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I want to self-publish a book called "Tweets on Entropy" - but I need a cover. Do you have suggestions for a good cover? Some rules:
1) It can't be a joke There are lots of jokes about entropy but I don't want them on the cover of my book. I want the cover to be artistic, inspiring, maybe even secretly teach some deep fact about entropy... yeah, I'm like that.
2) It can't have equations in it. I like equations, but my book is full of equations already.
3) It can't be a picture of Shannon, Boltzmann or Gibbs. I admire these guys immensely, but I don't want the cover of my book to be a picture of someone.
Here is a cover I made in less than 10 minutes. There could be something better.
It may help if you know what topics my book actually covers. Check out part 2 for that!
(1/2)
My book starts by explaining basic concepts from information theory, like Shannon entropy. Then I explain the principle of maximum entropy and how this leads to the Boltzmann distribution when you maximize entropy subject to a constraint on the expected value of energy. Then my big goal is to illustrate this by computing the entropy of hydrogen gas, and show why it's about 23 bits per molecule.
But to do this nicely, I need to introduce the concepts of partition function and free energy. Then I compute the entropy of a classical harmonic oscillator as a warmup problem, and then the entropy of a single classical particle bouncing around in a box. Next I compute the entropy of helium, which is a monatomic gas, and finally hydrogen, which is diatomic.
So, it's focused on foundations of the math and physics of entropy. It only covers a tiny portion of what one might want to know, but it tries to explain that stuff clearly, rather than racing through the calculations like most books do.
I say almost nothing about the 2nd law of thermodynamics (since it's very hard to explain when and why that law actually holds), or entropy in quantum mechanics, or black hole entropy, or various other sexy topics. It's all about what entropy in classical stat mech, and how to compute it, and what those calculations actually mean.
(2/2)
1. A number of a pictures of gas molecules from ordered to mixed?
2. some picture of Maxwells demon at work
@thomasfricke @johncarlosbaez I was thinking of roughly the same idea as your 1st suggestion, but maybe something more abstract? Like squares perfectly arranged in a lattice on the bottom of the cover that get gradually distorted, some of them missing, some shifting/rotating from the grid, and at the top it's just a sparse free "gas" of random squares.
@johncarlosbaez the title repeated all over the cover in rows and columns. The words in the center are black. The surrounding words grey. The background white. As you move from the center, the number of misspellings or misshapen letters increases.
@quodvideo - that's good.
@johncarlosbaez a complex life form interacting with a less complex one or natural feature? Like a hermit crab.
@felipe - Thanks! That would be great for a more ambitious book, but alas my tweets only go from the foundations of entropy in statistical mechanics to computing the entropy for an ideal gas, with a careful study of all the weird numbers that show up in the final formula.
I should have said this... I'll edit my tweet.
@johncarlosbaez If you stack the words like
Tweets
on
Entropy
you may make „Tweets“ disintegrating. Which is is kind of fitting :)
@zerology - that would be cute. Indeed I'm only using the word "tweets" in the title because Twitter is dead. But I want the randomization to increase as we read further, in keeping with the Second Law.
= 
log
) @johncarlosbaez
Perhaps something illustrating something surprising, like entropy driving complexity.
Fully ordered array of atoms on one side, fully disordered on the other side, and "complexity" in between?
Fractal whorls and eddies of the swirling atoms if it doesn't make the image overly complex.
@dougmerritt - alas, my book says nothing about complexity or how entropy drives complexity! I'll talk about the 2nd law of thermodynamics in one or two pages, and mainly say how hard it is to understand the conditions under which this law holds. I can imagine another book all about that... but that would be a mammoth project! I would have to work hard to outdo H. D. Zeh's The Physical Basis of the Direction of Time.
I realized I'd better explain what my book here is actually about, so I added a part 2 to my post here outlining it. My book is about the stuff people *don't* always talk about.
@johncarlosbaez I’d have a flick through pointillist paintings at various scales of closeup until you find something interesting that stimulates a line of thought?
