Days since: 90

Character reset

Sometimes you feel like you spec'd the wrong stats, or went down the wrong skill tree. Not in a way that makes your character special, quirky, or unique, but just straight up worse at everything.

But in this game there are no resets.

So what's your only option here?

Comment on set theory as foundations

Response to a comment on a Youtube video. 

Comment: The "Do mathematicians always think numbers like this" question reminds me of computer science. When writing code, you don't need to know the exact assembly language instructions to know what a function does, or even the exact workings of the processor to do that instruction, the level of abstraction given by the name is enough and most people use that instead to go faster

My response follows:

Not sure if this might be too subtle/not useful for non-mathematicians, but I will post here regardless for anyone interested.

So, you raise a good analogy with the programming thing, and although practically speaking it's okay to think of numbers as abstractions, unpacking into nested sets, this mental model is actually a bit limiting and narrow-sighted. Numbers existed/were thought of/used by mathematicians for centuries before we decided to trick undergraduate math students into thinking that "everything is sets". It's kind of like saying that a car, and really everything in the world, is just Legos. I mean, sure, Legos are extremely versatile and you can think of everything as Legos but with extremely weird shapes and joints. This is... certainly a way of looking at things, but to insist that this is foundational, definitional is misleading. On top of that, there are competing theories which can lay claim to be "foundational" for mathematics, which other people have pointed out here.

Set theory is more of a tool that exists within, and alongside, other mathematical tools, rather than something that "underpins" numbers, and mathematics in general, as might be suggested here. It's just unique in the sense that it works to model a lot of mathematics, so it's a great tool to help mathematicians answer mathematical questions, about math itself.... if, of course, you decide to CAST numbers as SETS in this particular way. Indeed, there are times where casting everything into set theory is useful, esp. when you're asking mathematical questions about mathematics, e.g. "is mathematics consistent?" In fact these types of questions, fundamentally, are what motivated the whole mathematical community's foray into set theory and logic. But to turn around and claim that numbers, and for that matter all of math, is sets, is quite misleading, to the detriment of mathematics (which is a whole 'nother discussion). 

This is far better expressed by mathematician Andrej Bauer: 

When logicians speak of "foundations" of mathematics, they may give the impression that they are "building the cathedral" starting from its foundation. But it is much better to view what they are doing as a study of how the cathedral is built and how we can improve it. For instance, logicians have observed the fact that almost all of modern mathematics can be expressed in the language of set theory, but this does not mean that we need to "secure" set theory before the rest of mathematics can be done. History is my witness: geometry, algebra, and analysis existed before set theory and logic came along. 

Notice the key phrase CAN be expressed, not MUST be expressed. It's important not to confuse "A can be modeled as/written as/depicted as B" for "A is B". 

Put in computer terms, it's like the difference between "C++" itself and "C++ as implemented on a particular machine". C++ code itself isn't an abstraction of assembly language, if anything it's just a part of the C++ standards doc filed with the ISO. But if I compile and run it on my Dell, it gets compiled into assembly or CPU instructions or what have you. But that's a decision made by the computer, not C++. C++ is C++, and numbers are numbers.

Should mathematics be a humanities subject?

I saw this comment on a Facebook math group recently and ended up leaving a wordy reply. 

Some people say "math is part of the Humanities" and I disagree strongly. It seems that in some sense mathematics is related to science as just like science, math attempts to discover universal truths outside of human opinion. This isn't to say that it can't also be related to philosophy as it gets more abstract or that it cant be seen as a type of art (after all, we know some elegant proofs).

If we came across an alien civilization, their art, music, philosophies, and ideas will be different from ours. But their mathematics, just as their science will be the same as ours. Because it needs to be. Their pi would be our pi, they would just have a different way of expressing it.

My response below:

I'm honestly okay with math being humanities. Makes it feel more warm and approachable, as it should be. A de-humanization of mathematics (i.e. viewing it as some kind of universal entity external to the human realm) would be detrimental to mathematicians and non-mathematicians alike.

In my humble opinion, mathematics is created as needed by human minds through an intense series of abstractions -- but abstractions nonetheless, of real, human experiences and learned patterns.

Yes, there's a kind of universality to mathematics, but mathematics within the human context is expressed in terms of human thoughts. It is written by humans, to humans, and at the end of the day for (often extremely abstracted) human purposes and interests.

Yes, you can always extrapolate and say that mathematical theorems "exist" as some kind of objective "thing" and that we're just discovering them in a very selective and human way... but that's neither here nor there. I guess that interpretation is not that interesting to me. In a sense everything is "discovered" -- poetry, literature, what have you.

