It would be nice if people had any better terminology than "an IQ of 300". IQ is a relative measure: it currently peaks at ~196, based solely on the current human population. Any 200+ scores you see in headlines are just numbers spat out by IQ tests with wacky tail behavior.
The real equivalent is something like Stockfish, AlphaZero, etc. that performs at superhuman level across _all_ domains. It is something that beats any human at any competitive activity. Arguably, super human intelligence exists already in the form of corporations, institutions, and state actors. Organized collectives of humans augmented by computers are obviously more capable than any individual across domains. “Country of geniuses in a datacenter” is simple enough to get the idea across, but something more like “company in a datacenter” or “state actor in a data center” might be more useful terminology for describing relative capabilities.
It provides an unlimited license specifically for reading and writing spec-compliant files, which could conceivably open you up to issues if you have implementation errors or attempt to extend the spec.
> The point is, why predict that the growth rate is going to slow exactly now? What evidence are you going to look at?
Why predict that the (absolute) growth rate is going to keep accelerating past exactly now?
Exponential growth always assumes a constant relative growth rate, which works in the fiction of economics, but is otherwise far from an inevitability. People like to point to Moore's law ad nauseam, but other things like "the human population" or "single-core performance" keep accelerating until they start cooling off.
> And note, there are good reasons to predict a speedup, too; as models get more intelligent, they will be able to accelerate the R&D process.
And if heaven forbid, R&D ever turns out to start taking more work for the same marginal returns on "ability to accelerate the process", then you no longer have an exponential curve. Or for that matter, even if some parts can be accelerated to an amazing extent, other parts may get strung up on Amdahl's law.
It's fine to predict continued growth, and it's even fine to predict that a true inflection point won't come any time soon, but exponential growth is something else entirely.
> Why predict that the (absolute) growth rate is going to keep accelerating past exactly now?
By following this logic you should have predicted Moore’s law would halt every year for the last five decades. I hope you see why this is a flawed argument. You prove too much.
But I will answer your “why”: plenty of exponential curves exist in reality, and empirically, they can last for a long time. This is just how technology works; some exponential process kicks off, then eventually is rate-limited, then if we are lucky another S-curve stacks on top of it, and the process repeats for a while.
Reality has inertia. My hunch is you should apply some heuristic like “the longer a curve has existed, the longer you should bet it will persist”. So I wouldn’t bet on exponential growth in AI capabilities for the next 10 years, but I would consider it very foolish to use pure induction to bet on growth stopping within 1 year.
And to be clear, I think these heuristics are weak and should be trumped by actual physical models of rate-limiters where available.
> By following this logic you should have predicted Moore’s law would halt every year for the last five decades. I hope you see why this is a flawed argument. You prove too much.
I do think it's continually amazing that Moore's law has continued in some capacity for decades. But before trumpeting the age of exponential growth, I'd love to see plenty of examples that aren't named "Moore's law": as it stands, one easy hypothesis is that "ability to cram transistors into mass-produced boards" lends itself particularly well to newly-discovered strategies.
> So I wouldn’t bet on exponential growth in AI capabilities for the next 10 years, but I would consider it very foolish to use pure induction to bet on growth stopping within 1 year.
Great, we both agree that it's foolish to bet on growth stopping within 1 year. What I'm saying that "growth doesn't stop" ≠ "growth is exponential".
A theory of "inertia" could just as well support linear growth: it's only because we stare at relative growth rates that we treat exponential growth as a "constant" that will continue in the absence of explicit barriers.
Solar panel cost per watt has been dropping exponentially for decades as well...
Partly these are matters of economies of scale - reduction in production costs at scale - and partly it's a matter of increasing human attention leading to steady improvements as the technology itself becomes more ubiquitous.
This is where I’d really like to be able to point to our respective Manifold predictions on the subject; we could circle back in a year’s time and review who was in fact correct. I wager internet points it will be me :)
Many people seem to assert that "constant relative growth in capabilities/sales/whatever" is a totally reasonable (or even obvious or inevitable) prior assumption, and then point to "OMG relative growth produces an exponential curve!" as the rest of their argument. And at least the AI 2027 people tried to one-up that by asserting an increasing relative growth rate to produce a superexponential curve.
I'd be a fool to say that we'll ever hit a hard plateau in AI capabilities, but I'll have a hard time believing any projected exponential-growth-to-infinity until I see it with my own eyes.
The 8.7e45 "restricted" number in that repo rules out certain patterns of pawn promotions. It looks like the 5.68e50 "general" number is the true upper bound, allowing any promotions possible.
Thanks for that link! I was looking for that answer a few years ago, but I couldn't find anyone who had carried it out all the way through (with the cost of "switching control" fully accounted for), nor many people who were even aware of the 75-move rule.
The 50 move rule is still there: either player has the right to claim a draw after 50 moves without a pawn move or a capture. So the game can end then if either player wishes it to (and it almost always will end, because at least one player can expect no better than a draw).
After 75 moves, however, it's not optional, the game has ended. It's still a draw if the game subsequently "ends" in checkmate or a loss on time, though maybe not the players sign the score sheet, move on to the next round, etc.
I'd be skeptical of the performance of any getBits() implementation. With the traditional approach ((X >> A) & B), you'll have to redundantly bit-shift all the data above the field you're aiming for. The other option would be to mask prior to the shift, but then you have a redundant copy of the data below the field.
Also, there's no great story for getting a large byte blob into or out of a BigInt, short of converting it all to ASCII hex and back. I ran into that limitation when attempting to use BigInts for arbitrary-precision arithmetic.
For simple data storage, I'd rather just use a Uint32Array and split/merge bits over element boundaries as appropriate.
The lack of control over the scale to switch between absolute and relative error seems like somewhat of a shortcoming: it only works when you have values in the rough vicinity of 1.
In any case, what I usually want from an error metric is a clear interpretation of what it means, apart from just looking nice. Absolute error is good for measurements where the major error sources are independent of the value, while relative error is good for accuracy loss in floating-point arithmetic (though it gets a bit involved with catastrophic cancellation, where you want to take everything relative to the original input scale). Without a principled reason to do so, I wouldn't want to clump together absolute and relative thresholds and distort their meaning like this.
I used it to pick the constants that minimized error in an approximation of inverse trigonometric functions (-π to +π). Found that it provided a good balance between minimizing either the relative or absolute error.
> Is C really "pure noise" if you can get A back out of it?
If you throw out B, then there's no possible way to get A out of C (short of blindly guessing what A is): that's one of the properties of a one-time pad.
But distributing both B and C is no different than distributing A in two parts, and I'd have a hard time imagining it would be treated any differently on a legal level.
It doesn't seem to have much in the way of validation, e.g., it will indiscriminately let you use either ']' or '}' to terminate an object or array. Also, it's more lenient than RFC or json.org JSON in allowing '\v' for whitespace. I'd treat it more as a "data extractor for known-correct JSON". But even then, rolling your own string or number parser could get annoying, unless the producer agrees on a subset of JSON syntax.
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