Of Particular Significance

I hope you all had a good Twosday. Based on what I saw on social media, yesterday was celebrated widely in many parts of the world that use Pope Gregory’s calendar. I had two sandwiches to in honor of the date, and two scoops of ice cream.

In the United States, the joy continues today, it being now 2/23/22. Though not quite as wonderful as 2/22/22 on Tuesday, it’s still another nicely symmetric number worthy of note. In fact we get a full week of this, including 2/24/22 tomorrow, 2/25/22 on Friday, and so on, concluding on 2/29/22 … uhh, (oops) I mean, 2/28/22, because 2022 is not a Leap Year. For some reason.

In other countries, where it is 23/2/22, the celebration is over for now … because without symmetry, where’s the love? Ah, but they’re just more patient. They’ll get their chance in a month, when it’s 22/3/22, a date that will go unnoticed in the USA but not in Europe.

But what, exactly, are we getting so jazzed about? After all, what is the significance of it being the 22nd or 23rd date of the second month of a year labelled 2022? Every single bit of this is arbitrary. Somebody, long ago, decided January would be the first month, making February month number 2; but it wasn’t that long ago that March was the first month, which is why September, October, November and December (7, 8, 9, and 10) have their names. It’s arbitrary that January has 31 days instead of 30; had it been given thirty, the day we call the “22nd” would have been the “23rd” of February, and our celebration would have been one day earlier. And 2022 is arbitrary two too. Other perfectly good calendars referred to yesterday by a completely different day, month and year.

This, my friends, is exactly what General Relativity (and the rest of modern physics) tells you not to do. This is about putting all of your energies and your focus on your coordinate system — on how you represent reality, instead of on reality itself. The coordinate system is arbitrary; what matters is what actually happens, not how you describe what happens using some particular way of measuring time, or space, or anything else. To get excited about the numbers that happen to appear on your measuring stick is to put surface ahead of substance, math ahead of physics, magic ahead of science. It’s as bad as getting excited about how a word is spelled, or even what word is used to represent an object; a rose by any other name.

But we humans are not designed to think this way, it seems. We cheer when we’ve driven a thousand miles, a milestone (hah) which combines the definition of mile (arbitrary) with the fascination with the number 1,000 (which only looks like an interesting number if you count with ten fingers, rather than 12 knuckles, as the Babylonians did, or eight tentacles, as certain intelligent sea creatures might do.) We get terribly excited about numbers such as 88, or 666, which similarly depend on our having chosen to count on our ten fingers. A war was ended on 11/11 at 11:00 (and one was started on 22/2/22 — coincidence?)

Celebrating birthdays is a little better. No matter what calendar you choose, or whether it even lasts a year (as, for example, in Bali), the Sun appears to move across the sky, relative to the distant stars, in a yearly cycle. When it comes back to where it was, a year has passed. If we define your age to be the number of solar cycles you’ve experienced, then that means something, no matter what calendar you prefer. Your birthday means something too as long as we define it not by the arbitrary calendar but by the position of the Sun on the day of your birth.

Similarly, the solstices that mark the days with the shortest daylight and shortest darkness, and the equinoxes that have days and nights equal in duration, are independent of how you count hours or minutes or seconds, or even days. It doesn’t matter if your day has 24 equal hours, or if you divide your daylight into 12 and your darkness into 12, as used to be the case. It doesn’t matter what time zones you may have arbitrarily chosen. If you want to mark days, you can use the time that the Sun is highest in the sky to define “noon”, and count noons. A year is just over 365 noons, no matter what your calendar. The time from solstice to solstice is about half that. But the date we call “December 25th” does not sit on a similarly fundamental foundation; it shifts when there’s a leap year, and sometimes it’s three days after the solstice and sometimes four. Many other holidays, driven by Moon cycles rather than a Sun cycle, are even less grounded in the cosmos.

Being too focused on coordinates can cause a lot of trouble. The flat maps that try to describe our spherical Earth make all sorts of things seem to be true that aren’t. They all make the shortest path between two points impossible to guess. Some wildly exaggerate Greenland’s size and minimize the entire African continent. Most of them make it difficult to imagine what travel over the north or south pole is like, because there’s a sort of “coordinate singularity” there — a single point is spread out over a whole line at the top of the map, and similarly at the bottom, which makes places that are in fact very close together seem very far apart.

A coordinate singularity of a more subtle type prevented scientists (Einstein among them) from realizing for decades that black holes, which were once called “frozen stars,” have an interior, and that you could potentially fall in. The coordinates originally in use made it seem as though time would stop for someone reaching the edge of the star. Bad coordinates can obscure reality.

Physics, and science more generally, pushes us to focus on what really happens — on events whose existence does not depend on how we describe them. It’s a lesson that we humans don’t easily learn. While it’s fine to find a little harmless and silly joy at non-events such as 22/2/22 or 2/22/22, that’s as far as it should go: anything that depends on your particular and arbitrary choice of coordinate system cannot have any fundamental meaning. It’s a lesson from Einstein himself, advising us on what not two do.

Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON February 23, 2022

Last time I described an easy way for you to determine the size of the Moon — easier than the famous techniques used by the classical Greeks. (We don’t need to know the Earth’s circumference, as they did, if we’re ok with a moderately precise estimate.) Once you’ve done that, there’s an simple method, well known since classical times, for figuring out how far away the Earth’s companion is. That’s what I’ll describe in this short post.

(What’s not so easy is to determine the distance and size of the Sun. The classical Greeks failed in their efforts. We’ll need a more modern approach… but that’s for next week.)

