17 papers, 2.6 sigmas, and 1 event
The LZ experiment recently announced (1 September) a new result through a talk and preprint paper.
The paper documents something strange: a single, unexplained event that could be consistent with an interaction with a Dark Matter particle. The data were analysed using frequentist, and specifically Fisherian, statistical methods described here. In particular, evidence was quantified using a \(p\)-value, that is, the probability of obtaining data that were at least as extreme as that observed given the background-only (i.e., no Dark Matter) hypothesis. The \(p\)-value was about 0.5%. For historical reasons, this is communicated as \(2.6\sigma\), as 0.5% corresponds to the probability mass contained in the tail of a Normal distribution at \(Z = 2.6\).
Hey ho, you might think. That ain't much evidence for an extraordinary claim, especially since it is contingent on their background and detector modeling to the 1 rogue-event level, and given all we know about \(p\)-values, the replication crisis, and the strength of evidence. That said, it might just about be below a threshold proposed by Benjamin et al. (2017) in social and medical sciences, thought not close to the physics typical requirement of \(5\sigma\) for a discovery.
In the two days that followed the paper, however, there were 17 theory papers that presented particular models of Dark Matter that could explain that 1 event. Hmm. I haven't read them well enough to comment on how well-motivated these explanations are, though the most popular appears to be a Higgsino explanation (see e.g., Fan & Reece), where a supersymmetric partner of the Higgs plays the role of Dark Matter. However, a paper today suggests Higgsinos may be in tension with so-called sideband results from LZ. That means, they would predict Dark Matter signals in other searches performed by LZ, but none were seen.
There was a particular statement in Fan & Reece that caught my eye:
The look-elsewhere correction depends on the total number of models that were fit to the data, and as such is arguably too conservative when, as we will argue, there is one particularly compelling model to focus onHmm. One of the infamous things about \(p\)-values is that they depend on the experimentalists' analysis plan. That is, they depend on what the experimentalists would have done, were the data different. Part of computing them correctly thus involves correcting for the look-elsewhere effect (LEE). This means, correcting for all the things you, the experimenter, would have looked at had the data been different. There is a famous reductio ad absurdum about a statistician and electrician, by Edwards and Pratt, described here that shows how strange this can be. The long-and-short of this is that the \(p\)-value depends on the experimentalists' analysis plan, which should ideally be declared before data collection. I don't think it's reasonable to claim after the fact that
Ah! But I was only interested in this subset of tests anyway (which happened to include tests that produce the smallest \(p\)-values). Let's just use those ones. Thus the \(p\)-value is smaller!This would have been perfectly fine pre-data. I would have no objection to pre-data, or pre-unblinding of data, someone saying, let's use an analysis plan that only performs these tests to maximise the statistical power for these particular Dark Matter models that we find plausible. Post-data, however, it's too late, at least within a frequentist paradigm.
On the other hand, perhaps Fan & Reece are subconsciously thinking as Bayesians. In Bayesian frameworks, we don't need to consider the sampling plan or what we'd have done were the data different: our conclusions depend only on the data we did observe. This is connected to the likelihood principle. In that case, perhaps a more charitable interpretation is that:
Ah! I don't care about your error rates and what you'd have done were data different. I just care about what I should believe given the data at hand. The Dark Matter models that explain the event were a priori plausible to me. Given that, I am more inclined to believe that they explain the data.I think that's a defensible point of view.
Tags: dark-matter, statistics, physics
Tall Tales and Wee Stories
Read Tall Tales and Wee Stories, a collection of Billy Connolly's stand-up material. I chose it to distract myself from other matters going on, and it mostly did the trick. I didn't know many of Connolly's routines, though remember his voice and manner from TV and from some VHS tapes my parents had in the 90s.
The routines are often funny, though occasionally misogynistic to a modern reader. Obviously something is lost on the page, especially the chaos, spontaneity, and physicality of his live performance, such as the one about getting drunk from the feet upwards. I was surprised by the lack of reflection, nostalgia, politics or social commentary in his material: I presumed he'd draw on his years as a welder or his working-class upbringing, but the routines are somewhat apolitical.
I'm part way through another AI/tech/society book, and then I plan to tackle a classic: Dickens or Hardy, something like that. Connolly's book was amusing, but didn't feel altogether rewarding.
Dreaming is for free
Read a heartbreaking story about a landslide at landfill site that killed 30 people in Guinea. Was appalled to realize that these occurrences are so common in the global south that they have their own Wikipedia entry. What an awful metaphor for the world we've created. Don't let anyone tell you a better world isn't possible.
WALL-E in rep
Watched WALL-E at a cinema in Qingdao, which is the center of the Chinese film industry, similar to Hollywood in the US. Chose it as it was in English and family friendly. What with the spate of remakes, I wasn't sure if it was a new version of an old film. However, as they were also showing Shawshank Redemption, it didn't come as a surprise that it was in rep.
I was pleasantly surprised by WALL-E and found it alarmingly prescient (2008). A monopolistic company, 'Buy N Large', de facto controls the world and trashes it. Robots are left behind to clean up the mess while humans escape in a spaceship. The humans become infantilised and alienated from each other, as their lives are organized by a system of robots that control the ship. The humans degenerate both physically and mentally.
