I left my Twitter account sitting disused and locked, on the off chance that one day I would have a use for it that I couldn’t foresee at the time. Today, after months of that not happening, I finally got around to deactivating it. Anything from “@blakestacey” won’t be from me.

# The Parable of the Muffins

Let’s try to make a profound statement about reality by thinking hard about baked goods.

I promise this is going somewhere.

A certain bakery has a special deal on muffins. They sell mystery boxes for those who like to live dangerously: mix-and-match sets of three muffins apiece. Each day, Alice, Bob and Charlie buy a mystery box together, and each day, Alice, Bob and Charlie take one muffin apiece back to their respective laboratories for analysis. They each have two testing devices — say, a device that can test whether a muffin is positive for dairy, and another device that can test whether it is positive for tree nuts. We’ll call these $X$ tests and $Y$ tests for short. Each day, Alice chooses either to do an $X$ test or a $Y$ test. Bob likewise chooses, independently of Alice, and so does Charlie. Importantly, each muffin can only be tested *once.* Maybe the test destroys the muffin, or maybe it takes so long to do one that they eat their muffins immediately afterward. Whatever the rationale, one test per muffin — that’s a rule of the parable.

We can write what they choose to do in a compact way. For example, if all three of them choose to do the $X$ test on their respective muffins, we’ll write $A_X B_X C_X$. If Bob and Charlie choose to do the $Y$ test but Alice goes instead with the $X$ test, we’ll write $A_X B_Y C_Y$. And so on. We can also write the results compactly, using $+1$ to stand for a positive result and $-1$ to stand for a negative one. (We could also record the outcomes with zeros and ones, or with trues and falses, greens and blues, etc. Using $+1$ and $-1$ is just a notation that will turn out to be helpful in a moment.) So, for example, if Alice chooses $Y$, Bob chooses $X$ and Charlie goes with $Y$, the results might be $(+1, -1, -1)$. Or they might be $(+1, +1, +1)$, or perhaps $(-1, +1, -1)$.

Over many days of muffin investigation, comparing their notes, they find a dependable pattern. Whenever *two of them* choose to do the $Y$ test, then the *product of their results* is always $+1$. The specific outcome varies randomly from day to day, but there’s never only one $-1$, and they never get all three results being $-1$. From this pattern, they can draw a couple conclusions. First, once two of them obtain their results, the result of the third is predictable. Let’s say their choices are $A_Y B_X C_Y$, as in the previous example, and both Alice and Bob get the result $+1$. Then we can predict that Charlie will get $+1$, because that’s the only way the product of the three numbers can be $+1$. Or, suppose their choices are $A_Y B_Y C_X$, and both Bob and Charlie get a $-1$. The two of them report their results and wait for Alice. Knowing Bob and Charlie’s results, we can predict that Alice will report a $+1$ outcome, because that’s the only way the product of the three outcomes is $+1$. A minus times a minus makes a plus, and so a third minus would spoil the plus.

If we had used a different notation for the outcomes, like “green” and “blue” instead of $+1$ and $-1$, then we could express this pattern by saying that whenever two of them choose to do the $Y$ test, an even number of the results will be blue.

Now, we deduce something else from the pattern. We can make a prediction about what happens under very different conditions. What about the days when all three choose to measure $X$?

Continue reading The Parable of the Muffins

# Consolation

For the rest of my life, whenever a research project doesn’t work out or I think back over the questions on which I failed to make progress, I will at least be able to say, “Hey, I didn’t try to do psychology research on a chatbot.”

# Celebrity

A couple years ago, I became an official textbook author.

For reasons that made sense at the time, I gathered all the homework problems together at the end into a chapter called, well, “Exercises”. And now I keep getting spam invitations to conferences and special issues of journals no one has ever heard of, asking me to share my pivotal work “in the field of Exercises”.

# The Lunn–Schrödinger Equation?

Wikipedia claims that Arthur C. Lunn discovered what we now call the Schrödinger equation some years before Schrödinger. I wonder if there is more to say about this than what the references cited there provide (they have the feel of being faithful recollections, but are light on specifics).

In a 1964 interview, the physicist Karl Darrow calls the story “impossible to check”. And in another interview, Robert Mulliken (not to be confused with Robert Millikan) shares the story of Lunn having “sent a paper to the Physical Review which was turned down and which anticipated the quantum mechanics”. Mulliken heard the story from the physical chemist William Draper Harkins. Similarly, Leonard Loeb told Thomas Kuhn that Lunn “was probably a misunderstood genius, and who was completely frustrated, because his one great paper with his one great idea was turned down by a journal”.

