Lidia Poët & measuring criminals' skulls

I've been watching The Law According to Lidia Poët on Netflix. In season 2 episode 3, a serial killer is murdering women in Turin.

Lidia meets a famous professor Cesare Lombroso, who claims he can identify criminals by the shape of their skulls. Of course, he thinks Lidia an intellectual inferior, and has full confidence in his theories.

Without any spoilers: basically someone has taken Lombroso's theories to the extreme, and is killing off women who purportedly are inclined to criminality – based on their skulls.

Did some digging, and Cesare Lombroso was indeed a real person, who had those theories (that skull characteristics are associated with criminal behaviour).

In fact, here's one of his papers: “Illustrative Studies in Criminal Anthropology”, from 1891.

For today's eyes, it’s a strange read.

Lombroso doesn't just talk about skulls – he says "born criminals" have distinguishable walks, gestures, sense of smell, taste, and other characteristics (compared to "occasional criminals").

An excerpt:

Walk.– A study which I have made with Perachia, shows us that, contrary to the case of normal men, the step of the left foot of criminals is generally longer than that of the right; besides they turn off from the line of the axis more to the right than to the left; their left foot, on being placed on the ground, forms with this line an angle of deviation more pronounced than the angle formed by their right foot ; all these characteristics are very often found among epileptic

He attributes this distinction to natural selection.

I encourage you to scan through the paper. Strange, but fascinating.

The Netflix episode presents a thought experiment: if we knew someone would commit a crime, is it moral to take pre-emptive action? As we know, Lombroso's theories didn't stand up to scientific scrutiny. So the answer is of course "the killer was wrong and an extremist". And if you could predict someone's future behaviour? Well that's explored in Minority Report and other stories!

The Time a Futurama Writer Devised a Whole New Math Theorem for an Episode

In Futurama’s season 6 episode “The Prisoner of Benda,” the crew ends up using a futuristic device to switch minds with each other. Over the course of the episode, everyone’s minds get thoroughly shuffled up. This would be simple to fix, but there’s a catch: two people who’ve already switched brains can’t do so again. So you’ll probably need new, un-switched people to untangle it all, but how many?

As the gravity of the situation sinks in, the Professor – in Bender’s body, naturally – utters one of my favourite lines of the series: “I’m afraid we need to use... math!”

Futurama | We'll Need to Use....Math!

But the episode was written by mathematics PhD-holder Ken Keeler, who actually devised a proof that forms the solution in the episode. While Keeler has been keen to downplay it, it has since become known as Keeler’s Theorem or the Futurama Theorem, and has been published in an academic journal.

Keeler’s Solution

Ken Keeler’s solution uses group theory to solve the problem. In particular, it uses the S_n symmetric group, with n being the number of people involved. The group basically collects the number of permutations that can be done on n elements. For his solution, he needed n + 2 elements – with two new people – so the group becomes S_n+2.

You can read the paper for the full mathematical details – “k-cycles” and all – but the basic idea is simple. You split the original bodies into two groups, all elements up to some person i, and then all the rest from i + 1 to n. Then, you go through the first part, switching each person with the first new element, x – since x is new, these switches have never happened before. For the remaining people (i + 1 onwards) you switch them each with y. Finally, you switch x with i + 1 and y with 1.

This makes everything almost right, with the exception that you may need to switch x with y right at the end. However, this works because they’ve never switched in this process.

The paper referenced above finds some cases you can solve with fewer additional people, and other authors have since worked to generalise the solution for bigger and more complicated mixtures. Not only did Keeler solve a legitimate mathematical problem, it even inspired mathematicians to take it further.  

Interstellar's realistic black hole

In the movie Interstellar, it's well known that they used sophisticated physics to generate the visuals – including eliciting the help of Nobel laureate Kip Thorne.

Cool fact: they also published a paper describing the physics model they used: Gravitational lensing by spinning black holes in astrophysics, and in the movie Interstellar.

From the sounds of it, they did tweak a few aspects (straying from the actual physics) to make the final visuals work for the movie, which is understandable. But you got to commend the effort, and most would agree the final product is pretty amazing.

Patrick Jane lie detection through pulse-sensing

Patrick is "The Mentalist", who helps police solve murders.

The show aired between 2008-2015, and I just started watching it after seeing a few reels/clips on social media.

A logician rivalling Sherlock, plus the mentalism of course.

One skill Patrick frequently showcases is detecting lies by sensing changes in someone's pulse.

Obviously, the show takes (giant) liberties with Patrick's "skills". So I'm not expecting everything Patrick does to be "evidence-based".

But pulse-sensing seems believable to some degree, and I wanted to see what actual science may exist.

If you think about it, what Patrick is doing is basically administering a polygraph test (using his own natural devices). Of course, a polygraph test senses much more than a person's pulse or heart rate.

In any case, as a starting point, it seems instructive to ask "do polygraph tests work" (as lie detectors)?

That's exactly what this 2025 study examines.

It's a fascinating research paper. What the researchers did:

Dow, Jeu, and Watkins present the first published empirical analysis of polygraph reliability. Starting with the universe of cases where an individual was convicted and was subsequently exonerated on the basis of DNA evidence ... the Authors take advantage of a natural experiment that results from the conviction of individuals subsequently determined with near certainty to be innocent. By ascertaining which cases of the wrongfully convicted individuals included a polygraph examination, and by studying how those examinations were interpreted, then, because the individuals are now known to be innocent, the Authors were able to determine the reliability of these polygraph results (which were obtained before the actual innocence of the subjects was known).

And their conclusion?

polygraphs yield unreliable conclusions in approximately 50 to 65 percent of all cases-worse than a coin flip. This failure rate represents a reason for caution in all contexts where polygraph examinations are routinely used, including criminal investigations.

