Live and Let Dice

How many ways are there to die? The answer is actually five, if by “die” you mean “roll a die” and by “rolled die” you mean “Platonic polyhedron”. The Platonic polyhedra are the solid shapes in which each polygonal face and each vertex (meeting-point of the edges) are the same. There are surprisingly few. Search as long and as far as you like: you’ll find only five of them in this or any other universe. The standard cubic die is the most familiar: each of its six faces is square and each of its eight vertices is the meeting-point of three edges. The other four Platonic polyhedra are the tetrahedron, with four triangular faces and four vertices; the octahedron, with eight triangular faces and six vertices; the dodecahedron, with twelve pentagonal faces and twenty vertices; and the icosahedron, with twenty triangular faces and twelve vertices. Note the symmetries of face- and vertex-number: the dodecahedron can be created inside the icosahedron, and vice versa. Similarly, the cube, or hexahedron, can be created inside the octahedron, and vice versa. The tetrahedron is self-spawning and pairs itself. Plato wrote about these shapes in his Timaeus (c. 360 B.C.) and based a mathemystical cosmology on them, which is why they are called the Platonic polyhedra.

An animated gif of a tetrahedron


An animated gif of a hexahedron


An animated gif of an octahedron


An animated gif of a dodecahedron


An animated gif of an icosahedron


They make good dice because they have no preferred way to fall: each face has the same relationship with the other faces and the centre of gravity, so no face is likelier to land uppermost. Or downmost, in the case of the tetrahedron, which is why it is the basis of the caltrop. This is a spiked weapon, used for many centuries, that always lands with a sharp point pointing upwards, ready to wound the feet of men and horses or damage tyres and tracks. The other four Platonic polyhedra don’t have a particular role in warfare, as far as I know, but all five might have a role in jurisprudence and might raise an interesting question about probability. Suppose, in some strange Tycholatric, or fortune-worshipping, nation, that one face of each Platonic die represents death. A criminal convicted of a serious offence has to choose one of the five dice. The die is then rolled f times, or as many times as it has faces. If the death-face is rolled, the criminal is executed; if not, he is imprisoned for life.

The question is: Which die should he choose to minimize, or maximize, his chance of getting the death-face? Or doesn’t it matter? After all, for each die, the odds of rolling the death-face are 1/f and the die is rolled f times. Each face of the tetrahedron has a 1/4 chance of being chosen, but the tetrahedron is rolled only four times. For the icosahedron, it’s a much smaller 1/20 chance, but the die is rolled twenty times. Well, it does matter which die is chosen. To see which offers the best odds, you have to raise the odds of not getting the death-face to the power of f, like this:

3/4 x 3/4 x 3/4 x 3/4 = 3/4 ^4 = 27/256 = 0·316…

5/6 ^6 = 15,625 / 46,656 = 0·335…

7/8 ^8 = 5,764,801 / 16,777,216 = 0·344…

11/12 ^12 = 3,138,428,376,721 / 8,916,100,448,256 = 0·352…

19/20 ^20 = 37,589,973,457,545,958,193,355,601 / 104,857,600,000,000,000,000,000,000 = 0·358…

Those represent the odds of avoiding the death-face. Criminals who want to avoid execution should choose the icosahedron. For the odds of rolling the death-face, simply subtract the avoidance-odds from 1, like this:

1 – 3/4 ^4 = 0·684…

1 – 5/6 ^6 = 0·665…

1 – 7/8 ^8 = 0·656…

1 – 11/12 ^12 = 0·648…

1 – 19/20 ^20 = 0·642…

So criminals who prefer execution to life-imprisonment should choose the tetrahedron. If the Tycholatric nation offers freedom to every criminal who rolls the same face of the die f times, then the tetrahedron is also clearly best. The odds of rolling a single specified face f times are 1/f ^f:

1/4 x 1/4 x 1/4 x 1/4 = 1/4^4 = 1 / 256

1/6^6 = 1 / 46,656

1/8^8 = 1 / 16,777,216

1/12^12 = 1 / 8,916,100,448,256

1/20^20 = 1 / 104,857,600,000,000,000,000,000,000

But there are f faces on each polyhedron, so the odds of rolling any face f times are 1/f ^(f-1). On average, of every sixty-four (256/4) criminals who choose to roll the tetrahedron, one will roll the same face four times and be reprieved. If a hundred criminals face the death-penalty each year and all choose to roll the tetrahedron, one criminal will be reprieved roughly every eight months. But if all criminals choose to roll the icosahedron and they have been rolling since the Big Bang, just under fourteen billion years ago, it is very, very, very unlikely that any have yet been reprieved.

Chicks, Dicks and H.B.D.

Britain has recently been entertained by a cat-fight conducted at Twitter, The Observer and other loci of liberalism. Or perhaps “cat-and-castrated-tom-fight” is a better way of putting it. In the cat corner: a pair of self-righteous feminist egomaniacs called Julie Burchill and Suzanne Moore. In the castrato corner: lots of self-righteous transsexual egomaniacs and their supporters. It’s been one of those fights you wish both sides could lose, but it’s also been interesting from a hateful, bestial and demonic point of view. That is, from an HBD POV. HBD stands for human bio-diversity and is about looking at how human biology influences social, cultural and political patterns. Transsexuality is obviously a biological phenomenon, but I think feminism and female writers are too. Read on, if you’re man enough, and I’ll explain how.

The fight started when Suzanne Moore wrote an essay about “female anger” for an anthology published by the booksellers Waterstones. I don’t know or care what the anthology was about, but Moore’s essay included these lines:

The cliché is that female anger is always turned inwards rather than outwards into despair. We are angry with ourselves for not being happier, not being loved properly and not having the ideal body shape – that of a Brazilian transsexual. (Moore article)

Moore was then politely challenged on Twitter by a transphilic woman who detected a hint of transphobia in her remark. Moore refused to retract it and was even sarcastic about the notion of “intersectionality”, i.e., the multiple oppressions suffered by, say, black homosexuals with bad legs, who will suffer not just from racism, homophobia or disabledism, but from all three. Finally, pushed too far, Moore announced that:

People can just fuck off really. Cut their dicks off and be more feminist than me. Good for them. (Transphobic tweeting)

Moore then left Twitter because of the “bullying” she was experiencing. Her friend Julie Burchill came to her defence in The Observer (i.e. The Guardian-on-Sunday) in an article that began like this:

Hey trannies, cut it out

Where do dicks in terrible wigs get off lecturing us natural-born women about not being quite feministic enough? (Burchill article)

Burchill went on to excoriate “dicks in chick’s clothing” and “bed-wetters in bad wigs” who have had their “nuts taken off”. Further uproar ensued, the “transsexual community” complained long and loudly, and The Observer withdrew the article and apologized for the offence it had caused. All this has been entertaining but also, I think, an example of the poisoning of politics described by Britain’s Chief Rabbi, Jonathan Sacks:

Sacks: Multiculturalism threatens democracy

Multiculturalism promotes segregation, stifles free speech and threatens liberal democracy, Britain’s top Jewish official warned in extracts from his book The Home We Build Together: Recreating Society… [Jonathan] Sacks said Britain’s politics had been poisoned by the rise of identity politics, as minorities and aggrieved groups jockeyed first for rights, then for special treatment. The process, he said, began with Jews, before being taken up by blacks, women and gays. He said the effect had been “inexorably divisive. A culture of victimhood sets group against group, each claiming that its pain, injury, oppression, humiliation is greater than that of others.” (Multiculturalism threatens democracy, The Jerusalem Post)

