Travel the Universe with a sheet of A4

March 26, 2021 7:42 PM

Metric Paper & Everything in the Universe (SLYT by CGP Grey) See also (some previously): Powers of Ten, The Super Zoom, The Known Universe, Timelapse of the Entire Universe, The Size of Space
posted by gwint (39 comments total)

I know intellectually that it doesn't take all that many doublings of anything to get to really crazy scales, but I'm still always surprised when I see stuff like this.
posted by wierdo at 7:45 PM on March 26, 2021 [2 favorites]

How big is the observable universe?

A4 x 2^184 also known as Aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa....
posted by Avelwood at 8:35 PM on March 26, 2021 [3 favorites]

the size of space is cool.
My firminent belief is there is nothing behind stars, a view widely dispersed.
posted by clavdivs at 8:50 PM on March 26, 2021 [2 favorites]

Well I feel bad for being absolutely utterly insignificant but I feel good for being able to correctly identify the music.
posted by aubilenon at 10:17 PM on March 26, 2021 [1 favorite]

Smooth transition
nothing to nothing

Planck Links - walking the plank to the edge of my sanity.
Staring into a starlit sky keeps me grounded.

Thanks so much for posting gwint.
posted by unearthed at 10:29 PM on March 26, 2021

So can we stop using US Letter now, please?
posted by How much is that froggie in the window at 11:02 PM on March 26, 2021 [18 favorites]

What comes to mind is an old Gary Larson Far Side cartoon: two ants are sitting atop a mushroom, hugging their knees and staring up at the night sky and one is saying 'You know, there's nothing like staring at all the stars to make you feel tiny and insignificant...'
posted by y2karl at 12:09 AM on March 27, 2021 [2 favorites]

Eh, I prefer the proportions of US letter, but will readily acknowledge that the A sizing is far superior as a system. I feel much the same way about Fahrenheit vs. Celsius. Celsius is better in every respect except at being sufficiently precise in setting a goddamned thermostat to a comfortable temperature. I swear to god metric units were all conceived by robots.
posted by wierdo at 12:31 AM on March 27, 2021 [4 favorites]

MeFi more “Space [...] is big. Really big. You just won't believe how vastly hugely mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space.”
posted by BobTheScientist at 12:43 AM on March 27, 2021 [4 favorites]

I feel much the same way about Fahrenheit vs. Celsius

As much as I hate imperial units and wish we could leave them behind forever, there is something nicely human-scale about some of them. That 0 to 100 degrees spans most human experience of "really cold" to "really hot" feels natural, compared to -20 to +40. And having people, rooms, and cables be more than a few and less than a hundred length units is handy. I suggest we switch to decidegrees and decimeters. It's no weirder than making the kg a base unit.

Also, neat videos. Thanks!
posted by eotvos at 4:00 AM on March 27, 2021 [1 favorite]

Don’t miss the sequel to Timelapse of the Entire Universe, Timelapse of the Future, posted previously.
posted by TedW at 4:31 AM on March 27, 2021

Imperial is the vinyl of measurement systems.
posted by condour75 at 5:13 AM on March 27, 2021 [4 favorites]

Imperial is the vinyls of measurement systems, surely?
posted by scruss at 5:59 AM on March 27, 2021

Even worse, the US "Imperial" measurement system isn't even the actual UK Imperial measurement system. It's most noticeable in volumes. The US ounce isn't an Imperial ounce, an Imperial pint is 10 oz, and an Imperial gallon is 20% bigger than a US customary one.

When I'm converting measurements from cookbooks, or even scaling recipes, it's way easier to convert everything to metric, do the math in a sensible base 10, then convert it back to whichever base 12 or base 20 wackadoodle unit system the recipe is written in.

My favourite realization on unit scales though is talking to astrophysicists about stellar temperatures. They'll refer to solar temps as 5000 or 6000. When seom naive chem undergrad asks whether they mean Celcius or Kelvin, the answer is "Sure, which ever one you like." (K+273=C, a difference too small to matter on those scales).
posted by bonehead at 6:10 AM on March 27, 2021 [1 favorite]

When I'm converting measurements from cookbooks,

The sphere of the observable universe; what's the volume of that in tablespoons?
posted by otherchaz at 6:56 AM on March 27, 2021 [2 favorites]

2.4x10^85 US tablespoons (or 2.0x10^85 Imperial Tbsp).
posted by bonehead at 7:14 AM on March 27, 2021 [2 favorites]

Warning: Pedantry

This is an interesting analogy but I missed at least a couple of minutes of it, distracted by his use of the word "exactly" in "A0 is exactly one square meter." It would have been easy to leave out that word, still make the point, and be correct, because

a) it's mathematically impossible for any of this to be exact for any choice of integer side lengths because the side length ratio by definition needs to be an irrational number, and

b) even without working the whole thing out, the last digit of the area has to be a 9 so it's clearly not true using the information on the screen at the time he says it (upon actual calculation the area is 51mm² short).

