/sci/ - Science & Math

>>11395196

>99% of contemporary physics
>Quantum mechanics is a tiny fraction of physics. Because it has no results.

So you have misunderstood 100% of contemporary physics then

>>11393662
Also please understand that disagreeing about fundamental questions of reality does not necessarily make someone a bad or incompetent physicist. They might be perfectly capable, possibly a Nobel laureate too, there is always a bit of crackpottery in brilliant physicists.

We can produce functional airplanes that can be put into service without building and testing prototypes using the continuum model of matter in Aerodynamics while the same people could believe matter is made of small atoms. Rather than worrying whether it is true that matter is continuous, science focuses on whether the model provides verifiable results. If it works, the model will be used, if not, the model is refined or discarded. This leads to interesting work in all areas of science where sometimes people employ mixture of models (e.g in nanophysics matter can behave like individual particles in some places and like a continuum in other places).

Maybe it's not a bug, but a feature of modern physics that people can have different philosophical views about the same fundamental topic.

>>11393662
Same reason the Greeks refused to deal with infinity and irrationals: psychological difficulty. The Greeks thought mathematics must be about constructible magnitudes from compass/straight edge only. Some physicists and philosophers thought physics must be about measuring preexisting property of nature. The new paradigm saying such property is inherently ill defined is too hard to swallow.

>>11392746
>If none of them explain the observations well

No. Quantum Mechanics' empirical success is unparalleled in history. All experiment results are accurately predicted and explained with the Hilbert space formalism and Born's rule. There's nothing ambiguous and controversial about its experiments/observations aspect. The semiconductor, microelectronic, well pretty much all of modern electronics are built from those successes.

The problem is when people look at the wavefunction or the measurement process (to get the probability of event through Hermitian operator acting on wavefunction) they can't just accept that it's the end of the line, they have to ask "what are the physical things behind all that math", "what are they like?" and that leads to different interpretations. Some of them just add more untestable things to the theory, some of them violate locality etc

The Copenhagen view is we don't care, it is not QM's job to speculate about ontological questions such as 'what are really there?' or 'what are they like', this latter question tries to connect QM to human intuitions, but human intuitions are classical, and will lead you to misunderstanding. QM concepts are not `like` anything, they are their own things, and their only descriptions are the math. That's the end of the line. I believe a physical theory only needs 3 components:
- The physical phenomena: the empirical evidence about physical objects gathered by observation or experimentation
- The formalism: provides the mathematical description of the phenomena and enables the physicist to make precise quantitative predictions. In this case this is provided by the Hilbert space formalism
- The link between the formalism and the phenomena. Born's rule does just that. It states the relationship between eigenvalues of the operator (the formalism), and the probability of events (the phenomena).

So nothing is missing in the physics.

>>11391575
Nah we can all agree that all scientists discover novel things in different parts of the physical world: biologist, chemist, medical scientists, etc you dont want to go back to the time when there was only physicists doing the discovering. Anyway I don't think it has to do with public fame, physicists are more popular among the lay audience simply because of the media.

In fact discovering something novel about our world is a fruit hanging so low that even some mathematician in late 19th century studying functional analysis already discovered something novel about our world as several decades later some other mathematician axiomatized quantum theory and it turned out the only way to get correct physical results is to view physical measurements as Hermitian linear operators acting on vectors on Hilbert space. (The same dude also helped pushed the Copenhagen view into the orthodoxy it enjoys today with his no hidden variable theorem, which is another great discovery of physics done by a mathematician).

And let's not forget that the discovery of computing originated from Entscheidungsproblem, one of Hilbert's problems. The idea of computers was basically discovered during axiomatizing first order logic, by mathematicians. Physicists could never have discovered the P vs NP aspect of the very physical problems that they work with on daily basis.
Similarly biologists could never have discovered the computational complexity aspect of evolution either.

These ideas are all novel aspects of our world, and I would say the computers are essential in modern era.

This unreasonable success of axiomatizing physical theories is exactly what modern physicists try to emulate, as mentioned here >>11389844 , of course some people still have psychological problem against this new trend, because it doesn't provide enough `ontology` behind formulas, they insist that physics has to come back to its classical regime in late 1800s.

>>11387321
>math evangelist talks about how it's actually got a bunch of potential (this word is here to save face) applications in cryptography

No offense but you dont know any real number theorist. If you ask any serious mathematician 'hurr what is the application of number theory in the real world' they might reluctantly give you an example in cryptography but what they truly think is 'you shut your fucking mouth what is the application of the real world in number theory?'.
Real mathematicians are not embarrassed at all that other people haven't figured out how to use their results in `practical applications`, like some tool that primitive humans couldn't make use of.

