Well, that’s everything

January 8, 2024   Issue #666

About this newsletter

Ooo, meta

Wow, Issue 666! Quite a kilometerstone. You know what this means, right? When you’re 2/3rds of the way through reading this, you’ll be 2/3rds of the way to reading 1,000 issues! Assuming you’ve read the previous 665. Get thee to the archive.

[CORRECTION: ARG! Bruce Dawson on Blue Sky noted that this is incorrect. You’d have to read 2/3rds of the way through issue 667 to get to 2/3rds of 1,000. Issue 666 is 2/3rds of 999. I forgot this started at Issue 1, not Issue 0, and made the old “last year of the century” mistake. So anyway, ignore that bit above, which I leave intact to show that I blow it sometimes.]

Besides the usual way people think of the number, 666 is interesting. Mathematically, it’s the sum of the first 36 natural numbers: 1 + 2 + 3 + 4… + 34 + 35 + 36 = 666. Numbers like that are called triangular numbers, due to the way you can arrange them as dots in a triangle. It’s also a Harshad number, meaning it’s evenly divisible by the number you get when you add up its digits (6 + 6 + 6 = 18, and 666 / 18 = 37).

It’s also a lotta issues of BAN. Good thing I enjoy writing these! And you, apparently, like reading them. I have no plans to stop (though I do have plans coming up soon for some changes), so stick around. There’s lots more Universe to poke at.

A Bit o’ Science

The entirety of science is too much for one sitting. Here’s a morsel for you.

[Note: That subheading is ironic, if not an outright lie, as you’ll see in a moment.]

Via the terrific Orbital Index newsletter I found a paper that is pretty cool: In it, the scientists are trying to explain… everything.

I mean that literally. The paper (which is short but still head-spinning) starts with the premise that by graphing some characteristic against another, some fundamental truths can be uncovered. This is not news; that’s how a lot of science is done (like the HR diagram in astronomy, which plots the luminosity of a star versus its temperature, and reveals a lot — a lot — of important stuff about how stars work).

But in this case the scale of their graph is what made me smile. It’s large. Very, very large:

The graph plots the mass of an object on the y-axis (the outer scale shows the mass in terms of the mass of the Sun, aka one solar mass, which is about 2 x 10^33 grams, and the inner scale in just grams). The x-axis at the bottom is size, measured in centimeters (at the top it’s in megaparsecs, where 1 Mpc is equal to 3.26 million light-years, a convenient-ish distance unit in astronomy because galaxies are separated by distances like that). But note, critically, that both axes are in logarithmic scale. I explained this in excruciating detail in an earlier (but fun! I swear!) article about music, but it’s a way of compressing a huge range into something readable. The number listed on an axis is the power of 10 to that quantity. So, on the outer y-axis scale, an object plotted at the value of 0 has 10^0 = 1 solar mass. An object at a value of 2 has 10^2 = 100 solar masses. Same along the x-axis, with an object at 0 being 1 cm in size, and an object, say, 5 is 10^5 = 100,000 cm or 1 kilometer wide.

So look at the inner y-axis now. That range goes from something 10^-50 grams in mass, which is ridiculously lightweight (an electron has a mass of about 10^-27 gm, or 0.0000000000000000000000000001 gm) up to 10^60 grams. The mass of the entire observable Universe is roughly 10^56 grams, so this plot covers literally everything. Everything.

What’s fun is to look for trends, looking at where things fall on the graph and seeing if there’s a pattern. A bacterium, a flea, a human (assuming a mass of 70 kg and a size of half a meter; they approximate everything as a sphere which, on this scale, is fine), a whale, Earth, the Sun… these all have roughly the same density (their mass divided by their volume), so they fall on a straight line (the reason behind this has to do with the way objects at the same density get more massive with the increase in size). These objects are all made of atoms.

On the other hand more dispersed objects like star clusters, galaxies, and clusters of galaxies are less dense. Their individual components, like stars in clusters, are made of atoms, but the cluster as an object itself is much larger and so has a lower density. Same with galaxies. A lower density means they’re farther over to the right, and their larger sizes puts them higher up in the graph.

There are lots of other things in this graph, mostly explained in the paper, or stuff you already know if you have like 20 years experience dealing with Big Bang physics. Don’t worry about them; I haven’t for the purpose of this article.

The point the paper makes with this graph is that there are regions where things get screwy. If you have a lot of mass (so, higher up) squished into a small volume (so, to the left) at some point you get an object so dense it becomes a black hole. That’s the “Forbidden by Gravity” part to the upper left.

On the other hand, if you have an object that is incredibly low mass and very small, quantum mechanics rears its head and says, nope, the Uncertainty Principle means you can’t know anything about them. That’s the lower left part of the graph, “Quantum Uncertainty”.

So what’s this mean, exactly? That’s… complicated. But one thing they look at is the question, is the Universe itself a black hole? When plotted, the cosmos falls on the line that demarks black holes — meaning the Universe itself is as dense as a black hole for a black hole the size of the Universe — so it’s a legit question. They argue that it might be true but not necessarily. We can only see out to a certain distance (the observable part of the observable Universe) and the Universe itself extends out much farther than that — I explain this in more detail in Crash Course Astronomy, so give that a watch. It depends on what’s outside our cosmic horizon; if there’s nothing, then yeah, we’re inside a black hole by definition. But if the rest of the Universe is like what we see locally, then we’re not. I’m still mulling that one over, honestly. It’s a weird thought.

They also discuss teeny weeny black holes — smaller than an atom but with considerable mass, which are theoretical but my have been created in the first moments of the Universe — which may or may not exist, and how they might affect the early Universe. And take a look at the black triangular region all the way on the left: Anything in there would be too massive and too small to exist: It’s forbidden by both gravity and quantum mechanics. We shouldn’t ever find anything that would go there, since it’s doubly taboo. Weird.

I don’t want to go into too much detail — because a) it would take too long, and 2) I don’t understand everything they’re discussing since it’s not my field — but the whole point is that a big part of science is looking for trends, and a fantastic way to do that is graphing stuff, so why not graph everything?

I love this idea, and I wonder what else can be gleaned about the entirety of existence by examining different versions of this graph. To quote every textbook I had in grad school: I leave that as an exercise to the reader.

Et alia

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