221–230 of 317 posts
Interesting, but is the required combination of EML gates less complex than using other primitives?
Like when the Apollo guidance computer was made, the bottleneck was making integrated chips so they only made one, the NOR gate, and a whackton of routing to build out an entire CPU. Horribly complex routing, very simplified integrated circuit construction
What would physical EML gates be implemented in reality? Posts like these are the reason i check HN every day
This is amazing! I love seeing FRACTRAN-shaped things on the homepage :) This reminds me of how 1-bit stacks are encoded in binary: A stack of zeros and ones can be encoded in a single number by keeping with bit-shifting and incrementing. Pushing a 0 onto the stack is equivalent to doubling the number. Pushing a 1 is equivalent to doubling and adding 1. Popping is equivalent to dividing by 2, where the remainder is t…
Did you just explain base-2 numbers on the HN forums as if it were novel?
Earlier quoted context omitted.
I think that you may have replied before I saved my entire response, so I am not sure how much of it you had read before replying yourself. I have replied to your last statement: > "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." As I have explained above, what you propose does not work. It…
> As I have explained above, what you propose does not work. It works in functions with 3 or more parameters, but it does not work in binary functions, because you cannot make binary functions from unary functions (without using some auxiliary binary functions). I have no idea what you're trying to say. If you can use one parameter to identify a desired function, then obviously you can use a function of arity n+1 to…
This requires expressing binary functions, like addition and multiplication.
You cannot do this by using only the set of unary functions, which can indeed be generated by a function with 2 parameters, one of which selects an unary function.
One thing I wonder now: NAND is symmetric while this isn't, could something similar be found where function(x, y) = function(y, x)?
This could have some interesting hardware implications as well - it suggests that a large dedicated silicon instruction set could accelerate any mathematical algorithm provided it can be mapped to this primitive. It also suggests a compiler/translation layer should be possible as well as some novel visualization methods for functions and methods.
I'm not too familiar with the hardware world, but does EML look like the kind of computation that's hardware-friendly? Would love for someone with more expertise to chime in here.
It gets a bit more difficult for the complex domain because you need rotation.
EDIT: please change the article link to the most recent version (as of now still v2), it is currently pointing to the v1 version which misses the figures. I'm still reading this, but if this checks out, this is one of the most significant discoveries in years. Why use splines or polynomials or haphazardly chosen basis functions if you can just fit (gradient descent) your data or wave functions to the proper computati…
write x#y for 1/(x-y).
x#0 = 1/(x-0) = 1/x, so you get reciprocals. Then (x#y)#0 = 1/((1/(x-y)) - 0) = x-y, so subtraction.
it's common problem to show in any (insert various algebraic structure here ) inverse and subtraction gives all 4 elementary ops.
I haven't checked this carefully, but this note seems to give a short proof (modulo knowing some other items...) https://dmg.tuwien.ac.at/goldstern/www/papers/notes/singlebi...