To me, mathematics as we know is a distillation of human thought. It's a human activity that serves a higher-order need for truth, without regard to specific application. We package and serve this in the form of results: lemmas, theorems, definitions. If philosophy can be considered a "humanities" subject, I'm okay with math being one.

You do hit upon an interesting idea when you mention "universal truths outside of human opinion". Although it seems a little offensive to the humanities to imply that they seek truths subject to human opinion (lol)... There are certainly different approaches within the humanities vs mathematics as it is done today. Tickles different parts of the brain, so to speak... so maybe there is some kind of hard distinction to be made along those lines.

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Japan

What does it mean to apologize? 

Imagine a scenario between Bob, the "victimizer", and Alice, the "victim" of some event, E. 

Alice expresses that Bob should apologize. But Bob retorts, oh my God, what do you want me to do? I'm sorry okay? I already bought you dinner that one night to make up for it, why are you still upset about it, and besides that was like three months ago? Really what do you want me to do about it, when will you get over this? Can you please just forget about it and like, never talk about it again? 

When Bob asks "what do you want me to do about it" the assumption is that it's Alice's job to teach Bob how to apologize properly. I suppose it's also Alice's job to teach Bob how to be an empathetic human being and learn to listen, really listen, to why Alice is upset.

Unsurprisingly none of this makes Alice feel any better about it or forget it. Worse still, the longer this goes on, Alice is sure that Bob will feel even more justified in using the "that was X months ago" excuse. 

Not only that, the following week Bob has a total change of heart and refuses to talk about E at all, refusing to admit any sort of responsibility. 

Throughout all of this Bob's close friend Charles wants to have an opinion about the matter and takes Bob's side. Bob, after all, supplies a lot of Charles' electronics through his store and even draws him really cool cartoons. I mean never mind that Charles once literally blew up Bob's place, it's all in the past anyhow. 

Anyways, Charles comes in saying that Alice should forgive Bob because I mean, Bob really did buy her that expensive dinner and he's a real nice guy, honestly and he's done so much for her so just be reasonable, okay? In private, Charles and Bob discuss how unreasonable Alice is being, sometimes surmising that Alice may just be trying to manipulate Bob into feeling bad, or even trying to extort him. 

Alice is left trying to justify her feelings to them by listing out those things Bob hasn't done. She mentions how Bob keeps waffling back and forth, says things which suggest he hasn't learned a thing and even contradicts the apologies he's made before, and most importantly constantly tries to avoid the subject or is more interested in burying/forgetting the past than actually confronting, resolving, and committing to that resolution.* 

But Alice knows that these are not the main point -- the real diagnosis being that Bob is not taking Alice's feelings seriously and listening to her, made clear by the above list, and the fact that whenever Alice tries to talk about how she feels, the automatic reaction from Bob (and Charles) is to doubt her or talk about why her feelings are wrong. The assumption, of course, being that Alice is being petty or manipulative. 

On the national level, is an apology any different? Just because it is between two groups of people rather than two people, does it mean that feelings are not involved? Is it only a formal act, involving reparations and a formal statement, maybe a monument or two, a footnote in the history books, and it's over and done with? 

When you apologize and the other person is still hurting, the move is not to say "well I apologized already so if something's still wrong you're the problem". What changes when you take this to the group, national level? 

It is a highly non-empathetic act to, as the apologizer, to set the terms of the "apology" yourself, and expect that the victim feel better about it. It is straight up offensive to explicitly cast doubt on the victim and their feelings on the matter. This often takes the form of saying things like "But I already apologized" or "Get over it already", which directly implies that the victim is being either petty or manipulative. And really, in what kind of apology is that the move? 

In my personal opinion, which I believe many share in this instance, I don't think the victim has to provide "facts and logic" to justify why they are feeling bad about something. If they feel that a particular apology was insufficient, that's because it was. At the very least, if they are incapable of apologizing properly, the apologizer shouldn't say or do anything to make it even worse. And third parties incapable of feeling how the apologizee feels should mostly stay out of it if not to offer general support. 

Is it possible that the Koreans government and Korean people are deliberately trying to make themselves feel worse, victimized? Sure. But I wonder why that is the natural conclusion for some people. It seems really off. 

You know, isn't it weird that collectively, Jews don't actively protest and say angry things about Germany, at least not to the extent that Koreans do about Japan? It can't be, can it, that Germany actually properly apologized, that their government and history books are consistently transparent about the matter, or that they have an amazing track record of atonement and establishing anti-fascist policy in government and education despite the lingering anti-Semitism of some? It's not anything to do with the fact that the conservative Japanese government is and has always been far too prideful and nationalistic to admit that their country has any history of wrongdoing, much less war crimes, rape, torture, massacre and that as a result their people are barely educated on the subject? No, of course not! It has to be Korea itself which is the matter.