toth
Joined 12 years ago
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Comment · 1 year ago
Comment · 1 year ago
> An example you'll see in say a modern C compiler is that if you write the obvious loop to calculate how many bits are set in an int, the actual machine code on a brand new CPU should be a single population count instruction, C provides neither intrinsics (like Rust) not a dedicated "popcount" feature, so you can't write that but it's obviously what you want here and yup an optimising C compiler will do that.
C compilers definitely have intrinsics for this, for GCC for instance it is `__builtin_popcount`.
And apparently it has even standard language support for it since C23, it's `stdc_count_ones` [1] and in C++ you have `std::popcount` [2]
[1] https://en.cppreference.com/w/c/numeric/bit_manip.html [2] https://en.cppreference.com/w/cpp/numeric/popcount.html
Comment · 1 year ago
I think you shared the wrong link. Based on a quick youtube search I think you meant this one
Comment · 1 year ago
For pytorch the analogue is Named Tensors, but it's a provisional feature and not supported everywhere.
Comment · 1 year ago
That seems uncharitable. I for one enjoy the tidbits he posts in is blog.
Comment · 1 year ago
> In a different world, we settled on a system of notation based on continued
> fractions rather than decimals for writing non-integers. In this world, nobody
> marvels at the irregularity of pi or e, the fact that they seem to go on for
> ever without a pattern - both numbers have elegant and regular representations > as infinite sums of fractions.
There are some less widely-known topics in math that seem to make some of those that learn them want to "evangelize" about them and wish they had a more starring role. Continued fractions are one.
Now, don't get me wrong. Continued fractions are very cool, some of the associated results are very beautiful. More people should know about them. But they never will be a viable alternative to decimals. Computation is too hard with them for one.
Also, while e has a nice regular continued fraction expansion [1], that is not the case for pi [2]. There is no known formula for the terms, they are as irregular as the decimal digits. There are nice simple formulas for pi as infinite sums of fractions (simplest is probably [3]) but those are not continued fractions.
[1] https://oeis.org/A003417 [2] https://oeis.org/A001203 [3] https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80
Comment · 1 year ago
Well, actually... the "main" function is handled specially in the standard. It is the only one where the return type is not void and you don't need to explicitly return from it - if you do it, it is treated as if you returned 0.
(You will most definitely get a compiler error if you try this with any other function.)
You might say this is very silly, and you'd be right. But as quirks of C++ go it is one of the most benign ones. As usual it is there for backwards compatibility.
And, for what it's worth, the uber-bean counter didn't miss a bean here...
Comment · 1 year ago
Those points are true of current AI models, but how sure are you they will remain true as technology evolves?
Maybe you believe that they will always stay true, that there's some ineffable human quality that will never be captured by AI and value creation will always be bottle-necked by humans. That would be nice.
But even if you still need humans in the loop, it's not clear how "democratizing" this would be. It might sound great if in a few years you and everyone else can run an AI on their laptop that is as a good as a great technical co-founder that never sleeps. But note that means that someone who owns a data-center can run the equivalent of the current entire technical staff of Google, Meta, and OpenAI combined. Doesn't sound like a very level playing field.
Comment · 1 year ago
I can't understand how you reach your conclusion.
At present, if you have financial capital and need intellectual capital you need to find people willing to work for you and pay them a lot of money. With enough progress in AI you can get the intellectual capital from machines instead, for a lot less. What loses value is human intellectual capital. Financial capital just gained a lot of power, it can now substitute for intellectual capital.
Sure, you could pretend this means you'll be able to launch a startup without any employees, and so will everyone. But why wouldn't Sam Altman or whomever just start AI Ycombinator with hundreds of thousands of AI "founders"? Do you really think it would be more "democratic"?
Comment · 1 year ago
Actually `e^(sqrt(n) pi)` is very close to being an integer for a couple of different `n`s, including 67 and 163. For 163 it's much closer to an integer, but for 67 you get something you can easily check in double precision floats is close to an integer, so I thought it worked better as a joke answer :)
FYI, the reason you get these almost integers is related to the `n`s being Heegner numbers, see https://en.wikipedia.org/wiki/Heegner_number.
Comment · 1 year ago
Charitably it was a joke, as was my quip about `e^(sqrt(67) pi)`. It is a funnier joke without a disclaimer at the end, but unlike GP I couldn't bring myself to leave one out and potentially mislead some people...
What I meant was that I didn't know that `e^pi - pi` is another transcendental expression that is very close an integer. You might think this is just an uninteresting coincidence but there's some interesting mathematics around such "almost integers". Wikipedia has a quick overview [1]. I didn't realize it before, but they have GP's example and also the awesome `e + pi + e pi + e^pi + pi^e ~= 60`.
Comment · 1 year ago
Very nice, didn't know about that one!
In a similar vein, Ramanujan famously proved that e^(sqrt(67) pi) is an integer.
And obviously exp(i pi) is an integer as well, but that's less fun.
(Note: only one of the above claims is correct)
Comment · 2 years ago
> Are you just being overawed by IQ tests, which are notorious for measuring only ability to pass IQ tests?
People like to say things like this, but nothing could be further than the truth. There is a vast literature showing that IQ predicts things like job performance, school performance, income and wealth [1]. IQ is highly persistent across time for fixed individuals. Yes, "intelligence" is not a precisely defined concept, but that doesn't mean that it isn't real. A lot of useful concepts have some vagueness about, even "height" to take the example parodied in the OP.
And "super intelligence" is admittedly even vaguer, it just means sufficiently smarter than humans. If you do have a problem with that presentation just think of specific capabilities a "super intelligence" would be expected to have. For instance, the ability to attain super-human performance in a game (e.g., chess or go) that it had never seen before. The ability to produce fully functional highly complex software from a natural language spec in instants. The ability to outperform any human at any white-collar job without being specifically trained for it.
Are you confident that a machine with all those capabilities are impossible?
[1] https://en.wikipedia.org/wiki/Intelligence_quotient#Social_c...
Comment · 2 years ago
Right, it's a limit at infinity
And FWIW all major C/C++ have for a long time have had a an intrinsic for this. In clang it even has the same name, Visual Studio it's something like just '_popcount'. So it has long been easy to roll your own macro that works everywhere.