myWindoonn

Over three millennia ago, humans had the Bronze Age, which included two global markets (copper and tin) and had international trade without any central authority setting the prices.

You just said it. Scientific fields are not differentiated arbitrarily; they drift apart as their experimental needs diverge. Chemistry and particle physics used to be one field, back before the cost of particle accelerators diverged from the cost of chemistry labs.

Oh, you're not from the USA? So, uh, we have a lot of mass shootings. A common point of discussion is whether we should publically discuss the details of mass shootings, because discussion can easily excuse and glorify the shooters.

The dog whistle in your earlier post is that the mean old liberals wouldn't let you talk about violence committed by Muslims, but fortunately Donald's fans were there to give you a space; how generous of them.

Humans lost the war against memes, if there could have been a war, millennia ago. We are now ruled by memes like "language" and "currency" and "justice".

Sure, and see also https://en.wikipedia.org/wiki/BLIT_(short_story)

But, uh, any evidence that that's real? We should be careful with Gödel's results here; the Gödelian incompleteness of the human mind is that a human cannot consistently believe that everything they believe is true. It has nothing to do with sanity and perception: https://en.wikipedia.org/wiki/Doxastic_logic

Weird hill to die on, IMO. Remember when we were younger and there was immense pressure on cable news to stop sharing the details of mass-shooting incidents because it was glorifying the shooters and their violent means? What Reddit is doing is what we asked cable news to do.

(Also, like, stop blowing your dogwhistle so damn loud.)

Well, most of the claims and structures of that period have been discredited. We do talk about them a little, but mostly in the same way as the pre-Socratic Greek philosophers: They were wrong, and it's interesting to examine how they were wrong.

On one hand, I agree with you. I've had no problem studying philosophy just with what's free on the Internet, and haven't bought philosophy books since high school. On the other hand, you should not be in charge of hiring anybody whatsoever, as you are biased against people based on their life experiences.

Your snark is unhelpful. Here's some things philosophy undergrads should know from category theory:

* Size issues. All the problems in set theory are back with a vengeance. Exploring size issues makes it clear that Russell's Paradox is not a fluke.

* Topoi. A topos is a generalization of the past few millennia of maths, and their existence shows that maths is a multiverse rather than a single collection of rules. Some topoi witness refutations of LEM, making them valuable counterexamples.

* Yoneda's lemma. The core of pragmatic philosophy is that objects are not separable from their effects in the world. Yoneda's result takes that to its logical conclusion: An object is equivalent to all of its effects under transformation.

* Equivalence of categories. Rel is equivalent to its dual (Rel is daggered) and so is Hilb; the category Set* of sets with an extra point is equivalent to the category Pfn of sets and partial functions. These show us that parts of maths are self-symmetric beyond group theory.

In addition, why shouldn't adjunctions be covered at some point? Adjunctions can't be studied without category theory (look up "Galois connections" for a history) and they're hard to avoid once we're talking about enough categories of note. I bet that the adjointness of syntax and semantics is very relevant to philosophy of language.

Conway showed that Collatz-like functions are as hard as Halting, by creating a language called FRACTRAN whose programs are Collatz-like functions: https://esolangs.org/wiki/Fractran

In Lojban, "zoho" is an alternate spelling of https://vlasisku.lojban.org/zo'o which means "as a joke" or "in a joking manner".

As a PNW native antifascist, this reads like FUD. Evans isn't perfect, but you'd have to be completely out to lunch to miss what the Proud Boys are doing in the Portland/Vancouver area.

The proposed PoS scheme for ETH will run afoul of regulators as soon as a big-enough crime is financed on ETH. I do not need to put effort into destroying those things; they are ticking time bombs. PoS separates participants into pigs and chickens, and the pigs could find themselves liable as money handlers.

It's too bad that AGPL wouldn't have been more effective; this seems like a dead end for copyright-based copyleft in France. We'll have to make extra effort to phrase things in terms of contract-based copyleft.

Although, doesn't this suggest a meeting of the minds? Free Software is usually proffered and consumed without such a meeting. So was a contract actually formed? I'm skeptical.

I imagine overwhelming miners with legitimate but expensive work. The way to generate this work is relatively sensitive to low-level blockchain parameters. BTC happens to fit the approach, but ETH doesn't. This isn't surprising because the approach was originally invented for BTC alone, prior to the proliferation of many different blockchains.

I think that you're overreacting a little to an imagined strawman. We already teach kids a decategorified set theory in order to give them an understanding of counting. We don't take the next step into category theory, which is to explain mappings between sets: If I can trade one sheep for two goats, and I have five sheep which I all trade for goats, how many goats do I get?

Remember: Sets are 0-categories, so set theory is 0-category theory.

Arithmetic is just decategorified set theory. The main advantage of teaching arithmetic via set theory is that it allows for building intuitions about counting.