In the end, humanity is saved by a robot, WALL-E, who finds beauty in a single weed growing amongst trash on Earth, and love in a fellow robot. I enjoyed the themes of endstage capitalism, environmental destruction, technology leading to alienation and decay, and the unusual resolution that it was a robot that rekindles what it means to be human. I didn't understand the lack of cultural and ethnic diversity amongst the humans on the spaceship: were only English-speaking white people saved?
The Machine Stops
Read The Machine Stops by E. M. Forster. I hadn't previously associated him with science fiction, so it was a surprise that he wrote this book. However, the book focusses on human connections and alienation and thus perhaps isn't dissimilar thematically from his other works. The book imagines a future where we live our lives through machines, including communication and experiences. I found the Machine's preference for $n$-th hand information intriguing: first-hand and second-hand sources were considered partisan and unreliable. The society thus prefers depersonalised, smooth, generic lectures and historical accounts. Any of this sound familiar?
Mechanical analogy for qubit measurement
I have designed (but not yet built) a toy to illustrate measurements of a qubit state on \(x\)-, \(y\)- and \(z\)- axes. You place a ball into this system of pipes. To perform a measurement on an axis, you tilt the board. Under gravity, it rolls along the pipe, hits a fork and with approximately equal probability goes left or right, along another pipe and into a small trap.
When you make a repeat measurement, by resetting the board to the level position and tipping it the same way, you get the same outcome, as the ball is trapped.
When you perform a new measurement on a different axis, the ball is elevated above level, escapes the trap, rolls to the center, rolls down the next axis, and again goes randomly into one of two traps after hitting a fork.
This shows several features of a qubit system: there are two possible outcomes for any given axis; a measurement is performed in a chosen basis; changing the basis and performing a new measurement does not preserve the previous state. E.g., performing a \(y\)-measurement after an \(x\)-one destroys whatever \(x\)-state it was in. Repeat measurements, though, give the same outputs. These are features of projective measurements that disturb the state and are repeatable.
You can see the board as a classical hidden-variable-style analogy for measurement outcomes on a qubit state. The outcomes appear probabilistic to us because of our ignorance of microscopic details of smoothness of the pipes, the speed of the ball, the exact way we tip the board etc. If we knew them all, though, we could in principle apply classical mechanics and figure it out. If this were used in a classroom demonstration, it could be used to contrast classical ignorance and genuine quantum behaviour.
It does not show, and cannot show, interference, entanglement or superposition, however. Why not? The ball goes through a single path, a single fork. There's just no way for a ball to classically go through a superposition of two routes. Thus, this kind of mechanical model cannot be extended to cover multi-qubit correlations, as shown by Bell-type inequalities.
Tags: quantum-mechanics
Is QBism Bayesian?
I've been exploring QBism, an interpretation of Quantum Mechanics (QM) based on or inspired by Bayesian inference. The appeal being that mysteries about the ontic or epistemic nature of the wavefunction and about the collapse of the wavefunction could be resolved in this perspective.
I found it confusing and incoherent. There is nothing mathematically Bayesian about it. We don't describe beliefs with probability theory alone, as we use a wavefunction, and we don't update them using Bayes' theorem alone, as we need the Born rule. It is, though, Bayesian in spirit, in that the wavefunction is interpreted personally and epistemically: it isn't real or ontic, it something that we create in our heads to describe a quantum state. The collapse of a wavefunction isn't real either, it's just an update we do in our heads, analogous to Bayesian updating from prior to posterior. In later works this is explicitly stated and the B is said to stand for Bruno de Finetti rather than Bayes, as much like de Finetti said that probabilities didn't exist, QBism says wavefunctions don't exist in a physical, ontic way.
Sounds wonderful at first glance, until you ask a few more questions. Why are we using wavefunctions to describe our epistemic state (cf. probabilities)? Why do we use the Born rule to associate probabilities with outcomes? If the wavefunction is epistemic, what is it that we are ignorant about? If the measurement and update are all in our heads, what determines which random outcome we observe?
I found the answers to these questions vague and handwavy, as they involve 'agents', 'agent experiences', and 'normative rules'.
Tags: quantum-mechanics, bayes
Neuromancer
Read Neuromancer by William Gibson (1984). A seminal, genre-defining work of cyberpunk fiction. High-tech; low-life. The book is extraordinarily fast-paced and frantic, with rapid scene switches, character aliases, and twists, and no explanatory text on the technologies or lexicon. This makes it a challenging read.
Whilst I didn't especially enjoy it as a novel, I recognized it as a masterpiece of science fiction, introducing the cyberpunk vision of the future that felt so eerily like our present. There is no sign of global governance, order, or rules; only mega-corporations that control big tech. Humans are somewhat redundant: the hyper-wealthy aristocratic Tessier-Ashpool family are cryogenically frozen, awakening only periodically to check that AIs are running their finances appropriately. On his hero's journey, our protagonist, Case, saves no one, averts no disasters, and is manipulated by AIs. I did see Case as our hero, though. He survives the ruthless criminal underworld of Chiba and chooses to take a step closer to the truth and personal meaning.