Slug is a Drug

Collins Complete Guide to British Coastal Wildlife
Collins Complete Guide to British Coastal Wildlife, Paul Sterry and Andrew Cleave (HarperCollins 2012)

Living by a river is good, but living by the sea is better. This means that the ideal might be Innsmouth:

The harbour, long clogged with sand, was enclosed by an ancient stone breakwater; on which I could begin to discern the minute forms of a few seated fishermen, and at whose end were what looked like the foundations of a bygone lighthouse. A sandy tongue had formed inside this barrier and upon it I saw a few decrepit cabins, moored dories, and scattered lobster-pots. The only deep water seemed to be where the river poured out past the belfried structure and turned southward to join the ocean at the breakwater’s end. (“The Shadow Over Innsmouth”, 1936)

Lovecraft would certainly have liked Collins Complete Guide to British Coastal Wildlife, a solid photographic guide to the flora and fauna of the British coast. There are some very Lovecraftian species here, both floral and faunal. Among the plants there’s sea-holly, Eryngium maritimum, a blue-grey shingle-dweller with gothically spiky and veined leaves. It has its own specialized parasite, Orobanche minor ssp. maritima, “an exclusively coastal sub-species” of common broomrape (pg. 94). Among the Lovecraftian animals there are the cephalopods (octopuses and squids), echinoderms (sea-urchins and starfish) and cnidarians (jellyfish and sea-anemones), but also the greater and lesser weever, Trachinus draco and Echiichthys vipera, which are “notorious fish, capable of inflicting a painful sting to a bather’s foot” (pg. 278).

Limacia clavigera

Orange-clubbed sea-slug, Limacia clavigera


But the strangest and most wonderful creatures in the book might be the sea-slugs and sea-hares, which are brightly coloured or enigmatically mottled, with surreal knobs, furs and “rhinophores”, or head tentacles. If LSD took organic form, it might look like a sea-slug. Greilada elegans, “orange with blue spots”, Flabellina pedata, “purple body and pinkish-red cerata”, Catriona gymnata, “swollen, orange and white-tipped”, resemble the larvae of some eldritch interstellar race, destined to grow great and eat worlds (pp. 218-222 – “cerata” are “dorsal projections”). As it is, they stay tiny: the orange-clubbed sea-slug, Limacia clavigera, gets to 15mm on a diet of bryozoans, the miniature coral-like animals that are Lovecraftian in a different way. That “Limacia”, from the Latin limax, meaning “slug”, is a reminder that sea-slugs have an accurate common name, unlike Montagu’s sea snail, Liparis montagui, and the sea scorpion, Taurulus bubalis, which are both fish, and sea ivory, Ramalina siliquosa, which is a lichen. This book includes a land slug too, the great black, Arion ater, but it has none of the charm or beauty of its marine relatives.

Arion ater is included here because it’s “particularly common on coastal cliffs, paths and dunes” (pg. 239). The land snails that accompany it have charm, like the looping snail, Truncatella subcylindrica, and the wrinkled snail, Candidula intersecta, but they don’t have the beauty and variety of marine shell-dwellers, from the limpets, scallops and cockles to the wentletraps, cowries and whelks. And the violet snail, Jacintha jacintha, which rides the open ocean on a “‘float’ of mucus-trapped bubbles” as it feeds on the by-the-wind sailor, Velella velella. Layfolk would say that Velella and its relative Physalia physalis, the Portuguese man-o’-war, are jellyfish, but they’re actually “pelagic hydroids”. And Physalia is a colony of animals, not a single animal.

Sample page #1

Sample page #1


Both jellyfish and hydroids are related to sea-anemones and corals: they’re all classified as cnidaria, from the Greek κνιδη, knidē, meaning “nettle”. In short: they all sting. Some swim and sway too: the colours, patterns and sinuosity of the cnidaria are seductively strange. There are strawberry, snakelocks, gem, jewel, fountain and plumose anemones, for example: Actinia fragacea, Anemonia viridis, Aulactinia verrucosa, Corynactis viridis, Sargartiogeton laceratus and Metridium senile. The tentacles of the last-named look like a glossy head of white hair and the snakelocks anemone sometimes has green tentacles with purple tips.

