Is it possible to perform an infinite number of actions in a fixed period of time, can a mythological hero pass countless walls of gods and reach the realm of his object, and also: a mathematical paradox of infinity
Marius Cohen
Thompson's lamp paradox
The light bulb (or lamp) paradox was proposed by the English philosopher James Thompson (Thompson), and its essence: an electric circuit turns on and off a light bulb alternately, so that the first action (lighting the light bulb) takes half the time of the second, and each additional action takes exactly half the time of the action that preceded it. As a result, the bulb performs an infinite number of operations in a cumulative time of one second. At the end of that second will the light bulb be on or off? On the one hand, the light bulb must be in one of its two possible states: on or off, but on the other hand, since the circuit performs an infinite number of operations, then after each switching on operation comes a switching off operation and after each switching off operation comes a switching on operation, that is, it is impossible for the process to end no By turning on the light bulb and not by turning it off!
The solution to the paradox: It is tempting to think that the solution to the paradox is physical. That is, that such an electric circuit is not technologically possible (due to the fact that the limiting speed in nature is the speed of light, for example), or that from a certain point onwards the duration of the operation will be so short that the bulb will not have time to turn on or off, and it will remain in one of its two states until the end of that second in which the circuit operates .
Such a pragmatic solution may be suitable for any attempt to perform infinite physical actions for a limited time, for example to alternately press two letters on the keyboard, say A and B, so that the duration of each keystroke is twice as short as the keystroke that preceded it (since the series of keystrokes lasts a finite period of time , it is possible to ask which letter was pressed last; but since the number of keystrokes is infinite, after each keystroke of the letter A, the keystroke of the letter B is made and vice versa). Even in this case it can be argued that there is a physical limit to the speed of tapping (whether human or mechanical), so the number of tappings in any given period of time must be finite. Thompson himself presented the paradox in order to prove that it is impossible to perform an infinite number of operations in a finite period of time, and some believe that the physical solution is indeed the correct solution to this paradox¹.
But physical limitations do not solve the logical problem (even if Thompson was right in stating that it is impossible to perform an infinite number of operations in a finite period of time). Let's assume that there were no technological or other limitations on the construction of the electric circuit described above and its operation. Will the bulb be on or off at the end of the second? Since the real problem is a logical (or mathematical) problem, obviously its solution should also be one.
If so, the problem lies in the fact that the question of whether the light bulb will be on or off is asked about its condition after the series of on and off operations is over. But there is no determination in the definition of the problem regarding the state of the bulb outside of this series. As part of the series, we know that after each switch-on operation a switch-off operation occurs and vice versa, but since all the series operations take place before one second passes, it is impossible to conclude anything about the state of the bulb at the end of that second. This state must be set separately, and it can be set as we wish: light bulb on or light bulb off.
Below is another paradox of infinity, proposed in 1964 by the philosopher Jose A. Benardete (Benardete).
Paradox of the Gods
A hero from some mythology, where countless gods show interest and involvement in human actions (but are unaware of each other's desires), decides to set off from his village to a nearby village. However, none of the infinite gods is interested in the success of his journey. Therefore one of them decides that when the hero reaches the middle of the road, he will put an impenetrable wall in front of him. A second god, who is unaware of the first god's decision, decides to put a wall in front of our hero when he reaches the quarter of the way. A third god conspires to do this when the hero reaches the eighth of the way, and so on and so forth, when each of the countless gods decides to erect a wall in the hero's path, halfway from the village gate to the point where some other god decides to erect his wall.
In this way, our hero is not able to take even one small step outside his village, since the attempt to go any distance will be prevented by the appearance of an impassable wall. However, if the hero does not leave the village, then none of the gods realizes his intention to block his path with a wall, and it turns out that our hero is prevented from carrying out his planned journey without any wall actually blocking him.
Solving the paradox: here too the assumption that the theoretical existence of an infinite number of gods is impossible does not solve the paradox, because even in this case the problem is logical and not physical. Also, many tend to imagine the mythological hero taking his first step outside the village, and immediately being blocked by an impenetrable wall. After the first wall was erected (right at the entrance of the village), the other gods no longer need to intervene. Exactly one wall was placed near the gate, and it was the one that prevented our hero from setting off.
But exactly how far from the village gate was the wall placed? If we assume that it was placed only one meter away from him by the god who decided on this distance in advance, then there is another god, who decided to place a wall half a meter away from the gate, so that the hero would never have been able to complete the first meter of his journey. But in his attempt to pass a distance of half a meter, he was supposed to be stopped by another wall a quarter of a meter from the gate. But even this distance he cannot reach, due to the wall that is supposed to block his path at a distance of an eighth of a meter from the gate, and so on, and so on: at any distance from the gate where we suppose the only wall blocking his path was placed, we will find that the hero of the story had no chance of making this distance due to a wall Another was already supposed to block his way. But if no wall is placed in his path in the end, what prevents our hero from leaving the village?
Well, the solution lies in the fact that the gods' wishes are not compatible with each other: each god intends to erect a wall at the point he has chosen if and only if the hero of the story reaches it. However, the hero will reach this point if and only if another wall did not block his way there. Hence every god will build a wall if and only if no other god has preceded him and built a wall in front of him. But since there is no god who has chosen a certain minimum distance from the village gate to place his wall (that is, such a distance that no other god has chosen shorter than it), then in order for any god to be able to erect a wall in accordance with his original intention, the infinite number of gods who have chosen shorter distances from the gate must give up their intention - they to do this.
Hence, if the hero begins his journey, it is not logically possible for the wishes of all the gods to be realized, and in fact only two situations are possible: either no god will realize his intention, and the hero will complete his journey as planned, or only a finite number of gods, from those who chose greater or equal distances At a given distance from the village gate, they will stick to their original plan, while the countless other gods, who chose shorter distances, will abandon it. Any other situation is not logically possible (and just for the sake of clarification: if a god does not erect a wall because another god did it before him, he is definitely acting according to his original design).
For dessert - a mathematical paradox of infinity
If we add all the natural numbers (that is, the positive integers), it is clear that the result will be infinite in size. However, if we add all the whole numbers (including the negative ones), what will be the result of the addition? We will try to solve the exercise by arranging these numbers in pairs (except for the number 0) in this way:
We will now try to solve the same exercise again, and this time by arranging the numbers in pairs in this way:
What, then, is the correct result of the exercise, and how is it possible that two arithmetic expressions, which according to all the rules should be equal, give different results?
146 תגובות
The whole universe can be seen as a kind of cellular automaton
See the Wikipedia entry
http://he.wikipedia.org/wiki/%D7%90%D7%95%D7%98%D7%95%D7%9E%D7%98_%D7%AA%D7%90%D7%99
fresh:
You are the one lying.
If anything from what I said seems wrong to you - point it out and explain your reasons instead of making false accusations.
Everything I said is true - at least as far as I know.
I can be wrong too but I don't lie.
Michael why lie?
You have the right not to understand what I am saying and not to agree, but I do expect integrity from you.
fresh:
You keep lecturing about things you have no idea about.
After all, we've already seen that you don't even know how to solve an elementary school arithmetic problem:
https://www.hayadan.org.il/against-laws-of-movement-2303082/#comment-196360
http://www.ynet.co.il/articles/0,7340,L-3515410,00.html
In fact if space-time is continuous, then numbers cannot exist at all in the sense of "things" or "objects", the only sense they can have is that of infinite ill-defined "processes". And I'm not just talking about numbers like the root of two, all numbers: complex, real, irrational, rational, whole, and natural. None of these types of numbers will exist, in the sense of an object, everything will be a process.
For example the number 1 in a continuous world would be ...1.00000 or maybe ...0.999999
The number 1 in a continuous world is meaningless. For literature to have a well-defined meaning as obiects the world must necessarily be discrete.
In a discrete world like ours, numbers like pi or root two exist but only up to a certain limit of accuracy after the decimal point, beyond this precision (which can be very much after the decimal point) root two or pi or third becomes meaningless.
Recommended further reading
http://he.wikipedia.org/wiki/%D7%A8%D7%A6%D7%99%D7%A4%D7%95%D7%AA_(%D7%A4%D7%99%D7%9C%D7%95%D7%A1%D7%95%D7%A4%D7%99%D7%94)
The comments that I think are more interesting in the YNET article are 17 21 28 35 42 53 59
They all explain what I tried to explain at length.
And an excellent book that I recommend: Godel's theorem and the problem of the foundations of mathematics.
The links are to the "Continuity (philosophy)" entry in Wikipedia
And to "The logic behind Zenon's paradoxes" in YNET.
In fact if space-time is continuous, then numbers cannot exist at all in the sense of "things" or "objects", the only sense they can have is that of infinite ill-defined "processes". And I'm not just talking about numbers like the root of two, all numbers: complex, real, irrational, rational, whole, and natural. None of these types of numbers will exist, in the sense of an object, everything will be a process.
