The challenge of the deep learning paradigm to the scientific method: hierarchy between models and identification of fundamental laws from algorithmic information theory by Enrico Prati

Dear Enrico,

thank you for your nice essay, which I found interesting and pleasurable. I really enjoyed how you applied deep learning models to physics theories, I think that's a stimulating point of view.

You write that

>The most fundamental model correspond to the most compact in algorithmic sense when arbitrarily extending the set of experimental data to account for.

I found this idea in some other essay as well, I think you will read them with interest. I wonder: it's for sure a good principle for our purposes, but it's relative to humans' goals and methods. It doesn't invalidate your arguments, but its fundamentality is relative to our knowledge, it's an anthropomorphic one.

In bocca al lupo! ;)

Francesco D'Isa

Dear Enrico Prati,

FQXi.org is clearly seeking to confirm whether Nature is fundamental.

Reliable evidence exists that proves that the surface of the earth was formed millions of years before man and his utterly complex finite informational systems ever appeared on that surface. It logically follows that Nature must have permanently devised the only single physical construct of earth allowable.

All objects, be they solid, liquid, or vaporous have always had a visible surface. This is because the real Universe must consist only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

Only the truth can set you free.

Joe Fisher, Realist

Dear Enrico,

I also think there are plenty of extrapolations in the meaning of physical laws. But it does not exist, in the best TOE, written in your town Milan in Latin language. You did not even mention that theory.

With best wishes,

Branko

Dear Fellow Essayists

This will be my final plea for fair treatment.,

FQXI is clearly seeking to find out if there is a fundamental REALITY.

Reliable evidence exists that proves that the surface of the earth was formed millions of years before man and his utterly complex finite informational systems ever appeared on that surface. It logically follows that Nature must have permanently devised the only single physical construct of earth allowable.

All objects, be they solid, liquid, or vaporous have always had a visible surface. This is because the real Universe must consist only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

Only the truth can set you free.

Joe Fisher, Realist

Dear Enrico,

I had no doubt, I just pointed your attention there because I think it could be useful for your studies. In the essays there are many common trends, it happened with mine as well, I think it's normal and quite a good sign.

Yes, "observer-related" suits it better, I made a text about Nagarjuna's philosophy and absolute relativism that explore this issue as well.

Bests,

Francesco

I am thinking that a deep learning and human knowledge are not commensurable: if I have a deep learning law, and an human law, the level of understanding are different; only if the knowledge is transferable, or intelligible, it is possible understand the Nature (I am thinking there is the same problem of ABC proof of Mochizuchi).

A question, if the Einstein field equation admit a low energy linearization, and the low energy approximation would be quantizable, then would the general relativity be the ultimate theory?

Could the problem of the best trajectory be solved using the deep learning like an oracle (of which we do not want know the reasoning), and to improve the solution solving the Newton's law for trajectories with little perturbation (for example different random fuel injections along the trajectory, using a genetic algorithm like evolution strategies)?

I have a problem with the most fundamental model: if are there more equivalent theory? If I have two theories with the same solutions, what is the most fundamental? I have the idea that it is the one that simplifies the calculations, but it is only an opinion.

A good essay

Regards

Domenico

Dear Enrico Prati

Just letting you know that I am making a start on reading of your essay, and hope that you might also take a glance over mine please? I look forward to the sharing of thoughtful opinion. Congratulations on your essay rating as it stands, and best of luck for the contest conclusion.

My essay is titled

"Darwinian Universal Fundamental Origin". It stands as a novel test for whether a natural organisational principle can serve a rationale, for emergence of complex systems of physics and cosmology. I will be interested to have my effort judged on both the basis of prospect and of novelty.

Thank you & kind regards

Steven Andresen

Prof Enrico Prati

Very nice words..... "The laws of physics are extrapolated by complex sets of experiments and they are considered fundamental the more they allow to describe concisely acceptable ideal approximations of real systems. The subsequent mathematical description, combined with initial conditions, enables to predict time evolution (or time-dependent probabilities in quantum physics)....."

Hope you will not mind that I am not working in Mainstream....