I think this would bother me less if it wasn't a member of larger class of squaring-the-circle-style common misconceptions about how numbers work, which he's unintentionally perpetuating by claiming exactness. I know the answer is really "1, within manufacturing tolerances" but that's very different from the Cosmic Numerology vibe of the video overall.
posted by range at 8:06 AM on March 27, 2021 [4 favorites]

I found it pretty shite, really, and I'll tell you why: it leaves you on a note of desolation, rather than an appreciation for everything we have at the human scale. The best one of these zoomy things, IIRC, begins and ends on a picnic blanket.

Our significance in the cosmos isn't numeric, it's in feeling joy at being alive, and empathy for the suffering of other beings. It's in taking what we were given, making it just a little bit better, and passing it on to the next generation.

Bleakness, tbh, is bullshit.
posted by seanmpuckett at 9:54 AM on March 27, 2021 [4 favorites]

Also I was kind of disappointed he didn't just use the paper numbering system. A8 is a sixteenth the area of A4, and A-3 is eight times the size of A0 for example.
posted by seanmpuckett at 9:57 AM on March 27, 2021 [1 favorite]

2.4x10^85 US tablespoons (or 2.0x10^85 Imperial Tbsp).

Confirmed. I love metafilter.
posted by eotvos at 10:02 AM on March 27, 2021 [1 favorite]

The animation of our galaxy lacks the central bar.
posted by meehawl at 10:32 AM on March 27, 2021

Appreciate the peer-review.
posted by bonehead at 11:02 AM on March 27, 2021 [1 favorite]

In regards to U.K. vs US Imperial units, I blame capitalism. In US Imperial units a pound of coffee is now just 12 ounces. A half gallon of ice cream is now smaller.
posted by njohnson23 at 11:39 AM on March 27, 2021

God I miss A4 paper and C5 envelopes. You could always fold an A4 paper in half and have it fit in a C5 envelope. I don't know why size 7 envelopes exist. If you don't look carefully you can mistake them for size 9 envelopers and then NONE OF YOUR SHIT FITS. Meanwhile a C6 envelope is tiny compared to a C5.
posted by Your Childhood Pet Rock at 12:46 PM on March 27, 2021 [1 favorite]

otherchaz: "The sphere of the observable universe; what's the volume of that in tablespoons?"

WHICH FUCKING CUP, AMERICA

posted by signal at 5:52 PM on March 27, 2021

Also, that thing with paper and shrimp and things they sell in hardware stores where the bigger the number is the smaller the thing being sold is?
Stop that.
posted by signal at 5:53 PM on March 27, 2021 [2 favorites]

Thank you for reminding me of wire gauge and similar measures so I have a better way to reference A sizes larger than A0 in my head. A0000000000 (ten-ought) sounds way better than asking for A-9 (A minus 9) when I need a sheet of paper sufficient to cover a neighborhood or small town.
posted by wierdo at 7:14 PM on March 27, 2021

What about the league, can't fathom a dram of a decameter, sounds like a record label.
posted by clavdivs at 7:23 PM on March 27, 2021 [1 favorite]

Powers Of Ten Two
posted by fantabulous timewaster at 9:17 PM on March 27, 2021

The best one of these zoomy things, IIRC, begins and ends on a picnic blanket.

A large influx of bees oughta put a stop to that!

Also, "made of nothing" is an oxymoron.
posted by flabdablet at 12:04 AM on March 28, 2021

If I were to make one mark on the world as a science communicator, it would be to put the misconception that “atoms are mostly empty space” into the same useful-but-wrong dustbin as the Bohr model (where we pretend electrons travel around the nucleus like little planets).