For example the number 1 in a continuous world would be ...1.00000 or maybe ...0.999999
The number 1 in a continuous world is meaningless. For literature to have a well-defined meaning as obiects the world must necessarily be discrete.
In a discrete world like ours, numbers like pi or root two exist but only up to a certain limit of accuracy after the decimal point, beyond this precision (which can be very much after the decimal point) root two or pi or third becomes meaningless.
Recommended further reading
http://he.wikipedia.org/wiki/%D7%A8%D7%A6%D7%99%D7%A4%D7%95%D7%AA_(%D7%A4%D7%99%D7%9C%D7%95%D7%A1%D7%95%D7%A4%D7%99%D7%94)
http://www.ynet.co.il/articles/0,7340,L-3515410,00.html
The comments that I think are more interesting in the YNET article are 17 21 28 35 42 53 59
They all explain what I tried to explain at length.
And an excellent book that I recommend: Godel's theorem and the problem of the foundations of mathematics.
Pine:
A minor chance.
This is one of the articles that came to me at some point and after skimming I decided it was too difficult to skim and I put off reading it (the well-known sin of "when I turn I will change").
After he disappeared, I don't even remember a keyword that should be used to search for him, but I will try in XNUMX because it interests me too.
Michael,
Any chance you can find the article or a link to it? Just out of academic curiosity 🙂
Not urgent, if you happen to find it then don't forget to bring it here.
Pine:
I must point out that the discrete space is definitely a physical possibility that has not been discounted.
There are ways to deal with the wave equation and as far as I know (I had an article that I downloaded to a stolen laptop and I don't have the strength to look for it again) one of the ways being tested as a synthesis of relativity with quantum theory is based on such a space.
All I wanted to clarify for you is that the fact that he heard somewhere and sometime about a separate space does not make this space a magic solution to all problems, including the problem of the conflict in the Middle East, and that in general it is better that he only speak about what he understands and will also be open to listening to those who understand better than him.
Ra'anan presented the discrete space as a solution to Zenon's paradox.
He did this without understanding what a paradox is and without understanding what a solution is and along the way he talked about a lot of things that he does not understand.
I am aware that I myself rounded corners in the discussion in the sense that I did not open up interesting issues of quantum theory that could emerge from it in an associative way, but I had no other choice because I wanted to argue with Ra'anan and not with myself. It was important for me to confront Ra'anan with the fact that he makes statements that, at least from his point of view, are baseless.
Michael, I meant that I am sorry in the sense that, despite his attempt to bring a theory that seems interesting and beautiful, I am forced to interrupt him with a number of truths.
I read your exchange, and I saw that indeed he did not understand that a number of philosophical questions in the past, have long been answered by scientific principles, and these are not philosophical questions because the very assumptions and points of view are wrong and incomplete to begin with. But it didn't bother me.
But when he started to confuse with simple and basic terms I had to "raise a voice" and stop him. To deny the idea of continuity already contradicts all mathematics and hence all the sciences (chemistry, physics, etc.) that came out of it. Who knows what wrong conclusions we would reach if we assumed that the sinusoidal equation of a wave function (or other equations that can be used to describe a wave in different language conditions) is discontinuous?
fresh:
I wonder where you get the courage to argue about things about which you have not the slightest idea.
I have no doubt that you have never studied Hadova.
Pine:
But why regret?
fresh,
I'm sorry to agree with Michael - Hadova does clearly define continuity. Not only does it represent continuity, but it also goes to second order, third order continuity and beyond (see the term differentiability).
The only place where the ideas of "discrete" are used is quanta (hence the name quanta) and even that only refers to discrete energy levels (assuming continuity of the equation of motion of a particle). Oh that there really isn't a discrete space (including time). On the contrary - the wave equation could not exist in a discrete world.
You have the right to think that HCV represents continuity. But you are wrong.
fresh:
You must have heard the expression "you don't scare a pigeon with wine".
fresh:
Enough lecturing about things you don't understand!
The accepted solution to the paradox is the one that uses the tools of Hadova and not your solution.
In Hadua there is no assumption of a discrete space. On the contrary. In Hadua they define exactly what continuity is.
I have already explained why the mathematical solution given to Paradox became possible only after the invention of the Hadva and the concept of a limit that limits infinity, that is, assumes the assumption of a discrete space.
And for response 125:
You don't understand!
I claim that you will not be able to find any combination of trajectories that will bring the two particles to the same point at the same time! You will not be able to do this with any set of laws of physics!
I don't expect to learn anything from such a route. I expect you to learn something from the fact that you fail to build such routes!
fresh:
But that's the whole point!
I claim that you have not explained anything and that to explain what is happening one must be able to answer the trivial question I asked.
What becomes clear in all this discussion is that while in normal mathematics and with the assumption of a continuous space there is no problem in dealing with the question of saying where the arrows are at any moment, where they will meet and when it will happen, in the method you are talking about there is no way to do this and in fact - even more so - no I just asked this question because for those who understand mathematics it is easy to see that the impossibility of meeting exists precisely in your method. That is, while in the world known to everyone - it is possible to leave the world as it is and only correct the mathematical mistake made by Zenon, in the world you describe the meeting is really mathematically impossible!
And I still think there is no point in the coordinates I mentioned, they are only one potential route out of a large number of possible potential routes. Nothing can be learned from this, it is a random path that results from random starting conditions and is subject to physical laws that are not yet fully known and probably will never be fully known. Therefore, there is no point in talking about another route. And I beseech you again, what knowledge do you think you will gain from such a chance path that tells you?
The paradox you just posed is exactly Zeno's paradox.
I have already explained many times how the quantization of space solves Zenon's paradox both in this article and in this one:
https://www.hayadan.org.il/against-laws-of-movement-2303082/
.and you are welcome to read my comments on the subject. I can't do more than that.
By the way, Ra'anan: for some reason, when I asked you to describe the trajectory of one particle - you didn't call out to God and all the scientists for that.
Since you didn't see that it invalidates your theory, you had no problem describing the trajectory.
Now I ask for a very similar thing - the same thing - only for two particles.
I guess you tried, saw you couldn't, and decided the only course of action was to start making excuses.
fresh:
So tell me how you allow yourself to claim that it solves the Zenon problem?!!!
Here is a Zenon paradox that fits the problem:
Two arrows are shot simultaneously from A to B and from B to A.
A is at (0,0) and B is at (13, 11)
The arrows will never meet because in order for them to meet they first have to reduce the distance between them to half the original distance, then to a quarter, then to an eighth and so on.
I have no problem getting out of the paradox with its correct explanation.
You suggested that quantization of the space would do the job and that the entire conventional treatment of the problem is incorrect.
As part of the accepted mathematical methods, the arrows will meet and it is possible to calculate exactly where and when this will happen.
Your method should solve the same problem so please - explain how!
In addition, I also think that this question is not relevant, what will knowing the route at a coordinate level give you? What understanding are you seeking to infer from these coordinates?
I didn't squirm even for a second. Only an omniscient can answer such a question. It's not that I'm avoiding it, there's simply no practical possibility to answer such a question, not for me, not for any scientist, and even if I had all the scientific knowledge available to humanity today, and all the best technical measurement equipment that humanity has today, it still wouldn't be possible to answer on this question.
I've already explained to you why it's impossible to describe such a route, I can't do more than that. What's more, I don't understand why it is so important for you to know this route. In my opinion, you should look at this idea at a general level of principle, at the level of the "big picture", and less at the level of specific coordinates.
fresh:
I must point out that what you are doing seems really dishonest to me.
You claim that the division of space into segments solves problems like Achilles and the tortoise and like Zeno's arrow, but as soon as I give you exactly such a problem you start twisting.
fresh:
You're just avoiding it.
I said that the particles will not meet, and to show that they will meet, I agreed that you determine what laws of physics you want - the laws that will most help you create a meeting between them (of course, within reasonable limits - the particles must move from the starting point to the destination point without going backwards or delaying for no reason at any point).
The starting conditions are completely defined - it is clear from which point each particle comes out, when it happens and at what speed it moves.
All you have to do is describe the route.
What is so complicated here?
In order to describe for each of the two particles at which point it is after each unit of time, I need to know perfectly and with perfect accuracy the initial conditions which means what are all the physical characteristics of the two particles in which medium they exist if there is one at all and any other physical information and to know with certainty and perfection (and not only as a good approximation) the laws of physics that apply to the above scales. these perfectly, and suppose I could also know the laws of nature perfectly, only then could I tell you that the particles will meet exactly at the space-time coordinate (x,y,z,t) and all this only under the assumption that there is no coincidence/chaos as a law of nature.
fresh:
Note that I tried to simplify the problem very much.
The speed of the particles is the same (one unit of distance per one unit of time), they leave their starting points at the same time, and the laws of physics are whatever laws you want
fresh:
I did not understand a word.