It's exactly the same situation when you teach math for kids in high school and one of the dumbest loudest kids with rich parents asks you 'what is the point of study algebra I'm never gonna use them :((', and you have to humor them with some applications because their parents are benefactors of your school.

>>11390425
>>11390397
In the real world all people who study math appreciate CS, it's almost part of regular undergrad math introductory class to learn some computability, complexity, algorithms, like right after constructing real numbers from ZFC and right before introductory Model theory. I've only seen people shitting on CS on this specific site lol

And I dont know where you get the idea that mathematicians dont like type theory when category theory has been their lingua franca for the last 50 years or so, and type theory is the syntax of categorical construction (free cartesian closed category, free topos etc.)

>>11390099
Just wanna say I appreciate your hard work. Well done.

>>11388836

Framing unrelated objects in terms of math can have the surprising effect of helping learning, understanding and creating new objects

I think most people who do math make those connections everyday, and some even wrote books about it

https://www.goodreads.com/book/show/23360039-how-to-bake-pi

So specialization doesn't necessarily make you know one single topic and blinded to other topics. Most specialists can make connections and gain insights and see patterns between rather unrelated things. It surely isnt about forgetting how to do basic trivial tasks like cooking or cleaning. This line of thinking 'I know how to change diaper and pitch manure so I am more human than that guy who is a good specialist, because knowing the things I happen to know is what being human is about', that is clearly just cope lol

>>11388816

If you specialize in a single skill, doesn't mean it is gonna be the only thing you're good at. Knowledge does not exist in isolation from each other like the brainlet in picture imagines. They are more like an interconnected web, and if you're good at something you're gonna be more efficient in learning many other things.

>>11388760
>actually believes being a corporate slave working overtime to optimize profits for rich businessmen while your wife fucks her yoga coach is a better life than sipping tea in comfy aircon office thinking about algebraic structures and spending leisure time with family writing textbooks for future generations with support from your wife
> cope level: David X. Li

>>11387381
Well, I'm listening to the P vs NP part of this interview https://www.youtube.com/watch?v=2BdBfsXbST8

When Knuth talked about classification of graphs, he spoke of classes of graphs that are closed under taking minor (shrinking edge to a vertex or deleting edge), one such class is planar graphs, but the description of such classes is clearly complicated, so kinda analogous to NP problem

Then he mentioned Robertson Seymour theorem https://en.wikipedia.org/wiki/Robertson%E2%80%93Seymour_theorem which tells you for any such class there is a finite list of graphs that can serve as a test, if it's not in the class, you can shrink it down to one in that list of bad minimal graph. When the class is planar, the list simply contains two graphs K(5) - everyone among five neighbors or K(3,3) - the connecting 3 utilities to 3 houses without crossing meme problem on sci

1:04:00 this dude asked "why do you bring up this theorem" lol obviously the finite list of bad minors is analogous to the finite exponents in a hypothetical algorithm to solve an NP problem, it's finite but it could be 2, 20 or 20000 so it might not be useful. I'm a layman in this topic but I can see that. Knuth brought this up as a case where P is not useful in practice.

So Knuth explained the obvious, then 1:06 this dude asked again why Knuth holds the intuition that P = NP is possible when it could be so counter intuitive, this annoys me, Knuth just explained that above (he gave an example that can give an intuition as to why P = NP might not be so paradoxical) Then the interview became a bit meandering about some Aliens shit lmao, idk this guy might be a good AI coder but he doesn't strike me as particularly clever.

>>11386790
Just go to viXra, there are too many similar theories.

The only way for a new theory about gravity to be considered worth a 20 minutes read is that it has to either
- predict something in principle testable that GR didn't predict or
- respect the invariances of existing established theories (like how QFT upgrades QM and SR, and how String upgrades QFT)

Also if the author doesn't understand what a Tensor is or what a manifold is (i.e someone like Tesla) then he is automatically dismissed in talks about gravity or space-time, I know this sounds unfair but physicists are humans too, they have limited lifetime. Not knowing modern math put your theory below Leo Vuyk's raspberry multiverses in the list of candidate theories.

>>11385757
>>11385853

Agreed. He's kinda similar to Penrose or even Atiyah or Einstein, long stellar career during prime years, followed by crankery in old age. It's a good observation that old physicists can be that way. There are many exceptions though.

>>11384540

I heard somewhere that Einstein is particularly successful with his female cousins.

And how can we not mention Schrodinger who fathered children from a variety of women, some of them his colleague's wife, some of them underage teens. After formulating his wave equation he literally couldnt stop impregnating young women around him, sometimes in FMF threesomes, also he kept detailed log of all of them.

