## Friday, January 31, 2014

### Mac Pro

An exciting day for me as my Mac Pro arrived! After unpacking, the first challenge was finding that little booklet that accompanies Apple products. I opened up the Pro (the outer casing just slides up) and pulled out of their slots the existing RAM, replacing it with new chips (ordered from OWC two days ago — arrived yesterday). I wasn't sure how I was going to hook it up but, since I had an extra HDMI cable kicking around, I ended up just connecting it to my Samsung TV (for now). I got a ten-year-old Apple extended keyboard and a Kensington trackball out of storage and away I went.

When I got to the desktop, there was no menu bar. I thought this might have been an OSX Mavericks default thing, but no. After some time looking for online instructions on how to enable the menu bar it finally dawned on me that this might be a display issue. Indeed, shoving the cursor to the top of the screen and clicking I was able to engage a menu that had merely been cut off. I played with the Displays in System Preferences without success. Finally I managed to get a proper desktop by engaging the Samsung TV's display preferences — specifically the Screen-Fit option.

I spent some time updating the software. The pre-installed Keynote, Pages, and Numbers refused to update and, after a half-hour-or-so online chat with a couple of Apple employees, I was advised to apply for the Apple Up-to-Date program, which I did. Within an hour I received redeem-codes for the programs, installed them on my iMac, after which the updates on the Mac Pro proceeded without further ado.

## Saturday, January 25, 2014

### Divide by the sum of the base-7 digits

Consider a number divided by the sum of its base-7 digits. If it goes evenly, repeat the procedure with the quotient. Continue thus until either the quotient arrived at is not evenly divisible by the sum of its base-7 digits, or the number 1 is reached.

There are only a finite number of positive integers that reach 1, the largest being