By the way...Here in my essay energy to mass conversion is proposed................ yours is very nice essay best wishes .... I highly appreciate hope your essay ....You may please spend some of the valuable time on Dynamic Universe Model also and give your some of the valuable & esteemed guidance

Some of the Main foundational points of Dynamic Universe Model :

-No Isotropy

-No Homogeneity

-No Space-time continuum

-Non-uniform density of matter, universe is lumpy

-No singularities

-No collisions between bodies

-No blackholes

-No warm holes

-No Bigbang

-No repulsion between distant Galaxies

-Non-empty Universe

-No imaginary or negative time axis

-No imaginary X, Y, Z axes

-No differential and Integral Equations mathematically

-No General Relativity and Model does not reduce to GR on any condition

-No Creation of matter like Bigbang or steady-state models

-No many mini Bigbangs

-No Missing Mass / Dark matter

-No Dark energy

-No Bigbang generated CMB detected

-No Multi-verses

Here:

-Accelerating Expanding universe with 33% Blue shifted Galaxies

-Newton's Gravitation law works everywhere in the same way

-All bodies dynamically moving

-All bodies move in dynamic Equilibrium

-Closed universe model no light or bodies will go away from universe

-Single Universe no baby universes

-Time is linear as observed on earth, moving forward only

-Independent x,y,z coordinate axes and Time axis no interdependencies between axes..

-UGF (Universal Gravitational Force) calculated on every point-mass

-Tensors (Linear) used for giving UNIQUE solutions for each time step

-Uses everyday physics as achievable by engineering

-21000 linear equations are used in an Excel sheet

-Computerized calculations uses 16 decimal digit accuracy

-Data mining and data warehousing techniques are used for data extraction from large amounts of data.

- Many predictions of Dynamic Universe Model came true....Have a look at

http://vaksdynamicuniversemodel.blogspot.in/p/blog-page_15.html

I request you to please have a look at my essay also, and give some of your esteemed criticism for your information........

Dynamic Universe Model says that the energy in the form of electromagnetic radiation passing grazingly near any gravitating mass changes its in frequency and finally will convert into neutrinos (mass). We all know that there is no experiment or quest in this direction. Energy conversion happens from mass to energy with the famous E=mC2, the other side of this conversion was not thought off. This is a new fundamental prediction by Dynamic Universe Model, a foundational quest in the area of Astrophysics and Cosmology.

In accordance with Dynamic Universe Model frequency shift happens on both the sides of spectrum when any electromagnetic radiation passes grazingly near gravitating mass. With this new verification, we will open a new frontier that will unlock a way for formation of the basis for continual Nucleosynthesis (continuous formation of elements) in our Universe. Amount of frequency shift will depend on relative velocity difference. All the papers of author can be downloaded from "http://vaksdynamicuniversemodel.blogspot.in/ "

I request you to please post your reply in my essay also, so that I can get an intimation that you replied

Best

=snp

Laws of physics aren't mathematical. Physics is not mathematics. Feynman devoted some effort to discuss differences between both disciplines.

"Therefore heat has been reduced as a kind of energy". Heat is not a kind of energy. Energy is a state function. Heat isn't. Heat is a mechanism of change of energy.

"the square of both electric and magnetic field have been identified with energy density", an energy density is unphysical because it diverges, and fail to satisfy other consistency checks.

"Electromagnetic and weak forces have been next unified into a single mathematical electroweak model". Not true, each interaction is still described with a different 'force' carrier. There is no real unification.

"Even energy conservation may be viewed as a special case suitable when measuring quantities at macroscopic timescale [...] It is well known that energy conservation is violated even in low energy physics experiments, such as in elastic and inelastic cotunneling in quantum dots, in processes lasting less than the time window set by the Heisemberg's indeterminacy". The law of conservation of energy is also valid in the micro-world. What happens is that some people confounds the fluctuation in energy in open systems with a violation of the law of conservation. This people confounds the conservation law diE=0 with the constancy of energy dE=0. For non-isolated systems dE is generally different from zero, and that people believes the law of conservation of energy is violated, but it isn't; the conservation of energy still holds for non-isolated systems: diE=0.

