Simple things can sometimes baffle advanced minds. If you take a number, reverse its digits, add the result to the original number, then repeat all that, will you eventually get a palindrome? (I.e., a number, like 343 or 27172, that reads the same in both directions.) Many numbers do seem to produce palindromes sooner or later. Here are 195 and 197:
195 + 591 = 786 + 687 = 1473 + 3741 = 5214 + 4125 = 9339 (4 steps)
197 + 791 = 988 + 889 = 1877 + 7781 = 9658 + 8569 = 18227 + 72281 = 90508 + 80509 = 171017 + 710171 = 881188 (7 steps)
But what about 196? Well, it starts like this:
196 + 691 = 887 + 788 = 1675 + 5761 = 7436 + 6347 = 13783 + 38731 = 52514 + 41525 = 94039 + 93049 = 187088 + 880781 = 1067869 + 9687601 = 10755470 + 7455701 = 18211171 + 17111281 = 35322452 + 25422353 = 60744805 + 50844706 = 111589511 + 115985111 = 227574622 + 226475722 = 454050344 + 443050454 = 897100798 + 897001798 = 1794102596 + 6952014971 = 8746117567 + 7657116478 = 16403234045 + 54043230461 = 70446464506 + 60546464407 = 130992928913 + 319829299031 = 450822227944 + 449722228054 = 900544455998…
And so far, after literally years of computing by mathematicians, it hasn’t produced a palindrome. It seems very unlikely it ever will, but no-one can prove this and say that 196 is, in base 10, a Lychrel number, or a number that never produces a palindrome. In other words, a simple thing has baffled advanced minds.
I don’t know whether it can baffle advanced minds, but here’s another simple mathematical technique: sum all the digits of a number, then add the result to the original number and repeat. How long before a palindrome appears in this case? Sum it and see:
10 + 1 = 11
12 + 3 = 15 + 6 = 21 + 3 = 24 + 6 = 30 + 3 = 33 (5 steps)
13 + 4 = 17 + 8 = 25 + 7 = 32 + 5 = 37 + 10 = 47 + 11 = 58 + 13 = 71 + 8 = 79 + 16 = 95 + 14 = 109 + 10 = 119 + 11 = 130 + 4 = 134 + 8 = 142 + 7 = 149 + 14 = 163 + 10 = 173 + 11 = 184 + 13 = 197 + 17 = 214 + 7 = 221 + 5 = 226 + 10 = 236 + 11 = 247 + 13 = 260 + 8 = 268 + 16 = 284 + 14 = 298 + 19 = 317 + 11 = 328 + 13 = 341 + 8 = 349 + 16 = 365 + 14 = 379 + 19 = 398 + 20 = 418 + 13 = 431 + 8 = 439 + 16 = 455 + 14 = 469 + 19 = 488 + 20 = 508 + 13 = 521 + 8 = 529 + 16 = 545 (45 steps)
14 + 5 = 19 + 10 = 29 + 11 = 40 + 4 = 44 (4 steps)
15 + 6 = 21 + 3 = 24 + 6 = 30 + 3 = 33 (4 steps)
16 + 7 = 23 + 5 = 28 + 10 = 38 + 11 = 49 + 13 = 62 + 8 = 70 + 7 = 77 (7 steps)
17 + 8 = 25 + 7 = 32 + 5 = 37 + 10 = 47 + 11 = 58 + 13 = 71 + 8 = 79 + 16 = 95 + 14 = 109 + 10 = 119 + 11 = 130 + 4 = 134 + 8 = 142 + 7 = 149 + 14 = 163 + 10 = 173 + 11 = 184 + 13 = 197 + 17 = 214 + 7 = 221 + 5 = 226 + 10 = 236 + 11 = 247 + 13 = 260 + 8 = 268 + 16 = 284 + 14 = 298 + 19 = 317 + 11 = 328 + 13 = 341 + 8 = 349 + 16 = 365 + 14 = 379 + 19 = 398 + 20 = 418 + 13 = 431 + 8 = 439 + 16 = 455 + 14 = 469 + 19 = 488 + 20 = 508 + 13 = 521 + 8 = 529 + 16 = 545 (44 steps)
18 + 9 = 27 + 9 = 36 + 9 = 45 + 9 = 54 + 9 = 63 + 9 = 72 + 9 = 81 + 9 = 90 + 9 = 99 (9 steps)
19 + 10 = 29 + 11 = 40 + 4 = 44 (3 steps)
20 + 2 = 22
I haven’t looked very thoroughly at this technique, so I don’t know whether it throws up a seemingly unpalindromizable number. If it does, I don’t have an advanced mind, so I won’t be able to prove that it is unpalindromizable. But an adaptation of the technique produces something interesting when it is represented on a graph. This time, if s > 9, where s = digit-sum(n), let s = digit-sum(s) until s <= 9 (i.e, s < 10, the base). I call this the condensed digit-sum:
140 + 5 = 145 + 1 = 146 + 2 = 148 + 4 = 152 + 8 = 160 + 7 = 167 + 5 = 172 + 1 = 173 + 2 = 175 + 4 = 179 + 8 = 187 + 7 = 194 + 5 = 199 + 1 = 200 + 2 = 202 (15 steps)
