Ptak Science Books

Drowning in Numbers--Arithmetical Harvesting by Monroe and Texas Instruments

JF Ptak Science Books  Post 1704

The Monroe calculator must have seemed the same sort of inspired salvation to the 1930's generation as the hand-held Texas Instruments calculator (with paper feed!) that I saw displayed in a glass-domed pedestal at Barnes and Noble in Manhattan in 1973.  Small, compact, and with fantastic calculatign capacity--and expensive.  It was in a very real sense a glimpse into the future.  For the general, garden-variety Monroe, it certainly offered its users a much smaller, tidier machine than some of the brutes of the decade or two preceding it--make no mistake, there were some big bruising accounting Monroes that were truck busters.

But the Monroes that appeared in these ads from LIFE magazine in the late 1930's were certainly populist, and easily transportable.  And they cost about as much (with some smoke/mirrors adjusting for inflation and etc) in 1937 as the $450 TI  cost in 1973. (The TI machine was produced just seven years or so after its first hand-held was introduced--I'm unsure of the 450 price tag, though I think it about correct.  The TI SR-50 without a paper trail cost about $150 in 1974.)

Monroe is an old company (begun in 1912) company that produced hand-cranked and electromechanical calculating devices.  The Monroe salesman's handbook that I have here from 1929 shows versions of their machine that were lightweight and versatile (at 38 pounds) to behemoths for insurance companies that were truck-haulable.  Monroe became part of Litton before reappearing again on its own, trying to compete in the hand-held market with its own electronic display calculator--a device that cost $269 in 1972.  Monroe was basically "done" by the 1960's.

I think that for most people Texas Instruments is produced hand-held calculating devices--it is of course a vast concern, with a long history that gets catapulted during WWII when the formerly geology-based company gets involved in military electronics.  Fast forward, TI created FLIR and MERA, laser-guided control systems for PGMs (laser-guided bombs/precision-guided munitions), launch and leave glide missiles, and so on. IT was also involved in the earliest work in microminiaturization, producing (by Gordon Teal) the first commercial silicon transistor (1954) and the first integrated circuit (by Jack Kilby) in 1958. And so on.  Its a big, old company.

And as much as each company was offering a similar god-send to their generationally-distanced mathematician/number cruncher, TI simply didn't have ads like Monroe.  And I've always iked to see numbers-on-the-move.

Numbers in Dreams

JF Ptak Science Books   Post 1703

Thinking big thoughts in dreams is generally not a common thing, as anyone who has read their own semi-conscious half-awake memory notes of a dream-based inspiration could attest.  But it does happen: 

Paul  McCartney¹ dreamed the song Yesterday, Gandhi dreamed the source of non-violent resistance, Elias Howe  dreamed of the construction of the first sewing machine, and Mary Shelley the creation of her novel Frankenstein... For good or for ill, William Blake was evidently deeply influenced by his own dreams; on the other hand, Rene Magritte was deeply influenced by dreams but didn’t use any of his own for his paintings.  Otto Loewi turned an old problem into not one in a dream, finding a solution to the prickish problem of whether nerve impulses were chemical or electrical (and resulting in the Nobel for medicine in 1935); the fabulous discovery of the benzene ring came to August Kekule in a dream as well.  Artists have been representing people in dreams and dreamscapes for many centuries: Durer depicted a dream in a 1525 watercolor, for example, and thousands of artists have depicted famous biblical dreams (Joseph of Pharo) for long expanses of time.

What struck me, though, in this illustration found on the other side of the page of the Illustrirte Zeitung² (for August 1932) that I used for yesterday’s post about damming Gibraltar and Shakespeare’s memories, was the depiction of someone dreaming mathematical thoughts…or at the very least, dreaming numbers.  People have undoubtedly dreamed much in mathematics, but I can not recall seeing illustrations of these dreams.

I'm differentiating here from something like a Poincarean inspiration, or vision, or thunderstrike--I'm talking about drop-dead asleep sleep, dreaming sleep, REM and all that. Also I'm differentiating this from imaging mathematical thought, as in the work of Francis Galton in 1880 in which the subject of mentally seeing the process of mathematics is perhaps first addressed. I wrote a short piece on that here, way back in Post 9. )

The numerical sequence in this dream doesn’t look like anything to me:  the backwards radicand doesn’t strike anything common in my head.  The geometrical drawing under the portrait in the dreamer’s room though is the impossibly iconic Pythagorean theorem, and there is a nice picture of a conic section in the foreground; but the artist, who improbably signed the work “A. Christ”, doesn’t offer much of math in the dreamscape.  Still, it is a rare depiction of someone dreaming about math. 

Notes
1. "I woke up with a lovely tune in my head. I thought, 'That's great, I wonder what that is?' There was an upright piano next to me, to the right of the bed by the window. I got out of bed, sat at the piano, found G, found F sharp minor 7th -- and that leads you through then to B to E minor, and finally back to E. It all leads forward logically. I liked the melody a lot, but because I'd dreamed it, I couldn't believe I'd written it. I thought, 'No, I've never written anything like this before.' But I had the tune, which was the most magic thing!" from Barry Miles (1997), Paul McCartney.
2.  this is really a great sheet of paper, coming from issue 4492, pp 518-519.  Two pictures of dreams on one side, with three visionary images on the other (the Gibraltar dam, a sub-polar submarine, and a futuristic Indian railway/bridge.