Failing that, check out some Bridget Riley for very colourful exactly-tuned uncertainties.
@johncarlosbaez a superhero figure, representing biological life, saying “I eat entropy for breakfast”.
@johncarlosbaez maybe a boiling liquid from where the words of the title are bubbling up or so 
@number137 - that could be good!
@johncarlosbaez or something black hole related.
@ehud - unfortunately my book does not discuss black hole entropy (except in one sentence) or entropy in biology. It has a very narrow focus, which is why it's able to be 100 pages long.
I realized I'd better explain my book, so I added a part 2 to my post here explaining it!
@johncarlosbaez I don’t think that should determine the cover, though. It can be aspirational.
@ehud - The cover of my book will reflect what's inside.
@johncarlosbaez it's a little more phase-space-y but what if each word of the title was written by only one continuous curve and then below the typography, the 3 curves start interacting with each other, merge and split (nonlinearity I guess?) further and further into a chaotic pile of spaghetti that continues downward to the bottom of the title page
Edit: or maybe even the curves overlap so much that they start to form a single unbroken color when the page ends
@johncarlosbaez May I ask you when you need the cover image? I might try to sketch a new drawing.
@mariamannone - hi! Great to see you here! There's no particular deadline, and since I'm self-publishing I can keep changing the cover.
I'm afraid I'm extremely fussy, in idiosyncratic ways that would be impossible for anyone but me to predict. But if you show me a rough sketch of a drawing I can decide if I like the basic idea. And even if I don't love it, I might use it on my blog, to "advertise" the book.
Suggestions: it should be simple and somehow illustrate the material actually in the book.
@johncarlosbaez Thank you!! :) I would be very honored. I sent you a sketch from my German email.
@bks - this is too much like the actual experience of reading the book. 
@johncarlosbaez just comparing formula for the N-particles in a 3d box to the formula for a single particle in a 1d box I can see how N-->1, V-->L, 3/2-->1/2..... but also 5/2-->1/2?? That certainly is mysterious!
@highergeometer - yes, it's actually that 5/2 that launched me on my quest to understand the entropy of a gas in detail! I could explain it, but maybe you can wait for the book?
You've certainly proved that we share a sense of what counts as mysterious.
It's also mysterious that Planck's constant shows up in the supposedly 'classical' formulas.
@johncarlosbaez I can wait for the book 
@johncarlosbaez A clear box with a few colourful rubber band balls bouncing inside.
(I'm thinking of the entropy explanation of rubber band stretching)
@johncarlosbaez
A few ideas:
Child blowing dandelion seeds
Bartender mixing/pouring cocktails
Coronal mass ejection
Bucket full of dice being poured out onto the ground
Fire
@johncarlosbaez How about a picture of the Maxwell's demon? Wikipedia has the idea here: https://en.wikipedia.org/wiki/Maxwell%27s_demon?wprov=sfla1
I think drawing a schematic representation of it should be simple with any sw you have available. For example doing vector graphics with .svg image description file might be a way.
@johncarlosbaez When is the book coming?
@kornai - maybe a few weeks? I'm still writing it.
@johncarlosbaez Your idea is very good, it has a potential, I can play with it, if I have some time.
@johncarlosbaez That's actually a neat design challenge: "how many ways can you make letters disintegrate." I've got two:
@johncarlosbaez Another option could be repeating the title multiple times, making it progressively fuzzier.
@BartoszMilewski - yes, that's good. Did you see this?
https://mathstodon.xyz/@mattkenworthy@mastodon.social/112772973324157439
But you and I are thinking of a stochastic process.
@johncarlosbaez @BartoszMilewski
A 10x10 grid with each cell containing say 32x32 pixel images.
One image is coherent, a well recognised object. The rest with the same pixels moved to random locations.
The image would portray the statistical un-likelihood of "ordered" configurations.