Lunn did apparently try to present what sounds like a grandiose paper (“Relativity, quantum theory, and the wave theories of light and gravitation”) at the American Physical Society meeting in April 1923, but his paper was only “read by title”. The abstract ran as follows:

This paper is a preliminary report on a theory originally sought in order to meet the recognized need for a reconciliation between wave theory and quantum phenomena; its scope of adaptation proves to be quite wide. It includes (1) a wave theory of gravitation in quantitative connection with optical, electronic, and radioactivity data; (2) a related general suggestion of a theory connecting molecular properties with properties of matter in bulk; (3) alternatives for some of the current features in the theories of atomic structure; (4) a new interpretation and deduction of formulas for series and band spectra, using in lieu of the quantum condition a substitute directly related to long familiar physical notions; (5) a modification of Lagrangian dynamics which promises to be of service in the study of complex atomic and molecular structures; (6) a non-quantum theory of specific heat and black radiation. Results so far reached deal mostly with problems approachable by elementary methods or approximate computations. A set of formulas has been obtained which yield computation of the electron constants $e$, $h$, $m$ and mass ratios, assuming from observation only the Rydberg constant, velocity of light, gravitation constant, and Faraday constant, with results in each case in practical agreement with measured values.

Darrow says, “I know that in 1924 he wanted to give a twenty or a thirty minute paper before the American Physical Society in Washington, but then authorities of the Society refused him more than ten minutes”.

Lunn’s abstract in the 1924 proceedings has a similar explain-everything atmosphere:

Relativity, the quantum phenomena, and a kinematic geometry of matter and radiation.A. C. LUNN, University of Chicago. The theory indicated in an earlier paper (Phys. Rev. 21, 711, 1923), has since been developed, extended in scope, and so ordered as to permit of treatment as a deductive space-time geometry. It unites the treatment of the quantum phenomena with the rest of physical theory in a way that yields to illustration by familiar physical images. It resolves into matters of choice a number of hitherto controversial alternatives in the interpretation of phenomena, and allows freedom of use of a range of concrete types of representation including many other concepts commonly discarded. Among special topics more recently found to affiliate with the scheme may be mentioned the Stark and Zeeman effects and fine structure, resonance potentials, and the intensity and distribution of general x-radiation. Improvements have been made in the setting of the formulas connecting $e$, $h$, and $m$ with pre-electron data. A program has emerged for the foundation of a trial mathematical chemistry by determination of types of atoms, valence, number of isotopes, atomic weights, and spectrum levels.

I can easily imagine a paper with that attempted scope being incomprehensible to whoever had the task of evaluating it, and so any really good morsels within it would have been lost.

# Underappreciated

An underappreciated aspect of the original *Dracula* story is that the way he goes out is basically, “And this is how we do things in Texas.”

Continue reading Underappreciated

# Friends Don’t Let Friends Learn Physics From Yudkowsky

With the demise of Reddit, we have lost /r/SneerClub, the Internet’s hot spot for mocking those who proclaim allegiance to capital-R Rationality and related ideologies like longtermism. Somewhere in between the discussions of heavy stuff like sexual harassment in Effective Altruism culture and total frivolity were the rambles about science. I thought I would pull a couple such comments out of the archives and edit them into something shaped like a blog post. So, consider this your Attention Conservation Notice: if you’d rather not work through a self-admittedly rough explanation of how Eliezer Yudkowsky’s claims about quantum physics are just silly, exit now.

Yudkowsky clearly intends to argue that the scientific community is broken and his brand of Rationalism(TM) is superior, but what he’s actually done is take all the weaknesses that physicists have when discussing quantum foundations and present them in a more concentrated form. There’s the accepting whatever mathematical formulation you learn first as the ultimate truth, the reliance upon oversimplified labels and third-hand accounts rather than studying what the pioneers themselves wrote, the general unwillingness to get out of the armchair and go even so far as the library…

Continue reading Friends Don’t Let Friends Learn Physics From Yudkowsky

# Reflection

I am always grateful that the pulp fiction I read in my childhood included mysteries as well as science fiction, so I internalized the notion that some people are just out to scam you.

# Life Is All Downhill From This Joke

Rest of world: (sobbing) You can’t just call everything a pudding!

J. J. Thomson: (points at atom) pudding

# Venting

I confess myself a bit baffled by people who act like “how to interact with ChatGPT” is a useful classroom skill. It’s not a word processor or a spreadsheet; it doesn’t have documented, well-defined, reproducible behaviors. No, it’s not remotely analogous to a calculator. Calculators are built to be *right,* not to sound convincing. It’s a bullshit fountain. Stop acting like you’re a waterbender making emotive shapes by expressing your will in the medium of liquid bullshit. The lesson one needs about a bullshit fountain is *not to swim in it.*

“Oh, but it’s a source of inspiration!”

So, you’ve never been to a writers’ workshop, spent 30 minutes with the staff on the school literary magazine, seen the original “You’re the man now, dog!” scene, or had any other exposure to the thousand and one gimmicks invented over the centuries to get people to put one word after another.

