A Daily History of Holes, Dots, Lines, Science, History, Math, the Unintentional Absurd & Nothing |1.6 million words, 7500 images, 3.9 million hits| Press & appearances in The Times, The Paris Review, Le Figaro, MENSA, The Economist, The Guardian, Discovery News, Slate, Le Monde, Sci American Blogs, Le Point, and many other places... 4,000+ total posts
I came upon a short notice in the Scientific American (January 30, 1892) for Louis-J. Troncet's ingenious and very popular instant-calculator. It was a small and powerful machine (10x6cm) that Troncet had patented in 1889, and was issued in a small book-like folding case, with the accordion folding bit containing multiplication tables. It was quick and easy to use, sold for a few dollars, and became a cheap arithmetic staple for decades.
(I'm pretty sure that the image that appeared in Scientific American, above, was the one used in the article by G. Mareschal, “Calculateur mecanique instante,” in La Nature, in 1890 (pp. 307-308).
Here's a color image of the Troncet at the National Museum of American History:
[Source: http://americanhistory.si.edu/collections/search/object/nmah_690248 For another visit with the Troncet see the History of Computers site http://history-computer.com/CalculatingTools/Gadgets/Troncet.html]
There's a LOT of artistic license in this title, but I like the idea of these acoustical plans as containers of what things sounded like in the halls and auditoriums that no longer exist. This is a big leap of faith given that the work that went into these images was conducted before the first truly scientific/mathematically rigorous architectural acoustics existed. But I like tot think of them as reconstructions of sound in a particular environment. The drawings are also beautiful, inn their way.
Image source: Theodore Lachez, Acoustique et Optique des Salles de Reunions, printed in Paris in 1879. This is the second edition, with 116 text illustrations in the 518pp--these are almost entirely images of plans or elevations of music halls (for the study of seating and the room's acoustics, etc.). This edition also contains sections on the acoustics of "sales de debats parlementaires" and an examination of the "singular and curious" acoustics of the new Paris opera house.
The book is for sale on the blog's bookstore; and/or you can have a look at it in full text online, here, at Google Books: https://books.google.com/books?id=MjoIAAAAIAAJ&pg=PA315&source=gbs_selected_pages&cad=3#v=onepage&q&f=false
“Cataloguing is an ancient profession; there are examples of such “ordainers of the universe” (as they were called by the Sumerians) among the oldest vestiges of libraries.” ― Alberto Manguel, A History of Reading (and also translator of Borges and co-editor of A Dictionary of Imaginary Places, a book worthy of high consideration as the The Book that you could have with you on a desert island.)
[On the other end of the infinite library, see an earlier post here on "The Library of One Book", here: http://longstreet.typepad.com/thesciencebookstore/2009/10/the-library-of-one-book.html]
In Jorge Borges' "The Library of Babel" (published in 1944 and translated into English in 1962) we find that an infinity, or a universe, or a heaven, is declared to be a sort of endless library, stocked with hexagonally-shaped rooms books filled with books, all the same size, with the same number of characters. The rooms are endless, as are the books, which are written in every conceivable language and containing 29 necessary elements (including the alphabet, and the period, comma, and very interestingly concluding with the space). There are endless varieties of possibilities, and the place is staffed by librarians who have interests and obsessions from, well, A to Z, or Az^Z^Z^Z to ZA^A^A and so on, until we run out of time. (Others have done some smart thinking on Borges' great thought experiment/short story, and have estimated the size of the library in terms of stacked orders of magnitude beyond the atoms of the universe--but you can find all of that stuff elsewhere with a quick google search.)
And then there's this sample fro Borges on what sorts of books make up the library:
"...the detailed history of the future, the autobiographies of the archangels, the faithful catalog of the Library, thousands and thousands of false catalogs, the proof of the falsity of those false catalogs, a proof of the falsity of the true catalog, the gnostic gospel of Basilides, the commentary upon that gospel, the true story of your death, the translation of every book into every language . . ."
Here's how you arrange an infinite library: you don't.
The books are not sorted to any sort of classification, only collected to the point that they are together.
