For some reason, voiced consonants are much funnier than unvoiced consonants. Is this culturally invariant? who has done the research
Calling the pope "the bope" is literally one of the funniest things possible. Young bope. The antibope
colinearity is weird cuz like
it’s sort of like an equivalence relation… but it takes three arguments
like, there’s a notion of symmetry (if points x y z are colinear, than any permutation is) there’s a notion of reflexivity (x x y are colinear) and there’s a notion of transitivity (if x y z and y z w are colinear, then x y w and x z w are colinear) and just from that you get “equivalence classes”, which are… lines.
like that’s, very equivalence-relationish, yknow?
so now, we oughta drop the symmetry condition, and get… like. some sort of order notion?
you are correct, of course, but like
yknow, categories! categories are categorified ordered sets and groupoids are categorified equivalence relations, so… if we categorify here, what do we get? some sort of… weird categorial incidence geometry?
i mean the appropriate context to work in here is… distributors, right? profunctors?
In caramelo’s book she internalizes the notion of composition as being a relationship that three arrows can be in? like, f and g and h=gf are in a “one being the composition of the other two” and my thought is in this case you would probably have something like
given a… 3-domain morphism f: X->Y->Z and a 3-domain morphism g:Y->Z->W you get two… composites? X->Y->W and X->Z->W? The associativity axioms are going to be… take a long time to list
I mean, using the nerve you can think of a category as a simplicial set with unique inner horn fillers. It sounds like maybe what you want is a functor from the full subcategory of Delta^op on all objects except the 1-simplex, with unique inner horn fillers, adding the condition: a diagram on the union of the 1- and 2- faces of the 3-simplex extends uniquely to the whole 3-simplex. That way you have something sort of like a category where you threw away morphisms but you still have "compositions" (2-simplices) and a higher associativity law.
I’m really enjoying Eco’s The Island of the Day Before, which features this absolutely true story as a major plot point. It’s making me rediscover an attraction to a genre I don’t know the name for, “novels where the plot is a transparent skeleton to have the characters talk about ideas.” Only examples I know are other Eco books, The Magic Mountain, and maybe White Noise.
Some of Greg Egan’s books are sort of similar (I’m thinking of the “Orthogonal” trilogy mainly, others I read too long ago to remember), in that the plot is a thin excuse to have the characters talk about weird fictional science
mx-bones-deactivated20160831
I drew/made characters based off of chess pieces
Reblogs are better than Likes
full picture of the pawns:
Britain has decided to leave Europe. Where will it go? Adrift without a leader, it will likely be carried north on the warm North Atlantic Current. Fluid dynamics simulations suggest it will eventually lodge between Iceland and Greenland. The fate of Northern Ireland is less certain.
I’m finally understanding,. Phew, think i’m finally understanding,. Nor do i think i’m finally understanding,. Neither nor do i think thats so neat if they rereleased it on eshop first, and then see how they work, and their actions as good, i mean first rate, in contrast to everything lowly, low-minded, common and plebeian. Neither nor there but it’s not especially difficult, for the love of everything fraggable, epic fail, minecraft, xbox, dirt clumps, the air, and even return to the lizards.
I’m so glad kalny is finally beginning to understand
crabs are so gentle, they can be so kind. their claws? precise little things, so careful in the sand, so careful with food. they do what they must to live and wave their claws to express their joy to the world for giving so much to them, for giving such kindness to these creatures known as crabs. please be gentle to crabs
i was on. a new sleep medication last night
Verbal brain noise: “Wallace and Gromit in ‘The Wrong Aesthetic’”
memeufacturing-deactivated20161
youre pissed off because the trolley was supposed to come at 3:30 PM but it’s 3:53 PM now
Eight Rainbows! WOW Lehigh Valley, PA [960 x 960]
I quite like that Pounded in the Butt by my Book, ‘Pounded in the Butt by my own Butt’ is a thing, but it just feels cheap and uninteresting to add another layer of ‘book’ to each sequel. They should keep going up further levels of abstraction.
-Pounded in the Butt by the Concept of Being Pounded in the Butt by Books, Butts, and Other Objects Not Usually Associated with Butt-Pounding
-Pounded in the Butt by the Ascending Levels of Abstraction Embodied in Chuck Tingle’s ‘Pounded in the Butt’ Series
-I’m not sure what the fifth book in the series would be, but I’m pretty sure it would be some sort of basilisk.
Pounded in the Butt by the Human Mind’s Incapacity to Deal with More Than a Few Levels of Recursion, Condemning Us to Die in the Shallows of an Incomprehensible Intellectual Ocean, Drowning in Trivialities While Being Pounded in the Butt.
Pounded in the Butt by the least complicated string that represents a Turing Machine whose behavior is not computable under ZFC and whose syntax consists only of clauses of the form “Pounded in the Butt by X”
postmarxed-deactivated20190429
Tired of The Discourse? Try…
TECHNO-PRIMITIVISM
I am alone in an asteroid cave hitting the LOUD KUSH I delved from my
AUTOMATED HYDROPONIC DANK SPACE WEED MINE!!!!
MEET ME THERE!!!
@jadagul (splitting off the infinite trolley thread which is getting long)
So there’s a lot to unpack there.
My post was assuming the usual real line, not the long line. In the regular real line, you just can’t get aleph-1 people into it without having aleph-1 people in some arbitrarily small interval. (Sketch of proof: choose an epsilon > 0. The line is a union of countably many intervals of length less than epsilon, and a countable union of countable sets is countable, so at least one interval must have uncountably many people in it).
