They don't measure every package, and it isn't exact. But the packages are all pretty much the same, so as long as their quality control on how much goes into each package is reasonably accurate, they're all close enough.

The impact that killed most of the dinosaurs didn't kill all life on Earth. But the dinosaurs were very large animals high on the food chain, and when food chains collapse, those animals are the first to go. Smaller animals, like the ancestors of the mammals that dominate the planet today, had an easier time surviving.

It also didn't kill all of the dinosaurs. We know the survivors as "birds".

> In the US, any private entity can end its relationship with you for any reason

Well, no, they can't, there are many rules against discrimination by private entities.

It just so happens that most of those rules have loopholes built in for religious beliefs.

The air is rotating along with the surface of the Earth. And so is the plane. The movement of a plane is relative to the moving surface.

Except for very near the poles, or a few supersonic aircraft, a plane traveling "west" is in fact still being carried eastward by the Earth's rotation. It's just traveling eastward less quickly, so its position relative to the surface moves westward.

> The follow-up question is: why don’t “we” see that yet?

We do see it. It has consequences along the coasts everywhere in the world.

The reason it's not, like, submerging entire continents is that most land is more than 9 inches above sea level.

It would surprise me if that were accurate for the SAT even back then.

I'm not a healthy, fit control. Even in the more-fit of those two states I was still way overweight and not particularly fit.

In this case, "axiom" is a bit misleading. It's an assumption, but not an axiom.

Relativity arose out of the observation that the speed of light was the same for all observers, which had become clear by the time relativity was developed. What relativity does is goes back and says "okay, what assumptions about physics are wrong in order for that to be possible?"

It turns out the wrong assumption was the idea that all observers, regardless of position or movement, agree on lengths in space and time.

Think of AD and BC dates as positive and negative numbers.

The Aztec Empire proper was around from 1428 to 1521 AD, that is, the years "+1428" to "+1521".

Ancient Egypt was around from about 3100 BC to, depending on exactly where you draw the line, 30 BC, that is, the years "-3100" to "-30".

Which is bigger? -3000 or +1428? Obviously, the positive one. The Aztecs came many, many centuries after the Egyptians.

Many, many languages have already died out. The world has far fewer languages today than it had 100 or 200 years ago, as people switch to using the dominant language of their region.

For example, you probably think of Ireland as an English-speaking country. But until a few hundred years ago, it wasn't. Irish Gaelic was the most common language in Ireland for most of its history; they swapped to English after England took over Ireland. (Gaelic speakers still exist, but it is now a shrinking minority language in Ireland, not the dominant one.) The same went for Wales and Scotland, both of which originally had their own languages (Welsh has been revived, Scottish Gaelic is mostly fading), and in the distant past, even England itself.

In general, since the rise of large nation-states during the middle ages, the world has been moving steadily towards using fewer and fewer languages. And that process has sped up a lot in the more interconnected world we live in today. There are only about 7,000 languages left in the world, and many of those are spoken by a tiny group of elderly people and will be lost as those people die without passing the language on.

That's a pretty big "if", though. A lot of tests are written by hand and bias away from long answer streaks and first/last answer choices.

I wouldn't take my personal experiences as some sort of proof. If you're looking for guidance on your own health, talk to your doctor. (Notably, I have not, to my knowledge, had covid.)

If you ever learn a foreign language, this is an example of grammatical case, which English usually doesn't mark (pronouns are the exception to that rule), but which a lot of other languages do on all nouns.

Strictly speaking yes, since "Joe and I" is the subject of the verb "went", "I" is correct (and English word order demands "Joe and I" and not "I and Joe").

"Me and Joe" is still very common in casual English speech, though.

> After how long, would you say? Weeks, months, years?

Well, empirically, I notice it after a few weeks and have mostly reset after a few months, but this is deeper than my knowledge goes. (The rates probably vary by a lot of factors, like sex and age among others.)

It's not hard, in the sense that it's not difficult to do in principle. It's just energy-intensive and therefore expensive, and it requires facilities that are themselves expensive.

> Will deconditioning cause your resting heart rate to go back up?

Yeah, because your body won't keep putting in the resources to maintain the higher level of fitness.

> Wouldn't your heart need to beat more forcefully to move the same volume of blood completely around your body at 60bpm than at 100bpm, though?