“It provides examples for teaching the art of critique!”

Why not teach with examples, just hear me out here, by actual humans?

“Students can learn to write by rewriting the output!”

Am I the only one who finds passing off an edit of an unattributable mishmash as one’s own work to be, well, flagrantly unethical?

“You’re just yelling at a cloud! What’s next, calling for us to reject modernity and embrace tradition?”

I’d rather we built our future using the best parts of our present rather than the worst.

# A Picture for the Mind: the Bloch Ball

Now and then, stories will pop up in the news about the latest hot new thing in quantum computers. If the story makes any attempt to explain why quantum computing is special or interesting, it often recycles a remark along the lines of, “A quantum bit can be both 0 and 1 simultaneously.” This, well, *ehhhhh…* It’s rather like saying that Boston is at both the North Pole and the South Pole simultaneously. Something important has been lost. I figured I should take a stab at explaining what. Our goal today is to develop a mental picture for a *qubit,* the basic unit that quantum computers are typically regarded as built out of. To be more precise, we will develop a mental picture for the *mathematics* of a qubit, not for how to implement one in the lab. There are many ways to do so, and getting into the details of any one method would, for our purposes today, be a distraction. Instead, we will be brave and face the issue on a more abstract level.

A qubit is a thing that one *prepares* and that one *measures.* The mathematics of quantum theory tells us how to represent these actions algebraically. That is, it describes the set of all possible preparations, the set of all possible measurements, and how to compute the probability of getting a particular result from a chosen measurement given a particular preparation. To do something interesting, one would typically work with multiple qubits together, but we will start with a single one. And we will begin with the simplest kind of measurement, the *binary* ones. A binary test has two possible outcomes, which we can represent as 0 or 1, “plus” or “minus”, “ping” and “pong”, et cetera. In the lab, this could be sending an ion through a magnetic field and registering whether it swerved up or down; or, it could be sending a blip of light through a polarizing filter turned at a certain angle and registering whether there is or is not a flash. Or any of many other possibilities! The important thing is that there are two outcomes that we can clearly distinguish from each other.

For any physical implementation of a qubit, there are three binary measurements of special interest, which we can call the $X$ test, the $Y$ test and the $Z$ test. Let us denote the possible outcomes of each test by $+1$ and $-1$, which turns out to be a convenient choice. The *expected value* of the $X$ test is the average of these two possibilities, weighted by the probability of each. If we write $P(+1|X)$ for the probability of getting the $+1$ outcome given that we do the $X$ test, and likewise for $P(-1|X)$, then this expected value is $$ x = P(+1|X) \cdot (+1) + P(-1|X) \cdot (-1). $$ Because this is a weighted average of $+1$ and $-1$, it will always be somewhere in that interval. If for example we are completely confident that an $X$ test will return the outcome $+1$, then $x = 1$. If instead we lay even odds on the two possible outcomes, then $x = 0$. Likewise, $$ y = P(+1|Y) \cdot (+1) + P(-1|Y) \cdot (-1), $$ and $$ z = P(+1|Z) \cdot (+1) + P(-1|Z) \cdot (-1). $$

To specify the preparation of a single qubit, all we have to do is pick a value for $x$, a value for $y$ and a value for $z$. But not all combinations $(x,y,z)$ are physically allowed. The valid preparations are those for which the point $(x,y,z)$ lies on or inside the ball of radius 1 centered at the origin: $$ x^2 + y^2 + z^2 \leq 1. $$ We call this the *Bloch ball,* after the physicist Felix Bloch (1905–1983). The surface of the Bloch ball, at the distance exactly 1 from the origin, is the *Bloch sphere.* The points where the axes intersect the Bloch sphere — $(1,0,0)$, $(-1,0,0)$, $(0,1,0)$ and so forth — are the preparations where we are perfectly confident in the outcome of one of our three tests. Points in the interior of the ball, not on the surface, imply uncertainty about the outcomes of all three tests. But look what happens: If I am perfectly confident of what will happen should I choose to do an $X$ test, then my expected values $y$ and $z$ must both be zero, meaning that I am *completely uncertain* about what might happen should I choose to do either a $Y$ test or a $Z$ test. There is an inevitable tradeoff between levels of uncertainty, baked into the shape of the theory itself. One might even call that a matter… of principle.

We are now well-poised to improve upon the language in the news stories. The point that specifies the preparation of a qubit can be at the North Pole $(0,0,1)$, the South Pole $(0,0,-1)$, or anywhere in the ball between them. We have a whole continuum of ways to be intermediate between completely confident that the $Z$ test will yield $+1$ (all the way north) and completely confident that it will yield $-1$ (all the way south).

