Moreover, EML is complete in a way that your suggested function isn't: If you take a finite combination of basis functions, can it build periodic functions? Hardy proved over a century ago that real (+,-,/,*,exp,ln) can't do this (and answering the paper's unresolved question about similar real-valued functions in the negative). EML being able to build periodic functions is a lot less surprising for obvious reasons, but still pretty neat.

It gets a bit more difficult for the complex domain because you need rotation.

[0] https://github.com/francisrstokes/githublog/blob/main/2024/5...

It's also pretty easy to find a set of patches that have to be applied in order. Then someone copies those patches onto another divergent tree, which has it's own set of custom patches without renaming. This is dangerous in git and probably sensible in pijul.

Haven't use pijul in practice, but it's not hard to imagine being better than git here.

This is simply a reflection of my beliefs though, not an objective reality of the world. I trust that the TRM for my chip accurately reflect the details I can't observe for myself. Many devs don't even go that far down and trust that their OS, or programming language to behave as they expect. We're all dealing with black boxes on some level.

To quote a reasonable definition from an actual scholar on this subject, Jesper Sorensen:

    Thus, magic is generally conceived of as referring to a

This pretty much perfectly describes how programming is perceived by normal people. I could also quote Malinowski, who argued that magic must have a kind of "strangeness" to differentiate it from non-ritual speech. And programmers regularly describe difficult bits of code as magical (e.g. magic constants, or fast inverse square root) even though these are easily explained in most cases.

Anyway, another lens to look at kinship relationships through is as a resilience strategy to volatile conditions. Any given stress (drought, job losses, etc) are unlikely to affect everyone equally, so the network functions as a safety net under many conditions.

Venture capital applies a similar strategy in the other direction if you squint a bit. It's impossible to predict who will succeed a priori, so the capital is spread to many different bets simultaneously in the hope that the successes outweigh the failures over time. Many of the "rituals" in the VC ecosystem (ghost hiring, puffery, fad chasing, etc) aren't particularly useful for any individual company's success, but I don't think many people here on HN are going to argue it's not economically effective as a whole.

All I did was keep it offline. Didn't even need charging, because it got enough power when I loaded it with new books every couple of weeks.

Regarding algebra, we know very little about precolonial mathematics. Maya mathematics we've figured out from the calendar system and has zero plus the basic operations. Aztec mathematics seems to have had the same, and we're pretty sure they understood fractions based on how they recorded land area (recording field dimensions) and unit conversions between different length measures. Our knowledge is limited by the very small amount of preservation there was, not because they didn't invent other mathematics.

Similarly people in what's not the US had leisure time for things like experimentation, hobbies, and pet birds. We know they had preferences on certain numbers (3 & 4 acted as their equivalents of lucky 7, for example).

Plus, many of the groups around them did not use the same script despite having comparable levels of technological development. The Maya, who did have true writing, were not massively more advanced technologically.

Moreover, we have records from some of these precolonial intellectual traditions in the Americas. The nahua genre of huehuetlatolli is an excellent example in many ways. The selectively preserved bits we have resemble something closer to Confucianism than mathematics, but keep in mind we have a narrow selection from a single genre in a much wider landscape.

In what's now US territory, proto-writing systems (emoji are a modern example of these) existed. There were also intellectual traditions associated with them, particularly among southwestern groups like the Puebloans. Those are relatively closed to academics for a variety of historical reasons and consequently understudied, but we know they existed.