Here, for comparison, is the sequence for 140 using uncondensed digit-sums:
140 + 5 = 145 + 10 = 155 + 11 = 166 + 13 = 179 + 17 = 196 + 16 = 212 (6 steps)
When all the numbers (including palindromes) created using condensed digit-sums are shown on a graph, they create an interesting pattern in base 10 (the x-axis represents n, the y-axis represents n, n1 = n + digit-sum(n), n2 = n1 + digit-sum(n1), etc):
(Please open images in a new window if they fail to animate.)
And here, for comparison, are the patterns created by uncondensed digit-sums in base 2 to 10:
In terms of the highest levels of the United Kingdom’s counter-cultural community, it seems to be compulsory for non-conformists, mavericks, free-thinkers et al to be committed readers of The Guardian (which was nicknamed The Grauniad by Private Eye in honour of the misspellings once common there). Naturally enough, committed Guardian-readers use the special dialect of English known as Guardianese (which is also found in The Times Literary Supplement, The London Review of Books, etc). And there are a lot of such Guardianistas in the counter-cultural community, trust me. So the obvious question arises:
Myriads, myriads, off the wall,
Who is the Grauniest of them all?
Continue reading Homotextuality…
The Sky at Night: Answers to Questions from Across the Universe, Patrick Moore and Chris North (BBC Books, 2012)
Astronomy, one of the most successful and far-reaching of all sciences, has been largely based on almost nothing. Human beings have pushed their knowledge of the physical universe out over huge stretches of space and time without using anything physical, in the everyday sense of the word. This is because astronomy is largely based on the collection and analysis of tiny, weightless particles known as photons, which can’t be touched, tasted, smelt, or heard, only seen. And sometimes not seen either: visible light is only a small part of the electro-magnetic spectrum occupied by photons at different wavelengths and energies. Move a little in one direction and you meet invisible ultra-violet; move a little in the other direction and you meet invisible infra-red. Move further and you’ll meet radio-waves and gamma-rays. To make all those visible, we need technology, but we also need technology to collect the visible light of dim or distant celestial objects.
That technology is called the telescope and without it modern astronomy wouldn’t exist. The telescope opened a door in the attic of the universe just as the microscope opened a door in the cellar. But astronomy was an advanced subject well before the telescope was invented, in part because it is an essentially simple subject. Unlike human beings and animals, planets and stars behave in relatively stereotyped, predictable ways. That’s why their behaviour is so easily expressed and analysed using mathematics. Thousands of years ago, men could create mathematical models of the universe and accurately predict celestial behaviour in detail. But they couldn’t create mathematical models of animal or human behaviour and make accurate predictions. We still can’t do that, but we’ve getting better and better at applying mathematics to the photons we collect from the sky. Patrick Moore (1923-2012) was the eccentric BBC presenter of a series called The Sky at Night and devoted his life to those photons, particularly the ones that bounced off the surface of the moon. He wasn’t a professional astronomer or an advanced mathematician, but he could recognize the importance of mathematics and the devices that run on it:
What single technological advance over the past 53 years has facilitated the greatest increase in our knowledge and understanding of the cosmos?