The many seem to be written in indefinable languages. Some of the librarians spent their time pursuing the holy grail--since all books that could ever be published would be present here, which theoretically include an index to library, or some sort of organizing principle.
But since there was no verifiable organizing principle at play here, the library was useless as a "library", though for the individual bits, it was perfectly fine. The structure though just turned into a long, endless, shelf. This might explain why the caretaker/librarians of the place are so desperate.
I cannot recall a mention of a card catalog, which I guess could be as all-powerfully impossible as the library, given that the library is not-classifiable. This is particularly true when you consider that there must also be a catalog of the arrangement of all possible false catalogs of all possible false books in the library, in addition to the true catalog. Perhaps the cards from this catalog would take up all of the space in the universe that would bump up against our own.
On the other hand, the logician W.V.O. Quine has written in a short piece that the Borges library is finite, because at some point there will come a time that all that can be written or will be written has been written:
"It is interesting, still, that the collection is finite. The entire and ultimate truth about everything is printed in full in that library, after all, insofar as it can be put in words at all. The limited size of each volume is no restriction, for there is always another volume that takes up the tale -- any tale, true or false -- where any other volume leaves off. In seeking the truth we have no way of knowing which volume to pick up nor which to follow it with, but it is all right there."
He reduces this argument elegantly but completely without the humor of Borges, and says that all that is known can be represented in two symbols from which everything else can be derived--a dot, and a dash. He writes:
"The ultimate absurdity is now staring us in the face: a universal library of two volumes, one containing a single dot and the other a dash. Persistent repetition and alternation of the two is sufficient, we well know, for spelling out any and every truth. The miracle of the finite but universal library is a mere inflation of the miracle of binary notation: everything worth saying, and everything else as well, can be said with two characters."
"The ultimate absurdity is now staring us in the face: a universal library of two volumes, one containing a single dot and the other a dash. Persistent repetition and alternation of the two is sufficient, we well know, for spelling out any and every truth. The miracle of the finite but universal library is a mere inflation of the miracle of binary notation: everything worth saying, and everything else as well, can be said with two characters. It is a letdown befitting the Wizard of Oz, but it has been a boon to computers." [Quine's "Universal Library" is found at Hyperdiscordia, here: http://hyperdiscordia.crywalt.com/universal_library.html]
Quine's approximation cuts way down on the size of the library, which evidently would not fit in the known universe, which opens the gates for Heaven, which I think doesn't depend on such restrictions--unless of course it was too big for that, which means believers would be in trouble, and none too happy with being kicked out of paradise to make space for a book.
Nicholas Saunderson (1682-1739) was an extraordinary mathematical talent—he was also blind (from about the age of one), and invented, principally for his own uses, what I think is the first mathematical calculator designed specifically for the use of the blind. He was supremely gifted and creative, and rose to become the fourth Lucasian professor at Cambridge, succeeding the expelled William Whiston, who had in turn succeeded Isaac Newton—Saunderson also held the post for one of the longest periods of time, 1711-1739. HE was friend and associate to Newton, Whiston, Roger Cotes, Halley, De Moivre and others during a particularly rich intellectual period in the history of physics and the maths.
His calculator was smart and simple, based on a cribbage-board –like device, that was able to perform arithmetical and algebraic functions—it consisted of nine rows and was worked with two pins, the positioning of the pins on the engraved board telling the user their value. (There was another calculator for the blind constructed by Meyer (below, left) using a sort of reverse principle to the Saunderson model where it was the shape and placement (leaning or not, for example) of the pegs in the hole that annotated value rather than their placement on the board.
The Saunderson computer was described in his The Elements of Algebra…,1 published at Cambridge in the first edition just after the author’s death, in 1740. The device was described in the book by John Colson (who succeeded Saunderson to the Lucasian chair), who commented that it was via the use of the device that Saunderson could compose his treatise on algebra. (At right is another Saunderson-based calculator allowing for the construction and study of geometrical figures).
