Maybe-Mathematical Musings

*someone finds a counterexample to my theorem* ok well obviously i didnt mean it for that case asshole

- Delta from Proofs and Refutations

we are going to have to start considering the possibility that trump is driven, at least partially, by a belief that a trade deficit is a type of budget deficit, because they both have the word 'deficit' in them

a lot of people think Trump's policies will be bad for the American national interests, but will they also be bad for Chinese national interests? it seems like there are four possible outcomes to reducing the American trade deficit / Chinese trade surplus:

it's interesting to see what outcomes people see as more likely, and how they correlate with their opinion of Trump in general.

I don't feel like this engages at all with what the other poster was actually saying, which actually seems to match things he has said pretty well and it's completely fucking wild if that's what's going on and nobody in his own party is able or willing to reign in this acting on the basis of a fundamental misunderstanding of what is even going on

Oh yeah, the consensus among, like, everyone I read is that Trump has gotten himself convinced that a trade deficit is something that costs us money. The general psychoanalysis guess is that he is so zero-sum in his thinking that someone has to be winning, but also some amount of being confused about "deficit" is involved in there.

But yeah, it sure seems like he thinks a ten billion dollar trade deficit with another country means we're losing ten billion dollars to them.

How is that not the only thing the media are talking about?

surely that ought to be a big fucking deal

Like fuck I thought the Brexit bus was bad; here you've literally got rule by effectively no one because the person in power literally doesn't understand the things that he's doing

Media structurally wants to explain the underlying reasoning of political decisions. It's not set up to explain that there basically isn't one.

Like even leaving out the way Trump may not realize that a trade deficit doesn't cost money, on-the-record administration spokespeople have given multiple diametrically opposite explanations of what they're trying to do. You literally have one guy out there explaining this is a setup for a negotiation while another guy is explaining they aren't going to negotiate and these tariffs are the end goal. That's actually happening.

So what I'm hearing is that you get these sit-downs between, like, business reporters and subject experts where the business reporters ask the experts to walk them through the logic of what the tariff plans are supposed to achieve, and what the administration is thinking, and the experts try to explain that this isn't possible because there is none. And the reporters try to "drill down past that" to what the actual underlying logic is.

but "he has this specific false belief" IS the reason! surely this would make some journalist's life if they could actually get the public at large to understand this, preferably in an interview thats really embarassing for the other guy

Yeah, I dunno what to tell you, the way the news media is set up makes it bad at handling this sort of story.

There's no scoop. There's nothing to uncover. You're just reading the President's public statements and interpreting them and realizing that he has no idea what he's talking about. But "interpreting public statements and realizing they're incredibly stupid" fits under "opinion", not under "news".

If he were secretly saying that, but publicly saying something else that would be a story. Or if you could get members of his administration to reveal that secretly he...anything. But he doesn't secretly anything. He just has a totally unjustified policy.

(Side note: this is one of the ways Trump has gotten away with so much. You can't write a scoop that he's doing unethical and illegal things. He'll just tell you!)

But the media wants to uncover things, so by reflex they're trying to uncover the secret logic. Even though there is none.

Now, you can include this in a story, but you can't write a story about it. E.g. the literal second sentence of this HuffPost article from today:

But the article is "about" the effect of the remarks on the market, because that's a thing you can write a story "about".

we are going to have to start considering the possibility that trump is driven, at least partially, by a belief that a trade deficit is a type of budget deficit, because they both have the word 'deficit' in them

a lot of people think Trump's policies will be bad for the American national interests, but will they also be bad for Chinese national interests? it seems like there are four possible outcomes to reducing the American trade deficit / Chinese trade surplus:

it's interesting to see what outcomes people see as more likely, and how they correlate with their opinion of Trump in general.

I don't feel like this engages at all with what the other poster was actually saying, which actually seems to match things he has said pretty well and it's completely fucking wild if that's what's going on and nobody in his own party is able or willing to reign in this acting on the basis of a fundamental misunderstanding of what is even going on

Oh yeah, the consensus among, like, everyone I read is that Trump has gotten himself convinced that a trade deficit is something that costs us money. The general psychoanalysis guess is that he is so zero-sum in his thinking that someone has to be winning, but also some amount of being confused about "deficit" is involved in there.

But yeah, it sure seems like he thinks a ten billion dollar trade deficit with another country means we're losing ten billion dollars to them.

How is that not the only thing the media are talking about?

surely that ought to be a big fucking deal

Like fuck I thought the Brexit bus was bad; here you've literally got rule by effectively no one because the person in power literally doesn't understand the things that he's doing

Media structurally wants to explain the underlying reasoning of political decisions. It's not set up to explain that there basically isn't one.