Tony Davies (Shoreham-by-Sea, West Sussex)
I think we’ve got to say here the development of electronics in astronomy. Old-fashioned photography has gone out, and electronic devices have taken over. They have led to amazing advances, in all branches of science, not just astronomy. Coupled with the advances in electronic computing, they have allowed discoveries astronomers could only dream of even as recently as a decade ago. So I must say the advent of the Electronic Age. (“Patrick Moore and the Sky at Night”, pg. 424)
I can almost hear Patrick Moore’s slightly clipped, almost stuttering tones as I read that answer. He was an odd character, but I think he led a worthwhile life and odd characters are attracted to subjects like astronomy. It’s on the philatelic side of science and this description by George Orwell of his job in a bookshop might also apply to astronomy:
Like most second-hand bookshops we had various sidelines. We sold second-hand typewriters, for instance, and also stamps — used stamps, I mean. Stamp-collectors are a strange, silent, fish-like breed, of all ages, but only of the male sex; women, apparently, fail to see the peculiar charm of gumming bits of coloured paper into albums. (“Bookshop Memories”, 1936)
Women also mostly fail to see the peculiar charm of astronomy. One of the reasons I like it is that it contains a lot of big ideas and tantalizing possibilities, from the lingering birth-bawl in the Cosmic Microwave Background to the prospect of life beneath the ice-cap of Jupiter’s moon Europa, by way of T.L.P., or Transient Lunar Phenomena, the mysterious fleeting changes that occasionally occur on the moon. This book covers all of those and much more. Another reason I like astronomy is that, so far, it hasn’t often involved killing things and cutting them up. Or worse, not killing them and still cutting them up. H.G. Wells couldn’t have written The Island of Dr Moreau (1896) about an astronomer and part of H.P. Lovecraft’s genius was to combine the grandeurs and glories of astronomy with the intimacy and viscerality of biology. Lovecraft would certainly have liked this book. This sounds like a giant cosmic conspiracy right out of a story like “Dreams in the Witch House” (1932):
…our Galaxy is moving relative… to the Universe… at a speed of around 600 km/s… The cause of the motion, enigmatically known as the “Great Attractor”, was a mystery for several decades, partly because whatever is causing it is hidden behind the material in the disc of our Galaxy. The source of the motion is now thought to be a massive cluster of galaxies in the constellation of Norma, which is attracting not just our Galaxy and its immediate neighbours, but also the much larger Virgo cluster. (“Cosmology: The Expansion of the Universe”, pg. 208)
It’s a large and complicated universe out there and it’s amazing that we’ve managed to learn so much about it from our own tiny corner, using mostly nothing but light and working mostly nowhere but the earth itself. But that is the power of mathematics: Archimedes said of levers that, given a place to stand, he could move the world. Using the lever of mathematics, men can move the universe standing only in their own heads. The co-author of this book, Dr Chris North of the School of Physics and Astronomy at Cardiff University, is one of those men. He does the heavy intellectual lifting here, answering the most advanced questions, but I’m sure that he would acknowledge that Patrick Moore was one of the world’s greatest popularizers of astronomy. The questions themselves range from the naïve to the nuanced, the elementary to the exoplanetary. But I was surprised, given that this is a book issued by the Bolshevik Broadcasting Corporation, that almost all of them seemed to be asked by white males, sometimes from hideously unvibrant parts of Britain like County Durham. Was there no edict to invent some astrophile Ayeshas and Iqbals from Bradford and some budding Afro-physicists from Brixton?
Perhaps there was, but Moore ignored it. He was an old-fashioned character with old-fashioned views, after all, and he says here that he was introduced to astronomy by a book, G.F. Chambers’ The Story of the Solar System, that was published in 1898 (pg. 409). So his astronomy touched three centuries. He also met three very important men: Orville Wright, the first man to fly properly; Yuri Gagarin, the first man into space; and Neil Armstrong, the first man on the moon. Those were three steps towards our permanent occupation of space. To understand what attracts men there and the questions they hope to answer, this book is a good place to start.
Что касается нас, то никогда мы не занимались кантиански-поповской, вегетариански-квакерской болтовней о “святости человеческой жизни”. Мы были революционерами в оппозиции и остались ими у власти. Чтобы сделать личность священной, нужно уничтожить общественный строй, который ее распинает. А эта задача может быть выполнена только железом и кровью.
Л.Д. Троцкий, Терроризм и коммунизм, IV. Терроризм.
As for us, we were never concerned with the Kantian-priestly and vegetarian-Quaker prattle about the “sacredness of human life”. We were revolutionaries in opposition, and have remained revolutionaries in power. To make the individual sacred we must destroy the social order that crucifies him. And this problem can be solved only by iron and blood.