Describe for each of the two particles at which point it is after each unit of time.
It is said that a unit of time is the time it takes to move from one point to its neighbor (horizontally or vertically).
Show me a pair of such trajectories of the particles where they are at the same point in the plane at a point in time (this is the definition of a meeting). What is so hard to understand? Or is the quibbling because you understood but couldn't execute?
Michael
Although you have a lot of florium interrogationum arguments against me in which you attribute a lot of claims to me that I don't make at all, I will reply.
What is the definition of "steps"? If the definition of one step is one discrete time unit, the particles will necessarily meet only if there is a minimum of two time units, in one unit they are at the departure point and in the second they meet. Their meeting coordinate will be a function of initial conditions and the laws of physics.
fresh:
Just for fun - come and model for us the trajectories of two particles that leave simultaneously from the point (0,0) and from the point (11,13) and tell us after how many steps they meet.
fresh:
I try to formulate things at a level that you can understand them and you take the few slogans you remember from modern cosmology and preach to me that, so that you understand, I did not use them (although you know that I often explain them to anyone who wants to understand them).
You make it worse by trying to explain things to me.
Go study them before you start explaining them.
Beyond that, you are talking nonsense.
From your words it does appear that the particles I was talking about will not meet, but I no longer have the strength for this silly argument because you do not understand every second word of my words.
"In the physics we know, there are straight lines"? What do you mean? Where did you get it?
"In the physics known to us, a particle that is not acted upon by a force moves in a straight line" It is not clear what you mean by that. The entire universe from the moment of the big bang and all the particles is in constant motion and energy and is developing in every possible direction you can imagine and also ones you can't imagine. The shape of the universe is the result of opening data and laws of nature, which create all the chemical and structural particle interactions and the patterns in nature, I am not different that we will not exert force on the particle, whether we give the particle force or whether it will not have force to navigate it in space? In the physics I propose there are straight and curved lines and some lines you can only imagine.
"In the physics we are familiar with, it will be enough if we know exactly the position of a particle at two points in time in order to predict its position at any additional point" - it depends on a philosophical point of view if there is an understandable randomness in nature or determinism, and this is exactly the case in "my" physics, there is no contradiction from the point of view This is between the types of physics, and it is not clear to me why you insist that in the physics I propose this cannot be done.
I have already said that the particle does not "remember" anything, the particle is a "slave" of the laws of nature, it does not decide on any spatial path on its own (and this is true whether the laws of nature include randomness at a quantum level or not)
What the uncertainty principle means is that you cannot know both position and momentum in one discrete time unit, and this is very logical because in one discrete time unit you cannot know momentum because momentum is a function of speed and in order to know speed you have to compare the particle's position at least between two discrete time units , therefore my idea fits the uncertainty principle perfectly.
"According to your description, a situation is also possible in which one particle will move from A to B and a second particle will move at the same time from B to A and they will not meet at all on the way" - I never claimed that.
By the way, fresh.
According to your description, a situation is also possible where one particle will move from A to B and a second particle will move at the same time from B to A and they will not meet at all on the way.
In fact, in the vast majority of cases, this will be exactly the case.
fresh:
Another attempt.
I do not make a distinction between a particle and an arrow.
You started talking about an arrow, so I treated it in the same context.
In the physics we know, there are straight lines.
In the physics you propose there are no straight lines.
In the physics we are familiar with, a particle that is not acted upon by a force moves in a straight line.
In the physics you propose it moves in a zigzag pattern.
In the physics we are familiar with, it would be enough if we knew exactly the position of a particle at two points in time to predict its position at any other point.
In the physics you propose this cannot be done.
At this point, a feeling like "OK. This is just another aspect of the uncertainty principle" may develop, but this feeling is not correct because according to your description, this is not about random movement, but about the direction the particle "remembers" in some way.
In other words - beyond the fact that the uncertainty principle does not allow us to measure the position of the particle, you add the claim that even if we knew its position precisely with as many measurements as we wanted along the way, we would not be able to predict the path of its progress.
Even if you want to change your claim now and claim that the particle decides to continue its path randomly and not according to the "original direction" given to it, you will get a completely different distribution than the one obtained from the known wave function.
To Michael
I'm sorry but it's not clear why you make a separation between a particle and an arrow, assume that this particle is one of the trillions of particles that the arrow is made of.
It is a philosophical idea that there will never be the technology with such a resolution that is necessary to conduct an experiment that can confirm or disprove it, and therefore there will never be a scientific journal that will publish it, let alone a philosophical journal, if there is such a thing at all.
to the point
No problem, get a cancellation on the phrase "free will" and replace it with randomness.
A refresher, what is this nonsense: "Free will means randomness"
Will is a mental concept, free is an undefined concept, random is a mathematical and philosophical concept.
fresh:
Another attempt even though I had already lost hope.
The arrow remembers nothing. He always continues on his path without any deviation except for the deviations caused by forces applied to him.
If no force acts on it, it will fly in a straight line.
Your particle at every point has to make a decision where to continue and this decision depends on its distant past at the time it clicked - nothing in the distant past at all changes its speed and direction at a given moment determine where it will be at the next moment.
This.
If you didn't understand then you didn't understand.
You are welcome, of course, to try to publish your theory in some scientific journal.
I assume that the path you will take when you are thrown from all the stairs will be similar to that of the particles in the space you describe.
If the laws of nature are deterministic, it is theoretically possible to predict its spatial path with perfect precision, and if there is free will, i.e. randomness that is understood in nature, there is no way to predict this coordinate path perfectly.
The particle "remembers" the angle just like the arrow remembers it. Where is the problem here? There are laws of nature and the particle can only move through the coordinates that the laws of nature allow it to move in, it is not that the particle decides on its own, it obeys the laws of nature.
fresh:
I said I don't have the strength anymore, so this is my last response on the matter.
If a particle moved from (0,0) to (1,1) then even if they tried to give it a different direction than 45 degrees - they failed to do so.
The particle has no way of "remembering" what was the intention of the one who launched it, therefore this intention does not affect it and it will continue to move at exactly 45 degrees.
This is a point I repeat to you in all the comments from 94 and you simply ignore it.
How can the particle "remember" at what angle it is launched after the path it actually traveled is 45 degrees?
You do not offer any mechanism that allows him to do this and your words are disconnected from all logic.
Good night
If you shoot an arrow at a target and hit it there is a certain coordinate path pressure and if you move the target a meter to the right and send another arrow its path will be through other coordinates, why don't you ask what caused the pressure to suddenly change the path without reason?
I didn't say that the deviation in the path is without any reason, the reason for the deviation is the launch angle, any different launch angle you choose will have a different coordinate path, where is the problem here?
There is no obligation to launch a particle at exactly 45 degrees in order for it to reach 10,10 even if the angle is 40 degrees it is possible that the path will start the trajectory through the coordinates (0,0) (1,1) (2,2) (3,3)....(10,10) ,XNUMX), because these are the smallest scales that exist, it is not the coordinates of a checkered paper page.
Oh, Ra'anan... I have no more strength.
You do not provide any clue as to the way in which the particle decides to suddenly deviate from the trajectory.
According to you, two particles can travel as long as we want, pass exactly the same points along the length and then, suddenly, for no reason at all, separate?
Come on! If you believe this then there is nothing to try to explain to you.
If we launch the particle at an angle of 45.1 degrees, it will both pass through 10,10 and will not necessarily pass through 13,13.
fresh:
The problem is that in order for it to pass through (10, 10) it has to be launched at exactly 45 degrees, so from this point it will inevitably reach (13, 13)
Why do you think that a body that moved from (0, 0) to (10, 10) will necessarily also move to (13, 13)? A body is free to pass through any coordinate path that the laws of physics allow it. If a particle is launched at an angle of exactly 45 degrees, it must indeed reach 13,13, but if we launch it at, let's say, 46 degrees, it will reach 11,13. Where is the problem here?
fresh:
You are not answering my question.
A body that moved from (0, 0) to (10, 10) will necessarily also move to (13, 13).
Here you are deciding on directions of movement that contradict all the laws of physics.
After all, a body launched in the direction of (13, 13) will also pass through (10, 10). How is he supposed to, at this point, suddenly decide to turn around? It's just bullshit!
(0,0) (1,1) (2,2) (3,3)….(10,10) (10,11) (11,12) (11,13)
This is how a body moves between coordinates.
Describing a relation within the discrete part itself is meaningless, to describe any relation you must have at least two discretes or two spatial slots.
fresh:
I was afraid that your mathematical training is not sufficient to explain the matter to you in correspondence and my fear of this increases following your response.
In the first question, a contradiction will be received following any answer that defines the ratio between the diagonal distance and the horizontal distance as different from the root of two, and if you say that there is no root of two in nature, you are in trouble, but the second question is more interesting, so I will explain to you the meaning of the brackets.