@johncarlosbaez I've always liked the use of sand as a visual aid for entropy, sand castles dissolving away, perhaps a twitter logo embossed on a beach being washed away by the tide or blown away on the wind.
@mustard @johncarlosbaez I love this idea. Many have experienced castle destruction firsthand, along with the sound, feel, loss, and ephemerality of that complete dissolution of order.
@johncarlosbaez As a significant visual component: a falling bird morphing into an X
(the bird's based on emoji, the X you'll have to Not Use The Official One)
@flippac - Fun idea!
Taking it perhaps too seriously:
I'm not really trying to get too deep into the Twitter/X stuff on my book cover. Indeed it may be distracting to call the book "Tweets on Entropy", but that's what it actually is, with a lot of later tweaks.
@johncarlosbaez "Small posts..."? Not as catchy, but means things like thread size or material from other platforms are still accurately covered. Not sure we'll be talking about tweets in five years.
@flippac - Good point - it will be bad if someone reads the title and goes "huh"? I may eliminate "Tweets" from the title and call the book something like "100 Short Lessons on Entropy".
@johncarlosbaez @flippac I like that more, actually. "Tweets on Entropy" sounds more superficial, like a pile of casual musings. "100 Short Lessons on Entropy" matches the tone of the material better, I think. Or, to make it sound a little more ambitious, what about "Entropy in 100 Short Lessons" or "Entropy in 100 Small Steps"?
@bstacey - indeed the depth of the treatment keeps growing almost against my will as I keep polishing things, because my desire to be precise is pulling me toward analysis. To prove a version of the Third Law I'm starting to want epsilons and deltas! 
So by now they're less like tweets and more like lessons. But there's something comical about "100 short lessons", because the word "short" is undercut by the large number "100". Sort of like "A Tiresomely Large Number of Brief Essays on Entropy". Which if I were going for a joke title would actually be good.
@johncarlosbaez @bstacey @flippac epigrams? aphorisms?
@abuseofnotation @bstacey @flippac - they are definitely not epigrams or aphorisms. Some of them are moderately strenuous, e.g. this:
@johncarlosbaez Since you plan to start from information theory, you could also call it: 42 bits on entropy, which may also open up a new space of associations for the illustration. @abuseofnotation @bstacey @flippac
@SylviaFysica @johncarlosbaez @abuseofnotation @flippac "The Crying of Bit 42"
@bstacey @SylviaFysica @johncarlosbaez @abuseofnotation @flippac A whole series: “Gravity’s Textbook”, “5.”, “Feynman & Gell-Mann”, “Coherent Space”, ….
@SylviaFysica @johncarlosbaez @abuseofnotation @bstacey @flippac I’d immediately buy a book called “Bits on Entropy”
@dabacon @SylviaFysica @abuseofnotation @bstacey @flippac - it's too bad that "Bits of Entropy" doesn't quite work as a double entendre.
@johncarlosbaez @flippac I think that would be a good idea as tweets will probably go the way of mp3 players in ten years - I like something like you said or the variant “entropy in one hundred vignettes” or some play on ‘one hundred years of solitude’ (“one hundred pages of entropy”)
@johncarlosbaez @flippac looking forward to reading it - I have been really wanting to properly understand something about it since reading Hasok Chang’s marvelous book Inventing Temperature
@boarders - Great! I haven't read that book. I should. Does Chang mention that the reciprocal of temperature is more fundamental than temperature? That's one of my points....
@johncarlosbaez I don’t recall off the top of my head - his point is one from the philosophy of science - that observation is “theory-laden” in the following sense: when we first invented thermometers we measured 0 °C and 100°C (say) and then linearly marked off the other points on the scale - but this relies on us knowing mercury linearly expands under temperature - how could we know that without some prior measuring equipment (and as you know it is not strictly speaking true)? The same could be said for measuring force in classical mechanics, there is a certain kind of puzzle in how we get off the ground empirically without holistic theories of the world (in this case an actual full-fledged theory of what temperature is fundamentally)