Leon Trotsky, Terrorism and Communism, 4, Terrorism.
As a life-long socialist, it’s impossible to deny that, yes, there are a few self-righteous windbags on the left. And in terms of issues around self-important halfwits, again, yes, as a life-long socialist, it’s far from not unimpossible to disrefute the notion that, yes, they aren’t unknown on the left either. But they are, I must insist, the exceptions that prove the rule. And to me, personally, the rule, i.e. the non-exceptions, is/are best represented by the award-winning author’n’academic China Miéville (b. 1972), who has done for science fiction and fantasy what Karl Marx (b. 1818) did for politics and economics. Okay, I have heard it suggested that Miéville’s writing is as exciting and unpredictable as his hair. In reply to that, all I’d have say is this: “Read one of his award-winning books, monkey-funker!” I’ve also witnessed it adumbrated that he has a torturer’s face. In reply to that, I would simply say this:
1) No he hasn’t.
2) And even if he has it’s woefully misleading because
3) He is (at the time of writing) a member of the Socialist Workers Party.
And can you imagine a potential torturer belonging to a Trotskyist party like the S.W.P.? Well, there you go, then. Anyway, as a keyly committed comrade in the Mythopoetic Miéville Massiv, it’s been very difficult to process my emotion at an angst-y article recently written by my heresiarchic hero about his beloved revolutionary corps d’élite (i.g., the S.W.P.). Yes, super-intellect China Miéville, award-winning author’n’academic, has discovered that a Trotskyist party – a Trotskyist party – can be not just a wee bit authoritarian, but also a wee bit dishonest, too. And also a wee bit anti-democratic, in addition! And is he pleased? You’re monkey-funkin’ right he isn’t! You may, like me, find it difficult to credit what you’re reading when you engage issues around his curt’n’concise cri du cœur. Yes, check out his non-self-righteous non-windbaggery for yourselves, comrade-skis: The Stakes.
The S.W.P. Central Committee? “Catastrophic errors of principle and process”? “Belief-beggaringly inadequate and arrogant”? By the Goat with a Thousand Young, whatever next?!? Speaking personally, for myself, I’ve not been so gobsmacked since I heard that Andy Coulson, former Downing Street Press Secretary, had been involved in something a teensy bit dodgy while editing The News of the World (prop. R. Murdoch).
P.S. Don’t neglect to engage the other engagements around the topic of Trotsko-toxicity in terms of that shining ornament of the Far Left, the ever-readable Lenin’s Tomb (prop. R. Seymour). Here are some tantalizing titbits:
I first became aware of the very serious nature of the allegations against Comrade Delta in late Autumn 2012 (not long after they had been made); as a result of a number of comrades, most of whom I have known for several years, contacting me to express their understandable grave concern. It immediately became clear to me that the information comrades had been given at the 2011 SWP Conference – that Comrade Delta had had an affair which had ended but that he had continued to hassle the woman (now referred to as Comrade W) afterwards – was quite seriously inaccurate. It adds insult to injury to recall that the session in which we were given this misleading information at the 2011 conference was turned into a kind of Delta love-in, culminating in a standing ovation for him (even at this stage it was effectively a standing ovation for having an affair) – but this demonstrates the effect that stage-managing a conference can have. Some party members resigned in protest at this time.
I recently started a degree, and was stunned to discover a whole new world of intersectionality, gender politics, and critical studies of which I had been unaware. I felt unequipped by what I had learnt so far during 8 years of membership to meet these new analyses head on. Now I feel like I exist in two discourses; a classical Marxist tradition – and the language and ideas I have had to develop to be able to continue to apply Marxist ideas in my studies, in talking and activity with other students, and in making sense of new understandings of oppression. I do not believe the latter conflicts with the former, but there is no space to discover how they interrelate within the party at the moment.
We do reject the bourgeois system of justice but in this case aspects of the bourgeois process were used, and having read the available documents relating to this case it is not convincing that there was a there a clear analysis and understanding of what aspects of an investigatory and quasi-judicial process were accepted and which were rejected. Clear decisions around process needed to be made and then fully explained to the complainant so that she was aware of what exactly she was getting into, its limitations and how effective it could possibly be in terms of her need for a resolution and could make her own choice on that basis.