Like even leaving out the way Trump may not realize that a trade deficit doesn't cost money, on-the-record administration spokespeople have given multiple diametrically opposite explanations of what they're trying to do. You literally have one guy out there explaining this is a setup for a negotiation while another guy is explaining they aren't going to negotiate and these tariffs are the end goal. That's actually happening.

So what I'm hearing is that you get these sit-downs between, like, business reporters and subject experts where the business reporters ask the experts to walk them through the logic of what the tariff plans are supposed to achieve, and what the administration is thinking, and the experts try to explain that this isn't possible because there is none. And the reporters try to "drill down past that" to what the actual underlying logic is.

we are going to have to start considering the possibility that trump is driven, at least partially, by a belief that a trade deficit is a type of budget deficit, because they both have the word 'deficit' in them

a lot of people think Trump's policies will be bad for the American national interests, but will they also be bad for Chinese national interests? it seems like there are four possible outcomes to reducing the American trade deficit / Chinese trade surplus:

it's interesting to see what outcomes people see as more likely, and how they correlate with their opinion of Trump in general.

I don't feel like this engages at all with what the other poster was actually saying, which actually seems to match things he has said pretty well and it's completely fucking wild if that's what's going on and nobody in his own party is able or willing to reign in this acting on the basis of a fundamental misunderstanding of what is even going on

Oh yeah, the consensus among, like, everyone I read is that Trump has gotten himself convinced that a trade deficit is something that costs us money. The general psychoanalysis guess is that he is so zero-sum in his thinking that someone has to be winning, but also some amount of being confused about "deficit" is involved in there.

But yeah, it sure seems like he thinks a ten billion dollar trade deficit with another country means we're losing ten billion dollars to them.

I think if you're going to do anything hundreds of times, you should get good at it.

If you're going to have a sandwich for lunch every day, you should spend that time getting better at making the sandwich, understand what works and what doesn't, how to be efficient and get the most out of it.

If you're going to bike to work, you want to get good at biking, right? Perfect your form, make it easy, economical, make it feel good.

There was a time when I thought that this was what everyone believed was the correct thing to do, but I guess it's not. Not everyone builds up a series of life hacks and optimizations and refinements for everything they do. There are, out there, people who make themselves a cup of coffee every morning but have never thought about how to make that cup of coffee better: it's exactly as good as the first time they made it, and there was never any experimentation or adjusting of the variables to see whether it could be better.

I don't want to say that this is wrong, but it definitely feels weird to me.

While on the one hand, I do think "the problem with food waste" seems to be, like, industry-scale and hard to solve at home.

And then I come to recipes that call for "1 tsp tomato paste". Dude, if you wanted me to throw away a 6 oz can of tomato paste, you could just say so.

1) what's even the point of 1tsp of tomato paste

2) freeze it: tablespoons (or whatever size is convenient) on a sheet of parchment on a quarter/eighth sheet pan; once they're solid, transfer to a more conveniently-tessellating container

3) to my concern, somehow, i go through tomato paste fast enough when i have it that i don't freeze it anymore

there is such a thing as squeeze-tube tomato paste. i exclusively get it in tubes due to the 6 oz can problem described above. it's great.

I don't know how this helps you, other than to point out that your problem has been solved by capitalism for other people, but not you?

So, sorry about that.

Yeah, I use it but it still goes bad. I just don't use tomato paste enough generally.

(My mistake for putting the comment in the tags)

Your mistake for not using tomato paste enough.

I saw this and just assumed it was a Wheel of Time meme.

You guys are gonna flip when you find out about technology

No, imo there's some insight here. Other techs tend to be developed to solve some problem and yes, they often displace jobs by doing that. But the way people are trying to use LLMs is imo different and way more directly this. They didn't replace the factory workers with a half-finished incredibly buggy device that wasn't really developed for or suitable to do their jobs; there's a real desperation to not pay people on display here

I've been sitting on this for a while because phaeton-flier is basically right but also it shook an idea loose in my brain.

So first of all, phaeton is right because on some level the point of technology is to avoid paying wages. We want to replace human labor with...not human labor...so that humans can get more stuff for less labor. That's a good thing!

And like if AI systems do, in fact, allow us to do the work that white collar workers currently do much cheaper, that's a great thing. If it lets people learn math without the help of specialized labor that's great, albeit maybe not great for me personally if that's all it does.

Of course that's a big if, which is Loki's point. There's a lot of deployment of AI systems that are not really fit for purpose yet. But this makes a lot of sense if you're familiar with a concept that gets a ton of play in tech circles.

