AI and Physics: new Math?

The recent development of AI presents challenges, but also great opportunities. In this clip I will discuss the implications for math -
do we need new structures?

Mind also my backup channel:

[classic_sci_fi]

Likely it depends on how the AI models are trained. Perhaps we can discourage them from dividing by zero?

[gustavorabino]

I remember the AI described in the novel "Hyperion" telling one of the characters that while humans may have developed the relativistic drive to travel a the speed of light the portal technology discovered and managed by AI could've never been discovered by humans as it was totally beyond our capacity to understand. Indeed AI comes at the time were we have reached a limit in our ability to comprehend reality even with the use of mathematical tools or constructs, we simply can't go beyond of our capacity as humans.

[stevenverrall]

Anyone who has used Chat GPT to construct simple budgets knows that it routinely makes addition errors.

If it can't reliably add, it can't be trusted at all to perform advanced mathematics. While algorithms can be trained to check the consistency of advanced mathematics, I don't see how AI could develop or even apply any new mathematics.

AI can only ever know about mathematics that has already been developed. Even then, it routinely messes up--just like people do. However, expert mathematicians and theoretical physicists are able to detect and correct their own errors.

[Gunni]

"Whatever you say, +1", just so people can see how NEW algorithms are. And where they lead to. Infinite information is too much for our memory capacity. Same will happen to A.I. It's not a matter of Filtering out a solution, but to have the facts. And you just can't make a machine with enough Memory, because DISCOVERIES still take place. And you can literally write EVERYthing on a paper. "Possibilities" are endless. How did "Science" miss that one?

[RicardoFlor]

Professor, Tell us about muons and mesons please I dont think the evidentes of rhem are conclusives.

[maciejnajlepszy]

The world's obsession about AI will one day turn into something so bad that only few can believe it now. And it can come sooner than we think.

[walterbrownstone]

Matter =1, Space =0.
Basic AI math can be told to presume 1+0=0 and then produce a whole kaleidoscope of meaningless jibberish based on 1+0=0.. Then I sell the jibberish to the government, I am a genius. Absolute evil genius.

[nightmisterio]

Quaternions and Clifford's Algebra

[rayoflight]

Current AI machines are some statistical monsters which can utilise efficiently a difference in probabilities of one thousandth of one percent.
Therefore a Montecarlo event generator, followed by a simulator to test the effectiveness of the event into reality, may be a solution for your proposition.
Greetings,
Anthony

[MeyouNus-ljde]

It's impossible for something to be both contradictory and true.

1) Calculus Foundations

Contradictory:
Newtonian Fluxional Calculus
dx/dt = lim(Δx/Δt) as Δt->0

This expresses the derivative using the limiting ratio of finite differences Δx/Δt as Δt shrinks towards 0. However, the limit concept contains logical contradictions when extended to the infinitesimal scale.

Non-Contradictory:
Leibnizian Infinitesimal Calculus
dx = ɛ, where ɛ is an infinitesimal
dx/dt = ɛ/dt

Leibniz treated the differentials dx, dt as infinite "inassignable" infinitesimal increments ɛ, rather than limits of finite ratios - thus avoiding the paradoxes of vanishing quantities.

2) Foundations of Mathematics

Contradictory Paradoxes:
- Russell's Paradox, Burali-Forti Paradox
- Banach-Tarski "Pea Paradox"
- Other Set-Theoretic Pathologies

Non-Contradictory Possibilities:
Algebraic Homotopy ∞-Toposes
a ≃ b ⇐⇒ ∃n, Path[a, b] in ∞Grpd(n)
U: ∞Töpoi → ∞Grpds (univalent universes)

Reconceiving mathematical foundations as homotopy toposes structured by identifications in ∞-groupoids could resolve contradictions in an intrinsically coherent theory of "motive-like" objects/relations.

3) Foundational Paradoxes in Arithmetic

Contradictory:
- Russell's Paradox about sets/classes
- Berry's Paradox about definability
- Other set-theoretic pathologies

These paradoxes revealed fundamental inconsistencies in early naive attempts to formalize arithmetic foundations.

Non-Contradictory Possibility:
Homotopy Type Theory / Univalent Foundations
a ≃ b ⇐⇒ α : a =A b (Equivalence as paths in ∞-groupoids)
Arithmetic ≃ ∞-Topos(A) (Numbers as objects in higher toposes)

Representing arithmetic objects categorically as identifications in higher homotopy types and toposes avoids the self-referential paradoxes.

4) The Foundations of Arithmetic

Contradictory:
Peano's Axioms contain implicit circularity, while naive set theory axiomatizations lead to paradoxes like Russell's Paradox about the set of all sets that don't contain themselves.

