John C. Baez

I met Sasha and Anna Shulgin at a big party they held at their house. No, I have no scandalous or fascinating tales to report! They seemed nice. I mainly talked to my friends.

I think you could get an example you want by looking at QED with two charged spin-1/2 fields in the Lagrangian, say an "electron field" and "proton field". Then you'd get stable bound states - lots of them! - that act like "atoms" and "molecules". And I think they should appear in the S-matrix.

Btw, did you get my point that you can't treat positronium as a mere spin-0 particle in S-matrix theory, at least not without major errors, because it has a spectrum of energy, angular momentum and energy states just like hydrogen? (Not to mention it's unstable, so you don't see it at infinity.)

You mean you're disabled by doing so much learning?

And there are parts of the novel that look like this!

The stories have been unified and modified in various ways, with some not being included.

So I liked it, though there's a certain amount of gore. The SCP website seems to be a collection of > 10,000 short stories about an organization that battles malign entities that need to be controlled: "Secure, Contain, Protect". I suspect qntm is one of the better authors here.

(3/n, n = 3)

"SCP-3125 pervades all of reality except for volumes which have been specifically shielded from its influence. This is it. This is our only safe harbor. This room represents the length and breadth of the war."

(2/n)

The book is mainly metaphysical horror, e.g. when Wheeler enters that capsule a video tells her:

"You've guessed already that SCP-3125 is not in this room. In fact, this is the only room in the world where SCP-3125 is not present. It's called 'inverted containment'."

(1/n)

So, to repeat, I said very sketchily that "cohomology" is roughly a composite of three ideas: thinking of a thing as a special kind of ∞-thing, and then simplifying it by "abelianizing" (a better word is "stabilizing"), and then studying it by its maps out to other stable ∞-things.

Yes, there's a way to understand all this. I alluded to it, but in a tiny bit more detail: there's a kind of "abelianization" map from homotopy types to *stable* homotopy types, or more generally spectra, where generalized cohomologies live. "Deriving" is part of this story.

Elliptic kittens?

You're right: the mediant depends on the numerators and denominators. Or, if you like, it's a way to take two vectors and create a new vector (simply their sum).

Nonetheless it's an important thing!

en.wikipedia.org/wiki/Mediant...

Yes, this is a way to think about what vector addition does for ℝP¹.

YouTube video by Andrea Joshua Asnicar There Is No Antimemetics Division - Ep 1 - SCP Horror Short Series

You can also watch at least some of the episodes as videos here:

(7/n, n = 7)

www.youtube.com/watch?v=w-Ii...

The surprise is what they find in there... but I won't give that away.

I believe the novel is more polished than the individual episodes, which you can find in written form here:

scp-wiki.wikidot.com/antimemetics...

(6/n)

During the exit cycle, a purge system rigged to the airlock flushes the occupant's memory by flooding the airlock with amnestic gas for three minutes.

A senior Antimemetics Division staff member must visit SCP-3125 every six weeks (42 days).

END OF FILE

(5/n)

This includes written and electronic notes, photographs, audio and video recordings, sound, electromagnetic and particle-based signals and psi emanations.

(4/n)

This airlock is programmed to allow only one person to enter the containment unit at a time, and to remain locked until this person exits before allowing another person to enter.

Under no circumstances may any coherent information be allowed to leave the containment unit.

(3/n)

This containment unit is a 10m by 15m by 3m cuboidal room clad in layers of lead, soundproofing and telepathic shielding. Access is through an airlock system at one end of the containment unit.

(2/n)

I'm enjoying the novel "There Is No Antimemetics Division".

I'll quote some for you:

.....

Item #: SCP-3125
Object Class: Keter
Special Containment Procedures: SCP-3125 is kept inside
Cognitohazard Containment Unit 3125 on the first floor of Site 41.

(1/n)

en.wikipedia.org/wiki/There_I...

Determining the mediant of two rational numbers graphically. The slopes of the blue and red segments from the origin to two points in the first quadrant are two rational numbers, using these as two edges of a parallelogrom, the slope of the diagaonal, drawn as a green segment, is their mediant.

The 'mediant' of two fractions a/b and c/d is (a+c)/(b+d).

Beginners sometimes add fractions this way by mistake.

But it's important in number theory...

... and I just learned it has a simple geometrical meaning, too!

Everything in math is weird when students first meet it. So it's possible that only teachers think "Riemann integrals via limits" are not too weird while "Riemann integrals via nets" is not too weird. I guess you have to try teaching something to see if it's actually too weird for the students.

Please, be subcilious.

Is there a difference between

It's trivial that (2) implies (3)

and

(2) implies that (3) is trivial ?

Physicists use approximations that for mathematicians would require a whole new set of theorems to justify. But the good part is that this gives mathematicians lots of fascinating things to work on! Like, can we generalize unitary reps of the Poincare group to ones with complex mass?

I guess you're talking about @gregegansf.bsky.social's generalization of the Grace-Daniellson inequality?

en.wikipedia.org/wiki/Egan_co...

I'll have to read about this, but for starters positronium has infinitely many internal states, mathematically just like hydrogen, characterized by n, l, m and s quantum numbers. Apart from that you may be right!

Collect these figurines based on Hieronynus Bosch's paintings!

Then cower in terror as they come alive at night and climb into your bed.

Starting at $34.50 here:

www.amazon.com/s?k=bosch+fi...

The case of positronium is vastly simpler: QED is an abelian gauge theory where we don't need BRST quantization, it's not confined so the electrons positrons and photons actually *exist* as asymptotic states, and we don't need a supercomputer to understand their bound states.