daynthelife

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.

Just to add some data points, I’ve flown spirit many times (at least 20), have never paid any more than the base cost, and have never had any issues. Maybe it’s just that I go in with the expectation that I’ll receive no special service, but my overall experience has been fine.

Of course, I wouldn’t fly spirit if I had a complex flight itinerary or needed to be 100% sure I would arrive when expected. Then again, I’ve had more issues with other airlines (looking at you Alaska) as well, so go figure.

All that being said, the invisible variable most of us miss is plane maintenance. I don’t know what spirit’s record is in particular on this axis, but some airlines really skimp on maintenance costs, sometimes leading to entirely preventable disasters ([0] to name one of many)

[0] https://en.wikipedia.org/wiki/Alaska_Airlines_Flight_261

What about nation states? Do you really think the US military will avoid working towards AGI if they think it would give them a tactical advantage? Or the CCP? Or North Korea? Personally, if AGI gets developed, I’d rather the first iteration be in the hands of someone who doesn’t also have access to nuclear weapons.

Return of the Obra Dinn is also an amazing game with entirely 1-bit rendering.

https://store.steampowered.com/app/653530/Return_of_the_Obra...

All too prescient: https://www.destroyallsoftware.com/talks/the-birth-and-death...

One parody I expected to see, but didn’t, is the notion that instead of modifying the predicates on the “greatest possible X”, we can instead modify the word greatest.

For instance, suppose I define a custom quality “Quux”. An object is more quux the more purple it is, the more it resembles a unicorn, the more it exists, and the closer it is to the center of Time Square.

We can certainly conceive of a maximally quux object — imagine a purple unicorn in the middle of time square. Therefore, by Anselm’s argument, since quuxness is increasing with existence, there must actually be a purple unicorn in the middle of Time Square.

> It's like if all we remembered about Newton was alchemy.

It’s ironic you say this. Like Freud, and unlike Newton, alchemists did not use scientific methodology. Also like Freud, alchemists get an unfair treatment by modern society, being remembered only for their mistakes. Medieval alchemists developed and refined distillation and crystallization, discovered acids and minerals, and developed metallurgy through the extraction of metals from ore. Just like psychology after Freud, the scientific field of chemistry grew rather naturally out of the advances made in alchemy.

My issue with one based indexing is more philosophical in nature. I truly believe to the core of my being that zero is the first number, and that indexing from one is simply wrong. The evidence leading me to this conclusion is that I have yet to know of a single instance where a procedure or mathematical formula becomes simpler when indexing from one; yet there are so many that become simpler when indexing from zero. To this extent, I find it almost offensive that a language geared toward mathematicians would intentionally choose to index from one.

> The world population is on track to peak at a level only marginally higher than the current population.

What makes you assume that trajectory will continue if the average lifespan suddenly increases 3-5x?

If it weren’t for the one based indexing, I would use Julia for almost all my math research. Overall it is a very well designed language, and a ton of things just work.

But I can’t for the life of me understand how any language designer signed off on one based indexing.

This is probably a controversial opinion, but I think we should be careful what we wish for. Death is a necessary part of life. Without it, society will stagnate, overpopulation will become even more rampant, resources will become more scarce, and dictators will hold power for unbounded lengths of time.

As hard as it is to say for someone whose mom is battling cancer, I feel similarly about a complete cure for cancer. Death ultimately needs a way to come for us all. The alternative is so much worse.

There are some contexts in which division by zero is defined in a meaningful way. The most common such situation is the real projective line or its complex analogue, the Riemann sphere [0]. We’ll focus on the latter, since it has a richer structure. The Riemann sphere is essentially just the complex plane “closed up” (compactified) by adding a point at infinity. The metric is defined such that points of very large norm are all close to infinity, and hence to one another.

Any nonzero number divided by zero is infinity. Zero divided by zero is undefined. The operation of adding 1 has a parabolic fixed point at infinity.

The Riemann sphere is not a group, but it still has many very nice properties. For instance, the set of analytic maps from the Riemann sphere to itself is precisely the set of rational functions (together with the constant map infinity).

A much more profound statement is Thurston’s characterization of rational functions [1], which states that every orientation preserving branched covering map F from the sphere to itself is equivalent (topologically conjugate) to a rational map on the Riemann sphere, unless F satisfies a certain computable property.

In other words, maps on one of the most ubiquitous topological spaces, namely the sphere, are often best understood by introducing a structure where division by zero is allowed.

[0] https://en.m.wikipedia.org/wiki/Riemann_sphere

[1] https://pi.math.cornell.edu/~hubbard/ThurstonRatMaps.pdf

Is there a reason not to just install Linux (and dual boot into windows if you need it for some things)?

I suppose if it’s a work laptop they might not be too pleased with this.

Yes, but not by directly asking it.

`awk` users hate this one simple trick!

Not an original source, but the Wikipedia page [0] gives a good introduction. A contact manifold is then just a manifold equipped with a contact structure.