Now, there are other things one can do to a qubit. For starters, there are other binary measurements beyond just the $X$, $Y$ and $Z$ tests. Any pair of points exactly opposite each other on the Bloch sphere define a test, with each point standing for an outcome. The closer the preparation point is to an outcome point, the more probable that outcome. To be more specific, let’s write the preparation point as $(x,y,z)$ and the outcome point as $(x’,y’,z’)$. Then the probability of getting that outcome given that preparation is $$ P = \frac{1}{2}(1 + x x’ + y y’ + z z’). $$

An interesting conceptual thing has happened here. We have encoded the preparation of a qubit by a set of expected values, i.e., a set of probabilities. Consequently, all those late-night jazz-cigarette arguments over what probability means will spill over into the arguments about what quantum mechanics means. Moreover, and not unrelatedly, we can ask, “Why *three* probabilities? Why is it the Bloch sphere, instead of the Bloch disc or the Bloch hypersphere?” It would be perfectly legitimate, mathematically, to require probabilities for only two tests in order to specify a preparation point, or to require more than three. That would not be quantum mechanics; the fact that three coordinates are needed to nail down the preparation of the simplest possible system is a structural fact of quantum theory. But is there a deeper truth from which that can be deduced?

One could go in multiple directions from here: What about tests with more than two outcomes? Systems composed of more than one qubit? Very quickly, the structures involved become more difficult to visualize, and familiarity with linear algebra — eigenvectors, eigenvalues and their friends — becomes a prerequisite. People have also tried a variety of approaches to understand what quantum theory might be derivable from. Any of those topics could justify something in between a blog post and a lifetime of study.

**SUGGESTED READINGS:**

- E. Rieffel and W. Polak,
*Quantum Computing: A Gentle Introduction*(MIT Press, 2011), chapter 2 - J. Rau,
*Quantum Theory: An Information Processing Approach*(Oxford University Press, 2021), section 3.3 - M. Weiss, “Python tools for the budding quantum bettabilitarian” (2022)

# Tropes? In This Economy?

Somewhere on the list of problems with the Internet, no worse than ten-billionth place I should say, is that nobody has created a TV Tropes page for my *Daria*–*Sandman* crossover epic.

# Why I Expect to Fare Poorly in Job Interviews

“So, where do you see yourself in five years?”

“Dead from the next pandemic? Dead from civil war? Dead from the combination pandemic-and-civil-war?”

# Angry Pessimism

“How were you radicalized?”

“Preprints accepted by the *Virginia Law Review*.”

# Blunt Pessimism

*I’m really not feeling that good about our ability to handle the next epidemic that comes our way.* —BCS, January 2017

The Supreme Court today is drooling with eagerness to kill Biden’s vaccine-or-test mandate, on the legal rationale of “we declare that we can, so we will”. So, first, congratulations to Omicron. Second, this makes it even more plain that they’ll throttle the EPA on the same “fuck any regulators that want to actually regulate” basis, in a few months.

The Democrats will probably lose at least the House in November (the map isn’t turning out as gerrymandered as a lot of folks expected, but it’s still bad enough). That’s the chance of court reform gone, with a reactionary majority free to uphold theocracy, sabotage the vote, treat LGBT people as subhuman, attack labor rights, fuck over press freedom (if *Roe* is gone, *NYT v Sullivan* can hardly be safe).

The Democrats will lose the Senate in 2024 (the map will be terrible unless 2022 goes amazingly for them). Oh, and two years of Republicans running the House means two years of Benghazi!-ing, a shutdown or two, doing everything possible to make Trump president again. Did we mention that one factor in that nominally not-so-bad map has been “incumbent protection”, i.e., baking in the MAGA?

… OK, maybe Trump will be dead by then, or too ill to be propped up on two feet. DeSantis seems the most likely heir at the moment. But whatever.

And supposing Biden wins in ’24? Not a lot he’ll be able to do with both the Senate and (probably) the House against him.

Point is, we’re on a three-year train to Fuckedville while the planet cooks around us.

I’ve seen people cast about for analogies for what’s in progress/likely to be coming. Turkey under Erdogan? Hungary under Orban? The Time of Troubles? There always seems to be some ingredient that makes the analogy not quite match, for me, but not a single option on the table looks good.

What was that old Adam Smith line about there being “a great deal of ruin in a nation”? Right now, we’re in the middle of measuring just how much ruin there is.

(Apropos, how much ruin is there in a health-care system?)

Autocracy is here. It just isn’t evenly distributed, yet.

# PEM-diss

So, there’s a joke going around BirdSite about how scientists said “the internet will revolutionize the sharing of information and eliminate barriers to communication”, and what we got is viral tweets asking for the solution to “4 + 8 x 3 – 7, no calculators!!”

Nobody has answered “24x – 3”.

(Grandpa Stacey voice) I am disappointed.