40090274859335788188225568958946114753008293347953175307173216438617812041555279623245865158433989020626979196127925376719536463066943202165158879123115753785079089282793640091903556833926655783997154594289161232116101044714579121240616475797816175718660050822593870727643983209393172239451564000476429967804164112577663514902049782611642638387652639351006276378991504088440953822881824506926245966514963040000736614161156758934690996704884832607639278528354732245854666907653859254346591907729278186995119626281069810539346524668166171231605013177562186320341362087115862268089449413417647638277642047209420699562205067887315497916485984047479489310211370627319356060094500301725713900105120910701197104253117436639212500902642314176176967754312051840268795232231564024125267411543199976525204927541708786679816758575657980667513081688484501372900276995079844047822503749108162774331711019656062212497878785698569208460217904682951905411288417291826551415716078000233552616827475207210341514285121555751575441134399283505320677313761929657695840782124531572332588442099528937144165250184289803073385821791845909284971333115533197924549237472741867079666309831088832176663994090643038292403450620469240039382786840375357650171845483239864881868376636340925946996646785706327788942019760843817358046420110165297873316665218667309986852968308151914980109861255816132030094899126866728713978090367542979716058225895429295194207297444409428114690224793718858105439405028365635014177006033191195106091973264238591041056591447688345347096425755587171730534338260827764462028242056916005480589853515765864089539689949490780229330184685785893827574420324884514104456847507112315527845624705715303582403385098824135955821678344596336056449221276334860009653229579919137731666143204865856974858549099713061735336708747418929594760677046206036537198447075597441193263702819022900470439134462698668788248803875258982520998673154040971723246000322690663588338780282130172653742214062320339642980651332437592943224171993054278504854359263546513111508293137452801227303396833467880111969018400836956919418265829867587385464514229131616091155350352359987344887853698108073516675773966599621889517183012061233924452768645462660214005099381105533323925286404042847666102614749030207217427375546428039974955185046587777342073373801527021929645708531510107354271378582391987786332608126321798272426997044018165624866770048171105808016488238188289801308544677802188474644539742390690842248428997401476399010954819656592067781778703291889757954679498302069401401589325018144280087599532278107367903151149649200575433317349581179662094712894052336941995935158089574682049242371135766303405317333617059918464786830296092873607723446043773160610547278645024176648057510413700798874223247283413540627128291798831684104289783812109519627995369714012993163971461872686244749458099411550580146503461601748857853191027042128009474550163763421442030011736634544836079453887866911132961282642546949388578768339835845624161668674021819489723044668294972996997423875362731882339528027245606149737913469101024504136549552849759917083630366539409605504659561011785440345272778211465945693960720896567621969969082811639238016393851093246600903247987707991789982893268370340914432740301848602399384133541309133004765045945724615545504560252430675440785241940929800637869330405417472594113223551904980864884198100540690717524636636379084134321939117603083808987373406802510361535170295926711324895678515256387358372611315751426038086161408174212693132659421605854959177851387175215247272630481582104275216142647681484992006265256385073823101449946755442330251434072611011489208591071525519165345150834473188181963251496464787239046879191176057202681823756066807911350570696571416365892638067852245320918704458345943824312320158356113528232806739654094813862171549232903287378512320904267042814472764239592657055353795135816252806115279123777834378600455934649535749621601986287045846352331849132536698413203087525707996888614483678382817496804464755695026786614809413548315054727775622002491893507360222933168981350098069602745544880692844548161914242691954481967644658745708028218170823474907840566117715397438721084547595421235809009128516284771247412686929297166747924273183595558256149187553094692988422792885679295229828731648430259944575276876535059284962602025651564247674254961641303327067136820343570606305572710794009532899041484237145056396481252948208121293195293955066499814095083227206365565524478997083638007853145132760121614350459055718294903921968755626688776131622821943262038510531087337993411469959845109033850015746028838780928421937726067934065224646757252627968948602024554240345188812056557019930438014843762808997245846764508623318834940804266521012417189436145906314777397243820562742540006134033037797890593215167461055509964419803703129965420774258361409290750622155072090212298443017813234103132127967993050253187957756924572283399296498652057583661385290455882219424975377399318373244931565633364877586069108072644714859683638688770424939379193467063544688987844624228624247205955441197735403439459887097450104020193684565175047546198582440115835268718123063858197162132127571015278632833778510683979780534184475292335187466278947401076763810662399750205184968078564813253753559514481268830591427801643087836170980870565146296479969566879950986431989117581520467409581186824798648001708940283184463764630034743405896647862838818430708764981297899258485589028613929261169040191749894038083335510033454827457798132396634744308570096568006644461861208943095923030329281356018755810734378377890722570794284697707418194294698953112364072732053821462968057013810305937663419273519779308262603635181031709204706975137864123673673389746652359298764223256795650322005135012106617227408487832344213063757386025891329337543613990584854719922545294782142232296720520631751605489285364119476851574815545641853016892858351444380277340844050292111869425152072650972437614156199194581797893546437816320452146569512073424871341424421995845821366420601533448902732135660793193527473582840561865399234530347032833676527441445583718035934771654689666787986539415791379147997538937615589553377468156111114645881350167183786268670123661018578431393319437168263711324426050397765263367207253382559661860463697090083074542325857182683992721745520542403903747926889485124768140390471147892041301178940056769365494197657203060671809981976740860893858496811981329645117977446917074954385200549230224659873260454126053650211959542931832195809291013462962544694891228644468879102993507245061922720884257306136941735971027027897323720141951876732293091968290602574595066772225301644505395740366854399364361907936673806540051759442142234433808837456364413923460109598187266592396953273164025977573095883035930683609122387311759871669020849502221120675091612073626584261302003523531553137481158186131172626241101515098402454610021116809425957914212179101605181332671739827844671552277586007535053774283817581712197064353741549242785088859153239236838430990178303886234536118744437642497389754250755439371878096184678793025092321871455039500040305824307674862544485216813154870493294977549636437183966080364600262876101172520314461053033693239000742910781266762715316011336592993823705279006274004988895977499235007814639679237526355807064291823107834257782806922188435272733938760338024695343442669419544529844039516530458106118852146854958325173661000125143008498241984522423685248053771352436576577262153071086800388885154314639546535113040814564761013808760111497216000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
written in base ten, or

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
written in base seven.

