alt Hacker NewsThis is what has excited me for many years - the idea I call "scientific refactoring"
What happens if we reason upwards but change some universal constants? What happens if we use Tao instead of Pi everywhere, these kind of fun questions would otherwise require an enormous intellectual effort whereas with the mechanisation and automation of thought, we might be able to run them and see!
Replies
> What happens if we use Tao instead of Pi everywhere
Literally nothing other than mild convenience. It’s just 2pi.
I can write a sed command/program that replaces every occurence of PI with TAU/2 in LaTeX formulas and it'll take me about 30 minutes.
The "intellectual effort" this requires is about 0.
Maybe you meant Euler's number? Since it also relates to PI, it can be used and might actually change the framework in an "interesting way" (making it more awkward in most cases - people picked PI for a reason).
* Tau
I'm using LLMs to rewrite every formula featuring the Gamma function to instead use the factorial. Just let "z!" mean "Gamma(z+1)", substitute everywhere, and simplify. Then have the AI rewrite any prose.
Think of how this opened up EM:
https://ddcolrs.wordpress.com/2018/01/17/maxwells-equations-...
Not just for math, but ALL of Science suffers heavily from a problem of less than 1% of the published works being capable of being read by leading researchers.
Google Scholar was a huge step forward for doing meta-analysis vs a physical library.
But agents scanning the vastness of PDFs to find correlations and insights that are far beyond human context-capacity will I hope find a lot of knowledge that we have technically already collected, but remain ignorant of.