There's an idea popularized in the 90s called "disruptive innovation", and it's something that the tech sector has as a major part of its self-image. That's why marketing and publicity materials describe everything as "disruptive" or as "disrupting a sector" etc.; all the tech people want to think they're doing disruptive innovation.

But the concept originally referred to something specific. Most innovation is incremental and iterative: this year's batteries hold 2% more charge than last year's or something. Sometimes you get a dramatic break where you develop something new and better, but also more expensive; early adopters pay a premium for the fancy new toy, and over time prices hopefully come down. (You can see that with e.g. big-screen LCD TVs, or with the iPhone.)

But there's a specific interesting category where you develop something new that's (a) not as good as previous technologies, but (b) so much cheaper that people use it anyway. This often shows up with a mass-production technique. Clayton Christensen liked the example of the Model T, which wasn't better than previous cars, but was affordable to a critical mass of people. Another common example is the personal computer, which wasn't nearly as good as a minicomputer but accessible to the home consumer. I'm also thinking about synthetic fabrics: early synthetics were shitty, but also dirt cheap so useful when you didn't care about fabric quality.

So a disruptive innovation often doesn't face real practical competition from pre-existing companies, because it's shitty but cheap so it opens up a new market. But then often the shitty but cheap tech improves over time! Modern PCs can do way more than the classic mini-computers did (and one of Google's innovations was figuring out how to run everything on banks of PCs rather than on custom built single boxes). Modern synthetic fabrics are really good, and can do stuff that you can't do at all with natural fibers (or can but only wildly expensively).

So the story nearly every tech company tells itself about itself is that it's a disruptive innovator: producing a cheap product that will eventually improve and displace the luxury product. And to be clear, this isn't a bad thing: disruptive innovation is a huge engine for prosperity and quality of life. But most of the time, the story is just not true—most innovation isn't disruptive!

And furthermore, if your innovation is really disruptive that means you have to be pretty particular about who your market is—at least for now. What makes it disruptive is generally that it's not good enough for a lot of obvious users of the technology—but cheap enough that a bunch of non-obvious users will use it.

And taken from that perspective, a lot of the AI weirdnesses make sense, right? The chatbots are (a) cheaper than people and (2) not as good as people at most things you want people to do. Plausibly, that opens up a whole bunch of new options for things we can maybe do that we just couldn't do at human-living-wage prices.

But crucially, if you're pitching a disruptive innovation you have to accept that, like, established conservative institutions with money are not your target audience. So like hospitals should be the last people you sell to. You're making something crappy and unreliable but so cheap that you can do things it's not worth hiring a human to do. "Custom header image for a blog post" fits that category; "diagnosing a cancer patient" doesn't.

But since every tech company tells itself it's doing disruptive innovation, people have lost track of that implication, and so we get what we see.

Dyson – "The Question of Global Warming":

But doesn't Nordhaus's model have exponential growth built in? Like, we explicitly count the dollar saved now and the 54 dollars it becomes in the future.So if that's the justification for the discount rate we would be double-counting.

A discount rate in finance make sense to me for valuing investments, it's just measuring opportunity cost. But does it make sense in this other activity, turning a curve of wealth as a function of time into a single "welfare" number?

Yeah, this sounds right to me. Compare this old post by Robin Hanson which also says that it makes sense to apply discounts when considering donations to the future. But Nordhaus applies the discount rate to the consumption.

There is no opportunity cost there, by assumption the money is consumed rather than invested...

But I guess there is also a different argument for discounting, which assumes that humans just have discounting built in? Like, presumably this evolved because evolution has to decide how much to "invest" at different life stages, but now it's part of human nature, and if you search your feelings you know it to be true that the future is less valuable...

There are a few reasons people give for discounting consumption that way. (Beyond the "humans just discount the future, psychologically; deal with it" point.)

One is increased uncertainty: the 50 USD payout a hundred years from now is way less certain than the 1 USD payout now.

One is economic growth: If we're all fifty times richer in a hundred years, 50 USD then is practically speaking equivalent to 1 USD now, in terms of relative impact.

And the third is that you kind of need to assume discounting for any of the analyses to make sense. With zero discounting, we never get to consume anything and that fails the absurdity test.

I think the "50 USD then is practically speaking equivalent to 1 USD now" would come out of the U in his equation (from diminishing returns), so it still seems like double-counting.

Okay, in theory I think that's maybe correct, but any actual computation is going to denominate utility in dollars rather than abstract utility so you would exponentially discount.

(Also, looking at the integral you can see point 3: if you don't have a decay somewhere the integral isn't gonna converge!)