This number takes 2046 steps to reach 1. I have plotted the count of positive integers (out of a total 693633 available) that take n steps (from n = 0 to n = 2046) to get to 1 in a graph. The smaller, darker-blue plot at the bottom-left is the count of positive integers (out of a total 15095 available) that take n steps (from n = 0 to n = 440) to get to 1 in the base-10 version of the procedure.

## Thursday, January 02, 2014

### When adders multiply

I had occasion, yesterday and today, to do some Google Books sourcing of quotations involving snakes doing arithmetic. It's a bit of a challenge getting full quotations from snippet views but it can often be done.

This list is not meant to be comprehensive. I just wanted to put in one place a number of items more-or-less bound by the word-play under scrutiny. Here and there, I've taken the liberty to make small editorial alterations that involve punctuation. [My thoughts are in square brackets.]

Oliver Corwin Sabin, Washington News Letter, 1900.

Another writer tells us that the first man was called Adam, and a curse laid upon him by his Creator because he falsified the word of God by adding to it, and his name therefore was probably Add-am.
The writer further argues in this puerile vein that the serpent in the garden of Eden was cursed by God for the same reason, and hence we have the word adder applied to a very deadly serpent. The writer was not aware of the fact that may be learned from any good dictionary of the English language, that adder is a corruption of the Anglo-Saxon word atter, which meant deaf, and was applied to a small, venomous snake that was reputed to lie with one ear flat to the ground, and its tail in the other ear, that its sleep might not be disturbed by noises.
Any concordance to the Scriptures will inform the writer of this curious Adamic theory, that the Hebrew word Adam, has three meanings, the same being respectively, earthly, ruddy, beautiful, and it never had any reference to addition, although he being the father of all living things might well have given a name that referred to multiplication.

Ambrose Bierce, Kings of Beasts (The Snake), 1902; taken from Collected Works, 1912.

I can tell you, though, about the snakes in the Garden of Eden, all exceptin the one which was tempted by Eve. When they had all been made, Adam he called them together and give them their names, and then he waved his arms and said: 'Now go 4th into all the waste places of the earth and multiply.'
"They all slided away only but jest one, which lay still and shook its head, real sad. Then Adam he said: 'Why dont you do as I said? Off with you to once!'"
"But the snake, it spoke up and sed, the snake did: 'If you please, sir, Ime willing to go 4th, but I cant multiply. Ime a adder. You told me so your self.'"

Brewers Journal (attributed to Baltimore American), 1907.

THE EXPLANATION
"I wonder why the snakes a man sees when he's been drinking multiply so fast?"
"I suppose because the kind of snakes he sees are adders."

Irvin S. Cobb, Who's Who at the Zoo, Hampton-Columbian Magazine, October 1911.

The secretary bird moons around seriously, doing sums in its head and, as if to add to the mathematical aspect of Zoo life, there are the rabbits multiplying rapidly and the great Egyptian asp which is considerable of an adder itself.
If you resent that last allusion as bordering dangerously upon a pun, do not blame me. I stole it from an English comic weekly ...

[Cobb's piece was much reprinted. The "multiplying rapidly" aspect of mathematics appears in Bray Studio's 1919 animation Bobby Bumps' Pup Gets the Flea-enza: "Flu germs are great mathematicians. They can multiply rapidly."]

Webster Method, 1918.

Rabbits multiply and some snakes are adders, but G.F. Butt, of John S. Metcalf Co., says, it takes a shark to figure elevator contracts.

[I don't get it. See comment (at end).]

Journal of the American Institute of Homeopathy, 1922.

