It is a surprise to many that the math used in physics is a weird kind of handwavy math.
"Quantum field theory is mathematics that has not yet been invented by mathematicians." quantamagazine.org/the-mystery-at…
The math in physics is not as rigorous as found in math but it works with extreme accuracy! Maps (i.e. models) are not the territory, but you want your maps to accurately represent the territory.
As Feynman has said "It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong."
So, what is it about 'curve-fitting that people don't seem to understand?
The theories and math invented by physicists are so powerful that they can perhaps model anything! So how do we know that they are not just curve-fitting to match experimental data?
There exists a fundamental truth here between our models of reality and reality itself. We simply are devoid of the mathematics to rigorously and comprehensively model reality. Reality at present is beyond what can be captured by current math.
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I'm composing this tweetstorm from a tweetstorm of a dream I had. It begins with the idea that Ptolemy's model of the movement of the planets was extremely accurate.
Ptolemy's model was accurate enough to be very useful for navigators of their time. But it worked well because it was finely tuned to fit with observed experimental data.
But was wrong with Ptolemy's model is that it did not correctly capture cause and effect. The earth and the planets revolve around the sun due to gravity and not everything revolves around the earth. This was the Copernicus model which he paid gravely for proposing.
It occurs to me that modern society has led to the perspective that we have immense control of our lives. This was not always true in the past where people could die for many reasons out of their control.
The modern understanding of the word 'tragedy' is that it when someone suffers for something that they could have avoided entirely. That there exists this means of control one's destiny and that it was ignored.
We see this play out on a mass scale with our actions in the pandemic (facemasks and vaccinations) and our absence of risk mitigation against climate change. But we remain utterly perplexed as to why people can't see the tragedy that is happening in slow motion?
It's becoming depressingly obvious that we have to depend on stupid people to do the right thing (see: vaccination and climate change).
We've been under the false assumption that stupid people can be convinced by good arguments and reason. You will have to throw away that assumption forever!
Explain to me why the CDC has masks-wearing guidelines that appeal only to smart people? The damn problem with smart people is that they assume most people are smart enough to understand good reasoning. Wrong!!!
It is patently absurd that so many researchers in cognitive science believe in a magical local rule (i.e. Hebbian learning, gradient descent, free energy, neural circuitry, etc) that leads to complex intelligence. I guess humans just never get tired of their reductionist methods.
But yet we have made tremendous strides using just local rules like gradient descent and massive computation to emulate intuition found in human minds.
Deep Learning methods appear like a bottom-up process, but it's actually a top-down process where an observational error is propagated down the layers perturbing weights along the way. An observational error can only be identified at the top.