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Passing through a later and edited edition of Jacques Ozanam (RECREATIONS MATHEMATIQUES ET PHYSIQUES, Qui Contiennent Plusieurs Problemes d’Arithmetique, de Geometrie, de Musique, d’Oprique, de Gnomonique, de Cosmographie, de Mecanique, de Pyrotechnie, & de Physique. Avec un Traite des Horloges Elementaires. Nouvelle Edition, Revue, Corrigee & Augmentee... and published in Paris in 1749-1750) looking for possible expansions on what he wrote on the Knight's Tour--a chess/math problem where the knight starting at, say, the center position must be moved to touch every square of the board in 64 moves--I found this little diagram showing the spaces to which a knight may not move:
It seemed just a little unusual to me--not being a reader of chess literature--to see what seemed the negative of the knight's movements on a truncated board. But I guess this is what we calculate and just not entirely "see" while playing.
The original problem in the 1672 edition of Ozanam's Recreations looks like this (and titled "faire parcourir au cavalier toutes les cases de l'echiquer"):
in which the knight starts off life at the top right square (h8) and finishes at f3. In the 1803 edition of the work it is pointed out that the knight can be started from any square and moved 64 times to accomplish this same feat.
Here are four further examples of solutions to the knight problem:
And as they say, many more are available.
A more modern version of the solution, this on a 24x24 grid:
"The name Magic Square, is given to a square divided into several other small equal squares or cells, filled up with the terms of any progression of numbers, but generally ah arithmetical one, in such a manner, that those in each band, whether horizontal, or vertical, or diagonal, shall always form the same sum." --from the very busy Charles Hutton's translation of Jean Etienne Montucla's edition of Jacques OzanamRécréations mathématiques et physiques (1694, 2 volumes, revised by Montucla in 1778, 4 volumes) and the whole thing revised in an English edition of 1844 by the appropriately-names Edward Riddle, and available online at Cornell's collection of historical mathematical monographs.
That was sort of a simple introduction to magic squares, tortured by my note on the quote's parentage. Nevertheless, leafing through a copy of Ozanam's work I found a lovely little (literally speaking, as it is about 1/2 inch by an inch) 3x3 multiplication magic square for the happy sequence of 1, 2, 4 ,8, 16, 32, 64 and 256. (That means that each of the nine numbers may appear only once, and that the product (4096) must be the same for each column and row). It is a nice little problem, and I was just surprised to see it in such spare simplicity.
And since we're at it slightly, a few pages further on I found this nice series of 3x3 magic squares for numbers 1-25:
These also are a half-inch (or less) and about two inches long...they're just very attractive.
But I guess I cannot leave the subject of "pretty" magic squares without referencing a "beautiful" one, and this being one of the earliest inclusions of a magic square in Western printmaking, and surely one of the most beautifully-encumbered one in general, from Albrecht Durer's mega-popular masterwork, Melancholia (printed 1514). The magic square had been around for at least 2,000 years at this point, starting up evidently in China between 650-1000 BCE before making its way west through the Arab lands and then through India, and finally into Europe around the 13/14th century, and then into art prints with Durer in 1514.
[Detail]
I doubt that Abraham's Rees' "Magic Circle of Circles" (published ca. 1814) is "pretty", and I'm not so sure it is "beautiful", but I am sure that it is "elegant".
Ditto his "Magic Square of Squares" (published ca. 1814):
In any event these are just a few samples that I had close to the top of my head--no doubt there are endless others, but these are some that have attached themselves longest to me (with the exception of the Ozanam, which are new).
There is a terrific find on Alex Bellos'website exhibiting Alan Turing's “report cards” for his time at the great Sherborne School from 1926-1930 (and which were transcribed by archivist Rachel Hassall), from the time when Turing was 14 to 19 years old. Turing (1912-1954) I think needs no introduction for his importance to mathematics and computing (and code breaking during WWII), and it is very interesting—thrilling even—to see how his instructors were coming to grips with the developing genius. Even at such a school as Sherborne (a very old school with 39 headmasters overseeing the place since 1437) where the teachers were I am sure familiar with gifted pupils, The comments on the reports of Turing's progressed showed that many weren't quite sure about what Turing was all about. Obviously Turing as a boy was very gifted, but many instructors reported as many hindrances to his intellectual development as there were advances—more, even.
Perhaps people at the school didn't know exactly how to deal with him; perhaps they did, but still at the end of the day Turing had to meet the common standards of the school. Or perhaps not—I really can't tell from the transcripts presented by Bellos and I don't know the intricate history of the school. But certainly as time progressed Turing's abilities were more readily recognized, but early on it seems that his talents didn't overwhelm his many supposed shortcomings, the faults of the parts larger than the whole of what he could accomplish. In instructors' comments across all of his disciplines, Turing was “capricious”, “untidy”, “lacking in life”, “need(ed) concentration”, “depressing unless it amuses him”, “careless”, “absent minded”, “un-methodological”, “slovenly”, (made) “mistakes as a result of hastywork”, and so on. He “could do much better” though one instructor felt that “he may fail through carelessness”. All of which may well have been true—from the outside. These statements may have simply been the result of teachers not being able to reach a boy genius, and perhaps the boy couldn't be reached, at least early on in his academic career.
