He Say, He Sigh, He Sow #39

— Croyez-vous aux idées dangereuses ?
— Qu’entendez-vous par là ?
— Croyez-vous que certaines idées soient aussi dangereuses pour certains esprits que le poison pour le corps ?
— Mais, oui, peut-être.

  Guy de Maupassant, « Divorce » (1888)

“Do you believe in dangerous ideas?”
“What do you mean by that?”
“Do you believe that certain ideas are as dangerous for some minds as poison is for the body?”
“Well, yes, perhaps.”

Amateur ’Grammatics

There is much more to mathematics than mathematics. Like a tree, it has deep roots. Like a tree, it’s affected by its environment. Philosophy of mathematics is concerned with the roots. Psychology of mathematics is concerned with the environment.

On Planet Earth, the environment is human beings. What attracts men and women to the subject? What makes them good or bad at it?And so on. One interesting answer to the first question was supplied by the mathematician Stanislaw Ulam (1909-84), who wrote this in his autobiography:

“In many cases, mathematics is an escape from reality. The mathematician finds his own monastic niche and happiness in pursuits that are disconnected from external affairs. Some practice it as if using a drug.” – Adventures of a Mathematician (1983)

That’s certainly part of maths’ appeal to me: as an escape from reality, or an escape from one reality into another (and deeper). Real life is messy. Maths isn’t, unless you want it to be. But you can find parallels between maths and real life too. In real life, people collect things that they find attractive or interesting: stamps, sea-shells, gems, cigarette-cards, beer-cans and so on. You can collect things in maths too: interesting numbers and number patterns. Recreational maths can feel like looking on a beach for attractive shells and pebbles.

Here’s a good example: digital anagrams, or numbers in different bases whose digits are the same but re-arranged. For example, 13 in base 10 equals 31 in base 4, because 13 = 3 * 4 + 1. To people with the right kind of mind, that’s an interesting and attractive pattern. There are lots more anagrams like that:

1045 = 4501 in base 6
1135 = 5131 in base 6

23 = 32 in base 7
46 = 64 in base 7

1273 = 2371 in base 8
1653 = 3165 in base 8

158 = 185 in base 9
227 = 272 in base 9

196 = 169 in base 11
283 = 238 in base 11

2193 = 1329 in base 12
6053 = 3605 in base 12

43 = 34 in base 13
86 = 68 in base 13

But triple anagrams, involving three bases, seem even more attractive:

913 = 391 in base 16 = 193 in base 26
103462 = 610432 in base 7 = 312046 in base 8
245183 = 413285 in base 9 = 158234 in base 11

And that’s just looking in base 10. If you include all bases, the first double anagram is in fact 21 in base 3 = 12 in base 5 (equals 7 in base 10). The first triple anagram is this:

2C1 in base 13 = 1C2 in base 17 = 12C in base 21 (equals 495 in base 10)

But are there quadruple anagrams, quintuple anagrams and higher? I don’t know. I haven’t found any and it gets harder and harder to search for them, because the bigger n gets, the more bases there are to check. However, I can say one thing for certain: in any given base, anagrams eventually disappear.

To understand why, consider the obvious fact that anagrams have to have the same number of digits in different bases. But the number of digits is a function of the powers of the base. That is, the triple anagram 103462 (see above) has six digits in bases 7, 8 and 10 because 7^5 < 103462 < 7^6, 8^5 < 103462 < 8^6 and 10^5 < 103462 < 10^6. Similarly, the triple anagram 245183 (ditto) has six digits in bases 9, 10 and 11 because 9^5 < 245183 < 9^6, 10^5 < 245183 < 10^6 and 11^5 < 245183 < 11^6:

7^5 < 103462 < 7^6
16807 < 103462 < 117649
8^5 < 103462 < 8^6
32768 < 103462 < 262144
10^5 < 103462 < 10^6
100000 < 103462 < 1000000
9^5 < 245183 < 9^6
59049 < 245183 < 531441
10^5 < 245183 < 10^6
100000 < 245183 < 1000000
11^5 < 245183 < 11^6
161051 < 245183 < 1771561

In other words, for some n the number-lengths of bases 7 and 8 overlap the number-lengths of base 10, which overlap the number-lengths of bases 9 and 11. But eventually, as n gets larger, the number-lengths of base 10 will fall permanently below the number-lengths of bases 7, 8 and 9, just as the number-lengths of base 11 will fall permanently below the number-lengths of base 10.