The study gives a few case studies:

Corey Batchelor insisted he had nothing to do with either the robbery or murder of Lula Mae Woods, who was found dead in 1989 in Chicago, Illinois. During their interrogation, police told Batchelor he had failed a polygraph exam. Confronted with this bogus claim, Batchelor confessed to a murder he did not commit. He served twenty-seven years before being exonerated.

Justin Black suffered a similar fate. In 2007, he was charged in West Virginia with the 2002 murder of Deanna Crawford. After maintaining his innocence from the outset, including during a polygraph examination, Black confessed to the crime after being told he had failed the exam. He served eleven years for a crime he did not commit before being officially exonerated in 2021.

In Nebraska, James Dean began to wonder whether he really might have been an accessory to the murder of Helen Wilson. Informed he had failed a polygraph and would face the electric chair if he did not come clean, Dean confessed to participating in a crime he had nothing to do with. He served five years before being exonerated in 2009.

Even a confession doesn't prove guilt.

So, all in all, not so good for Patrick Jane -- even if he could read pulses as good as a polygraph!

Is a "Mind Palace" an actual thing?

The "mind palace" concept comes up quite often in pop culture. Unsurprisingly, it appears in Sherlock too!

My impression was that the mind palace is a real thing. Found a cool (top 1% cited) paper that tested it.

And indeed the mind palace does work – it improves memory outcomes, and interestingly also "rewires" the brain.

The hound of baskervilles mind palace

The paper uses the term method-of-loci, and not "mind palace", which is basically the same thing. From the credo summary, method-of-loci means:

placing imagined information along a familiar route to aid remembering

The researchers trained lay persons with method-of-loci techniques used by "memory athletes".

The results:

• Before the training, participants could remember about 26 to 30 words (from a list of 72 words).

• After 6 weeks of practicing the method-of-loci technique (for 30 minutes a day), participants were able to recall over 60 words (from a similar list).

• After four months (without daily practice), participants still performed better than the baseline.

And it wasn't just a "useful memory tool" (like how you use a calculator for math) – the training actually altered brain networks.

It sounds like actually training the brain, like how you'd train a muscle.

So the good news: we can actually train to improve our memory. (Though we probably won't be able to reach Sherlock's level!)

Enola Holmes investigates death of matchbox factory girls

In her first case (in the movies), Enola Holmes solves the case – the dying matchbox factory girls. She works alongside Sarah Chapman to uncover the truth: phosphorus from the matches are causing the workers to become ill and die.

In this scene, we see the workers striking after learning about the phosphorus poisoning:

Enola Holmes and Sarah Chapman won the battle for truth.#enolaholmes2 #losangeles #shorts

As it turns out, the events are based on a real story – the 1888 Bryant & May strike.

And this paper looks into the medical reasons behind the workers' poisoning.

The researcher analyses historical reports and compares them with known chemistry, and concludes that the workers suffered from "phossy jaw".

From the credo summary:

the epidemic lasted from about 1858 to 1906, caused painful exposed jawbone, and had reported mortality of 20%. Workers handling match materials as mixers, dippers, and boxers were affected in relation to exposure duration ... yellow phosphorus could react with water, carbon dioxide, and amino acids such as lysine (a protein building block) in the body, producing amino bisphosphonates (bone-affecting chemicals) resembling alendronate and pamidronate. The article says this explains the similarity to modern bisphosphonate-associated osteonecrosis (death of bone tissue).

In real life, there was no Enola Holmes – but there was Sarah Chapman and other workers who stood up for their rights.

Hinokami Kagura (sun breathing)

In Demon Slayer, Tanjiro's special technique is sun breathing. With the skill, Tanjiro is able to momentarily up with power/speed, sending flames through his body and blade.

Tanjiro does it again😱 Thunder breathing and Hinokami Kagura | Demon Slayer Kimetsu no Yaiba

Breathing techniques do exist e.g. for meditation or sports. But is there an actual breathing technique that comes close to the Hinokami Kagura?

This paper explores a Tibetan meditation technique – called g-Tummo (or "inner fire" breathing) – that could be a candidate.

Check out the credo summary to see how the researchers carried out the experiment and what they found.

But briefly, they found that seasoned Tibetan meditators were able to raise their body temperature (to up to 38 degrees) through a combination of a breathing technique and mental visualisation.

It's not entirely clear to me why the practitioners do this, but it sounds like raising body temperature is part of the ritual to heighten mental concentration somehow.

Not quite Hinokami Kagura, but with some similarities – and cool nonetheless.

House MD: mirror therapy for phantom pain

In one of the series' neatest (and most unhinged) scene, House sedates and ties up his neighbor Murphy -- only to cure him from his phantom pain:

Phantom Limb Pain | House M.D..This "miracle" treatment is one of House's most memorable -- given its deceptively simple setup (a cardboard box and a mirror) and the instant and total relief brought.

I always wondered how scientifically truthful it all was, so I decided to look it up.

It turns out the idea has been around since at least 1996.

Does it work? Over the years, it sounds like there's been some back and forth -- with some studies claiming mirror therapy does work, and others saying it doesn't.

This seems to be the latest review study on the mirror therapy. From the credo summary:

The review counted 21 of 32 studies as effective, meaning pain fell by at least 50% or 2 points on a 0–10 scale. Eleven studies did not meet that threshold. Treatment varied in setting, teaching, movement technique, exercise delivery, session length, frequency, and overall duration; most features appeared in both outcome groups. A 15-minute daily session for four weeks was common among successful studies, but was not established as best.

From what I gather, it sounds like yes mirror therapy does work, and is commonly practiced.

But the immediate and dramatic effects on House are well -- a dramatisation.