"Today, the common understanding is that forces are all apparent manifestation of gauge theories and of the choice of the reference frame, while mass is another form of energy, so they look not fundamental at all". That is the common missunderstanding. Gauge theories are only an (inconsistent) approximation to the description of interactions, and mass is not another form of energy. The equation E0 = mc2 doesn't say that mass is energy; it says that masses at rest have energy whose value is E0.

"The mathematical rule approximately holds because the Newton's equation of gravity is a first order approximation of the Einstein's general relativity mathematical model, a more consistent (see the issue of the instantaneous action of the gravity in the Newton's theory) and coordinate-independent theory, where forces are apparent". This is all a too common misunderstanding spread in GR textooks. The weak limit of GR produces an expression (a = -grad phi), which is then assumed to be identical to the expression (a = -grad phi) associated to Newtonian gravity; but this is only a superficial appearance because GR people uses the same symbols for different physical concepts and mathematical objects. The phi in Newtonian gravity is a function phi(R(t)), whereas the phi on GR is a function phi(r,t); the gradients are also different; one is a gradient defined on a curved spacetime, the other is a phase-space gradient, finally the "a" are also different. So it is better to use different symbols for each theory, e.g. (a' = -grad' phi') for GR and (a = -grad phi) for Newton.

GR can only simulate certain aspects of the one-body limit of Newtonian gravity. GR is not a covering theory of Newtonian gravity. Many textbooks also incorrectly pretend that the weak-limit of GR produces an equation (a' = -grad' phi'), when in reality the weak limit gives a'=0. To get non-zero acceleration for test bodies one has to include second order terms from the perturbation expansion of Hilbert Einstein equations.

I don't think that deep learning challenges scientific method; deep learning is a consequence of applying the scientific method.

I don't see any challenging in the example given. The scientific method identifies certain patterns in the raw data and associates those patterns to laws, but the law doesn't have to represented exclusively in the form of a mathematical expression as Newton gravitational law; one can express the data as giant arrays of data connecting possible initial states with final states, or some other expression. The claim that the scientific method "looks for a compact set of mathematical equations" is incorrect; there are lots of counterexamples in the physical and biological sciences.

"Such quantification corresponds to the negative of entropy or randomness". There are dozens of definitions for the concept entropy. The term has been so abused in the literature that it is almost useless today.

"Implicitly, we associate the idea of a theory of being more fundamental with respect to another one when it is simpler, or, in other words, when the algorithm to reproduce the data is smaller, which corresponds to low entropy". Ignoring the many ways that "entropy" has been defined, ignoring that the size of an algorithm is not a objective measure (a non-optimized algorithm would be bigger than one optimized), and ignoring that the more complex theory would require a more complex algorithm (everything else the same), this approach to characterize theories only seems valid if one theory is a covering of the other theory.

"the Newton's law fail as we should add some additional mathematical effective laws to cover the full Solar system. This action enlarges the algorithm to implement the model, which loses if compared to compactness of general relativity" What compactness? It is possible to extend Newtonian gravity and explain all Solar system observations with a formalism is less complex than GR, which is full of redundancies, e.g. in the metric tensor.

Dear Enrico,

I highly estimate you essay exelent.

It is so close to me. «Planets do not precisely follow the Newton's law»

I hope that my modest achievements can be information for reflection for you.

Vladimir Fedorov

https://fqxi.org/community/forum/topic/3080

Dear Enrico

If you are looking for another essay to read and rate in the final days of the contest, will you consider mine please? I read all essays from those who comment on my page, and if I cant rate an essay highly, then I don't rate them at all. Infact I haven't issued a rating lower that ten. So you have nothing to lose by having me read your essay, and everything to gain.