[Image source for Saunderson portrait: https://en.wikipedia.org/wiki/Nicholas_Saunderson#/media/File:Nicolas_Saunderson.jpg]
!. Here's a link for a later-n-the-century (1792) edition of the Saunders book via the Internet Archive: https://archive.org/details/selectpartsofsau00saun
Also see MacTutor History of Mathematics biography of Saunderson, here: http://www-history.mcs.st-and.ac.uk/Biographies/Saunderson.html
There's a box in the studio that is filled with all manner of antique and semi-antique adding/calculating/etc. instruments, from slide rules to blast effects of a nuclear weapon to air speed to the gas mileage for a 1959 Rambler. Some are wood, some metal, but my favorites I think are those made of paper (a large revolving baseball from 1961 for calculating world series records is my favorite in that area....that, or the radiation measurer made of paper to place alongside A Body Part to check on its incremental-or-not growth following nuclear detonation).
The there are the little bits that maneuvered the little bits, as seen in this uncovered little gem, the "Fraction of an Inch Adding Machine" (shown above). It was patented in 1952 by K.P. Jaeger (http://www.google.com/patents/USD169941), and is stamped "Sheradco, Inc., Detroit" on the reverse of the metal plate.
It does a relatively simple task as stated--adding diverse fractions--and it does so quickly; as a matter of fact, it is far quicker than you can do it online, even with a converter. This is basically two steps--you put a pen or pencil head in the outer ring hole for the first fraction and move the dial clockwise until you come to the stop; then you do the same for the next fraction, and the result is instantly displayed. For operations above 1, you just need to keep track of the whole numbers yourself. Unfortunately it doesn't teach you anything about fractions, but neither does your digital calculator teach you about anything calculating.
This is just a smart and pretty instrument that works very nicely indeed, and I just wanted to share it.
[I did find a lovely post on how to make your own! It also provides a pdf of base plate and the rest of it as well: http://www.evilmadscientist.com/2007/make-your-own-1952-fraction-of-an-inch-adding-machine]
While looking for it on Google Patent Search I bumped into some other similar devices, and I just wanted to take a moment to note the beauty of the possibility of their interior base dials. Just one sample here for the moment: the "Dial Adding Machine" of E.T. Knopke, 1952, which is so full of numbers and potential and mathematical poetry:
This is one of those fascinating bits that you come across that in the moment are just thrilling, but overall really doesn't have anywhere particular to live in your memory. Still, it was curious to find this data on the positions and pay to the members of the U.S. Navy in 1820 and to see the amount and distribution of pay, and to see the aggregates.
The pay ranges (for example) from $100/month for (52) Captains, $50/month for ( 52) surgeons, $40/month for (10) chaplains, $20/month for (21) sailmakers, $18/month for (24) cooks, $12/month for (1388) able seamen, $10/month for 1370 ordinary seamen, and $7/month for (278) boys.
[Source: can't remember. This is a detail from a loose, folding sheet from a U.S. government document from 1820, probably looking at the finances of armed forces, or some such.]
So it looks as though the total pay for U.S. naval personnel in 1820 (excluding "rations", which I believe included food and housing allotments) was $867, 578.00 (or pretty close to that) for 4,550 sailors/etc., which is about $200 per year per person, on average. 41% of that total outlay went to the 3,158 able and ordinary seamen, who composed 71% of the total naval force. So it looks like if your removed the pay for "boys" then the highest paid officer made about ten times what the lowest paid seaman made, which by today's standards is pretty corporate-responsible (a la Ben & Jerry's).
I'm not yet finding what a carpenter/laborer would make in salary for that year for comparison, but I will add that here later.
I've written a number of times on this blog about my interest in collecting the artwork of children--kid art from say before 1900--and how difficult it is to actually find examples. Most of that has been serendipitous, finding scribbles and drawings of notebooks, and ledgers, and free endpapers of schoolbooks, that sort of thing. There are a number of reasons for this scarcity--the greatest being lack of paper, and pencils, or paints; that, coupled with the stuff needing to survive multiple generations of house cleans and moves and so on, well, it just means that not a lot has survived.