This is actually the accepted way to represent points in two-dimensional space by two coordinates - let's say X and Y.
The point (0, 0) is at the origin of the axes (where both X and Y are zero) and the point (13, 11)
It is the one where X is 11 and Y is 13.
Since it is a square mesh - all the points where you can pass are with whole X and Y.
11 and 13 are prime, so there is no crosshair point on the way between (0, 0) and (13, 11).
Therefore you could give me two types of answer:
The first type of answer is that the body cannot pass at any point on the way (and since 11 and 13 are not the only primes and there are primes as large as I want, it would follow from the fact that there are sections as large as I want that a body can move between their ends without passing at any point on the way (and as large as I want this also means a million light years).
The second type of answer is that the ganaf "compromises" and passes certain points along the way.
It was said that you would say that it passes through the point (6, 6).
In such a case, I would ask you what differentiates - in your opinion - between a body that reaches (12, 12) and one that reaches (13, 11) and how does the ball decide, after traveling between (0, 0) and (6, 6) whether to continue to (13, 11) or to (12, 12).
Michael
You are welcome to prove mathematically.
Regarding question 1, let's assume that the diagonal is indeed different, although I really have no idea if that is the case.
And regarding question 2, the question is not so clear to me, and what are the numbers in brackets?, but a body that moves through these individual units does not have to move in a certain order. Lighting and closing of the lamps according to the order one after the other. And it may also be that a body does not have to move through successive units, that is, to skip several units.
(as well as any fractal tiling)
fresh:
And I can prove mathematically that any non-fractal tiling will result in a contradiction.
I can't tell you what shape this spatial tiling has, but I can definitely say that it's not a fractal tiling like the Sarpinski triangle, because then it has no end.
fresh:
I told you I could prove a problem with any structure you suggested.
If you want to continue with the cube structure - do not hesitate - answer the questions I presented to you in response 80.
There is no evasion here, this is honesty.
Suppose the structure is a cube, what internal contradiction could there be in such a case? Why does it matter if the shape is a cube or a sphere or even any other "non-engineering" XNUMXD shape. I'm not talking specifically about what form because I really don't know, I'm talking about the fact that, in principle, there must be such a unit.
fresh:
Note that I wrote "Phenitzit" instead of "Panimit" this is bread for a tsunami and that is why the saying "Shelk your bread on the surface of the water" was written.
fresh:
This is already evasion.
I inform you that I can find a Phoenician contradiction in any structure you propose.
I have a general method to do this, but it seems to me that it would be too difficult to explain the method to you, so I tried to get you to define the structure precisely to show you the bug in this specific structure.
If you can't specify the structure - there is no justification for your confidence in the idea, what's more, I assure you that I can prove that any structure you are able to propose has a problem.
I don't know what the shape of the tiling of space-time is, or what exactly this lattice or network looks like, it could possibly be any three-dimensional shape, a cube, a pyramid, a hexagon, an ellipse or a sphere, it seems to me that it makes the most sense that it is a cube because it is a shape that does not leave spaces between the pixels and fills the entire space, what I am sure of is that some discrete unit that cannot be further divided must exist, whatever its form may be.
fresh:
The previous comment was of course intended for you
I apologize for not having the strength to read the entire endless thread.
1. Do you claim that the diagonal length unit is different in length from the horizontal and vertical one?
2. Let's look at units in the grid you're talking about. I still remain in two dimensions. What are the points (according to their order) through which a body passes that starts its movement at (0,0) and ends it at (11,13)
"To deal with questions related to rates of change, Newton - and separately from him also the German mathematician Gottfried Leibniz - invented a new branch of mathematics: differential and integral calculus. This Torah changed the face of the earth, both literally and metaphorically. But again, the ideas this discovery inspired were different for different people. Physicists set out to look for other laws of nature, which could explain natural phenomena in terms of rates of change. They found a multitude of such laws governing various phenomena: heat, sound, light, flow dynamics (gases and liquids), elasticity, electricity, magnetism. The most esoteric modern teachings dealing with elementary particles still use the same kind of mathematics, although the interpretation, and to some extent the implicit worldview, is different. However, mathematicians have found a completely different set of questions to ask. First of all, they spent a lot of time grappling with the question of what the phrase "rate of change" really meant. To calculate the speed of a moving object, you need to measure where it is, find where it has arrived after a very small interval of time, and divide the distance it has traveled by the elapsed time. However, if the body is accelerating, the result depends on the time interval you chose. Both mathematicians and physicists had the same intuition regarding handling this problem: the time interval used should be as small as possible. Everything would be wonderful, if only an interval of size zero could be used, but unfortunately this is not possible, since both distance and elapsed time would be zero, and a rate of change of 0/0 is meaningless. The main problem with non-zero intervals is that no matter which one you choose, there will always be a smaller interval with which you can get a more accurate result. What would be really useful is the smallest possible non-zero time interval - but there is no such thing, since given any non-zero number, the number that is half of that number is also non-zero. Everything would work out if it was possible to get a small margin at an infinite rate - "infinitsimal". Unfortunately, difficult logical paradoxes arise in the context of infinitesimals; In particular, if we limit ourselves to numbers in the conventional sense of the word, there is no such thing. Therefore, for about two hundred years, humanity was in a very strange situation in relation to the Bible. Physicists used it, with great success, to understand nature and predict its behavior; mathematicians were troubled by the question of what its true meaning was and how to construct it so that it would function as a properly established mathematical theory; and philosophers claimed that all of this Nonsense. It all gets resolved in the end, but you can still find big differences in approach."
Taken from a book I'm reading now called "The Numbers of Nature: The Unreal Reality of Mathematics" by mathematician Ian Stewart
http://lib.cet.ac.il/pages/item.asp?item=12127
The diagonal of the discretes is the unit of length, it is the physical definition of a diagonal unit of length!, length units of cm inches, etc. are only for our convenience as humans who have access to scales and standards that are different from Planck's scales, you can read about Planck's units in Wikipedia. What you are actually asking is how many units of length are there within the most basic unit of length there is, and the answer to that is that within the most basic unit of length that exists in nature, there is only one unit of length, and that unit is itself. And in this it is different from a pixel of a screen, a pixel of a screen consists of an infinite number of those basic units that cannot be divided, and therefore you can ask about such a pixel the question of the type you asked, i.e. how many units of length does it have diagonally. It is possible that there is no distance between the discretes themselves, meaning they are adjacent to each other without a gap, if there is a gap between them then this gap does not belong to our space-time, they belong to something else. The stuff we are made of and the time we are in can only exist within these discretes.
Ok, refresh:
So let's stay on the level for a moment.
These are pixels like on the screen, right?
I mean - they are arranged in the form of squares - right?
Now tell me - if we define the distance between two pixels as a unit - how many units is the length of the diagonal of these squares?
You are welcome to trap me
Good night.
I already said that space is discrete and so is time, just like there are pixels on a screen, the same space only in three dimensions + time dimension, there is no continuity neither in movement nor in time. And the directions in which you can move are only from discrete to discrete, so if you want to move just for example 12 degrees while passing only one discrete, it is not possible. At a distance of one discrete, you can only move in the right, left, forward, backward diagonals of 45 degrees, and also in the Z axis up and down and diagonals 45 of the Z axis, like a Hungarian cube. In the small scales there is no freedom of movement as it seems to us to have from the perspective of scales where humans experience the world. And in each direction the minimum distance that can be traveled is the same distance, and is the distance of one individual or one slot.
fresh:
I understood you very well.
The truth is that there are endless questions that can be asked, but most of them are difficult to clarify on the website, so I chose this simple question.
Do you see this as a lack of understanding of your words?
I won't dwell on it because it's stupid to explain to you that I do understand and will ask another question.
How, in your opinion, is the space organized?
Can it be moved in any direction?
Is the minimum distance that can be traveled the same in each direction?
Keep in mind that these are just introductory questions and I'm preparing a trap for you based on the answers you give
If I understand correctly, you are asking how it is possible to skip those minimal sections? And without going through any point in the middle? And I ask what are you talking about?
What skips are you talking about? I wasn't talking about any skips. And what point? And in the middle of what? I'm talking about measurable time space and you're asking me about particles? I don't think you understood me at all even though you read.
fresh:
this is simply amazing.
You want to tell me that in all the times you said you had already given the answer you dared to do so without knowing what the question was?
But in your response 61 you actually repeated my question almost exactly, so you actually do know what it is.
Listen - you are really confusing.
For the avoidance of doubt - the question appears in response 60 and its extension appears in 62
what a question?
By the way, fresh:
I went back and read everything you wrote in the link you provided and indeed - as I remembered - there is no answer to my question there.
fresh:
Stop being evasive and answer specifically.