After the cnidaria come the annelids, or segmented worms, which can be beautiful or repulsive, mundane or surreal, free-living or sessile. For example, the scaleworms are “unusual-looking polychaete worms whose dorsal surface is mostly or entirely covered with overlapping scales” (pg. 129). They’re reminiscent of the sea-slugs, though less strange and more subdued. But segmented worms gave rise to the wild variety of the crustaceans, including crabs, sea-slaters, lobsters and even barnacles, one species of which is a parasite: Sacculina carcini forms a “branching network” (pg. 178) within the body of a crab, particularly the green shore crab, Carcinus maenas. You would never guess that it was a barnacle and you might not guess that an infected crab was infected, because the yellow “reproductive structure” of the barnacle looks as though it belongs to the crab itself.

Sample page

Sample page #2


And there’s a photograph here to prove it. In fact, there are two: one in the barnacle’s own entry, the other in the entry for the green shore crab. I like the way the guide gives extra information like that. In the entries for sea-lavender, Limonium vulgare, and thrift, Armeria maritima, there are small photographs of insects that feed “only” or “almost exclusively” on these plants: the plume moth Agditis bennetii, with very narrow wings, and the more conventional moth Polymixis xanthomista (pg. 90), respectively. Those insects, with Fisher’s estuarine moth, Gortyna borelii, and the Sand Dart, Agrotis ripae, are stranded in the wild-flower section, as though they’ve been deposited there by a stray current. The fiery clearwing moth, Pyropteron chrysidiformis, is stranded in another way: in Britain, it’s “entirely restricted to stretches of grassy undercliff on the south coast of Kent”. It looks like a wasp wearing make-up. The scaly cricket, Pseudomogoplistes vincentae, isn’t attractive but is romantic in a similar way: it’s “confined to a handful of coastal shingle beaches in Britain and the Channel Islands” (pg. 17).

Also confined is the bracket fungus Phellinus hippophaeicola, which is “found only” on the trunks of sea buckthorn, Hippophae rhamnoides (pg. 54). Its photograph appears with its host, but the full fungus section is only one page anyway. It includes the “unmistakable” dune stinkhorn, Phallus hadriani, whose scientific name means “Hadrian’s dick”. It’s “restricted to dunes and associated with Marram” grass (pg. 50). But fungi flourish best away from the coast. Not that “flourish” is the right word, because fungi don’t flower. Nor do seaweeds, the giant algae that have to survive both battering by the waves and exposure to sun and wind. They cope by being tough: leathery or horny or chalky or coralline. And though their colours are limited mostly to green, brown and red, their geometry is very varied: leafy, membranous, thong-like, ribbon-like, whip-like, fan-like, feather-like, even globular: punctured ball weed, Leathesia difformis, and oyster thief, Colpomenia peregrina, for example. The book doesn’t explain why “oyster thief” is called that. Landlady’s wig, Desmarestia aculeata, red rags, Dilsea carnosa, and bladder wrack, Fucus vesiculous, are self-explanatory.

And there’s a bluntness to names like wrack, kelp and the various weeds – bean-weed, bead-weed, wire-weed – that go well with the rough, tough life these plants lead. That’s why rainbow wrack, Cystoseria tamariscifolia, sounds so odd. But it lives up to its name: it’s “bushy and iridescent blue-green underwater” (pg. 36).

Seaweeds are at the beginning of the book; birds, fish and mammals are at the end. After the strangeness, surreality and beauty of some of the plants and invertebrates, the higher animals can seem almost mundane. Evolution hasn’t found as many spinal solutions as non-spinal, because the invertebrates have been around much longer. It’s been working longest on the fish, so the variety of shapes is greatest there: rays and flounders, lampreys and eels, sea-horses and pipe-fish, the giant sun-fish and the largest animal native to Britain, the basking shark, Cetorhinus maximus. Some of the names seem ancient and long-evolved too: saithe, pogge, goldsinny, weever, dab, goby, blenny, shanny and brill. The last-named, Scophthalmus rhombus, is a flatfish with a typically ugly head. As the book notes: “In their early stages, they resemble conventional species. But during their development the head shape distorts so that, although they lie and swim on their sides, both eyes are on top” (pg. 257).