To see this in action, consider the simplest example: number-lengths in bases 2 and 3. There is no anagram involving these two bases, because only two numbers have the same number of digits in both: 1 and 3 = 11 in base 2 = 10 in base 3. After that, n in base 2 always has more digits than n in base 3:

2^0 = 1 in base 2 (number-length=1) = 1 in base 3 (l=1)
2^1 = 2 = 10 in base 2 (number-length=2) = 2 in base 3 (l=1)
2^2 = 4 = 100 in base 2 (l=3) = 11 in base 3 (l=2)
2^3 = 8 = 1000 in base 2 = 22 in base 3 (l=2)
2^4 = 16 = 10000 in base 2 = 121 in base 3 (l=3)
2^5 = 32 = 1012 in base 3 (l=4)
2^6 = 64 = 2101 in base 3 (l=4)
2^7 = 128 = 11202 in base 3 (l=5)
2^8 = 256 = 100111 in base 3 (l=6)
2^9 = 512 = 200222 in base 3 (l=6)
2^10 = 1024 = 1101221 in base 3 (l=7)

Now consider bases 3 and 4. Here is an anagram using these bases: 211 in base 3 = 112 in base 4 = 22. There are no more anagrams and eventually there’s no more chance for them to occur, because this happens as n gets larger:

3^0 = 1 in base 3 (number-length=1) = 1 in base 4 (l=1)
3^1 = 3 = 10 in base 3 (number-length=2) = 3 in base 4 (l=1)
3^2 = 9 = 100 in base 3 (l=3) = 21 in base 4 (l=2)
3^3 = 27 = 1000 in base 3 (l=4) = 123 in base 4 (l=3)
3^4 = 81 = 10000 in base 3 (l=5) = 1101 in base 4 (l=4)
3^5 = 243 = 100000 in base 3 (l=6) = 3303 in base 4 (l=4)
3^6 = 729 = 23121 in base 4 (l=5)
3^7 = 2187 = 202023 in base 4 (l=6)
3^8 = 6561 = 1212201 in base 4 (l=7)
3^9 = 19683 = 10303203 in base 4 (l=8)
3^10 = 59049 = 32122221 in base 4 (l=8)
3^11 = 177147 = 223033323 in base 4 (l=9)
3^12 = 531441 = 2001233301 in base 4 (l=10)
3^13 = 1594323 = 12011033103 in base 4 (l=11)
3^14 = 4782969 = 102033231321 in base 4 (l=12)
3^15 = 14348907 = 312233021223 in base 4 (l=12)
3^16 = 43046721 = 2210031131001 in base 4 (l=13)
3^17 = 129140163 = 13230220113003 in base 4 (l=14)
3^18 = 387420489 = 113011321011021 in base 4 (l=15)
3^19 = 1162261467 = 1011101223033123 in base 4 (l=16)
3^20 = 3486784401 = 3033311001232101 in base 4 (l=16)

When n is sufficiently large, it always has fewer digits in base 4 than in base 3. And the gap gets steadily bigger. When n doesn’t have the same number of digits in two bases, it can’t be an anagram. A similar number-length gap eventually appears in bases 4 and 5, but the anagrams don’t run out as quickly there:

103 in base 5 = 130 in base 4 = 28
1022 in base 5 = 2021 in base 4 = 137
1320 in base 5 = 3102 in base 4 = 210
10232 in base 5 = 22310 in base 4 = 692
10332 in base 5 = 23031 in base 4 = 717
12213 in base 5 = 32211 in base 4 = 933
100023 in base 5 = 301002 in base 4 = 3138
100323 in base 5 = 302031 in base 4 = 3213
102131 in base 5 = 311120 in base 4 = 3416
102332 in base 5 = 312023 in base 4 = 3467
103123 in base 5 = 313102 in base 4 = 3538
1003233 in base 5 = 3323010 in base 4 = 16068

Base 10 isn’t exempt. Eventually it must outshrink base 9 and be outshrunk by base 11, so what is the highest 9:10 anagram and highest 10:11 anagram? I don’t know: my maths isn’t good enough for me to find out quickly. But using machine code, I’ve found these large anagrams:

205888888872731 = 888883178875022 in base 9
1853020028888858 = 8888888525001032 in base 9
16677181388880888 = 88888888170173166 in base 9

999962734025 = 356099992472 in base 11
9999820360965 = 3205999998606 in base 11
99999993520348 = 29954839390999 in base 11

Note how the digits of n in the lower base are increasing as the digits of n in the higher base are decreasing. Eventually, n in the lower base will always have more digits than n in the higher base. When that happens, there will be no more anagrams.