A more in-depth discussion can be found in many differential topology texts, e.g. page 581 of [1].

[0] https://en.m.wikipedia.org/wiki/Contact_geometry

[1] Lee, Introduction to Smooth Manifolds https://math.berkeley.edu/~jchaidez/materials/reu/lee_smooth...

Better than all other major browsers != good

Since the only real competition is chromium, safari, and edge, the bar is astoundingly low.

Do you have any advice for working around the 10,000 token rate limit when using aider? It seems to be a huge limiting reagent, as it makes it pretty much impossible to use on large files.

Conversely, there’s a running joke that you’re in big trouble if Terry Tao takes too much of an interest in your topic of study, since he will inevitably solve all but the hardest problems in the field.

The sci-fi plot I’ve wanted to write combines this with the idea of a non-orientable universe. A space shuttle goes off in search of habitable planets and happens upon a planet that looks exactly like earth, but with the continents reversed. It is earth, but as the travelers have done a full loop around the non-orientable universe, they now have a mirrored frame of reference. So they have to learn to survive as aliens among humans, not being able to eat the same food despite knowing everyone.

(Of course, this reader would have to suspend disbelief regarding the fact that earth should be billions of years in the future when the travelers arrived, and that the travelers would most likely be composed of antimatter upon arrival due to CP symmetry)

On a related note, starting from a circular orbit, it takes

1/(2sqrt(2) - 3) ~ 5.83

times more energy to throw an object to the center of a gravity well than it does to throw it out of orbit.

It doesn’t matter how close your initial orbit it, or whether you’re orbiting around the Sun or Sagittarius A*. The ratio is always the same, though gravitational assistance from other bodies often affects the calculations in practice.

I expect we’d send a satellite outside the Milky Way long before we get one anywhere near the center of the galaxy. Not that either mission seems particularly feasible with current technology.

The original email [0] actually describes it better than Wikipedia imo.

[0] https://seclists.org/bugtraq/1998/Dec/79

The “<A” notation indicates that the head of the Turing machine is positioned at the rightmost point to the left of the “<“, and is in state A. [0]

For instance, the notation `0^\inf 1^3 <B 0^2 1 0^\inf` is equivalent to `0^\inf 1 1 (B1) 0 0 1 0^\inf`.

[0] https://www.sligocki.com/2021/07/17/bb-collatz.html

That question is implicitly suggesting that the universe was created. If that turns out not to be the case, then not even an omniscient being could answer it correctly. It would be equivalent to asking “describe the true process by which the Earth came to be flat.”

Of course, humanity does not understand everything about the universe. For instance, there is still the huge open problem of unifying general relativity with quantum mechanics, which is essential to understanding the very early universe (the standard model starts to lose accuracy prior to 10^(-32) seconds after the Big Bang [0]).

But that does not mean humanity will never understand such things.

And in case you are thinking “we’ll never know for sure; we’ll only have theories”:

I contend that all knowledge is inherently probabilistic. To claim to know something with absolute, 100% certainty is a fallacy [1]. After studying math my whole life, I am pretty confident that multiplication of integers is commutative. Is it possible that I have misunderstood numbers for my whole life, or that I am hallucinating right now, or that all of humanity has made the same mistake throughout all of history without realizing it? Yes. Just very, very improbable.

But that does not take away from the notion of understanding. One can understand an idea, while simultaneously recognizing that there is a small chance their understanding is flawed.

[0] https://en.m.wikipedia.org/wiki/Inflationary_epoch

[1] The notions of “probability 1” and “certain” are actually distinct; for instance, if you flipped a coin for every integer, the probability that at least one would turn up heads is 1, even though it is possible for them to all land tails. That being said, the existence of real-life phenomena (cosmic rays, parasites, etc.) that could affect our minds at any given time ensures that no claims of knowledge can ever have probability exactly 1.

Analytic number theory has seen a fair number of such conjectures. The first that comes to mind is the Pólya conjecture [0]. The conjecture stated that for any positive integer N > 2, there are at least as many positive integers less than N with an odd number of prime factors as there are with an even number. The smallest counterexample is N = 906,150,258. [0] https://en.m.wikipedia.org/wiki/P%C3%B3lya_conjecture

The issue with sets is that they don’t capture the notion of multiplicity. One would like to say sqrt(0) = {0,0}, but {0,0} is just equal to {0} as a set. The CxC/~ formalism captures the possibility of multiplicity as well as the fact that the output always has size 2.

As an aside, the notation R x R means ordered pairs of reals. So for your definition, you would instead want 2^R as the codomain (i.e. the set of subsets of R).

The codomain should not be Z×Z — firstly, the square root is usually not an integer, but more importantly, there is not a canonical ordering of the pairs you get, especially if we allow negative/complex inputs. The map we really want is

sqrt: C -> (C×C)/~,

where C is the complex numbers and ~ is the equivalence relation generated by (a,b) ~ (b,a) for all a,b in C.