Intelligent life.

And mathematical theory also not: it is immanent.
Mathematics doesn't help, at all, ever, in telling you what the universe is like. It's a system of rules about how to make statements and prove them correct (or incorrect), and then a set of axions from which one can derive statements and prove them correct. It is just a game that minds can play. Very much like chess.

Having said that, there is a very difficult to understand connection between mathematics and reality. How come that we can make models of the universe (for example Newton's theory of gravitation, which is proven every time we drop a wine glass on the hard floor of the kitchen), and the "game" of mathematics happens to help us build the models? Let me give you a much easier example of that. We have Peano's axioms, which in mathematics help us define what integers are and how they work. In a nutshell, Peano's axioms define the system of counting: We start with 0, we add 1 and get 1, we add 1 and get 2, and so on. You can try that in your kitchen, by pulling a few apples from the fruit basket: Put one apple on the counter. Put another apple next to it, and you have 2 apples. Put yet another apple next to it, and you have 3 apples. But mathematics doesn't know anything about apples. It only knows about integers, and rules for incrementing their number (and doing many other fascinating things with them).

What you just did is a scientific experiment. You counted apples, you built a model of how the number of apples increments when pulling them from the fruit basket, and that model happens to follow Peano's axioms and the properties of common integers. That shows that there is a connection between mathematics and the world.

And now comes the place where magic happens, where philosophers of science are dumbfounded: Find an orange in the fruit basket, put it on the counter. You have 1 orange. Put another orange next to it, and you have 2 oranges. The miracle is: Why does the same mathematical theorem apply to oranges that we have already experimentally proven (many times, since we learned to count when the kindergarten teacher brought apples) on apples? There is nothing in mathematics that says that counting oranges should follow the same law. I could make a mathematically consistent model that says: If you put another orange next to 1 orange, you now have 42 oranges, and if you remove one orange again, you go from 42 to e^(i*pi). Nothing in mathematics says that oranges have to follow the rules of normal integers. The miracle is that Peano's axioms apply to ALL fruit (and to squirrels and bricks and all objects we interact with in everyday life).

Yet, there are objects in the universe for which normal counting rules don't apply. An example are electrons: take one electron, put it on the counter. Take another electron in the same state (same energy level, same spin), and just try putting it next to it. It just won't work, you will never get to two electrons. Pauli's exclusion principle says so, and detailed studies of atomic spectra have proven that. In electrons, 1+1 is not 2, it can't be done. Another fun weirdness of electrons happens with normal geometry: Take one electron, put it in a an electron basket on your kitchen counter (a thing that is just like a fruit basket is for apples, it is possible to build magnetic "traps" that hold individual particles, but for electrons it is extremely difficult). Now take the fruit basket, and spin it around on the counter by exactly 360 degrees. You would think that after that rotation by exactly a full circle, the electron is exactly like it was before. You can try this experiment on apples and oranges (and on pions and Higgs bosons), and they work just like apples, and after a 360 degree rotation they're back in their original state. Well, I'm sorry to tell you that on an electron it WON'T work: after spinning it by 360 degrees, it internal rotation is backwards. To get it back to its original state, you have to spin it by a multiple of 720 degrees (two full rotations), not a single one.

Experimental physics does not help here: it is built from the perception.

This is yet another very deep and philosophical question. The wife (now ex-wife) of a physicist friend was a famous cultural anthropologist, and she often asked this question: Are the laws of physics (models of reality) that we have found through experimentation and theory dependent on our cultural background. As an example, European white men found F=ma=m d2x/dt2, and F=mg, Newton's laws of motion and of gravity. Would a different culture have found different laws? The example typically discussed (following Margaret Mead) is: Would Samoans have come to different results when studying coconuts falling from palms that Newton did when studying apples falling from trees?