The misconception that “atoms are mostly empty” comes from illustrations in textbooks that show protons and neutrons as colored balls that are about the same size. A caption nearby explains that protons and neutrons have about the same mass, while the electron is 2000 times less massive, so the electron is included in the illustration as a smaller ball. Then there is some (correct) text about how the protons and neutrons are packed close in the nucleus, but the volume of the nucleus is only 10^-15 = 0.0000 00000 00001 the volume of the atom. There may even be a (correct) statement that, while we know the size of the protons and neutrons, the electrons are “point particles” whose size is “too small to measure.” It’s either stated explicitly, or the reader is left to believe, that the list of things which could fill the atom has been exhausted, and that the atom must therefore be nearly all vacuum. But that conclusion is wrong. The atom is full of electrons, which get bigger when they are cold.

The colored-ball model, where protons and neutrons are one size and electrons are smaller, makes intuitive sense because all the materials normal humans interact with on a daily basis all have approximately the same density: the same density as water, within a factor of five or so. (You’ve probably handled styrofoam but never aerogel; your experience wearing gold jewelry does not prepare you for the experience of handling a gold brick.) The major exception is air, a thousand times less dense than water, which many educated adults sometimes forget is a material that carries mass at all. If protons, neutrons, and electrons were all made of “particle-stuff” with comparable density, then the big-ball/small-ball model would be a good one. But: they’re not, and it’s not.

We talk about the “intrinsic size” or a proton or neutron because there are short-range interactions that you can only detect below a certain length scale. Some of those short-range nuclear interactions are responsible for “hard-core repulsion” among nucleons, so nuclear matter has the same density whether the nucleus is small or large. A hopper full of tennis balls has constant density, for the same reason. Also, if you force two protons closer together than this “hard core,” these short-range interactions excite internal degrees of freedom and you get something that’s not-a-proton-anymore. Intrinsic size makes sense for protons and neutrons.

Electrons have a “natural size” from electromagnetism, which is slightly bigger than a proton or a neutron. But when you interact with electrons, there is absolutely nothing that changes at this length scale. Electrons do have an “extra interaction” that “turns on” at a particular length scale, which is about 1000 times shorter than the radius of a nucleon. But that’s not special to the electron: every particle that we know about participates in the weak interaction. And no matter how hard we look, the electron doesn’t seem to have any sub-structure that we can excite. Everything interesting that happens when electrons interact at short distances seems to be something interesting about the vacuum, not anything particular to the electron. It’s less that “the electron has zero size” and more that “the electron doesn’t have any size”: questions about intrinsic size, applied to the electron, give nonsensical or contradictory answers.

But there is an extrinsic size parameter associated with an electron, because there’s no such thing as an electron at rest. The de Broglie wavelength of any particle goes like the inverse of that particle’s momentum. And if you figure out how fast an electron trapped in an atom is moving, and turn that into a wavelength, what you get is ... the size of the atom. If there are lots of electrons trapped at the same atom, they take on increasingly baroque shapes that occupy the same volume with “zero overlap.” A low-math analogy might be to imagine a conch shell, which takes up a lot of volume but also has a long empty spiral where the snail used to live, and to imagine a design where you could get two conch shells to nest, one inside of the other.

(This extrinsic size isn’t special to electrons either: people use cold neutrons to study the structure of crystals, because the low-momentum neutrons are bigger than the distance between atoms and therefore interact with many atoms at once.)

I think that “cold electrons are huge” is just as pithy as “atoms are mostly empty space,” while also being more correct, being more interesting, and having more predictive power.
posted by fantabulous timewaster at 9:41 AM on March 28, 2021 [9 favorites]

Even "empty space" isn't empty. There's weird incoherent shit going on everywhere all the time; some of it occasionally sticks around long enough to be observable.
posted by flabdablet at 10:05 AM on March 28, 2021 [1 favorite]

That's a really nice perspective, fantabulous timewaster. I think you mention it in passing in there but I wanted to point out that I think the "mostly empty space" model is probably a direct descendant of popular accounts of the Rutherford/Geiger experiments, where the disconnect between the "physical" (electron) dimensions of an atom and its behavior when you throw nucleons at it is pretty astonishing. But to first approximation that gets reported as it being mostly empty space, which is kind of true if you're an incoming alpha particle, but then leaves us kind of unequipped to explain why nuclei end up so far apart from each other in bulk materials.
posted by range at 10:24 AM on March 28, 2021 [1 favorite]

