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Why is there anything at all? The fundamental question of metaphysics: Part two: On reality as a mathematical structure

"The whole of nature, in all its phenomena, is only mathematics... All these objects themselves, sounds, lights, stars, zodiac signs, are nothing but numbers in combinations and combinations-combinations of many kinds." (Descartes)

Is all this nothing but the self-realization of mathematics?
Is all this nothing but the self-realization of mathematics?

Marius Cohen

Preparation for what is to come

בThe first part of the article We saw how difficult it is to answer the fundamental question of metaphysics: "Why is there anything at all?"

This difficulty led the philosopher William James to call it "the darkest question in all philosophy". The fact of the existence of the universe, about the space and time that make it up and the matter and energy that fill it, is paradoxical: for the mind cannot tolerate either the possibility that the universe suddenly came into existence full of nothing - for nothingness cannot provide a primary cause for creation - nor the alternative possibility that the universe has always existed (as, for example, Aristotle and Newton believed) without any transcendent reason for its existence. We saw that the philosopher Arthur Witherall claims that in this case all the usual explanations fail and that we are confronted with something enormous, something beyond the comprehension of common sense. There is no doubt that the difficulty of answering the fundamental question requires looking for unconventional solutions to the problem, and such is the solution proposed in this part of the article: contrary to our intuitions, according to which we exist in a concrete physical world, The Platonic-Pythagorean thesis Examines the possibility that the universe is nothing but an abstract mathematical structure, which as such is not required for a transcendent reason for its existence.

Explanations based on reducing theories

In the first part of the article, we dismissed the various attempts to answer the fundamental question of metaphysics: "Why is there anything at all?" If so, what types of explanation consistent with modern science are still available to us?

Well, one of the types of explanation that science uses a lot, and in the eyes of many physicists even constitutes a complete explanation for phenomena of any kind, is an explanation based on reducing theories. Reduction of theories is the position of one field of knowledge (to be called below secondary) on another field of knowledge (below first) Through Reduction. Reduction is basing the concepts of the secondary domain on those of the primary domain and a logical-mathematical derivation of the laws of the secondary domain from the laws governing the primary domain.

A simple example of reduction is deriving the mechanics of a rigid body from the mechanics of point bodies. Basic concepts in the mechanics of a rigid body, such as angular velocity, angular acceleration, torque, torque constant, rotational energy and angular momentum, are all defined using concepts that are used in the mechanics of point bodies, and laws that characterize the mechanics of a rigid body are derived from the laws of mechanics of point bodies (laws Newton, for example). In cases where the field of secondary knowledge includes concepts that cannot be defined using concepts from the field of primary knowledge, a match must be assumed between the relevant concepts of the two fields of knowledge to allow the derivation of the remaining components. Thus, for example, in the reduction of thermodynamics to mechanics, an adjustment is required between the concept of temperature (in thermodynamics) and the concept of the average kinetic energy of molecules (in mechanics), and this is because temperature is a basic concept in thermodynamics, and is not defined using concepts from the field of mechanics. On the basis of this correspondence, all thermodynamic phenomena can be explained using the laws of mechanics. Such an explanation, based on a reduction through the matching of concepts, a reduction which is actually a determination of identity between the teaching objects of these concepts (that is, that these are different names for the same phenomenon), is called Explanation based on identity explanation by identification)). This type of explanation, although it fits well within the framework of causal explanations, is not a causal explanation in itself: the temperature of a body is not caused by the average kinetic energy of molecules, but is itself such energy (although the energy of molecules is what causes the mercury in the thermometer to expand and to boil, but equally it can be said that the temperature in the room is the one that causes the mercury in the thermometer to rise, and that the water temperature is the one that brings the water to a boil).

The prevailing assumption in science today is that the set of phenomena in nature, including chemical processes, biological systems, and even psychological states, is based on fundamental physical laws that act on physical objects (a position called Physicalism). Based on this assumption, and due to science's many successes in reducing theories, the concept developed at the beginning of the 20th century that science should aspire and put the whole of the natural and life sciences above physics itself. Today we indeed know how to derive chemical phenomena such as solubility, acidity and speed of a reaction from the fundamental forces acting between the elementary particles and from the equations of quantum mechanics (although the calculations are often long and tedious, and in many cases the calculation power of advanced computers must be used for this). Today we also explain many biological phenomena (mainly at the molecular level), such as cell metabolism, DNA replication, neural communication, and the like, based on chemical reactions and physical processes. And so, despite the many difficulties that arise on the way to placing biology as a whole over physics (difficulties stemming at least in part from the complexity of biological systems), the mainstream in science assumes that this is not an impossible task. Even psychological states are today better understood in the context of physiological activity (hormonal and nervous, for example) and chemical reactions in the body, and even if the nature of the connections between these two last fields of knowledge is still not clear enough, it is not unreasonable to assume that the gap between them will continue to narrow, perhaps until its complete elimination . The main obstacle in this chain of reducing theories may be the attempt to derive the phenomenon of consciousness from some physical theory, and this is due to the uniqueness of the subjective experience that characterizes it, and which is different from anything else known in nature. No one is clear how, if at all, physical processes are capable of evoking mental experiences, although recently there has been significant progress in our ability to link defined states of consciousness to specific neural activities. In any case, we will adopt here the position of the mainstream in science, which is that all of nature at its various levels is based in one way or another on objects and physical laws, whether we ever discover them or not. We accept the The physicalism assumption As a basic premise, without committing to the fact that we will ever actually succeed in reducing the totality of phenomena in nature to the basic physics equations.

If so, it is possible to arrange the natural phenomena in a kind of hierarchy of fields of knowledge, at the base of which is physics, and above it in order: chemistry, biology, psychology and perhaps also sociology, with the laws of each level supposed to derive in principle from those of the levels below it. But is physics really the most basic level in this hierarchy? Although this is the opinion of most scientists, a trend is currently developing in physical research that examines the possibility that this hierarchy has an even more basic level, which is pure mathematics. According to this conception, the physical universe is in fact an abstract mathematical entity, so that it is basically possible to reduce the physical to the mathematical. The prominent representatives of this concept are physicists such as Max Tegmark, John Barrow and Kikir Shoshani, and even the writer of these lines deals with the subject. This position is indeed met with quite a bit of opposition from the scientific community (mainly due to the lack of possibility of empirical examination of it), but it fits well with the insights of modern science, and it has an explanatory power that deserves the attention it deserves: and that is exactly what we will try to do here.

Mathematical structures

The notion that the physical universe is nothing but a mathematical entity makes use of the concept Mathematical structure, a concept that originated in the 19th century, but only in the second half of the 20th century did it begin to gain the attention it deserved. We will try to understand this concept before returning to the fundamental question of metaphysics.

A collection of objects that maintain certain relationships between them is commonly called system. Thus, for example, one can define a family system whose objects are a certain group of people, and whose relationships exist between them are family relationships: husband, wife, son, sister, uncle, etc. a building, on the other hand, is an abstract creation consisting of a collection of abstract objects, which maintain a set of abstract relationships between them, and which do not have any additional property beyond the fact that they maintain this set of relationships. The objects and relationships of a structure are abstract in the sense that they do not carry any content, that is, it is impossible to say anything about them, beyond the fact that they maintain the particular set of relationships that establish the structure. A system's collection of objects and relationships, on the other hand, has meaning. Thus, for example, in a family system every object is a human being (with all that implies), and relationships such as one's mother or one's brother have a biological meaning (and perhaps also a social or legal one, as needed). In other words, what distinguishes a system from a structure is that the components of the system have content, while the components of the structure are contentless, and characterized only by the way in which they are linked to the other components of the structure.

It is common to call structures whose legality characterizes them a rich deductive investigation of them Mathematical structures.1 The systems of geometry and arithmetic, for example, have such structures, and by virtue of these systems are considered mathematical (according to the above definitions, geometry and arithmetic are systems because their objects have content: point, line, number, connection, multiplication, etc.). It is important to clarify that many mathematical structures represent systems that are not precisely numerical or computational in nature, and this is especially evident in various branches of modern mathematics (in set theory, for example), where dealing with non-numerical abstract objects is commonplace.

Mathematical structuralism

It is a realist-Platonist position regarding mathematical structures. It attributes to mathematical structures an existence that is not conditioned on their pronunciation by any intelligence. According to this position, the structure representing Euclidean geometry would have existed, and in it there would have been a true Pythagorean theorem even if no intelligence had developed in the universe that would have conceived the structure and discovered the theorem, and even if a physical universe had not existed at all. Without a universe, there would not be concrete systems demonstrating the various mathematical structures, but the internal structural truths of these structures (such as the Pythagorean theorem) would exist in any case, and this is what justifies the structuralist position. According to this position, when we define a structure we do not invent it but describe an existing structure. And to remove doubt, this existence of structures is not physical but Platonic, meaning outside of physical space and time.

The Platonic-Pythagorean thesis

The position that the universe is a mathematical entity can be formulated using The Platonic-Pythagorean thesis, which has four principles that include, among other things, an answer to the fundamental question of metaphysics:

1. Reality is nothing but a mathematical structure: the so-called "physical" objects at the base of reality are nothing but the abstract objects of this structure, and the laws of nature are an expression of the legality that characterizes the set of relationships that these objects maintain among themselves. It is a reductive position that identifies the physical elements of nature with the elements of an abstract mathematical structure (an identity-based explanation).

2. The "physicality" we attribute to reality stems from the way in which our consciousness, which is also part of this mathematical structure, perceives its abstract environment. Our consciousness works in such a way that it experiences reality as tangible, and because of this we interpret it as "physical" (that is, "physicality" is an epistemological, not an ontological, aspect of reality).

3. This metaphysical picture provides an immediate answer to the fundamental question of metaphysics: the universe as a mathematical structure does not need a transcendent reason to exist! It has a Platonic existence like any other mathematical structure, which is not conditioned by the existence of a "physical" universe or by an intelligent consciousness that conceived it.

4. There is no ontological "physicality", that is, one that differs from a mathematical structure. On the other hand, there are countless mathematical structures, with the complexity of some of them allowing the appearance of consciousness (as part of the mathematical structure), which perceives its abstract environment as "physical". Because of this, these cognitive-supporting structures can be called "physical".

The reason why this thesis is called Platonic-Pythagorean is that, although it is customary to use the term "Platonic" in the meaning of "abstract", Plato himself perceived the world of ideas as separate from physical reality, while the Pythagoreans, according to Aristotle's testimony, claimed that "things themselves are numbers" .

If so, the thesis unfolds a radical metaphysical picture, according to which - contrary to our intuitive perception of reality - the physical world in which we exist is not ontologically different from abstract mathematical structures. In other words: physical reality itself is nothing but a mathematical structure, while its "physical" constituents (whatever they may be: elements of space-time, elementary particles, strings, membranes, or any other "physical" objects) are the abstract objects of this mathematical structure And the laws of nature are an expression of the set of relationships that these objects maintain among themselves. This metaphysical image provides an immediate answer to the fundamental question of metaphysics: if all reality is nothing but a mathematical structure (and we, who exist in this mathematical reality, interpret it as "physical" because of the way consciousness works), then the universe, as a mathematical structure, does not need a transcendent reason to Exist! It exists platonically like any other mathematical structure, which is not conditioned on the existence of a physical universe or an intelligent consciousness that will conceive it (as mentioned, on the basis of the structuralist position presented above). Just as it is not correct to ask "What caused Euclidean geometry?" or "Why do numbers exist?" Likewise, it is not correct to demand a causal explanation for the existence of the mathematical structure that constitutes our universe: the universe is nothing more than an abstract mathematical structure, and since mathematical structures are not created but simply exist (Platonic), the universe, as a mathematical structure, does not need some kind of super-being to create it. , and it didn't even "appear" out of nowhere for no reason, it simply exists by virtue of being a mathematical structure!

If our reality is indeed nothing more than a mathematical structure, two questions immediately arise: one, are there possible additional mathematical structures, the validity of which allows the emergence of consciousness with consciousness (which is characterized by subjective experiences such as sensory perception and emotions)? And the second, in addition to these mathematical structures, is there also some kind of "real" physical reality (that is, one that is not a pure mathematical structure)?

Well, if our reality is nothing but a mathematical structure, then theoretically there may be additional mathematical structures (whether similar in their laws to the mathematical structure that constitutes our reality or completely different), which enable, due to their special laws, the appearance of cognition. We call such structures Recognition-supporting structures (We will refer to the not simple general question, how recognition can even appear in an abstract structure later). It can be assumed that only a small part of the total number of existing mathematical structures are cognition-supporting, and perhaps even only one of them is such (our reality). However, the existence of cognitive-supporting mathematical structures does not necessarily follow that there does not also exist a "real" physical entity (that is, one that is not an abstract mathematical structure), which may therefore be perceived as "real", and the question begs whether such a "physical" existence is also possible, in essence is not a pure mathematical structure, and that its "physicality" is not conditioned by the existence of a consciousness that perceives it as such. Well, not only does the Platonic-Pythagorean thesis not need a "real" physicality, one that is ontologically different from mathematical structures, but it even rules out the possibility of its existence: after answering the fundamental question of metaphysics on the basis of the structuralist position, the assumption of the existence of a "real" physicality will open renews the vicious circle of searching for a causal explanation or some other for the so frustrating question: "Why is there anything at all?" And it seems that on the basis of "Ockham's Razor", according to which of two theories with the same explanatory power the more economical one should be preferred, there is no justification to assume that there is anything beyond abstract mathematical structures (and this after it is possible to explain the existence of reality as a whole through them).

If so, assuming that "real" physicality does not exist, any mathematical structure that supports cognition can be defined as physical, since the mode of operation of cognition is such that it perceives its mathematical environment as tangible. Despite the uniqueness of the phenomenon of recognition, it is part of our reality (the physicalism assumption), and if the reality in which we exist is nothing but a mathematical structure, then there may be additional mathematical structures that support recognition. The picture of the world that such recognition creates on the basis of subjective experiences is a picture of a "physical" reality, and therefore these structures can also be seen as "physical". Tagmark himself prefers to see every mathematical structure as having a physical essence, but it seems that such a position is not justified for two reasons: first, there is no real justification for considering mathematical structures such as those that represent Euclidean geometry or arithmetic to be physical, and second, since we have established that the term "physical" is an epistemological term Only, it would be correct to see a mathematical structure as physical only if there appears in it a consciousness that experiences it as such.