It's good that you didn't tell me that there are all your answers in the world and that I'll just search the world.
https://www.hayadan.org.il/against-laws-of-movement-2303082/
There are all my comments on the subject. If there are any more questions, feel free to ask, no need to beg.
fresh:
I didn't see any explanation you gave. In any case - not a convincing explanation.
Maybe I missed something and didn't see it.
What's the problem with repeating the explanation or giving an exact link to it?
Why didn't you end the argument this way instead of starting to argue about history?
I am asking you - begging you - I did not find the explanation. Mom, explain again or point exactly to another place where you gave it.
fresh,
The paradox of Achilles and the tortoise is solved in a continuous space - take in, think and read.
For you one more time:
It is possible to pass an infinite number of points, the distance between which shortens rapidly in a finite time, because the time of passing from point to point also shortens rapidly.
And here is the "mental" leap you need to make:
The sum of the infinite rapidly shortening times (of the transitions from point to point) is ** finite! **
It is not easy to understand this but it has been proven beyond any doubt!
That's it, I said, and you should look for clear sources from me on the subject
Michael
What dodge? Who dodges? I have already answered this, and more than once.
On the other hand, the question you asked is a well-known trapping technique whose purpose is to exhaust the speaker by making him repeatedly answer the same question that is phrased differently each time.
A known evasion method.
I have already answered this either here or in the article about Zenon's paradoxes
fresh:
so you said
Maybe you can tell us how?
By the way, particles whose trajectories intersect exactly in the middle of such a section will not collide?
Michael
The solution I propose explains how to skip those minimal sections without going through any point in between.
fresh:
All that Zenon has shown us is that he is wrong.
His problem can be solved mathematically in continuous space, only he - like you - did not know mathematics.
The "solution" you offer does not, as I have told you many times, solve anything because it does not explain how those minimal sections and more can be skipped without going anywhere in between.
I must reiterate that I am not claiming that space is not quantum. I only claim that nothing you say indicates that and no thought experiment or other known to humanity requires such a conclusion.
I can refine your claim and also claim that the sections are alternately green and purple. It will have exactly the same effect as your words.
Some people get confused and call the blooming of musings in the air in the name of philosophy.
There is no serious philosopher who sees it that way. In fact the most serious philosophers are the scientists.
It has already been said about the type of "philosophy" you are talking about that to be a theoretical scientist you need paper, a pencil, an eraser and a trash can, but to be a "philosopher" you only need paper and a pencil.
Lenaam and Michael
Mathematics is not the world, it is only symbols that represent it. The question of whether infinity actually exists in the world or rather minus infinity which represents scales of space-time is a philosophical and not a scientific question because no experiment will confirm or disprove it, there is no microscope that reaches these scales and there is no camera that can take pictures in such short time dimensions, therefore until devices are invented Such, and they will probably never be invented, we will not agree with each other. Therefore the answer to this question must also be philosophical or logical in the meantime, and Zeno showed us very nicely that when we assume that time-space is continuous we reach a contradiction, therefore space-time is necessarily discrete, at least In our universe, what is beyond our universe, i.e. what is sometimes referred to as the BULK of the multiverse, if this BULK exists at all, does not necessarily have to be discrete.
fresh,
You're too busy giving me grades and don't spend enough time thinking - maybe because of the time. Try again when you wake up…
fresh:
It seems you are already completely confused about the time.
Where did I talk about equations that use irrational numbers?
Your answer refers partly to Noam's words and partly to his own.
You probably don't even understand what a paradox is.
A paradox is a situation in which a set of considerations that appears to the inventor of the paradox to be legitimate leads to a conclusion that does not correspond to reality or is in contradiction to a conclusion arising from another legitimate set of considerations.
Therefore every paradox is based on a set of considerations.
Go to sleep.
I meant Michael...
Good night
Lenaam
So what if there are equations that use irrational numbers? What does that even have to do with it?, you probably don't understand what I'm saying at all.
To refresh, I don't remember someone showing me that discrete space does not solve this apparent paradox, and what is Zenon's system of considerations anyway? What considerations? Zeno invented a thought paradox and did not create any system of considerations.
By the way, fresh:
The joke is that you started talking about dividing the space into non-divisible units as a "solution" to the Zenon problem.
Already when you did this I showed you that it doesn't solve anything because if you accept Zenon's system of considerations (which in my opinion is wrong but not in your opinion) then it is clear that Zenon would claim that there is no way to get past the small sections.
You didn't answer that.
You just skipped it because it doesn't fit your goals.
fresh,
You insist on thinking that in the real world there is no place for infinite numbers. It's a mistake. There are quite a few equations that use irrational texts when the result is sometimes - not always - completely rational.
In short, the separation between mathematics, which includes infinite numbers, and "your" reality, which does not include infinite numbers, and thus you think to solve the difficulties that infinite numbers do bring ** is not correct**
Oh yes, I understand the difference between pi and a decimal fraction with 3000 digits after the nearest point in value...
pleasantness
It is not that I am making an artificial separation, it is you who is making an artificial union, where such a union does not make sense. Reality does not have infinite precision, mathematics does because mathematics is a mental thing and not a physical thing, the difference between the root of two or pi as a physical length and these numbers as mathematical concepts is so minuscule and negligible from a practical point of view and at the same time so large and significant in terms of world view . I'm sorry you don't understand that.
Shenomach = that is formulated
refreshed
You make an artificial separation. The numbers pi, e, root 2 and many more are irrational numbers, infinite in length. Despite this, there is almost no equation in "your" world of physics that does not use them. What will be the area of a circular garden that you decided to build in your house, whose radius is exactly 1 m?
The answer is exactly pi. But you will immediately declare the burning of Carthage and claim that the area of the garden cannot be divided into infinite parts. But the meaning of the claim that the ** exact ** area of the garden is a pie - is that its area is described by a number with an ** infinite ** length. If you claim otherwise, then either Pi is indeed rational or the theorem of the area of the circle is incorrect.
And I understood very well that you meant repetition of an idea, and what's wrong with that? I just want people to understand me correctly. I only talk about it where I think it's relevant of course.
By the way, I would like to hear instead of personal accusations against claims that contradict the content of my words, if there are any...
To Noam my friend
FYI, I delved into Cantor. And there is no contradiction between me and him. The fact that there exists in mathematics a concept called infinity and even different intensities of infinities does not require the actual existence of infinity. Therefore, as I have already mentioned, a distinction must be made between mental/conceptual/mathematical infinity, and physical reality.
fresh,
It's not the first time you "understand by hand".
This sentence has an additional meaning to the one you mentioned and it is the real meaning:
We mean a person who constantly repeats the same sentence, whether it is related to the subject or not.
I have already told you before, your insistence on eliminating the concept of infinity from your world, only causes you harm. I kindly suggest you to start delving into the cantor example.
To Noam
This sentence means "an opinion or view that a person adheres to in many and voices it often". In some cases, the phrase also expresses tireless stubbornness, determination and adherence to a goal.
So I would like to thank you for the compliment although I allow myself to assume that you meant stubbornness in the bad sense.
I read "Hasbarach" and he would have given you a failing grade in math.
Indeed - in the way you try to tie everything to this unfounded theory you remind Cato.
To remind you - Cato's activity was in the field of politics and not in the field of science.
fresh,
Have you heard of the old Cato, who used to end every speech with the sentence "and Carthage should be burned"?
I already explained why the Pythagorean theorem does not contradict, I recommend you read.
fresh:
The Pythagorean theorem says that the remainder of a right-angled and isosceles triangle is the perpendicular multiplied by the root of two.
By simple considerations of number theory it can be shown that there is no size to divide both the length of the perpendicular and the length of the hypotenuse.
If the space was divided into segments as you claim, these segments would divide both the perpendicular and the remainder.
It's not really clear to me why I'm bothering you because you're done telling me not to understand.
My previous comment.
Container
A. The Pythagorean Theorem does not contradict anything, and even if you continue to declare every day until the end of time, that the Pythagorean Theorem contradicts it still will not make the Pythagorean Theorem a contradiction
Ra'anan the prophet who is ready to beat his teachings everywhere without taking into account the fact that the findings (like the Pythagorean theorem) contradict it.
In the current case it is even more ridiculous because it has already been explained here why when you apply logic correctly you do not encounter a paradox so there is no need to "save" us through baseless prophecies.
There is no paradox here if we assume that space-time is discrete (quantum).
The paradox exists only if it is assumed that space-time is continuous (that is, it is possible to divide a spatial dimension or a time dimension infinitely without stopping at any point)
And therefore space-time is necessarily discrete (quantum). And when humanity has a good enough microscope or a camera that shoots in slow enough motion it will be proven.
The Paradox of the Lamp: There was one lamp. Turn it on, turn it off. Turn it on, turn it off. Turn it on, turn it off. But we gave her a set time for each action, and decided the number of actions. How does this lead to a paradox? There are three formulations of the concept of paradox, one is true, one is not, and one itself tries to create a paradox.