Some triple anagrams

2C1 in base 13 = 1C2 in base 17 = 12C in base 21 (n=495 = 3^2*5*11)
912 in base 10 = 219 in base 21 = 192 in base 26 (2^4*3*19)
913 in base 10 = 391 in base 16 = 193 in base 26 (11*83)
4B2 in base 15 = 42B in base 16 = 24B in base 22 (n=1067 = 11*97)
5C1 in base 17 = 51C in base 18 = 1C5 in base 35 (n=1650 = 2*3*5^2*11)
3L2 in base 26 = 2L3 in base 31 = 23L in base 35 (n=2576 = 2^4*7*23)
3E1 in base 31 = 1E3 in base 51 = 13E in base 56 (n=3318 = 2*3*7*79)
531 in base 29 = 351 in base 37 = 135 in base 64 (n=4293 = 3^4*53)
D53 in base 18 = 53D in base 29 = 35D in base 37 (n=4305 = 3*5*7*41)
53I in base 29 = 3I5 in base 35 = 35I in base 37 (n=4310 = 2*5*431)
825 in base 25 = 582 in base 31 = 258 in base 49 (n=5055 = 3*5*337)
6S2 in base 31 = 2S6 in base 51 = 26S in base 56 (n=6636 = 2^2*3*7*79)
D35 in base 23 = 5D3 in base 36 = 3D5 in base 46 (n=6951 = 3*7*331)
3K1 in base 49 = 31K in base 52 = 1K3 in base 81 (n=8184 = 2^3*3*11*31)
A62 in base 29 = 6A2 in base 37 = 26A in base 64 (n=8586 = 2*3^4*53)
9L2 in base 30 = 92L in base 31 = 2L9 in base 61 (n=8732 = 2^2*37*59)
3W1 in base 49 = 1W3 in base 79 = 13W in base 92 (n=8772 = 2^2*3*17*43)
G4A in base 25 = AG4 in base 31 = 4AG in base 49 (n=10110 = 2*3*5*337)
J10 in base 25 = 1J0 in base 100 = 10J in base 109 (n=11900 = 2^2*5^2*7*17)
5[41]1 in base 46 = 1[41]5 in base 93 = 15[41] in base 109 (n=12467 = 7*13*137)
F91 in base 29 = 9F1 in base 37 = 19F in base 109 (n=12877 = 79*163)
F93 in base 29 = 9F3 in base 37 = 39F in base 64 (n=12879 = 3^5*53)
AP4 in base 35 = A4P in base 36 = 4AP in base 56 (n=13129 = 19*691)
BP2 in base 36 = B2P in base 37 = 2PB in base 81 (n=15158 = 2*11*13*53)
O6F in base 25 = FO6 in base 31 = 6FO in base 49 (n=15165 = 3^2*5*337)
FQ1 in base 31 = 1QF in base 111 = 1FQ in base 116 (n=15222 = 2*3*43*59)
B74 in base 37 = 7B4 in base 46 = 47B in base 61 (n=15322 = 2*47*163)

Heads and Tells

I have a natural history book that has a photograph of a mole as it emerges from a patch of bare soil, digging itself up with its forepaws. But the photograph has been posed: the mole’s obviously dead. Its colour is wrong and you can see that there’s no tension in its body.

But the photograph might fool a hasty glance. The difference between tense life and flaccid death is small and there’s no clue in the mole’s eyes, because you can’t see them. It’s a mole, after all. In this photo, on the other hand, you can’t miss the eyes:

Ruby-tailed wasp, Chrysis ignita

Chrysis ignita, Ruby-tailed wasp

But an insect’s eyes don’t generally change when it dies, so the wasp’s eyes don’t refute or confirm a suspicion I have about the photo: that it’s also posed with a dead subject. I’m much less certain than I am about the mole, but then a dead insect is harder to read than a dead mammal. Insects have chitinous exoskeletons, not skin or fur over muscles, so their bodies don’t obviously lose tonus when they’re dead.