CPG Grey's cosmic journey was great, but the actual details of paper sizes is as you would expect overly exacting, baroque and complex. https://en.wikipedia.org/wiki/Paper_size You have heard of A4 but what are B4 and C4? They are sizes in between the A sizes. This was all originated by the German national standard of course, but the Swedes then said "why not D, E, F and G too? If US letter is 8.5x11" where did US alternative 8x10" and 8x10.5" come from? Herbert Hoover said so. And don't get me started on the archaic French size names.
posted by thefool at 12:08 PM on March 28, 2021

QED provides us with a pretty good idea as to why electron orbitals are where they are and, to a lesser degree, why atoms arrange themselves in the way they do in macro scale materials. It is, in a very real sense, true that atoms are mostly empty space. Not exactly, since it is also true that an electron could be anywhere in the cloud of probability that makes up said electron's corresponding orbital and those regions fill most of the space we would consider "inside" an atom. We very much know how big an electron isn't, so it isn't exactly accurate to say that the space in the cloud of electrons surrounding the nucleus isn't mostly empty, though.

All of space is filled with some probability of a particle existing in that location, yet vacuum is still a phenomenon that happens, so I find it hard to say that the unrealized possibility of a particle is enough to say that a volume is not empty. At some level beyond time that doesn't map to our human experience, sure, but when talking about the way things work for those of us stuck in that metaphorical river, not so much.
posted by wierdo at 2:25 PM on March 28, 2021

Sure, but what does it mean to say that an electron “is somewhere within” an orbital? It means that electron somehow has a position uncertainty Δx which is much smaller than the characteristic size of the orbital. If your mental picture of how nucleons and electrons look is a big-ball/small-ball model, you might say an electron has been “found” when its position uncertainty Δx is like the size of nucleon. But an electron which is localized so precisely has an enormous momentum uncertainty Δp; nearly the entire phase space for such an interaction has the electron ejected from the atom afterwards. You may have determined where the electron was, but you’ve done so destructively. Make an electron hot, and it gets small enough for you to decide you have found it.

The “probability cloud” interpretation comes from the era before relativistic field theories, and seems to rely on a semiclassical notion of “a particle.” People who use field theories to solve problems tend to be unbothered when I say something like “cold electrons are big.”
posted by fantabulous timewaster at 7:03 PM on March 28, 2021 [1 favorite]

Sure, a cold electron is big in one sense, but in other senses it isn't. They've gotta be pretty cold to measure their magnetic moment, but the volume in which it is detectable is still much less than the distance (the space in which the probability amplitude is zero or close enough not to matter) between the innermost orbital and the nucleus.

It's probably more fair to say that if you ignore the particle half of the wave-particle duality, the question of how much empty space there is in an atom is functionally meaningless, as so many questions are in QM more generally. Whether you believe it's all waves or it's both, you end up in the same place making the same predictions anyway. The electrons in my fist are going to exert a force on the electrons in my face if I punch myself no matter whether the volume is filled with electron-ness or not. Either way the two collections will stubbornly refuse to occupy the same quantum state as one another, resulting in a sore jaw and a sore hand regardless of what I think about what it means for space to be empty.
posted by wierdo at 7:47 PM on March 28, 2021

Exactly. "Could I put something there" is a much better test for emptiness than "Can I imagine something there".
posted by flabdablet at 7:52 PM on March 29, 2021 [1 favorite]

Sure, but what does it mean to say that an electron “is somewhere within” an orbital?

Experimentally, it means that if you punch electrons with a certain energy, you can get some position and momentum data that looks like an orbital. That's pretty much all we've been able to do for the past half-century or so. We can locate down to the inter-atomic scale, but I'm not aware for work that allows intra-atomic spatial resolution... yet.

A favorite bugaboo of mine is that we still have no certainty that electrons (or any sub-atomic particles) travel in anything like a continuous path, whether as a wave packet or what ever. That is an electron could, by the models we have now, instantaneously flit from position to position within its orbital (or state) without crossing the space in between in a way that would be meaningful to us at our level of scale. Indeed, quantum teleportation seems to be supported by evidence of multi-well structures and evanescent transitions, to name but a few.

So the question of where an electron is in 3d space within a molecule or within an orbital state or within a structure band isn't obvious to me, and is significantly harder to answer in a way that we can analogize to understand in a classical, "this object is here" sense than might be obvious at first glance.
posted by bonehead at 6:22 AM on March 30, 2021 [1 favorite]