The rays aren’t distorted like that: they lie on their bellies, not on their sides, so their eyes don’t look distorted. Evolution has taken two different routes to the same ecological niche, the sea-floor. Camouflage is useful there, so both rays and flatfish have beautiful patterns: specklings, mottlings and spots. Other fish are colourful, but British fish can’t match the rainbow variety of fish in the tropics. Nor can British birds. The kingfisher, Alcedo atthis, is a rare exception and it “favours fresh waters”, except in winter (pg. 328). Truly coastal birds can be hard to tell apart: the knot, Calidris canutus, and the Sanderling, Calidris alba, are not as distinctive as their common names. Nor are the whimbrel, Numenius phaeopus, and the curlew, Numenius arquata. Both have long down-curved beaks and streaked, “grey-brown plumage” (pg. 342). But the whimbrel is smaller and rarer.

The gulls and terns can also be hard to tell apart, as can the skuas that prey on and parasitize them. “Skua”, which comes from Old Norse skúfr, is a good name for a gangster-like bird. I prefer “gull” in what is probably its original form, the Welsh gŵylan. The French mouette, for small gulls, and goéland, for large ones, are also good, and some French bird-names are used in English: avocet, plover and guillemot, for example. “Plover” is from Latin pluvia, “rain”, but the reference is “unexplained”, according to the Oxford English Dictionary. The reference of “ruff” might seem to be obvious: the male ruff, Philomachus pugnax, has a ruff of feathers in the breeding season, like a kind of gladiatorial costume: its scientific name literally means “the pugnacious lover-of-fighting”. But the female of this species is called a reeve, so perhaps ruffs have nothing to do with ruffs: the feminine form, “apparently made … by a vowel change (cf. fox vixen) suggests that [ruff] is an older word and separate” (OED).

This book uses “ruff” for both sexes: it doesn’t have space to chase etymology and give more than brief details of the hundreds of species it covers. The final species are the mammals and the final mammals are the ones that have returned to the sea: whales, dolphins and seals. After them comes a brief section on “The Strandline”:

A beach marks the zone where land meets sea. It is also where detached and floating matter is washed up and deposited by the tides, typically in well-defined lines. During periods of spring tides, debris is pushed to the top of the shore. But with approaching neap tides, tide extremes diminish and the high-tide mark drops; the result is a series of different strandlines on the shore. The strandline is a great place for the marine naturalist to explore and find unexpected delights washed up from the depths. But it is also home to a range of specialised animals that exploit the rich supply of organic matter created by decomposing seaweeds and marine creatures. (pg. 368)

Those specialised animals – sand-hoppers, kelp-flies and so on – have been covered earlier in the book, so this section covers things like skeletons, skulls, fossils and egg-cases – the “sea wash balls” laid by whelks and the “mermaid’s purses” laid by rays. Then there are “sea-beans”, tree-seeds that may have “drifted across the Atlantic from the Caribbean or Central America”. At first glance, seaweeds also seem to make a come-back in this section. Not so: a bryozoan branches like a plant but is “actually a colonial animal that lives just offshore attached to shells and stones”. Bryzoans are often washed ashore after storms. One of the commonest is hornwrack, Flustra foliacea, of which “fresh specimens smell like lemon” (pg. 254). When I first noticed that for myself, I thought I was having an olfactory hallucination. That’s the sea for you: always changing, always surprising. This book captures its complexity in 384 well-designed pages full of eye- and brain-candy.

Performativizing Papyrocentricity #21

Papyrocentric Performativity Presents:

Poems and ParachutesA Hell for Heroes: An SAS Hero’s Journey into the Heart of Darkness, Theo Knell (Coronet 2012)

I Am A KameraMezzogiallo: Life, Death, Eastern Europe, David Kerekes (TransVisceral Books 2014)

Where’s the Beef?Mein Kampf, Adolf Hitler (1925)

No Plaice Like OlmEuropean Reptile and Amphibian Guide, Axel Kwet (New Holland 2009) (posted @ Overlord of the Über-Feral)

Or Read a Review at Random: RaRaR

Lat’s That

In a magic square of numbers, all rows, columns and diagonals have the same sum, or magic total. Here is an example:

1*5*9
8*3*4
6*7*2

(mt=15)

Here’s another:

06*07*11*10
15*02*14*03
04*13*01*16
09*12*08*05

(mt=34)

