Lost in Math
February 16, 2021 12:01pm
These are some of the notes I put down while listenin to audiobook version of Lost in Math: How Beauty Leads Physics Astray by Sabine Hossenfelder ( twitter, youtube, blog).
It's impossible to test all the hypotheses that we have.
Over time, theories become bigger, more complex and harder to test and prove.
this is an expected evolution when using the scientific method, and physics might be the first area of science hitting a very hard wall in that regard
as noted in the book, it's not easy to just "come up" with new theories - they carry the burden of all previous experiments with them, and even validating that a new theory doesn't mess up what previously already worked is tremendously hard and demanding
physicists may try to use proof assistants to automatically check things - doing things manually is outdated anyway
In choosing which theory to test next, since we lack experimental data (because we are only yet to test the theory), we have to use unscientific parameters, like the beauty.
this one really is problematic
Beauty is not a scientific criteria, but maybe it is one coming from the experience ("throughout one's experience, one has seen what works and what doesn't, and can use that intuition to assess what *will* and will not work next").
without a concrete, quantitative comparisons, I'm fine with this one - it works for someone deciding what they themselves want to work on, but it's still problematic in teams - if different people have different intuitions and/or experience, then it's hard to decide once again
There're no reasons to believe that a fundamental theory is simple (or simpler when compared to lower resolution emergent levels), but in picking a direction to go, more "simplicity" is often a reason.
you could argue that less involved theory will let you test the hypothesis faster, and even if wrong, will waste less of your time then (computationally less demanding, and since the best task optimization strategy is "shortest job first", this one makes sense even)
complex theory at a higher resolution level doesn't necessarily mean that lower level theory is even more complex - it might happen that internal workings cancel themselves out so they leave a simpler theory at a lower level, but that's (probably) less probable then simple theory giving rise to more complex theory.
If we can't test the theory, is it science at all?
working on a theory can still lead to new findings and correlations and useful work. we can compare this to mathematicians working with objects that "don't exist" - and only latter did they found their purpose.
but is it recommended to work on a theory so large that it wastes decades - probably not, but again, work is not in vain.
Simplicity, beauty, elegance, naturalness ("fine tuning").
simplicity, beauty, elegance - it seems it's about collapsing the number of parameters that you can use to describe a particular subsystem, or an entire system - meaning that you have to hold less things in your head, and from time to time, your calculations can use the simplified version (especially if interested in doing approximations)
naturalness - for this one, I'm not sure. I am fine with "weird" numbers and ratios. They really *are* equally probably like any other numbers. Since I think that we're very far from "the theory of everything" (in an all-encompasing sense, not just quantum world and gravity), having any useful conclusion about whether certain numbers are fine or not is way out of our reach at the moment. It might be better to just focus on the data, instead of structure of out theory.
"Lost in math" is not just about physics or math. It's about scientific method, what "science" means and entails. Because of that, it requires a reading.
Scientific method requires extensions and improvements. I've thought about it before (topics for writing, computational science), but this book has reminded me of it yet again. Certain fields in science urgently require meta-scientific improvements.
Saying that "math" and "science" are one and the same is also an interesting topic. "Math" is simply a language used to communicate our ideas - a precise and strict language, that's what's good about it. But many opinions and theories exist whether (all) mathematical objects are "real", whether they *should* be real, and whether everything real is (necessarily) mathematical as well. These are, again, questions very far from our reach at the moment, I'm afraid. Disconnect lies in the fact that if we can describe something, it's natural and thus can be mathematically expressed, which means that we cannot work in the domain of things that aren't in our domain, yet we ask such questions. As our search space is space generated by fundamental primitives of our world, we can access only that part of universe's expresiveness, and go only as low as those fundamental parts (maybe not even that much if we're boarded from accessing lower levels due to some emergent phenomena). This whole talk inevitably reminds me of Death of functions?, because we're again questioning causality, scientific method, and mappings.
The conclusions that I can surely derive are: scientific method requires a bit of rethinking, and an entire science/math/computation requires probably even more rethinking.