2,302 karma · joined February 15, 2011
> I have no particular call for action. Please don’t cause any trouble for the journalist involved, both because that would be wrong, and because I suspect he did not personally want to write this and was pressured into it as part of the Times’ retaliatory measures against me.
(https://www.astralcodexten.com/p/statement-on-new-york-times...)
Before that, he did ask for public commentary on their plan to reveal his real name; maybe that's what you were thinking of.
(Before your post was edited, it was originally a comment that misrepresented the history of the NY Times piece by claiming he 'sent a flood of internet crazies' at them after they wrote it.)
There are different types of map that we call "X homomorphism" for different types of algebraic structure X (groups, rings, fields, vector spaces, modules, algebras, etc). In an abstract algebra course you'd probably first encounter the definition of a 'group homomorphism' (preserves the group's multiplication operation, whatever that is: f(x*y) = f(x)*f(y)), and then a separate definition of a 'ring homomorphism' (preserves the ring's addition and multiplication, which are the two operations you have on a ring - f(x+y)=f(x)+f(y) and f(xy) = f(x)f(y)), etc. The definitions are similar, but they are distinct: a group homomorphism is between groups, a ring homomorphism is between rings, etc. (There's also a more formal sense in which they're examples of the same thing, you'd look into category theory for more on that.)
So what's going on in your example? Well, you could define a simple type of algebraic structure where, for any instances of that structure, you can only ask the question "is x positive" for one of its elements x and get a yes or no answer, and then define 'homomorphisms' between such structures as maps that take 'positive' elements of the source space to 'positive' elements of the destination space (and vice versa). But I'm not sure you'd really be able to use it for much. (On https://en.wikipedia.org/wiki/Homomorphism#Definition, that'd correspond to having exactly one unary operation μ(x) = is_positive(x) and no other operations, not even addition.)
An example is reduction mod 5: it's a (ring) homomorphism because the relevant laws of arithmetic work just the same if you do arithmetic in the ordinary integers then reduce the result mod 5, or if you instead reduce all numbers mod 5 first and then apply special 'modulo 5' versions of those arithmetic operations. (E.g. 7 + 19 = 26 = 1 mod 5, but also (7 mod 5 + 19 mod 5) = (2 mod 5) + (4 mod 5) = 1 mod 5, where that last '+' is addition mod 5 instead of integer addition.) But you don't, given just '1 mod 5', know whether the original source integer was 1, 6, 21, -4, or any of infinitely many other choices.
Another example: projecting 3d space down to 2d by just dropping the third coordinate: (x, y, z) -> (x, y). That's a vector space homomorphism, but there isn't a way to recover the z-coordinate given just (x, y).
An example from the Haskell wiki mentioned above (I think you're referring to https://en.wikibooks.org/wiki/Haskell/Monoids#Homomorphisms) is the `length` function: given only the result of applying the homomorphism, `length(a)`, it's not possible to recover a.
(The rules do say that runners will be stopped and recalled if the reaction time limit is breached, which means that no race will actually happen in that case:
> 16.6 When a World Athletics certified Start Information System is in use, the Starter and/or an assigned Recaller shall wear headphones in order to clearly hear the acoustic signal emitted when the System indicates a possible false start (i.e. when the reaction time is less than 0.100 second). As soon as the Starter and/or assigned Recaller hears the acoustic signal, and if the gun was fired, there shall be a recall and the Starter shall immediately examine the reaction times and other available information from the Start Information System in order to confirm which, if any, athlete(s) is/are responsible for the recall. )
> the United States Supreme Court on November 20, 2023 rejected the Company’s petition to file an appeal against the orders passed by the US Court of Appeals, 7th Circuit
(I wouldn’t count impl trait in function parameters since that acts more like a generic type.)
That’s mostly incorrect, both are “otc” (over-the-counter) wherever you can buy them without a prescription. That’s what that means.
I don't think they are. Turing was a runner. He ran in the 2:40s for the marathon, which is a reasonably good amateur time even today, and was a few places away from making the British Olympic team.
(It's also ironic that you (understandably) refer to Bannister by his mile - he himself would rather have been remembered for his achievements in neurology.)
This is implausible to me: I'm on the west coast and my Alexa stuff wasn't working. Moreover, almost all Alexa devices in the US likely use us-east-1. This was true and hard-to-change as of a couple years ago.