In a certain sense there is no escaping the conclusion that the answer to the fundamental question of metaphysics is simple: there really is nothing! (where by "nothing" it is meant to talk about what is "really" physical): not physical space, not physical time, and not even any "really" physical essence. On the other hand, there are plenty of mathematical structures and at least one of them (our world) is also "physical" according to the concept presented here.

So is it all numbers? It seems that Pythagoras and his successors, who were fascinated by the numerical nature of natural phenomena (such as, for example, the relationship between the length of the strings and the interval of the sounds they produce) thought so. Even Descartes, the 17th century philosopher, came to the conclusion that "the whole of nature, in all its phenomena, is only mathematics... All these objects themselves, sounds, lights, stars, zodiac signs, are nothing but numbers in combinations and combinations of many kinds .”2 We are indeed used to seeing mathematics as a field that deals with numbers, but as we have already mentioned, in modern mathematics there are branches where the objects of research are objects of a different type, and mathematical structures are not necessarily numerical structures (topological structures, for example, are not numerical structures). Therefore, despite the great use of numbers in physical theories, it is not necessary that the mathematical structure of reality includes arithmetic.

Difficulties, problems and answers

The Platonic-Pythagorean thesis is counter-intuitive, since we perceive our world as having a concrete essence that is fundamentally different from mathematical structures. As such it raises quite a few difficulties, and here are some of them: First, the concrete physical world is perceived as fundamentally different from abstract platonic structures. Is it possible to explain this perceptual gap within the framework of the thesis? Second, how, if at all, can consciousness develop in an abstract Platonic structure? A third difficulty is in the question of how can a mathematical structure explain the dynamism of reality, which is characterized by constant change? And fourth, if reality is a mathematical structure, why exactly this structure?

We will try to answer these difficulties and show that despite being anti-intuitive in essence, the Platonic-Pythagorean thesis presents a plausible metaphysical picture.

First, the narrowing of the ontological gap between the physical and the mathematical, which is at the base of the reductive thesis presented, is completely unintuitive. This is due to the fact that the physical world, of which we are an integral part, we experience in a completely different way from the way we are introduced to mathematical structures. But the very distinct gap between the physical and the mathematical is not an ontological gap, but an epistemological gap only: according to the Platonic-Pythagorean thesis, reality is nothing but a mathematical structure, of which we ourselves are a part, we perceive reality, that is, the mathematical environment of which we are a part, through A cognitive mechanism that processes the information coming from the senses. This mechanism produces for us experiences of touch, color, sound, smell, heat, cold, solidity, wetness, and the like, and these subjective experiences give us a sense of the reality of the world (perhaps most of all, the experience of touch is what gives us a sense of tangibility, of physicality , and those who for some reason lose this basic ability "will always move in a blurred and dull world").3 On the other hand, we perceive the mathematical structures we think through a different cognitive mechanism, a rational mechanism (at least partly linguistic), which allows us to engage in mathematics and use it for our needs. Since these two cognitive mechanisms, the one that perceives reality, and the one that deals with mathematics, are different mechanisms, reality is perceived by cognition as ontologically different from abstract mathematical structures. Just as visual information is perceived in our consciousness in a different way than sound information because the cognitive mechanisms that process these two types of information are different from each other, so too our consciousness perceives reality as tangible (and interprets it as "physical"); Whereas she perceives mathematical structures as abstract, Platonic, because the cognitive mechanisms involved in the practice of mathematics are different from those involved in sensory perception. In fact, the essential difference between the mathematical structure that constitutes our reality and the mathematical structures we think is the fact that we ourselves are part of this mathematical structure (since we are part of the universe, which according to this thesis is a mathematical structure), and therefore we perceive it in a unique way: through the senses. The mode of operation of the cognitive mechanism that processes the sensory information is such that its product is characterized by tangibility, and this tangibility causes us to attribute to physical realities, while our knowledge of theoretical mathematical structures is not a product of sensory information processing. Therefore, it is not characterized by tangibility and consciousness does not label it as physical, but as abstract. From this it follows that the physical reality is a model that our consciousness creates for the mathematical structure, which itself is a part of it, and this through the sensory information processing mechanism that causes us to perceive our mathematical environment as "physical". If so, Physicality (in the sense of tangibility) is an epistemological and not an ontological aspect of reality.

Second, the emergence of abstract structure recognition. Cognitive activity, and in particular the phenomenon of qualitative consciousness (from the word quale; the experience of color, smell, pain, etc.), is so unique that even the assumption of physicalism does not prevent us from wondering how cognition can even appear in a mathematical structure that is an abstract Platonic creation. As we described above, narrowing the ontological gap between the physical and the mathematical allows us to understand that a mathematical structure may be perceived as physical by cognition that develops in such a structure, but it does not explain how cognition can even appear in it, and the possibility that cognition will develop as part of a mathematical structure seems intuitively implausible. However, we do not know (nor do we come close to knowing) how consciousness is possible even in a "real" physical world (one that is not possible to be reduced to an abstract structure). Therefore, the Platonic-Pythagorean thesis does not create the explanatory gap that already exists. Under the assumption of physicalism, which also dominates neurophysiological research, consciousness is indeed a product of matter, and therefore the possibility that material reality is nothing but an abstract structure also embodies the phenomenon of consciousness: any theory that succeeds in placing mental experiences on physical foundations will need only one more step To place consciousness on mathematical elements: determining the identity between the physical elements of nature and the elements of an abstract mathematical structure (explanation based on identity), which is the core of the Platonic-Pythagorean thesis.4

Third, static structure or dynamic structure. There are two main metaphysical positions regarding the nature of time: the first, the more intuitive, holds that time is dynamic, that is, that only the present (and according to another version also the past) is real, and that the world is characterized by real changes and Being (presentness) which is steadily progressing from the past to the future. The second position, the less intuitive but one that is consistent with insights that emerge from modern physics, holds that time is static In the sense that all times from then until eternity are equally real, and "being" is not real but is a point of view of consciousness: the "now" that someone will experience at a future point in time and the "now" that we will experience at some point in time in the past are just as real as the "now" that someone experience while reading these words. According to this position, the very passage of time is nothing but an illusion of consciousness (albeit a persistent illusion, as Einstein pointed out), when consciousness, spread throughout all the time points of its existence, experiences each of them as a different "now". It is legitimate to ask whether the distinction between static time and dynamic time stands up to empirical examination, but it does not matter for our purposes, since each of these classes corresponds to one of two types of mathematical structures: static time corresponds to a static mathematical structure (such as the structures of arithmetic or Euclidean geometry), while dynamic time Suitable for a dynamic mathematical structure (such as an algorithm that is applied to a data structure). It is understood that in none of these types of structures, whatever the structure underlying our reality may be, time does not have a "physical" essence, but is only perceived as such by consciousness. The same is true of the concept of space: there is nothing "spatial" within the mathematical structure, but the array of objects and relationships in it allows cognition to experience "spatiality" (by the way, several directions in modern physics hint at the possibility that space and time themselves are not fundamental dimensions in nature, but can be derived from essences more thorough).

Why this structure? As I recall, Leibniz asked not only "Why is there something and not nothing?" but also the requested addition: "Why should they be found this way and not otherwise?" Well, the Platonic-Pythagorean thesis also answers this question: the explanation that the universe is like this and not another, and that the laws of nature are like this and not others, is that out of the countless mathematical structures that exist, this is the mathematical structure in which we exist. Different mathematical structures have different objects and different sets of relationships, and this is the mathematical structure that constitutes our reality, and we experience it and nothing else because we are part of it and not of another structure. In this context, the question also arises as to whether the positing of reality (including space and time) on a mathematical structure does not commit to an eternal universe, i.e. one that had no beginning (since a mathematical structure also has no beginning - it exists platonically outside of physical space and time). But since the existence of mathematical structures is not in space and time, but on the contrary: according to the Platonic-Pythagorean thesis, space and time are internal to the mathematical structure underlying reality, and the question whether the universe is eternal or whether it had a beginning is an intra-structural question, and both possibilities are compatible with the universe being a structure Mathematical (it is possible to adapt mathematical models to both options).

The explanatory power of the Platonic-Pythagorean thesis

The Platonic-Pythagorean thesis, as presented above, is a hypothesis, and we have tried to show that despite being unintuitive, it is coherent. In fact, its ability to answer the fundamental question of metaphysics has great power, but any metaphysical theory or thesis that is put forward to solve a particular problem is tested not only for being coherent, but also for its ability to explain additional phenomena. Well, the Platonic-Pythagorean thesis has explanatory power beyond its ability to answer the fundamental question of metaphysics. It also answers two other pressing questions concerning physical research, to which satisfactory answers have not been given to date:

1. Why is nature subject to mathematical defiance? Since Galileo Galilei pointed out this fact, the phenomenon has become an assumption

Work in physical research, and any explanation in this field that is not mathematical in nature is considered an incomplete explanation.

2. How is it that the constants of nature are adjusted so delicately and precisely, that the appearance of intelligent cognition is possible

(Usually the question is asked about the appearance of life, but it seems more correct to put emphasis on

intelligence), since the smallest differences in these constants would have prevented it?

The book of nature is written in the language of mathematics

Galileo Galilei, who was the pioneer of quantitative experiments, and who analyzed their results with mathematical tools, claimed that the entire book of nature is written in the language of mathematics:

"Natural science is written in this great book, the world, which we look at for an hour, but the book can only be understood on the condition that we first learn to know its language and read the letters from which it is built. The language in which it is written is mathematics, and the letters are triangles, circles, and other geometric shapes without which we could never understand a single word in it; without which we are doomed to wander in a dark labyrinth."5

The new physics adopted this view of Galileo, which has since been established as a paradigm of physical research, which assumes that in principle the laws of physics can be formulated with the help of a mathematical formulation. The success of Newtonian physics, as well as all the branches of physics that developed simultaneously and following it, and which were based on various mathematical methods for cracking the laws of nature, did illustrate the importance of mathematics in understanding the world, and its power in predicting the results of experiments. Modern physics, whose discoveries led to far-reaching changes in our understanding of nature, brought this perception to its peak in three ways, and these are:

1. Using pure mathematical considerations to predict unknown phenomena. Thus, for example, Maxwell predicted the existence of electromagnetic waves based on the equations he received (and which are named after him); Dirac predicted the existence of the positron when the equation he used produced an electron with a positive electrical charge; Schwarzschild deduced the possibility of the existence of black holes and their properties from Einstein's field equations; Bohm and Aaronov predicted on the basis of pure mathematical considerations a surprising and completely unexpected effect in quantum theory (an effect named after them: Boehm-Ahronov effect); And another priest and priest.

2. Formulation of physical laws whose only expression is mathematical (wave function, for example), meaning they do not refer to any "physical" objects, but they have meaning in the broad context of the theory, and they yield measurable results. Quantum theory is rich in such examples, and in the physics of elementary particles we encounter conservation laws that arise from symmetries that have nothing but a mathematical expression. In general, modern physics is characterized by a growing blurring between the physical and the mathematical, with quite a few physicists now using the term "mathematical entities" when talking about essences that in the past were considered distinctly physical (such as electrons, for example).

3. Our ability to describe a physical phenomenon through mathematics is considered the ultimate understanding of it, while any explanation of the phenomenon that lacks a mathematical basis is considered an incomplete and insufficient explanation.

The use of mathematics to describe nature has become so self-evident that the fact that there is no agreed answer to the question of why this is so is hidden from many. To date, no satisfactory explanation has been found for the very fact that nature obeys mathematical laws (many scientists are so used to the success of using mathematics to describe reality, that they take it for granted). This phenomenon aroused and still arouses astonishment among many thinkers, physicists and mathematicians: Eugene Wigner, winner of the Nobel Prize in Physics, claimed that the fact that mathematics is so useful in the natural sciences borders on mystery, and that it has no rational explanation. According to Wigner, the ability to use mathematics to formulate the laws of physics is a wonderful gift that we do not understand, nor do we deserve; In a speech to the Prussian Academy of Science in Berlin in 1921, Albert Einstein expressed his astonishment at the fact that mathematics, which is a mental creation that is not conditioned by experience, is so suitable for describing reality; The physicist Richard Feynman, also a Nobel laureate in physics, claimed that it is amazing that through mathematics, which has nothing to do with the original (physical) thing, it is possible to predict what will happen; So is Michael Dummett, a contemporary philosopher, who writes about the relationship between abstract mathematics and physical reality, which is incomprehensible in light of the fact that the former is timeless, in contrast to the reality in which we exist. Dummett wonders how facts about abstract objects can have relevance to the physical universe; Mathematician Anthony Tromba wrote that the correspondence between mathematical structures and reality evokes a deep mystical feeling; And Isaiah Leibovich, one of our greatest philosophers, referred to the fact that mathematics corresponds to reality by saying (emphasis mine):

"This is a great metaphysical question. Why is this so? Already Pythagoras asks the question and states that the world is a number. This is a statement that has almost no meaning, but it expresses the fact that he had already thought about the question of why the laws of mathematics are known in reality. It really is a wonder... "6

Well, this is the solution offered by the Platonic-Pythagorean thesis to the mystery: the book of nature is written in the language of mathematics, because nature itself is a mathematical structure. As such, it is possible to describe it mathematically, and we can study it and predict its behavior (within the limitations arising from the laws of nature themselves, such as the uncertainty principle, or from the mathematical tools at our disposal). If so, the mystery of the connection between the actual physical world and some Platonic mathematical world is summed up in the fact that this Platonic world is able to represent reality with incredible precision, despite the essential ontological difference between the two. Why do the laws of physics, which apply to physical objects, have to obey mathematical principles abstracted from any meaning, which have nothing to determine their applicability to the real world (as Einstein, Feynman and Dummett wondered)? The Platonic-Pythagorean thesis closes the ontological gap between these two worlds: it is a virtual gap, which stems, as mentioned, from the way cognition works. According to this thesis, physical reality is nothing but a mathematical structure, and all natural phenomena are an expression of the mathematical legality of this structure. If so, the very fact that nature is characterized by mathematical behavior should no longer be surprising. This phenomenon is not a miracle or a wonder or a mystical phenomenon (as Wigner, Leibovich and Tromba say), but stems directly from the fact that reality is a mathematical structure in itself.