There is a story that you all probably recollect, that when Noah finally realized that his Ark was at last on the firm ground of Mount Ararat he opened the door and said to his cargo, "Now all you animals get out and go multiply." They all did, all but two snakes which did not move from their corner. Then Noah again opened the door and said, "Did you fellows hear what I said, go out and multiply." Whereupon one of the snakes, raised its head and replied: "We can't, Noah, we are adders."

[Currently the earliest incorporation of Noah.]

International Congress on Accounting, 1933.

You remember that Noah was shooing the animals out of the ark two by two, and saying to them in a helpful spirit, "Now, get out, be fruitful and multiply" and when he thought the Ark was empty he looked round and saw that it was not cleared, because in one corner there were two little snakes. He scolded them and said, "Get out! Be fruitful and multiply"; and they said "We cannot; we're adders."

The Michigan Technic (Stresses and Strains), October 1934.

After the flood was over, Noah went back to see if all the animals were out of the Ark. He found a pair of snakes in a corner weeping copiously. When he asked them what the matter was, they answered: "You told us to go out and multiply upon the earth and we cannot, for we are adders."

[This was reprinted in a number of trade journals in the 1930s and 1940s (mostly verbatim, except 'matter' is 'trouble', which makes me doubt this is the original, but at least it has a firm date; a Google-assigned 1930 date for one of the copies can't be assumed belonging to its provided snippet).]

Proceedings of the Grand Division, 1941.

I would like to tell you a little story, in that I have referred to mathematicians. The gentleman in that corner over there a while ago touched light on Noah, the man who built the ark to save a pair of each who were threatened by the great flood that lasted 40 days.
When the waters started to rise in this flood, Noah laid his gangplank and he said, "Come ye all here and take shelter."
After the flood had subsided, Noah said to these passengers on this boat, "I want you to go into all the corners of the earth and multiply."
So after the boat was thoroughly cleaned, so he thought, all the passengers had dispersed, there were two little snakes over in the corner. Noah said, "I thought I told you all to go into the corners of the earth and multiply."
One of the little snakes said, "Well, you did, Mr. Noah, but we are adders."

Jane Hedges (to William D. Hedges), WWII Letters of Three Brothers and Their Sister, October 1942.

I just heard a silly joke. "The Lord told two little snakes, to go forth and multiply. Instead, they went off to a corner and cried. Why? Because they were adders." That's the kind of stuff that circulates around this office.

The Michigan Technic (Ambrose McHigan), April 1946.

It is widely known that rabbits and guinea pigs are some of the most rapid multipliers. The snake out-does them though. Some snakes are adders at birth. The honors, however, go to the tiny organism, amoeba. It divides to multiply.

New Zealand Law Journal, 1947.

... He told all the animals to go out and multiply. Afterwards, he met two snakes, and they were just as he had seen them before, so he told them that they must multiply. They said, 'Well, we are sorry, Mr. Noah, but we are adders.' 'That is no good,' said Noah, 'you must multiply.' He was very pleased next time he saw them that there were a lot of little snakes about them. He said, 'Oh, I see you have learned to multiply.' They said, 'No, Mr. Noah, we did it by logs.'

[If the date is correct, this is currently the earliest mention of using 'logs' to solve the adders' dilemma.]

John Raymond Shute, The Seer (So Spake the Snakes), 1950.

"On that great day when the ark gently grounded on the highlands of the mountains, our mighty ancestor threw wide its doors and bade every pair of animals to go forth into the earth and multiply, so that there might be abundant increase. Out onto the land poured the foxes, the jackals, the lions and every manner of animals that had for many days and nights remained aboard the ark. Finally every pair was upon the good earth save a pair of snakes who lingered in the shade of the deckhouse. 'What now,' roared Noah, 'go ye forth also and multiply in the earth.' But the reptiles hung their heads and did make answer, saying: 'Kind sir, this we cannot do, for you see we know naught of multiplying, for we are adders.'"

Iron Age, April 1953.