Wrong: A paradox is something that doesn't make sense.
Correct: A paradox is a logical sentence, which humans, because of their irrationality, make completely wrong assumptions and then are surprised that the answer is strange, just like them.
The paradox: the number defined in this sentence + 1.
Regarding the "paradox" I said here: there is no number defined in the sentence! Wow! What a paradox!
Regarding the paradox mentioned at the end of the article:
I can think of another series: for every 10 positive numbers a negative number is made. How can this be done? 1,2,3,4,5,6,7,8,9,10,-1. 11,12,13,14,15,16,17,18,19,20,-2. You can of course continue in this way. So how is it still possible to arrange in another way and that it gets 0? (A question for thought - a short and wise thought.)
It is worth reading again - on repeat - this article and all the responses to the matter, which were conducted here in the context of the articles
The last ones.. really.. as a humble recommendation only.. I, for my part, will return to the harmonica, the bagpipes, the drawings... with a pen.. and the notebooks..
For the upside-down coffee..for the cigarette pipe - by the way, for those who are stressed about the matter..a new genius solution..
Electronic cigarette..men's shop..at Dizengoff Center - without mentioning names.
It's also worth sitting in the port of Tel Aviv... good ionization... oh one more thing... there's a cafe there
Nimrod..a company on the Keifak, and even a drink called..mohitha..ha.ha
So, Archie Chochem.. and have a good week.. Qantas.. in the strength of.. the good and kind ones who escaped
For our blessed affairs.
The riddle of Achilles and the tortoise is also relevant to our understanding of the theory of relativity. Suppose now that the tortoise starts the race at a slow speed, but accelerates. In this case, the tortoise is able to avoid Achilles even if his running speed never equals Achilles' speed. If we convert the tortoise into an astronaut and Achilles into horns- The light moving behind him towards him. The astronaut is not able to exceed the speed of light. But by continuously accelerating he is able (in principle) to get closer and closer to it. Under these circumstances, the light beam is never able to reach the astronaut.
The solution to the riddle of Achilles and the tortoise means that an infinite series of events can actually be completed in a moment (within a given time).
To Michael
In your words, I see a wild diversion and slander of innocent scientists.
When I see how your lust for B12 makes you lose your mind, I have to ask you if the detective's name was Michael by chance.
Cows have every right to live peacefully on their way to our plate.
But if we're going to be really serious, then how do you really know you've met a cow? It's not an easy problem because, as we know, not one cow is the same, therefore, isn't it possible that within the uncertainty of measurements, a cow could be, God forbid, an Athens, and not only that, Even if you talk to meet a cow on the Internet you can't be sure it's a horse pretending to be.
And don't be told that a cosmological principle can allow me to believe that it is a cow!
The use of Ockham's razor in this case can be used as a maximum... for slaughter.
Good night
Sabdarmish Yehuda
How did they know what a cow is if they haven't seen cows elsewhere? asked the detective who was investigating a case where a cow was murdered to rob her of B12 and arrested the three of them.
By the way,
In the book 'Perma's Last Theorem' (no need to worry, he finally came out right...) the following joke appears:
Three scientists are traveling in Scotland and see a cow:
The astronomer calls out: We have seen proof, all the cows in the whole world are black!
The biologist reads: Why, only the cows in Scotland are black;
The mathematician replies against them: it's all nonsense: we saw one cow (!) that we only know about one side of her (!) which is black.
In other words: the technical limitations always dictate the methodological limitations: in astronomy I compromise on levels of certainty that are lower than the levels of certainty that I would be willing to accept in other fields of science. This is a fact that we live with in Barra, but we must not forget the limitations that are built into it.
good week
to ask
Regarding the link in response 5, I agree with Michael that there is actually nothing new about what we already know from a previous discussion. We have two strange phenomena about spaceships flying in space. The first is the Pioneer Anomaly which appears at the edge of the inner solar system and talks about an unexplained wobble in the spacecraft's flight out of the solar system and the second is called the Play Bay effect and talks about an unexpected phenomenon of acceleration/wobble of several mm per second during the spacecraft's flight near the two planets. The conclusion reached in the article is that it is possible And here we are talking about the need to change the known laws of gravitation. This was also known to us.
So, I'm sorry, but for section five you will not receive any additional share of the cosmos in your name.
I'm trying to see what can be done with the dark mass you gave me. Maybe feed it to the animals you donated to Michael. The question is whether the quality of B12 will not change.
So have a good week
Sabdarmish Yehuda
א
borrowed:
According to what I saw, the link from comment 5 contained material similar to what you already provided in the previous link. I didn't find, therefore, anything new to say on the subject and maybe I messed up when I didn't simply say, thank you.
Regarding Einstein, most of those who have studied the subject have doubts, including Abraham Pace who wrote his in-depth biography Subtle is the Lord. I also think it is likely that he knew about the experiment but, as mentioned, it is not "known" in the conventional sense of the word
To the honorable Michael and Yehuda,
Thank you for the honor. There are scientists who invest millions of dollars and tens of years of their lives and those of their assistants, in order to go down in history, and here, thanks to you, I got to own an entire galaxy!!!!
As a sign of gratitude, I give Judah the ownership of the dark matter (which is not in her) and the black holes she has, and Michael the vegetarian the ownership of all the animals in her. Someone like him would do well to know how to preserve them.
good week. And well fed.
Bye
For some reason you did not refer to the link I provided in response 5 to this page. A follow-up article to the issue of the spacecraft orbit anomaly.
To Michael: Lorenz referred to Michelson and Morley's experiment from 1897 in a famous article ten years later. There is no doubt that Einstein was familiar with the experiment.
To all those interested who asked me. Michael and I name the galaxy NGC4736 as the "Shaul Galaxy" to which the nice commenter, the uplifted, Shaul, first directed us.
The idea there was first brought up by Michael, and I humbly join in the honor we gave Saul.
This spiral galaxy is very interesting because for its rotation it does not need an additional dark mass as is required in all other spiral galaxies.
For those interested:-
http://space.newscientist.com/article/dn13280-galaxy-without-dark-matter-puzzles-astronomers.html
may we have a nice week
Sabdarmish Yehuda
To Roy Cezana
Today my first-born daughter who joined the sacrifices, brought the pure corpses of my walkers without calculation. I must point out that I am not sure that we have worsened the global warming situation because we only used one bag of archaeological charcoal and added to it some twigs from our immediate surroundings, such as are supposed to be regenerated in the Ben Shemen forests. Considering that every dead cow always stops spreading the aromas of the well-known greenhouse gas - methane, we haven't worsened the situation in a significant way.
I want to point out that in the sin of the sacrifices many sinned, blue which is on the seashore, and the sacrifices were all around me a fat son and under every fresh tree, a great multitude (and very hungry).
And as for the young and beautiful Beiti, she enrolled in geography and environmental sciences. She justified her choice in the future need to save the planet, and in the fun she was going to experience on the expected trips for the environmental studies. For your information, Beiti studied five units in the subjects of English, geography, chemistry and four units in mathematics, so she is not only beautiful like her mother but also smart like her father.
And as a leader, the celebration was closed by the "Sandwich? His beautiful wife and my sweet and probably smart granddaughter. It was really, really, really fun.
to Arya Seter
Welcome back to our borders, we haven't heard from you in a while.
And Michael
It is true that the Saul galaxy did not give Newton a decisive blow, but it is the lower limit of the possibility of being explained by Newton. Beyond that there can only be magic solutions.
So let's see what a day boy is.
Sabdarmish Yehuda
Aryeh Seter:
I'm not sure I understood your question, but if I did, then you represent a surprising turn in the discussion and return to the topic of the article :)
If I'm guessing correctly (and again, I'm not sure that's the case because your words are lacon) your question refers to the paradox of the gods.
What I tried to claim in my response (and I still claim) is that the source of the problem there is that we allow ourselves to refer to a physical system and its properties in a mathematical model that we did not bother to define within it the full mathematical equivalent of the physical phenomenon. As a result, we encounter logical problems arising from unfounded assumptions we make regarding undefined entities.
It seems that your words refer to the question of how it would be correct to map the physical world into the mathematical model and this is indeed a respectable question that the entire science of physics tries to answer. I did not pretend, in my response, to answer this question.
Yehuda:
I agree with most of what you said except for the hypothesis that the dark mass takes a hit from the Saul galaxy.
In my opinion, the dark mass theory (as opposed to the dark mass itself) actually receives confirmation from this galaxy because it shows that the movement of galaxies does not require different laws of gravity, therefore galaxies where the stars rotate faster are probably affected by another factor that is not a change in the laws of gravity. The dark mass is definitely a possible factor that is consistent with the findings and is therefore an excellent candidate to be that "additional factor".
I repeat that I personally have no known real reason to think that the dark mass is not a normal mass and that the whole idea of a special type of mass seems to me, at this point (and according to Ockham's Razor), unnecessary.