The problem of fine-tuning the constants of nature

One of the open questions today in physical research is how is it that the laws of physics (including the constants of nature such as the constant of gravity, the constant of fine structure, and more) are adjusted in a very precise way, so that they allow the existence of intelligent life? It can be shown that a gravitational constant small by a fraction of a percent would have prevented the formation of galaxies and stars; A large gravitational constant by a fraction of a percent would shorten the age of the universe to such an extent that the universe would converge back to a singular point even before life had time to develop; A slightly different electromagnetic force would have caused the chemical reactions necessary for the formation of organic matter to not occur, and so on. The smallest changes in the laws of physics and its constants would create a universe in which life could not form at all, and the chance that precisely this fine-tuning would characterize our world tends to zero. Physicist Brandon Carter (Carter) first proposed one of the currently accepted answers to this problem, and it is based on a statistical explanation that assumes multiple universes: the chance of winning the big prize in the lottery is slim, but when millions of lottery tickets are purchased, there is a very high probability that someone will win the prize (even Because the winner himself, who estimated his chances of winning as zero, will be very surprised by his winning). Similarly, if there are countless universes, each of which has different laws of physics and physical constants, then there is a high probability that at least some of them are adjusted so that the development of intelligent life is possible in them, and in the end the questioning about the exact adjustment can of course only occur in these universes.

It is possible to imagine scenarios in which a multiplicity of different universes may be possible, and here are some of them: In the first scenario, there is an endless cycle of great explosions in our universe, whether each such cycle ends in the collapse of the universe into a singular point or, in a more modern version, in an eternal expansion, As each such cycle has its own laws of nature and physical constants. Admittedly, in this way the conditions for the development of life will not be created in most cycles, but in some of them (including the current cycle) the laws of nature will allow life and intelligence, and only in those cycles (including the current one) can the question of fine-tuning arise.

In the second scenario, our universe is just one of countless universes that exist side by side in some kind of superuniverse, infinitely larger than the visible universe (perhaps even infinite), and in which great compensations that occur in it from time to time (or maybe even all the time) lead to the creation of new universes, each One of its characteristics is that only some of them meet the physical conditions that allow the development of life.

In a third scenario there are universes that exist simultaneously, each universe with its own space-time (such as those created according to Everett's interpretation of the relative state of quantum theory, and more on that later). It is possible that each of these countless universes has its own physical constants, and the huge amount of universes that exist at the same time makes it statistically possible that in some of them the conditions suitable for the existence of life will develop.

Of course, these scenarios are speculative and cannot be confirmed or refuted today, but the last "scenario" is particularly problematic since it requires introducing countless other universes into the picture of the world, which is already quite complex, each of which is subject to different laws of physics, which causes several difficulties:

  • What is the mechanism that enables the physical existence of countless "parallel" universes? We find it difficult to explain even the existence of one physical universe, much less the existence of countless such universes.
  • Where (and when) are these universes? The possibility that each such universe has its own space-time is insufficient (although it has no logical flaw), especially in light of the lack of a mechanism capable of explaining the formation of these universes.
  • Why do the laws of physics differ from location to universe?
  • The ontological price we are required to pay just to explain the fine-tuning phenomenon of the physical constants is enormous: countless whole universes (for all their mass and energy).

And this is where the Platonic-Pythagorean thesis comes into play: the assumption that reality is a mathematical structure immediately solves the difficulty inherent in the possibility of the existence of these multiple worlds. The thesis provides, without any ontological cost, an infinity of universes of all possible types (as abstract mathematical structures), whose Platonic existence nowhere and at no time does not need any special production mechanism: mathematical structures simply exist, they are not created. Also, as Platonic creations, these mathematical structures do not exist in physical space-time, so the question "where are they" (or "when are they") is not relevant to them. If so, the Platonic-Pythagorean position, according to which the universe is nothing but a mathematical structure, provides a solid basis for the statistical explanation of the mystery of fine-tuning: all the infinite mathematical structures have the same status: they exist platonically, but the legality of some of these structures, including our universe, is such that allows the The emergence of intelligent recognition (of course, due to the subtlety of the "tuning" necessary for this, the proportion of mathematical structures whose legality allows this is extremely small). In these universes (which, as we saw above, can be seen as physical), and only in them, the question of fine tuning may arise. Since the existence of all these universes is Platonic, the unbearable ontological cost that applies to an infinite number of "physical" universes (in the intuitive sense of the term) does not apply to them.

The possibility of the existence of multiple ("parallel") worlds, which are ontologically equivalent to the actual reality in which we exist, has also been proposed in other contexts of physical research. For example, Hugh Everett's interpretation of quantum theory, an interpretation called Meaning of the relative position, but is better known by its popular name The interpretation of the multiple worlds. Any such theory of multiple worlds is ontologically uneconomical, since in these theories we are talking about physical worlds, and usually innumerable of them, so that even if the theory succeeds in solving one problem, it undoubtedly creates another problem. The Platonic-Pythagorean thesis provides an economical and simple ontological basis for any theory of many worlds: innumerable mathematical structures, which differ from each other, whether to a small degree or not, exist (Platonically), and there is no need for a special mechanism to create them.


The Platonic-Pythagorean thesis, despite being counter-intuitive, seems to provide a metaphysical framework in which a plausible answer can be given to the frustrating question: "Why is there anything at all?" To date, no theoretical framework has been found that might answer it. The mere fact that the question can be answered within the framework of the Platonic-Pythagorean thesis is enough to justify it, however, as we have seen, this thesis has an additional power: it provides an explanation for the incomprehensible fact that the universe is subject to mathematical regularity, and it offers an economical ontology for theories of multiple universes (such as The one that offers an explanation for the fact of the "fine tuning" of the constants of nature).

It is also possible that this thesis has a psychological advantage in accepting the "oddities" of modern physics, as they are expressed in the theory of relativity (for example: the relativity of distance and time, the relativity of simultaneity), in quantum theory (for example: superposition, quantum entanglement) and in the various attempts that are made to unite these two theories ( For example, multi-dimensions, discontinuous space and time). The "common sense" has difficulty accepting these peculiarities of nature, but there is a certain psychological relief in understanding that space and time are not "physical" entities as we intuitively perceive them, but rather mathematical objects: and that the validity of the structure to which these objects belong determine their properties. Since different mathematical structures (such as, for example, the structures of various non-Euclidean geometries) are the playground of modern mathematics, it is easier for human cognition to accept "mathematical oddities" than "physical oddities".

And we will end with a sentence, which offers a unique perspective to the Platonic-Pythagorean thesis:

Our world is a mathematical structure in which an awareness of being such has developed.


1 Deductive: using logical inference rules.

2 Bergman, Shmuel Hugo, The history of the new philosophy from Nicolaus Cusanus to the Enlightenment period,

Jerusalem: Mossad Bialik (2002), p. 150.

3 Ackerman, Diane, A journey to the senses, Dorit Lands (translator), Tel Aviv: Mater Publishing (1997).

4 It seems that a functionalist theory of the mind, which is the most accepted theory in this field today,

It is a worthy candidate for the defense of the possibility of the emergence of recognition in a mathematical structure.

5 in a circle, a wolf, Three Copernican revolutions, Tel-Aviv: Haifa and Zamora-Beitan University (1999), p. 65.

6 Ziv, Yossi, "Conversation with Yeshayahu Leibovitz", Zvi Yanai (editor), thoughts 65 (July 1993), p. 13.


Dr. Marius Cohen He teaches philosophy at Ben-Gurion University.

for further reading

Shoshani, Yakir, Matter and Spirit - The Spiritual Foundation of the Universe, Ministry of Defense - Publishing House (2008).

Barrow, John D., Pi in the Sky, Toronto: Little, Brown & company (1994).

Hut, Piet, Mark Alford and Max Tegmark, “On Math, Matter and Mind”, Foundations of Physics, Volume 36, Number 6 (June, 2006).

Shapiro, Stewart, Philosophy of Mathematics: Structure and Ontology, Oxford: Oxford University Press (1997).

Shoshani, Y., "Apriorics and the Proliferation of Elementary Particles in Parallel Subuniverses", Physics Essays, Vol 11, No. 4 (1998).

Steiner, Mark, The Applicability of Mathematics as a Philosophical Problem, Cambridge, Massachusetts: Harvard University Press (1998).

Tegmark, Max, "The Mathematical Universe", Foundations of Physics, Vol. 38, no. 2, pp. 101-150 (February 2008).

117 תגובות

  1. Shanir Harel,
    Four years ago we knew something that could have dismantled all this confusion with one question. About the axioms, "someone had to put them down".. and what about the question "why is there anything at all?", not only does it exist the moment it is asked, but someone has to ask it in order to be a question. All this fugitive metaphysical discussion proceeds from the assumption that there is something.
    In addition to this, it is useful to use a simple heuristic tool: instead of many arguments, there is confusion in the understanding of the terms.
    happy holiday to those who take a look at Pena that the power of the web is this. I was just looking for material on Galileo...

  2. Alik:
    I have nothing but to return and refer you to my previous response.
    If you understand her - you will understand that there was nothing in your response.

  3. Hello to Michael Rothschild
    The first time I thought you were trying to respond to my words, but in retrospect it seems that I was wrong, because even in your second response there is no actual reference to my understanding that you disagree with Marius Cohen's proposed solution to the metaphysical question "Why is there anything at all?", and in my opinion refute it.
    Wonder then why you found it appropriate to direct your arguments specifically to me, as the main impression that emerges from them is that all your eyes are focused on a crusade that you are conducting elsewhere and on two different fronts:
    A. One - the "objective existence of mathematics", which you claim you have conclusively proven. I have no idea how you proved this, and if you come up with a link that shows the proof I will definitely want to look at it, although - and this is the main thing - even such a proof will not disprove my claim that the a priori existence of eternal ideas without any dependence is not possible. As I have mentioned, belief in such an existence posits mathematics as a transcendent entity from which the way is open to difficulties such as transcendent intelligence and a transcendent God.
    In short, we are talking about different questions that are on different levels.
    B. The second front is the matter of "the existence of God" which in your opinion is a delusional idea that probably does not require a reasoned refutation, because your opinion on the matter is authoritative enough to obviate any need for further discussion.
    I have no problem with any opinion on this matter, nor did I express any opinion regarding the existence or non-existence of God, although - after you raised the issue - I stated a well-known fact that from a metaphysical point of view it is an open question. It is true that, like those who believe without reasoning in the existence of God, you have every right to deny his existence, also without reasoning, and in any case I am not a party to the debate between you and them.
    And since no actual dialogue was created between us, I am right to retire quietly and let you conduct your holy war in God in the name of the eternal mathematical ideas, and without interference.
    And finally, I will once again express my gratitude to Marius Cohen for his excellent article that fascinated me and made me very excited.

  4. Alik:
    I suppose we could also find people who would disagree with the conclusion that one plus one is two (certainly there are some because everyone who disagrees with the objective existence of mathematics disagrees with that).
    I have well reasoned the reasons for my belief that mathematics has an objective existence.
    I have not yet heard a single argument against. All the reasons put forward were along the lines of "there are many people who believe otherwise".
    It was said eat shit - 100 billion flies cannot be wrong
    Likewise, the question of the existence of God who intervenes in what is happening in the world. There is a debate that originates from the survival power of the religion (I emphasize - the survival of the religion - not the survival of those who believe in it) and not from the correctness of this delusional idea.

  5. To Michael Rothschild, thank you for your response to my response.
    As a matter of fact, there is no disputing your full right to see the assumption that mathematics is a discovery of a solved question, nor am I saying that you are wrong, but the fact is that among the scientific or philosophical community, the question is undecided. The assumption that the world behaved according to the same laws before the existence of man, and will probably continue to behave this way even after the existence of man, is not relevant to the question of whether mathematics is a discovery or an invention. The important thing is that there is a necessity for some kind of existence whose rational aspect allows the existence of abstract ideas, and as I mentioned in my response to the article, it can be any rationality; human, divine or otherwise. A state of the absence of any existence cannot allow the existence of any ideas.
    And on the subject of "God", the difference between the argument for the existence of eternal abstract ideals that do not depend on other existence, and the argument for the existence of an eternal divine being that also does not depend on other existence - is a big question mark. After all, there is no agreed upon definition of the divine being, and in any case it is not claimed that it is not mathematical. And so it is surprising that people who zealously reject the correctness of God's existence - a rejection that is legitimate in itself - some of them, cling to the belief in the existence of eternal abstract ideas detached from physical existence. After all, this argument is only a fragment of an argument that the abstract ideas are intelligent, which can lead to the assumption that they themselves are the divine being.
    And finally, science rules out, and rightly so, the introduction of ghosts into the equations, but when we are dealing with metaphysical questions, I recommend you, and everyone, not to be afraid or intimidated about "bringing God into the picture". After all, even if this does not appeal to every ear, the metaphysical question about the existence of "God" is also not resolved, and the preoccupation with it has given rise from the beginning of Dana to our days, arguments that consider the eternal divine being a discovery (or revelation) - similar to those who claim that eternal mathematics is a discovery, And there is probably quite a bit of work left to try and settle this question.

  6. Alik:
    In my opinion, even if some people say that the question of whether mathematics is a discovery or an invention is not resolved, the question is completely resolved.
    I don't think anyone among those who claim that the question is unsolved thinks that the world did not behave according to the same mathematical laws even before there was man.
    On the contrary! Anyone who uses mathematics in the field of cosmology, geology or paleontology presupposes that these laws have always governed the world.
    Otherwise there would be no meaning, for example, to dating based on radioactive decay of elements or running the stars back in their current orbits to conclude that there was a big bang.
    Also the fact that the mathematics discovered by different people is the same indicates that mathematics is not dependent on a person.
    I have already talked about it a lot in this discussion and others and I will not repeat things more than I did.
    In my opinion - precisely the attempt to describe (as if it is possible at all) a world without mathematics, is tantamount to bringing God into the picture.