But something about the posture of the wasp looks wrong to me. So do its antennae: trailing on the ground, not held up. I’m far less certain than I am about the mole, but I’m suspicious. And I’m interested in my suspicion. Photographs are usually harder to read than moving pictures. There’s less information in them, because they record an object in an instant of time. You might say that you have to go by the geometry, not the trajectory.

Or lack of it. Dead things don’t have trajectories, unless an external force imposes one on them. So it’s the geometry – slumped limbs, slightly twisted heads – that betrays the true status of some of the subjects in the book Living Jewels, which collects photographs of tropical beetles. They’re museum specimens and some may have been dead for years or decades. Exoskeletons don’t corrupt and decay like skin and muscle, so the beetles retain their beauty.

And they don’t look blatantly dead. Not the way mammals would. There’s less information in an insect’s exoskeleton, so the difference between life and death is harder to read. Emotions are harder to read in an insect too. What would a photo of an angry beetle look like? Insects’ faces are immobile, like masks, which is one reason they seem so eerie and alien.

People are different: there’s lots of information in our faces and postures, let alone our voices. And sometimes imposture (and im-posture) is easy to read. We’re all familiar with false smiles and fake laughs. For me, it gets interesting when information is restricted and you can’t see someone’s face. How much can you tell from the back of a head, for example? Or a hand? Sometimes a lot. That’s why I’m interested in these photos of people adopting a stereotyped attitude of despair: slumped and heads-in-hands:

posture 1

posture 2

posture 3

posture 4

posture 5

posture 6

I don’t think any of the photos are of genuine emotion: they’re too clean and carefully lit, for one thing. And you wouldn’t expect them to be real. But the difference between posed despair and the real thing is often very slight. There are subtle differences in the outline of the body and its muscle tension. There’s a term for this in poker: tells, or slight give-aways in the posture or expression of an opposing player. The heads above tell me that the despair is being acted. So do the hands. And the outline of the bodies.

This photo I’m less certain about:

Deserter by Charles Glass

Deserter by Charles Glass

That might be real despair in a real soldier — I haven’t read the book, so I don’t know what the provenance of the photo is. The way his right foot is pointing slightly inward looks convincing to me. But I’m not certain. The photo might have been posed. If it was, the soldier was a good actor. With a posture like that, there’s little scope to express emotion: with less to do, you have to act more.

And with less information, the mind has to work harder. That’s why I find this an interesting topic. How do we read falsity or veracity in very small things like the angle of a hand or outline of a body? And will computers be able to imitate us? And then surpass us? If so, there must be mines of information buried beneath the surface of old photographs. At the moment, we intuit that information or miss it altogether. One day, computers may be able to trawl archives and come up with new facts about the psychology and relationships of historical figures, simply by reading tiny tells in expressions and postures.

I Say, I Sigh, I Sow #12

The quickest way to improve your life is to stop watching TV.

White Dot — the International Campaign against Television

The Mill to Power

Reading about Searle’s Chinese Room Argument at the Stanford Encyclopedia of Philosophy, I came across “Leibniz’s Mill” for the first time. At least, I think it was the first time:

It must be confessed, however, that perception, and that which depends upon it, are inexplicable by mechanical causes, that is to say, by figures and motions. Supposing that there were a machine whose structure produced thought, sensation, and perception, we could conceive of it as increased in size with the same proportions until one was able to enter into its interior, as he would into a mill. Now, on going into it he would find only pieces working upon one another, but never would he find anything to explain perception. It is accordingly in the simple substance, and not in the compound nor in a machine that the perception is to be sought. Furthermore, there is nothing besides perceptions and their changes to be found in the simple substance. And it is in these alone that all the internal activities of the simple substance can consist. (Monadology, 1714, section #17)

Andererseits muß man gestehen, daß die Vorstellungen, und Alles, was von ihnen abhängt, aus mechanischen Gründen, dergleichen körperliche Gestalten und Bewegungen sind, unmöglich erklärt werden können. Man stelle sich eine Maschine vor, deren Structur so eingerichtet sei, daß sie zu denken, zu fühlen und überhaupt vorzustellen vermöge und lasse sie unter Beibehaltung derselben Verhältnisse so anwachsen, daß man hinein, wie in das Gebäude einer Mühle eintreten kann. Dies vorausgesetzt, wird man bei Besichtigung des Innern nichts Anderes finden, als etliche Triebwerke, deren eins das andere bewegt, aber gar nichts, was hinreichen würde, den Grund irgend einer Vorstellung abzugeben. Die letztere gehört ausschließlich der einfachen Substanz an, nicht der zusammengesetzten, und dort, nicht hier, muß man sie suchen. Auch sind Vorstellungen und ihre Veränderungen zugleich das Einzige, was man in der einfachen Substanz antrifft. (Monadologie, 1714)