The statements in general—especially in the maths—I think are fascinating things. It may be easy to judge some of the remarks as intemperate, the teachers unable to clearly see the genius-in-the-making who (70 years later) we can so clearly see today. I think the remarks need more careful consideration than that, and that is where they become interesting.
Here are some selection from reports on Alan Turing, 1926-1930, below; a more full list exists at the Bellos site, here.
Subject: Mathematics
1926. Works well. He is still very untidy. He must try to improve in this respect
1927. Very good. He has considerable powers of reasoning and should do well if he can quicken up a little and improve his style.
____. A very good term’s work, but his style is dreadful and his paper always dirty.
____. Not very good. He spends a good deal of time apparently in investigations in advanced mathematics to the neglect of his elementary work. A sound ground work is essential in any subject. His work is dirty.
____. Despite absence he has done a really remarkable examination (1st paper). A mathematician I think.
____ I think he has been somewhat tidier, though there is still plenty of room for improvement. A keen & able mathematician.
These lovely images weren’t intended to show people living in the Renaissance and Baroque eras how to actually record data on their hands—they were intended rather as templates to show how they could use their fingers and hands for calculating and as memory devices. Much like Frances Yates has shown us so beautifully in The Art of Memory and how info and data was stored in imagined and compartmented palaces in the mind (relying upon images), the hands were also used as a theatre of memory in addition to extended calculation.
These mnemonic devices were necessary—especially during the Renaissance—because of the general lack of and access to affordable vellums or paper and writing instruments. Having notebooks filled with memoir or history o calculation was generally not something that was happening for even the not-wealthy but not struggling class. These mental images were used widely in the areas of religion, palmistry, astrology mathematics, astronomy, astrology, alchemy, music, and other such fields. The first image (from a German manuscript) of the hand-theatre was found and deciphered by Claire Richter Sherman (Folger Shakespeare Theatre) and is religious in nature, an intentional piece of memory for the devoted and for devotions. The needs of religion were splayed out as the hand was opened and fingers flexed, and working from thumb to pinkie, from finger tip and joint—“do God’s will, examine your conscience, repent, confess”, and so on, and above all be content with your lowly penitente stature. If there were 28 of these admonitions or reminders at different points of the hand and you memorized them all, it would be a much simpler time to recall and keep them in order if you merely had to touch a part of your hand where that memory should be to invoke what it was you were supposed to do. Therefore you could theoretically cast about with your creator with your hands in your pockets—if you had pockets.
The next two images (including the enlargement of the hand section) are from a work from 1587 entitled Musique and are attributed to John Cousin the Younger (1522-1597). The basic premise for this device—it seems to me—was to be able to order the different chords of 20 different instruments. Another musical hand mnemonic was the Guidonian hand, a survivor of Medieval times, and possibly named after Guido of Arezzo (a musical theorist), and was an aid to singers learning to sight sing.
The entry for the Guidonian hand in Wiki explains it use rather well: “The idea of the Guidonian hand is that each portion of the hand represents a specific note within the hexachord system, which spans nearly three octaves from "Γ ut" (that is, "Gamma ut") (the contraction of which is "gamut", which can refer to the entire span) to "E la" (in other words, from the G at the bottom of the modern bass clef to the E at the top of the treble clef). In teaching, an instructor would indicate a series of notes by pointing to them on their hand, and the students would sing them. This is similar to the system of hand signals sometimes used in conjunction with solfege…” The final two examples come from Jakob Leupold’s (1674-1727) Theatrum Machinarum (1724)—this was a complex work involving nine sections and addressed the theoretical aspirations of engineering (load, flexure, that sort) and its applications to its daily practitioners. In one section of the book he sought to explain the connections (and correlations) of hand motion and symbolism to the origins of the number systems, carrying it out further still into body language, so that two people conversant in these symbols could talk and bargain between themselves in economic/body terms. Barbara Maria Stafford, in her Artful Science, Enlightenment,
Entertainment and the Eclipse of Visual Education (1994) points out the long history of this tradition, and that it reached far back into misty time: Leupold knew that Appian, the Venerable Bede, and Aventinus had been fascinated by manuloquio, or natural language with the hands. He thus linked counting to a global….medium of prearranged gestures…”
This fine cartoon appeared in the 23 September 1865 issue (page 114) of the London Punch magazine, poking a little fun at the recent meeting of the British Association for the Advancement of Science, which had just finished its 35th meeting in Birmingham. Its attendees and contributors read like a "who's who" of the heights of mid-19th century British sciences (across fields of geology, physics, physiology, chemistry, mathematics, statistics (and economics)): attending and contributing were JC Adams, Airy, Hooker, Thomas Graham, Wheatstone, Nasmyth, Fairbairn, Murchison, Lyell, Huxley, Thomson, Maxwell, Tyndall and of course numerous others (also including foreign members).