By claiming “pain, injury, oppression” and so on, transsexuals want to make themselves immune from criticism. Saints could be trusted to behave well when immune from criticism, but saints wouldn’t demand to be so. Transsexuals are, I think it’s safe to say, no more saintly than Jews, blacks, women or gays. All the same, I also think Moore and Burchill have shown bigotry – in the proper, rather than politically correct, sense – towards transsexuals. This transphobic twosome obviously don’t like their feminist franchise being challenged by transsexuals, i.e., people who were born in men’s bodies, but think they’re really women and have had surgery to prove it. From my own bigoted, biocentric point of view, I am happy to accept that bodies do not always match brains and that someone with a female mind can be born in a male body. Or vice versa. It’s an interesting phenomenon, scientifically speaking, but it must also sometimes be a distressing phenomenon, psycho-socially speaking. Burchill’s sneers about “phantom limbs” and “bed-wetters in bad wigs” don’t show much female solidarity, let alone imaginative sympathy. But then she doesn’t seem to accept that a real woman can be born in a male body:

Shims, shemales, whatever you’re calling yourselves these days – don’t threaten or bully we [sic] lowly natural-born women, I warn you. We may not have as many lovely big swinging PhDs as you, but we’ve experienced a lifetime of PMT and sexual harassment, and many of us are now staring HRT and the menopause straight in the face – and still not flinching. Trust me, you ain’t seen nothing yet. You really won’t like us when we’re angry.

That is echt essentialism – indeed, physio-fascism. Burchill seems to believe that you can’t be a real woman unless you’re born in a female body. The bit about “lovely big swinging PhDs” is a sneer too, but a funny one: Burchill is an entertaining writer who combines masculine vigour with feminine illogic. Look at her reasoning here, for example:

…their lot [i.e., transsexuals] describe born women as “cis” – sounds like syph, cyst, cistern; all nasty stuff…

If “cis” is nasty because it sounds a bit like “cistern”, presumably “sister” would be even worse. Like Burchill, Suzanne Moore has no time for the nasty male invention of logic; unlike Burchill, she isn’t an entertaining or amusing writer. I’d never read anything by her before this cat-fight and I don’t intend to read anything again. The fight itself seems a good example of narcisso-sisters playing tyranny-trumps and poisoning politics, as the Chief Rabbi warned. Burchill and Moore themselves seem good examples of testotero-sisters: they’re masculinized in both psychology and physiognomy. It’s not just their aggression and coarseness: take a look at their faces:

Suzanne Moore and Julie Burchill

Suzanne Moore and Julie Burchill

I suggest that Moore and Burchill, despite their female bodies, are less psychologically female than some transsexuals who were born in male bodies. Both of them are left-wing and opponents of biological determinism, but they are cruder in their bio-determinism than the supposedly right-wing psychologist Hans Eysenck (1916–97), who was writing about HBD before HBD existed under its present name. In his book Sex, Violence and the Media (1978), Eysenck discussed that idea that “there is a strong biological determinant which predisposes individuals in the direction of greater or lesser ‘maleness’”:

Some of the strongest evidence for this point of view comes from the work of Dr Wilhart Schlegel, a Hamburg physician who made an exhaustive study of the shape of the pelvis in men and women. In men, typically, the pelvis is shaped like a funnel, tapering down to a narrow outlet; in women, the pelvis is shaped more like a tube, with a broad outlet. There is much variety within each sex; thus there are men with tube-shaped pelvis outlet structures, and women with funnel-shaped ones. What made Schlegel interested in the pelvic outlet is that its shape is apparently determined at the foetal stage by precisely the kind of hormonal burst [determining masculinity or femininity] already described; if such androgenic material is supplied, the pelvic shape will be masculine; if not, feminine. This led Schlegel to study in detail the social and sexual behaviour of men and women having typical and atypical pelvic shapes, using over a thousand men and women in his researches. (Op. cit., H.J. Eysenck and D.K.B. Nias, Maurice Temple Smith, London, 1978, pg. 230-1)

Schlegel discovered a strong correlation between pelvic shape and behaviour:

A masculine-type pelvis correlated with leadership, an active sexual role, dominance and a preference for a younger sexual partner, in men and women alike. A feminine-type pelvis correlated with empathy, suggestibility, and compliance. In other words, behaviour in both sexes seemed to be determined by the same hormonal factors which originally produced skeletal features of the pelvis, namely androgen secretion at the foetal stage.

