And the math will set you free by Cristinel Stoica

I have asked Dr. Foster, the moderator of this competition and he claims that he did not remove it and for me to enquire of the person at the site. I posted a revised comment to your site, and that has been removed. I will repost for a third time.

Ruefully,

Joe Fisher

Dear Dr. Stoica,

You wrote: "Some may hope that there are things in the universe which can't be described by mathematics. But can you name those things?" Thank you ever so much for asking. Please read and try to understand my definitive answer:

Accurate writing has enabled me to perfect a valid description of untangled unified reality: Proof exists that every real astronomer looking through a real telescope has failed to notice that each of the real galaxies he has observed is unique as to its structure and its perceived distance from all other real galaxies. Each real star is unique as to its structure and its perceived distance apart from all other real stars. Every real scientist who has peered at real snowflakes through a real microscope has concluded that each real snowflake is unique as to its structure. Real structure is unique, once. Unique, once does not consist of abstract amounts of abstract quanta. Based on one's normal observation, one must conclude that all of the stars, all of the planets, all of the asteroids, all of the comets, all of the meteors, all of the specks of astral dust and all real objects have only one real thing in common. Each real object has a real material surface that seems to be attached to a material sub-surface. All surfaces, no matter the apparent degree of separation, must travel at the same constant speed. No matter in which direction one looks, one will only ever see a plethora of real surfaces and those surfaces must all be traveling at the same constant speed or else it would be physically impossible for one to observe them instantly and simultaneously. Real surfaces are easy to spot because they are well lighted. Real light does not travel far from its source as can be confirmed by looking at the real stars, or a real lightning bolt. Reflected light needs to adhere to a surface in order for it to be observed, which means that real light cannot have a surface of its own. Real light must be the only stationary substance in the real Universe. The stars remain in place due to astral radiation. The planets orbit because of atmospheric accumulation. There is no space.

Warm regards,

Joe Fisher

Dear Cristi,

now I had the chance to read your essay. Very interesting. In many parts, we both agreed (or as Pauli expressed it in a letter to Heisenberg: "boring agreement" ;-)

But at one point I went farther than: in my opinion at the center of modern math is structure (as you explained in one section). Math is not a simple theory to relate one number to another, it is rather a theory of structures. Even this structures will be also important in the future for other sciences. You mention model theory and even this point is crucial: one can change the model (including the logic), i.e. one can change the math completely and only the structure is left.

Maybe an agreement again?

Torsten

Dear Cristi,

thanks for your words and vote, which I will give back! Other essays concentrated on the close relation between math and physics to forecast experiments. But not yours and I like it (and also your scientific work).

Best

Torsten

I get a little worried when Goedel comes into the picture. This is not because I don't think at some point this might rear its head, but because as you say this is misapplied. I think the real question is whether because we are a part of the universe that our attempt to completely codify the universe runs into this sort of incompleteness. We are in a way a piece of the universe that is working to encode its foundations, which is similar to a formal system listing or computing all its Goedel numbers. We may have an issue of this sort with the so called measurement problem and our inability to rectify quantum mechanics and measured outcomes with our macroscopic based thinking.

I am not sure one could say that 19th century physics was a unified theory as such. There were the three main areas of classical-Hamiltonian mechanics, thermodynamics, and electromagnetism. Thermodynamics ran into trouble with classical mechanics over the issue of time reversal invariance. Electromagnetic theory was not able to figure out how an arrangement of charges could be stable in a classical mechanical form. Then of course there was that annoying black body problem. I think physics then was filled with open questions that betrayed any idea of unification. I suppose in many at the time were confident that as Raleigh put it that all would be working once that black body problem is solved.

LC

Dear Cristinel,

About "And the math will set you free", it may be but only after you have realized the truth - and only "The truth shall set you free".

Man is a created being absolute as he cannot create himself. The Creator is the God of man - the God who divides as well as the God who unites. Everything that we know of as well as things that have never ever crossed our mind are all already ready out there - there is not a little one bit more or a little one bit less. Why? Because our God is the One Perfect God who misses nothing.

Mathematics is left only to be discovered. The patterns are all already part of the nature of the universe for our minds to unravel. It is all abstract as it is in harmony with the power endowed with our mind to work with abstract objects and structures. So mathematics is only mental and there is no "physical" reality in mathematics. But there are realms beyond the mental, beyond our endowed mental powers. So with the mind, as well as with mathematics, you cannot understand those unreachable realms.

Time is one realm completely beyond the mental understanding of man and mathematics. Time is only metaphysical. Since ancient time, time is taken to be absolute and its nature is almost as mysterious as the nature of God. To say we know of the nature of time is as good as saying we know the nature of God - which we cannot do. So in Newtonian mechanics time is just the variable 't' - there is no assumption that 't' could have properties that man can understand. It was the case until Einstein's relativity theories which presumed man has the ability to ascribe properties to 't' - that there is a Lorentz factor that have the properties of 't' implied within it. If the Lorentz transformation is "truth" that could describe physical reality, it would mean that man, through his thinking, could understand and give properties to God the Creator - which we cannot. The treatment that Isaac Newton gave to time, just a single variable 't', actually is an acknowledgment that man cannot know God except that "God is God". So there is only absolute time.