An Episode in the History of Anticipation: Death at Archimedes' Door

JF Ptak Science Books   Post 1665

Earlier in this blog there appeared an entry on the death of Archimedes--actually, it was a piece on an image depicting the killing of the great mathematician.  It is a pretty gruesome affair, even by the very early 18th century standards under which the engraving was made--gruesome still by today's standards, what with the man's head being cleaved laterally in two by the summoned Roman Centurion. I'm not an historian of these images of Archimedes, but I can say that for whatever I am, I have not seen anything quite so graphic dealing with the man's death.

The usual images of Archimedes coming to his end show him working a problem in his dust/sand/earth "chalkboard", absorbed to such an extent in his thinking that he doesn't hear the chaos outside his rooms, and doesn't sense the approach of the soldier who finds Archimedes unresponsive to his calls and therefore a threat, and so kills him.

[Image source:  Titus Livius, Romanae historiae principia, libri omnes.  Printed in Frankfurt by Feyerabend, 1578.]

Looking at this image (above) brought to mind another in the history of anticipation--not knock knock knocking on Heaven's door, but the opposite, and the opposite of that, the opposite of  knocking on Death's door, or at Death's door:  Death knocking at our door. 

The title of this emblem--Cunctos mors una manet/death is all that remains--is meant to remind us

of our common foe.  It is the work of  one of the great engravers of his time, Otto van Veen (teacher of Rubens),  and appears (along with next image and 100 others) in his Q. Horati Flacci emblemata.  Imaginibus in acs incisis notisque illustrata, printed in Amsterdam in 1607 by H. Verduss.

--All images and most translations courtesy of the splendid work at The Emblem Project/Utrecht, here.--

Part of the legend (which appeared in four languages) of the image leaves us with the following reminders, choice bits on the folly of forgetting our common end:

La terre embrasse tout comme mere commune --Mother Earth embraces us all

Moritur sutor eodem modo ac Rex.--The King died the same as the shoemaker

Death is the thing that sucks the rivers of lives, "Del rico al pobre, del soldado al Papa", From rich to poor, soldier of the Pope.

and so in image and word telling us that death will seek us out, whether king or shoemaker, rich or poor--and that in the coming end the Earth will take us all.  Archimedes didn't hear that one coming; nor did he care, I think. 

THis last image brings to mind Archimedes' work in the dust, though the intent of teh emblem ("Estote prudentes" //Be ye therefore wise // Be Cautious) wouold have been completely lost on him.

The legend translates (Thanks to the Emblem Project for this):

When the serpent sees that it is going to be attacked with, Lethal wound, it protects its head with artful care. Here lie the dwellings of the soul, the sanctuary of the truth. Hence comes life that is to be hoped for by every body.

Surely Archimedes could relate to his lines and the expressions of his thought as the dwellings of his soul (if he actually believed in a soul), though I guess you could say that the artful deception of the serpent's head finally wound up killing him via the Roman soldier.

Letali serpens cùm se videt esse petendum
Vulnere, sollicita contegit arte caput.
Hîc animæ sedes positæ, verique recessus: (here placed the seat of the soul, in artful covering...)
Hinc spiranda omni corpore vita venit

In any case I was drawn to the similarities of these two events, and the bit of anticipation that seems common between them. 

An Episode in the History of Multiplication

JF Ptak Science Books  Post 1657

 

Many thanks! to Ray Girvan and Thony Christie for solving this multiplication problem!

Ray Girvan (JS Blog--Journal of a Southern Bookreader) http://jsbookreader.blogspot.com/2011/11/taglientes-multiplication-by-columns.html

Thony Christie (Renaissance Mathematicus) http://thonyc.wordpress.com/2011/11/10/1202/

Giovanni Tagliente was many things, though perhaps he wasn't mathematically inclined, not really.  He was however a very capable putting together books and addressing some elementary needs of the working classes  that reached out into the mass of the great unwashed offering instructionals on how to do the basics of--in this case-- applied mathematics, as with this book, Libro de abacho...¹, this edition printed in Venice in 1564.    This was a  small, pocket-sized book², a references on how to do the stuff of daily (and not so daily) calculations, and in principle was a concise, Humanist guideline for getting through the daily bits of the calculating and mercantile life.

The above image is a woodcut diagram "explaining" how to do multiplication.

To the 21st century eye however the actual explanations of how to conduct Tagliente's approach to actually "doing" the math might not be so evident.  They seems to be inspired acts in helping the reader understand the process, say, of multiplication, though it does appear a little mysterious, and explanations for the actual process are--as the author(s) says--self-evident in the woodcut, and are not elaborated in the text. 

I've been unsuccessful thus far in determining how the product to the problem of 9876 x 6789  (67.048,164) was reached via adding the individual results of the factors' multiplications,  though seeing the individually parts of the calculation is apparent³ (explained below).

I thought that this would be easier, because it was after all easier once upon a time, at least to people not me. 

I think that I get a D+ on this one.  All I really wanted to say is that Tagliente's diagrams are pretty. 

History of the Future--John von Neumann's Crystal Ball & the Computer, 1949.

JF Ptak Science Books   Quick Post

John von Neumann contributed a major piece of prescient thinking in the 1949 volume of Proceedings/Computation Seminar, December 1949, assembled by Cutherbert Hurd of the IBM Applied Science Department. [The entire contents of the volume is available here.] Von Neumann (1903-1957)--perhaps the most advanced mind of the 20th century, a man whose work made the other advanced minds say "how did he do that?"--was a staggering polymath who made contributions in many fields, not the least of which was in the creation of the modern computer.  His one-page contribution to this volume was a deep  insight into the possibilities of the machine.  In 1949. Check out this terrific piece by the great Claude Shannon, "John von Neumann's Contributions to Automata Theory" here.