  7. Marius Cohen's article is instructive and fascinating throughout, and the thesis presented in it is charming and challenging, but at the same time it raises a number of questions, and I will address the thought of them.
    The fact that the thesis is based on the Platonic method regarding abstract ideals that do not depend on the existence or non-existence of the physical universe of which we are a part, creates a fundamental problem that deserves to be examined. Plato, as is known, gave "tangible meaning" to the idea of ​​ideals in his theosophical worldview, which included the demiurge ("the creator god" or "the working artist") who created the world while looking at abstract ideals, and according to which he created it. But regardless of the theosophical aspect, there is significant doubt regarding the claim that the abstract ideas exist without any dependence on the existence of a physical universe, or on the existence of any intelligence. At the very least, this is a questionable assumption.
    The thesis presented in the article relies on a kind of eternal a priori world "made of" abstract ideas, some of which are mathematical structures, one or more of which may include algorithms - which were/are used for the development of an intelligence with an epistemological characteristic that produces a perception of a dynamic physical universe.
    What is it similar to? For those who hear about the big bang theory, and imagine in their mind's eye a kind of vast and empty space in which there once existed some point or void or a small ball that at a certain moment exploded and created the galaxies and stars. This is of course absurd because space (and time) is a result of the big bang and not its "habitat" - but the human imagination has difficulty dealing with the extreme situation of the uniqueness of the big bang. Simply put, I would like to argue that just as there is no existence for empty space without a big bang, so too there is no existence for mathematical structures or any abstract ideas* without the existence of intelligence (human, divine, or otherwise), even if the human imagination has difficulty dealing with an extreme state of non-existence .
    Moreover, it seems that there is a contradiction hidden here in the spirit of the contradictions presented in the article itself against scientific (naturalistic) arguments claiming that the universe has always existed, or ontological (ontological) arguments regarding the necessity of God's existence. Indeed, the same can be said for those who argue about the "necessity" of the eternal existence of ideas and abstract mathematical structures (which, by the way, are not "more abstract" than God). In other words, one gets the impression that the very aesthetic thesis presented here secretly crept into a barren manipulation of concepts, in which the eternal existence of a physical universe or the eternal existence of God was replaced by the necessary eternal existence of ideas and mathematical structures.
    I am afraid that the bold answer proposed in the article to the question "Why is there anything at all?" falls into these, despite the impressive reasons supporting it, and it remains at this point a brilliant thought exercise.

    * Regarding the independence of mathematical structures, it is worth mentioning, by the way, that the question of whether mathematics is a discovery or an invention is undecided, as can for example be found in Mario Livio's book "Is God a Mathematician".

  8. Can anyone relate the idea of ​​the mathematical abstraction of the universe with the ideas of David Lewis in the context of multiple worlds?

  9. Invalidating own imperfection invalidates.

    Anyone who disqualifies others, is himself disqualified, with the same deformity he infects others.

  10. thank you for sharing
    It's just a shame you don't do it from the psychiatrist's couch.

  11. In my opinion, physics and mathematics will give way to newer and more accurate sciences in the future.
    Just as today they don't count with stones, so in the future they will use a more precise science than mathematics.

  12. Shinir Harel:
    It seems to me that you missed an important point in the article's claim.
    The claim is not that out of the multitude of existing possibilities, one has been realized, but that all of them are being realized.
    It is a theory of multiple worlds that actually removes the difficulty of breaking symmetry of any kind - including the physical ones.

  13. I do not accept the division between the mathematical and the physical, because as we mentioned before - we do not understand the essence of physical reality at all.

    If we say that every reality in our world can be defined "theoretically", or mathematically, the question will still be asked - why does it exist. Saying that existence is within mathematics is actually saying that the property of "existence" of any object is not an optional property, but is required. We understand that any theoretical or mathematical idea may or may not exist, but the author of the article claims that an idea "carries its existence" within itself, meaning that there is no need for the attribute of existence, it is not an optional thing.

    This is actually the claim that reality is "committed". The ancient Greeks dealt a lot with this discussion and the writer stuck to Aristotle's definition, although Aristotle included much more, and cleaned it of some defects found in the above article. In fact, Aristotle separated the attribute of existence itself from any other theoretical structure, but he claimed that existence itself is obligatory, it is not optional, and it "joins" every theoretical structure and its existence.
    But you can think otherwise. One can think that every theory is only possible, and the feature of existence is not something immanent in it, nor does it necessarily join and sustain it.
    And how will we decide? In my opinion, this is a logical equivalent to Kant's creation paralogism and there is no absolute logical decision.
    But nevertheless it is worth asking the following question: even if all realities exist, this does not release us from the obligation to explain how within our "mathematical structure" certain characteristics developed out of an abstract singularity. If you claim that it was in a non-causal way, that this "mathematical structure" does not include a developmental sequence at every stage - this will be the abandonment of science.

    Words from another direction:
    The above article is added to the chain of answers that build the world in the following way: at the base there is a theoretical concept, whose theory includes the fact that it exists. This concept is enough to explain the existence of everything else, "rest" which in our view consists of concepts whose existence is not part of their theory.
    This is a fascinating direction that must be continued to be developed, but in my opinion it is impossible to arrive at the assumption that everything possible exists, neither Ockham nor Popper would approve such a leap and it is impossible to hide behind a reduction to mathematics to claim that there is actually not too much of an assumption here. Although the symmetry behind this idea is attractive, in our reality there was a symmetry breaking that needs to be explained. Apparently, the Big Bang model indicates that a certain possibility was realized even though there were other possibilities, and this is what needs to be explained.

  14. Logical gates, "one zero", there is no.
    They have infinite formula changes, as the size of the network, as the size of consciousness.
    hall. Does everything take place outside the box?
    Does everything that is written exist and everything that exists has been written?
    If I were a Rothschild?
    Everything remains in the fence maybe as long as it is not turned differently.

  15. Shinir Harel:
    In my opinion you are completely wrong and things were explained well - both in the article and in the comments that followed.
    1. The basic claim of the article is that every possible mathematical structure exists in practice and so does the structure in which we live.
    There are mathematical structures in which the Big Bang is a component, and the mathematical structure in which we live is one of them.
    According to this concept - the concept of time is not part of nature but part of the mathematical structure.
    I assume that if this assumption is correct - there is no escaping the conclusion that in fact - a world exactly like ours exists countless times because our existence does not detract from the ability of our mathematical structure to come to life again.
    I said that I have several reasons to think that this hypothesis is incorrect, but none of the reasons are the ones you pointed to.
    2. After one comes 2 and no more 1.
    3. The axioms of a mathematical structure are part of the structure.
    They have no proof and there is no need to prove them either.
    There are different sets of axioms from which different worlds are created.
    Only within those worlds can the "correctness" of the axioms be tested experimentally.
    For example - the axioms of Euclidean geometry are not true in our world and we know this as a result of an experiment, but experiments carried out in our world do not say anything about the results of those experiments in another world based on other axioms.
    All this is not important in terms of mathematics and also in our world where Euclidean geometry does not exist, Euclidean geometry can be discussed. This is because the mathematical theorems (which are true in every possible world) are always formulated in the form "if such and such conditions (the axioms) are met, then such and such also holds - the conclusion".
    Since the sentence begins with a condition - it cannot be hidden by experiment or calculation in a world where the condition is not met.
    In fact - all this has already been explained in the current discussion, but you probably didn't read it.

  16. Unfortunately, the solution presented in the article loses its value due to several failures, here are two for example:

    1. A physical problem: according to the currently accepted theory, the physical universe began with a singularity, a singularity that physically does not include "information" that would allow breaking symmetry, and determining certain values ​​for constants and forces (which were created only later). Since the magnitudes were determined only after the singular phase, it is impossible to use the mathematical argument presented here (which is actually nothing but the entropic principle) to solve the problem of their determination. We must refer to the physical aspect - how were they determined from the singularity, from the big bang? Without solving it there is no value. Trying to say that they were determined directly from mathematics contradicts the big bang theory.
    In other words: an attempt to explain that our universe started from a number of basic building blocks, or mathematical axioms, would have solved the problem. But according to the Big Bang there was an initial stage that preceded the definition of the constants and forces, so it is necessary to explain how they arose from it, and they cannot be presented as the starting points.
    1. Conceptual problem: "mathematical structure" - this concept assumes that there is an independent mathematical existence, but in fact this is not the case, and I will explain: does a mathematical structure have an independent, independent existence? The answer is negative.
    A mathematical structure is composed of two completely different parts: axioms, and development. It is true that the relationship between the axioms and everything that follows from them is real, independent, having an independent existence and so on. But the axioms themselves - there is no mathematical truth in them. They are concepts that do not derive from anything, do not represent any truth. They are a starting point that has no reason.
    Only after certain axioms have been established - and this stage is not mathematical at all - can you start using mathematics. This completely devalues ​​the article. It is impossible to explain existence itself, nor their unique characteristics, behind mathematical necessity, because there is no mathematics without axioms, and axioms have no necessity and no explanation, and nothing to do with mathematics at all. They do not exist by themselves.
    "Mathematical structure" must begin with arbitrarily determined axioms. The rest of the "structure" is just the long-winded language of humans, who fail to see the meaning of the axioms without filling tables with diverse symbols. The need to "develop a structure" is nothing but a human need, but in fact only the axioms exist. And these axioms - they have no existence by themselves, someone had to assume them, or they were determined arbitrarily.
    Therefore, there is no meaning to the claim that the universe is a mathematical structure, because it is a concept that originates from the weakness of the human mind. One can only claim that the universe is a certain collection of axioms, which have no existence on their own. Some consciousness had to determine them, or they were determined arbitrarily.
    Therefore, we returned to the basic options: either initiation by consciousness that established axioms, or service initiation that established axioms. The article did not advance the understanding of the subject.

  17. Shlomo:

    I have nothing but regret for your withdrawal from the discussion. It would have been interesting to hear your learned opinion in dealing with the arguments raised.

  18. To Michael and Liza
    It seems to me that we have slipped into a theological debate that drags on like a tail after a discussion of the comeback of classical philosophy, and if that is not enough, the discussion has also become loaded with repetitions. It might be appropriate to end here. And since I had the right of the first word, I tell myself enough.

  19. To Shlomo:

    I don't blame you for claiming something against Judaism.
    My argument is that you are distorting the true essence of scientific activity in a tendentious manner (whether out of a desire to protect religion, in your case it is Judaism, or out of a lack of honesty or understanding regarding the true essence of scientific activity).
    And regarding the examples you gave, I do not doubt that much wisdom can certainly be found in the sources of Judaism (of which I am not knowledgeable). However, there are wisdom writings in other religions as well, even those that were not directly influenced by Judaism such as Buddhism.
    The saying that "in science there is a current similar to religion" is unfounded and, as mentioned, it is motivated by non-material considerations. In the institutions engaged in scientific activity there is nothing that can even be called a religious activity.
    The strict standards of scientific work not only leave room for challenging existing theories and presenting alternatives, they also establish benchmarks by which different theories can be distinguished. This is what gives scientific activity the ability to develop and learn from mistakes.
    Science has changed countless times the basic picture of the world that it tries to represent. The changes that have been made are not random, but there is a clear direction in the development of science - as science develops, it accurately describes and finds more of the observations collected from the world around us. This is the touchstone of science that determines the direction of its development - nature determines for science what is a more correct description of reality. Science has never claimed and will never claim that it has the theory that describes reality as it really is. If there is anything that can be learned from the scientific activity of the last centuries, it is that theories are temporary and not absolute.
    The scientific establishment not only accepts these standards, it encourages them. Criticism is not a marginal part or a byproduct of scientific activity. It is the heart of science and the thing that drives its development.

    This has no counterpart in any religion and that includes Judaism.

  20. Shlomo:
    It is really interesting to meet a religious person who has not heard of the chastity vigils.
    Since the Torah is claimed as a book that gives an answer to all questions while it is far from providing the goods, there are issues on which religious people can argue, but anything that the religion has established - there is no debate about it, and the one who argues, many times - death.
    The philanthropist will argue that the observance of modesty is an unusual thing that even religion opposes, but beyond the fact that this is clearly not true, he will still have to confront the fact that in our century (1966) in the Jewish and democratic state of Israel, the Rabbinical Court ordered a deaf woman who was widowed before she had children to be raped by my brother her husband (who was married to someone else) so that she could remarry.
    Of course, there is no need to repeat the refutation of the nonsense you keep repeating about science being a religion even though he never commanded anyone to do anything because of science.

  21. to Liza
    According to my understanding, Judaism is in no way similar to Catholicism, nor to the religion of science, in this respect that there are no binding dogmas (there are even two different versions of the creation at the beginning of the book of Genesis). Every current is legitimate and it is possible to challenge almost everything (and there are also many who challenge without a problem, and without encountering censorship or excommunication) and you can even argue with God about his decisions (see Abraham and the case of Sodom). The boycott of Spinoza stemmed from the perception that he actually renounces belief in God itself, which is the basis of every religion.
    To give you an example of a challenge to conventions, I will point out to you a discussion that took place thousands of years before Leibniz's question came up, and the topic of the discussion has a certain resemblance to this question, at least in terms of radicalism:
    "Tano Rabnan: two and a half years Beit Shamai and Beit Hillel were divided. They say: It is more comfortable for a person who is created than not. And they say: It is easier for a person who was not created than he was created. They enumerated and finished: it is easier for a person who was not created than he was created. Now that he has been created - he will fumble with his actions." (Irobin XNUMXb). It is clear that the discussion itself can be perceived as heresy (since in the story of creation God gives the creation of man the grade "very good"), and the conclusion of the discussion is a matter of general doubt. And such examples can be found in abundance. But I don't see much interest in it, since my whole argument was that in science there is a current similar to religion. I have never tried to claim that Judaism is a science and you will not find even a hint of it in anything I say. It is also clear that over the generations various currents in Judaism have made great and even horrifying mistakes in understanding the world in which they live, apart from the political consideration: the fanatics of the Second Temple, Rabbi Akiva and his false Messiah, and closer to our time the rabbis in Europe did not understand the essence of the Nazi threat.

  22. Shlomo:

    I agree with some of your points. The fervor in which people (including scientists) condemn theories (among other things scientific) can indeed be reminiscent of religious belief. You can see a lot of evidence of this phenomenon on this site.
    My objection to this claim is that it is valid for any cultural phenomenon (and not every cultural phenomenon deserves to be called a religion). Some argue that every idea (or meme as Dawkins called it) fights and competes for its place in consciousness. This is true for religion, science, politics, economics, art, etc...

    However, another phenomenon that can be noticed (among other things in your comments, although it is worth noting that in a smaller dose) is an attempt to make artificial comparisons between religion and science, thereby defending religion and elevating the status of science. The "religion of science" is such an attempt (which, by the way, is also a kind of meme that competes with my meme that I haven't found a name for yet).
    When you create an analogy between religion and science based on some similarities that we have agreed to exist between the two, you unwittingly create new similarities that did not exist before, and about which one should be careful (see the example of the plane, the bird and the vacation). Such is the parallel between a religious establishment and a scientific establishment - when has any scientific establishment tried to tell people how to get married? Or with whom to marry? Where does each of these institutions get the ideas they advocate? What is the rational basis for interviews with whom he is identified? When was the last time any religious establishment recognized a fundamental error in its understanding of the world? When was the last time any religious establishment changed its basic assumptions?
    All of these are completely different between the two and constitute their identity.
    Given all of this, I would have no difficulty at all in saying:
    The religious establishment is for the scientific establishment
    As an apple is to an orange

    post Scriptum
    Brief news update:
    The "scientific establishment" updated Copernicus' model of the solar system and Galileo's laws of motion were also updated.
    The "scientific establishment" documents and acknowledges the multitude of mistakes made by the scientists who belong to it. A whole scroll of such mistakes can be recorded from the records of this establishment itself.
    What mistakes has Judaism made in understanding our world in the last two thousand years?