No. You don't need as much blood flow when your blood is more efficiently carrying oxygen, and it doesn't have to push as hard when it's not getting as much resistance from your arteries.

> And are these your own actual numbers, or are people more likely to see a more modest decrease in resting heart rate, like from 70bpm to 60? 100 seems awful high for "resting"!

It is high, yes. It's typical of someone with poor physical fitness, but not healthy. 60 bpm is a fairly normal healthy resting pulse. But the thrust of the explanation - that the heart does less work by having mild stress during exercise and less stress the rest of the time - stands either way.

Sine is y/r, and cosine is x/r.

If you multiply x, y, and r by the same value - which is what happens if you make the circle bigger - the values of sine and cosine don't change, and therefore neither does the sum of their squares.

Your blood pressure is higher while you're exercising at first, but it becomes lower on average as a result of exercise (in much the same way that exercise raises your heart rate during exercise, but lowers your average heart rate).

The reason is that exercise:

• Causes your body to store and carry oxygen more efficiently, by improving oxygen storage in your muscles, increasing the density of of red blood cells in your blood, and increasing the amount of hemoglobin in those red blood cells. This reduces the amount of blood flow required to support your body's operation.

• Increases the size and strength of your heart, which no longer has to work as hard to pump.

• Stretches out your blood vessels, making them more flexible to blood flow. The stiffness of blood vessels is a big part of high blood pressure, and contributes to the buildup of deposits on the sides of the blood vessels that contribute to e.g. heart attack or stroke.

When your body is storing oxygen more efficiently, your body doesn't have to "ramp up" to handle everyday tasks. You feel this as being less out of breath from small bits of exercise, like jogging for a moment to catch a bus or climbing a flight of stairs. It can also run quieter when you're stationary, because fewer, gentler heartbeats are needed to sustain your body's background oxygen usage. That reduces the overall stress on your body, and lets your body heal itself under low stress in between bouts of heavy exercise in a way that it can't if it's constantly under stress.

For example, I find about 30 minutes of relatively strenuous exercise a day drops my resting heart rate from ~100 beats per minute to ~60. Even though it spikes up to like 150 bpm during that exercise, that's only for 1/48th of the day, and it's running half as hard for the other 47/48ths. My low-fitness heart has to beat about 144,000 times a day, while my high-fitness heart has to beat 4,500 times during the exercise (using the 150 bpm number) and 84,600 times for the other 23.5 hours of the day, for a total of 89,100 beats - barely half as many.

The sheer amount of material involved is far, FAR too large for this to be practical.

Let's take a single mountain. I'll use Mount Diablo, a small mountain near my home in the San Francisco Bay Area.

Mount Diablo is roughly a (right circular) cone with a base radius of about 5 kilometers and a height of about 1 kilometer. (It's actually taller than this in terms of height above sea level, but here I'm just going to count its size starting at the surrounding land where the slopes fade into the background.)

The formula for the volume of a cone, then, gives us V = (1/3)Ah, where A is the area of the base and h is the height. That's (1/3)(pi * (5 km)^(2))(1 km) = about 26 cubic kilometers of rock. That's enough to blanket the entire state of California in a few inches of gravel, which should give you an idea of just how much material we're talking about here.

It's made mostly of sandstone, with some inclusions of denser rocks like basalt, so let's estimate a density of about 2.5 grams per cubic centimeter (a bit higher than the density of sandstone). 26 cubic km times 2.5 grams per cm^3 is 6.5 x 10^13 kg.

Okay, that's a big number. How big is that?

Well, it turns out to be approximately a quarter of all Earth moved by all humans worldwide every year. If we combined the entire earthmoving capacity of all of humanity, we could move four Mount Diablos each year, to the exclusion of literally every other construction project ever undertaken by mankind. (We'll set aside the fact that the actual logistics of this would be impossible, since you'd also have to be carting all that rock away, and the fact that we're cutting through hard bedrock and not soft soil.)

And to cut a pass through a mountain range, you need far more than that. A typical mountain range is something like 20 or 30 peaks "thick", and those peaks are typically quite a bit taller than Mount Diablo. Even just building a road through such places is a pretty serious engineering task; destroying the mountains entirely would be the greatest engineering task ever undertaken by mankind by a huge margin.

