daynthelife

Not defending GP, but your claim that actual truth "obviously exists" is equally condescending and empty of backing evidence.

Would you say the continuum hypothesis (or its negation) is "actual truth"? Or does the "actual truth" become something closer to "actually, there are models of ZFC where CH holds as well as models where it doesn't hold, or maybe ZFC is already inconsistent; we don't really know, nor can we."?

Similarly, on the subject of astronomical reference frames, I'd argue the "actual truth" is closer to this:

> Any reference frame that locally obeys Newton's law of inertia is equally valid. Some are more useful than others depending on the problem you are studying. The notion of an "absolute center" is purely semantic, and a meaningless human construct, until one places bounds on the system under study, wherein the center of mass becomes the most reasonable choice at sub-cosmological scales.

GR says that any falling (or orbiting) reference frame is equally valid, locally obeying Newton's laws. So in a precise sense, geocentric and heliocentric reference frames are equally valid. Both can claim to be "actual truth". Of course, a heliocentric reference frame is a lot more useful for studying planetary orbits since it gives rise to simpler equations of state. But that doesn't make the geocentric frame "wrong".

Put differently, would you say a heliocentric reference frame is also "wrong" since the sun is actually orbiting around Sagittarius A*?

Taking your argument to its logical conclusion, one would conclude that the [comoving reference frane](https://en.wikipedia.org/wiki/Comoving_and_proper_distances) is the only "true" one. And at last there is real validity to this claim, since the CMB does pick out a preferred velocity at each point in spacetime. But it is pretty impractical to use comoving coordinates to study problems outside of cosmology.

Ultimately, it stops being a matter of "right" or "wrong" but rather one of picking the right tool for the job you're working on.

As mathematician, I actually agree. We could do a lot more to communicate ideas in a way non-experts can understand.

For instance, most people are familiar with polynomials. Take a polynomial in x (with integer coefficients) and substitute x for 5t everywhere. So for instance, 2x^3 - 8x + 3 becomes 250t^3 - 40t + 3.

The Rees algebra Z[5t] (here Z is the integers) is then just the set of all polynomials you can get this way.

If Wikipedia introduced it like this, I don't think most people would have a problem understanding.

The concept is not (at least not always) actually that complicated, like others are implying. It's our communication that is lacking.

Editions do not fragment the ecosystem at all. A crate written in rust 2015 can depend on a crate written in rust 2024 and vice versa. There are no forced upgrades.

The only maintainers it causes a burden for are the compiler developers (and tech debt within the compiler). But this is pretty much unavoidable if the language is to evolve while remaining backwards compatible -- e.g. it's not like the c++ compiler has a lower rate of tech debt accrual.

Out of curiosity, did it shift up or down for you? I've had perfect putch from a young age, but now at 30 I hear everything a semiton higher (so e.g. a B sounds like a C to me, and I have to manually subtract the semitone to infer the real pitch and hope that I am not overcorrecting)

My read of GP is that there is a cycle economy between "bitter lesson" style domain-general scaling and domain-specific adaptation once the scaling plateaus for the latest tech.

I love this! If I were to suggest any improvements:

- Have a play-by-play view so users can see plays they missed

- Make the "between innings" tabs clickable rather than forcing users to wait for the cycle (cycle by default, pin if user clicked a tab)

- show glove on right hand for outfielders that throw LH

- maybe show baserunners taking leads rather than keeping a foot on the base

To the extent that's true, the same would then apply to any sufficiently intelligent life. So if that's the crux of the argument, it has nothing to do with AI being a great filter.

It always bothers me when people suggest that AI could be the "great filter" in the sense of Fermi's paradox. Yes, AI may well wipe out biological life, but all evidence suggests AI will have a much easier time with space travel compared to biological life, and it will emit much louder signals unless it is intentionally staying silent.

It clearly doesn't use minimax, since it doesn't play the best move for black in the critical line, leading to a mate in 5 instead if a mate in 6.

Best line is N4 N5, Nx6+ K7, R4 N3+!, K2 N5, N8! Kx8, Rx5#. The site has black instead play Kx6 on the third move, allowing a faster mate.

The site plays Kx6 instead. You're right though that I was generous with the exclams; all the moves are easy to find in reality.

It frustrates me that the site does not give the strongest defense for black. The position is mate in 6, not 5:

1. N4 N5

2. Nx6+ K7

3. R4 N3+!

4. K2 N5

5. N8! Kx8

6. Rx5#

> Theoretically you can max out every 5 hour window, but they lose money on that.

No, there is a weekly limit as well. Maxing out a single 5h window uses ~10% of the weekly limit

I find a lot of motivation from topology. If you plot a smooth degree d curve over the complex numbers, it forms a surface of degree g=(d-1)(d-2)/2. In the case of a cubic, we get genus 1, i.e. a torus. Now tori admit a very natural group action, namely addition in (R/Z)^2. And sure enough, if you pick the right homeomorphism, this corresponds to the group action given by the elliptical curve.