Previously pre-posted (please peruse):
Language doesn’t create the world, but it can manipulate the way we see it or can focus our attention on things we were overlooking. When I read a book on architecture and learnt about the three classic forms of column – Doric, Ionic, and Corinthian – I started to see them everywhere in towns and cities. Something similar happened to me because of this book. After leafing through its colour photos, I suddenly started noticing moss much more. And it’s worth noticing, both scientifically and aesthetically. It’s a humble but fascinating plant and has a surprising beauty and variety: Thuidium tamariscinum, common tamarisk-moss, for example, looks as though it should be with the ferns, because it has a similar branching structure. Lichens aren’t beautiful in their own right like mosses, but they can create beautiful patterns and colours on rock and stonework. And like mosses, they’re something humble that should make us humble: they’ve been around for much longer than we have and may be around long after we’re gone.
The same is true of ferns and grasses, though I have to admit that I still find it hard to see much interest in grasses. I know that interest is there, but they still seem dull. Ferns don’t, despite being a simpler plant. But they have a romance that grasses lack. You could call them the Celts of the vegetable kingdom: pushed to the fringes by later invaders. Where once they ruled the world, now they’re confined to specialized habitats. Damp ones. Meeting ferns at home can be refreshing in all sorts of ways: the air is cool and moist and their green is easy on the eye. I like their fractal structure too and there’s even a fern that refreshes the nose: mountain fern, Oreopteris limbosperma, which has a “strong almost citron scent released by brushing past or rubbing the leaves”. The scientific names are fascinating too and books like this are spiritually refreshing in our increasingly soulless, mechanized and electronic world. Leafing through Grasses, Ferns, Mosses and Lichens is like taking a walk through woods and mountains without leaving your chair. Lots of people like flowers and trees, and lots of places host them. These botanical groups are much more specialized and easy to overlook, confined to the fringes of our world, and have a cult-appeal that reminds me of obscure forms of music or art.
Pre-previously posted (please peruse):
Mushrooms, Roger Phillips
Led Zeppelin, Ray Tedman (Titan Books, 2011)
The most important thing in this big book of photographs is, of course, Robert Plant’s hair, which often looks remarkably like mine in both its colour and its curliness. There’s also little to choose between me and Robert Plant in the sex-god stakes, so I’ve often wondered precisely whose gigs my mother was attending in her youth (related rumours circulate, muso mutato et mama mutata, about at least one other keyly committed core component of the counter-cultural community). These aren’t unusual thoughts for me when I look at a book about Led Zeppelin: their hair interests me more than their harmonics. I usually get bored well before songs like “Whole Lotta Love” and “Stairway to Heaven” are over and I would much rather listen to the Beatles or Black Sabbath, even at their worst, than to Led Zeppelin, even at their best.
But, at their best, before their locks were shorn as the 1970s ended, Led Zeppelin did look much more like rock-gods than either the Beatles or Black Sabbath. One thing all three bands have in common is their classic quadrivalency: there are four men in each filling the four standard rock roles. I’ve outlined my humorous theory of the classic guitar-bass-drums-vocals line-up elsewhere, so all I’ll say here is that Led Zeppelin fit the theory well. Each member has a distinct personality as he plays a distinct instrument. Each is also distinct in appearance: Jimmy Page is rake-thin, Robert Plant well-built, John Paul Jones average, and Bonzo stocky. Bonzo always had facial hair too, which must say something about his psychology. The colour of his hair certainly says something about his psychology. Like skin-colour and eye-colour, hair-colour is a chemical phenomenon: different colours signal different chemicals or different levels of chemical in the body, and so in the brain. Lighter hair, like lighter skin and eyes, tends to go with a more introverted, less aggressive personality and it may be significant that Robert Plant and John Paul Jones, with lighter hair, are said to have been the two best-behaved members of Led Zeppelin. Black-haired Bonzo was notoriously bestial and also the heaviest drinker. Jimmy Page wasn’t violent, despite having black hair, but his somatype, or body-shape, doesn’t predict violence.
