51–60 of 144 posts
I think it is very intuitive that more space beats the pants off of more time. In time O(n) you can use O(n) cells on a tape, but there are O(2^n) possible configurations of symbols on a tape of length n (for an alphabet with 2 symbols), so you can do so much more with n space than with n time.
Lookup tables with precalculated things for the win! In fact I don’t think we would need processors anymore if we were centrally storing all of the operations ever done in our processors. Now fast retrieval is another problem for another thread.
> if we were centrally storing all of the operations Community-scale caching? That's basically what pre-compiled software distributions are. And one idea for addressing the programming language design balk "that would be a nice feature, but it's not known how to compile it efficiently, so you can't have it", is highly-parallel cloud compilation, paired with a community-scale compiler cache. You might not mind if some…
Earlier quoted context omitted.
If you have rows of racks of machines, isn't that 3 dimensions? A machine can be on top of, behind, or next to another that it's directly connected to. And the components inside have their own non-uniform memory access. Or if you're saying heat dissipation scales with surface area and is 2D, I don't know. Would think that water cooling makes it more about volume, but I'm not an expert on that.
That example would be two dimensions still in the limit computation, since you can keep building outwards (add buildings) but not scale upwards (add floors)
Lookup tables with precalculated things for the win! In fact I don’t think we would need processors anymore if we were centrally storing all of the operations ever done in our processors. Now fast retrieval is another problem for another thread.
Reminds me of when I started working on storage systems as a young man and once suggested pre-computing every 4KB block once and just using pointers to the correct block as data is written, until someone pointed out that the number of unique 4KB blocks (2^32768) far exceeds the number of atoms in the universe.
It's basically how deduplication works in ZFS. And that's why it only makes sense when you store a lot of repetitive data, e.g. VM images.
Lookup tables with precalculated things for the win! In fact I don’t think we would need processors anymore if we were centrally storing all of the operations ever done in our processors. Now fast retrieval is another problem for another thread.
Reminds me of when I started working on storage systems as a young man and once suggested pre-computing every 4KB block once and just using pointers to the correct block as data is written, until someone pointed out that the number of unique 4KB blocks (2^32768) far exceeds the number of atoms in the universe.
What a strange, sad way to think about this. Academia is perverse.
Earlier quoted context omitted.
Except that there are collisions...
This might be completely naive but can a reversible time component be incorporated into distinguishing two hash calculations? Meaning when unpacked/extrapolated it is a unique signifier but when decomposed it folds back into the standard calculation - is this feasible?
Earlier quoted context omitted.
O(n^(1/2)) really, since data centers are 2 dimensional, not 3 dimensional. (Quite aside from the practical "we build on the surface of the earth" consideration, heat dissipation considerations limit you to a 2 dimensional circuit in 3-space.)
More fundamentally O(n^(1/2)) due to the holographic principle which states that the maximal amount of information encodable in a given region of space scales wrt its surface area, rather than its volume. (Even more aside to your practical heat dissipation constraint)
Earlier quoted context omitted.
Except that there are collisions...
This might be completely naive but can a reversible time component be incorporated into distinguishing two hash calculations? Meaning when unpacked/extrapolated it is a unique signifier but when decomposed it folds back into the standard calculation - is this feasible?