Comments URL: https://news.ycombinator.com/item?id=45533489

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# Comments: 0

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.

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

https://youtu.be/EL7Au1tzNxE

https://docs.pytorch.org/docs/stable/named_tensor.html

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

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...

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.

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"?

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.

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`.

[1] https://en.wikipedia.org/wiki/Almost_integer

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)

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...

The mean of the n-dimensional gaussian is an element of R^n, an unbounded space. There's no uninformed prior over this space, so there is always a choice of origin implicit in some way...

As you say, you can shrink towards any point and you get a valid James-Steiner estimator that is strictly better than the naive estimator. But if you send the point you are shrinking towards to infinity you get the naive estimator again. So it feels like the fact you are implicitly selecting a finite chunk of R^n around an origin plays a role in the paradox...

I think that ship has sailed, but I think it's unfortunate that "ReLU(x)" became a popular notation for "max(0,x)". And using the name "rectified linear unit" for basically "positive part" seems like a parody, like insisting on calling water "dihydrogen monoxide".

So it's not enough to make them smaller and cheaper, they also have to be made much less prone to these complications. I am sure that will happen in time, but I am also sure we'll be able to grow people new lungs in time

All this versatility comes at the expense of ease of use. It could certainly do a better job of making the simple common use cases more straightforward.

gnuplot arguably has similar power and versatility and it does make the simple stuff easier.

One thing that matplotlib is IMO bad at is interactive plots. They are very slow, and the controls are not intuitive. 99% of the time you just want to zoom and pan and those should be default actions.

gnuplotlib looks interesting and I will have a look, but these days most of the plots I do are in jupyter notebooks and I really want inline interactive plots so I don't think I will use it much. FWIW, what I use currently is plotly - the interactivity is very good (way better than matplotlib's) and plotly.express is very easy to use for the simple use cases.