We can see that Leibniz’s argument applies to mechanism in general, not simply to the machines he could conceive in his own day. He’s claiming that consciousness isn’t corporeal. It can’t generated by interacting parts or particles. And intuitively, he seems to be right. How could a machine or mechanism, however complicated, be conscious? Intuition would say that it couldn’t. But is intuition correct? If we examine the brain, we see that consciousness begins with mechanism. Vision and the other senses are certainly electro-chemical processes in the beginning. Perhaps in the end too.

Some puzzles arise if we assume otherwise. If consciousness isn’t mechanistic, how does it interact with mechanism? If it’s immaterial, how does it interact with matter? But those questions go back much further, to Greek atomists like Democritus (c. 460-370 BC):

Δοκεῖ δὲ αὐτῶι τάδε· ἀρχὰς εἶναι τῶν ὅλων ἀτόμους καὶ κενόν, τὰ δ’ἀλλα πάντα νενομίσθαι.

He taught that the first principles of the universe are atoms and void; everything else is merely thought to exist.

Νόμωι (γάρ φησι) γλυκὺ καὶ νόμωι πικρόν, νόμωι θερμόν, νόμωι ψυχρόν, νόμωι χροιή, ἐτεῆι δὲ ἄτομα καὶ κενόν.

By convention sweet is sweet, bitter is bitter, hot is hot, cold is cold, color is color; but in truth there are only atoms and the void. (Democritus at Wikiquote)

Patterns of unconscious matter and energy influence consciousness and are perhaps entirely responsible for it. The patterns are tasteless, soundless, colourless, scentless, neither hot nor cold – in effect, units of information pouring through the circuits of reality. But are qualia computational? I think they are. I don’t think it’s possible to escape matter or mechanism and I certainly don’t think it’s possible to escape mathematics. But someone who thinks it’s possible to escape at least the first two is the Catholic philosopher Edward Feser. I wish I had come across his work a long time ago, because he raises some very interesting questions in a lucid way and confirms the doubts I’ve had for a long time about Richard Dawkins and other new atheists. His essay “Schrödinger, Democritus, and the paradox of materialism” (2009) is a good place to start.

Elsewhere other-posted:

Double Bubble
This Mortal Doyle
The Brain in Pain
The Brain in Train

Material Whirled

When we are conscious of being conscious, what are we consciousness-conscious with? If consciousness is a process in the brain, the process has become aware of itself, but how does it do so? And what purpose does consciousness-of-consciousness serve? Is it an artefact or an instrument? Is it an illusion? A sight or sound or smell is consciousness of a thing-in-itself, but that doesn’t apply here. We aren’t conscious of the thing-in-itself: the brain and its electro-chemistry. We’re conscious of the glitter on the swinging sword, but not the sword or the swing.

We can also be conscious of being conscious of being conscious, but beyond that my head begins to spin. Which brings me to an interesting reminder of how long the puzzle of consciousness has existed in its present form: how do we get from matter to mind? As far as I can see, science understands the material substrate of consciousness – the brain – in greater and greater detail, but is utterly unable to explain how objective matter becomes subjective consciousness. We have not moved an inch towards understanding how quanta become qualia since this was published in 1871:

Were our minds and senses so expanded, strengthened, and illuminated, as to enable us to see and feel the very molecules of the brain; were we capable of following all their motions, all their groupings, all their electric discharges, if such there be; and were we intimately acquainted with the corresponding states of thought and feeling, we should be as far as ever from the solution of the problem, “How are these physical processes connected with the facts of consciousness?” The chasm between the two classes of phenomena would still remain intellectually impassable.

Let the consciousness of love, for example, be associated with a right-handed spiral motion of the molecules of the brain, and the consciousness of hate with a left-handed spiral motion. We should then know, when we love, that the motion is in one direction, and, when we hate, that the motion is in the other; but the “Why?” would remain as unanswerable as before. — John Tyndall, Fragments of Science (1871), viâ Rational Buddhism.