Mother Goose for the Space Age (1958): "I Have Thunk, So I Cannot Am!"

JF Ptak Science Books  Post 1633

The history of Mother Goose--but real and imagined--is a long and winding story, the blending of the old stories to more modern times almost as odd as the stories themselves.  This entry is what I think is the first "Space Age" version of the tales, though mostly it concerns itself with the ideals of Mother Goose more so than the stories themselves. 

The physics-esque approach to the old idea rests in the verses of Frederick Winsor in his The Space Child's Mother Goose, printed by Simon and Schuster in 1958, the stories helped along by some fine and tech-intricate drawings by Marian Parry.  The poems are occasionally delightful as works in themselves; but when you grade the work on a curve of science poems/funny science, it gets an even higher grade.  Let's face it--there weren't that many works in this genre in the 1950's/'60's, so it gets a little help just for being a friend to the lonesome in the pop-science-poem arena.  (The text for the volume can be found here; and if you wanted to own it you may purchase it from our blog bookstore, here.)

 

Did Galileo Know That He Was Galileo?

JF Ptak Science Books     Post 1610

Here's an interesting lead sentence I found in 3QuarksDaily via Salon:

  "Karl Marx did not know what we know: he did not know that he was Karl Marx."

The author suggested that Marx would've had a better time in his life had he known what influence he wielded in what he was writing--basically, Karl Marx didn't know that he was KARL MARX.  It is an interesting--and frightening--idea to think of someone laboring like that laboring (as it were) away in relative obscurity, or at least relative to the monumental influence it would come to have.

The real question is not how many people might be in this category of not knowing who we know them to be, but if everyone is in this category at one point or another, and how long it took for them to understand the lasting significance of their work.  But for right now I'm interested to know what people think of the following ten science personalities, and to answer (in a simple survey), if they knew the significance of their work.

The survey is simple and fairly straightforward, and asks questions regarding Copernicus, Harvey, Galileo, Einstein, Maxwell, Newton, Turing, Darwin, Lucretius and John Von Neumann. 

You'll have a chance to view the survey results at the end.  Thanks!

Follow this link to the survey.

 

Buried by the Numbers--Literally

JF Ptak Science Books   Quick Post

A metaphorical statement is not often seen in its literal sense, graphically displayed--especially in mathematics.  But I did stumble across this example in the 15 June 1885 issue of Punch, or the London Charivari.  It was used to illustrate an inglorious poem on an inglorious topic that we don't need to go into just now, but the tail-piece does exhibit the curious image of being buried by numbers.

 

History of Lines--a Note on the First Appearance of the Addition ("+") Sign

JF Ptak Science Books   Post 1575  [Part of the History of Lines series]

The history of lines is full and rich with symbols, some of which have absolutely nothing to do with the extension of trust and belief and hope and fear--unless you're a young student studying math or chemistry or physics.  One symbol in the maths that seems to have no exact age except to say that it is semi-ancient is the addition sign.  (It will be interesting in this series on the history of lines to address the origins of  other symbols like the sign for pi, division. multiplication, percent, inequality,  equality and so on.)

I say "semi-ancient" because the symbol for addition is a hieratic form of the Egyptian hieroglyphic, looking like a capital "A" in a way, without the horizontal crossbar.  The earliest appearance of a symbol for addition in Europe was in the 13th century, with the letter "p", appearing in various forms, as well as the word "plus", "used in connection with the Rule of False Position"¹.  The concept also appears as the word itself, as "et", or "and", which just so happens to closely resemble the symbol that the concept would become a few centuries later.  The earliest appearance of the symbol we would recognize instantly today as an addition sign came in the 1489 book by Wideman, the Behenunde und kuepsche Rechnung (seen above in detail and in full, from the 1532 edition of the work), while the first time the "+" appears in an algebraic equation for the first time 25 years later, in a work by Vander Hoecke.  

It is interesting to think of the life of these symbols before they became themselves. 

I am not certain of this, but it seems that the first "+" printed in the United States did not occur until the 20th edition of James Hodder's² Arithmetic³ was printed in Boston in 1719, and this at the press of James Franklin (1697-1735), the fourth child of ten in the Franklin family that included Benjamin (1706-1790).  So it is entirely possible that 13-year-old Ben helped his older brother print the first addition sign in the British Colonies. 

Notes:

1. D.E. Smith, The History of Mathematics, volume II, p. 397

2. Hodder in 1672 wrote "note that a + (plus) sign doth signifie Addition, and two lines thus = Equality, or Equation, but a X thus, Multiplication," no other symbols being used."  (Smith p395)

3.  In his introduction, Hodder says:

Are there More People than Knots? Finding the Structure of Matter in Smoke Rings

JF Ptak Science Books   Post 1541 (Part of the Series Blank, Empty & Missing Things.)

Embedding a circle in 3-D Euclidean space is another way of looking at a simple and substantial elements of human activities.  Knots have played a large role in human history over a long period of time--not just for connecting things, or determining speed, but also in design, the appearance of, say, objects that would later be known as  Borronean rings that appear in Tibetan Buddhism (endless knots as keys to infinity) to the Celtic knots (decorating, say, the Book of Kells).

