I wonder if anyone would find Einstein's field equation aesthetically pleasing.
On Mathematical Beauty in Physics
11–20 of 56 posts
Re: On Mathematical Beauty in Physics
#12I found the book "Our Mathematical Universe" by Max Tegmark, a physicist, a pretty good read. His idea is basically that the universe isn't explained by math, it IS math. To get to what he means by that he provides a good review of theoretical physics/cosmology/quantum mechanics. No idea how other physicists think of his work but for someone not in the field who has some interest I thought it was a good overview and…
Keeping in mind that Tegmark's idea is 2,500 years old and the basis of Western civilization. Pythagoras was the biggest philosophical influence on Plato. And, according to Aristotle (150 years later), Pythagoras believed that "all is number".
Thales (the "first" Greek philosopher) believed that the underlying principle of the world was water, a kind of flowing force. Anaximenes, his student, believed the underlying principle was air, a sort of bouncing around set of particles.
Pythagoras believed that underneath everything, the most basic underlying principle was math. And not just that: he believed that the natural harmonies in mathematics led to the natural harmonies in the kosmos (a term he is credited with introducing, along with the term "philosopher").
Re: On Mathematical Beauty in Physics
#13I wonder if anyone would find Einstein's field equation aesthetically pleasing.
Yes for sure.
Re: On Mathematical Beauty in Physics
#14It's an interesting opinion. And just like the concept of beauty that it mentions, it is subjective.
Math is a human language, written and interpreted by humans. Without human interpretation, math means nothing, just like any other language. And just like any physical model.
We cannot separate ourselves from nature, hence we cannot "truly" state anything about nature in an absolute sense, only relative to us.
I wish physics (and math for that matter), were a little bit more like computer science, in which usually there's an "interpreting machine" (a lot of times a Turing machine), which in a way acts as the explicit observer of the system, without which the system just doesn't make sense (literally, as sense can only be given to something by an interpreting-observer).
Re: On Mathematical Beauty in Physics
#15I expected this to be an a new article or report of Sabine Hossenfelder's work, but apparently the author S is someone else?
Hossenfelder's counterpoint, disussed on HN in the past:
https://www.amazon.com/Lost-Math-Beauty-Physics-Astray/dp/04...
"A contrarian argues that modern physicists' obsession with beauty has given us wonderful math but bad science
Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades. The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria. Worse, these "too good to not be true" theories are actually untestable and they have left the field in a cul-de-sac. To escape, physicists must rethink their methods. Only by embracing reality as it is can science discover the truth."
Hossenfelder's blog: http://backreaction.blogspot.com/
Re: On Mathematical Beauty in Physics
#16It's an interesting opinion. And just like the concept of beauty that it mentions, it is subjective. Math is a human language, written and interpreted by humans. Without human interpretation, math means nothing, just like any other language. And just like any physical model. We cannot separate ourselves from nature, hence we cannot "truly" state anything about nature in an absolute sense, only relative to us. I wish…
Aren't measurements of some natural system objective? We just convert/summarize these measurements to representations that facilitate, to humans, a better understanding of Nature.
Re: On Mathematical Beauty in Physics
#17I think it’s mostly a case of the drunk looking for his keys under the lamp post because that’s where the light is. We have no idea how much there is to know about reality. We do know how to describe some parts with mathematics, but who knows how much there is out there which is not possible to describe with mathematics. We may just be discovering infinitesimally small part ls of reality which math happens to describ…
Math is a description of our reality. If we discovered something that math couldn't explain we'd expand math to explain it.
Re: On Mathematical Beauty in Physics
#18It's an interesting opinion. And just like the concept of beauty that it mentions, it is subjective. Math is a human language, written and interpreted by humans. Without human interpretation, math means nothing, just like any other language. And just like any physical model. We cannot separate ourselves from nature, hence we cannot "truly" state anything about nature in an absolute sense, only relative to us. I wish…
Aren't measurements of some natural system objective? We just convert/summarize these measurements to representations that facilitate, to humans, a better understanding of Nature.
Who performs the measurements? What instruments are used to perform those measurements?
If there's someone or something performing the measurements, then they depend on that someone or something to interpret them.
You are right that measurements and models facilitate a better human understanding of nature/ourselves. However, it is important to keep in mind that these things are maps, not the terrain.
Re: On Mathematical Beauty in Physics
#19I think it’s mostly a case of the drunk looking for his keys under the lamp post because that’s where the light is. We have no idea how much there is to know about reality. We do know how to describe some parts with mathematics, but who knows how much there is out there which is not possible to describe with mathematics. We may just be discovering infinitesimally small part ls of reality which math happens to describ…
Math is a description of our reality. If we discovered something that math couldn't explain we'd expand math to explain it.
How does that square with something like godel's incompleteness therom?
Re: On Mathematical Beauty in Physics
#20Earlier quoted context omitted.
Aren't measurements of some natural system objective? We just convert/summarize these measurements to representations that facilitate, to humans, a better understanding of Nature.
Who performs the measurements? What instruments are used to perform those measurements? If there's someone or something performing the measurements, then they depend on that someone or something to interpret them. You are right that measurements and models facilitate a better human understanding of nature/ourselves. However, it is important to keep in mind that these things are maps, not the terrain.
A measurement can be the interaction between two sufficiently decoupled subsystems.
But I don't really understand why there needs to be some "interpreter." Nature could be some computer/system that is minimizing Action over all possible trajectories. Humans attempt to communicate an approximation to this truth by writing down nonlinear differential equations.