benkuykendall
Joined 11 years ago
Joined 11 years ago
So, as stated, this is impossible since it violates the Time Hierarchy Theorem.
The actual result of the paper is that any poly-time computable function can be computed with poly-many tokens. Which is... not a particularly impressive bound? Any non-trivial fixed neural network can, for instance, compute the NAND of two inputs. And any polynomial computable function can be computed with a polynomial number of NAND gates.
But if I were watching Star Trek, they would definitely just ask the computer to grab the fields and it would be a done deal!
Well... other than the 18th Amendment.
However, it reminded me of an older approach to signal filtering that I just recently learned about: the superheterodyne radio receiver. It's a simple idea that enabled us to build cheap, tunable radios. YouTube video if you're curious: https://www.youtube.com/watch?v=hz_mMLhUinw. Definitely an accessible introduction to a neat trick in signal processing!
results = list(get_some_stuff(...))
assert len(results) = 1
result = results[0]
into result = one(get_some_stuff(...))
I guess you could also use tuple-unpacking: result, = get_some_stuff(...)
But the syntax is awkward to unpack a single item. Doesn't that trailing comma just look implausible? (Also I've worked with type-checkers that will complain when a tuple-unpacking could potentially fail, while one has a clear type signatures Iterable[T] -> T.)> Bit rotation can be implemented using a combination of bit shifting and or operations, and on a hardware level, with different locical XOR ports. That’s of course just one way, and you still need a way to identify the number without confusing it with another figure. Although I don’t think that last was implemented: if you select your starting bits in a smart way, there won’t be any overlap. The identification system here uses 14 bits, and all of the figures have either 6 or 7 1s, making it even possible to completely ignore bit rotation and just rely on the relative position of the enabled bits to do the identification. I’m of course merely guessing at this point.
Not sure what it means to "completely ignore bit rotation" and "just rely on the relative position of the enabled bits", those sound like the same thing to me.
To throw my speculation out there, I wonder if this is just done with a lookup table. If we use a byte (generous) to identify each figure, then a table indexed by all 2^14 bit patterns will take less than 17kb. No need to do anything more clever.
""" The Mars Religion
When you hold on to a belief so strongly that neither facts nor reason can change it, what you are doing is no longer science, but religion. So I’ve come to believe the best way to look at our Mars program is as a faith-based initiative. There is a small cohort of people who really believe in going to Mars, the way some people believe in ghosts or cryptocurrency, and this group has an outsize effect on our space program.
At NASA, the faith takes the form of a cargo cult. The agency has persuaded itself that re-enacting the Moon landings with enough fidelity will reward them with a trip to Mars, bringing back the limitless budgets, uncomplicated patriotism, and rapt public attention of the early sixties. They send up their rockets with the same touching faith that keeps Amtrak hauling empty dining cars across the prairie, dreaming of the golden age of rail.
Outside of NASA, the Mars faith shades darker. It is part of a transhumanist worldview that holds mankind must either spread to the stars or die. Elon Musk, the Martian spiritual leader, has talked about the need to “preserve the light of consciousness” by making us a multiplanetary species. As he sees it, Mars is our only way off of a planet crawling with existential risk. And it's not just enough to explore mars; we have make it a backup for all civilization. Failing to stock it with subsistence farming incels would be tantamount to humanity lying down in its open grave. """