Maybe-Mathematical Musings

@jadagul

I math, I dance, I argue weird philosophy on the internet.

8,149 posts

Higgledy piggledy isn't a difficult rhythm to write in if you can take time. But it is tricky to write a good higgledy piggledy where you sound natural and rhyme.

#poetry #higgledy piggledy

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Formal experiments make it so tempting to irritate followers with a conceit forcing unnatural snytax and wording on sentiments lacking in substantive meat. Rather than keeping a regular meter a proper expression of well-defined views has to conform to the structure of thought and proceed at the rhythm of actual news.

There's a linguist, Anne Cutler, who studied how everyday speech is affected by rhythm and rhyme. She wrote "The perception of rhythm in language". It's easy to read and it's well worth your time.

#language #linguistics #anne cutler #the perception of rhythm in language

Are all conditionally convergent series that don't converge absolutely 'equally' conditionally convergent? Or is there some way to measure whether one series converges more conditionally than another?

Ooh!

One of my favorite calc II theorems is the Riemann series theorem, which I would argue says that all conditionally convergent real series are equally conditionally convergent.

Specifically, if a series of real numbers converges conditionally, then by rearranging the terms of the series you can get the sum to be any real number, or infinity, or minus infinity, or \pm infty. The sum is determined by the order of the terms, and not by the terms themselves!

Sketch of proof: think about adding just the positive terms of the series. If that sum were bounded, then it would converge absolutely, and same with the negative terms. So the positive terms sum to infinity, and the negative terms sum to negative infinity.

Now pick a target L. Add up positive terms until you're above L, then negative terms until you're below, then positive terms until you're above, then... You'll never run out of either side, but the terms have to individually go to zero, so this converges to L.

In a complex series things are a little bit more complicated. Some series can be rearranged to get any complex number; some have some specific line in the complex plane they can be rearranged to sum to.

#math #analysis cw #riemann series theorem #calculus

For some reason, my brain is convinced the second line of a higgledy-piggledy should be "Cedric Diggory", with the first name pronounced as three syllables.

More recently it's also decided the third line should be "Sind einer Hand breit", with "Hand" drawn out for two beats, which makes even less sense.

Found myself wanting to say that "consuming text is easy and passive, unlike video which requires active effort to watch" and then realized this is the opposite of what basically every other human being would say.

#well. on tumblr you get the thunderous applause.

Yeah. I posted the same thing to Bluesky and got two (2) likes. And one of those is someone I met here!

(To be fair I have more followers here, but not a hundred times more.)

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Found myself wanting to say that "consuming text is easy and passive, unlike video which requires active effort to watch" and then realized this is the opposite of what basically every other human being would say.

#well. on tumblr you get the thunderous applause. #I recall watching Hank Green talk about how under intense stress he didn’t want to read a bunch of text #he wanted a video to explain things to him #and even though it should have been obvious that a VIDEO CREATOR likes video #my mind was moderately boggled #what do you MEAN you find video EASIER and lower effort #that’s not a real thing - via @tuesdayisfordancing

markwateneymemorialcrater

If I’m searching for specific info. Text is far easier to scan through. I am so tired of all tutorials and guides being videos now. Give me illustrated text files. I don’t want scrub through a 20 minute video for the 40 seconds of relevant info.

Video can be great for some things. But I think part of where someone might feel reading is “passive” while video is not, is that video is easy to ignore and let play on the background. You haven’t actively focus. But reading, you just naturally focus so it doesn’t feel as active.

kata4a said:

I don't know if this matches your experience, but one of the salient differences for me is that I can control the rate at which I read text. which is of course, a property of it being more "active," but it's a kind of "activeness" that feels less...stressful? energy intensive? like I'm not actually going to miss anything if I space out for a bit (because the text won't like, keep going without me)

I do think the two of you have basically nailed what I'm actually feeling.

Sure, you can put video on in the background and exert literally zero effort, but then I'm not going to process it either.

In practice, if I want to actually absorb the content of a video, I need to get headphones set up, turn it on, commit to spending some time watching it, and if I get distracted in the middle I lose everything, so it requires (1) a startup cost and (2) continual focus.

But for, say, a text website, I can just open a tab, and whenever I want to I can click over, read a bit, and then move on with my life. And that seems so low-investment to both start and stop that it feels very low in actual effort. If I leave the tab open the text will Get Read without me having to try to make that happen.