  23. to Liza
    As for my beliefs, I see myself as a general and unchurched Jew, because I do not belong to any sect or religious movement, I do not kiss the hands of any rabbi, I do not pay taxes in any synagogue, and I do not receive a salary or even a writer's salary for my faith. Just a small believer in a big God.
    And as for the analogy, as you call it. First I must make it clear that I am in no way claiming that science as such is a religion. There are many scientists who believe in God and of course do not believe in the religion of science and do not belong to the church of reason. And there are also many other scientists who, even if they do not believe in a higher power, do not accept the main body of the metaphysical dogmas, which make the church of the mind what it is.
    But out of the universities and the academic community, a religious establishment was gradually created, over hundreds of years. This establishment competed with the corresponding establishment of the Christian religion (mainly) in the war for control of consciousness and of course for the favor of economic and political power (ie, money, power, respect and influence). Willingly or not, this establishment, which I call the Church of Reason, has developed a narrative that will compete with the religious narrative. This narrative is supposedly "scientific", but in fact it is just as religious - if not more so - than the proper religious narrative. It includes martyred saints like Copernicus or Galileo. It includes defining moments such as the "monkey trial" in Salem or a man stepping on the moon. It includes scriptures such as Darwin's "Origin of Species" or Marx's "Capital" or Karl Popper's "Free Society and its Enemies", or nowadays the books of Hawking and Dawkins and many others - every sect and current and its scriptures. But the main point of comparison in the analogy, and the main point of the scientific-religious narrative, what makes the religion of science a religion, and the church of reason its establishment - is the basic assumptions and the identity in the status of the basic assumptions in the religion of science and in other religions. Notice, for example, with what fierceness and with what abysmal piety and admirable consistency Magonen Michael R. Ours about Darwin's theory, for example, and what a holy fury, including curses and blasphemies and expressions of disdain directed towards those who try to dispute its validity in any way. And all of it, let's remember, is a theory - that is, a kind of hypothesis, and essentially a belief. Exactly what lies at the foundation of all other institutionalized religions.
    Well, when you have some basic faith, in God or in his absence, in nature or in man, in reason or in fate; And when you later have an establishment that seeks to instill this faith, preserve it, expand the audience of believers, and all this with the help of people, writings and events that gain mythical status, and a hostile to contemptuous treatment of anyone who tries to challenge the faith, and many more lines of similitude and complete identities; Given all of this, it will be difficult to claim that the comparison between the Church of Wisdom and a religious church is like comparing apples to oranges.
    (By the way, Marius Cohen, thanks to whom we are debating here, published an article at the time in which he tries to distinguish science from religion, and there is a link on the website)
    As for morality, it seems to me that the highest value in Jewish morality is the sanctity of life. God is a living and existing God, He gave us a spirit of life and the Torah is in the sense of "and you lived in it". As for the question of good and evil in this context, it is true that sometimes you are in a situation where you must do evil. For example: "The one who killed you is the wise one to kill." But this is the extreme, rare case, while the rule is that for the sake of life one must stick to the good and stay away from the bad.

  24. And besides, Shlomo, do you really think that a position that includes internal contradictions is really preferable?

  25. Shlomo:
    In addition - you are just confusing the brain.
    Thousands of people shouted that Deri was entitled and only the prosecution claimed that he was guilty and yet they convicted him.
    There is a difference between the authority attributed to person A and that attributed to person B.

  26. Shlomo:
    It is said about this "eat shit because there can't be trillions of wrong bacteria"

  27. To Michael Rothschild:
    If I understood your words correctly, when all humans, or close to it, accept the beliefs of the scientists, they must be treated seriously, as reliable witnesses, let's say, and hence also that the theory they accept is serious and reliable. But when almost all of these people themselves do not accept - at the same time and at the same time - a certain scientific theory or even accept its opposite - they are in the sense of those who have turned off their minds, and hold stupid opinions. Any novice lawyer will tell you, Michael, that it is better not to refer to such witnesses at all and not to completely trust their testimony and judgment. Why don't you reveal your true opinion, a cabalistic glimpse from your words about everyone who disagrees with your opinion? Namely, that about 2.5% of humanity, all of whom are believers in the religion of science and members of the establishment of the Church of Reason, are the only wise, enlightened, and seriously knowledgeable, and all the rest are just fools, liars, mentally retarded and poisoners of wells? What is this fake populism for you? He gives you nothing, complicates it with contradictions and refuses to exhaust your arguments.

  28. Shlomo:

    I would love to join the interesting discussion that arose here.
    Can you share your beliefs with us? What church do you belong to?

    Regarding the analogy that you seem to like very much:
    It is true that a similarity can be found between religion and science. between scientists and priests. Between church and university. Is this enough to call science a religion?
    There are similarities between many things (in fact, it's hard for me to think of two concepts for which no similarities can be thought of). Between an apple and an orange, between a horse and a cow, between a bird and an airplane, etc... Is an apple an orange? Is a horse a cow? Is a bird a plane?
    Just to clarify, I believe that the power of analogies is greatest. The ability to find an analogy between fields or concepts that seem completely different, is reserved for virtuous individuals and is, in my opinion, the highest measure of a person's intellectual abilities. However, not every analogy is a useful or instructive analogy or one that brings with it insights. Analogies must be used judiciously.
    Saying that there are similarities between a bird and an airplane does not mean that on my next vacation in Europe I will fly on the wings of a cormorant.
    By implying that religion and science are the same, you are ignoring the great difference between the two.
    Of course science can be called religion based on certain similarities. Of course, sometimes in a certain context scientists can be called clerics - but this would be as a criticism of a deviation from strict scientific norms and not the other way around. Religion is a symbol of mental fixation. The essence of science is a repeated challenge to outdated dogmas.
    Science can also be called religion out of hidden motives, for example out of a desire to elevate the status of religious beliefs to the status of science, which few would disagree with. But these comparisons are stupid. Anything can be called anything else but most of the time it will be worthless.

    And if we are talking about values, the discussion about morality is definitely a proper discussion. Are you a relativist? Or do you think good and evil are absolute?

  29. Example:
    To get an answer you have to ask a question. You didn't. At least not in a way that allows you to understand exactly what your illness is.
    To give you a diagnosis - the anamnesis must be continued.
    How many times a day do you suffer from these hallucinations?
    How many times a day do you enjoy them?
    Why do you feel an irresistible urge to use words you don't understand?

  30. An example of axioms!
    *-The Big Bang- a stupid assumption that is based on dynamite and watching a supernova.
    And today the whole exalted community of scientists is busy debunking this nonsense.
    Also, if one plus one equals two (there is no truly perfect one in cosmic nature,
    Apparently also in the elementary particles) so what's wrong with the pi ratio?
    Can we get an answer Mr. Rothschild:

  31. Shlomo:
    I have always said that everyone has beliefs and that I repeat it for those who perceive slowly does not indicate that I am convinced of false claims.
    Also, the fact that I say some things that are self-evident, such as the fact that the scientists as a community usually do not stick peas in their ears - something that can be seen as another law of that community does not indicate that I am convinced that you are lying.

    All human beings believe in the things that scientists believe in, but because they have turned off their minds - they do not see that these beliefs contradict their other beliefs.
    Shutting down the mind is also what causes you not to understand that the fact that 90% of people believe in the existence of a higher power is not in contradiction with the claim that everyone believes in critical thinking, the laws of logic and the fact that the input of the senses has a connection to reality (and these are the only beliefs of the scientific community as a community - regardless of beliefs/ Personal conclusions that some scientists come to. For example - I assume that most scientists today do not have any faith that is related to you in my time actually there is and there is).

    So it is true that a large majority of people hold stupid beliefs in addition to the necessary beliefs that science holds - but this, as mentioned, is only a result of their willingness to hold contradictory beliefs.

  32. to Michael Rothschild
    "Every person has beliefs," you write, "and the beliefs that science is based on are beliefs that are shared by all human beings." You admit, then, that science is based on beliefs. Elsewhere in your response you refer to the "scientific community", everyone knows what it is. And in another place you even acknowledge the existence of a law that the scientific community wants to preserve. It seems to me that little by little you are convinced, Michael. Because if we already have faith, and law, and an institution that seeks to uphold them, we have religion. I also noticed that in another place you yourself use the concept of the church of the mind, although in quotation marks. Nice, Michael, nice.
    As for your assertion that the beliefs on which science is based are shared by all humans, it seems to me to be a bit sweeping, if not just a wild exaggeration. For example, according to all surveys known to me, at least 90% of the people in the world believe in the existence of a higher power (some kind of god), while only a very small minority, 2.5%, completely reject the existence of God (the rest are partial believers in God or those who do not want to take position). But it is precisely this rejection of the existence of God that underlies the main scientific dogmas of the type of Darwinism. So perhaps it is more correct to say that a large majority of people in the world actually reject the beliefs that stand at the foundation of the religion of science. And no, I didn't forget the second part of the sentence you wrote."Although some people are not ready to accept the conclusions of their beliefs and continue to adhere to contradictory beliefs as well." I mean, what? That more than 90% of people (the "part") are morons and deniers who continue to adhere to beliefs that contradict those of science, even though they actually believe in science and its beliefs?
    I notice that you avoid with remarkable consistency the comparison between the Nazi religion and between the communist religion and the capitalist religion. Is Marxism-Leninism in the style of Stalin, or capitalism in the style of Ayn Rand or Milton Friedman, in your opinion, logical, and encouraging critical thought (that is, strictly scientific), as opposed to Nazism? Only we will know.
    And as for my understanding of the concept of "tautology" - I have already read your definition of the concept, and it seems to me that in order to have a proper discussion on this matter, you should be a little more interested in the subject.

  33. And by the way, Shlomo, you have no idea what a tautology is, but it's not important.

  34. Shlomo:
    Regarding A - it's just a gross lie. The scientific community does not have any laws, it does not have any coercion and it does not have any characteristics of religion.
    Regarding B - this is another nonsense. What they did at the Hebrew University is far from enough to restore logic to our districts. The appointment of a man who tells us that because God told him something then the conclusions of science are not correct as chief scientist of the Ministry of Education is an act of unbelievable madness - especially when this man also declares that he intends to fight science. It would be fine if they appointed him chief rabbi of the Ministry of Education but chief scientist? You exaggerated!!!
    Regarding c - you define the desire to understand reality as it is - without inventing an imaginary friend as a religion - again - this is simply nonsense and I have already explained what the characteristics of a religion are and why science is not a religion.
    Every person has beliefs and the beliefs that science is based on are beliefs that are shared by all people even though some people are not ready to accept the conclusions of their beliefs and continue to adhere to contradictory beliefs as well.
    As for D - this is another quibble.
    I said that Nazism is a religion - it is true. Does this make logic and critical thinking a religion? how? After all, Nazism does not make sense and does not encourage critical thought! Just like the other religious establishments - it bothers to turn off the mind.
    So it's true - the "Church of Reason" has one and only law of conduct and it is the law that says "not to turn off the mind" but it is a self-evident law - for some reason you do not call the community of people who uphold the law "not to amputate the legs if there is no medical need" by name religion.
    Nazism is a religion and therefore it excludes itself from the "Church of Reason".
    The logic of your delusional claim is similar to the claim that because the Nazis ate then anyone who eats is religious.
    Regarding the - we have no escape from moral relativism in the sense that those who determine what is moral and what is not are human beings - neither God nor any other external entity.
    It could be terrible if evolution had not instilled in us over many years - a fairly uniform sense of what is moral and what is not. All the fatal differences of opinion on the subject are the result of religions. None of them are the result of adherence to logic and critical thinking.

  35. to Michael Rothschild
    The thought that I caused you to waste your time must have claimed me for the entire time and I apologize. And if you also felt the syndrome of poisoning my words - you can raise my apology with some presumption, and from now on you are exempt, as far as I am concerned, from any reference to my words, although I would be happy even if you did not take advantage of it. But since I do not have such sweeping reservations about your words and I have not earned myself a corresponding exemption, I will allow myself a few comments:
    A. I absolutely agree that religion is a law, and no less a custom and tradition, and in short: a foundation of faith. Whereas a church is the religious establishment (usually paid) that exploits the faith and controls the religion over the believers, sometimes even by coercion. Usually the church also engages in missionary preaching. All these definitions also apply to the religion of science and the church of reason.
    B. There is no necessity that for a religion to be created there must be a deliberate intention to create it. Nor is it necessary to believe in any god to establish a religion. For example: the Buddhist religion. Buddha certainly did not seek to create a religion, and God was irrelevant to him. But anyone who sees the faithful lighting incense in front of a huge golden statue of the Buddha, knows immediately what is in front of him. And similarly the Church of the Mind. Just a few weeks ago, the president and the rector of the Hebrew University in Jerusalem announced a few minutes of silence and silence in their institution when it seemed to them that the new chief scientist was violating the sacredness of their faith. And when there is faith, scriptures, priests and pastors, followers and devout believers, it is a religion, even if its leaders and believers call it Chapdukulu. By the way, even at the beginning of the "Enlightenment" period there were some thinkers who sought to institutionalize their faith as a formal religion with science at its core.
    third. At the foundation of the religion of science are mainly the beliefs in rationalism (hence the term church of reason), naturalism and objectivism. The main war of this religion is directed against the monotheistic religions, and at the same time it establishes for itself an ecclesiastical example based on the beliefs mentioned at the beginning of the paragraph and sets up its own narrative that will explain the history of the universe and the human race in such a way that it contradicts or at least ignores God as creator.
    d. When you say that Nazism is actually a religion, dear Michael, you only agree in my opinion (although it is not clear to me why you do not treat the other sects of the religion of science in a similar way. Is the blood of those killed in the Nazi concentration camps redder than the blood of those killed in the Gulags? Or the blood of The innocent Japanese who perished in Hiroshima and Nagasaki? Or the blood of the Haifa Bay and Kishon rioters? Why do you agree with me that Nazism is a religion - and are silent about communism and capitalism?). In the twentieth century, a tremendous religious war was fought between the three main sects of the religion of science (like the Reformation wars between the Catholics and Protestants at the time, or the Shia and Sunni wars in Islam today). In the various pasts of the front stood the racist religion (scriptures: The Protocols of the Elders of Zion, Mein Kampf, etc.), the Marxist religion (scriptures: Marx and Engels, Lenin and Stalin) and the capitalist religion (scriptures: Adam Smith, and closer to our time, Ayn Rand and Milton Friedman). And just as Catholics and Protestants believed in God and Jesus his prophet, what the three scientific religions (which also exist in our time) have in common is their belief in Darwinism, evolutionism, rationalism, objectivism and naturalism. It is clear that the branches of the Church of the Intellect that deal with the exact sciences or the various natural sciences, such as mathematics, physics or chemistry, were happy to cooperate with the ecclesiastical establishments in their countries and made available to them without any moral considerations and while taking strictly scientific objectivism the most terrible forces of destruction, then as well as now.
    God. All of this is of course nicely related to the article here. Those who believe that at the foundation of the universe stands a good and benevolent God, cannot advocate moral relativism. And those who believe that the basis of the universe is a Platonic idea of ​​a mathematical structure cannot but advocate moral relativism. And speaking of a Platonic idea - it's a shame that the author of the article did not choose the idea that Socrates and/or Plato themselves placed at the top of the hierarchy - the idea of ​​the good (about 1000 years after our Hebrew ancestors) and instead went for Pythagorean mysticism.