Size Versus Distance

Even the early classical Greeks knew something about the Sun, just from the fact that the Moon and Sun appear roughly the same size to our eyes — that is, they occupy about the same amount of sky. If the Sun is twice as far away as the Moon, its diameter must be twice as big, in order that it appear the same size. That’s illustrated in the figure below. If it is ten times as far away, its diameter must be ten times as big. If it’s four hundred times as far away, its diameter is four hundred times as big. (Spoiler: that last one’s the truth; but we’ll get to it later.)

If the Moon is a distance L away from you, and another object twice as far away appears to be the same size in the sky, then that object’s diameter must be twice the Moon’s diameter D. This logic applies more generally to objects further and nearer than the Moon.

You can run this logic in the other direction; if something perfectly blocks the Moon, then if it’s ten times closer than the Moon its diameter must be ten times smaller. If it’s a billion times closer than the Moon, it must be a billion times smaller.

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON February 18, 2022


Having confirmed we live on a spherical, spinning Earth whose circumference, diameter and radius are roughly 25000, 8000, and 4000 miles (40000, 13000, and 6500 km) respectively, it’s time to ask about the properties of the objects that are most obvious in the sky: the Sun and Moon. How big are they, and how far away?

If the Moon were close to Earth, then at any one time it would only be visible over a small part of the Earth, as indicated in light blue. But in fact (except at new moon) about half the Earth can see it at a time.

Historically, many peoples thought they were quite close. With our global society, it’s clear that neither can be, because they can be seen everywhere around the world. Even the highest clouds, up to 10 miles high, can only be seen by those within a couple of hundred miles or so. If the Moon were close, only a small fraction of us could see it at any one time, as shown in the figure at right. But in fact, almost everyone in the nighttime half of the Earth can see the full Moon at the same time, so it must be much further away than a couple of Earth diameters. And since the Moon eclipses the Sun periodically by blocking its light, the Sun must be further than the Moon.

The classical Greeks were expert geometers, and used eclipses, both lunar and solar, to figure out how big the Moon is and how far away. (To do this they needed to know the size of the Earth too, which Eratosthenes figured out to within a few percent.) They achieved this and much more by working carefully with the geometry of right-angle triangles and circles, and using trigonometry (or its precursors.)

The method we’ll use here is similar, but much easier, requiring no trigonometry and barely any geometry. We’ll use eclipses in which the Moon goes in front of a distant star or planet, which are also called “occultations”. I’m not aware of evidence that the Greeks used this method, though I don’t know why they wouldn’t have done so. Perhaps a reader has some insight? It may be that the empires they were a part of weren’t quite extensive enough for a good measurement.

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON February 17, 2022

Even if you’re working from home, so that you’re spending the day at a fixed location on the Earth’s surface, you’re not at a fixed location relative to the Earth’s center. As the Earth turns daily, it carries you around with it. So where are you headed today? Presumably Earth’s spin takes you around in a big circle, right?

That’s great. Which circle?

Point to it, right now.

Let me ask that again, in case that wasn’t clear. With your feet on the ground, looking whichever direction you choose, please show me the circle you’ll be taking today on your travels.

Most people who hazard a guess imagine that if they face east (toward the rising Sun, which here is into the plane of your screen), they are traveling on a circle that cuts vertically into the ground. But this is true for very few of us.

No idea? In my experience, many people have never even thought about it. Those who are willing to hazard a guess have to think for a moment to figure out that the Earth is rotating west to east — that’s why the Sun appears to rise in the east and set in the west. Once they are clear on that point, many people face east, and then indicate a circle that goes straight ahead, which would be combination of east and then down, as you can see in the figure.

To say that another way, if you imagine the circle of travel as being the edge of a disk, that disk would face east-west and slice directly down into the ground.

For the vast majority of us, it turns out this guess is not correct.

So where are we headed? People located at the equator or the poles can answer this more easily than the rest of us, so let’s start with them.

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON February 14, 2022

I’ve received various comments, in public and in private, that suggest that quite a few readers are wondering why a Ph.D. physicist with decades of experience in scientific research is spending time writing blog posts on things that “everybody knows.”  Why discuss unfamiliar but intuitive demonstrations of the Earth’s shape and size, and why point out new ways of showing that the Earth rotates?  Where’s all the discussion of quantum physics, black holes, Higgs bosons, and the end of the universe?

One thing I’m not doing is trying to convince flat-earthers!  A flat-earther’s view of the world is so full of conceptual holes that there’s no chance of filling them.  Such an effort would be akin to trying to convince a four-year-old Santa Claus devotee that the jolly fellow can’t actually fly through the air and visit half a billion homes, stopping to eat the cookies left for him in every one, all in one night.  Logic has no power on a human whose mind is already made up.  (If you’re an adult, don’t be that human.)

Instead my goals are broader, and more contemplative than corrective.   Here are a few of them.

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON February 11, 2022

In my last post I gave you a way to check for yourself, using observations that are easy but were unavailable to ancient scientists, that the Earth is rotating from west to east. The clue comes from the artificial satellites and space junk overhead. You can look for them next time you have an hour or so under a dark night sky, and if you watch carefully, you’ll see none of them are heading west. Why is that? Because of the Earth’s rotation. It is much more expensive to launch rockets westward than eastward, so both government agencies and private companies avoid it.

In this post I want to describe the best proof I know of that the Earth rotates daily, using something else our ancestors didn’t have. Unlike the demonstration furnished by a Foucault pendulum, this proof is clear and intuitive, involving no trigonometry, no complicated diagrams, and no mind-bending arguments.

The Magic Star-Pointing Wand

Let’s start by imagining we owned something perfect (almost) for demonstrating that the Earth is spinning daily. Suppose we are given a magic wand, with an amazing occult power: if you point it at a distant star, any star (excepting the Sun), from any location on the Earth, it will forever stay pointed at that star. Just think of all the wonderful things you could do with this device!

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON February 7, 2022

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