Related but distinct is that watching movies/TV can be stressful because fiction can be stressful, and in a movie I can't control the rate at which I'm experiencing it. That's also very definitely something I experience but wasn't what I was thinking about when I made this post.

Found myself wanting to say that "consuming text is easy and passive, unlike video which requires active effort to watch" and then realized this is the opposite of what basically every other human being would say.

tbh "religious liberty" always felt like a uniquely weak reason that you should be allowed to do something. "I know it seems bad, but have you considered that I'm doing it because it's important for no reason?"

idk like. even modern secular liberal societies display such a common penchant for using innocuous feature of religion as an excuse to harass and legally punish the other that an instinct to carve out protections for religious practices seems indisputably useful? otherwise you get situations like France's "muslim women can lose their jobs for wearing hats, even ones required to do said job," nominally coming from a place of secularism and no state religion and feminism and in fact just an excuse to harass muslim women.

so i think understanding "religious liberty" as providing a degree of presumptive (but not infinite) protection is a good instinct for society to have bc people are always trying to figure out new excuses to be dicks to members of social groups they don't like and religion is a major axis along which this dickish behavior occurs.

The other thing is, religious liberty frequently protects choices and behaviors over which people are willing to defy the state at great personal cost.

Insofar as we take "liberalism as armed truce between competing ideologies" seriously, it makes sense to be especially demilitarized on topics where people are especially willing to escalate.

#politics #religion #liberalism

One response to Gödel incompleteness is to postulate iterated consistency statements: instead of just PA one can work in PA+CON(PA)+CON(PA+CON(PA)), etc. Alan Turing’s phd thesis was about iterating this process transfinitely many times. I think at least the first few steps are usually considered unproblematic, we “know” PA is consistent, so we may as well postulate it.

But just consistency is not enough for this to be sound. Someone on mathoverflow pointed out this counterexample: If T is some consistent logical theory, then by Gödel’s incompleteness theorem T+¬CON(T) is consistent too. However, CON(T+¬CON(T)) implies CON(T), so T+¬CON(T)+CON(T+¬CON(T)) is not consistent. It feels pretty paradoxical, a theory that is consistent only as long as it doesn’t know it is…

I’m not sure what the philosophical implications are (any references to discussion is welcome). It would be a pretty funny cosmic joke if PA was consistent but PA+CON(PA) was not.

I feel like a lot of issues with Gödel stuff resolves itself when you drop the whole concept of “truth” from the situation.

(This is why I take issue with saying PA “is” consistent—you can prove its consistency under a number of axiom systems, I think including ZF, but that’s passing the buck to those systems.)

So what this says is, if you have a system of tools T that can’t generate a contradiction, we know by Gödel that T+¬CON(T) is also a tool system that can’t generate a contradiction. But if you add in another tool of course you get more degrees of freedom, and more potential to generate a contradiction somehow.

I feel that only shifts the problem to the other half. Like sure, if you stop thinking about truth then it’s not weird that one set of axioms is contradiction-free and another one isn’t. But then it is instead mysterious why Turing thought he could unproblematically postulate that infinitely long series of axioms! :)

I don’t see why it would be problematic. You can postulate whatever axioms you want!

The question is whether this models anything useful, and the answer is, obviously, “No, once the word ‘transfinite’ shows up you’re definitely not modeling anything useful.”

It’s much easier to just drop the assumption that every number has a successor; that’s an empirical approximation good enough for describing, like, grains of sand on a beach, but not actually useful for anything. And then the whole incompleteness thing drops right out because of course it relies on unphysically large quantities.

Sure, you can go with finitism. The problem isn't that it doesn't work; the problem is that it's a lot of extra effort to solve fake problems. You never have to worry about those issues in any real problem so you can just go ahead and axiomatically assume they never come up at all.

If you just go ahead and let the natural numbers be infinite, the real numbers be complete, and every set have a choice function, you get to avoid making a lot of really fiddly arguments and don't lose much of anything.

#math #logic #godel #godel incompleteness #axiom of choice #analysis

One response to Gödel incompleteness is to postulate iterated consistency statements: instead of just PA one can work in PA+CON(PA)+CON(PA+CON(PA)), etc. Alan Turing’s phd thesis was about iterating this process transfinitely many times. I think at least the first few steps are usually considered unproblematic, we “know” PA is consistent, so we may as well postulate it.