Another new joke which we printed here some time back (the one about the two snakes in Noah's Ark who couldn't go forth and multiply because they were adders) has brought forth a torrent of two letters with an engineering flavor.
Mr. D.J. Foskett wrote from London that "the story was inaccurate because the snakes were found in the middle of the forest which was then cut down so that, although adders, they could multiply by logs." And Mr. W.E. Brainard of Hughes Aircraft, California, wrote that Noah should have chopped down a tree and built a table from its logs. Adders can easily multiply if they have a log table." One more case of great minds and hands across the sea.

Bryan Morgan, Total to Date, 1953.

... in fact, were like those snakes which were loath to repopulate the world after the Flood: they said that they were adders and found it hard ...

[I can't nudge snippet-view to show me anything of this passage.]

Journal and Proceedings of the Institution of Agricultural Engineers, 1954.

You might remember the story of Noah when the Ark came to rest on dry land. He was evacuating the animals and to each one he said: "Go forth. Go forth and multiply."
He said that to the waiting Snake who replied "We can't multiply because we are adders."
Then Noah noticed Mrs. Snake with a family of little snakes.
"What is this?" he said, "I thought you couldn't multiply."
"Oh, we did that by logarithms," replied Mr. Snake.

Anatol Rapoport, The Language of Science (Wistar Institute symposium address), April 1959.

On releasing the animals from the ark, Noah bid them to go forth and multiply. Suddenly two little snakes spoke up, "But we can't multiply — we are adders." Thereupon Noah constructed a table from rough-hewn lumber and said, "Here is a log table. Now you adders can multiply."
The puns on "adders" and "multiply" are obvious. However there are two more puns, barbs aimed at the viscera of the mathematician: "log table", i.e., a logarithmic table is a device which reduces multiplication to addition.

[Rapoport's address was reprinted in Readings for Technical Writers (Blickle & Passe, 1963) and The World of Words (Kottler & Light, 1967).]

George Gamow, Matter, Earth, and Sky, 1965.

At this point the author cannot resist telling a story of what happened when Noah's Ark, loaded with animal couples of all species, finally landed at Mt. Ararat. As a lion and a lioness, a deer and a doe, a rooster and a hen, etc., were coming onto solid land, Noah was giving them instructions to spread out and to multiply. Next spring, walking around the land which was again flourishing after the Great Deluge waters receded, Noah was enjoying the sight of little lion cubs, yearlings, baby chickens, etc., running around. But then he found a couple of snakes that had no offspring. Didn't I tell you to multiply?" asked Noah in anger. "Why didn't you?" "Sorry, Sir," answered the snakes, "we can't multiply because we're adders." A year passed, and Noah, walking around his property, found under a big table (built for the family's outdoor meals) the same two snakes — surrounded by a dozen or so newly-born offspring. "You told me last year," said Noah in surprise, "that you couldn't multiply because you're adders. How is it that you managed to multiply?" "Oh, sir," said the papa adder proudly, "you see, we've found a log table!" Let us hope that this story will persuade those students who do not know how to use the log table to learn this art.

[A very verbose retelling of the pun. I include it because author Gamow had a following.]

Inland Members' Service Bulletin, December 1968.

An Adder That Multiplies. With that we've come full circle. We realize that a computer adds by adding, multiples [sic] by adding, subtracts by adding, and divides by subtracting by adding. It's a cross between a snake and a rabbit — an adder that multiples [sic]. Get it! And man can these things add!

Sarah Fullton, via Scot Morris, Omni (Games), July 1979.

To bear offspring, Noah's snakes were unable.
Their fertility was somewhat unstable.
He constructed a bed
Out of tree trunks and said,
"Even adders can multiply on a log table."

[cf. Michael Stueben, Twenty Years Before the Blackboard, 1998:

To reproduce, Noah's snakes were unable.
Seems their fertility was somewhat unstable.
So he made them a bed
Of tree trunks and said,
"Even adders can multiply on a log table!"

... attributed, alas, to Anonymous. There are forces afoot attempting to obscure one's 15 minutes of fame.]