  36. Nature is not mathematical - we are.

    During evolution, there was probably a preference for creatures that are able to build computational models that represent the environment they are dealing with, and with their help try to predict
    and improve their chances of survival.

    Therefore, if we reduce all the "layers of explanations" we have to the world of phenomena, we will indeed arrive at a pure mathematical model that describes the physical / chemical / biological reality, etc... but this model will describe the way in which we are built, and not how what surrounds us is built...

    We are locked inside consciousness... and there is no pill that can get us out of it 🙁

  37. Shlomo:
    You ignore what you are told and pour out your poison without any shame.
    That's why I will explain to you one last time because it seems that you do not understand.
    "Religion" is a word of Persian origin and means "law".
    Of course, this refers to the law that dictates the way humans behave and not to the law of nature.
    A church - in case you didn't know - is a religious institution.
    That's why the "Church of the Mind" is nonsense. There is no such thing and nothing bad has yet happened because people thought logically.
    You allude to the crimes of the Nazis and ignore the fact that Nazism was really a religion.
    It had murderous and idiotic rules of conduct that in no way stemmed from reason.
    In fact - all religions are based on turning off the mind - that is - on replacing critical thought with commandments that come from an indisputable source.
    The monotheistic religions invented God for this and Nazism invented the theory of race.
    The fact that they used terms from the theory of evolution is only because people are stupid enough (like you) to buy this bullshit.
    Evolution talks about what happens in nature and not about how one should behave.

    But I really think I'm wasting my time on you. After all, I didn't actually say anything new here, I just emphasized obvious things and if you wrote the nonsense you wrote, you certainly did so knowing all these facts and deliberately ignoring them.

  38. To Michael
    Nevertheless, one more small thing before the stars appear and the dumplings are served: almost all religious establishments have committed, and some of them still commit, horrific crimes and clearly immoral acts, and in my eyes at least their actions are doubly bad because they take God's name in vain. But all these crimes, throughout history, are not
    We are approaching, not even cumulatively, what the Church of Reason did during the last century, and what it continues to do in this century. And I'm talking about math. Counting human and animal skulls, and mathematically measurable physical damage to our wretched planet. Happy holiday again.

  39. Michael Rothschild
    A. When the author of the article says that 'physical reality itself is nothing but a mathematical construct', he is claiming exactly the opposite of what you are saying about his claim. Note the words "is not but". In other words, there is nothing real in reality other than being a mathematical structure.
    B. You will not find a loyal partner from me in any war against any religious establishment - including the religious establishment you belong to, or its supporters, despite attempts at denial. As for morality, please note that I wrote that "the starting point of faith is distinctly moral". While the starting point of every religious establishment is the utilization of faith for the needs of the mediators between the believer and his God. All the rest after the holiday. Happy holiday.

  40. * What is the mechanism that enables the physical existence of countless "parallel" universes? We find it difficult to explain even the existence of one physical universe, much less the existence of countless such universes.

    The answer to this question is actually very simple: we must conclude that there is more than one location, because the properties of our universe indicate this, such as the specific values ​​that the constants of nature receive. This is like finding a distant planet, where only a single (and fairly developed) organism exists, without any evidence that other life exists or has ever existed on this strange planet. It will be much more difficult for us to explain the origin of this mysterious organism, than the origin of all the billions of life forms on KDA (evolution). This is an example of a situation where giving an explanation for a single case is infinitely more complex and complicated than giving a general explanation for multiple cases.
    Therefore, in this case, "Ockham's Razor" actually dictates that the most probable possibility is that there are multiple universes, not one. And this is also the answer to the fourth question, which is actually the same as the first question only with a slightly different wording.

  41. Shlomo:
    I do not agree with any of your claims.
    Let's start with the tautology thing, when I read it I still thought you were just confusing yourself and not waging a war against the truth here.
    A tautology is a self-evident thing (not necessarily easily but necessarily as a conclusion of a set of axioms accepted by all) without the need to be based on information that comes from the world itself.
    For example - all math sentences are tautologies.
    This is not the case here - because here. Here in the interpretation there is a claim about the world which we perceive as "outside of mathematics".
    It is true that the claim is that its existence is derived from mathematics, but this is a claim that until you have proven it, you are not entitled to claim that it is a tautology.

    Of course, reading the continuation of your words, I already understood that the truth does not interest her at all and you are actually in a holy war against it.
    The starting point of religion is not morality.
    On the contrary.
    It tries to mobilize man's (natural, evolutionary) desire to behave morally and sells him a "morality package" whose entire function is to make him a loyal servant of the religious establishment.
    Because she sells it along with explicit instructions not to be convinced by the facts - she manages to work on a lot of people.
    This is why the religious think it is moral to stone Sabbath breakers and homosexuals.
    They are so disconnected from true morality that it is simply unbelievable.

    Of course there is also no church of the intellect.
    There's just a collection of people who didn't let a stupid meme system turn their brains off.
    Of course, these people also have something to say about morality, and what they have to say about this matter is of much greater value than the lies of religion.
    Those who are interested in understanding something about the relationship between religion and morality - should read the book "Religion arose on its creators" by Yaron Yedan.
    Those who are interested in hearing something about the connection between reason and morality, are invited to watch, for example, the following link:

  42. To Moses

    Sir, if science does not suit you and seems to you like a competing religion to your private religion (instead of understanding that it is a universal and cross-faith way of life) then please go read the Hidberot or other sites that pretend to science what it is not and leave the real science lovers alone.
    Science is the mechanism for the pursuit of the truth and not a religion whose purpose is to determine what the truth is and then use various means to make people think it is the truth. The billions you milk from the state can help you steal the minds of many children, but it will not turn a lie into the truth.

  43. To Abraham Cohen

    Your first question to the author of the article is a burst into an open door, since he himself admits in his article right away that there is no possibility of empirical examination, as he says: "This position does encounter quite a bit of resistance from the scientific community (mainly due to the lack of possibility of empirical examination of it)" but at least I do not see this as a disadvantage , because I do not believe that it is possible to take too seriously the truth of the measure established by Karl Popper regarding the validity of scientific theories. This is because Popper's theory, itself, cannot truly live up to the standard he set. And if his theory is not scientific - then it is clear what it is: ideological. It simply fits into the basket of abstract assumptions of the church of reason, and that's why Popper gained the status of an ecclesiastical saint in the religion of science.
    The basis of the theory in this article is a definite tautological theorem. In one of the author's many formulations: 'Physical reality itself is nothing but a mathematical structure, while its "physical" components are the abstract objects of this mathematical structure' which is like saying that 'a donkey is a juvenile animal with four legs and long ears, whose physical characteristics are the abstract objects of its structure' The serious mathematician.”
    It's just that while according to our "intuition" it seems to us that the donkey's youth, short legs and long ears are its reality, the author of the article wants to convince us that its true reality is its mathematical structure, which does not depend on time, place or any material.
    The rest of your questions show the connection you are looking for between the theory presented here and human morality. But as far as the Church of Reason is concerned, any advantage of such a theory is the disconnection from morality. While the starting point of the faith is clearly moral ("And God saw that it was good" as the raison d'être of creation), the Church of the Mind seeks to disassociate itself from any morality, in part to justify its boundless cooperation - which pays its priests well - with the political and economic forces which actually lead to the destruction of our world. That is why a "mathematical structure" as the Archimedean point of creation can be so enchanting to believers of the religion of science, being devoid of any moral aspect.

  44. You are right, Michael.
    I'm sorry if I offended anyone, that's not what I meant.
    Have a good week and happy spring holiday.

  45. my age:
    Are you ready to take us out of your dreams?
    What is this chatter?
    Do you really not understand that math is not a language?
    Do you think that discrediting people who understand better than you is a better method than making claims with substance?

  46. The pragmatic approach uses a lot and especially mathematics, fact!
    And this is in order to develop and improve the industry, industrial products and our quality of life.
    hall. Mathematics is also used as imagination games, and recreation and amusement for some people.
    People who are extreme in the mathematical interest elevate this language to a limitless philosophical value,
    that the distinction between the number and the measure is not really important.

  47. Mathematics is indeed a language (a human language to describe what exists and "can exist" in the universe).
    But for a language of interpersonal communication such as Hebrew and English,
    Mathematics, after all, also pretends to predict the future.
    The ability to predict the future is valid to a small and laboratory extent, developments cannot be predicted
    that are influenced by influencers' io-branch.
    For example: Is it possible to predict what a jungle will look like in three generations of trees,
    For rough details and fine details, such as the location of the trees, and the distribution of ants on a tree
    certain at a certain time. That's not it.

  48. Mathematics like any language needs consistency and repetition
    And our universe is indeed consistent and cyclical.

  49. Uri, you missed the whole point. For a long time, physicists tried to build a mathematical model that would describe and predict the results of experiments done on particles, quantum mechanics. The only model, as of today, that predicts relatively accurately the results of the quantum experiments is a model of randomness. Does this necessarily mean that nature is indeed random?
    Coins, ripples of waves or clouds also appear random because they arise from phenomena with chaotic behavior that simulates randomness.

    In any case, we are going off topic here. Regarding the article, there is no phenomenon in the world that cannot be treated mathematically. Therefore, mathematics is considered the "language of nature" and your disdain for the ability of mathematics to describe the world and perhaps even to be the world (as the current article suggests) is puzzling to me. You claim that mathematics is failing and limited but many others claim that it is man's greatest achievement. Do you know a phenomenon that cannot be described with the help of mathematics?

  50. Uri, you missed the whole point. For a long time, physicists tried to build a mathematical model that would describe and predict the results of experiments done on particles, quantum mechanics. The only model, as of today, that predicts relatively accurately the results of the quantum experiments is a model of randomness. Does this necessarily mean that nature is indeed random?
    Coins, ripples of waves or clouds also appear random because they arise from phenomena with chaotic behavior that simulates randomness.

    Anyway we surf here. Regarding the article, there is no phenomenon in the world that cannot be treated mathematically. Therefore, mathematics is considered the "language of nature" and your disdain for the ability of mathematics to describe the world and perhaps even to be the world (as the current article suggests) is puzzling to me. You claim that mathematics is failing and limited but many others claim that it is man's greatest achievement. Do you know a phenomenon that cannot be described with the help of mathematics?

  51. Ori:
    I collected some of the responses of people who know how to appreciate what they get.
    I did this because there are also morons like you who should be given another chance to understand where they live.
    Regarding your claims about the limitations of mathematics - they merely present your personal limitations in understanding it and as mentioned - you ceased to interest me a long time ago.

  52. Machel
    If you went to the trouble of saving all the quotes of those you misled and licked you, it makes you a little brat in need of input and reinforcements for your inflated ego. You have not responded to any of the limitations of the math I presented because you have no answer other than your arrogance at the expense of humiliating others.
    Good, so now you will rewrite all the quantum physics they have done in the last hundred years and cancel the quantum uncertainty feature with the wave of your hand. You claim that there is no uncertainty, but this has already been conclusively proven in the laboratory, see Bell's theorem.

  53. Uri, you understand everything the other way around. In nature there is no randomness but things that happen as a result of a certain reason, the problem is that we don't always know the reason or can calculate it. For example, the decay of a radioactive particle, the only model that currently exists to explain the phenomenon is a mathematical randomness model. Randomness, like infinity, are mathematical concepts that very impressively describe and predict physical phenomena.
    If you think about it to the end, there is really no infinity and no randomness in nature. The same coin or cube, every fall obeys very deterministic laws, although they are sensitive and have chaotic behavior, the closest model to presenting them is randomness, but there really is nothing random here. Even pie, which apparently requires an infinite level of precision for its description, is a finite size called "pie" and the mathematical model that describes it will be... 3.14. The one that ends here is the mathematical model, not the physical element pi which represents a relationship between completely physical elements.

    What is beautiful is that mathematics can deal with any field and anything and probably also predict almost any phenomenon, the problem is with the power of calculation not in mathematics itself usually, to the point of the article's message that the entire world is a mathematical structure.

  54. Ori:
    A sample for your enjoyment:


  55. Machel
    You are arrogant and condescending as if you are the only one with qualified knowledge.
    Outside of arrogance you present nothing but insults there is nothing behind your ravings.
    You do not address even one question that I raised in a matter-of-fact manner, only the arrogance, arrogance of a rooster and the humiliation of the person in front of you and his cancellation. I clarified fundamental problems that mathematics is not designed to deal with and everything it does in these areas are only approximations. I presented additional problematic areas. You have not addressed any of these issues. You just presented yourself as having pride and dismissed my words and me and used words to humiliate.
    What did you show that you are a person without integrity and no morals at all and petty.

  56. That's it, Uri, I'm completely tired of you.
    I do not give orders and never have.
    on the contrary. In the army I was for many years in charge of many people and I never needed orders.
    It is true that since it was a framework of elite power in a computer unit and I could choose the best people, there were people much more intelligent than you, but here and there I also encountered stupid people and yet - I never gave an order to anyone.
    You are showing supreme ignorance here and I have no intention of starting to give you training that you should have acquired in kindergarten.
    Sweet dreams.