I think the answer is the following. Yes, we can express the same laws of physics many different ways. For example, Newton did all that with differential calculus (which he helped invent in the process). But we don't have to say that a = d2x/dt2, we can instead use integrals, and say that the acceleration is fundamental, and x = Int Int a dt2 (where Int is the big S-like integration symbol). Similarly, when it comes to more complex problems in mechanical motion, every physics graduate student learns to prove that Lagrange's method of solving them (with a Lagrange function, posing it as a minimization problem) is equivalent to the Hamiltonian method of solving them (with an operator). In quantum mechanics, it was quickly discovered that Schroedinger's wave functions and Heisenberg's matrices give the same "results" (real-world predictions), they are just more or less convenient to use for different set of problems. A similar theoretical revolution happened when Feynman's diagram made it much easier to calculate particle physics cross sections, and it was quickly found that they are actually equivalent to the old Lagrangian approach or S-matrix approach.

So here is the answer: Yes, Samoans would find the same physical laws, but they might express then very differently. Not just in a different language, but in a completely different formalism. After all, Galileo proved that coconuts and apples fall the same way (remember his famous experiment using the tower of Pisa, except that he demonstrated that a pound of feathers and a pound of lead fall down at the same acceleration ... oh wait, that's an old joke). But we all believe that concrete predictions of "true" physical models are independent of perception, and independent of culture and of how they are presented. And in that sentence, the word "true" means that the models match reality well. For example, if a hypothetical culture (let's call them Elbonians) came up with a model of gravity that says that both apples and coconuts fall downwards, while wine glasses fly up in the air if dropped, the Elbonian theory of gravity would be very quickly proven "false", not "true".

So my answer is: No, it's not just perception. There is really a number 3 out there. Whether we call that spatial dimensions, or degrees of freedom, or anything else, it is as real as our experiments have shown it to be.

By the way: Using thermodynamics to prove anything about the universe tends to drive people insane. Here's the introduction to the best textbook on that topic, by Kerson Huang: "Ludwig Boltzmann, who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics. Perhaps it will be wise to approach the subject cautiously."
 
Having said that, there is a very difficult to understand connection between mathematics and reality.

It is the question, why is Mathematics applicable?
Why this mental construct help engineers build something and physicists make their models of reality.

It is a very simple question, and it has a very simple answer.
After you discover it, you would say it is trivial.

But why you do not see it?
I must acknowledge that it took time until I recognized it.
The obstacle is how you see mathematics, influenced by the schools of mathematical foundations.
The problem is that the 'scientific method' is taught at school like a formula.

After you have the answer, you will also recognize how limited is science, physics.

So my answer is: No, it's not just perception. There is really a number 3 out there. Whether we call that spatial dimensions, or degrees of freedom, or anything else, it is as real as our experiments have shown it to be.
Yes, until you perceive the 4rth dimension.

About science in other cultures: what is science, follows our way of thinking, and all people think the same.
Why would their science be a different science from the one of the civilized western people?

I always had problems understanding Newton laws, till now. It mainly says there are 3 dimensions, the second
derivatives may be expressed as x''=F(t,x,x').

And what is 'Lagrangian Mechanics'? Useful mathematical tautology. It tells you how you convert the equations
if you know that the particles movement is restricted to a manifold. It allows you to insert your perception.

But why physicists understand it in a different way? Well they mix it with their mythology that include fantastic entities like energy, entropy, etc. These same physicists would mock about scientists of other cultures for their different mythology.
 
“When it was theorized that the quantum Hall effect could be observed in four-dimensional space,” said Mikael Rechtsman, assistant professor of physics and an author of the paper, “it was considered to be of purely theoretical interest because the real world consists of only three spatial dimensions; it was more or less a curiosity. But, we have now shown that four-dimensional quantum Hall physics can be emulated using photons — particles of light — flowing through an intricately structured piece of glass — a waveguide array.”

"Particle accelerators use powerful magnets that generate electromagnetic fields to guide and accelerate beams of particles to where physicists want them to go. Resonances can occur in the accelerator due to imperfections in the magnets, creating a magnetic structure that interacts with particles in problematic ways.