Non-Contradictory Possibility:
Homotopy Type Theory / Univalent Foundations
N ≃ W∞-Grpd (Natural numbers as objects in ∞-groupoids)
S(n) ≃ n = n+1 (Successor is path identification)
Let Z ≃ Grpd[N, Π1(S1)] (Integers from N and winding paths)

Defining arithmetic objects categorically using homotopy theory and mapping into higher toposes avoids the self-referential paradoxes.

[smftrsddvjiou]

“Thou shalt not make a machine in the likeness of a human mind.”

[konradcomrade]

Question about Neutrinos and their Antiparticles?
are they annihilating when they (even if rarely) bump into each other, or not? They cannot emit Energy or Gammas, can't they!

[tenbear]

It could work simply because it won’t have a human bias, but then it depends who programs it, because AI isn’t intelligent: it just has a capacity to process reams of information very quickly.

[stephene.robbins]

In actuality, you're in the heart of Penrose's critique of AI and why thought requires consciousness (his "non-computational thought"). Look at his example (in Shadows of the Mind) of a computation that does not stop/halt, e.g., the stacking of ever larger hexagonal numbers, folded as three-sided cubes, one over the next, invariantly making a larger cube (cubical number) - a dynamic visual transformation over time seen as a global whole.

[richardmarcus]

We don't need AI to solve the problems in our model of the universe. All that is requires is common sense, something none in the science community seem to possess. An AI will never be able to expand upon information we feed it if the information is wrong. The single fix to all the problems in physics today, is so simple it amazes me nobody has discovered it yet.

[LaurenDove-xx]

While the sphere is a fundamental form, it should be considered as the ‘final’ or ‘perfect’ form of nature. ‘Quantums’ or ‘units’ are not necessary for a universal explanation of Creation.
Fundamental physics does not require advanced math.

Excerpt from the ‘Home Study Course’ written by W&R Russell:
There is no point in the universe which is not continually extending and retracting in inward-outward explosions to multiply the black light of space into the white light of incandescent matter and to divide the white light to return it to the zero from which it came. Every particle of matter is a wave and every wave is completely filled with particles of matter which measure the electric potential at every point in every wave-field.

Figure 82 illustrates how the electric current multiplies the zero of the universal equilibrium by winding low electric potential spirally into high potential, and then unwinding it to zero for repetition in the next wave cycle.

The central sun in this electric cycle occupies a position in the electric current which is known to electricians as a loop of force. Wherever an electric current passes through a wire these whirling loops of force occur to form microscopic atomic systems which are identical with a solar system, a nebula or a galaxy like the Milky Way. This little sun in Fig. 82 is a true sphere and the orbits of all of its microscopic atoms revolve upon the place of its equator.

The same little sun is shown in Fig. 83 at the amplitude of a wave. By studying this diagram, in connection with Figures 84, 85, and 86, you may see the whole process of winding light gyroscopically, and spirally into spheres IN FOUR EFFORTS – then unwinding these spheres by four opposite efforts.

Spheres occur only at wave amplitudes and the fact of its four positive and four negative efforts is the basis of the octave wave from which our spectrum, our octave of the elements and our octave of musical tones are derived.

This 0, 1, 2, 3, 4, 4, 3, 2, 1, 0 octave sequence constitutes the heartbeat of the universe. It is the basis of our musical rhythms, our chemistry, our mathematics, our symmetry of design of all animal, mineral and vegetable forms and of our colour spectrum of light.

Within the octave light-waves of matter in motion lie all the secrets of Creation. To know the wave is to know God’s secrets and His processes.

The next lesson will expand this idea more fully, but we can go no further now until we clarify the wave-field principle itself. To do this we must make clear to you the principle of the cube wave-fields of space as we have make clear the centring physical bodies which have emerged from those wave-fields of space.

This mystery will be unfolded in lessons 41, 42, and 43, together with the secret of how positive and negative light turn inside-out and outside-in to radiate and gravitate light from zero to incandescence and back to zero.

In the meantime study these six pages of drawings carefully, for in them is the basis of all the arts and sciences of man.



Lauren Dove, author of ’The Design Equation - The Unified Theory and the Mathematics of Hidden Dimensions’

[BCarli]

Thank you. Very interesting ruminations.

[photinosman]

Can AI be used to validate (or refute) the logical/mathematical coherence and self-consistency of a new theoretical model (e.g. hypothetically, an alternative to quantum mechanics)? If so, how?

[johncampbell]

I have seen two sides to AI. One platform was proven to be little more than a Wikipedia reference engine, repeating dogma as if it was proven fact.

Meta AI however did surprise me, it managed to follow an alternative proposition to the accretion disc planetary formation hypothesis and recognise the validity of the arguments presented. Posing inciteful questions tondrill down on the concepts presented and acknowledge the answers provided. It agreed that the proposals were valid and reasonable.

So it really seems to depend upon the platform, whether or not it possesses actual intelligence or is just an established dogma peddling machine.

[lerssilarsson]

A Small Matter Of Programming i.e. a couple lines of Python code.