  57. Rach
    The probability is based on an existing phenomenon called a law. The math starts from this point. There is no mathematical expression that explains how the probability distribution occurs and why.
    The physical world is saturated with infinities and is based on the infinities. It is mathematics that reduces the infinities to approximations with error percentages.
    It is enough to examine the smallest particle, no matter which one you choose, it represents a collection of infinite sizes that mathematics approximates so that we can do something with it.
    You must have heard of perturbation theory. It took many physicists many years to find an approximate computational way for infinite quantum calculations.
    And by the same token, you may have heard that it is not possible to bridge the gap between relativity and quantum because of those infinities that no one has yet found a way to even calculate an approximation.

  58. And another Ori thing. Infinity is a pure mathematical concept, where do you have infinity in the physical world?

  59. Uri, what are you talking about? It is impossible to explain why a coin will fall an equal number of times on both sides? Have you heard of gravity? Weight? mass? friction? What is the problem with simulating a coin drop on the computer? And once we have done something on the computer it is pure mathematics because everything the computer knows how to do begins and ends with mathematics.

    And think what the computer is capable of doing, pictures, movies, music, robotics, that is, all of these can be calculated purely mathematically. What can't be calculated? Come and say the trivial answer "feelings". Not true, emotions can also be calculated because they are based on biochemical activity. ideas? same as above.
    So what exactly can't mathematics touch?

  60. Machel
    You are probably used to giving orders. It seems to you that you are the only one who understands and no one has the right to dispute your assertions.
    When I read your words I conclude from the content of the things that mathematics is your "example" the unshakable idol.
    And you think that no one has the right to challenge this determination.
    You make a false and fake claim and mislead others by saying that mathematics knows how to handle randomness and infinity perfectly and accurately. Everything that mathematics does in these areas is only "approximations".
    All these mathematical calculations represent an erroneous value of some magnitude, however small it may be, but mathematics is not structured in such a way that it can get rid of these errors completely for ever.
    ZA that the solutions are always approximately as accurate as you claim they are only up to a certain limit.
    The mathematical structure is built solely on approximations.
    If you could get rid of the approximations it wouldn't be the same math at all.
    Because you had to change many fundamental things in mathematics itself.
    But these are only the small problems.
    Mathematics itself works on rules of thumb, it cannot explain the laws themselves.
    For example, tossing a coin a large number of times will always give an equal average of falls for each face of the coin.
    Can mathematics explain the reason for the law behind this dispersion?
    No and there is no explanation. Mathematics accepts the aforementioned law as an existing fact and starts from there.
    Is mathematics able to explain the connections that are revealed within mathematics itself between different structures.
    Of course, it cannot only show the connection, but in no way explain why a certain connection exists.
    Because if she could explain the reason for even the most trivial relationship, it would be possible to predict the existence of additional relationships through this insight. But it is denied to you because mathematics is incapable of doing such things.
    If she was capable she would no longer be a mathematician.

  61. I don't understand why if the universe is physical, you might ask why it is sleeping, even though we have no clue about it and its nature (except for the knowledge of the phenomena). And if we say that he is mathematical then we will understand that mathematics is eternal?

  62. A. Ben-Ner:
    I forgot to reiterate what I said here already in previous responses: mathematics is not created by man but is discovered by him. It exists with and without him and does not depend on him as such.
    Mathematical research creates the knowledge we have about mathematics but not the laws of mathematics and I have already mentioned many facts that confirm this claim beyond any reasonable doubt.

  63. A. Ben-Ner:
    I also make the distinction between mathematics and physics.
    This is evident both from my comments here and from my comments elsewhere.
    Also in this discussion you can read about things that I pointed out that exist only in mathematics and not in physics (the number i) and moreover - about mathematical structures that were created as such and only later it was discovered that they have a representation in physics (the non-Euclidean geometry) - as well as about mathematical structures that were thought to represent the Physics and later it turned out that they were not, but they continued to be valid mathematical structures (Euclidean geometry).

    I have also explained more than once that mathematics is built on axioms that describe models and there is no place for experiments, while physics deals mainly with experiments and the discovery of the mathematical model that is suitable for describing the findings arising from the experiment.
    In fact, physics deals with the discovery of those mathematical structures that have a representation in the structures that exist in our world.

    Physics is not God's creation because God is man's creation, but that is another matter.
    What the article we are commenting on (and I get the impression you haven't read) claims is that the mathematical models are sufficient and there is no need for structures outside of mathematics.
    I do not share this opinion (this opinion really does not distinguish between physics and mathematics, but it does so consciously and not out of a lack of understanding) but I do not know if you will ever find a way to refute or confirm it (although I have certain thoughts on the matter but they are not yet mature enough to be published And as I suggested to others to do - I usually think with my head and not with the keyboard).

  64. Ori:
    Maybe the first logical step for you to take is to stop telling me lies about what I say?
    What do you think?
    I did not say that mathematics is the vision of everything. for example. But that's just your stupid accusation from the last comment. There is such a lie more or less in every response of yours.
    You have heard some words about mathematics and it turns out that you do not understand them.
    If you had any idea about it, you would know that mathematics is the only tool we have to deal with infinity - including comparisons of different numbers and arithmetic operations between them.
    Mathematics is also the only tool we have to deal with randomness.
    Besides - I repeat - the fact that mathematics has a language does not mean that it is a language. It has a language because the other languages ​​do not provide the level of precision and sharpness needed to think about things accurately but the heart of mathematics is the real things it deals with and the heart of the practice of mathematics is pure thinking. All these are not language and changing the language will not help at all.
    And again - I repeat and implore you to reveal to us where you get the feeling that you know better than Gmark, the author of the article or me. Has your amazing mind created any fruit that serves humanity?

  65. To Michael
    I think that you do not make the necessary distinction between physics and mathematics
    Your claim that:
    "Mathematical structures are only discovered by man. Nature obeyed the laws of mathematics long before man was created"
    Here is a mistake, if only in the definition of the concepts of "physics" and "mathematics". With your permission I will explain briefly:
    Physics, the one we know today and the one not yet known, is nature in its total lawfulness.
    This is the definition of physics.
    Mathematics is the set of laws and rules as formulated by science, with the aim of investigating physics.
    Physics is God's creation and nature as a whole.
    Mathematics is the creation of man-science. This is perhaps the reason why the math is not perfect. There are some undefined points.

  66. Machel
    Mathematics is not the be-all-end-all as you try to make your mind up about it.
    Its main limitation is that mathematics is unable to handle randomness at all.
    In the same way, mathematics is not able to deal with infinity except by canceling it through limits and the like.
    However, mathematics is not designed to address this end directly.
    The technique of the borders is actually eye catching because you can never be infinitely precise.
    You must agree to a compromise on the level of accuracy or alternatively on the amount of error that suits you.
    Although in practice you are able to make technology using this method you always have a limit of accuracy.
    And so it is actually an eye catch because if, for example, there is some place in the universe where another language exists that does know
    Dealing with randomness and infinity, surely there is no mathematics there but something else entirely.

  67. Ori:
    You probably really don't understand what you are being told.
    The only one here who tries to close the width of the world of thought and allows himself to define mathematics as a language is you.
    I come back and suggest that you reveal to us what your "wide" world of thought has created. You jerk.
    And as for the style that cancels out other things - after all, this is where we started - all your responses - including the first of them boil down to exactly this - apart from the poor attempt to cancel out other things, there is nothing in them.

  68. Avraham Cohen,
    Regarding your paragraphs 3-7, what is the connection between theory for the good of man? There is among the people and also unfortunately among many researchers a tendency to look at science as a tool whose sole purpose is to improve human life. In my opinion, this is an important goal, but it is by no means the only one. What's more, basic research that stems solely from human curiosity (compared to applied research) has in many cases led to insights that made the applications possible. That is why theories should not be measured by the "improvement of the quality of life" that they provide.

  69. Machel
    The attempt to close the breadth of the world of thought and the breadth of reality into a narrow-minded framework is pathetic.
    In your approach, you remind me of the military approach that does not give room for questions, only for answers.
    Do you think the world will rise or fall by command. Is it at your whim or the whim of an army of pretenders
    Those who tell us here is the answer, we are the ones who understand and we own the thinking.
    In this you will stop the progress and allow only the militaristic approach that imposes a certain way of thinking.
    Your military approach is expressed in the way you answer that you tend to immediately dismiss the other person's opinion and damage his talent and abilities. This is a wild, violent and immoral approach by force will achieve nothing. do you think you can
    To give orders or orders and manage the world of thinking only according to the military rules is a big mistake.

  70. Ori:
    Not true.
    Mathematics is not just a language. This claim is so far from reality that it is hard to believe that anyone would try to base an argument on it, but it turns out that there are still those who do.
    It's really a waste of time to talk to you - what's more, you treat a respectable group of people with disdain, each of them put you in the small pocket of their pants that they threw away when they were already small on him at the age of 3.

  71. Machel
    Mathematics is a language and nothing else. Can you prove that this is the only possible language to control physical reality better. You will not be able to prove from the language itself something that is outside the definition of the language.
    There are many mental beings that mathematics is in no way capable of describing and quantifying.
    Mathematics is not able to describe everything related to human cognition and thinking itself.
    Human thinking is much smarter and richer than the language of mathematics.
    And yet the entire above article is pathetic because it tries to give an answer from a narrow field of knowledge about a much broader field
    From him human thinking and cognition. Doubts and questions originate in the human mind, these are the things that push a person to move forward. The attempt to present as if there is a solution is actually trying to dwarf and limit to a narrow place the magnitude of human thinking and cognition which is far beyond mathematics.

  72. falcon.:
    True, philosophy is philosophy.
    I said no?
    I only said that there is a difference between philosophies and the philosophy offered here stands out for the better among them.

    I see no point in talking to you and I've already explained that.
    There is a minimal level of understanding and debate that people who don't reach I find no point in wasting my time.
    In a world without mathematics you will not be able to do anything because mathematics is nothing but a development of logic and a world without mathematics is a world without logic. It's a world where there is no language (whose entire structure and laws are mathematical) it's a world where you can't cross the road because the fact that it's currently free and there's no car within kilometers doesn't mean that you won't be run over in a second (well, of course in such a world there are no roads and cars on the way rule but even if you are walking in Savannah and there is no road and a car there is no way to conclude that you will not be run over in a second by ten cars speeding on the freeway).

    ghost moon:
    you're back?
    I can be convinced but false claims are not the way to do it.

    I do not justify your thought.
    I brought Euclidean geometry as an example and the fact is that when you build a world that matches it (and I have described such a world) it really works and not just approximately.
    I have already brought the number i as an example in another discussion. It is a number that has no representation in reality and yet the mathematics based on it - when it yields real numbers - works in reality.
    The point is that the relationships between this number and the actual numbers are defined in a way that conforms to the laws of logic and therefore it is not possible otherwise. This is also due to the fact that the laws of logic do not depend on the existence of this or that reality.
    Many mathematical theories were discovered without any relation to the real world and only later it was found that they corresponded to some real thing.
    Non-Euclidean geometry is a good example of this.
    As soon as an actual structure fulfills the axioms of a mathematical structure - all the conclusions drawn as sentences arising from those axioms apply to it as laws.

    Avraham Cohen:
    Let's treat your response as a theory claiming that you are satisfied if the theory in the article will give a useful answer to the questions you presented.
    Now please ask the same questions about this theory and if the answers are not good - explain to us why you wrote it.

  73. The article and theories are interesting in terms of internal logic.

    Open questions for the author:

    1. Could there be a way/experiment to verify or disprove the theory?

    2. Is the theory able to predict any finding? (phenomenon, particle)

    3. Can the theory (correct or not) have any practical use?

    4. Does it have the potential to improve the quality of life?

    5. Is she able to bring balm to the patient?

    6. Can you bring food to the hungry?

    7. Does she have the ability to prolong life? (Literally)

    I doubt.

  74. Machal, in my opinion you exactly justify my claim. When Euclid and his peers created geometry they started from axioms that seemed to describe reality well. They built the entire structure on it. Only today we know that these axioms are nothing but an approximation of reality. That is, the beginning was based on the physical world (or what is considered such) and the continuation was an exploration of the meanings that derive from the axioms. So it is a combination of invention based on observations (the axioms) and investigation that led to the discovery and proof of the theorems that derive from them.

    Uri, you speak decisively out of a lack of knowledge. Rothschild did not invent the idea that mathematics is the vision of everything or that the world is a mathematical structure and your personal attacks on it are a bit unnecessary. I suggest that you read Mario Livio's book "Is God a Mathematician" which discusses the development of these ideas throughout history and maybe you will realize that the issue is not as simple and clear as you think.

  75. Machel
    A world without mathematics is no different from a world without television.
    Mathematics is simply the language used to control technology and physical reality.
    It is possible that there are additional languages ​​that may be much more efficient. It is possible that more efficient languages ​​will allow technology redundancy at a much higher level.
    It is equally possible that the place of television in such a world will be replaced by a much more efficient technology.
    Mathematics as it is today is not an effective language at all, there are many people who have difficulty using it.
    It is not an ideal language in many ways because it sets many limitations and boundaries.
    Your private tendency to love and adore this language as if it were the face of everything is completely pathetic.
    Just like your claim that you got money because you understood something. After all, it is only according to your own personal opinion.
    You got money because you managed to convince someone to give you money. Just as someone won in the stock market or casino.
    The fact that you imagine all kinds of stories that stand behind it are grandmother's stories.
    It's a matter of luck and nothing else. You had the right luck so you made money it has nothing to do with understanding.

  76. Michael, philosophy is still philosophy, the difference is mainly "quantitative" and any philosophy, good or bad, requires a maximum degree of skepticism, when the ambition should always be to try and attack it in one way or another.
    There are good "philosophies" and there are less... the main difference I see between the two is that a "good philosophy" expands the boundaries of thought and paves the way for a more accurate discovery of the truth while the "bad" one does not.

  77. Rah:
    Regarding the axioms you mentioned - it seems to me that you are not referring to the right thing.
    Which axioms of certain mathematical structures do not need the real world and experience in it in order for them to be correct in that mathematical structure.
    More than that: one of the axioms you mentioned - the axiom of parallels - is only true in Euclidean space and not in the world we live in, which since the theory of general relativity we know is not Euclidean!
    So here you have an entire body of mathematical knowledge (Euclidean geometry) that everyone knows what is true and what is not true in it - yet there is no structure in the physical world that obeys its axioms.
    Well - this is not entirely accurate because since we know the axioms of Euclidean space - we use it to represent structures that we ourselves created - such as the relationship between the amount of dolls that are bought and their total price - but these are man-made structures that were created based on our understanding of mathematics. These are not structures you would find in nature if there were no man.

