yaks_hairbrush

It works if you don't care about magnitudes, distances, or angles of complex numbers. Those properties aren't algebraic.

You're right that a business wouldn't lower prices if customers keep showing up. The basic causes of prices falling amount to two: increased supply, and decreased demand.

On the supply end, if competitors enter a given market and take some of your customers, you might lower prices to lure them back. And if people just can't afford (or otherwise don't want) to go to your salon/restaurant as often, then you might lower prices to lure them back.

As far as the current environment, we've got student loan payments restarting in a couple months after a three-year hiatus. A good number of folks who had some disposable income are going to have less. That'll impact the demand end of the equation. Won't necessarily cause deflation, but will at least lower inflation.

> It would be perfectly straightforward to fund that entirely by raising income taxes on the highest earners.

Even if you do that, you're still getting inflation. That'll hit everyone -- not just high earners. Loan forgiveness and payment pauses free up a fair bit of middle class budget and therefore increase the velocity of money.

> Based on what?

Someone with a high school diploma will earn on average $1.3 million over their lifetime. Someone with a B.S. averages $2.3 million. The college degree is thus worth, on average, $1 million in lifetime earnings.

Source: https://cewgeorgetown.wpenginepowered.com/wp-content/uploads...

> The fact is, a huge number of people have staggering amounts of student loan debt, and very little ability to repay that debt—and a legal prohibition on discharging it.

I believe I acknowledged that. Making provisions for discharging student loans via bankruptcy would be a really good idea. Much better at targeting student loan relief to those who need it.

> What does this situation gain us that would be lost if we simply cancelled all that student loan debt?

Cancelling all student loan debt would lead to some combination of higher taxes and inflation. No matter how you slice it, that would be a redistribution of wealth from the uneducated to the educated. That redistribution of wealth therefore goes the wrong way -- the uneducated are more likely to be poor, and the educated more likely to be rich.

> The question is if you think "most recent college graduates without wealthy parents" are a population worthy of government assistance.

And, quite frankly, I'd gravitate towards a "no" on this. When taken as a group, I'd expect college graduates to be able to pull off an income stream sufficient to pay down the student loans.

Of course there are individuals for whom student loans pose a real problem. There should be some realistic provisions for discharge in bankruptcy.

Considering our recent/current environment of low unemployment and high inflation, broad-based loan forgiveness is simply the wrong choice from a Keynesian economics perspective. The same is true of continuing the payment pause.

The length of the burst tells us the maximum size of the event. Imagine the event takes place instantly at the source, and that the source has some size. If we observe the event over two minutes, then the event size was two light-minutes.

In reality, these aren't completely instantaneous events. But any event duration at its source is going to decrease the event size. Take the extreme case: the event actually took place at its source over the course of two minutes. And we observed it over two minutes. We would have to conclude that the event had zero size.

Of course, the reality is that we have no idea how long the event took place at its source. All we know is that we observed it over two minutes. But that's enough information to conclude that the event we're seeing certainly occurred within a two light-minute sphere. If it had occurred over a larger sphere, we would have observed it over a longer period of time because of the time light takes to traverse the length of the source.

Maybe this: https://www.collaboraoffice.com/code/

Played this (or something very similar) growing up. We called it "squeak".

I have a macbook air with an egpu connected by a thunderbolt 3 port. I unplug the gpu when I want to take the laptop somewhere, and plug in back in when I'm at my desk.

The issue with schools is that they're daily large gatherings where the virus can be transmitted. Children can be carriers with schools providing the network effect for spreading covid-19.

FL300 (30,000 feet) is usually within the troposphere. And that's highly relevant, because the troposphere is well-mixed. Water vapor emissions at 30,000 feet are going to come back down, for the most part.

So, 500 million metric tons sounds like a lot, doesn't it? But there's the fact that it's getting dumped into an already big system: the atmosphere at large.

Let's check it out it percentage terms. According to wikipedia, the mean mass of water vapor in the air is 1.27 * 10^16 kg. To get the units correct, that aviation contribution is 5 * 10^11 kg. Dividing the latter by the former, we find that the annual commercial aviation water vapor represents 0.004% of the mean mass of water vapor.

That's rounding error.

Erm... I feel like you're maybe projecting and/or arguing a strawman. Acknowledging that humans are causing the climate to change is quite a far cry from demanding actions from China's population.

Good question! It means that the probably of finishing in the next increment of time is always the same. Just got up to the teller? There's, say, a 20% chance that you're done within the next minute. Been at the teller's desk for 30 minutes already? Still a 20% chance that you're going to be wrapped up in the next minute.

It was indeed established that Pluto had an atmosphere before the New Horizon flyby. The atmosphere is mostly seasonal. The air freezes when Pluto is far from the sun, and sublimates again when it's near.

> The issue is rather that we don't know what all that star stuff becomes once it goes into the black hole, though there are theories. The problem is that the defining feature of a black hole, its even horizon, by necessity means there is no way of knowing what theory is correct since nothing happening inside is supposed to matter to us.

Right. As far as "an observer at infinity" is concerned, all that in-falling matter gets asymptotically closer to the event horizon and never crosses it.

One way to reframe the situation which I quite like: Black holes have no insides.