Regarding the "Saul Minus" galaxy, I agree with the claim that if such a galaxy is discovered, the current theory of gravity will receive a serious shock (although my guess is that such a galaxy will not be discovered).
By the way, I also took advantage of the beautiful morning. I hiked the area and visited (unannounced) some friends I hadn't seen for most of the winter because they live too short to justify driving but too far to encourage walking in the rain.
Gentlemen will teach me. Is it not possible to look for the solution to these problems in quantum physics? I mean Planck length and Planck time. So you will say that this is a physical limit - that there is a minimum length and time below which it is impossible to go any further, and this does not solve the logical problem. But we are already used to the strangeness of quantum theory and maybe the physical limitation is also a logical limitation.
Have mercy on the animals, Yehuda. Between me and your family, we could eat all the animals.
By the way, I forgot to congratulate you and your beautiful young daughter on her acceptance to college. What field did she choose, if I may ask?
Shabbat Shalom,
Roy.
For some reason my name disappeared in the title of the previous comment. So to anyone who says anything, this is my response!
Sabdarmish Yehuda
To Michael
So apparently the Messiah is about to come.
Additionally
I must point out that the "Shaul" galaxy never stops making me think.
And it seems to me that we will once again agree on several conclusions:-
A. The "Saul" galaxy is proof that Prof. Milgrom's MOND theory is incorrect, because in this galaxy the change in Newton's second law formula, which is the basis of the above theory, does not take place.
B. The dark mass receives a strong blow here because we are required to agree that there is a huge area in the sky that is completely (or almost completely) free of it.
third. My personal conclusion.
If a galaxy is discovered whose rotation speed is lower than that expected by Newton, (it will be called "Saul Minus") then this galaxy will completely drop the dark mass, the dark energy, and with them Newton's laws to great distances.
Note that this has nothing to do with the willingness or unwillingness of Le Sage that she is lame anyway.
d. I am sure that people will not easily give up the "loved" dark mass and they will create a new cosmological concept to explain the "Saul minus" galaxy - "negative dark mass".
God. I wonder if someone has already talked about negative dark mass?
and. Because of its importance, the immediate step must be to carefully check the correctness of the inferred data for the Saul galaxy.
G. The time has come for a response also regarding a culinary part that is very much loved by my dear friend Roy Cezana and many others,
As you must have noticed, I must conclude that today is a beautiful day and there is nothing like a day like this to go swimming in the beauty of our beloved country and raise offerings and sacrifices (barbecue in Leaz} and here and there some beloved animals will donate their B12 to the welfare of Homo sapiens. So Yaer Ben Shemen will be the preferred address and my heart , my heart will be with all the vegetarians.
Be strong and courageous.
I would love to hear your opinion on conclusions from the "Shaul" and "Shaul minus" galaxies.
Have a nice and pleasant day.
Sabdarmish Yehuda
.
For me, most logical difficulties are revealed when I'm awake.
Yehuda:
I think it's time to raise a toast!
Shabbat Shalom.
Michael
To Michael
I'm trying to find things in your response that I don't agree with, and I'm having a hard time.
Perhaps on Le Sage, I still think that particles are able to bring attraction in their movement although, I admit, this is a situation that probably requires an inelastic collision at least in part, and therefore will also require explaining where the energy disappears. I think you also agree that it could cause gravitation. Admits that at the moment, there is a problem with Le Sage.
The disagreement between us probably only concerns the way we should treat the laws beyond the range of their experiments. You and most scientists believe according to Occam, to go with the simple law,
I am willing to compromise, up to a close range beyond the scope of the experiment/measurement, I am willing to agree according to Ockham, beyond that at ranges far tens of meters from the range of the experiment/measurement, I advocate using them with a very limited guarantee.
If one were to use my method, one would have to be careful with conclusions such as singular points, dark mass, dark energy, and the like.
Thank you for your insightful response.
It's a shame that sometimes we don't "understand" each other.
good evening
To Michael
The computer is having some trouble and it's hard for me to write a comment, that's why a structure came out
The reaction is strange.
I liked your comment.
I will delve into it and respond
ש
Your definition that "the laws are just the best guess we could guess based on the information we had".
Really good and I will use it in the future.
I agree with some of your words and some not, but mainly I am not a follower of the "fatigue exercises" that is how I define your religion.
good evening
Sabdarmish Yehuda
borrowed:
Your words are a private case of my claim that we do not know the answer to the question of whether Einstein knew about the Michelson-Morlay experiments or not.
Unfortunately he did not mention their names and the debate surrounding the question of whether he knew or not will probably never be decided.
Yehuda:
The truth is that I watched your response but you are wrong, so I will add the words you thought were unnecessary.
Already in my first response (which was not specifically aimed at you) I explained the difference between scientific research and the treatment of mathematical and logical paradoxes.
I explained, for example, that we allow ourselves to assume that the laws of nature continue to be valid even after the experiment.
In general, every law we discover is a generalization of the experiments we have done.
So how do we know if this is a legitimate generalization or an overgeneralization?
We have no way of knowing this except for the logic that is at our disposal and allows us to draw conclusions from the available information and from experiments that we conduct especially to test the validity of the law.
The theory of relativity, for example, still stands the test of all the experiments we conducted where we could. It also exists, as it turns out, in the same galaxy that for the sake of convenience and credit I will call the Saul galaxy.
These facts, as I mentioned, support the continued use of this theory, of course, only as long as it provides correct predictions.
On the other hand - the LeSage theory fails even without a special experiment and we devoted a special discussion to the subject, as you know. In this discussion I brought both my own refutations to this Torah and those of the great scientists and philosophers.
Therefore the LeSage theory cannot be accepted as a law of nature even for a moment.
If we return to philosophy, when you come to adopt ways of solving paradoxes it is better to be early and ask what a paradox is.
A paradox is a situation in which two seemingly legitimate ways of thinking give different and even contradictory results.
A paradox can be revealed in the realm of pure logic as well as in the realm of the interaction between logic and the real world.
The Achilles and the Tortoise paradox is in the realm of pure logic because all the entities in it are well defined and their definition allows conclusions to be drawn with their "behavior". The paradox is created here as a result of the fact that according to normal calculations of solving equations of motion we know that Achilles is supposed to get the tortoise, while according to the consideration of the mistake I presented we conclude that he will not get it.
In my response I argued that, in fact, the Paradox of the Gods is not in the realm of pure mathematics and in order for it to be considered as such, additional definitions must be defined that we did not pay attention to in the first place.
In the field of physics, we will encounter a "paradox" if the behavior of physical systems does not match the laws we know, but it is not really a paradox because from the beginning we knew that the laws were only the best guess we could guess based on the information we had. In any case - this kind of paradox will oblige us to re-examine the laws and adapt them to reality as we know it after the new experiment.
Until then - so that we don't just get bogged down in idle work - they invented Ockham's razor which says that a theory should not be complicated if the theory describes reality even without the additional complication (or in other words - the theory should not be complicated unnecessarily).
By the way, I apologize for the late response - a delay that will allow the questioner to watch it only on Mochash - but this delay was a commitment from my "religion".
Paraphrasing Einstein's words, if there is any behavior in me that deserves to be called "religious" - it is my almost obsessive adherence to fitness training.
Once every two days I devote five hours to this kind of training - an hour and a quarter to bureaucracy (traveling, changing clothes and showering), three quarters of an hour to strength machines and three hours to riding an exercise bike.
With such training I contribute to global warming about 1500 calories (not including the trips).
her face to ask,
The links you provide here are very helpful. Please do not stop your actions. The comments area is designed for exactly this purpose. It also expands the knowledge of other people interested in the field.
To Michael:
To the best of my recollection, the words with which the famous article opens are: "results of experiments done recently are instructive, etc.": which experiments are you referring to?
Some relevant links:
First article http://web.syr.edu/~ddawson/phy312/body
http://www.physicsbanter.com/799545-post1.html
To Michael,
I will find the reference and bring it
Another note to ask:
I think they say "Akhdal" and not "Akhdol"
This reminds me of the fact that on many doors in the malls of our country the word "urgent" is written instead of the word "urgent"
borrowed:
To the best of my knowledge, it is not clear if Einstein knew about the Michaelson Morley experiment when he formulated the theory of relativity and his motives were different (he, in any case, did not mention this experiment in the articles that revealed his theory) according to his testimony, these motives are related to thought experiments he did back in his youth.
Anyway, what I was trying to say in my words is that paradoxes should be faced with courage and not "bypassed" by alternative explanations. It seems to me that in many cases people take the "detour" way and thus they lose the real insight that may grow from identifying the mistake that caused the paradox.
To Michael
Must note that your explanation is exhaustive and thought-provoking. I will also note that he will definitely require me to go back and delve into the examples you gave.
