Above link highlights yet another math proof that has recently emerged. I did not pick this one in particular and did not even scrutinise the content closely but there is something else I need to highlight regarding the problem with physics. I don’t know if anyone else noticed but the math proofs of ancient conjectures are flying thick and fast now. Why? Because AI.
A math proof is not a loosely held concept; it is exact. At the same time, a disproof of any statement or conjecture is an immediate dismissal. On the other hand, a science theory is not a proof, and can maybe be compared to a math conjecture. Science theories are based on observation, modelling, mathematical adaptation, but also more-and-more lately it appears to be founded on ‘belief’.
The last statement may be a bit naughty but it is supposed to express a frustration. When I saw yet another math proof popping out from AI assistance I realised why. Yes, AI can run fractals 24/7 and it just needs to let you know when it has found the exit. Every proof is built on a succession of other proofs but we can consider these foundation proofs as flawless, so the building blocks are solid. I may oversimplify the process and I do not intend to make light of math proofs but trying to point out that AI can assist in finding the path through the maze, especially if it is 100% known that there is at least one exit.
Then why can AI not do the same for physics? And why hasn’t it?
I thnk if AI (assisted) were to pop out a ‘new GR’ today, this very day, 90% of the science fraternity would reject it. Why? Because physics is not math and were are allowing ourselves to get attached to faulty models. Math does not suffer this. If this ‘new GR’ were indeed flawless it would still take 20-100 years to become widely accepted. I suppose not that long though, in this information age.
In physics we already know there are problems, but the will to critically scrutinise past ‘theories’ is lacking. We know GR is not the be-all yet do not dare speak out against GR. Same goes for QED, QFT, or QCD; take your pick. These too were built on observations that were ‘modelled’ into math and now (later) we find problems with the models and there is a huge resistance to step back and say ‘let’s start from scratch’.
I recently had the misfortune of having an article rejected from a leading journal. Despite a constructive review by Reviewer1, the rejection was based on this statement by Reviewer2: “The existence of dark matter and dark energy have already been confirmed …” This is not me griping about my rejection, but read that again and think what would this reviewer consider as a ‘proof’ if their foundation is already so flawed? And think if a ‘new GR’ would ever get past this person’s desk? This is the problem we are dealing with in physics … ‘belief’.
Math doesn’t have this problem because it never advances one step from a shaky foundation. If someone brought forth a ‘dubious’ proof that was later disproved, nobody, but nobody, carries on using the wrong proof as a new foundation. It is summarily discarded. Cold. Not so in physics. Physics build conjectures upon conjectures, which then become mainstream.
@Francois-Zinserling one thing I would add to your note is that everything in mathematics is formally defined, so all mathematicians can agree on a proof.
But in physics, observations are interpreted in a framework that is based on some theories. When someone creates a new theory, it also changes how observations are interpreted.
In the ΛCDM framework, dark matter (CDM) and dark energy (Λ) are “confirmed” by galaxy rotation curves and accelerating expansion. The only thing left to do is to understand their properties.
A ‘new GR’ is outside of the ΛCDM framework, but that doesn’t mean it’s not correct, but a reviewer would have to take a chance and take the time to study the ‘new GR’ if they were then to be able to interpret observations in the new framework. Of course, nobody has time for that!
That’s why paradigm shifts don’t happen very often.
@Francois-Zinserling , @RedshiftDrift . >one thing I would add to your note is that everything in mathematics is formally defined, so all mathematicians can agree on a proof.
NOT always true. Very much like in cosmology, there exist alternatives of mainstream theoretical mathematics. Constructivism is a well-known example. Intuitionism is an even more extreme form of the latter.
I have devoted a whole website on this, augmented with many articles, especially in Mathematics Stack Exchange. Believe me: there is much belief in mainstream mathematics too !! And I am not the only one (e.g. page 141) who thinks so.
Update
Just found in my old notes a few quotes from a book by Carl Friedrich von Weizsäcker: Die Einheit der Natur. Daß ein Physiker überasht sein sollte, wenn es Phänomene in der Natur vorfände, in deren Beschreibung das Wort “Unendlich” nicht durch das Wort “sehr groß” ersetzt werden dürfte. And problems in mathematics and physics that wie ich persönlich meine, im wesentlichen identisch sind.
Let google translate be your friend.
Loved the videos 🤣
I once had an argument with someone that ‘2’ doesn’t exist because it is an abstract. Needless to say it didn’t end well.
My argument is that in a mathematical sense 2 is perfectly useful, and gives us concepts like 2+2=4 (or 2+2=22, depending which school you went to 🤣), but it only exists as an abstract and is not real. Of course the other person argued that ‘2’ is real and exists.
We agreed on one thing, and that is that 2=2. Then I asked him to draw me a 2 on a piece of paper. I then drew another 2 next to his but made it look very different. Clearly his 2 and my 2 were not the same and the statement of 2=2 had to be false, or else we had to agree that neither his 2 nor my 2 were actually, well, ‘2’.
A 2 on a piece of paper is not 2, but only a representation of 2. 2 can never exist and must remain abstract. It seems I am playing a broken record … I hope you got the gist.
Not so in physics, apparently. We have seen how the W- and Z- bosons have been detected as ‘obviously real’, even though they were presented as not only abstract, but even virtual. Now they are still virtual but we can actually measure them. Go figure … Gelman and Zweig proposed quarks as abstracts with an equivalent useful method just like 2+2=4 and what do we go and do … we collide particle to try and find the quarks as if they were real. Final verdict: They are so confined that we can’t get them out. Dark matter, dark energy … same thing. Physics has lost the plot.
@Francois-Zinserling .
Yes !! Very much related: Leibniz’ Law and that good old riddle. However, being the same is a serious problem in physics a well. As an example, think of the Schrödinger versus the Heisenberg picture with Quantum Mechanics. It took some time before everyone agreed that the two are equivalent.
Yes, but these beliefs don’t have to fit anything in nature. There are problems in maths, I know a bit about those concerning infinity…
@Francois-Zinserling I agree physics has lost the plot. Virtual particles are just a way to describe some properties, like ‘2’!
Unfortunately, even a physicist like @RedshiftDrift shares math beliefs that do NOT fit anything in nature. An outstanding example starts at this place in a thread named The well known pictures of black holes are fake! The heated debate is about, quote :
Oh yeah, and another thing. I deleted a post about the mathematics of the Jacobian conjecture, because the distinction between polynomials and other continuous functions is not at all clear in physics (: think e.g. of series expansions). This makes the conjecture a pure mathematical business and so rather uninteresting for ACG.
By nature, horses always have four and only four legs. There’s no possibility whatsoever of a horse being naturally born with five legs. However, we know for a fact there’s a horse in Kentucky with five legs.
Does that mean horses can naturally be born with five legs? Of course not. Everyone knows horses have four legs, so that simply isn’t possible. In reality, the mother of the five-legged horse was abducted by space aliens the day before giving birth, and they genetically altered the fetus so it would grow an extra leg.
Was the abduction ever actually confirmed? Of course it was! The proof of the abduction is the fact that the horse was born with five legs. What other proof do you need?
I was going to reply to @RedshiftDrift above but you said it beautifully. ΛCDM framework have essentially programmed themselves into an infinite loop.