I think actually their U has some kind of weird form which is supposed to model decreasing marginal utility. But I don't really get what they are doing, I would have expected it to be, like, a logarithm or something but instead they have parameter ϕ which is the "marginal utility" and they exponentiate and divide by it..?

They write

and then they also write

So it seems they have a "pure" preference ρ, but in addition they tweak the rate to also include uncertainty, and then the decreasing marginal utility somehow shows up as two different kinds of the greek letter phi, applied in the rate and in the utility function? I'm so confused...

Yeah, they're doing something fairly complicated. I think the rho represents the abstract case for "now better than the future", and then the g_r represents the fact that we'll be richer in the future. (The phi is measuring, basically, how much better off does being richer make us; if our income doubles we don't actually double our consumption, we tend to save a bit more proportionately.)

The U doesn't have exponential decay built in; the phi is constant and doesn't vary with t.

Dyson – "The Question of Global Warming":

But doesn't Nordhaus's model have exponential growth built in? Like, we explicitly count the dollar saved now and the 54 dollars it becomes in the future.So if that's the justification for the discount rate we would be double-counting.

A discount rate in finance make sense to me for valuing investments, it's just measuring opportunity cost. But does it make sense in this other activity, turning a curve of wealth as a function of time into a single "welfare" number?

Yeah, this sounds right to me. Compare this old post by Robin Hanson which also says that it makes sense to apply discounts when considering donations to the future. But Nordhaus applies the discount rate to the consumption.

There is no opportunity cost there, by assumption the money is consumed rather than invested...

But I guess there is also a different argument for discounting, which assumes that humans just have discounting built in? Like, presumably this evolved because evolution has to decide how much to "invest" at different life stages, but now it's part of human nature, and if you search your feelings you know it to be true that the future is less valuable...

There are a few reasons people give for discounting consumption that way. (Beyond the "humans just discount the future, psychologically; deal with it" point.)

One is increased uncertainty: the 50 USD payout a hundred years from now is way less certain than the 1 USD payout now.

One is economic growth: If we're all fifty times richer in a hundred years, 50 USD then is practically speaking equivalent to 1 USD now, in terms of relative impact.

And the third is that you kind of need to assume discounting for any of the analyses to make sense. With zero discounting, we never get to consume anything and that fails the absurdity test.

I think the "50 USD then is practically speaking equivalent to 1 USD now" would come out of the U in his equation (from diminishing returns), so it still seems like double-counting.

Okay, in theory I think that's maybe correct, but any actual computation is going to denominate utility in dollars rather than abstract utility so you would exponentially discount.

(Also, looking at the integral you can see point 3: if you don't have a decay somewhere the integral isn't gonna converge!)

Dyson – "The Question of Global Warming":

But doesn't Nordhaus's model have exponential growth built in? Like, we explicitly count the dollar saved now and the 54 dollars it becomes in the future.So if that's the justification for the discount rate we would be double-counting.

A discount rate in finance make sense to me for valuing investments, it's just measuring opportunity cost. But does it make sense in this other activity, turning a curve of wealth as a function of time into a single "welfare" number?

Yeah, this sounds right to me. Compare this old post by Robin Hanson which also says that it makes sense to apply discounts when considering donations to the future. But Nordhaus applies the discount rate to the consumption.

There is no opportunity cost there, by assumption the money is consumed rather than invested...

But I guess there is also a different argument for discounting, which assumes that humans just have discounting built in? Like, presumably this evolved because evolution has to decide how much to "invest" at different life stages, but now it's part of human nature, and if you search your feelings you know it to be true that the future is less valuable...

There are a few reasons people give for discounting consumption that way. (Beyond the "humans just discount the future, psychologically; deal with it" point.)

One is increased uncertainty: the 50 USD payout a hundred years from now is way less certain than the 1 USD payout now.

One is economic growth: If we're all fifty times richer in a hundred years, 50 USD then is practically speaking equivalent to 1 USD now, in terms of relative impact.

And the third is that you kind of need to assume discounting for any of the analyses to make sense. With zero discounting, we never get to consume anything and that fails the absurdity test.

A drink or two a night is much better for your health than getting genuinely drunk once a week which is too bad cuz the former is ghost-robot-domesticated animal and the latter is living-flesh-wild beast

Baffling.

Getting genuinely drunk once a week gets you drunk, which is bad and unpleasant and no fun.

Having one drink lets you taste and enjoy the drink without being affected much by the alcohol, which is much better. And you get to do it several times in a week!

If you guys were on here at 11 years old what would you be posting about

My uncle came in to visit for a week when I was 11.

He apparently told my mom "I don't mind the stories about Teddy Roosevelt. But if I have to hear one more explanation of string theory..."