Gauss did very early work (1)-as is so often the case-- on knot theory, as did William Thomson, Lord Kelvin,who visualized atoms as knots in the aether and who was perhaps inspired by P.G. Tait's experiments on smoke rings (2)  and who in turn had been influenced by  a paper of Hermann von  Helmholtz on vortex-rings in incompressible fluids, and organized the  stability of chemistry around this pricnipal.  In turn  P.G. Tait based his very solid work on knot theory in 1867 on this work of Kelvin and von Helmholtz. .(Kelvin's theory (3) was rather well received for several decades until it was not, but it did enjoy the support for a time by J.C. Maxwell.  Kelvin was a brilliant man who I think is too often remembered for some of the few hundreds of the millions of words that he wrote and lectured, not the least of which were his pronouncements at the every end of the 19th century on the impossibility of heavier-than-air flight.)   Tait--who also co-authored a very well respected textbook on Natural Philosophy with Kelvin--moved on to firmly establish knot theory and on the elements that makes knots different, formulating tables on how knots form, and in essence believing that he was fabricating a table of the elements. All of this work suffered a fatal blow when the great Michelson-Morely experiment (1887) (4) failed to detect the luminiferous aether. 

 

• [The first page of how knots come to be as they appeared in P.G. Tait's earliest work, though he by necessity kept the investigations to  relatively minimal degree: "We find that it becomes a mere question of skilled labour to draw all the possible knots having any assigned number of crossings. The requisite labour increases with extreme rapidity as the number of crossings is increased. ... I have not been able to find time to carry out this process further than the knots with seven crossings. ... It is greatly desired that someone, with the requisite leisure, should try to extend this list..."]

This was the beginning of the tabulation of knots, found in Tait's beautiful work.  To date some 7 billion tabulations have been identified, a number nearly equal to the of the world's population. Knot theory has taken shape as an area of study within the field of topology, which was developed in the 1850's through the 1870'sby Riemann/Listing/Mobius/Klein and then which received its algebraic foundation by Henri Poincare (5) just af ew years after Michelson-Morely and in the same year as Roentgen's x-ray, 1895.

Notes

1.  The Gauss linking integral,1833, carried forward by Johann Benedict Listing.

2. An interesting modern recreation of the Tait smoke ring experiment can be seen here. See malso: Silliman, Robert H., William Thomson: Smoke Rings and Nineteenth-Century Atomism, Isis, Vol. 54, No. 4. (Dec., 1963), pp. 461–47

3.  Lord Kelvin, Sir William Thomson, "On Vortex Atoms", Proceedings of the Royal Society of Edinburgh, Vol. VI, 1867, pp. 94-105. Reprinted in Phil. Mag. Vol. XXXIV, 1867, pp. 15-24.

--It was also Kelvin (along with A.A. Michelson) who spoke on the finiteness of physics, with Kelvin in particular stating at a British Association for the Advancement of Science meeting in 1900 that there would be nothing new in physics, and that all that was left was measurement.  I seem to remember a story about one of Einstein's uncle's (?) warning him against going into physics because there was nothing left new to do...I can't remember if this was before or after Roentgen.  In any event, Kelvin's statement was five years after Roentgen, but it didn't stop him from making his claim. 

4. On the Michelson-Morely experiment.

5.  H.Poincaré, "Analysis Situs", J. Ec. Polytech ser 2, vol 1 (1895) 1-123.

--The Journal of Knot Theory and Its Ramifications was founded in 1992, establishing a journal devoted purely to knot theory.

A Note on Teaching Math, Unexpected Art, and Picturing Things Differently

JF Ptak Science Books   Post  1427

Stereo viewing geometrical figures may or may not be useful--I find it a little off-putting, creating a slight dizzying effect, though I'm sure it helps others (particularly children?) see complex geometrical figures a little more easily., especially when it comes to crystalography images. Education was certainly what Henry Vuibert , the author of Les Anaglyphes Geometriques had in mind when he published the work in 1912.  He had a long history in mathematics education, having founded the firm that bears his name back in 1877, a publishing house specializing in school texts in the maths, physics and general sciences.  (We offer the book for purchase at out blog bookstore.)

Vuibert's book is a very early example of the use of the anaglyphe--examples of the use of the method go back to the 1850's, when d'Almeida used a version of the idea to punctuate lectures using a magic lantern; the (printing) process of the anaglyphe wasn't patented until the 1890's by L.D. DuHaron.  It does confuse me or remind me quite a bit of Oliver Byrne's beautiful monster The First Six Books of Euclid in which coloured diagrams and symbols are used instead of letters for the greater ease of readers... printed at the Chiswick Press by C. Whittingham for William Pickering in 1847.  The book is, well, unusual and probably not at all usefu1¹.  Bryne replaced all of the algebraic notation, identifying letters and almost all of the descriptive text with color and color codes, leaving Euclid mysterious, hidden, awkward, impervious, and, yes, beautiful². As a matter of opinion this work presages the cubists (and especially Piet Mondrian) by 60 years, and all by accident artwork. 

 

 

 

 

 

 

 

 

 

 

 

There are certainly much earlier works that tried to get at a fuller representation of geometrical objects, not the least of which was a 16th century Elements of Euclid in which the figures were cut-out paper, pasted into the book and attached to a string so that the reader could pull out the illustration and see it displayed in three dimensions. The elements of geometrie of the most auncient philosopher Euclide of Megara. Faithfully (now first translated into the Englishe toung…³, printed in London in 1570, was no doubt a great and exasperating labor of love, a complex "pop-up" book accomplished with sixteenth century technology.  (The photo below shows the Smithsonian Institution's copy.)

