isotropy

So…if we had already been using a base-12 counting system when metric came along, we would have the best of both worlds.

Without necessarily endorsing the article's ideas....I took this to be like the diamond-inheritance problem.

If service A feeds both B and C, and they both feed service D, then D can receive an incoherent view of what A did, because nothing forces B and C to keep their stories straight. But B and C can still both be following their own spec perfectly, so there's no bug in any single service. Now it's not clear whose job it is to fix things.

Offer non-diluting liquidation preferences for 996 and we can talk.

OOPs = "object-oriented programming", BUT it's a more restrained and thoughtful complaint than just "objects suck" or "inheritance sucks". He cabins it pretty clearly at 11:00 minutes in: "compile-time hierarchy of encapsulation that matches the domain model was a mistake"

Ouch: fair enough.

CERN, for managing highly-synchronized beam pulses applied km apart from each other: https://white-rabbit.web.cern.ch/

Empirically, human-flipped coins have about a 1% bias toward the same side they started on: https://www.ams.org/publicoutreach/math-history/hap7-fifty-o...

I've seen a db mock work when 1) there was a small subteam in charge of the OR-mapping, schema structure, and included a DBA; and 2) also a design policy from the architect that all objects had to come out of factories. Under those specific circumstances, having the mock - used solely as a per-developer object cache imitating the factory interface - was critical for unblocking the people working on business logic and front-end.

I wouldn't structure a team that way now.

I like this - nice playing around. We usually think of this kind of tree as having directed edges from parent to child, e.g. from set to element. In your graphs, you're erasing the direction of the edges, which uncovers a neat little symmetry that I never thought about before.

All the (non-limit) von Neumann ordinals are of the form X+1 = {X, {X}}, where X is the previous ordinal in the set. If you just look at trees of this form:

X+1: X <- node -> {X}, or X <- node -> node -> X

then you ignore the direction of the parent-child relation, you get this:

X+1: X -- node -- node -- X

So that's why your trees are symmetric as undirected graphs; and of course, every lower ordinal has its own version of this symmetry, which is also contained in the tree. All the large gaps between sections correspond to node--node edges of the larger ordinals. Kinda neat!

They are different: in the U.S. that's why "freedom of the press" is also written down in the First Amendment, and historically, that's exactly how the U.S. courts have interpreted the phrase "freedom of the press" - as a (pretty) general right for anyone to use any media technology they can access to spread any ideas they want. There are always some limits, but from the start "the press" meant "the printing press", not "institutionalized news organizations". It's a general technology-usage right, not a specialized right for a certain group. Everyone is allowed to do more than just talk, or even shout. People can have different opinions on how wise that right is, but in the US at least, you are indeed free to broadcast your nonsense to millions of people, if you have the resources.

Alice is taking a small unfair advantage of every member of the community at once. A community and its practices is a form of commons shared by the members, so it's vulnerable to the tragedy of the commons. If one member acts in a way that deliberately goes against the trust, that's inherently unfair to the rest of the members because it tends to push everything toward a breaking point. If her goal depends on the community's existence or function (which if it doesn't, why is she even around?), then whatever her goal, Alice has gone after it in a way that takes unfair advantage of everyone else's commitment to the system. Even if Alice's action doesn't cause a final breakdown, she's moved things in the wrong direction for her own purposes.

Tone-of-voice example (not mine): "It. Just. Works." vs "It juuuuust works."

Thank you for sharing so much of yourself with us these past months.

I'm not sure "it can be generalized to an undecidable problem" really explains why it's hard....

Hah! I agree with this. :)

In fact, according to the Esolang Wiki [https://esolangs.org/wiki/List_of_ideas#Mathematics] , Gregory Chaitin apparently has built a Diophantine equation whose parameters encode an entire Lisp interpreter.

Yeah, this is a little bit subtle. Please ignore the lack of rigor below, but this is my understanding: They aren't looking at a particular polynomial like 4x + 3y = 2. That has a solution x=2, y=-2, but they don't really care about the exact value for (x, y), just that it's integers. They're more interested in the parameters: (4, 3, 2), and in general Ax + By = C. If you like, it's almost like hyper parameter tuning: what are the parameter settings for (A, B, C) where I can get this shape of equation to "work", e.g. give me acceptable x and y? A "Diophantine set" is a family of parameters that all work. It turns out you can think of "parameters of a given shape of Diophantine equation" as an exotic programming paradigm.

Fermat: x^N + y^N = z^N. The Diophantine set only has the number N=2, because Fermat's Last Theorem tells us that no other possible N will work if x, y, z have to be integers. This is just a finite set.

Other polynomial expressions work with an infinite number of parameter settings: Pell's equation is x^2 - N*y^2 = 1. In this case, every N that is not a square will work. This is an infinite set.

