antognini

Orbital mechanics can be counterintuitive. There was a fairly basic orbital mechanics problem that caused some debate among physicists back in the 1970s. The problem went like this:

You are in a spacecraft orbiting the Earth. You distribute a bushel of apples throughout spacecraft so that they are at rest with respect to the spacecraft. After a long time, where do the apples end up?

Hannes Alfvén (more famous for Alfvén waves) argued that they would bunch up together in the middle of the spacecraft. But Michel Hénon (correctly) proved that half would end up in the bottom front corner, and the other half in the top back corner.

I wrote up a blog post explaining the solution a few years ago: https://joe-antognini.github.io/astronomy/apples-in-a-spacec...

Yes this is another important difference between human auditory perception and classical signal processing algorithms. Typically when processing audio we take a Fourier transform and then throw away the phase information. Mostly the amplitude information is all you need to understand a sound, but the ear actually is capable of picking up phase information.

(I thought this was discussed at some point in Lyon's book but it's admittedly been many years since I read it, so I can't remember for sure.)

If you want to get really deep into this, Richard Lyon has spent decades developing the CARFAC model of human hearing: Cascade of Asymmetric Resonators with Fast-Acting Compression. As far as I know it's the most accurate digital model of human hearing.

He has a PDF of his book about human hearing on his website: https://dicklyon.com/hmh/Lyon_Hearing_book_01jan2018_smaller...

Around 95% of the OpenAI engineers signed a letter to the board threatening to quit unless he was reinstated.

I'm guessing the idea is that in GR, the solution for a black hole with charge looks different from one without. So in principle you could infer the charge of a black hole based on the curvature of spacetime.

They do, but there's just not that much mass compared to stars.

This system, OJ287, is perhaps the most important system we have for understanding what happens to supermassive black holes after a galaxy merger. This is the so-called "Last Parsec Problem."

When two galaxies merge, their supermassive black holes fairly rapidly sink to the center of mass of the newly combined galaxy via dynamical friction and enter into a slow orbit around each other. Over time, the SMBHs kick out interloping stars, which removes energy from the orbit and causes the two SMBHs to come closer together. If the SMBHs were able to get within ~0.1 parsecs of each other, gravitational wave radiation could take over and cause the orbit to shrink fairly rapidly and lead to the merger of the two SMBHs.

However, the theoretical models we have generally predict that at about 1 parsec, the SMBHs have kicked out all the stars in their neighborhood, so the process stalls out. In practice we don't observe many SMBH binary systems (OJ287 being the main exception), so there must be some mechanism that causes these systems to shrink from 1 pc to 0.1 pc. But we don't know what it is. The hope is that detailed studies of the orbit of OJ287 can provide some clues as to what that missing mechanism is.

"If I have not seen as far as others, it is because giants have been standing on my shoulders." --Hal Abelson

I can't speak to OpenAI's specific setup, but a lot of startups will use a third party service like Carta to manage their cap table. So there's a website, you have an account, you can log in and it tells you that you have a grant of X shares that vests over Y months. You have to sign a form to accept the grant. There might be some option to do an 83b election if you have stock options rather than RSUs. But that's about it.

The music is notated as if there had been no detuning so that you can use the natural finger positions. (For example, a note that is notated as a C would actually sound as a B.) The trade-off is that it makes some of the intervals look wrong, but you do get used to it.

Bach's 5th cello suite also uses this technique where the A string is tuned down to a G. (The technical term is "scordatura.")

The Bach Cello Suites are deservedly famous, but if you are looking to branch out to other solo cello music I recommend listening to Zoltan Kodály's Sonata for Unaccompanied Cello. After the Bach Cello Suites it is probably the most important piece in the solo cello repertoire. One of the unusual features of the piece is that it calls for the bottom two strings to be tuned down half a step which gives the cello a darker timbre.

https://www.youtube.com/watch?v=phygv_Et9sQ

> The oldest maps in the world and in Europe are oriented North at the top

This isn't true, the oldest maps from the Middle Ages were oriented towards the East. (In fact the very word "orient" refers to the East.) The convention of putting north at the top is only a couple of centuries old.

It's nice to see this reference. I'm currently reading it and about halfway through (making my way through the chapter on Quantum Logic).

The discussion of the EPR paradox and the Kochen-Specker Theorem was really very illuminating.

Planetary and moon mass black holes are ruled out by gravitational microlensing surveys. Microlensing puts an upper bound on the mass of primordial black holes at ~1/5 the mass of Ceres.

Shameless plug, but I have a podcast about the history of astronomy and did an hour long episode on the Antikythera Mechanism a little while back if you're interested in more detail: https://songofurania.com/episode/022

The condition is the former. The probability distribution spans the full dimensionality of the space. Basically, the result will hold for an infinite number of dimensions and a finite number of steps. But it will also hold if you take both the number of steps and the dimensionality to infinity while holding the ratio N_steps / D constant with N_steps / D << 1.

The behavior of a random walk in a high dimensional space can be counter-intuitive. If you take the random walk trajectory and then perform principal components analysis on it, it turns out more than half of the variance is along a single direction. More than 80% is along the first two principal components.

To make matters even more surprising, if you project the random walk trajectory down into these PCA subspaces they are no longer random at all. Instead the trajectory traces a Lissajous curve. (For example see figure 1 of this paper: https://proceedings.neurips.cc/paper/2018/file/7a576629fef88...)