His face may predict high intelligence and high artistic achievement, however: he has always been a good-looking man. Good looks are related to symmetry, and symmetry is related to intelligence and coordination. Again, this isn’t an absolute rule: good-looking people can be stupid and bad at music, just as ugly people can be intelligent and good at music, and strange things can sometimes happen at the extremes of the bell-curve. But biology is about averages and tendencies, not absolutes, and biology is central to understanding human beings and their behaviour. That’s one of the things I find interesting about looking through this book, but there’s much more than individual biology at work here. Led Zeppelin followed fashions as well as setting them and faithfully reflected the look of the three decades in which they existed: the ’60s, the ’70s, and the ’80s.
Or first year of the ’80s, anyway: Bonzo died on 25th September 1980 and the band broke up. The book then follows Plant and Page into their solo careers and their occasional re-unions with Jones, but nobody looks as good as he did in the band’s mid-’70s prime, when their locks were longest and their testosterone levels highest. Endocrinology, or the science of hormones, is another essential part of understanding human behaviour and rock music at its loudest may influence hormones with more than its rhythms and melodies. High volume affects the entire body, not just the ears, and Led Zep were loud and proud, a band who shook the glands of their fans in more ways than one. As I’ve said, I’m not a big fan of Led Zeppelin myself, but if you are I can recommend this book. The photos range from the casual to the candid, the rampant to the risible, the phallocratic to the fan-worshipped, and there are regular biographical pages to guide you through the Led Zeppelin story. Oh, and there’s an index too, which books like this often lack.
Light and Shade: Conversations with Jimmy Page, Brad Tolkinski (Virgin Books, 2012)
I’ve seen too many bad bios about big beasts of the rock jungle to expect much when I pick up a new one, but I was pleasantly surprised by Light and Shade. It does descend into rock-journalese from time to time – Cream and Jimi Hendrix adopted “a new, heavily riff-driven mode of expression” in 1967, apparently – but the conversations with Page are interesting, intelligent, and even impish, as when Page reveals he can mock himself:
On your 1973 tour you started using your own private plane, the Starship. Was that a good thing, or did it just guarantee that the party could continue and you’d never have a moment of rest?
No, it was a good thing. It was a place where you could bring your music and books and create some semblance of continuity as you travelled from city to city. However, [our former tour manager] Richard Cole ran into one of the air hostesses on the Starship recently and she told him, “You know we made a lot of money off you guys,” and Cole asked her how. “Well,” she explained, “when people on the plane used to sniff cocaine, they’d roll up hundred-dollar bills to use as straws. Then after they were high or passed out, they’d forget about the money. So we would go around and grab all the money that was laying around.” That might’ve been true, but I’ll tell you one thing: They never got any of my money! [laughs]
(Ch. 7, “The tours were exercises in pure hedonism…”, pg. 172)
And now you know, if you didn’t already, why Page has the nickname “Led Wallet”: he has always been canny with his cash. But don’t be misled by the coke reference or the chapter-title: this isn’t Hammer of the Gods, the most notorious of the Zeppographies, so the sex’n’drugs side of Page’s rock’n’roll story doesn’t get anywhere near as much attention as his music, his metaphysics, and his mutating fashions. There aren’t many photos, but they’re all well-chosen and you can trace the evolution of Page’s looks, locks, and collaborations right from the 1960s to the present day. There are also contributions from John Paul Jones, Jack White of the White Stripes, publicists, guitar experts and fashionistas, so you do get a well-rounded portrait of an interesting and highly influential musician. I’m not a big Led Zeppelin fan and I still liked this book. And regretted the absence of an index. So it’s a shade light there. Otherwise, it should provide many pages of pleasure for Page-o-philes.
Frogs: Inside Their Remarkable World, Ellin Beltz (2005)
Everyone say “eye”. Because I think that is one of the most important reasons that frogs and toads are so endearing. Their large eyes and their large mouths make them seem full of character and full of interest in the world. Their four limbs and plumpness are important too, I think, and I suspect that looking at them activates some of the same regions of the brain as looking at a baby does. All that would certainly help explain why we like them. The Californian herpetologist Ellin Beltz doesn’t spend long examining the roots of the human affection for and interest in the batrachians, as frogs and toads are called. “Is it perhaps that frogs look and act rather like people?” she asks and then gets on with the science. But she herself is obviously a dedicated batrachophile and she’s written an interesting and exhaustive introduction to what is indeed a remarkable world. There are frogs smaller than a human fingernail, like Psyllophryne didactyla, the gold frog of southeastern Brazil, and frogs larger than a human head. Or one species larger than some heads, anyway: Conraua goliath, the goliath frog of Cameroon. There are also frogs, the Malaysian Rhacophorus spp.,* that fly, or glide, at least, on the extended webbing between their toes, and frogs that literally stick around for sex: “males of the genus Breviceps from southern Africa” have very “short front legs” and “use special skin secretions to glue themselves onto the females” (pg. 149). Elsewhere, the Australian desert spadefoot toad, Notaden nichollsi, uses a “smelly skin secretion” to ward off predators (pg. 58).