The more degrees of freedom a dynamic system exhibits, the more complex it is to describe mathematically. Particles moving through a particle accelerator are usually described using just two degrees of freedom, reflecting the two coordinates needed to define a point on a flat grid.

To describe structures therein requires mapping them using additional features in phase space beyond just the up-down, left-right dimensions; that is, four parameters are needed to map each point in the space."

They later continue...

..."What makes our recent finding so special is that it shows how individual particles behave in a coupled resonance," Bartosik says. "We can demonstrate that the experimental findings agree with what had been predicted based on theory and simulation."

So perhaps there is some indication or "ghost of 4d" as they desribe it, but not proof.

No experimental proof of existence of a 4D has so far been demonstrated. Only observations that can be mathematically described by using a hypothetical 4th dimension, hence the term '4D-ghost'. It's a hypothesis.

Perhaps the 4 parameters used in their mathematical description of their experimental observations are merely a convenient mathematical technique. Perhaps there is another explanation for the observations that does not require a hypothetical 4th dimension, that has not been thought of yet. Perhaps their experimental observations contain errors that have not been accounted for in their hypothesis. Has their experiment been repeated elsewhere, or is CERN the only place on the planet where these observations have be made? And perhaps I have not properly understood what I just read (almost certainly😂 ).

Perhaps no such experimental proof is possible for us. Perhaps no more dimensions than 3 exist. Indeed until the existence of a 4th dimension is proven by experiment, we shall have to conclude that it does not exist. The burden of proof lies with the person proposing the hypothesis. Extraordinary claims... require extraordinary evidence.

At least, that's my reading of it. Not that I have any expertise in this area, so you'd better not take much notice of what I say.
 
By the way: Using thermodynamics to prove anything about the universe tends to drive people insane. Here's the introduction to the best textbook on that topic, by Kerson Huang: "Ludwig Boltzmann, who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics. Perhaps it will be wise to approach the subject cautiously."
I once rented a room in a house owned by a fellow who was a full maths professor at one of the more well-regarded British universities. His research was on brownian motion. He told me one day that sometimes when he was deeply engaged in thinking about his work, he found it so absract and otherworldly that it used to make him feel physically ill.

I've worked with more than a few of what you might call 'high-IQ' people, or people "on the spectrum". They often seemed to pay a personal price for it.

Choose wisely...

choose-wisely.jpg
 
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I found the 1995 japanese animated version freely viewable here. It's excellent...
View: https://www.youtube.com/watch?v=7sYlHy_ycuU
Yeah, the 1995 movie is a fun watch, but in there, discussion of AI is a bit limited in there. The TV series (listed here) offers a more in-depth exploration of AI...

I think in Season 2, ep. 4, an AI-powered tank (called Tachikoma, and it's shown/depicted to have a 'personality' and judgement comparable to a 10-year-old kid) exclaims, "Jeez, gloomy AIs snap so easily!".
 
Hmm, it says release date 8th Dec 1995 under the video... maybe the guy who posted it got it wrong. So there's an earlier one... interesting! I guess I could always go and find the original manga too :). Gunm/Gally, aka alita battle angel, was the same, several iterations; the original gunm manga was very good, it's all online if you search for it.
 
Hmm, it says release date 8th Dec 1995 under the video.
The original 1995 version has no CGI in it, easy to spot in the title screens. I have both versions. It's mostly the same but 2.0 has some scenes replaced with CGI. Prefer the original.

View: https://www.youtube.com/watch?v=UJT0mLi23Ag


I found the 1995 japanese animated version freely viewable here. It's excellent...
Oops. Double checked, but yours is actually the 2004 "Ghost in the Shell 2: Innocence". The poster didn't just confuse the original with the 2.0 rerelease, he got the entire movie wrong. And I got thrown off by the CGI, while quick-skipping through it. There's also a third movie, Ghost in the Shell: Solid State Society" (2006). It follows the "Stand Alone Complex" series.