It shouldn't be surprising that two sheep plus two sheep is four sheep. We can go further. Suppose that we have lots of longhair sheep and shorthair sheep. If we choose some sheep, how many ways can we have some shorthair and some longhair? This gives exponentiation intuitively, so that we could ask how many ways we could choose zero sheep from a collection of zero sheep, or in other words, why zero to the zeroth power is one.

The parts of category theory that you're imagining, with the morphisms and natural transformations, doesn't have to be taught before arithmetic. It can be taught when lambdas are first introduced, when we write "f(x)" on the board for the first time.

I'm working on destroying proof-of-work blockchains. I have a plan for BTC, but I'm not sure how to approach ETH. Advice would be appreciated.

And yet, you provided none. Curious.

(I've been attacked by dogs multiple times, and indeed, they warn before attacking.)

u'i xo'o xu la pygy ku jai logji .i pe'i so'i valsi .iku'i na'e logji

Since nobody had the temerity, I'll answer. If nobody had to justify their existence, then our society would not need systems which destroy people. It's that simple, and the folks using downvotes instead of words should confront their biases.

You really don't want to try a Wikipedia slap-fight with me. From my original link, at the very top of the page, in the first paragraph:

> In mathematical logic, Goodstein's theorem is a statement about the natural numbers, proved by Reuben Goodstein in 1944, which states that every Goodstein sequence eventually terminates at 0. Kirby and Paris[1] showed that it is unprovable in Peano arithmetic (but it can be proven in stronger systems, such as second-order arithmetic).

Despite PA having such a big proof-theoretic ordinal, PA cannot prove Goodstein's theorem. We need SOL.

Also, as one constructivist to another: Nobody cares la~ Hopefully you know the difference between PA, which describes NNOs, and HOL, which is ambient in each topos. Just because some topoi have NNO (just because HOL can host PA) and topoi recognize Goodstein's theorem (because Goodstein's provable in HOL) doesn't imply that all NNOs can witness Goodstein.

Indeed, double-check your understanding with the following quirk: In the topos Diff for synthetic differential geometry, the natural numbers are decideable and countable, but the real numbers are not decidable (and in fact prove LEM false!) and uncountable. Due to smoothness requirements, the real numbers are fundamentally different from the natural numbers in Diff. These are two different objects, two different infinities, with two different topologies.

Proof-theoretic ordinal ε₀ isn't sufficient to prove Goodstein's theorem; the entire point is that PA has ε₀ as proof-theoretic ordinal and yet is not able to prove it.

The better point to make in the context of the parent comment is that ω is the first of many transfinite numbers; our ability to talk about multiple numbers "above infinity" is intimately related to the set theory which underlies Cantor's theorems. Infinities aren't just about some sort of mathematical game, but directly influence what we can define and describe.

Goodstein's theorem comes with a function on the natural numbers. Whether we can prove that the function works correctly, and indeed whether we can implement the function, depends on how big we allow infinities to be. https://en.wikipedia.org/wiki/Goodstein%27s_theorem#Sequence...

I will give you the charity here. I see what you're saying, and this would be an interesting discussion, but the author's chosen framing ruins it.

Nike is a poor choice for making this point, because their original business was making waffle-iron shoes in a garage. They could have stuck to being a specialty cobbler who only caters to the top stars of track-and-field sports. None of the abuses had to happen. The only sad thing that was obligatory in Nike's story was the death of Steve Prefontaine.

> It wouldn’t shock you to learn that Carlos hated the new Nike ads I texted to him. His exact words were, “I don’t want fucking activism from a sweatshop monopoly.”

As somebody who grew up in Oregon, this is precisely it. I don't just want Nike to change its outward branding; I want Nike to stop advertising. I don't just want friendlier campus life for women; I want Nike to stop employing. I don't just want Nike to move its sweatshops from one country to another; I want Nike to stop enslaving.

Nike should stop existing. Anything less is neoliberal simpering.

You're so close to having empathy for all people! Just keep going: What if nobody had to justify their existence?

Edit: Downvoters, try a little harder. Engage your emotional core. Really work those empathy centers. Think about it: If nobody had to justify their existence, and people just allowed each other to exist, then we wouldn't have to weigh whether sex workers are more deserving of rights than computer scientists. We could allow both; we could allow everybody.

Tone policing is boring. It sounds like you don't have evidence. Stop spreading anti-democratic propaganda; you sound like a cryptofascist.

I don't know why people are disagreeing with you. Look how many people are begging for "thoughts and prayers", a totally useless gesture with no medical benefits. Religious cures are an example of alternative nonsense. Ironically, it's not untested; we know that it doesn't work.

The author did not think through their argument very well. Mathematics is non-scientific (science requires maths!) and epistemic, so the existence of people who use science and maths for their epistemology is a counterexample to their entire framing.

Could we get a (2010) in the title?