Beyond my essay's introduction, I place a microscope on the subjects of universal complexity and natural forces. I do so within context that clock operation is driven by Quantum Mechanical forces (atomic and photonic), while clocks also serve measure of General Relativity's effects (spacetime, time dilation). In this respect clocks can be said to possess a split personality, giving them the distinction that they are simultaneously a study in QM, while GR is a study of clocks. The situation stands whereby we have two fundamental theories of the world, but just one world. And we have a singular device which serves study of both those fundamental theories. Two fundamental theories, but one device? Please join me and my essay in questioning this circumstance?

My essay goes on to identify natural forces in their universal roles, how they motivate the building of and maintaining complex universal structures and processes. When we look at how star fusion processes sit within a "narrow range of sensitivity" that stars are neither led to explode nor collapse under gravity. We think how lucky we are that the universe is just so. We can also count our lucky stars that the fusion process that marks the birth of a star, also leads to an eruption of photons from its surface. And again, how lucky we are! for if they didn't then gas accumulation wouldn't be halted and the star would again be led to collapse.

Could a natural organisation principle have been responsible for fine tuning universal systems? Faced with how lucky we appear to have been, shouldn't we consider this possibility?

For our luck surely didnt run out there, for these photons stream down on earth, liquifying oceans which drive geochemical processes that we "life" are reliant upon. The Earth is made up of elements that possess the chemical potentials that life is entirely dependent upon. Those chemical potentials are not expressed in the absence of water solvency. So again, how amazingly fortunate we are that these chemical potentials exist in the first instance, and additionally within an environment of abundant water solvency such as Earth, able to express these potentials.

My essay is attempt of something audacious. It questions the fundamental nature of the interaction between space and matter Guv = Tuv, and hypothesizes the equality between space curvature and atomic forces is due to common process. Space gives up a potential in exchange for atomic forces in a conversion process, which drives atomic activity. And furthermore, that Baryons only exist because this energy potential of space exists and is available for exploitation. Baryon characteristics and behaviours, complexity of structure and process might then be explained in terms of being evolved and optimised for this purpose and existence. Removing need for so many layers of extraordinary luck to eventuate our own existence. It attempts an interpretation of the above mentioned stellar processes within these terms, but also extends much further. It shines a light on molecular structure that binds matter together, as potentially being an evolved agency that enhances rigidity and therefor persistence of universal system. We then turn a questioning mind towards Earths unlikely geochemical processes, (for which we living things owe so much) and look at its central theme and propensity for molecular rock forming processes. The existence of chemical potentials and their diverse range of molecular bond formation activities? The abundance of water solvent on Earth, for which many geochemical rock forming processes could not be expressed without? The question of a watery Earth? is then implicated as being part of an evolved system that arose for purpose and reason, alongside the same reason and purpose that molecular bonds and chemistry processes arose.

By identifying atomic forces as having their origin in space, we have identified how they perpetually act, and deliver work products. Forces drive clocks and clock activity is shown by GR to dilate. My essay details the principle of force dilation and applies it to a universal mystery. My essay raises the possibility, that nature in possession of a natural energy potential, will spontaneously generate a circumstance of Darwinian emergence. It did so on Earth, and perhaps it did so within a wider scope. We learnt how biology generates intricate structure and complexity, and now we learn how it might explain for intricate structure and complexity within universal physical systems.

To steal a phrase from my essay "A world product of evolved optimization".