Of course there's the very old fashioned way of representing mathematical concepts, and that's with sticks and stones and blocks and such.  For visceral memory and practical applications, the idea is hard to beat, unless of course, you really beat it , which is difficult to do.  But to me that's just what Major G. Mackinlay did in his Realistic Arithmetic,  for Teaching Children the Elements of Arithmetic by Means of Special Blocks⁴, published in London in 1900--his ideas for the use of blocks was very sound and stable; his instructions (and in particular his illustrations) for what to do with the blocks was not.  I am reminded of inscrutable, badly translated and designed instructional manuals for tech stuff that need a manual for the manual. 

Here's one of the folding plates describing how to assemble the blocks:

Then there are other sorts of wooden (and etc.) three-dimensional models, such as the (600+) gorgeous geometric designs housed in the Institute Henri Poincare, transferred there from the laboratory of geometry of the Faculty of Sciences of the University of Paris in 1928⁵.  Most of these models were constructed around the time of vast change in mathematics and art (1900-1920), which means that many of them predate the revolutionary ascensions of  Cubism and non-representational art.

And as long as were at the point of unintentional and under-recogniozed epochal works, I think that there is a broad book that could be done on exactly this topic, calling into play such examples as Georgina Houghton, Victor Higo, Emily Vanderpoel, and many others. 

Georgina Houghton, for example, produced this non-representational painting in 1870 (or thereabouts):

 And Victor Hugo, from the 1860's

And Emily Vanderpoel (1900 or so):

In another, much earlier case of removing detail and adding abstraction for the sake of simplicity in representing an idea,  Erhard Schoen, in his Unnderweissung der proportzion und stellung der posssen liegent und dtehent, printed in Nurenberg  in 1538, presented these cubed figures (below).  He used simplified geometric form to stand in for the curvy humans, replacing them with proportional stacks of boxes which would more easily explain to the younger reader how to represent the human body in space and in proportion to other things. 

I think that these were monumentally combative images showing humans in a radical, previously unknown way, much like the moving-through-space-and-time photographs of the somewhat forgotten Etienne Marey, who in the 1870's created what was essentially the world's first "slow motion" device. One iteration of Marey's apparatus was basically a long series of ganged cameras recording a motion for a simple task at a given time frame and presented on a continuous strip of photographic paper, sort of like a motion picture with the camera speed set at three frames per second. The resulting images were phenomenal and showed people for the first time the exactness of all manners of simple motions--motions that no longer looked so "simple" once all of its aspects could be studied from captured photographic evidence.  Even the act of hopping over a small stool or bending to pick up a bucket of water were enormously revealing in a way like Robert Hooke's Micrographia displayed the great detail and complexity of the seemingly simple fly.  Perhaps the most famous of Marey's series of images was that of a galloping horse, which also for the first time revealed what exactly the horse's legs were doing and proving that almost every painter in the history of art represented the galloping horse incorrectly.  His series of photographs (as in this sample below) show a fairly close fit to the work of the futurists (like for example Duchamp) who would come into being after another four decades. 

  And Duchamp's Nude Descending (1912):

 

I do want to make it clear that this is just a simple note, a thinking-out-loud piece on how attempts to visualize things differently for the sake of explanation or education can come "unintentionally" close to what would become epochal works.  More later.

Notes

1. Augustus De Morgan, mathematician and logician, wrote a very highly critical book A Budget of Paradoxes in which he describes hubbub, fakirs, frauds, perpetual motion machines, squaring the circle efforts, millstones and other useless books in the maths, and in here he sniffily dismisses Byrne's work. At best, to De Morgan, the Byrne book is "curious". But useless and curious, as I have seen many thousands of times, does not mean that it can't be attractive and beautiful, and the Byrne book is probably the leading candidate in the Bad & Beautiful category.

2. In his Victorian Book Design McLean calls the Byrne book "...one of the oddest and most beautiful books of the whole century...a decided complication of Euclid, but a triumph for Charles Whittingham [the printer]".

3.  This is also the first appearance of Euclid in English.  The full title: The Elements of geometrie of the most auncient philosopher Euclide of Megara faithfully (now first) translated into the Englishe toung by H. Billingsley, citizen of London; whereunto are annexed certaine scholies, annotations, and inventions, of the best mathematiciens, both of time past and in this our age; with a very fruitfull praeface made by M.I. Dee, specifying the chief mathematicall scieces, what they are, and whereunto commodious; where, also are disclosed certaine new secrets mathematicall and mechanicall, untill these our daies, greatly missed. London, Imprinted by I. Daye, 1570.

4.  From the Report of the Annual Meeting of the British Association for the Advancement of Science, 1906:

 

5.  From the IHP website:  "Most of the models  were created by Martin Schilling in Leipzig between 1900 and 1920 and  a few of them  (in wood)  were made between 1912 and 1915 by J. Caron, Professor of Descriptive Geometry in charge of  the "graphic work" course at the ENS at the beginning of the century (between 1912 and 1915)."

Also this:   "In the thirties, the surrealists, led by Max Ernst, were interested in these geometric objects. André Breton alludes to them in  "Crise de l'objet" , an article  in the magazine  Cahiers d'Art (May 1936, No. 1-2, p. 21-26.). Man Ray took photographs of the models, which where published in same issue. He would later use them to compose what he called  "Shakespearean Equations". Many artists, painters, architects and sculptors drew inspiration from them."