Oh, dear god no. Nicotine inhalers exist, and I went to a doctor to get a prescription for them a few years before ecigs became prevalent. The doctor insisted that Chantix was the way to go. I reacted badly to Chantix.

I finally quit cigarettes by switching to ecigs, and eventually quit those as well. Actually, I just passed the 5 year mark nicotine-free a couple weeks ago.

Point is, doctors are happy prescribing Chantix, which is bad, and the better option may simply not be prescribed to folks for whom it would to a lot of good.

A secure service wouldn't have an easy way of getting at a user's password. They'd store the salted hash of a user's password, and not the password itself.

The definition I gave is, nonetheless, the accepted definition of the term. Can't find a citation for yours.

(Note: I do understand about utility, and how/why progressive tax systems help society. My only bone of contention here is that you're trying to redefine a specific term to have a different meaning.)

Definition of "regressive tax": A tax that takes a higher percentage of income from low-income earners than from high-income earners.

By definition, the tax system in the post you replied to is not a regressive tax system.

That's the big thing that jumps out at me. There are very, very few serious economic policies that have this level of agreement among economists.

Greg Mankiw did a list a while back about what economists agree on: https://gregmankiw.blogspot.com/2009/02/news-flash-economist...

(1) The US government did just that -- promised backpay for all unpaid work during the shutdown.

(2) Banks may not wish to give loans to folks who have bad/no credit, even with the assurance. Banks need a bit more than assurances that the government will pay their debtees -- they need assurances that they will get that money.

Probably a planet. The distinction between planet and dwarf planet turns on whether the body has demonstrated gravitational dominance. Planet Nine's existence (if it indeed exists) was inferred from alignments of other bodies' orbits, which makes for a very, very strong case that it's a planet and not a dwarf planet.

There are eight currently known bodies (apart from the sun) in our solar system which can tug hard enough to dictate terms of sharing/crossing their orbit. Pluto is locked into a 3:2 orbital resonance with Neptune. Neptune dictates the terms under which Pluto can have an orbit with anything close to its current parameters. That's what it means to be a planet. While there is theoretical space for borderline cases, none exist in our solar system.

I understand you'd like to focus on objects in hydrostatic equilibrium. Pluto, Ceres, the Moon, and Titan are really neat, but something happens when you tell their life stories: you end up referencing one or more of the eight heavyweights. By contrast, these smaller objects just don't get referenced very much when we talk about other bodies' life stories.

The large scale structure and history of the solar system has just 8 known characters that really matter, and that's what the definition of the planet captures.

One very important difference between the big bang and the interior of the black hole: Within the event horizon of a black hole, there is always a singularity in your future. In our universe, that singularity is in our past.

One interpretation: the big bang theory describes a white hole -- the time-reversed version of a black hole.

Can I get an email address? I'd love to follow up on this post more directly.

This is a really nice explanation -- it flowed really well, and I liked the sieve approach to proving the product-over-primes formula (the other standard way relies on a clever trick, and being clever is fun-but-not-good-for-exposition).

I did get hung up on the complex graph showing the first few non-trivial zeros. It's a very busy graph! I ended up realizing that you graphed the contours Re(zeta(s))=0 and Im(zeta(s))=0.

Off the top of my head: Yahoo! and DuckDuck Go might be ahead of Bing.

It is a man-made shift. Here's the quick-and-dirty version of the reasoning:

The earth's energy equation has three big components: sunlight in, reflected sunlight out, and blackbody radiation out. Measurements of these three items indicate that we are not currently in equilibrium. Instead, there's an excess of 0.6 Watts/square meter. That means the planet is warming.

How do we know it's us? We've increased the CO2 content of the atmosphere. CO2's absorption/emission spectrum happens to be quite strong precisely where earth's blackbody radiation is strong; it therefore reduces the energy out by blocking the blackbody radiation. A paper about this is [0]. I eyeball Figure 6a as indicating a theoretical radiative forcing of 2 Watts/square meter, given the amount of CO2 we've put into the air.

[0] https://rmets.onlinelibrary.wiley.com/doi/pdf/10.1002/wea.20...

Historically, quaternions came about as a way to try to reason about three dimensional physics. I mean, complex numbers were obviously really nice -- two dimensional numbers you could meaningfully add, subtract, multiply and divide. But they were only 2-D and we live in a 3-D world and we want to do 3-D physics.

So Hamilton was trying really hard to find a way to have 3-dimensional numbers that behaved nicely, and he couldn't do it. But he did find 4-dimensional numbers -- the quaternions. And they were really neat. You can use them quite well for classical mechanics, and electromagnetism, and even special relativity. So, why don't we?

We look at Maxwell's equations of electromagnetism today, and they're really nice, single-line vector formulas. You can also write them as nice, single-line quaternion formulas. Our notion of vector didn't exist at the time the quaternions were first used, and it was a boon to have quaternion notation to simplify some of these physical laws. Vectors and quaternions competed for a bit, and vectors won since they generalize to arbitrary dimensions.

Hidden inside of quaternion multiplication, you can find the three-dimensional versions of the dot product and cross product. And they do have some theoretically interesting properties for number theory and abstract algebra. In the end, however, sometimes items are discarded in favor of better items. I'd rate quaternions as one of the coolest items that ultimately wound up in the discard pile.