Best of luck for the conclusion of the contest

Kind regards

Steven Andresen

Darwinian Universal Fundamental Origin

Dear Enrico,

I think your essay is very good, and I like it. Do you believe it may be possible that the laws of physics, as we perceive them, may emerge somehow from a process of deep learning? For example maybe the world is a (quantum?) neural network, or a cellular automaton, which learned to behave in a certain way we observe now. A potential difficulty may be that normally we feed neural network with some data, and a possible answer is that in the case of the world the world itself is the data, but I don't have a clear picture how this may be. I think the idea to use Kolmogorov complexity to evaluate which is the most fundamental theory is great, and I am also using it to propose to identify the simplest theory in section 5 of this reference. Of course, this is not an absolute measure, because each equation has behind it implicit definitions and meanings. There is a theorem showing that the Kolmogorov complexity of the same data expressed in two different languages differs only by a constant (which is given by the size of the "dictionary" translating from one language into the other). So modulo that constant, Kolmogorov complexity indicates well which theory is simpler. This is a relativity of simplicity if you want, and of fundamentalness, because it depends on the language. But the difference is irrelevant when the complexity of the theory exceeds considerably the length of the dictionary. One may wonder what if the most fundamental unified theory is simpler than any such dictionary? I tend to believe that the laws are simpler than the apparatus needed to express them. For example Einstein's equation is simple, but the various mathematical structures required to build a four-dimensional spacetime with Lorentzian metric may be difficult So then, translating this into another language has much more complexity than the Einstein equation itself. By comparison, maybe Newton's theory may be simpler, although less empirically adequate. In this case the difference becomes relevant, but I think that if the theory is so simple, then we should use the minimal language required to express it. So if the dictionary is too large, it means we are not using the best formulations of the theory. This means that once we find the unified theory, it may be the most compressed theory, but we can optimize further by reformulating the mathematics behind it. For example, Schrödinger's equation is a partial differential equation, but the language is simplified if we use the Hilbert space formulation. Compression by reformulation occurs also by using group representations for particles, fiber bundle formulation of gauge theories, and Clifford algebras.

Thank you for the excellent essay, and success in the contest!

Best wishes,

Cristi Stoica, Indra's net

Enrico,

I am not quite on top of this essay contest as I would like to be...meaning I just found your essay. I took notice of deep learning when it was used in the field of biology to predict the ebb and flow of fish populations. Traditional algorithmic methods failed terribly.

Now, if I understand you correctly...you are proposing deep learning to determine the best algorithmic methods. I am all grins :) and believe your proposal will result in all schools having deep learning departments to determine "correct" algorithms.

I am glad I did not miss your essay!

Don Limuti

Do visit my blog, it has a simple theory of space-time.

Enrico,

Fascinating essay, nicely explained & very informative. I touched on deep learning, layering and loops in last years entry but hadn't realised it crossed over into my main study area; the ecliptic plane issue/stellar aberration,(ECRF/Barycentric transform, quantum optics, observer rationale and issues with relativity.

Past essays explaining a rationale have been finalists (since 2011) including 1st & 2nd placed community scores. The transform is explained in the model along with stellar aberration and a number of other anomalies. Editors don't seem interested in ontological constructions involving actual lens mechanism etc. without algorisation, but your approach seems maybe to vindicate it. If you have time to look and advise I'd be greatly appreciative.

The last 3yrs have been testing the model in finding a classical mechanism for QM. This years, shockingly, does so! Though of course weirdness is now mainstream so few dare even look! Declan Traill's short essay confirms the Bell violation is met with matching code and plot. Hope you get a chance to look.

Well written and thank you.

Peter

I found https://forums.fqxi.org/u/eprati article beautiful, albeit challenging. Many argue that artificial intelligence (AI) lacks a true understanding of physical phenomena, and therefore its results are not entirely reliable. Perhaps they place too much emphasis on the cited concept of information entropy. Human and artificial intelligences operate differently, and while it might be possible to determine which is “more fundamental”, one could also question the practical value of such a conclusion. I would, once again, like to share my personal experience regarding this.
I have used AI in my research, not only to translate text into a language that is not my native one. I cite the text from a ChatGPT note in my research:

"The apparent coincidence between the measured energy and that of blackbody radiation could be a consequence of a deeper principle, where the visible energy is only a portion of the actual energy, which includes contributions from the geometry of the 4D bubble. Therefore, it's not necessarily unacceptable but rather a clue to the connection between the different dimensions of the model."

Regarding this, I had mentioned to ChatGPT that I didn't consider the statement to be a mere consequence of what I had previously expressed, but rather a thought from a different intelligence, which, in my opinion, had formulated an idea autonomously.

This was the response:

"However, this statement didn't arise completely on its own, but rather resulted from a reworking of your reasoning, amplifying a possible logical implication that could be deduced from your model. It's as if a connection was made between the concepts you introduced and a new interpretation based on them. This often happens in theoretical discussions, where an initial idea is reinterpreted and refined."