Of course, the homeomorphism to (R/Z)^2 does not respect the geometry (it is not conformal). If we want the map to preserve angles, we need our fundamental domain to be a parallelogram instead of a rigid square. The shape of the parallelogram depends on the coefficients of the cubic, and the isomorphism is uniquely defined up to choice of a base point O (mapping to the identity element; for elliptic curves, this is normally taken to be the point at infinity). You still get a group law on the parallelogram from vector addition in the same way, and this pulls back to the precise group action on the elliptic curve.

The real magic is that the resulting group law is algebraic, meaning that a*b can be written as an algebraic function of a and b. This means you can do the same arithmetic over any field, not just the complex numbers, and still get a group action.

Rooks don't have taxicab geometry. Their metric space is compact even on an infinite board. I think you're thinking of the wazir: https://en.wikipedia.org/wiki/Wazir_(chess)

Sure, but who's reading the conversation to determine whether it "looks suspicious"? A regex? A neural network? Who decides the algorithm, and do you really can believe they won't ever change it to serve other more nefarious purposes like suppressing dissent?

I am confused how we can define a rotation number of the map from S^1 to R^3 defined at the end of the second paragraph. R^3 is nullhomotopic, after all...

My preference is semi-compatible with both conventions:

First = 0 Second = 1 Toward = 2 Third = 3 …

This way, the semantic meaning of the words “first” (prior to all others) and “second” (prior to all but one) are preserved, but we get sensical indexing as well.

Beat me to it!

Working in HFT, my favorite is 1 nanosecond ≈ 1 foot

Can you make the checkboxes indexed from zero?

(Maybe I am too dogmatic)

> You think mathematicians had it all wrong for centuries

As a mathematician, yes, I do. Pretty much everything becomes simpler if you treat zero as the first natural number.

> Incidentally, I find it amusing that in Europe, the ground floor is zero, while in the US, it's one.

I really think it makes no sense to number the ground floor as 1. This means if you want to know the height of the nth floor, you have to multiply the height of a story by (n-1).

There are a ton of other cases where you have to needlessly subtract 1 when people use 1-based indexing. To name a few

- Dates: why did the 21st century start on 1/1/2001? Why are the 1800s the 19th century? It doesn’t make any sense. If we indexed from zero, today would be 5/0/2023 (5 months, 0 days, 2023 years since the common era), in the 20th century. It all becomes so easy and intuitive. - Mathematical foundations: If we are using set theory to encode mathematics, how is the number 1 defined? As a set containing itself? This leads to paradoxes in many cases. As the set containing a different single element? Then we can call its contents 0. - Musical intervals: why do two thirds (ok, major and minor, but I’ll gloss over that) make a fifth? Does 3+3=5? The fact that musical intervals index from 1 significantly increases the cognitive burden for music theory. It becomes much easier when we index from 0. - Birthdays: Age is correctly indexed from zero, but it may seem counterintuitive that your first birthday is the day you are born. So when is your second birthday? The day you turn 1, of course. The word “third” sounds like 3, so it seems reasonable to me to introduce a new ordinal here (I like “toward”). - Computing: languages that use 1-based indexing are obscuring what is actually going on; they generally just subtract 1 internally from the user’s input. They have to, since indexing from 0 is fundamentally more efficient at the hardware level. 4 bits can only store 15 possible addresses if you throw away 0.

These are just a few examples and by no means an exhaustive list. Conversely, I have yet to know of a single instance where 1-based indexing makes more sense or simplifies things (aside from being more compatible with legacy features of our society).

After a while, when you think deeply about it, you start to feel that 0-based indexing is something closer to a fundamental truth, rather than simply a convention. Indeed, I propose that the only reason people find 0-based indexing counterintuitive is due to social conditioning.

And when you do need google, you can always just add `!g` to your search query. There are a bunch of other useful ones [0], my favorite is probably `!w` for Wikipedia.

[0] https://duckduckgo.com/bangs

I disagree on the zero-based indexing complaint. Indeed, the fact that Julia indexed from 1 is the sole reason I will never use an otherwise great language. I can’t comprehend how people came to the conclusion this was a good idea.

For anyone wondering if the speed of light is a concern, a good mnemonic is that a foot is roughly equal to a nanosecond. So a millisecond is long enough (by a factor of ~50000) that camera placement doesn’t matter.

One of many things I learned from [0] is that the vast majority drownings happen in crowded pools with a ton of floaties. It’s so easy to miss a kid falling in. Those floats are supposed to keep kids safe, but they’re a lot closer to being death traps.

[0] http://spotthedrowningchild.com/

Put more briefly, gravity does not produce a compressive stress in the phone in free fall. The external force from the table applied to the phone sitting atop it does create compressive stress. Ergo, the situations are fundamentally different.

The payload still contains a list of other inodes though

My hot take is that it should be called the L^(1/2) norm. Many theorems and formulas become a lot easier to state if you redefine L^p as L^(1/p).

For instance, under this notation, the dual of L^p is just L^(1-p). And Littlewood’s interpolation inequality is a lot easier to remember, since the exponents used come directly from the coefficients in the convex combination:

If r = ap + bq, where a and b are nonnegative and sum to 1, then |f|_r <= (|f|_p)^a (|f|_q)^b

They may well. But if we ban research altogether, the only ones with access will be governments. At least with an open system there would be some competition.