[Source: Scientific American, September 13, 1890]
Lack of paper or paper being too expensive was a big deal, and so kids used slates, which means that very little has survived on the slate itself. And to further point out the ephemeral nature of slate-written/drawn material, I present the slate eraser sponge! It is a little bit of a thing that fits over the slate stylus and allows a really thorough erasure/sponging of anything on your slate. No only was the slate stuff gone, it was double-gone.
This is also an invention that is remarkably well nested in the dustbin of abandoned and unnecessary useful inventions that worked superbly for about two decades, and were never heard from again.
The wonderful and occasionally problematic Fr. Athanasius Kircher (addressed numerous times in this blog, just check out a search under his name in the Google box at left) inferred by "anthropomorphic calculus" (so says Jan Bondesman, in A Cabinet of Medical Curiosities, pg 82) the size a human/giant must have been to accommodate (for example) an elephant tooth. So instead of dinosaurs you'd get these enormous creatures many time larger than a "Homo ordinarius"--as you can see in the scale, we have the enormous creature flanked by "homo ordinarius", then Goliath (still puny), "Helvetius Gygas", and "Gygas Mauritanius", all quite tiny compared to the big boy, who stood 200 cubits. (A cubit was a measure from he elbow to the fingertips, so depending on where you were, the cubit could be 17-20 inches or so; in any event the giant would have been 300-400 feet tall.) This image appears in Kircher's great Mundus subterraneus, quo universaw denique naturae divitae, published in 1668.
This original image is available for purchase via the blog's bookstore, here.
It is always difficult comparing value of objects over periods of time--this is especially so when trying to compare the value of wealth, in general. And so I won't be tempted to much to do this while relating the data of this interesting and tiny handout, The Distribution of Wealth in the United States, 1910. It was published in 1912 by Edward G. Hewitt (who curiously locates himself in "Brooklyn Borough", rather than just "Brooklyn" or the "Borough of Brooklyn", the incorporation taking place 14 years earlier) and presented in a bit of an odd way, at least to me, dividing the wealth into groups of families. It makes it a little hard to understand, even if there are only 22 divisions to the analysis.
What attracted my attention in this was the number of millionaire families, which was 7,737 in the total of 18,434,837 families--or about .4%--with an aggregate wealth of $26.9 billion, which was a 22.6% share of the national wealth stated at $115,000,000,000. That millionaires club would be about $24 million in 2014 dollars, using the Bureau of Labor Statistics inflation calculator.
Secondly, the much-discussed 1% here totaled 189,237 families with wealth of over $62,500, or about $1,494,545 or so in 2014 dollars.
Since "wealth" really isn't defined here it is difficult for me to extrapolate the differences between the 1% of 1910 and the 1% of 2015--especially so since I've seen several different current interpretations of what the modern 1% actually means.
In 1910 there were 7,737 families of millionaire status--today there are something like 5.4 million millionaires in the U.S., though that is counted as individuals, or about 1.6% of the population compared to .4% in 1910. And as my friend Jeff Donlan points out, it would be more useful to talk about the 24-millionaires club than simple millionaires, but I don't have access to that data, at least not for this half-hour post.
It is interesting that The Economist in 2012 stated that the average household income of the 1% was $1.2m in 2008, according to federal tax data. I find it very surprising that the 1910 1% (adjusted by BLS) comes in at $1.49m.
Again, this is all sorts of problematic, but even though stumbling around like I am here with these numbers it is very curious to see how closely those 1% numbers from 1910 and 2014 come together. It feels like this is wrong on many or all levels, and the 1910 data might all be junk for all I know, and that it is like saying that the stars are all the same size because that's what it looks like here on Earth, but it is strange about how those numbers worked out--at least here, using the stated data. I'm not saying that what I'm saying above has any value beyond indicating that there may be something interesting here...
This was a surprise, finding M. Bollee's article ("Sur une nouvelle machine a calculer") in the 1889 Comptes Rendus, pecking around in that big 10-pound volume looking for something else. It was very easy to miss if you weren't looking for it, just a few pages long in a 1000-page book. But there it was, nestled comfortably in pp 737-739. It these few pages Bollee describes his machine and with particular reference to his innovative approach to direct multipilication--a fine addition (ha!) to the long line of contributions by Babbage and Clement, Scheutz, Wiberg and Grant and Hamann.
