July 23, 2026 : Wondercab Mini (117A)

WELCOME

Comparing the relative densities (matter to empty space) of the Milky Way and a stretch of the human arm, by convening our Cabinet’s kitchen cabinet.

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The Main Event

Cabineteers Want to Know
(or Ren does, anyway):
Which is denser, the Milky Way or the Human Arm?

So I was meandering about the internet a few weeks back and I came upon this astonishing image at the ThisIsColossal website:

Just look at this thing!
or alternatively this video expansion of same.

This is a recent massive photomosaic of the 60 million stars that make up a small part of the core of the Milky Way as captured by the European Space Agency’s Euclid spacecraft (discussed here).

And it got me to wondering—as I suspect it may have you as well. And in my case, I decided to convene a meeting (by way of a group email) of our Wonder Kitchen Cabinet, as it were—an ad hoc grouping of friends who we regularly call on at times like this, in moments of free-floating perplex. I linked everyone to the Euclid photomosaic with its characterization, and went on to ponder, as follows:

I assume that even though the vista above is as seemingly dense as a wall, this must be an illusion in part caused by rendering what begins as a deep gaze into 3- or even 4-dimensional space across a two-dimensional surface.  That, in fact, light-years separate each individual pair of the 60 million stars (Yes? No?).

And my question is whether a similar electronic microscopic x-ray (or some such) vantage of an expanse, say, of a small stretch of my arm, would show a similarly dense vista of molecules or atoms or I’m not sure what, even though any two such entities would be similarly far, relatively speaking, from each other.

Yes? No?

Please illuminate? elucidate...

Ren

AND THE RESPONSES BEGAN POURING IN. TO WIT:

MICHAEL BENSON’S REPLY

{Michael Benson is the author of several utterly ravishing visual anthologies—several of those (Beyond; Far Out; Planetfall) surveying the macro-telescopically far-flung and far-distant, while his most recent, Nanocosmos, plumbs the infinitesimally electron-microscopic.}

Hi Ren,

Your assumption is correct that it’s an illusion. Atoms in your arm are way more tightly packed, they’re separated by only one to two times their own radius. Stars in the Milky Way, even in the tightly packed central areas, are more like between 0.1 and 1 light year in separation, or a million to ten million times their radius. So hundreds of thousands to millions of times more empty space than between atoms.

On the other hand, atoms are mostly empty within the sphere of their electron cloud. 

{An AI query amplifies this last point: “Atoms are mostly empty space. If you imagine the nucleus as a grape sitting on the 50-yard line of a football stadium, the electrons are like tiny gnats buzzing around the very top row of the stadium.” [1, 2, 3]}

BTW just a couple days ago I answered a question from Musee Magazine (about Nanocosmos) with this (a fragment of the whole answer):

That’s the power of the technology. And with macro imaging, in which an entire galaxy can be reduced to the size of a 11.5 x 11.5” book page, another extraordinary type of scaling is at play. And by the way, we’re so used to seeing things in 2D—we’re so trained to see things that way—that we rarely even think about that other form of reduction, namely the compression of the visual field down to a 2D piece of paper. So there’s not just a reduction in scale to consider, but depth compression. I mean, a galaxy can be 100,000 light years across—and we have the hubris to collapse that down into a flat image that can be held in one’s lap!

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WALTER MURCH’S REPLIES

{Walter Murch, another Cabinet regular, is the eminent film and sound director (Apocalypse Now; The Conversation; The Unbearable Lightness of Being; The English Patient, and so on) and the author most recently of the first volume of a memoir-cum-manual-cum-manifesto, Suddenly Something Clicked.}

Hola Ren :

Yes, with a proviso….  

If you were given a pair of magic mittens (thought experiment coming up!) and could gather all those Milky stars into a single “starball” (ignoring gravitational effects) and gently pat that ball into a sphere of Sun-like density (1,410 kg/m3), it would have a diameter of just less than the orbit of Uranus in our Solar System. 18 astronomic units, or 5.4 billion km.

(All numbers here are congenially approximate)

So all the stars in the Milky Way could easily fit within our Solar System, with a few planetary orbits to spare.

The volume of the Milky Way itself is 100,000,000,000,000,000,000,000 (1e23, in other words 1 followed by twenty-three zeros) times the volume of that starball. Which is to say: Lots of empty space. 

If you performed the same magic trick with all the stars in the observable universe, the starball would have a diameter of 6.6 light years. If that starball were centered on our Sun, it would not quite reach Alpha Centauri, the nearest star to us. Remember the diameter of the Milky Way is 100,000 light years. 

The volume of the observable universe is 1e30 times the volume of that first starball. That is like comparing a 1mm grain of sand to the volume of the planet Earth.

Now, your arm: it is made of atoms nestling close to each other, so the atoms are not like the stars, living far from each other. But each atom itself is full of emptiness, unlike a star. 

The volume of an atom (out to the furthest electron orbit) is 10,000,000,000,000 (1e13) times the volume of its nucleus.

So now we have three volumetric ratios of empty space compared to the baryonic matter within. (We are ignoring dark matter.)

The Observable Universe 1e30
The Milky Way 1e23
Your arm: 1e13

So the Milky Way is 1e7 (ten million) times denser than the Universe itself.

And your arm is 1e10 (ten billion) times denser than the Milky Way.

