The article was written following a lecture at the Society for Astronomy at the observatory in Givatayim
Yehuda Sabdarmish
Direct link to this page: https://www.hayadan.org.il/sevdermishyoum.html
The collection of the data and the derivation of the rules that operate on this data and the projection of these rules throughout the known universe is apparently a trivial act that should not lead to contradictions. Is this indeed the case? Is this natural action of finding rules and laws for the way the universe functions lacking?
The naturalness with which we operate in scientific research will be seen with the help of very simple examples that will easily define for us the way of finding legality in scientific research.
Let's first take an example of a simple invoice series:-
1, 2, 3, 4,
Let's look at these four numbers. It is clear to us that the natural continuation of this series is:- 5, 6, etc.
Let's take another simple series:-
5, 10, 15, 20, again it is easy for us to see the tribal continuation in numbers:- 25, 30, etc.
Everything is simple and logical.
This logic is not only in mathematics. For example:- Physics:-
We will take a spring, put different weights on it and measure its contraction.
1 kg 1 cm
2 kg 2 cm
3 kg 3 cm
4 kg 4 cm
When we ask how the spring will behave in the future, the answer will almost certainly be that if we put five and six kg on the spring, it will shrink respectively five and six cm.
Well what did we do? How did we know what to answer?
This rule that allows us the answer is called: "induction"
definition:
Induction is a method of learning by investigating many details in order to deduce from them the rule (principle, law) that unites them.
If N is the serial number of the members in the examples we have given, then:-
The rule attached to them in the first example is: - N becomes N
Likewise in the case of the spring (the third example)
In the second case, the attached rule is N becomes 5 * N
Are these rules the only option?, aren't there other rules that can also define for us the organs we have chosen?
For example, is there a possibility that the continuation of the second example, 5, 10, 15, 20, is 1, 6, ?
What is the rule in this case?, it is not difficult to notice that the rule here is a 24-hour clock, that is, five hours after 20:XNUMX (eight in the evening) one o'clock at night will appear, and then six o'clock in the morning, etc.
In other words, we found two rules, each of which defines the first four numbers we tested, but each gives a different continuation.
We will see also regarding the first example, we will bring another possibility
What if after 1, 2, 3, 4, we get 6, 7, 8, meaning we skipped 5?
The rule is for those who want to check:- N becomes an absolute value of:- IN*1.2 I
And what about the example of the spring? Couldn't there be the possibility that after 1, 2, 3, 4, appear:
4, 4, 4, … ? Sure!, when the spring cannot shrink more than four cm, and it doesn't matter what weight we put on it!.
From the examples we have given so far, three main important conclusions can be drawn:-
The first is known as "David Yom's induction problem",
The second is the reality of infinite possibilities for rules,
The third is "Occam's Razor"
We will explain the conclusions one by one.
The first conclusion is called "David Yom's induction problem":-
We cannot confidently draw conclusions beyond what we measured. (1*)
David Yom's induction problem shows us that the only possibility to expand the range of rules, principles and physical laws is only by increasing the range of our measurements, any increase in the range of rules without increasing the range of measurements, will amount to a wild guess!
A second important conclusion is the statement that:-
"Each set of measurements has an infinite number of rules that define them."
For example, we showed that the sequence of numbers:- 5, 10, 15, 20, can continue in all kinds of possibilities, all according to the rule that builds them, 5*N, or the rule of the twenty-four hour clock and more, there is no end to the possibilities of rules. (*2)
The third conclusion that we will define will help us decide which of the infinite number of rules we will choose. The way of selection is called:- "Occam's Razor" (*3) which says:-
"Among several correct options, choose the simplest one"
Choosing the simplest option in no way makes it more correct. Not in the measurement area we measured, certainly, certainly not beyond the measurement range either. The simple choice is for convenience reasons only. And really, what's the point in choosing a complicated option if you can get the same correct results in a simple way?
In addition, we must add and specify that the definition of the simplest is not an exact definition and sometimes the choice of the simplest is not unambiguous. Sometimes even the choice is a personal matter, depending on the user's personal knowledge. (*4)
The measurement range problem
These three conclusions show us that the extension of the scientific rules to larger ranges requires additional measurements in the aforementioned ranges. Ignoring this and using rules beyond the above ranges would amount to a wild guess lacking almost any scientific meaning.
We will now see how the range is increased and is it always possible?
In the first stage we will see differences in the possibility of increasing the range in mathematics and physics
The math is done in the head. In the head, you can build anything, there is no limit. I can always access to infinity and pull from there the data I need for my calculations and determining my rules and formulas.