The Alpha and Omega of Computer Questions; Asimov, 1953 and 1955

JF PTak Science Books  Post 1375

 

Following up on yesterday's post on the world's first (popularly-published) computer magazine (Computers and Automation)  is this Isaac Asimov short story on what might be the first great computer question.  The story in mind, "Question", appeared in the March 1955 issue of this same magazine, a two-pager sandwiched between an ad for Remington Rand UNIVAC and an article on computers and weather prediction.  It is the first appearance too of Asimov's massive computer of the future, Multivac, a giant machine with corridors and nooks where technicians could stop and have a seat to enjoy a cup of coffee.  And it seemed to at least one worker that it wasn't quite right to be sitting inside the machine, that the billion-tube, two billion relay computer was more than just a flow of electrons. (The ENIAC, which was basically the world's first computer, had 20,000+ tubes, so a billion as  conceived by Asimov would've been a very big machine indeed, a 500,000-ENIACs-sized behemoth.) And a very hot one.   The workers wondered if you could ever tell if the machine was alive, if it thought on its own, if it attacked aparat from its instructions and programs. 

As it turns out, the answer was positive, and not only that, but Multivac could speak.  Its answer to "the question" was "who...am...I...?", repeated several times in the closing sentence of this rocket-fast short story.  I guess that that would give you pause, as it would anyone had the question come to them from their own computer while communicating along the spine of the great global "mind", the Internet, and perhaps someday it will, at some time in the near-ish future when the height of our own computer-y heights looks as quaint to them as a half-million ENIAC idea of 1955's premier scifi writer looks to us today.

I know almost nothing about Asimov, but he seems to return to this idea of the Big Computer, Multivac, and ultimate question a few years later.  It seems as though there was an issue of serendipity involve with the structure of the "Question" story and that of another writer's ending for a story called "Problem for Emmy" by Robert Sherman Townes. Asimov admitted the similarities but also maintained that he didn't know of Townes and had never read his story--be that as it may, Asimov promised that he would never reprint the story, and it seems as though he never did.  But it looks as though he resurrected his idea somewhat, which is fine, because the whole idea of ultimate/penultimate questions and massive computers is a great genre. 

Asimov wrote a story called "The Last Question" in 1956, a year later, writing about a trillion years of human history in the space of another terrifically-short short story, the short story that Asimov found to be his own favorite.  If "Question" posted the ultimate question put to the super-colossal Multivac computer,  ultimate question in "The Last Question" may well then be the ultimate answer.  You'll have to see the ending of the story for yourself to see what it was--I can't spoil it. 

Notes:

1.  I'm just a little surprised that Asimov was hung up on tubes in 1953--transistors had been in the air by 1947/8, published in 1948, and pretty-published by 1952.  I figure he should've been aware of them and how they would transform computer construction.  Maybe not. Perhaps he just wanted to write about a billion-tube computer. "Multivac " stands for "muliple vacuum tubes", and then "multiple vacuum tubes analog computer", so using transistors might be a little at cross-odds with the name and the idea of the machine.  It woulod be interesting to put together a list of questions/answers of these early fictional machines, a longlist of which appears here.

2. The two characters in the story by the way are named "Alexander Adell and Bertram Lupov", both of which suggest the name Alexander Graham Bell to my head.

 

The World's First Popularly-Published Computer Journal

JF Ptak Science Books   Post 1374

Nothing quite gives you the taste for the ancient history of a very modern topic--like computers--than by looking through some of the earliest popular publications on the subject. This can actually be done pretty quickly if you wanted to just get a broad taste for the subject in its modern infancy--just reading the titles of the papers and taking in the advertisements might be enough. So here's two volumes of a very scarce and interesting journal by old Edmund Berkeley that may do this job perfectly.  Berkeley was a bona fide mover and shaker in the early days of electronic computing in the United States--he had a lot on his mind, contributed many written words and ideas, and also tried to make a fair living while doing so (there was a bit of Sideshow Ed in him for some of the things he tried to sell.  

Computers and Automation, the brainchild of the brainy not-child Edmund Berkeley, was the first popularly-published  magazine published regarding the computer, its applications, it programming, and really just about everything else.  (It appeared seven years after the Mathematical Tables and Aids to Computation  was published in 1943, almost entirely to the mathematics and engineering communities.) Computers was published by Edmund Berkeley & Associates in NYC beginning in 1952., beginning its publishing journey as The Computing Machinery Field, its name changing to Computers and Automation in February 1953 (in volume 2, number 2).   All issues have some fair space devoted to advertising, even though the issues generally ran between 32 and 40pp. Berkeley was a real-enough mathematician, engineer and computer pioneer, but he also had a pretty large taste for making these interests pay--which was essential, as the original print runs were not very large, though his advertisers were impressive. (According to the first issue, approximately 1200 people were on the mailing list for the journal, with around 2000 issues being printed each number. All told, this is not a large print run, and thus not many of the early issues have survived.)  He was not averse to being somewhat outre with his journal—in addition to having contributors like Grace Hopper and Alton Householder, he also had Fletcher Pratt and Isaac Asimov writing some pretty arresting pieces from the SciFi/Futurama point of view.