And another:

04*25*20*10*06
01*13*11*21*19
23*09*07*08*18
15*16*03*14*17
22*02*24*12*05

(mt=65)

And another:

35*15*10*18*11*22
05*25*33*12*07*29
34*30*04*14*21*08
02*16*27*17*23*26
03*24*09*19*36*20
32*01*28*31*13*06

(mt=111)

In all those magic squares, the magic total is fixed: the sum of all numbers from 1 to 36 is 666, so any individual line in a 6×6 magic square has to equal 666 / 6 or 111. In other kinds of magic figure, this rule doesn’t apply:

2*7*3
4***8
6*5*1

(mt=12)

6*3*4
2***8
5*7*1

(mt=13)

8*5*1
2***6
4*3*7

(mt=14)

8*1*6
4***2
3*5*7

(mt=15)

Continue reading Lat’s That

Who Guards the Guardianistas?

“…We’re not so much a reaction against what’s going on – it’s more down to the music that we’re into – but in terms of guitar music there hasn’t been much in terms of louder groups.” – Bored of cookie-cutter conformity in music?, The Guardian, 6/iii/ 2014.


Elsewhere other-posted:

Ex-term-in-ate!

Priamonds and Pearls

Interesting patterns emerge when primes are represented as white blocks in a series of n-width left-right lines laid vertically, one atop the other. When the line is five blocks wide, the patterns look like this (the first green block is 1, followed by primes 2, 3 and 5, then 7 in the next line):
5line

(Click for larger version)

Right at the bottom of the first column is an isolated prime diamond, or priamond (marked with a green block). It consists of the four primes 307-311-313-317, where the three latter primes equal 307 + 4 and 6 and 10, or 307 + 5-1, 5+1 and 5×2 (the last prime in the first column is 331 and the first prime in the second is 337). About a third of the way down the first column is a double priamond, consisting of 97, 101, 103, 107, 109 and 113. For a given n, then, a priamond is a set of primes, p1, p2, p3 and p4, such that p2 = p1 + n-1, p3 = p + n+1 and p4 = p1 + 2n.

There are also fragments of pearl-necklace in the columns. One is above the isolated priamond. It consists of four prime-blocks slanting from left to right: 251-257-263-269, or 251 + 6, 12 and 18. A prearl-necklace, then, is a set of primes, p1, p2, p3…, such that p2 = p1 + n+i, p3 = p + 2(n+i)…, where i = +/-1. Now here are the 7-line and 9-line:

7line

Above: 7-line for primes

9line

Above: 9-line for primes

In the 9-line, you can see a prime-ladder marked with a red block. It consists of the primes 43-53-61-71-79-89-97-107, in alternate increments of 10 and 8, or 9+1 and 9-1. A prime-ladder, then, is a set of primes, p1, p2, p3, p4…, such that p2 = p1 + n+1, p3 = p + 2n, p3 = p + 3n+1…

And here is an animated gif of lines 5 through 51:

lines5to51

(Click or open in new window for larger version or if file fails to animate)

No Plaice Like Olm

European Reptile and Amphibian Guide by Axel KwetEuropean Reptile and Amphibian Guide, Axel Kwet (New Holland 2009)

An attractive book about animals that are mostly attractive, sometimes strange, always interesting. It devotes photographs and descriptive text to all the reptiles and amphibians found in Europe, from tree-frogs to terrapins, from skinks to slow-worms. Some of the salamanders look like heraldic mascots, some of the lizards like enamel jewellery, and some of the toads like sumo wrestlers with exotic skin-diseases. When you leaf through the book, you’ve moving through several kinds of space: geographic and evolutionary, aesthetic and psychological. Europe is a big place and has a lot of reptilian and amphibian variety, including one species of turtle, the loggerhead, Caretta caretta, and one species of chameleon, the Mediterranean, Chamaeleo chamaeleon.

But every species, no matter how dissimilar in size and appearance, has a common ancestor: the tiny crested newt (Triturus cristatus) to the far north-west in Scotland and the two-and-a-half metre whip snake (Dolichophis caspius) to the far south-east in Greece; the sun-loving Hermann’s tortoise (Testudo hermanni), with its sturdy shell, and the pallid and worm-like olm (Proteus anguinus), which lives in “underground streams in limestone karst country along the coast from north-east Italy to Montenegro” (pg. 55). Long-limbed or limbless, sun-loving or sun-shunning, soft-skinned or scaly – they’re all variations on a common theme.