Léon Bollée: "Sur une nouvelle machine a calculer", in Comptes Rendus de l'Academie Sciences (Paris), volume 109, 1889, pp. 737-9. (You can purchase the original paper if you'd like by following this link to our Books for Sale page, under "Bollee".)
An image of the machine from The Manufacturer and Builder:
My friend Jeff Donlan (who writes a fine and insightful blog, At the Library) cent (ha!) me this article on the false tyranny of the penny--rather it is about getting rid of the penny, which the author claims has run its course of usefulness, swallowed by the history of economic need for it. Maybe it takes more money to deal with the one-cent piece than it is worth, I don't know--the author of the article goes through that along with a short history of other currencies dumping their minuscule and antiquarian denominations.
What I wonder about is what happens to the number "9"?
My made-up statistical reference notes that about half of all prices on all the stuff in the U.S. use at least one nine; many use two. What happens to people excitedly advertising ",..and all your's for only three small payments of $19.99!!! And what about gasoline prices which are $2.89 and 9/10? Assuming that we keep the nickel, prices will have to re-adjust to accommodate the five-cent piece, dropping the "9" in millions of prices. No doubt tens of millions of people will think that prices have been raised across-the-board.
And what will we do with this enormous surplus of 9s?
Seriously though why not just get rid of the whole lot of less-than-a-dollar currency? I know that would be very problematic, but no doubt it there will be less time between the introduction of the penny to its demise than there will be from now to the elimination of all coin-and-paper currency, After all, in for a penny, in for a pound.
Here's a fine piece of work on Charles Babbage from a very early period (volume 5) of Nature--succinct and tight and only two pages. (It was buried in the middle of the issue, which surprised me, as I thought he'd be placed up front rather than tucked into the middle. So it goes.)
"Characteristics of the Small-Scale Computers" looked innocent enough, 12" tall and one folded piece of paper, and published in 1956. The authors--John W. Carr III and Alan J. Perlis--were heavy hitters, and so I really wasn't very surprised to see what they had done "inside", though I was impressed and happy to see the data. Displayed on the 12x16" sheet of paper are 15 data points on 14 computers, many of them classic/famous: the 650 IBM, UNIVAC, Elecom, Alawac.
(Remember that when you're looking at purchase price and monthly rental amounts that the 1956 dollar is equal to about $8.70 in 2015 dollars, so that $3275/month for the 650 would be about $30k. The $136k for the Datatron is about a million today.)
This hand-out pamphlet seems to be a case where the sale of an edible product is made for the sale of its packaging.
The pamphlet shouts that CANDY IS DELICIOUS FOOD, which is certainly a correct statement if food=digestible. It tells/sells the story of candy as a profit-maker to the grocery seller, saying that "32% average gross profit on home consumption units", those delicious-sounding unit-things being the candy.
There are bits and pieces about candy display and placement, all on the advice of the maker of the stuff that in which the candy was wrapped--cellophane. The publisher and distributor of the pamphlet, the "Cellophane" Division of the E.I. du Pont de Nemours & Co. Inc., had a huge vested interest in candy sales: candy was mostly wrapped in Cellophane (starting with Whitman in 1912) and by the time du Pont achieved its water- and moisture-proof Cellophane in Delaware the product accounted (in 1938) for 25% of the company's profits. That's pretty big, and so candy as a major muncher of Cellophane would be promoted by du Pont as pretty big, too. And as food, for added Bigness.
The small $25 miracle/godsend to number crunchers everywhere was this small, nine-place, sliding-digit chain-adder mechanical calculator, set in nickel-plated metal, and which we see in this fantastic and half-bizarre ad in Illustrirte Zeitung for June 1922. The instrument was about eight inches long and came in its owns hard case, and was a very good instrument for the lowish-end market. The add of course is fantastic. ("Die Erloesung" could I guess be transliterated as "Deliverance!" from the drudgery of making calculations by hand.)