One thing that stands out to me about choral music is how much smoother it makes dissonance sound. Eric Whitacre is one of the most popular living composers of choral music and he routinely uses huge tone clusters in his works. When sung by a choir, his pieces sound dreamy and atmospheric, but if you were to play them on the piano they would be much more challenging to listen to. I have a theory that choral music tends to be sidelined by more "serious" classical music for precisely this reason.

As an addendum, for anyone interested in choral music I highly recommend listening to Caroline Shaw. She is among the most interesting new voices in the genre. Her piece Partita for 8 Voices [1] won the Pulitzer Prize a few years back. For a somewhat more accessible piece I also really like Its Motion Keeps [2].

[1]: https://www.youtube.com/watch?v=NDVMtnaB28E

[2]: https://www.youtube.com/watch?v=oT1PqR97urc

As a counterbalance to the "renegade" character of these kinds of podcasts I do recommend Sean Carroll's Mindscape podcast. He does a good job representing the "establishment" position in physics, so to speak.

A good episode to start with is "The Crisis in Physics" in which he (unusually?) argues that there is no real crisis in physics.

https://www.preposterousuniverse.com/podcast/2023/07/31/245-...

Based on the code in the repo it looks like they designed the chip in verilog and then ran it in a simulator. But if they have the verilog code in principle they could send it off to a fab and get real hardware back.

There's an interesting extension of the Central Limit Theorem called the Edgeworth Series. If you have a large but finite sample, the resulting distribution will be approximately Gaussian, but will deviate from a Gaussian distribution in a predictable way described by Hermite polynomials.

https://en.wikipedia.org/wiki/Edgeworth_series

> Right now I'm trying to figure out how to consistently make $1/day as a POC exercise.

You can do this with the following strategy:

1. Buy $10,000 of Treasury bonds.

It might be more interesting to target a particular Sharpe ratio rather than an absolute dollar amount since that will be proportional to the amount you invest.

> when the realignment caused ten days to be subtracted from the year, mobs across Europe attacked Jesuit houses to protest the time stolen from them

The outrage over the implementation of the Gregorian calendar had more to do with landlords in some areas charging a full month of rent for a month that lacked 11 days.

In addition to his more substantial pieces that others have mentioned, the real turning point in his music was a very small piece called Für Alina:

https://www.youtube.com/watch?v=jvXy69eF__Y

Prior to this he had composed in the dissonant, serialist style that was expected of "serious" art music in the middle of the 20th century. This was the first piece where he broke with the contemporary style and introduced his unique "tintinnabuli" style.

If you have even a basic familiarity with music theory it's worth taking a look at the structure of the piece because it's surprisingly simple for the effect. As the right hand plays the melody, the left hand simply plays notes from a b minor chord, with the particular note being whatever is just beyond one octave below the note that the right hand is playing. However there is one exception towards the end where the left hand plays a C# instead of a D as it would be expected to, and this marks the climax of the piece.

If anyone is interested in getting into cocktails I really can't recommend Cocktails with Suderman enough. The early posts are free and go into the theory of how cocktails are structured and why they work. Once you start to understand the structure of the major cocktails it makes it a lot easier to understand how you can play with the ingredients and make something new.

For instance, tons of cocktails fall into the "sour" category. They usually have proportions of 2:1:1 or 3:1:1 of a liquor, a sour, and a syrup. If you have rum, lime juice, and simple syrup it's a daiquiri. Swap out the lime juice for lemon juice and the rum for whiskey and you get a whiskey sour. Swap out the simple syrup for honey syrup and you get a Gold Rush. Use tequila, lime juice, and a blend of agave syrup and Cointreau and you have a margarita. Gin, lime, and simple syrup is a gimlet. And so on.

Also, as others have mentioned, the quality of the ingredients and the brands often matter a lot. A Manhattan calls for whiskey, sweet vermouth, and bitters, but the choice of whiskey and vermouth makes a big difference in the character of the drink. (And if you are using old vermouth that has been sitting out on the counter for a few years, or making a drink with bottled lime juice, it's just not going to turn out all that good.)

https://cocktailswithsuderman.substack.com/

This is a really good overview. However:

> It actually needed more cycles to explain than the geocentric version of the model!

This part is not true. The main advantage of Copernicus's model was that it reduced the number of epicycles needed. In the Ptolemaic system every planet (except the Moon and Sun) required an epicycle with a period of one year, which we now know was needed in order to account for the relative motion of the Earth on its own orbit. In a heliocentric system these epicycles could be eliminated. Copernicus presented his model more in terms of it requiring fewer calculations.

That's not exactly what is meant by luxury beliefs. Luxury beliefs aren't simply beliefs that rich people hold. It more refers to social opinions which would (allegedly) impose high costs on the poor, but from which the wealthy would be insulated from the consequences. Something like "defund the police" is usually pointed to as an example of a luxury belief. The poor, who live in high crime areas, would see crime go up and bear the brunt of the consequences. Whereas the rich, who live in pricey, low crime neighborhoods, wouldn't see much of a change and would be able to afford private security anyhow if they did.

How does Kete differ from REBOUND? (https://rebound.readthedocs.io/en/latest/)

Worth noting that this paper is from 2009.

For anyone interested they released the code about a decade later: https://arepo-code.org/getting-started

There's a pretty detailed description of TPUs in the latest edition of Hennessy's Computer Architecture. (Hennessy was also involved with the design of the early TPU architectures if I recall right.)