But just consistency is not enough for this to be sound. Someone on mathoverflow pointed out this counterexample: If T is some consistent logical theory, then by Gödel’s incompleteness theorem T+¬CON(T) is consistent too. However, CON(T+¬CON(T)) implies CON(T), so T+¬CON(T)+CON(T+¬CON(T)) is not consistent. It feels pretty paradoxical, a theory that is consistent only as long as it doesn’t know it is…

I’m not sure what the philosophical implications are (any references to discussion is welcome). It would be a pretty funny cosmic joke if PA was consistent but PA+CON(PA) was not.

I feel like a lot of issues with Gödel stuff resolves itself when you drop the whole concept of “truth” from the situation.

(This is why I take issue with saying PA “is” consistent—you can prove its consistency under a number of axiom systems, I think including ZF, but that’s passing the buck to those systems.)

So what this says is, if you have a system of tools T that can’t generate a contradiction, we know by Gödel that T+¬CON(T) is also a tool system that can’t generate a contradiction. But if you add in another tool of course you get more degrees of freedom, and more potential to generate a contradiction somehow.

I feel that only shifts the problem to the other half. Like sure, if you stop thinking about truth then it’s not weird that one set of axioms is contradiction-free and another one isn’t. But then it is instead mysterious why Turing thought he could unproblematically postulate that infinitely long series of axioms! :)

I don't see why it would be problematic. You can postulate whatever axioms you want!

The question is whether this models anything useful, and the answer is, obviously, "No, once the word 'transfinite' shows up you're definitely not modeling anything useful."

#math #logic #godel #godel incompleteness

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One response to Gödel incompleteness is to postulate iterated consistency statements: instead of just PA one can work in PA+CON(PA)+CON(PA+CON(PA)), etc. Alan Turing’s phd thesis was about iterating this process transfinitely many times. I think at least the first few steps are usually considered unproblematic, we “know” PA is consistent, so we may as well postulate it.

But just consistency is not enough for this to be sound. Someone on mathoverflow pointed out this counterexample: If T is some consistent logical theory, then by Gödel’s incompleteness theorem T+¬CON(T) is consistent too. However, CON(T+¬CON(T)) implies CON(T), so T+¬CON(T)+CON(T+¬CON(T)) is not consistent. It feels pretty paradoxical, a theory that is consistent only as long as it doesn’t know it is…

I’m not sure what the philosophical implications are (any references to discussion is welcome). It would be a pretty funny cosmic joke if PA was consistent but PA+CON(PA) was not.

I feel like a lot of issues with Gödel stuff resolves itself when you drop the whole concept of "truth" from the situation.

(This is why I take issue with saying PA "is" consistent—you can prove its consistency under a number of axiom systems, I think including ZF, but that's passing the buck to those systems.)

So what this says is, if you have a system of tools T that can't generate a contradiction, we know by Gödel that T+¬CON(T) is also a tool system that can't generate a contradiction. But if you add in another tool of course you get more degrees of freedom, and more potential to generate a contradiction somehow.

#math #godel #godel incompleteness #logic

Leaving aside all the partisan bullshit around mail-in ballots, I feel like being able to cast my ballot absentee just makes me a flat-out better voter. Not in that "oh, I'm making the superior choice to all these people who disagree with me" but rather that I'm casting votes that are more accurately in line with my values and politics because I can take my time on it. If I showed up at the ballot box and had to make a decision about [Random Government Position #17] I probably would either not vote or cast a pointless vote based on name recognition or something. Even if I brought all the voter guide mailers sent to me, there are still positions that don't get mentioned or people who aren't discussed, or whatnot.

When I vote at home, I take maybe 5-10 minutes on some candidates (which still feels like not a lot) and that would just be utterly unacceptable sitting in a polling booth with a line going around the block, but is totally something I can manage over a weekend, a bit at a time.

When I do my research for casting my (long, California) ballot, the judgmental part of me goes "how can we possibly allow people to vote in person when the choices are this weighty?"

I think you're "supposed" to do all the research and fill out the ballot at home, and then bring that in to the polling place and just transfer your conclusions.

And that doesn't not work, but it does very much add an extra step in the middle.

#voting #politics #us politics

An intersection of my and my readers' interests: Andrew Gelman on Scott Alexander.

#andrew gelman #scott alexander

Based

edward-blake-unknown-knight

"But but if their unarmed they might be trying to feed their family, think if they have a mental illness, the morality of it all"

Yea sooo anyway!!

"If you kill a burglar you're evil because you value your stuff over a human life!"

No, if you decide to burgle someone it's because you value their stuff more than your own life.