Abbracci forti (or fifty!)

W xo

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TED CHIANG’S RESPONSE

{Ted Chiang, one of our most celebrated authors of science and speculative fiction, is the writer, among others, of Stories of Your Life and Others (which includes the novella that formed the basis of the film Arrival) and the subsequent collection Exhalation.}

Ren, you’ve gotten excellent answers from Michael and Walter. I will just add a minor observation, which is that stars are visible from great distances because they radiate light on their own. Individual atoms do not, so any attempt to visualize atoms requires shining some kind of light at them. The wavelengths of visible or ultraviolet light are too long to resolve atoms, so you need X-rays (or perhaps some type of particle beam). But even then, the wavelength of X-rays is not that far off from the size of the atoms themselves, so the resolving power is not great, and X-rays aren’t well reflected; they usually go between the atoms, meaning you have to illuminate the sample from behind. So it’s a bit like trying to get a clear picture of a jungle gym by throwing a bunch of tennis balls through it and seeing how their paths are changed. 

This image was one of the ones used to deduce the structure of DNA:

You can see how abstract it is, and how different it is from conventional representations of the double helix.

Also, X-ray crystallography works because the regular arrangement of atoms in a crystal makes it possible to get useful information out of how the X-rays are diffracted. The sample is rotated and the difference between the diffraction patterns at different angles provides information about the arrangement. The atoms in your arm are in highly irregular configuration, so my guess is that it would be a computationally intractable problem to deduce anything from the diffraction patterns of X-rays going through your arm.

This does suggest a thought experiment: if the stars did not emit light, how would we form a picture of the Milky Way? If we assigned stars a certain albedo, or reflectance, what kind of light source would we need to get a good picture? Are we using a point source situated inside the galaxy, or some kind of planar light source located outside the galaxy?

Ted

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MARGARET WERTHEIM WEIGHS IN

{Margaret Wertheim, curator of her own substack, Science Goddess, is a physicist-turned-science-writer, author among others of The Pearly Gates of Cyberspace: A History of Space from Dante to the Internet and Physics on the Fringe) and the cofounder, with her twin-sister Christine, of the ongoing-mass-community project bridging hyperbolic geometry and ecological activism, the Crochet Coral Reef.}

Here’s my response re the star/atom photo issue.

Walter and Michael nicely address the space issues here. I want to respond to something Ted says.

Ted raises the issue that we can only really see atoms by bouncing light off them. Or x-rays, or particles. Very true. He also points to the famous Photo 51 that played a key role in the elucidation of the structure of DNA. That “photo” is not a photo in the classical sense, rather its a diffraction pattern. Technically the pattern in this image is not the structure of DNA but the Fourier Transform of the structure of DNA. Crystallography is a science in which people capture Fourier Transforms of atomic or molecular structures and then use this transform to determine the real-world structure. So this is not ‘photography’ per se. Those versed in reading transforms become very adept at seeing the real-world structures captured by them. I learned to do so in optics classes at university. 

All photos have in, some sense, a one-to-one light correspondence with the thing they are an image of. Whereas diffraction patterns capture the composition of waves that make up the structure of something. Holograms do the same thing. Indeed, a hologram is a fourier transfrom of the object it represents. The word “represents” is specific here: photos depict objects, but transforms represent them in a dual space of waves. The FT is also the mathematics behind the Shroedinger equation, and wave-particle duality is a real-world playing out of the duality of real-world space and transform space. FTs are used in vast areas of physical and techno-sciences including data-science, sound analysis, music synthesis, interpretation of seismic signals, and much much more. Fourier imaging represents an entirely other kind of imaging to photography. It’s a modern marvel. Indeed the FT has been called the most useful piece of mathematics ever.

I’m semi-obsessed with the FT and its many applications, and am working on a long essay about it and its relationship to optics, quantum mechanics and data science, due out one of these days.

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AND BLAISE AGÜERA Y ARCAS ROUNDS OUT THE FIELD:

{Blaise, another Cabinet regular, is a polymathic leader in computational vision and photography, machine intelligence and large language modeling, and much else, long affiliated with Google. He is the author of the novella Ubi Sunt, and more recently a short book What is Life? and a longer one, What is Intelligence? and yet another forthcoming: On Giving a Shit: Consciousness, AI, and Why We Care.}

Ren, you already have all the good physics answers a humanist could wish for here, so I’ll just add something brief.

Because of the vast differences in scale here, our eyes are far from ideal instruments to resolve either atoms or stars. (Indeed, in the case of atoms, they can’t even be resolved in wavelengths we can see, as others have pointed out.) Also, for opposite reasons of scale, neither atoms nor stars are affordances in our Umwelt, by which I mean, our bodies, unaided by technology, can’t manipulate either one, either with tweezers or cosmic mittens. That makes the very question of their unmediated “reality” even more nebulous than reality usually is (for, of course, we never see anything “as it is”... in fact that phrase can’t really mean anything). So no matter what we do to visualize atoms or stars, let alone compare those visualizations, it’s an act of mediation, translation, and ultimately metaphor.

SO GOOD, OKAY THEN, I’M GLAD THAT’S ALL SETTLED…

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See you next week!

{Note: All of the stars in this issue of the Cabinet, details from the photomosaic at the top, are contained within that little red lozenge at the center-left of this wider angle view of the Milky Way.}