In general, with questions like this, it's worth just doing some back-of-the-napkin calculations to see roughly how large the thing you're trying to do is. Even if I didn't have all that info available, I could say something like:

• Mountains are much more than 1 km high.
• Mountains are much more than 1 km wide.
• The volume of a thing is roughly length * width * height, so mountains have a volume of at least 1 km^(3), probably much more.
• Solids typically have densities of at least 1 gram / cm^(3) (that's the density of water, and most solids sink).
• There are 10^5 cm in 1 km, so there are 10^15 cm^3 in 1 km^3
• So we're talking about at least 10^15 g or 10^12 kg of rock.
• A bag of gravel at my local Home Depot probably costs me something like $10 = $10^1 per kilogram.
• So this is at least $10^13 worth of gravel.
• $10^13 is 10 trillion dollars, comparable to the entire budget of the United States government.
• Probably not worth it.

No, "imaginary" has a specific technical meaning in mathematics. It doesn't just mean "constructed for some purpose". It means a member of a particular set of numbers that solve equations of the form x^2 = a, for some negative number a. For example, 2i is an imaginary number that solves the equation x^2 = -4.

Sure, in the same way that, when you don't know about fractions, you can say 3 divided by 2 isn't possible, because there's no integer that, when multiplied by 2, gives you 3.

But you don't do that, because inventing the idea of a number 3/2 is pretty useful, and lets you do many calculations that you couldn't do without it. In particular, you get ideas like "3/2 is the same kind of no-solution-is-possible as 6/4 is".

Imaginary numbers are the same kind of thing. They aren't "impossible", and "imaginary" is just a name (you could call them the "Bob numbers" if you wanted to). They are a perfectly well-defined algebraic object. They're only imaginary in the sense that they don't fit onto the number line, and human intuition about numbers tends to come from ideas like length that happen to be real-valued.

But in practice, imaginary numbers show up all the time in descriptions of the world around us. In particular, they're critically important in quantum mechanics, where the fact that the states of particles aren't real-valued is essential to the theory (many quantum-mechanical phenomena actively require this). They also turn out to produce very compact representations of things like periodic behavior, as with a spring or a pendulum. And relativity tells us that the relationship between space and time is the same kind of thing as the relationship between the number "3" and the number "3i".

You could do all of this with objects that are just pairs of real numbers (a,b), defined in such a way that (a,b) "times" (c,d) = (ad + bc, ac - bd) and (a,b) "plus" (c,d) = (a + c, b + d). But the object you've invented has exactly the same properties as imaginary numbers do, so why add the extra complexity?

They aren't. They're circles (or they would be, if rain were falling throughout your field of view).

A rainbow appears in a circle of a particular size (the size has to do with the refractive index of water, so it's the same for all rainbows) centered around a point opposite the Sun in the sky (the "antisolar point"). But since the Sun has to be up for a rainbow to appear, the antisolar point is necessarily below the horizon, so less than half the rainbow is visible if you're on a flat surface.

If you're in a position where there can be rain "below" the horizon in your sky (as if, for example, you're in a plane or on top of a high mountain), you can sometimes see the full circle of the rainbow. But most people live on approximately flat surfaces or at the bottom of valleys, not near the tops of steep hills, and it's hard to get the geometry right to have the Sun above you and the rain below, so rainbows are normally just small portions of a circle.

Obesity - especially abdominal obesity - is part of a broad cluster of conditions collectively known as metabolic syndrome. This syndrome includes, among other things:

• Diabetes
• Cardiovascular disease
• High blood pressure
• High cholesterol (or more properly, high LDL and low HDL, the "bad" and "good" cholesterols respectively)
• High blood triglycerides (fats)

These things are all interrelated in complex ways.

For example, fat cells are related to insulin, in the sense that insulin stops fat cells from releasing their stored fat. Insulin, in turn, is related to high blood sugar, in that high blood sugar stimulates the release of insulin. But high insulin levels for extended periods can result in insulin resistance and hence diabetes, which causes high blood sugar to stick around and fat cells to improperly release fats into the bloodstream. Those floating fats can build up in blood vessels, causing high blood pressure and ultimately heart disease. And the poor circulation from that disease can combine with the poor circulation caused by diabetes to...

...yeah, like I said, complicated.

In part, becoming very obese is as much a symptom of underlying breakdowns in the way the body regulates energy intake as it is a cause of those breakdowns. It's all part of a bunch of feedback loops where which is cause and which is effect becomes kind of unimportant, because they're all causing and reinforcing one another.