A Note on the Advertisements: in short, they’re wonderful. For example, on the back cover of vol2/1 is Edmund Berkeley & Associates “SMALL ROBOTS”, advertising “Simon, the Mechanical Brains”, “Squee, the Robot Squirrel”, and other gadgets. To give you an example the other ads in this issue alone are for “The Circle Computer”, “General Ceramics Ferramic Cores”, “Magnetic Metals Co. Amplifier Cores”, Ross Ashby’s “Design for a Brain”, Consolidated Engineering’s SADIC System, Monroe Calculator’s Monrobot Electronic Calculator, George Philbrick’s “Computor (sic) products”, and a lovely two-page spread for Remington Rand. Further into the year are ads for Burroughs, IBM (604 ands 607), Electronic Associates Inc, Prokar capacitors, and many others.

Some of the subjects include: The ERA 1103 computer, NIMWIT, Applications of the Computer, what the computer *is*, Admiral Grace Murray Hopper’s compiler, mechanical translation, Harper’s subroutines, the cost of coding, computer “self-repair”, automation at Ford, and so on.  Also includes perhaps the earliest announcement of the first all-transistor computer (October 1954, IBM’s “new experimental transistorized computer” , the earliest (?) printing of Asimov’s Three Laws of Robotics in a scientific journal, and more.

Each section generally has three of the following categories (per issue) : computer glossary, roster of member organizations, who’s who, an annotated books and journals section, and other aligned concerns.  For example, there's this bit, an application (cut-out) card for "Who's Who in the Computing Field for December 1952"--utterly simple, it seems as though anyone who filled out the card was in, the "who's who" part of this that we normally celebrate with fame or achievement really was just telling the rest of the people in the field who was exactly who.

The contents:

Volume 2/1, January 1953. 45pp.

Householder, A.S. Brains, Electronic and Otherwise; Williams, S.B. (President, ACM) What Computers Do; Murphy, E.F. and E.C. Berkeley. Automatic Computers on Election Night.

Volume 2/2 , March 1953. 37pp.

Boehm, George A.W. Gypsy, Model VI, Claude Shannon, Nimwit and the Mouse; Paynter, Henry. Water and Computers; and the editor Berkeley, The Concept of Automation, and Berkeley (with Neil Macdonald, Berkeley’s other name). The ERA 1003 Automatic Computer

Volume 2/3, April 1953. 40pp.

Fletcher Pratt, The Art of Solving Secret Ciphers and the Digital Computer; Berkeley, Avenues for Future Development in Computing Machinery;  Gene Hegedus, Hungarian Prelude to Automation..

Volume 2/4. May 1953. 33pp.

Grace Murray Hopper,  Compiling Routines; A.D. Booth, Mechanical Translation; Marshall Stone,  Medical Diagnosis.

Volume 2/5. July 1953.

Yehosuha Bar-Hillel (the great logician),  Machine Translation; George Boehm, Robot Traffic Policemen; Rudolf Flesch,  How to Talk to Computers.

Volume 2/6. September 1953.

Tommaso Fortuna,  The Soviet Union: Automatic Digital Computer Research.; Wainwright, Lawrence Wainwright,  Digital Computer Questionnaire; and a general DISCUSSION: “How to Talk About Computers”, with GG Hawley, Samuel Scharff, C.B. Crumb, and EC Berkeley.

Volume 2/7. October 1953. 36pp.

Brown, David W. Brown Computers in the Factory; Neil (Berkeley) Macdonald,  The Flood of Automatic Computers. 

Volume 2/8. November 1953. 40pp.

John W.Carr  III. Who Will Man the New Digital Computers?; E.F. Cooley,  Electronic Equipment Applied to Periodic Billing; Glenn.Hagen,  Air-Floating: a New Principle in Magnetic Recording of Information.

Volume 2/9 December 1953. 36pp.

Clippinger, Richard Clippinger, How a Central Computing Laboratory can Help Industry; R.T. Wiseman, “Combined” Operations in a Life Insurance Company instead of “fractured operations”.

These are the contents for 1953; the volume for 1954 bulks up a little, but is still under an inch thick.   The MTAC journal stays quite slender throughout its pre-1960 life (it has virtually no advertisement and is entirely academic), and there are more and more computer articles appearing in old stand-by associated journals like the Proceedings of the Institute of  Radio Engineers (which by 1959 will published a massive supplemental volume called "the Computer Issue" which I'll talk about soon.  For the time being, I just wanted to make an inroad into this journal--I'll expand on he articles in just a bit. 

An Elementary and Perhaps Useful Cheat Sheet for Names of Big Numbers

JF Ptak Science Books

I thought to include this little cheat sheet for the names of large numbers—I didn't know the name for some big number, and had to go and find it. Here's a bunch that I cobbled quickly together to serve as a recipe should you ever need a big-number-name and not know it.  I've only used the modern American and British versions of these names, and I've avoided numbers that just won't work for me here (as I'm just looking for simple stuff) like

(~ googolplex^{1,941,887,670,000}), (years),  which is the "scale of an estimated Poincaré recurrence time for the quantum state of a hypothetical box containing a black hole with the estimated mass of the entire universe, observable or not, assuming a certain inflationary model with an inflation whose mass is 10⁻⁶ Planck masses."  so says University of Albert physicist Donald Page, quantum cosmologist and Stephen Hawking co-author. 

A googol is already a big number at 1x10¹⁰⁰; a googolplex is terrifically larger, being 10^googol,  or. 10(10¹⁰⁰).

I've left out almost everything, actually, including the beautiful numbers from ancient India, including the sublimely-named "untold" as exactly 10^10*2122  appearing in Bodhisattva's maths in the Avataṃsaka Sūtra..

Hindu theology incorporates spectacular leaps of time, numbers which jump geometrically, reaching ever greater heights, describing a small part of a small bit of teh beginning of the Cycle of Brahma.  (See far below.)