Sample page

Sample page from European Reptile and Amphibian Guide


And that’s where aesthetic and psychological space comes in, because different species and families evoke different impressions and emotions. Why do snakes look sinister and skinks look charming? But snakes are sinuous too and in a way it’s a shame that a photograph can capture their endlessly varying loops and curves as easily as it can capture the ridigity of a tortoise. At one time a book like this would have had paintings or drawings. Nowadays, it has photographs. The images are more realistic but less enchanted: the images are no longer mediated by the hand, eye and brain of an artist. But some enchantment remains: the glass lizard, Pseudopus apodus, peering from a holly bush on page 199 reminds me of Robert E. Howard’s “The God in the Bowl”, because there’s an alien intelligence in its gaze. Glass lizards are like snakes but can blink and retain “tiny, barely visible vestiges of the hind legs” (pg. 198).

Other snake-like reptiles retain vestiges of the fore-limbs too, like the Italian three-toed skink (Chalcides chalcides). The slow-worm, Anguis fragilis, has lost its limbs entirely, but doesn’t look sinister like a snake and can still blink. Elsewhere, some salamanders have lost not limbs but lungs: the Italian cave salamander, Speleomantes italicus, breathes through its skin and the lining of its mouth. So does Gené’s cave salamander, Speleomantes genei, which is found only on the island of Sardinia. It “emits an aromatic scent when touched” (pg. 54). Toads can emit toxins and snakes can inject venoms: movement in evolutionary space means movement in chemical space, because every alteration in an animal’s appearance and anatomy involves an alteration in the chemicals created by its body. But chemical space is two-fold: genotypic and phenotypic. The genes change and so the products of the genes change. The external appearance of every species is like a bookmark sticking out of the Book of Life, fixing its position in gene-space. You have to open that book to see the full recipe for the animal’s anatomy, physiology and behaviour, though not everything is specified by the genes.

Pleuronectes platessa on the sea-floor

Pleuronectes platessa on the sea-floor


The force of gravity is one ingredient in an animal’s development, for example. So is sunlight or its absence. Or water, sand, warmth, cold. The descendants of that common ancestor occupy many ecological niches. And in fact one of those descendants wrote this book: humans and all other mammals share an ancestor with frogs, skinks and vipers. Before that, we were fish. So a plaice is a distant cousin of an olm, despite the huge difference in their appearance and habitat. One is flat, one is tubular. One lives in the sea, one lives in caves. But step by step, moving through genomic and topological space, you can turn a plaice into an olm. Or into anything else in this book. Just step back through time to the common ancestor, then take another evolutionary turning. One ancestor, many descendants. That ancestor was itself one descendant among many of something even earlier.
Olm in a Slovenian cave

Olm in a Slovenian cave


But there’s another important point: once variety appeared, it began to interact with itself. Evolutionary environment includes much more than the inanimate and inorganic. We mammals share more than an ancestor with reptiles and amphibians: we’ve also shared the earth. So we’re written into their genes and some of them are probably written into ours. Mammalian predators have influenced the evolution of skin-colour and psychology, making some animals camouflaged and cautious, others obtrusive and aggressive. But it works both ways: perhaps snakes seem sinister because we’re born with snake-sensitive instincts. If it’s got no limbs and it doesn’t blink, it might have a dangerous bite. That’s why the snake section of this book seems so different to the salamander section or the frog section. But all are interesting and all are important. This is a small book with some big themes.