"But can we find a property of time that can't possibly be described by mathematics? In fact, time was best understood due to mathematics, in relativity and thermodynamics."

Actually, time cannot be understood; within physics, there should not be any attempt to incorporate any understanding of time. It is because relativity try to assume that there there is a way to discover some property of time through inventing relative time dependent on the motion of a frame or that of the observer that both the special and general relativity theories can only be invalid. Any theory of physics founded on the Lorentz transformation can only be invalid as the Lorentz transformation cannot be physical - meaning it can never be a valid physical theory describing the working of our physical universe.

Best Regards,

Chan Rasjid.

Very nice essay, Cristi -- with the broad range of profound and interesting questions that one has come to expect from you. Well done.

A couple of things:

Being a student of Yaneer Bar-Yam (who by the way was just appointed as visiting professor to the MIT media lab) -- I appreciate your reference to his theory of multi-scale variety, which I regard as one of the most important theoretical advances in science today. It encompasses network-connected phenomena across every scale of physical self-organization, which brings me to the second thing:

Your claim that " ... we can't prove the mathematical universe hypothesis by Tegmark's method."

If one is a rationalist in the sense of Karl Popper, no scientific theory is ever proved. That is, no amount of empirical evidence that validates a theory, is proof that the theory is true -- only a falsifiable criterion makes a theory scientific at all. And Tegmark's criterion is very clear and unambiguously stated: if the universe is shown to be fundamentally based in randomness, the mathematical universe hypothesis is falsified.

There is also no ambiguity in Popper's position. Long ago, Popper made an important reversal of himself -- as important as Hawking's reversal in the case of black hole information loss -- that Darwin's theory of common ancestry is a falsifiable theory, after all. Not because we can refute common ancestry by a single experiment, but because biology is incoherent without the theory, and the auxiliary hypotheses that support the theory are clearly falsifiable.

In the same sense, I think that multi-scale variety can be seen as a unifying theory of complex systems, and Tegmark's MUH as a unifying theory of mathematical physics.

All best,

Tom

Hi Cristi,

I didn't interpret Tegmark's falsifying criterion into existence. He states it explicitly in his book (p.356): "Looking toward the future, thee are two possibilities: If I'm wrong and the MUH is false, then physics will eventually hit an insurmountable roadblock beyond which no further progress is possible; there would be no further mathematical regularities to discover even though we still lacked a complete description of our physical reality. For example, a convincing demonstration that there's such a thing as fundamental randomness in the laws of nature (as opposed to deterministic observer cloning that merely *feels* random subjectively) would therefore refute the MUH. If I'm right, on the other hand, then there'll be no roadblock in our quest to understand reality, and we're limited only by our imagination!"

I explore this falsifying criterion in my essay.

The question of computability enters because Max approaches the hypothesis the same way that Wigner describes the role of mathematics in physics: discovery of physical regularities leads to discovery of mathematical regularities. I argue that if MUH is true, it has to work both backward and forward -- i.e., discovery of mathematical regularities leads to discovery of physical regularities. MUH is true if, and only if, the hypothetical final theory is mathematically complete.

(By student of Bar-Yam, I didn't mean a classroom student but rather a follower. He is a dozen years younger than I -- showing once again that there's little correlation between age and wisdom.)

Best,

Tom

Hi Cristi,

As I told you in my FQXi page, I have read your pretty Essay. Here are some comments:

1) I find the title very intriguing.

2) I think the most brilliant text ever written is Einstein's 1915 paper on general relativity!

3) The idea that all human creation and knowledge is a point in the interval [0, 1] is upsetting!

4) I disagree with Smolin's statement that "there is no mathematical object which is isomorphic to the universe as a whole". I think we merely do not know if such a mathematical object exists or not.

5) Congrats for generalizing the Weyl curvature hypothesis, you know that I am an estimator of your research work.

6) I do not think that you are too reductionist in claiming that there is a mathematical structure which is isomorphic to the universe described by the extended list of propositions. In fact, I agree with you.

7) I am not completely sure of the real existence of a a theory of everything, but it should be a great pity if it does not exist! The same for black holes!

8) Your statement that "if we can understand the universe, it is because this immense complexity can be reduced to a small number of laws" is very intriguing. It I think should have been appreciated by Einstein who claimed that "The most unintelligible thing about the universe is that it is intelligible at all."

In any case, the reading of your intriguing Essay was interesting and enjoyable. It surely deserves the highest score that I am going to give you.

I wish you best luck in the Contest.

Cheers, Ch.