Faces, like pelvises, are shaped by hormonal factors and I suggest that Moore and Burchill have masculinized faces. I also suggest that, as female writers, they are not unique in this. Another example of a masculinized female writer seems to be Hilary Mantel, winner of last year’s Man-Booker Prize for her novel Bring Out the Bodies. Mantel has been placed under scientific analysis by Eysenck’s protegé Chris Brand at his g-Factor blog:

Hilary Mantel

Hilary Mantel

Incomprehensible bug-eyed leftist old bag authoress Hilary Mantel was welcomed by the London Review of Books to put in her two pennorth slagging off the gracious, cheerful and pregnant Duchess of Cornwall… Broad-beamed Mantelpiece was a leftie born and bred – a matter which her publishers had contrived to conceal for several years. Of Irish parentage, she was raised a Catholic by parents who separated (she never saw her father after age eleven). She gave up Christianity at twelve and progressed to full-blown socialism, as was readily compatible with her studies at the London School of Economics and the University of Sheffield. Her own lack of husband and family was perhaps traceable to gynaecological problems so serious that she had been treated by doctors for psychosis during her twenties. (IQ & PC – By Chris Brand, Monday, February 25, 2013)

Mantel’s unusually broad features seem to occur elsewhere among female writers:

L-R: Jane Austen, Harriet Beecher Stowe, Pearl S. Buck, Iris Murdoch

L-R: Jane Austen, Harriet Beecher Stowe, Pearl S. Buck, Iris Murdoch

L-R: Joyce Carol Oates, Maya Angelou, Alice Walker, Arundhati Roy

L-R: Joyce Carol Oates, Maya Angelou, Alice Walker, Arundhati Roy

I suggest that the particular genre in which a writer works would also be reflected in her – or his – biology, but female writers are a small, self-selected group and don’t seem typical of women in general. This also appears to be true of female politicians. I first began to notice their unusual features in the 1990s among women like Hillary Clinton and Madeleine Albright:

Hillary Clinton and Madelaine Albright

Hillary Clinton and Madelaine Albright

Like Moore and Burchill, Clinton and Albright are left-wing and opponents of biological determinism. But the reality may be that a rejection of biological determinism is itself, in part, biologically determined. The subjective self-confidence and aggression of a masculinized woman may lead her to deny any influence of biology on politics, even though there is more and more evidence that such influence exists:

The GOP has a feminine face, UCLA study finds

At least when it comes to female politicians, perhaps you can judge a book by its cover, suggest two UCLA researchers who looked at facial features and political stances in the U.S. House of Representatives. “Female politicians with stereotypically feminine facial features are more likely to be Republican than Democrat, and the correlation increases the more conservative the lawmaker’s voting record,” said lead author Colleen M. Carpinella, a UCLA graduate student in psychology.

The researchers also found the opposite to be true: Female politicians with less stereotypically feminine facial features were more likely to be Democrats, and the more liberal their voting record, the greater the distance the politician’s appearance strayed from stereotypical gender norms. In fact, the relationship is so strong that politically uninformed undergraduates were able to determine the political affiliation of the representatives with an overall accuracy rate that exceeded chance, and the accuracy of those predications increased in direct relation to the lawmaker’s proximity to feminine norms. (“The GOP has a feminine face, UCLA study finds”, Meg Sullivan, September 27, 2012)

Faces and pelvises are indirect guides to brains and it would be very interesting to have more direct data about the brains of female politicians, whether left- or right-wing. It would also be interesting to know how many children they have and the sex-ratio of those children, because that is also influenced by hormonal factors. Like Burchill and Moore, Hilary Mantel and Hillary Clinton would no doubt dismiss HBD as hateful, but all of them are biological entities and none of them can escape HBD. Neither can I or you or any other human being, but the more we know about ourselves the better we may be able to understand politics and culture. And the more we know about human biology, the more we may also understand that some forms of politics are far less caring and compassionate than they claim to be.