I'll save the suspense—the largest number identified here is 1x10^3003, which is a millinillion, and it looks like this:
100.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000. 000.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000. 000.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000. 000.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000. 000.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000. 000.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000. 000.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000. 000.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000. 000.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000. 000.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000. 000.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000. 000.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000. 000.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000. 000.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000. 000.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000. 000.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000. 000.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000. 000.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000. 000.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000. 000.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000. 000.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000. 000.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000. 000.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000. 000.000.000.000.000.000.000.000.000.000.000.000.00 0.000.000.000.000.000.000.000.000.000.000.000.000.

000.000

 And the rest (I'm sorry to say that one cannot make columns in typepad posts):

10⁶ Million

10⁹ Billion

10¹² Trillion

10¹⁵ Quadrillion

10¹⁸ Quintillion

10²¹ Sextillion

10²⁴ Septillion

10²⁷ Octillion

10³⁰ Nonillion

10³³ Decillion

10³⁶ Undecillion

 

An X-Ray of Cubism? Jouffret and Visualizing the Fourth Dimension, 1903 and 1906.

JF Ptak Science Books   Post 1361

Is this an X-Ray of Cubism?

Emile Jouffret brought an amazing and lovely pair of books to the mathematical dining table, both coming at about the mid-point of a period of perhaps the most sweeping multidisciplinary revolutions in human history.  Published in 1903¹ and 1906² [and both originals available at our blog bookstore] they both may have had an impact as a visualization tool for the newest movement in art since the creation of Impressionism (1850's-1870's): Braque and Picasso's  Cubism. When you compare the illustrations in the Jouffret books you cannot help but to see a connection to the work of (the morally-lonely) Picasso (and especially in his 1910 portrait of the movement-molding art dealer Ambroise Vollard, below). Georges Braque and the that the two would make in 1906, the first year of the Cubist movement. 

Jouffret's 1903 book was hardly the first on the topic, though it may be the first of the major, book-length treatments of the topic, as well as the most  heavily illustrated.  Thinking on the fourth dimension goes back as far as Kant, at least, and the real work begins in the first half of the 19th century.

The first major³ work arrives with Hermann Grassmann's "Die Lineale Ausdehnungdlehre" (Theory of Linear Extensions) in 1844 (and the subsequent translations of the work as well as original work by Arthur Cayley); followed by Ludwig Shclafli (1814-1895) "Theorie der vier flachen...." (Theory of Continuous Manifolds, 1852 but not published until 1906), Riemann's 1854 speech (which was not published until 1867 and which appeared translated by William Kingdom Clifford in Nature in 1873, G.F. Rodwells "On Space of Four Dimensions" (Nature, May 1873),  Dodgson/Carroll's  Through the Looking Glass (1872) deep references, Zollner "On Space of Four Dimensions" 

(April 1878 and subsequent publications, and who is referenced in Kandinsky's [difficult -to-me On the Spiritual in Art of 1912), W.I. Stringham (1847-1909) "Regular Figures in n-Dimensional Space" (American Journal of Mathematics, 1880), and E.A. Hamilton Gordon, "Fourth Dimension", April 1887, to name some of the major figures.  And then of course comes Edwin Abbott's Flatland, a Romance of Many Dimensions, by a Square (1884) and Charles Howard Hinton, who published a number of different works beginning in 1880 ("What is the Fourth Dimension?", 1880 plus Scientific Romances 1884, and The Fourth Dimension, 1904) and lasting through the turn of the century.  There is also H.G. Wells, whose The Time Machine began to appear in parts as early as  1894, though it did appear in the same issue of the  Science Schools Journal as the Hamilton Gordon article, in April 1887, as the "Chronic Argonauts"). Wells' also approaches the fourth dimension in "The Plattner Story", in 1896 and The Invisible Man in 1897. Other literary contemporaries of Wells who used the fourth dimension in their work include Oscar Wilde ("The Canterville Ghost", 1891), George Macdonald (Lilith, 1895), and Joseph Conrad and Ford Maddox Hueffer The Inheritors, (1901)--the most convincing and scientific of all of these literary efforts though lies with Wells. From about this point on--from the time that Jouffret enters the scene in 1903--the fourth dimension has become part of the culture, and a popular culture at that...especially after the Cubists begin their assault on visual representation in about  1906.

The Jouffret books are beautiful, and very interesting--they would have been better served with a bibliography, which would have been very nice to have--that said, Jouffret does have a fair number of footnotes to earlier work, so it is not as though his work is without attribution.  But it is a very interesting adventure. (Just a note--the fourth dimension and non-Euclidean geometries would get their first bibliography in D.M.Y. Sommerville's classic  Bibliography of Non-Euclidean Geometry in 1911, which is a must-have for all of those interested in this topic...it is massively packed with all manner of major and minor works as well as obscuriana.  It is not, unfortunately, annotated.)

1. Jouffret, E.  Traite Elementaire de Geometrie a Quartre Dimensions et Introduction a la Geometrie a n-Dimensions. 

2.  Jouffret. Melanges de Geometrie a Quatre Dimensions.  Paris, Gauthier-Villars, 1906.  220pp.

3. Most of the data in this long and winding sentence has been culled from Linda Dalrymple Henderson's terrific The Fourth Dimension and Non-Euclidean Geometry in Modern Art, Princeton, 1983--most of my references come from the first 45 pages or so of her book, which is the Bible of all modern works on the fourth dimension/math/physics/art.