The power of good examples is that you can "upgrade" them with a simple transformation of replacing certain words with others and get the required conclusion again.
For example, I will quote exactly the excellent example you gave in your response to show the negation of "overgeneralization":-
"I walk around my house and ask all the people I meet there what is their country of residence. They all answer me "Israel" and I allow myself to conclude that all the people in the world live in Israel." End quote.
Now if we make a transformation, and where it says "home" we will write "Chinese restaurant" and instead of "Israel" we will write "Chinese food". And the question will be: - "What do you eat?". We will get a new example.:
"I walk around a Chinese restaurant and ask all the people I meet there what you eat. They all answer me "Chinese food" and I allow myself to conclude that all the people in the world eat Chinese food."
It is clear to us that we can also draw the same conclusions against overgeneralization from the "new" example of Chinese food.
This is a very important rule, Michael, so important that I really want to give another example:-
"I walk around my house and ask all the planets I meet there what revolves around them. They all answer me "gravitation" and I allow myself to conclude that all the planets in the world and with them all the stars, and we will also add to them all the galaxies in the world, all of them, all of them, without leaving As a rule, spin because of "gravitation".
Every extra word is superfluous.
May we have a quiet weekend, and recovery for those injured in the attack.
Sabdarmish Yehuda
A small addition to Michael,
It seems to me that paradoxes are mostly resolved by bringing up for discussion a point hidden in the assumptions that, due to its simplicity, no one dares to challenge it and address it, until the paradox solver arrives, and dares to do so, and uses that point as an Archimedean point for a new look at everything - this was Einstein's revolutionary approach in relation to For the famous experiment of Michelson and Morley: usually when we talk about speeds we ignore the fact that speeds are relative to time; Einstein not only 'remembered this', but mostly was ready to challenge the absoluteness of this intuitive concept and claim that 'this is where the dog is buried' and thereby solve the entire problem.
Einstein himself described that there are two types of science: the theories, and the theories that give rise to new thoughts and an overview of those 'inferior' theories. It goes without saying that the last type was the type he liked more, because he does not have to use experiments but ride on the experiments of others. Einstein also claimed that this kind of science is more 'clean' and 'beautiful'.
Shabbat Shalom
To Michael, Yehuda and all our dear friends. Continued article on the subject we have already discussed.
To Avi Blizovsky: I think you should see it as a compliment that discussions started on your site are continued by surfers as parasites on other topics. In any case, if things bother you, say so, and I'll stop bringing the links. Shabbat Shalom.
Fix copy problem:
In the above response, where n-2 is written, two to the power of minus N should appear
The error was caused by the site's editor software that did not correctly handle the superscript that was in the original text
The answer given by David to the dessert paradox is of course the correct answer as anyone who studied high school math knows.
I would like to refer, however, to the article itself and will do so by quoting the response I sent on this subject to "Galileo". This response also contains a reference to another paradox - the paradox of Achilles and the tortoise - but I decided to quote this part of it as well because it may contribute to understanding things.
A paradox always arises from an error of judgment.
Maybe a mistake that is hard to find but a mistake nonetheless.
The solution to the paradox is not achieved by presenting a completely different way in which a logical solution is obtained, but by finding the error in the original way and pointing it out. Any other act does not resolve the contradiction. This is the reason for the importance of paradoxes - their solution forces us to delve deeper and solve fundamental problems in our thinking.
I will briefly explain what I mean using the Achilles and the Tortoise paradox presented in the previous issue.
The Achilles and the Tortoise Paradox says that Achilles will never catch the Tortoise.
He reaches this conclusion by describing an infinite series of events in which indeed Achilles has not yet obtained the tortoise and this series is indeed a series that exists in reality, but at this very point the error of judgment enters when concluding from the existence of that infinite series of events that Achilles will never obtain the tortoise while all The events in question, although their number is infinite, all take place before a certain time (the series of periods of time separating them converges), so it is not correct to conclude from their existence anything about what will happen after this time.
In other words - it was correct to conclude from them that Achilles would not get the tortoise before an hour (say) 10:00 but it was incorrect to conclude that he would never get it.
The error is an "overgeneralization" error and can be likened to the following error:
I walk around my house and ask all the people I meet there what is their country of residence. Everyone answers me "Israel" and I allow myself to conclude that all the people in the world live in Israel.
In a framed article it is worth noting here that we do not always limit ourselves in this way and sometimes there is justification for not limiting ourselves.
If, for example, we look at the scientific enterprise, it is regularly "flawed" by what I described a moment ago as a mistake because we conducted all our experiments in the past and our conclusions regarding the laws speak for the future as well.
We allow ourselves to do this because we believe in the correctness of a certain axiom regarding the laws of nature - an axiom that says these laws do not change over time.
In the problem of Achilles and the tortoise, of course we do not rely on this type of axiom regarding the location since the movement is defined by the change of location with the progress of time.
The answer given in the "upside down" section to the paradox of the gods seems to me to be flawed on several levels:
On the methodological level, it is flawed in that it does not point out the error in consideration that led us to the wrong conclusion.
On the descriptive level, it is based on an apparent contradiction between the decisions of the gods and themselves, a contradiction that, in my opinion, does not exist.
To increase the motivation to face the problem more courageously, I will first present another version of it: suppose all the gods build the walls independently - neither of each other nor of the hero's departure, and then - after the walls are built, the hero sets out.
Of course the hero can't move because he's stuck in a wall, but which wall? After all, no wall is the first?! In other words - for each wall we can prove that he will not reach it at all because the walls in front of him were supposed to stop him before that.
So what's going on here? We ran into exactly the same problem without mixing the gods' decisions into the story.
In my opinion, the solution to the paradox lies in recognizing the fact that we involve physical intuitions in our thinking about a mathematical model in which we have not defined how physics works.
This sentence sounds a bit floaty and in the following paragraphs I will try to bring it down to the ground.
The example of the series of walls we are dealing with demonstrates to us a simple mathematical fact, which is that although an order relation is defined between any two numbers (greater, smaller, or equal), not every infinite collection of numbers has a first or last number, even if all the numbers are in a given finite range.
Another example that illustrates this fact is the collection of all numbers between zero and one, without zero and one themselves.
We are talking about a world where a person can be in motion and can also stop or be stopped, that is, move from a state of motion to a state of no motion.
The claim that the person stops at a point whose distance from the village is zero is a definite claim that says that until the moment they reached point zero the person was in motion and after that moment he was no longer in motion.
On the other hand - the claim that a person stops at the first point after zero or at the smallest of the numbers whose form is 2-n is not defined because there is no such number - as mentioned, these are groups of numbers that do not have a first term.
If the person is in motion for some time and it will be as little time as we want after reaching the gates of the village he will necessarily pass not only through one wall but through an infinite number of walls.
So what's going on here anyway? After all, if we build the walls, it is clear that the person must be stopped, so what kind of wall stops him despite everything?
Our inability to answer stems from the fact that our feeling regarding the concept of stopping stems from our experience in the physical world and from the fact that in the model we are talking about there is no definition of what causes a person to stop (because as mentioned, the first wall he encounters is not a defined concept!).
As soon as we introduce an unequivocal definition of the stopping conditions into the story - the problem will disappear.
This can be done by a more realistic model of the physical world - one in which there are no walls of zero thickness and an infinite series of walls in a finite domain is not possible at all.
This can be done by adopting another aspect of the physical world according to which we are stopped by electromagnetic repulsion of particles and this repulsion is actually the accumulation of the repulsions created by the whole group of walls and not by a single wall.
It is possible that this rejection will stop him a little before all the walls or exactly at the zero point or after he passes through several (infinite) walls.
No matter how we look at it, what we must not do is to base ourselves on a model in which the conditions that cause a stop are not defined and then be surprised that we do not know when the man stops.
And what happens when the gods build the walls exactly under the conditions defined in the problem in its first formulation?
Here we have to ask if these conditions have even been defined.
In the interpretation given by Marius Cohen to these conditions, they are not defined at all because he describes the action of each god as a result of the action of the god before him and since there is no first god, then the mode of action of the gods is not defined at all. This is one way to deal with the paradox, but it is actually a simpler paradox than the paradox in the original definition of the problem. If you read the problem as a language, then the way the gods work is not defined by the work of their predecessors, but as a function of the hero's arrival at a certain point. The dependence that Marius Cohen introduced on the action of the other gods is a conclusion and not a given. What is this conclusion based on? Again - it is based on the same stopping condition that he allowed himself to "copy" from the world of physics without defining it in the mathematical model.
Infinite commutativity
As we know, commutative (commutative) connection does not (necessarily) hold for an infinite column. In such a case, the commutativity holds only for a positive column, or every column is absolutely convergent...
The correct answer is 0 since in the second series the negative numbers are one term behind so that eventually it will be necessary to subtract infinity from infinity and the result will be 0 as in the first series.