In physics it is impossible, we are limited, especially when it comes to large sizes: the masses, the density, speed and especially when we also have the large ranges.
To overcome part of the above physical problem, devices were invented that are capable of measuring distances, for example: telescope, spectroscope, measuring wavelengths, measuring the Doppler effect, measuring cosmic particle radiation such as neutrinos and more. But the solution is extremely partial and most of the universe still remains without the possibility of accurate measurement.
That is:-
There is no guarantee that all the laws, principles and rules we have found will be correct even outside the range of measurements we have measured. For example in the following cases:-
In very large masses - such as black holes, or very small - opaque parts,
Very large matter density - such as neutron stars, or very small - interstellar space, enormous speeds - close to the speed of light, or tiny -
High accelerations - such as a super nova explosion. or small accelerations - such as the peripheral acceleration of rotating galaxies,
Large physical sizes - such as the universe, or tiny sizes - such as singular points,
And especially - at very large distances such as between galaxies, or very small - inside the nucleus of the atom,
Or in different directions than we measured!
At this stage of scientific research we have reached a situation where we know what we cannot research, and therefore scientific research had to focus on attempts to increase the range.
Any unjustified increase in range had to include presenting a "warning light" to the reader, who would accept the conclusions with a "limited guarantee", but human nature has a strong desire to generalize about everything, it is something psychological inherent in people to define what they have developed or discovered as true for all The universe began from the beginning of time, in various religions for Aristotle to Newton, Einstein and others. Everything is true in the whole world, from the smallest particles to the most massive bodies. But are there any measurements that will justify this? There are none!
Of course, the need for backup exists. After all, it is impossible to do such an act without the backing of any scientific principle. Well, this is done by arbitrarily giving three properties to the universe:-
Isotropic - property that makes the universe uniform in all directions
Homogeneous - a property that makes the universe uniform everywhere.
(no name)- a property that makes the universe uniform for any existing or assumed physical size.
The above three qualities together are called the cosmological principle.
(Author's note:- In fact, only the first two properties are known as the cosmological principle, but the reference to the laws of nature in the cosmological principle is as if the third property is also included in the principle even without it being stated, therefore I decided to associate it with the principle as well).
The definition of the cosmological principle:-
There is no favorite place in the universe. The conditions of the universe will look the same from wherever the viewer chooses to watch from.
To this must be added the addition arising from the third conclusion: "There is no preferred size in the universe."
Let's go back and emphasize again:- the above three qualities were actually given arbitrarily, without any substantiation of scientific measurements, just a casual belief that maybe this is how it should be.
Even the few cases in which there are proofs that the cosmological principle is correct do not show its correctness in every case.
There is no doubt that if David Yom were alive today, his outcry and anger would be great, because in fact this is not a matter of principle, but at best "disgust" or "hope".
To show the problematic nature of the "cosmological principle" and the psychology behind it, we will tell the story of a man we all know: Isaac Newton and the discovery of the gravitation formula:-
Newton's gravitation formula was developed to explain the movement of the planets known at the time, starting with the planet Mercury, which is 0.39 astronomical units from the Sun, and ending with the last planet known at the time - Saturn, which is 9.54 astronomical units from the Sun. Based on these data, the cycle time of the planets, and Kepler's laws that were known in his time, Newton arrived at his well-known formula.
But we must not forget two important facts:
A. This formula was proven at this point only for these distances. It was impossible to say at that stage anything absolute about the formula at larger or smaller distances (David Yom).
B. There could be infinitely more similar formulas. Naturally, Newton chose the simplest formula (according to the principle of "Ockam's Razor"), but it is not necessarily the correct formula even for other larger or smaller distances!
But that didn't stop Newton from stating that gravitation works from the edge of the universe to every two pieces of matter at any distance. Isn't this too overwhelming a decision? Surely he didn't check it at every point in the universe? (*5)
But since then, the discovery of the distant planets: Uranus- (1781), Neptune- (1846) and especially Pluto- (1930), which moves at a distance between 30-50 YA from the Sun, and Henry Cavendish's experiment and finding the gravitation constant increased confidence in the formula.
Now that the proven limits of the formula have increased so much doesn't that prove that Newton's formula will always be correct? The answer is unequivocal: no! The astronomical sizes are much larger.
Parallax measurements, measurements using cupid stars and finally measurements using Hubble's constant, determined the size of the visible universe: fourteen billion light years which is one billion million astronomical units. To remind you, Newton's gravitation formula is proven up to fifty astronomical units only!