Performativizing Papyrocentricity #20

Papyrocentric Performativity Presents:

Clive AliveC.S. Lewis: A Life, Alister McGrath (Hodder & Staughton 2013)

Ink TuneNick Drake: Dreaming England, Nathan Wiseman-Trowse (Reaktion Books 2013)

Stan’s FansAwaydays, Kevin Sampson (Vintage 1998)

Words at WarPoetry of the First World War: An Anthology, ed. Tim Kendall (Oxford University Press 2013) (posted @ Overlord of the Über-Feral)


Or Read a Review at Random: RaRaR

Miss This

1,729,404 is seven digits long. If you drop one digit at a time, you can create seven more numbers from it, each six digits long. If you add these numbers, something special happens:

1,729,404 → 729404 (missing 1) + 129404 (missing 7) + 179404 (missing 2) + 172404 + 172904 + 172944 + 172940 = 1,729,404

So 1,729,404 is narcissistic, or equal to some manipulation of its own digits. Searching for numbers like this might seem like a big task, but you can cut the search-time considerably by noting that the final two digits determine whether a number is a suitable candidate for testing. For example, what if a seven-digit number ends in …38? Then the final digit of the missing-digit sum will equal (3 x 1 + 8 x 6) modulo 10 = (3 + 48) mod 10 = 51 mod 10 = 1. This means that you don’t need to check any seven-digit number ending in …38.

But what about seven-digit numbers ending in …57? Now the final digit of the sum will equal (5 x 1 + 7 x 6) modulo 10 = (5 + 42) mod 10 = 47 mod 10 = 7. So seven-digit numbers ending in …57 are possible missing-digit narcissistic sums. Then you can test numbers ending …157, …257, …357 and so on, to determine the last-but-one digit of the sum. Using this method, one quickly finds the only two seven-digit numbers of this form in base-10:

1,729,404 → 729404 + 129404 + 179404 + 172404 + 172904 + 172944 + 172940 = 1,729,404

1,800,000 → 800000 + 100000 + 180000 + 180000 + 180000 + 180000 + 180000 = 1,800,000

What about eight-digit numbers? Only those ending in these two digits need to be checked: …00, …23, …28, …41, …46, …64, …69, …82, …87. Here are the results:

• 13,758,846 → 3758846 + 1758846 + 1358846 + 1378846 + 1375846 + 1375846 + 1375886 + 1375884 = 13,758,846
• 13,800,000 → 3800000 + 1800000 + 1300000 + 1380000 + 1380000 + 1380000 + 1380000 + 1380000 = 13,800,000
• 14,358,846 → 4358846 + 1358846 + 1458846 + 1438846 + 1435846 + 1435846 + 1435886 + 1435884 = 14,358,846
• 14,400,000 → 4400000 + 1400000 + 1400000 + 1440000 + 1440000 + 1440000 + 1440000 + 1440000 = 14,400,000
• 15,000,000 → 5000000 + 1000000 + 1500000 + 1500000 + 1500000 + 1500000 + 1500000 + 1500000 = 15,000,000
• 28,758,846 → 8758846 + 2758846 + 2858846 + 2878846 + 2875846 + 2875846 + 2875886 + 2875884 = 28,758,846
• 28,800,000 → 8800000 + 2800000 + 2800000 + 2880000 + 2880000 + 2880000 + 2880000 + 2880000 = 28,800,000
• 29,358,846 → 9358846 + 2358846 + 2958846 + 2938846 + 2935846 + 2935846 + 2935886 + 2935884 = 29,358,846
• 29,400,000 → 9400000 + 2400000 + 2900000 + 2940000 + 2940000 + 2940000 + 2940000 + 2940000 = 29,400,000

But there are no nine-digit sumbers, or nine-digit numbers that supply missing-digit narcissistic sums. What about ten-digit sumbers? There are twenty-one:

1,107,488,889; 1,107,489,042; 1,111,088,889; 1,111,089,042; 3,277,800,000; 3,281,400,000; 4,388,888,889; 4,388,889,042; 4,392,488,889; 4,392,489,042; 4,500,000,000; 5,607,488,889; 5,607,489,042; 5,611,088,889; 5,611,089,042; 7,777,800,000; 7,781,400,000; 8,888,888,889; 8,888,889,042; 8,892,488,889; 8,892,489,042 (21 numbers)

Finally, the nine eleven-digit sumbers all take this form:

30,000,000,000 → 0000000000 + 3000000000 + 3000000000 + 3000000000 + 3000000000 + 3000000000 + 3000000000 + 3000000000 + 3000000000 + 3000000000 + 3000000000 = 30,000,000,000

So that’s forty-one narcissistic sumbers in base-10. Not all of them are listed in Sequence A131639 at the Encyclopedia of Integer Sequences, but I think I’ve got my program working right. Other bases show similar patterns. Here are some missing-digit narcissistic sumbers in base-5:

• 1,243 → 243 + 143 + 123 + 124 = 1,243 (b=5) = 198 (b=10)
• 1,324 → 324 + 124 + 134 + 132 = 1,324 (b=5) = 214 (b=10)
• 1,331 → 331 + 131 + 131 + 133 = 1,331 (b=5) = 216 (b=10)
• 1,412 → 412 + 112 + 142 + 141 = 1,412 (b=5) = 232 (b=10)

• 100,000 → 00000 + 10000 + 10000 + 10000 + 10000 + 10000 = 100,000 (b=5) = 3,125 (b=10)
• 200,000 → 00000 + 20000 + 20000 + 20000 + 20000 + 20000 = 200,000 (b=5) = 6,250 (b=10)
• 300,000 → 00000 + 30000 + 30000 + 30000 + 30000 + 30000 = 300,000 (b=5) = 9,375 (b=10)
• 400,000 → 00000 + 40000 + 40000 + 40000 + 40000 + 40000 = 400,000 (b=5) = 12,500 (b=10)

And here are some sumbers in base-16:

5,4CD,111,0EE,EF0,542 = 4CD1110EEEF0542 + 5CD1110EEEF0542 + 54D1110EEEF0542 + 54C1110EEEF0542 + 54CD110EEEF0542 + 54CD110EEEF0542 + 54CD110EEEF0542 + 54CD111EEEF0542 + 54CD1110EEF0542 + 54CD1110EEF0542 + 54CD1110EEF0542 + 54CD1110EEE0542 + 54CD1110EEEF542 + 54CD1110EEEF042 + 54CD1110EEEF052 + 54CD1110EEEF054 (b=16) = 6,110,559,033,837,421,890 (b=10)

6,5DD,E13,CEE,EF0,542 = 5DDE13CEEEF0542 + 6DDE13CEEEF0542 + 65DE13CEEEF0542 + 65DE13CEEEF0542 + 65DD13CEEEF0542 + 65DDE3CEEEF0542 + 65DDE1CEEEF0542 + 65DDE13EEEF0542 + 65DDE13CEEF0542 + 65DDE13CEEF0542 + 65DDE13CEEF0542 + 65DDE13CEEE0542 + 65DDE13CEEEF542 + 65DDE13CEEEF042 + 65DDE13CEEEF052 + 65DDE13CEEEF054 (b=16) = 7,340,270,619,506,705,730 (b=10)

10,000,000,000,000,000 → 0000000000000000 + 1000000000000000 + 1000000000000000 + 1000000000000000 + 1000000000000000 + 1000000000000000 + 1000000000000000 + 1000000000000000 + 1000000000000000 + 1000000000000000 + 1000000000000000 + 1000000000000000 + 1000000000000000 + 1000000000000000 + 1000000000000000 + 1000000000000000 + 1000000000000000 = 10,000,000,000,000,000 (b=16) = 18,446,744,073,709,551,616 (b=10)

F0,000,000,000,000,000 → 0000000000000000 + F000000000000000 + F000000000000000 + F000000000000000 + F000000000000000 + F000000000000000 + F000000000000000 + F000000000000000 + F000000000000000 + F000000000000000 + F000000000000000 + F000000000000000 + F000000000000000 + F000000000000000 + F000000000000000 + F000000000000000 + F000000000000000 = F0,000,000,000,000,000 (b=16) = 276,701,161,105,643,274,240 (b=10)

Next I’d like to investigate sumbers created by missing two, three and more digits at a time. Here’s a taster:

1,043,101 → 43101 (missing 1 and 0) + 03101 (missing 1 and 4) + 04101 (missing 1 and 3) + 04301 + 04311 + 04310 + 13101 + 14101 + 14301 + 14311 + 14310 + 10101 + 10301 + 10311 + 10310 + 10401 + 10411 + 10410 + 10431 + 10430 + 10431 = 1,043,101 (b=5) = 18,526 (b=10)

They Say, They Sigh, They Sow #2

“Epitaxial mismatches in the lattices of nickelate ultra-thin films can be used to tune the energetic landscape of Mott materials and thereby control conductor/insulator transitions.” — On the road to Mottronics, ScienceDaily, 24/ii/2014.