(*Sp. = species, singular; spp. = species, plural.)
That species isn’t very dangerous, but the much smaller poison-arrow frogs of South America definitely are: “the golden dart frog, Phyllobates terribilis, is credited with producing ‘the most toxic naturally occurring substance’ ” (pg. 147). In captivity, deprived of the wild food from which they manufacture their toxins, the poison-arrow frogs are harmless, but their remarkable colours remain: they look like harlequins in all shades of the rainbow. Whether these rainbow frogs are also raines beaux, or “beautiful frogs”, as they might be called in French, is a matter of taste, but some frogs definitely are beautiful. So are some toads: the male golden toad, Bufo periglenes, is a vivid golden-orange. Or rather, was: it was once a tourist attraction as it swarmed “out to mate in great congregations” in the Monteverde Cloud Forest Reserve in Costa Rica, but “photographs seem to be all that remains of this exquisite amphibian” (pg. 43). Yes, the ugliness in this book isn’t supplied only by the villainous-looking cane toad, Bufo marinus, which has been munching and poisoning its way through Australia’s native wildlife since it was foolishly introduced there in 1935. There’s also ugliness in the story of what is happening to the world’s amphibians. They’ve been disappearing everywhere and most of chapter four, “Environment & Adaptation”, is given over to the threats they face from pollution, bacteria, viruses, and various fungi, including the chytrid fungus responsible for “chytridiomycosis, a fatal fungus disease that leads to thickening and sloughing of the skin and death by unknown causes” (pg. 118).
African clawed frogs, Xenopus spp., are “asymptomatic carriers” of chytrid fungus. Because they were once used in pregnancy tests, they have been introduced all over the world and may have helped the fungus spread. However, the ever-growing human population is perhaps the greatest threat to the survival of wild amphibia, as it is to fauna and flora in general. More people mean more roads and more cars, for example:
Roadkill numbers are immense. Frogs don’t even have to be hit by a vehicle; the force of its passing can literally suck them inside out. Hundreds of flattened and inverted corpses lie roadways on rainy nights. (pg. 121)
Some species may be disappearing without ever being recorded. Perhaps the strangest and unfroggy-est frog in this book is Nakisakabatrachus sahyadrensis, the Kerala purple frog of southern India, which has tiny eyes and dark, leathery skin. It lives underground most of the year and was only described by scientists in 2003. Its tiny eyes are part of its adaptation to underground life. Eyes are a guide to ecology in other ways: a batrachian’s angle of vision is a clue to its edibility. Frogs, whose eyes are usually positioned so they can see both ahead and behind, are edible and fear predators. Toads, which usually can’t see behind themselves, are inedible and don’t fear predators. I can remember once picking up a tiny toadlet, or juvenile toad, and feeling my fingers sting from the secretions it released. Among Beltz’ personal anecdotes in this book is one about what happened when she and a colleague found a Couch’s spadefoot toad, Scaphiopus couchii, on the U.S.-Mexico border:
It was drizzling, and I brought the toad into the car for a good identification. We were paging through the field guide and put on the defoggers to clear the windows when we were overcome by a wave of noxious vapor emitted by the toad. It was like teargas and we exploded out of the car, put the toad into a ditch and tried to air out the car. Whatever toxin the toad let loose that night, I was down for 24 hours, sleeping with runny eyes and all the symptoms of a major cold. My colleague was similarly affected. Other reports of noxious fumes from southwestern toads have been [made]. (“Frog Miscellany”, pg. 149)
Stories like that are part of what makes this such an enjoyable book and although, at 175 pages with lots of large photos, it’s too brief to explore thoroughly all the biological topics it raises, there are pointers to some interesting aspects of evolution – and mathematics. Try this description of the Eastern spadefoot, Scaphiopus holbrookii, and plains spadefoot, Spea bombifrons, which live in deserts in North America:
When the rains fall, they congregate at temporary pools to breed. It takes the eggs two weeks to hatch into tadpoles. At this point, more rain is needed; otherwise the pools dry up and the plant-eating tadpoles die. Some tadpoles become cannibalistic under these harsh conditions, permitting some individuals to survive long enough to transform into frogs by eating the bodies of their herbivorous relatives. (ch. 2, “Frog Families”, pg. 37)