Um, no? To all of this? If someone breaks into your house and tries to run at you(or any direction that could be interpreted as such in the moment) despite you pointing your gun at them and yelling "don't move!", then it's ok to fire and that has nothing to do with burglary, because anyone who charges someone with a gun can be reasonably assumed to have intentions alot worse than stealing a tv. If they're clearly no threat, like if you somehow know for a fact that they're not dangerous like these scenarios all imply, it's murder. Life>property, and one guy who, in this scenario, you know doesn't intend to harm you is not a mass of rioters trying to break into your property for who-knows-what and necessitating you become a Roof Korean.

If you see a stranger on your property, obviously you are obligated to give them the chance to retreat UNLESS it's immediately obvious they're a danger to your life or that of your family's.

But if you aim your gun at someone, tell them to stop, and they don't, you have a right to defend yourself, your family, and your property. You are not obligated to let someone walk off with your stuff, but you are obligated to give them a chance to stop and if they're not a threat to your life (for instance, if they're already leaving the premises) you aren't really within your rights to shoot to kill.

Shoot to maim, however? I'd say if you're breaking into someone's house to steal shit, taking a bullet is just the risk you have accepted to take, but I would support shooting to injure rather than kill in cases where there is no threat to life.

siryouarebeingmocked

Shooting to maim can still get you in serious legal trouble, because it looks better to a judge and jury if you used deadly force to kill someone. Personally, I'd rather avoid harming someone at all if I can. This does not include, obviously, if they're risking the life of myself or my family. Hopefully I'll never have to test this principle.

Rule 2

Shoot to maim and they're armed they then have the chance to attempt to return the favor, your job is to neutralize the threat and center mass is the biggest target meaning you have the best chance to hit it.

Warning shots could also get you arrested so those are also a bad idea,

because they get treated the same as "not" warning shots in most US states that I know of.

A warning shot is a live round that you fired at a point you probably don't know the end of. "I'm sure there's nothing in those trees/behind that wall" is often a true assumption, but because people can fucking die when it's wrong it's never a good one to make with firing so casually. And yes, firing into the air counts. That kills people every single year on the Fourth of July or New Years because some idiot doesn't know the risks and thinks they can just pop off rounds with no conseuences.

With the exception of the Navy and Coast Guard, we don't even do warning shots in the military anymore - they are simply too unpredictable to do safely even for trained and experienced shooters. So either shoot for IC, or don't shoot at all.

As far as home invasion is concerned, anyone in my house uninvited has two options. Either immediately surrender and follow all verbal commands, or I run a Failure to Stop drill through the midline of their body. I don't care which direction they are facing either. Just because the threat has turned their back does not mean they are no longer a threat. They could be running away, or they could also be trying to gain a tactical advantage. I don't know the answer to that question, so they will be treated as a threat until proven otherwise.

If they're running like, directly away from you without stopping, I'd say it's a reasonable assumption that they're not a threat. But if it's dark and in a cramped space(ie indoors), it'd be pretty hard to ascertain that's what's going on, and a much more reasonable assumption that someone who responds to "don't move I have a gun" by moving is a danger.

There have been more than enough tragic incidents where someone shot a person who turned out to be lost, looking for help, or even a family member or other fellow resident of the dwelling to make it clear that just unloading at a humanoid figure on your property or even in your home without at least trying to verbally warn first is probably a very bad idea.

That said, there have also been more than enough tragic incidents that make it clear that people busting into an occupied dwelling may well have intentions far worse than stealing and refusing to consider use of force in resisting home invaders is potentially allowing others to torment and murder your family in the worst way imaginable.

Laws like this are *not* in place for liberal namby pamby feelings.

A criminal is in the house and you catch them with a gun. They consider running away but you could shoot and murder them and be off scot free.

They can rush you with a knife, or run off. Knife is bad, let's say 50/50 chance they die or you die or both.

But if YOU're not allowed to fire IF THEY ARE FLEEING, then fleeing is actually a pretty good option for them.

You reeeeaalllly want the illegal assailant who is in your home to remember their life is NOT forfeit, and killing you will make their life much worse. That is what you want them thinking about at the time. And if they understand "so long as I don't escalate he won't escalate" your life is in a much safer place.

So yes, we try to use the law to not escalate from breaking and entering up to assault and murder.

