The Orion's Arm Universe Project Forums

Hi, a timeline question, and some math about encryption
(05-16-2018, 11:49 AM)Drashner1 Wrote: Another quick thought re modos matching transapients in the encryption dept by simply building up enough computronium:

It should be noted that transapient computronium is qualitatively superior to modosophont computronium, and at the S4 and higher level starts operating at levels that would tear apart processors held together by chemical bonds - so modos are literally incapable of building it. Transapients also presumably employ better/more efficient software design to go with better hardware, making the gap between their tech and modo even larger.

I suppose that modos could (in principle) still build massive amounts of computronium to make up the difference. But I'm not sure how much they would have to build to make up the difference.

Agreed. But encryption is one of the few problem areas where a simple brute-force search of all the keyspace is actually the most efficient algorithm (at least, it is if the cryptologist designing the code knew what they were doing, since that's exactly what they're trying to ensure). Unlike, say, chess, or go, or higher mathematics, there are no subtleties about pruning the search tree or recognizing abstract relationships and patterns -- the best you can possible do is just try every key as fast as you can. So, unlike most problems, it parallelizes (and can be attacked via Grover's algorithm) very cleanly -- if you want to try a billion keys at once, and you happen to have a computronium bank of a billion little processors available, the programming overhead for doing so is negligible. So this -- extremely atypical -- problem is the one area where toposophic barriers don't really apply: Denebolla collapse never kicks in, since the architecture for parallelizing it to arbitrary numbers of processors is trivial (well, up to one processor per key in your entire keyspace -- not usually a significant limit). But for more typical problems (like designing and manufacturing that computronium bank in the first case), that isn't true.

So yes, of course an archai will have access to far larger banks of far faster computronium than a mososophont. But usually the archai also has the advantage is also having a far more efficient architecture for handling complex problems, which lets them additionally use those computronium banks far more efficiently (since they're supernaturally-to-a-modosophont effective knowing how to prune the search tree, or recognize abstract relationships, or whatever's needed for this complex problem). But for a problem like brute-force trying every key (as opposed to, say using mathematics and logic to figure out a subtle flaw in the cryptosystem, if one exists, or trying to technotelepathize the message sender), an efficient architecture for handling complexity isn't needed -- the problem parallelizes trivially, no search tree pruning is needed, and (assuming that no subtle flaws in the cryptosystem exist) there's no more effective but more complex approach. So this is the area where an archai actually has the smallest advantage over a modosophont -- merely the level of advantage you'd assume from comparing the ratio of their nominal available processing power, without their usual huge algorithmic efficiency advantages on top of that. So brute-force search of a very large number of simple-to-check possibilities (in the absence of any clues suggesting where to look), like brute-force decryption, is one of the very few areas where a modosophont that had access to a moonbrain-sized sphere of S3 ultimate chips (assuming e knows how to use it, and yes, obviously that's unlikely) can do roughly as well as an S3 moonbrain that's built out of S3 ultimate chips.

This is related to the problem with P=NP in the OA setting. A really complicated problem can always be reduced to a simple (and easily parallelized) problem of just trying every possible answer in turn until you find the solution (as long as recognizing the solution when you have it isn't hard -- i.e as long as the problem is in NP). What P=NP says is "you would expect that, while that approach was theoretically possible, in practice it was ridiculously expensive way to solve such a problem compared to some more sophisticated problem-specific approach since it appears to require doing brute-force search of an impractically fast space -- but you're wrong: actually there's a general algorithm for searching the set of all possible solutions in a very reasonable time, vastly faster than looking at all of them, regardless of what your original problem was." So P=NP is saying something that seems extremely implausible -- that all possible inherent complexity is an illusion. That's why it would makes archai redundant: archai can handle supernatural-to-a-modosophont levels of subtlety and complexity. But P=NP means that if a modosophont can describe a problem and how to check that a possible answer is the solution, the apparent complexity doesn't matter, they can effectively check all possible solutions ridiculously much faster than that sounds like it would be possible to do (regardless of how complex or challenging the original problem was). So then you only need to hand a modosophont some moderately fast computronium (or even worse, if the P=NP algorithm also parallelized cleanly -- which seems even more implausible -- a moderately large bank of slow computronium), and then they can solve the sorts of problems that everyone had been assuming only archai could solve. Basically P=NP would provide an end run around the need for toposophic levels, putting S-infinity into a single algorithm: most apparently hard problems can be reduced to one easy problem, and solving that problem doesn't require transapient levels of complexity handling (unless recognizing whether an answer is a solution already inherently requires transapient levels of complexity handling).

Messages In This Thread
RE: Hi, a timeline question, and some math about encryption - by Roger - 05-16-2018, 01:16 PM

Forum Jump:

Users browsing this thread: 1 Guest(s)