There is no doubt that if we want to use Newton's gravitation formula at distances greater than fifty eleven, the formula must be proven at these distances. An attempt to ignore this contradicts the problem of induction raised by the English philosopher David Hume which we discussed.
Attempts to prove Newton's gravitation formula using the rotational motion of spiral galaxies failed, too much mass was missing. Nevertheless, in the science of cosmology, without any restraints, while basing themselves on the "cosmological principle" they talk about intergalactic attraction forces and even to the edge of the universe, even though this leads to "suspicious" conclusions such as - a huge amount of missing mass, holes Strange blacks, strange singular points and more. The justification for the use is mostly made only according to the "cosmological principle", with all the problems arising from it.
In conclusion:
There are several rules that help us in conducting scientific research, two of which are problematic and contradict each other.
On the one hand, the rule called:- "David Yom's Idduction Problem" which claims that what is true here is only true here and it is impossible to conclude from that about the rest of the universe,
On the other hand, the "cosmological principle", which claims that what is true here is also true throughout the rest of the universe,
The contradiction between "David Yom's induction problem" and the "cosmological principle" doubt is irreconcilable!
If scientific research continues to insist and progress based on rules and laws that were measured only in our limited area of the near universe, then the results and conclusions of such research are very flawed!
Remarks (*):
1. The story of David Yom's life is intertwined with his attitude towards the masses. He never made sure to give simple examples of his philosophical ideas, which caused him to clash with the scientists of his generation (the eighteenth century) who used to philosophize in Latin and feel elevated by the people. This is surely one of the reasons why he is considered the greatest of English philosophers.
The induction problem he defined was characterized by simple examples such as:-
You checked a hundred crows and saw that they were all black, what is the conclusion from that? Are all the crows in the world black? no and no! The only conclusion that can be drawn from this is that the hundred crows you checked are black, and nothing more!, other crows can be black or other colors!
2. The problem of finding an infinite number of rules is more significant when it comes to physical measurements, which are inherently uncertain, so deriving rules becomes more difficult, with many more possibilities because the data itself is not unambiguously defined. But always, the number of possibilities for the rules is infinite.
3. The story "Ockham's Razor" begins with the story of an extremely ascetic monk named William from the Occam area, in Scotland. His passion for asceticism was so extreme that he incurred the wrath of the Pope who excommunicated him. There are several versions of his rule - "Occam's Razor" I prefer to choose the simplest (!) which says: - "Among several correct options choose the simplest"
4. Below are several examples that show several options for choosing the simplest:-
First example:- If a 51 mm wide cloth ribbon is required for a certain job, most likely an American worker will be required to bring a two inch wide ribbon (1 inch = 25.4 mm approximately)
Second example: - On a construction site, pits had to be filled with concrete. The diameter of the drill that drilled the holes was R. But due to the presence of stones in the ground, and the vibrations of the drill, the drilled hole was larger. Three experts were required to ask how much concrete should be ordered to fill the pits? Below are the three answers received:-
A. Add 12% to the drill diameter R and calculate according to the new diameter.
B. Calculate according to the diameter of the existing drill and add a quarter to the final result.
third. The pit should be treated as if it were a square column with side R*2 (ie the diameter of the drill bit).
These three simple formulas did their job faithfully with the difference in results varying by less than two percent.
5. We must not forget that the known universe in Newton's time was relatively small. The known solar system at the time witnessed the planet Saturn, and apart from it, there was at most another count of Saturn planets that do not move. So Newton actually did not exaggerate too much when he said that his gravitation formula was proven for the entire universe known at the time.
bibliography:
Fat-El Yigal, Astronomy, A Guide to Knowing the Heavens, Cosmos Publishing (1998)
Meir Midev, N. Cypress, H. Netzer Haikum Fundamentals of Astrophysics, The Open University (2000)
Timothy Ferris, From Childhood to Adulthood for the Milk, Maariv Library (1991)
Yakir Shoshani, Thoughts on Reality, The Broadcasting University (1999)
Yuval Na'eman, Seder Man Akraai, Van Leer Institute in Jerusalem, Kabatz Ha'Uchaed Publishing House (1999)
Sabdarmish Yehuda, Thoughts on Newton's gravitation formula, "Astronomy" Betown Association.
Sabdarmish Yehuda, The weight of bodies in the universe changes, "Astronomy" in the association's publication.
A compilation of Yehuda Sabdarmish's articles on the Hidan site
https://www.hayadan.org.il/BuildaGate4/general2/data_card.php?Cat=~~~3351103~~~129&SiteName=hayadan