Of the figures I can identify in this image are Thomas Huxley and the not-beautiful Richard Owen at top left, discussing the principles of evolution in front of a small audience of skeletal/fossilized monkeys, and standing to their immediate right waving an instrument over chemical elements may be JAR Newlands. I am not sure who is presiding over the numerals at bottom left, but what attracts me the most is the zero is running away, screaming, from the other numbers seated calmly on tiny stools. Seated serenely at center juggling earth/spheres in the geologist Roderick Murchison, who appears prominently in the Punch report--I'm less sure about the two other geologists (one placing the Earth-chunk back into the globe, and the other placing a short-handled shovel into another globe, both in front of an audience of geologist's hammers...are they Charles Lyell and John Phillips?) Above them may be John Tyndall, working with an optical viewer in front of an audience of dividers and a telescope. And above the maybe-Tyndall is a steam hammer demonstrating itself to a set of jackknives and cutlery.
The text is pretty interesting in itself, not the least of which is another visit to the squaring of the circle (having just written about this two days ago), which goes like this:
"A few words on Squaring a Beadle who was arguing in a vicious circle. Illustrated pugilistically. (A portmanteau to itself, including gloves and change of linen."
I should be able to idenbtify these men though I'm afraid I can't; perhaps I'll have a little help with them.
Notes (including the contents of the volume published in 1866 of this Birmingham 1865 meeting):
Well, probably. The ad is by UNIVAC—fives years old at this point—and the lace-cuffed image pushing the virtues of the world's first commercial computer is that of John Napier's abacus, which he wrote about in 1617. The ivory calculating bones/rods method had been seen before in the history of the maths and calculation, but not published, and the idea employed in the elegant calculating device were very old, but Napier seems to have gotten to publish it first. (His work on logarithms is of tremendous importance, far more so than the abacus.)
The word “rabdologia” belongs to the title of Napier's significant book (where the title is the abstract): Rabdologia, or, The art of numbring by rods : whereby the tedious operations of multiplication, and division, and of extraction of roots, both square and cubick, are avoided, being for the most part performed by addition and subtraction : with many examples for the practice of the same ...
And I just want to say that since this ad was UNIVAC and it appeared in the November 1956 issue of the early computer journal, Computers and Automation, that the illustration got the “bones” correct. That is, the calculated product is correct.
The way these rods worked is as follows: in the illustration, the number rod on the extreme left (ranging from 2 to 9) is the multiplier; and the numbers at the top of the other rods represented the multiplicand. So we see that the lace-cuff is multiplying the number “76” (at the top of the two rods to the right) by, say, 7. Simply start writing the answer as follows: take the “2” from the 6 rod for your ending number; then add the numbers on the diagonal directly to the left of the two (4+9=13) and take the 3 and place it next to the two in the tens column, and carry the 1 to the next function, which would be 4+1=5. So the answer: 532. The bones could do more than this, of course, but for right now I'd just like to point out that the ad folks got this right--plus its nice to see a bunch of numbers used in public display that actually mean something. [See the Wolfram site for a nice explanation of how the bones work.)
John Napier's work in logarithms (published three years earlier in 1614) is the work for all time; the Rabdologia however would have been instantly appreciated by people like his father, who was master of the mint of Scotland. That said, I've read here and there that Napier considered his most significant published work to be his A Plaine Discovery of the Whole Revelation of St. John (1593), in which he practiced a theo-chronometry based in the Book of Revelation that among other things in its 300-pages predicted that the world would come to an end in 1688. Or 1700. He evidently considered himself a Theologian first and foremost, and what bothered him most was Pope Clement VIII, who he considered to tbe the anti-Christ--and so complications arose. Win two, lose one.
[I've just uploaded Tompkin's classic/first textbook on the digital computer (High Speed Computing), 1950, to the books for sale section of this blog, here.]
At first glance this math teaching tool looks a little on the obvious/antique/useless side, but I think that there are some good points to it in helping small children understand the concept of what a number "is" and relating the processes of addition and subtraction to the relationship of "numbers" to "things".
And as the inventor points out
and so on...
This certainly seems more beneficial and utilizable than the current practice in my daughter's third grade class, where a simple subtraction problem is turned into a double addition problem employing a number line, all in the name of teaching the children the concept of "number" and doing away with algorithms. I think that by the third grade, the concept of "number" has been established, though the board of edu-selection might be trying to re-visit a lost point of development somehow.
So with my daughter's class,take the problem 456-345= ______
This is made intoan addition problem, 345+ ____= 456.
The addition problem is turned into a number line, with 345 on the left far end and 456 on the right.
The children are told to add the requisite bits to 345 to get to a "zero unit" for each place value, and then add those for the solution to the problem.
So: 345+5= 350, 350+50=400; 400=50=450; 450+6+456. Add the 5+50+50+6= 111.
In this confusion a stab at the heart of understanding the concept of "number" has beenb made.
A step back from this would be a wise move to make.
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.
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 novelFrankenstein... 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.
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
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.
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.
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.)
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!
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.