Because a lot of the parameter sets are infinite like this, the size of the parameter set are instead measured using big-O notation. For Fermat's Last Theorem, {N=2} is constant, so big-O(1). For Pell's equation, {N not a square} is O(N). For other Diophantine expressions, the parameter settings are O(N^2), or O(2^N), or any other growth function you want that's achievable with Turing machines.

And this is the essence of what MRDP proved. Robinson, Davis, Putnam, and Matiyasevich over several papers proved that if you could encode a set that grew roughly like O(2^N), you also could encode any other computable set in the parameters. Approximately, demonstrating an exponentially-fast-growing family of parameters for some specific Diophantine problem was enough for Diophantine problems as a whole to be Turing complete. Matiyasevich's clinching discovery was a concrete example using the Fibonacci numbers.

Fusion: Turbulence, plus Naiver-Stokes was known to be hard, plus adding in EM fields, plus the exothermic state change of the nuclei fusing introduces discontinuous jumps in the free energy.

Collatz: if you replace 1 and 3 with arbitrary parameters, Conway showed that this class of problems is undecidable, so any particular instance could be arbitrarily hard.

Not OP but for me, it’s that public answers here are available to all of us. That’s great!

I read this as basically arguing that our filters throw up too many false negatives, like Kariko, in a high-risk/high-reward environment. It’s saying the cost of false negatives is way higher than the system realizes, and that’s because the system has drifted to be too much like the collaborative, incremental workplace that most of us live in. Typical work teams pay a high cost for false positives when hiring, so they guard against them at the cost of way more false negatives. The doesn’t work as well for moonshot fields.

Danny Calegari's essay "Disappointment" in the Notices (https://www.ams.org/journals/notices/202309/noti2782/noti278...) is a nice reflection on how to think - and try to feel - about failures.

NEVER assume that information learned because of your job is shielded from insider trading, even for a completely different company. From ten years ago, here are two data analysts from Capital One who thought they could use the data from credit card transactions to jump the gun on quarterly earnings reports for retail stores. Never traded Capital One stock. Didn't matter - SEC hammered them.

https://www.sec.gov/litigation/litreleases/lr-23216

Yes.

https://en.wikipedia.org/wiki/NBA_salary_cap#Individual_cont...

"The maximum player salary is based on the number of years that player has played and the total of the salary cap. The maximum salary of a player with 6 or fewer years of experience is either $25,500,000 or 25% of the total salary cap (projected for 2017–18), whichever is greater. For a player with 7–9 years of experience, the maximum is $30,600,000 or 30% of the cap, and for a player with 10+ years of experience, the maximum is $35,700,000 or 35% of the cap.[19][33] There is an exception to this rule: a player is able to sign a contract for 105% of his previous contract, even if the new contract is higher than the league limit.[34]"

Quantum key distribution solves the sharing problem and will arrive sooner, for a certain budget.

Thanks, I appreciate that! For you personally, are you thinking more code-focused, what-can-I-do-with-this, or more theory, what-is-a-qubit/quantum-gate kind of stuff?

Trying to explain is dodgy - it never works for jokes, either. But I think they represent a bundle of interesting contrasts that hits a sweet spot for a lot of us. Most people have made a Mobius strip out of ephemeral paper and thrown it away after fiddling with it; these are hard-wrought, complex artisinal craftings from the same family of ideas. The idea of "Klein bottle art" at first sounds rigid and limited, but the variation shows lovely creativity and artistic sense. They riff off the low humor of a dribble glass by mixing it with the sophistication of advanced math. The artist stays down-to-earth and accessible, even though he's clearly walked quite a way down a particular road of practice and experimentation that the rest of us are only going to admire from afar.

You may be thinking of Polya's result, which lets the walker go anywhere on the grid, so there are more possible states than Poincaré allows. For a discrete system, Poincaré assumes (roughly) that the space of possibilities is finite.

Yup, had this job as an undergrad, too, in a national lab on campus. Standard process was something like rinse in regular water, scrub with detergent, spray off with de-ionized water, 5-minute dunk in aqua regia, dunk in more de-ionized water, then alcohol rinse and set aside to dry.

Wore butyl gloves and apron and a face shield. Accidentally raised my hands above horizontal once and didn't notice a trickle of acid over the edge of the gloves. Next time that shirt came out of the wash the sleeves were shredded.

Our aqua regia bath was also about 10 gallons, but it was in a WW2-era fume hood and it looked like it was made of some kind of metal in a concrete shield, that had been partially eaten away. One time a cockroach the length of my thumb fell into the bath while I was working - I heard the splash, and by the time I turned my head to see what happened, it was mostly just exoskeleton. I quit that job pretty soon after that.

V. cool! It's off topic, but what do the algorithms look like in that task?

Oddly echoes Asimov's "The Feeling of Power": https://urbigenous.net/library/power.html

Well, only for 8 years.

1000 998 994 986 970 938 874 746 490 ooops