Definitely recommend hunting for the original 1995 "Ghost in the Shell" movie. You're going to find out "The Matrix" actually "borrowed" certain scenes from it ;)
 
That is not a better proof than the daily experience of having three degrees of freedom. We can say it is evident. My point was: is this not due only to our perception?
I guess we aren't very useful from an experimental point of view because we are part of the system itself. We have evolved to perceive the typical 3 dimensions in the way they are because it helped us, i.e forage, hunt (or probably invade cells in the earlier evolutionary steps).

Plus, apparently, there is no implicit direction of time because information is retained (although entropy increases), so who is to say that we only perceive time as "going forward" because it helped us hunt back in the day (again, probably as single cell organisms).

I recall (was it PBS spacetime? haha) that our brain even has evolved some element of "hard coding" to help us map out coordinates and predict positions (probably to help hunting). Interestingly this mapping is 2D which we then apply to 3D "at runtime".
 
It's all very strange.... I still can't get my head around the wave-particle duality, probability waves, quantum entanglement, cats in boxes, uncertainty principles and the rest. Now there's this new thing (to me, anyway) called dark energy (dark... what?) and another new thing called the higgs boson (huh?) that I know nothing at all about... better not start thinking about black holes and gravity waves either. So what IS this "reality" that we are living in? It all used to seem so simple, before I studied any physics..! :oops: :'‑(
 
It's all very strange.... I still can't get my head around the wave-particle duality, probability waves, quantum entanglement, cats in boxes, uncertainty principles and the rest. Now there's this new thing called dark matter and another new thing called the higgs boson that I know nothing at all about... better not start thinking about black holes either. It all used to seem so simple before I studied any physics..! :oops: :'‑(
Cats in boxes is easy. Its getting them out that is the tricky part.

(Can't help you with the rest. I never studied Physics past A-levels in school)
 
To say it with the words of Nobel price winner Richard Feynmann, you do the math , you do the calculations, you have a result , a prediction.
But don't try to understand, nobody does.
 
Perhaps this is the original 1995 version. Japanese with english subtitles.

This one has an english language voiceover.

All I want now is a copy of 'Airplane' from 1980 and my life will be complete. :)
 
I guess we aren't very useful from an experimental point of view because we are part of the system itself. We have evolved to perceive the typical 3 dimensions in the way they are because it helped us, i.e forage, hunt (or probably invade cells in the earlier evolutionary steps).
You have too big expectations of what is a proof.

It is only something that convinces (you). Also a mathematical proof is in principle that.

So what IS this "reality" that we are living in? It all used to seem so simple, before I studied any physics..!
In any case it is not the result of 'publish or perish'. For the last, scientists build always higher. One gets dizzy. I prefer to dig on the ground, and discover it is not so firm, they build on sand.

Not even the logical principles are given. It is for example perfectly rational to reject 'tertium non datur', what leads to a different kind of mathematics. What happens then with all these physical theories based on classical math?

And by the way, what means 'rational'?

But don't try to understand, nobody does.
Perhaps philosophers?

Maybe it's a good thing I became a C programmer... :)
As a (C) programmer, I would feel myself like the cat in the box. Who gets me out?
 
It's all very strange.... I still can't get my head around the wave-particle duality, probability waves, quantum entanglement, cats in boxes, uncertainty principles and the rest. Now there's this new thing (to me, anyway) called dark energy (dark... what?) and another new thing called the higgs boson (huh?) that I know nothing at all about... better not start thinking about black holes and gravity waves either. So what IS this "reality" that we are living in? It all used to seem so simple, before I studied any physics..! :oops: :'‑(
There are a few very good books on quantum physics for people who don't have a PHD. Jim Al-Khalili is one of my favorite authors in the subject but there are many. You're actually mixing things and putting quantum mechanics, cosmology and particle physics all together. Yes, they are linked but I suggest you tackle one argument at a time.
 
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