  78. Rah:
    For some reason, it is completely clear to me that mathematics stands on its own merits and that "nothing" is even possible that does not at least include it.
    I say again: you will not be able to get a good answer to the question "why is the math correct" because anything that you consider an answer will be something that is based on logic - that is - on mathematics.
    From here to the claim of the article the distance is still great and I am not ready to skip this distance easily but as mentioned, I have no problem with the claim that mathematics does not depend on anything and does not derive from anything. On the contrary - I'm sure this is the case.

  79. I am with Ra'anan on this issue and I could not have phrased what he wrote better. Mathematics on the one hand describes the physical world beautifully but if we remember where it started, with axioms derived from the physical world. For example, one line passes between two points or 1+1=2 are derived from experience that stems directly from the physical world and in fact it is hard for us to imagine a world where they are not true. Mathematics was built on top of the axioms, which indeed also predicts undiscovered physical phenomena. Is it so clear from this that mathematics is the vision of everything? Or is it possible that it is just a powerful theoretical tool of reality? (And I really don't have an answer).
    Another philosophical question that arises from the discussion is what is the definition of nothing? Can we really describe anything?
    Of course, nothing can be described in the negative way, we will remove all the things and be left with nothing. According to the article's method, is it possible for a world/state/universe even without a mathematical structure that is nothing real?

  80. There is a very clear application to the article, there is no problem to murder, steal, send spam messages and make noise between two and four as long as 4>3>2 holds

  81. fresh:
    It seems to me that if you read the discussion between me and Rah you will get an answer to some of your questions.

  82. Well done for the excellent article, and now for the review...

    I am not sure that the Platonic-Pythagorean thesis, although very interesting and thought-provoking, answered the question of why there is anything at all.

    Even abstract mathematics is a kind of something, it is not nothing. And so we are left with the same problem, why is there something, instead of nothing.

    Second, we need to know that a Platonic universe does not need a mechanism to create it, why assume such a thing?
    How do we know that the principle of thrift and minimalism of nature and Occam's razor does not also apply to Platonic universes? Because if the principle of parsimony also applies to a Platonic universe, then the problem of the precise adjustment is not solved, nor is the problem of the multiplicity of universes.

    Perhaps the laws of nature do not obey mathematical legality, rather mathematics represents and describes the laws of nature?
    The fact that through mathematics you can describe reality does not mean that mathematics is reality.

    And in any case, any theory that cannot be substantiated or empirically confirmed, even if it is very impressive, such as string theory, is actually philosophy, not that there is anything wrong with that, of course, because every scientific theory began as a philosophical thought in the mind of a scientist.

    And thanks again for the excellent article.

  83. Rah:
    This is definitely an answer - and even a very good answer to your claim that you don't see the difference because it shows a difference. It shows a feature that one faith has that the other faith does not have.
    Basically - you cannot expect a "winning" answer to the question because the only "winning" answers you (and not only you) can imagine are mathematical answers and such answers presuppose the independent correctness of mathematics.

    As I wrote to you in our previous email correspondence, and as I also wrote at the end of this response

    The laws of logic are laws of nature that are expressed in every place and situation and are so general and common that they were imprinted in us by evolution.
    Evolution discovers the laws of nature just as science does, only without any inspiration.
    It does this by an almost endless series of animal experiments on whose altar any creature that tries to "invent" faulty logic is sacrificed.
    That's why I wrote in the same response that deduction is an extreme case of induction.
    Because the logic inherent in you is a product of evolution, you cannot even imagine a world in which mathematics will not work because in such a world nothing can work, but this inability is not a sign of weakness because - as I said - precisely the creatures who did not suffer from this "weakness" extinct

    Just giving grades is not smart.
    In my opinion, the article expresses a deep and correct understanding of the Platonic Pythagorean thesis and in fact it does not matter at all whether the article talks about a thesis that you call Platonic Pythagorean or one that you call Carpucciolit Schmandrikaian because the name of the thesis is just a name and the content of the thesis that the article talks about is well clarified in the article and it is well clarified even if you are not I think it is appropriate to call the described thesis "Pythagorean Platonic".
    And no - the article is not based on the fact that he does not understand his own thesis.

    I do not claim that the thesis presented in the article is correct.
    On the contrary - my gut feeling is not correct - but it is definitely better than many philosophical theories.
    It is clearly superior to those of them that include an internal contradiction (and there are many of them).
    Nor does it leave open ends - which all other theories do - which in doing so they actually admit that after all the talk they do not answer the question they were formulated to answer.

    It is true that we currently do not know of a way to test this theory - even in principle.
    Maybe it will change and maybe not but it could be that any explanation of the reason for the existence of "something" is doomed to a similar fate.

  84. I liked the article very much. It's nice that there are also publications like this that challenge thinking and imagination...
    I would like to know, but what really causes the human consciousness to be created or the "consciousness part" of the animals for example... is it an accidental mathematical connection that simply becomes consciousness or is there something beyond that... something that is nevertheless responsible for such connections..?

  85. A very interesting article that enriches the reader, activates thought and it is hard not to agree with it intuitively.
    But if so, the thesis presented in it is not scientifically superior to any other philosophical thesis because even though it gives answers, it does not offer ways to test their correctness.

  86. It seems to me that there is a fundamental misunderstanding in the article regarding the Platonic-Pythagorean thesis and on this basis a whole world of misinterpretations is being built. To the readers: Please do not take what is said here as see and sanctify.

  87. M. This is not an answer, the fact that my imagination is limited still does not explain how something defines itself. In my understanding this is a kind of philosophical evasion similar to the religious argument which says that God has always existed. Ditto what Mishu says here. There are infinite mathematical structures, from where? How were the constants of each structure determined? In my understanding, this is simply a postponement of the question "what is the source of everything" to one level above. I really don't see a fundamental difference between the answer "God" and the answer - "a self-defining mathematical structure that was not created and no one created it either."
    The truth is that I liked Lisa's idea the most in the previous part of the article regarding the extent to which virtual creatures on the computer know about our world and with what tools they can tap into the programmer's world.

  88. Rah: The article actually addresses these questions, and raises the hypothesis that there are an infinite number of such structures, and that our universe is based on one structure among countless others, some of which (small) can have "consciousness" and some (large) cannot.
    In such a case, the question "who set the building laws" is not asked, because it is one building among countless existing buildings. What is meant by "self-defined", as I understand it, is that the very fact that you can think of a structure in which one or another constant is different than in "our" structure actually defines this structure.

  89. Ori:
    You just don't understand anything.
    I explained to you exactly what I got the money for and I really thank you for not accusing me of robbing the elderly.
    I explain to you again - I received the money for understanding things that others failed to understand.

    Beyond that, as mentioned, I find no point in arguing with you. Nothing can be learned from him except about your personality and that really doesn't interest me or - to use your expression - provokes one long yawn in me.

    Just try to imagine a world without God.
    Did you succeed? I'm sure it is.
    Now - try to imagine a world where the math doesn't work.
    I have no doubt that you cannot do it.
    So how can there be no difference?

  90. By the way from Kal:
    Money is said to have no smell, so it is difficult to trace its origin.
    But I saw a lawyer on TV who retired from the criminal field because she did not want to receive money that came from drug dealing and crime.

  91. Machel
    Indeed you admit and declare that faith is a completely private matter.
    As money you earn is your private business. As you know, money can be made in many and very private ways.
    Therefore you have no right to pretend and cancel one private belief and prefer another.

    Here is also Mr. Rah's argument:
    Demonstrates that you cannot differentiate and prefer one type of belief in a self-defining thing over another type.

  92. I still don't understand. What is the difference between saying "the world was created by God" and then the obvious question is how was God created and "the world is a mathematical structure" and then the obvious question is how it was created and who determined the laws of the structure?
    What is self-defined? Do you have another example of something that defines itself?

  93. By the way, Uri, people have already paid me a lot of money for my "private" girls.
    These are understandings that enabled the execution of things that before I understood them "privately" no one knew how to do and as a result were recognized and registered as patents.
    You constantly talk about the "purposefulness" and "value" of questions and their solutions, but you avoid the question of what purposeful and valuable thing you have ever done.
    As someone who has never asked a question or given a valuable answer in his life - you are not qualified to discuss the value of questions and answers.

  94. Machel
    You do not argue because you are not ready to admit that you are armed with words and not facts.
    Your argument about the mathematics has no basis except for your personal conclusion as an explanation of a phenomenon.
    There are other possibilities that you don't think of at all.
    Your conclusions elevate mathematics to some kind of deity that you bow to.

  95. Rah:
    The various mathematical structures do not need a reason for their existence because they are defined by themselves.
    If you remember the debate I had with Nadav, you also remember the distinction between what exists in power and what exists in practice.
    The mathematical structures are (in practice) a description of what exists in force - that is, of what can exist in practice.
    Everything else that actually exists needs matter or space or time to exist in.
    Mathematics does not need any of these.
    In fact, in addition to this, apparently talking about a "reason" for the existence of mathematical structures is not consistent because in order to say something is a reason for saying something else, the term causality must be used, which itself is nothing but a mathematical structure.

  96. point:
    Mathematical structures are only discovered by man.
    Nature obeyed the laws of mathematics long before man was created.
    If the laws of nature were not part of nature, different mathematicians would not reach the same mathematical conclusions.
    The fact is that the same mathematical structures and the same mathematical laws are discovered by people who have no connection between them (and in the past - even between their cultures).
    It has no equal in human works.
    You will not find two writers who will write the same story or two painters who will draw the same picture independently.

    Did I say I'm not arguing with you?
    I said!

  97. Machel
    You use the word "understand" "comprehension" etc. as a uniform standard that you are qualified to determine according to.
    After all, there is no uniform measure for understanding! Different people understand differently than you!
    However, the understandings that you are referring to have no implication or factual practical result that relies on an experiment.
    Not as a mathematical proof and certainly not a physical experiment in a laboratory.
    All you have are words and more words.
    Therefore the word understand refers only to what you yourself understand. according to your private beliefs.
    The "understanding" here is simply another description of the feeling that the article makes you personally.
    Someone else will have a different feeling.
    The arguments of the article are a tautology as long as the arguments of the article do not have a point of reference anchored in factual proof.

  98. I agree with Michael's opinion that this is one of the most interesting and impressive articles published here.
    One point that is not clear to me is why mathematical structures are different, why shouldn't there be a reason for their existence like we would expect a reason for other things?

  99. Mathematical structures do not exist. They are the fruit of our imagination and intellect.

    Why is there anything at all, that's a big question. But the answer may be that there is everything.
    There is still and there is not gone.

  100. Ori:
    I won't continue arguing with you because all you care about is attacking others and even your weapons are stupid.
    According to my words nothing happens from what you say happens according to my words.
    Where does it say that anything at all fills me with mystical feelings?
    You also do not understand the difference between religion and faith at all.
    Every person believes in something because without believing that he himself exists, that the input of his senses represents something from reality or that logic works, there is no way to function.
    While it is clear that all of these necessary beliefs are also the beliefs of the religious and it is also clear that the beliefs of the religious are supplemented with baseless beliefs that have no need or logic, but your lack of understanding on the matter goes far beyond the fact that you do not understand the difference between a logical and necessary belief and a stupid belief.
    Your main lack of understanding is in not distinguishing that a religion is a collection of rules of behavior (often convoluted) much more than a belief.
    What bothers me about religion is the element of the rules of behavior and not the stupid beliefs in it.
    With the beliefs I can argue but against the laws I feel it is a duty to fight.
    And if it is possible to fight the laws by challenging faith - how good!

    If we return to the topic of faith - all the things I believe in are things that everyone believes in and without faith in them you can't even have a conversation because you can't decipher a sentence.
    Mathematics is part of it.
    Do you think there is a sane person in the world who does not believe in the correctness of mathematics?
    I find no point in repeating here everything that is written in the article because if you did not understand the things as they were written in detail and at length in the article - you certainly will not understand them if I write them here in short.
    Nevertheless, it is important to emphasize, for the benefit of those readers who have some gray cells, that every field that we have ever come to the conclusion that we really understand is a field that has been given a mathematical description.
    As long as we have not described things mathematically, we do not think that the subject has been fully understood.
    This implies that even if there is something beyond mathematics - we probably won't be able to reach a perfect understanding of it.
    The article (like all the "egg chatterers" mentioned in it, each of whom dwarfs Uri) describes the possibility that nothing but mathematics is actually needed.

  101. Machel
    Apart from babbling eggs, is there any practical implication for the discussion in the article?!
    According to you, the theory fills you with mystical feelings.
    If so, you are no less a believer than believers in religions.
    Your faith is in these philosophies which conclude that nothing of one kind is actually nothing of another kind.
    You exchanged a cow for a donkey, so what's wrong with you because you will complain about other believers.
    You can't prove that your nothing is better than someone else's. Because you claim that their faith is nothing.

  102. Luke:
    The mathematical structures exist without any relation to the human mind.
    The human mind does not create them - it only discovers them.

  103. Does consciousness have the means to change the basic mathematical structure of the universe?

  104. MB:
    Indeed, in my opinion, this is one of the most beautiful articles that has ever appeared here.
    I have already mentioned it in many comments in the past and since it was not possible to point to it (because it was not displayed on the Galileo website) I referred to the links to the texts authored by one of the fathers of this theory - Tagmark.

  105. Ori:
    I have already asked you if you have ever provided the world with an answer that according to your criteria has value.
    I'm pretty sure you didn't because people who don't know how to appreciate such questions (and answers) are shallow people.

    Besides - regarding the "value" - don't you see value in the existence of a theory that has nothing mystical in it and has no place for God? Is there no value in fighting the stupid beliefs that cause so much damage to the human race?

  106. A very deep and powerful article... I enjoyed every moment, even when I didn't understand everything, the article ignites the mind and consciousness to interpret the infinite universe in a different phase. Marius Cohen... Thank you very much

  107. is there an answer!? But what value is there in an answer that cannot be applied.
    Besides talking, these conclusions have no results in the metaphysical world, certainly not in the physical world.
    This answer does not help to solve even the smallest math problem.
    The end result is you started with a question that leads to nothing and ended with the same nothing.

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