Elsewhere other-posted:

Double Bubble
The Brain in Pain
The Brain in Train
This Mortal Doyle

Blue is the Killer

Eye Bogglers by Gianni A. Sarcone and Marie-Jo WaeberEye Bogglers: A Mesmerizing Mass of Amazing Illusions, Gianni A. Sarcone and Marie-Jo Waeber (Carlton Books 2011; paperback 2013)

A simple book with some complex illusions. It’s aimed at children but scientists have spent decades understanding how certain arrangements of colour and line fool the eye so powerfully. I particularly like the black-and-white tiger set below a patch of blue on page 60. Stare at the blue “for 15 seconds”, then look quickly at a tiny cross set between the tiger’s eyes and the killer turns colour.

So what’s not there appears to be there, just as, elsewhere, what’s there appears not to be. Straight lines seem curved; large figures seem small; the same colour seems light on the right, dark on the left. There are also some impossible figures, as made famous by M.C. Escher and now studied seriously by geometricians, but the only true art here is a “Face of Fruits” by Arcimboldo. The rest is artful, not art, but it’s interesting to think what Escher might have made of some of the ideas here. Mind is mechanism; mechanism can be fooled. Optical illusions are the most compelling examples, because vision is the most powerful of our senses, but the lesson you learn here is applicable everywhere. This book fools you for fun; others try to fool you for profit. Caveat spectator.

Simple but complex: The café wall illusion

Simple but complex: The café wall illusion

The Power of Babel

“…par la suggestive lecture d’un ouvrage racontant de lointains voyages…” – J.K. Huysmans, À Rebours (1884).

The language you know best is also the language you know least: your mother tongue, the language you acquired by instinct and speak by intuition. Asking a native speaker to describe English, French or Quechua is rather like asking a fish to describe water. The native speaker, like the fish, knows the answer very intimately, yet in some ways doesn’t know as well as a non-native speaker. In other words, standing outside can help you better understand standing inside: there is good in the gap. What is it like to experience gravity? Like most humans, I’ve known all my life, but I’d know better if I were in orbit or en route to the moon, experiencing the absence of gravity.

And what is it like to be human? We all know and we’ve all read countless stories about other human beings. But in some ways they don’t answer that question as effectively as stories that push humanity to the margins, like Richard Adams’ Watership Down (1972), which is about rabbits, or Isaac Asimov’s The Gods Themselves (also 1972), which is about trisexual aliens in a parallel dimension. There is good in the gap, in stepping outside the familiar and looking back to see the familiar anew.

Continuing reading The Power of Babel

Mi Is Mirror

I hope that nobody thinks I’m being racially prejudiced when I say that, much though I am fascinated by her, I do not find the Anglo-American academic Mikita Brottman physically attractive. It is her mind that has raised my longstanding interest, nothing more.


This is because, for me, Ms B is like a mirror that reverses not left and right, but male and female.

Obviously, we’re different in a lot of ways: I don’t smoke and I don’t have any tattoos, for example.

But there are big similarities too.

We were born in the same year (1956) and we were both keyly core contributors to seminal early issues of the transgressive journal Headpress Journal.

And we have various other things in common, like our mutually shared passion for corpse’n’cannibal cinema, our Glaswegian accents and (at different times) our season tickets for Hull Kingston Rovers.

So it is that, looking at Ms B, I have the uncanny experience of seeing myself as I might have been, had I been born female.

But it’s not just uncanny.

It’s horrifying at times too.

Okay, I’m comfortable with the idea that, born female, I would have been less intelligent and more conformist. So I don’t mind that Ms B is a Guardianista. Not particularly. I can face the fact that I would quite likely have been one of them too, as a female.

But there are worse things than being a Guardianista, believe it or not.

Ms B has a PhD in EngLit.

A PhD!

In EngLit.

It’s not at all easy for me to face the fact that I might have had one too, as a female. It really isn’t. But how can I deny it? I might have. That despicable, deplorable, thoroughly disreputable subject might have attracted me. In fact, it would probably have attracted me.


But it gets worse still.

Ms B is a psychoanalyst.

A psychoanalyst.

Ach du lieber Gott!

See what I mean by “horrifying”?

I mean, even if I’d been born female I wouldn’t have sunk to such depths, would I? Would I? No, I have to face facts: I might. But I don’t think so. I have a feeling that there’s more to Brotty’s interest in Freud than her gender statusicity and her key commitment to core componency of the counter-cultural community.

But I’d better say no more. Verb sap.