Comment by peterlk
14 hours ago
Reminds me a bit of the coolest talk I ever got to see in person: https://youtu.be/FITJMJjASUs?si=Fx4hmo77A62zHqzy
It’s a derivation of the Y combinator from ruby lambdas
14 hours ago
Reminds me a bit of the coolest talk I ever got to see in person: https://youtu.be/FITJMJjASUs?si=Fx4hmo77A62zHqzy
It’s a derivation of the Y combinator from ruby lambdas
If you've never worked through a derivation/explanation of the Y combinator, definitely find one (there are many across the internet) and work through it until the light bulb goes off. It's pretty incredible, it almost seems like "matter ex nihilo" which shouldn't work, and yet does.
It's one of those facts that tends to blow minds when it's first encountered, I can see why one would name a company after it.
Have you gone through The Little Schemer?
More on topic:
> No comparable primitive has been known for continuous mathematics: computing elementary functions such as sin, cos, sqrt, and log has always required multiple distinct operations.
I was taught that these were all hypergeometric functions. What distinction is being drawn here?
Hypergeometric functions are functions with 4 parameters.
When you have a function with many parameters it becomes rather trivial to express simpler functions with it.
You could find a lot of functions with 4 parameters that can express all elementary functions.
Finding a binary operation that can do this, like in TFA, is far more difficult, which is why it has not been done before.
A function with 4 parameters can actually express not only any elementary function, but an infinity of functions with 3 parameters, e.g. by using the 4th parameter to encode an identifier for the function that must be computed.
> Hypergeometric functions are functions with 4 parameters.
Granted, but the claim in the abstract says:
>> computing elementary functions such as sin, cos, sqrt, and log has always required multiple distinct operations
And I don't see how this is true as to hypergeometric functions in a way that isn't shared by the approach in the paper.
> Finding a binary operation that can do this, like in TFA, is far more difficult, which is why it has not been done before.
> A function with 4 parameters can actually express not only any elementary function, but an infinity of functions with 3 parameters, e.g. by using the 4th parameter to encode an identifier for the function that must be computed.
These statements seem to be in direct conflict with each other; you can use the second parameter of a binary function to identify a unary function just as you can use the fourth parameter of a quaternary function to identify a trinary one.
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