On the long line things are different. We do have to back up and define things more carefully, because typically a “measure” only outputs a real (or complex) number or infinity, and so you can’t have a set with measure aleph-1. But it’s easy enough to route around that (as long as you can define the idea of adding infinite cardinals sensibly, which I think you can).
Then sure, you can take the long line and put one person in each [0,1) interval. There will be aleph-1 people on the track at “the same density” as the aleph-0 track.
But this is where we get back to my original complaint, which is that some (almost all!) people will never get hit by the train. Not only will they not get hit in finite time, they won’t get hit in countably infinite time. The train doesn’t have a way to get off the “usual” line onto the “long” part of the long line.
Basically, we say something is countable if for every element, you know how many elements you have to go through to get there. The set may be infinite but each individual element is only finitely far into the list. Which means you can ask questions like “when does the train hit this person?” Or “how many people will get hit before this person gets hit?” and have well-defined answers.
In uncountable sets, by definition, you can’t ask those questions. You can order an uncountable set (which means that for any two elements, you can ask which comes first). And if you believe in choice you can well-order an uncountable set (which means that for each element, there’s a “next” element–but not necessarily a “previous” element! There is, however, a “first” element). But none of that is enough to ask questions like “who is the fifth person to get hit?” or “How long will it take before John gets run over?”
So yeah, if your set is “the set of points on the real line” then there’s a natural “total order”. (Although there isn’t really a natural well-order). So you could say “after time t=1 these (uncountably many people) have been run over.” But you couldn’t ask who gets hit first or anything.
My understanding is that “countable” is a description of a cardinality of a set, not of its order type, which is (confusingly) the aspect that is relevant for questions of counting one by one.
(This is just the point @bowtochris made about the original post, except until now I was too confused to understand it)
So, for instance, consider ω+1. ω is just the order type of the natural numbers:
0 < 1 < 2 < 3 < …
Then ω+1 corresponds to taking the natural numbers and adding on an extra element that’s greater than all of them:
0 < 1 < 2 < 3 < … < 0′
This thing has the same cardinality as the usual natural numbers, so it’s countable. But with order type ω, for any number, we can define how many steps it takes to get there. With order type ω+1, we can’t do this with 0′. (And since the original picture just stated the cardinality, we can’t tell which of these we are dealing with.)
Of course, since these are both countable, we can put them in one-to-one correspondence, and thus rearrange the one with 0′ to the one where you can count to anything, including the numbers what 0′ gets mapped to. So at worst this seems like an “ordering issue” rather than some issue with 0′ being “so far out” that it can’t be counted to.
But now consider the uncountable case. Specifically, consider the first uncountable ordinary ω_1 (used to make the long line). It orders all the countable ordinals, of which there are uncountably many. So from one perspective, this contains all sorts of things you can “never count to.” On the other hand, for any x∈ ω_1, the set of elements of ω_1 less than x is countable. So wherever you are in ω_1, any inability to “count to that point” is again just an “ordering issue,” no worse than in the above case.
I guess this is just another way of stating your point that the train can’t ever get to “the ‘long’ part of the line.” However, I don’t think this makes the original picture or problem somehow ill-defined. There’s nothing wrong with depicting the uncountable people on the second track as a first one followed by a second one etc. – this implies that they are well-ordered, but ω_1 is well-ordered (even without the axiom of choice, I think?).
On either track, you can have various order types, implying various people who can’t be reached by counting – you can even have countably many of these on the first track. But on the second track, no matter what the order is, you must have uncountably many people who can never be hit. I’m not sure the “uncountably many” is the important part here – it also just seems important that you can have zero people who can never be hit on the first track, but can’t on the second. But “people who can’t be hit” isn’t a concept that applies only to the second track – it’s just that on the first track you have somewhere between 0 and aleph_0 of them, while on the second you have aleph_1 of them.
Of course none of this is at all in the spirit of the original problem, since it gives you no way to hit “more people” on the second track. Which is I guess what you’ve been saying. But I don’t think this is because you can’t possibly answer “how long until John gets hit?” for the second track. As on the first track, the answer will either be “[some finite time t]” or “never.”
(I should say, again, that I am a a complete newb at all of this and am basically just thinking through the process of learning basic stuff about infinite cardinals and ordinals. So I apologize if this is tedious or irritating for that reason.)
(On another, uh, track entirely – it’s funny how utilitarianism breaks down with infinities. You could add another person to one of these tracks without changing the cardinality, like in Hilbert’s hotel, but surely that’s bad and not neutral, right?))
If the second track gets to be parametrized by the long line, then surely time can be parametrized by the long line as well. Then everyone on the second track gets hit eventually - it's just that most of them get hit "after the end of time".
But the main thing is the mental attitude. If you are running late and believe that saving time requires Fancy Driving you will probably make poor decisions that put people at risk. A better viewpoint is that your arrival time is already fixed once you step out the door, and the best you can do is get there safely.
ilzolende
Fancy Cycling definitely saves me several minutes each morning (at a cost of increased risk of my own death, as well as making a few pedestrians who overestimate the difficulty of bringing a bicycle to a complete stop uncomfortable), though.
Since you are very young, an increased risk of death could cost you 80 years, in which case I hope you are saving a lot of minutes each morning in exchange.
ilzolende
The only way I can avoid the intersection that is probably the place where you should probably look for me if I die in the next 6 weeks would be by adding several blocks to my commute and probably almost doubling the travel time. And I doubt my risk is that increased, I’ve never heard about fatal accidents along that route.
Surely passing through a certain intersection is never intrinsically Fancy