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What comes to mind is studying Category Theory and Abstract Algebra.
MIT 6.890 https://ocw.mit.edu/courses/electrical-engineering-and-compu...
Basic idea is map a hard problem A (e.g TSP) to some other problem X (e.g chess) by finding “gadgets” then you know X is at-least as hard as A (a lower bound on X).
So the answer I have isn't exactly what you're looking for, which I think is an algorithmic/machine learning architecture that can transfer concepts found in problems. Just wanted to share for anyone interested that there is in depth research and theory developed in cognitive science concerning the way people use what the field calls conceptual blending to make sense of unfamiliar subjects with familiar concepts. May…
The Way We Think is not a book I will forget.
There is Frame Innovation by Kees Dorst. It takes at look at complex problems NOT by slicing them up and trying to solve each ‘slice’ but rather tries to look at the entire situation as a whole and -with your team- formulate a better and more desired situation. It uses ‘frames’ from other disciplines and tries to achieve a multidisciplinary view where each field combines knowledge. The idea is not always to solve the…
That’s called Mathematics. For example, most NP-complete problems we know of were proven to be NP-complete by showing them to be no easier than some other problems we know to be NP-complete. https://en.wikipedia.org/wiki/NP-completeness#NP-complete_pr... : “The easiest way to prove that some new problem is NP-complete is first to prove that it is in NP, and then to reduce some known NP-complete problem to it” As a se…
We're taught so much about the mechanics and details about mathematics in school, that I've never taken a step back to understand it from a fundamental/philosophical level for what it is. Beautiful answer.
This game is of course an imperfect information game (you don’t know your opponents hole cards). We have lots of great algos for perfect information games but not imperfect.
So what the researches did is they mapped hold em to a perfect information game by tweaking it: now nobody knows their hole cards and all players must publicly announce their strategy to a “referee”. Then the referee looks at the players cards and places bets on behalf of the players. A player’s strategy looks something like: if I have a pair of aces then I want to raise 94% of the time and call 6% of the time and fold 0% of the time etc etc.
You know your opponent’s strategy too (as they have announced it like you did to the referee) so you can now iterate and optimise your strategies which will approach a Nash equilibrium.
It's possible that we could decompose the complex problems into simpler ones and the solution for a subset could be shared. Although in most cases I feel that the effects will be at least slightly different as far as the n-order effects.
For example, the solution to inflation could be tying a number to automatically adjust based on CPI. This might make sense for a SS payment and COLA. It might not make sense for basis adjustment of school property taxes as other variables could adjust the revenue need, like decrease in students or increase in funding from other sources. It looks like they map on the surface, but not when you dig deeper.
That’s called Mathematics. For example, most NP-complete problems we know of were proven to be NP-complete by showing them to be no easier than some other problems we know to be NP-complete. https://en.wikipedia.org/wiki/NP-completeness#NP-complete_pr... : “The easiest way to prove that some new problem is NP-complete is first to prove that it is in NP, and then to reduce some known NP-complete problem to it” As a se…
There were two men trying to decide what to do for a living. They went to see a counselor, and he decided that they had good problem solving skills.
He tried a test to narrow the area of specialty. He put each man in a room with a stove, a bucket of water, and an empty pot on the stove. He said, “Boil some water in the pot.” Both men filled the pot with water from the bucket and turned on the burner to boil the water.
Next, he put them into a room with a stove, a bucket of water, and a pot full of water on the stove. Again, he said, “Boil the water in the pot.” The first man immediately turned on the burner. The counselor told him to be an Engineer. The second man emptied the pot and proudly said that now the problem is reduced to the previously solved problem. The counselor told him to be a mathematician.
This version from: https://www.davidmarcus.com/Humor/MathJokes.htm and other versions at https://www.math.utah.edu/~cherk/mathjokes.html
How do we map programming to understanding genetic codes?
How do we map psychological research or zoological data to operations research?