Consider the evolutionary mathematics of this cannibalism. It’s easy to understand genes instructing an individual to eat. Less easy to understand are genes that might instruct an individual to let itself be eaten. But the tadpoles in a temporary pool can be seen as a kind of super-organism. The super-organism initially has many mouths to turn algae and so on into tadpole-flesh. Then, as the pool shrinks, the super-organism begins to eat itself, having exploited the resources of the pool with maximum efficiency. It’s possible there is even a class of tadpole that exists to put on flesh fast and then be eaten by its siblings. It would never breed, but evolutionarily speaking that behaviour would be no more paradoxical than the sterile workers among ants, bees and wasps. Or the juvenile birds that let themselves starve to death in an over-crowded, underfed nest. The apparently suicidal genes of a cannibalized tadpole or sterile worker or starved nestling do not survive in that non-breeding individual, but they promote behaviour that enables unactivated copies of themselves to survive better in other individuals – as Richard Dawkins explains in The Blind Watchmaker (1986).
Swimming in another kind of pool is responsible for other evolved features in batrachians: their sometimes vivid colours or cunning camouflage. For millions of years, images of batrachians have been created in the chemical sludge of predators’ brains. And so, like snakes and wasps, batrachians signal their toxicity with colour. Or use colour to disguise their outlines or blend into the background. But batrachians are also like octopuses and other cephalopods: they can change their colour using special structures in their skin called chromatophores. One of the briefest but most interesting sections in this book discusses this shade-shifting and the cells responsible for it: the melanophores (responsible for black and brown colouration), xanthophores (yellow), erythrophores (red and orange), and iridophores (responsible for iridescence in the poison-arrow frogs). But what is briefly mentioned is extensively illustrated: almost every page has one or more colourful photographs of frogs and toads, usually in what appears to be their natural habitat.
There are also diagrams of batrachian anatomy and evolutionary relationships and pictures of art and sculpture in chapter five, “Frogs in Myth and Culture”. You’ll learn in the evolutionary discussions that toads aren’t a distinct group, because they don’t have a single common ancestor distinguishing them from frogs. But they look different to us and chapter five says that they were sacred to Heqet, the Egyptian goddess of childbirth and fertility. She’s depicted with an almost scientifically precise green toad, or Bufo viridis, on an ivory obstetric wand found near Thebes and dating from “around 2000 to 1700 BCE” (pg. 131). That “BCE”, like the “humanmade objects” mentioned on page 47, is a reminder that Ellin Beltz is a modern, and politically correct, American, unlike a Californian born in the Victorian era whose absence can’t, alas, be called a flaw in this book. The Auburn writer Clark Ashton Smith (1893-1961) and his interplanetary toad-god Tsathoggua and man-slaying toad-witch Mère “Mother of Toads” Antoinette aren’t famous and Beltz may never have heard of them. Instead, she discusses Shakespeare and the three toad-toxin-brewing witches of Macbeth (1611), Mark Twain and “The Celebrated Jumping Frog of Calaveras County” (1867), and Kenneth Graham and Toad of Toad Hall from Wind in the Willows (1908).
In short, she covers all the batrachian bases, from biology to books by way of batrachophagous bats and a bee-eating Bufo japonicus. The batrachophage, or frog-eater, is the fringe-lipped bat, Trachops cirrhosus of Central America, which tracks its prey by homing in on their calls. And here’s another acoustic anecdote to end on, demonstrating that Hollywood’s hegemony is partly herpetological:
Chorus frogs, Pseudacris spp., include the Pacific treefrog, Pseudacris regilla, the “ribbet frog” known to every movie fan. At some time in the early days of talkies, someone recorded frogs in a pond, probably near the famous Hollywood sign. The same audio loop is used over and over again in movies, leading to hysteria among amphibian researchers who hear “ribbet” in darkest Africa, South America and Australia… The Pacific treefrog is actually restricted to the western edge of North America. (ch. 2, “Frog Families”, pg. 49)