>>11384662
Yes, I think engineers do use the results from his paper to design algorithms behind the hardware of medical imaging, there are like bazillions of 'l1 recovery sparse signal', 'sparse approximation', 'compressive sampling' type algorithms in the years following that publication until today. No, they are not tinkering around randomly when they write the programs from those algorithms.

from cursory googling
https://people.eecs.berkeley.edu/~mlustig/CS/CSMRI.pdf
https://authors.library.caltech.edu/10092/1/CANieeespm08.pdf
etc.

I don't know if the engineers can derive results such as Restricted isometry https://en.wikipedia.org/wiki/Restricted_isometry_property or the robust uncertainty principles and all the bounds involved, but I know that this paper https://arxiv.org/pdf/math/0409186.pdf shows there is a way to get around the fundamental limitation of Nyquist Shannon sampling theorem and thus created a new paradigm for signal processing.

I think the main reason people think Tao is a meme is because he gained a lot of fame without being a theory builder, i.e he didn't create any theory so that lay people can quote and go 'woo wee' but he's more of a problem solver, he solves specific technical problems that are incomprehensible to non experts, so it's a reasonable question to ask how come this guy is famous, what has he done. The answer is nothing you could appreciate unless you spent years studying the relevant research literature.

>>11384686
You can just ignore those articles that has low citation or too high ratio of self citation, I'm not even looking at them. There are ridiculously many papers cited by people from different fields it's actually hard to keep track of.

>>11384649
>>11384638
But Terrence Tao's publications are not comparable to the publications you guys talk about.
They actually lead to new field and impact people's lives (if you go to the hospital and use MRI scan for your rectal cancers you should thank him)

>>11384471
Can you unironically find a single mathematician (let alone pure mathematician) with this much citations by engineers/scientists?
https://scholar.google.com/citations?user=TFx_gLQAAAAJ&hl=en

and it's not even something he cares too much about.


Anyone here applying to be his student? don't be shy guys!

>>11384487
>101 rep on Scifi & Fantasy

lol he probably has been lurking that site for a year but hasn't had enough courage to ask the first question.

>>11384040
Yeah it's pretty cringey when people who struggle with exercises from Velleman's How To Prove It rave about Godel's theorems.
Those who believe mathematics can be reduced to formal logic in this day and age probably have autism, and I would say the incompleteness results are useful for keeping these special folks from wasting their time, much like the energy conservation law keeps special folks from spending their entire life trying to construct perpetual motion machines just because there are some combinations of cogs and wheels they haven't tried.
But then again, most mathematicians don't have this sort of autism, and clearly the average student of physics can cope with conservation of energy.

>>11384009
You can assign numerical codes to formal arithmetic expressions then locate the 'this sentence is false' expression using the diagonal argument.

>>11383688

Absolutely no one should have ever been surprised that mathematical truth cannot be equated with theoremhood in some finite axiomatic system.
An infinitude of mathematical truths are uninteresting trivia, with no obvious route to being proved. I think even Gauss knew this.
E.g check if the digits of square root of 47 is contained in the decimal expansion of pi^101. Well, we can just calculate out the sequences of digits and check. If it's true, you can find the digits that match, but no amount of just grinding out the digits and checking will ever prove it: there are always more digits to check. If it's not true, same problem, you cant disprove it. That is an unprovable mathematical fact. It is also a very, very, very uninteresting one.

All Gödel did was find a clever way to construct a provably unprovable mathematical fact, given any consistent and finite set of axioms to work with. The work is clever piece of technicality but in no way profound. It should have come as no surprise at all. And surely it never really impacts most of mathematics, except for some narrow branch.

At Hilbert's time it would have made more sense to have this sentiment that mathematics took some dark turn due to the incompleteness theorem, because it killed Hilbert's meme program. But it has been a century since then, it should've been clear that Hilbert's vision was too idealistic, and of course he was overconfident. Godel's theorem marks the boundary of Enlightenment, not its refutation (boundary that first rate mathematicians should've seen coming long before it was reached). Again I think philosophically, this stuff was known since Gauss who spent a lot of time staring at natural numbers, if we drop Godel's paper on Gauss's office, he would skim over it and wouldn't have cared much for it and continue sipping his tea and read his geodesic survey and cartography, which would actually impacts math and physics century later (differential geometry, General Relativity, etc)

>>11383167
I'd prefer more people think like this, it keeps the dumb people out of universities.

>>11383241
I mean the racial bonus for the top grad schools (Harvard, Princeton, Caltech etc)

>>11382791
There's no need for hate, we just need to realize that proper CS is a branch of math which studies abstract computing machine, whereas meme CS is the study of the computing machine you can buy from Amazon with $900