***If you are ever in a fight with someone stronger and bigger than you, for your own safety, do not pull out a knife.

It's also why "attempted murder" has so much lower penalties than "murder". You want the person, with every fiber of their being, to want to change their mind, or to flub the shot, or to otherwise fail at their original goal. As a liberal society, we need the attitude toward crime to never be "well, I've gotten this far, I'm already totally fucked, might as well go the rest of the way."

Chen Sheng and Wu Guang were both army officers who were ordered to lead their bands of commoner soldiers north to participate in the defense of Yuyang (simplified Chinese: 渔阳; traditional Chinese: 漁陽). However, they were stopped halfway in present-day Anhui province by flooding from a severe rainstorm. The harsh Qin laws mandated execution for those who showed up late for government jobs, regardless of the nature of the delay. Figuring that they would rather fight than accept execution, Chen and Wu organized a band of 900 villagers to rebel against the government.

Finished Final Fantasy XVI yesterday. (I don't think I've even blogged here about FFXV yet, and I finished that months ago. Having a built-in audience for my thoughts at home takes away some impetus to blog about them.)

Overall, very good game. And I have a lot of thoughts about it but they're all fundamentally kind of silly, because I don't have the right sort of reference class.

So for instance, FFXVI is by far the most realistic-looking game I've played. But FFXV is the second-most realistic looking, third place goes to FFXIII, and fourth might go to FFXII. This tells you more about what games I play than about this game specifically.

But embracing my lack of reference frame, I feel like my two biggest complaints about FFXVI is that it has too much voice acting, and too many in-combat cinematics.

The voice acting at its best is great. Pretty much every major plot sequence was acted and animated extremely well. I never regretted listening to that. But they committed to voicing everything. A lot of sidequests, especially, have a bunch of little back-and-forths about why I need to kill six snow moose and where the snow moose live and not only am I bored listening to this get voice acted out, I can tell the voice actors are also kind of bored by it. That all would have been better as straight text.

Similarly, the game had a lot of very cool, very impressive cinematics. But they kept interrupting my (fun!) combats to show them to me, instead of letting me just have a battle. I wound up finding the hunts and miniboss battles fun but kind of dreading the boss fights, because they all felt rigged—generally in my favor, sometimes against me, but just generally rigged.

I tend to prefer it when the game sets up a puzzle in the combat engine, then lets me engage with it. But the boss fights would put up a health bar, and then at unpredictable points in it shunt me over to a Cinematic Clash which would do various amounts of damage to me and to the boss and then drop me in a different arena in a different phase.

(I also kinda didn't like the checkpoint system; it felt like it didn't allow/require me to actually learn the boss properly to beat them and advance. I understand why they don't restart you from the beginning of the fight; some of those fights are annoyingly long. But I didn't like what they settled on.)

But I think all these complaints are dangerously close to "New games are too new and not like the games I grew up with, where everything was conveyed through text because they couldn't do anything else."

#video games #jrpgs #final fantasy #ffxvi #final fantasy xvi

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Here's my personal Old Man Yells At Cloud moment: I don't think that D&D should be held entirely responsible for the 'Americanization of fantasy' that people keep grumbling about. I would posit that JRPGs are equally responsible for it, if not even MORE. While many of the tropes from the modern genre did originate in D&D, they were codified through that genre and spread much further through simple volume.

Oddly, while mainstream JRPGs do have a lot of Dungeons & Dragons influence in them, many of the particulars that Western gamers tend to parse as "Americanised" fantasy aren't a product of that influence. As near as I can tell, it's really mostly a product of the Dragon Quest franchise being intensely preoccupied with the German Renaissance, and that preoccupation bleeding out into every other piece of Japanese fantasy media that's biting on Dragon Quest. There are a huge number of JRPG tropes that read as "generically medieval" to American audiences that are actually the-German-Renaissance-by-way-of-Dragon-Quest, and we can't blame that one on D&D by proxy – none of the big-name D&D settings do that.

(With respect to the obvious follow-up question of why the Dragon Quest franchise is so preoccupied with the German Renaissance, that one's beyond my expertise!)

It is always funny to me how many JRPGs start you out in Generic Medieval/Early-Modern Europe (apparently in the German Renaissance), and then eventually you travel to the Mysterious Exotic Orient that has samurai and ninja.

I sometimes wind up uncomfortable with the exotic otherization. And then I remember that this is being written by Japanese people, and that makes it much funnier.

(But also makes the bits where the Japanese emperor is noble and good and the Chinese stand-ins are contemptible evil machinators read very differently!)

#video games #jrpgs

The photos I've seen online really don't do the White House justice.

#politics #us politics #trump

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