A Daily History of Holes, Dots, Lines, Science, History, Math, Physics, Art, the Unintentional Absurd, Architecture, Maps, Data Visualization, Blank and Missing Things, and so on. |1.6 million words, 7500 images, 4.9 million hits| Press & appearances in The Times, Le Figaro, Mensa, The Economist, The Guardian, Discovery News, Slate, Le Monde, Sci American Blogs, Le Pont, and many other places… 5000+ total posts since 2008.

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Author: JF Ptak

Seeing Mathematics as it “Happens”
JF Ptak Science Books (an earlier post from 2008 expanded and corrected somewhat)

I wanted to return and add a bit to an earlier notice concerning a series of drawings that I found utterly fascinating—what seems to be among the earliest illustrations of the active formation representing visualized human thought. (I know that this titling is ungainly, but it seems to be the least inelegant solutions to stating the idea of what the images represent.) In 1873 Miss H. R. Hudson wrote an article¹ on her visualization of numbers–and later and more famously Sir Francis Galton approached this same issue first in an article in Nature² that included a number of fascinating presentations of the “suspended” numbers. Working further through this thesis he greatly expanded it, resulting in a 26-page chapter called “Number-Forms” in his book Inquiries into Human Faculties and its Development ³(1883, with a second edition appearing in 1909). Galton includes another 71 images of visualizing arithmetic, plus others on general images of mental images of numbers and letters—there is also a small but beautiful section on associations between colors and numbers and letters. (These are all depicted in the first four images on this page.)

G.T.W. Patrick (a professor of philosophy at the state university of Iowa) published one of the earliest papers in response to Galton’s work. In “Number-forms”⁴, published in the Popular Science Monthly in 1893, Patrick addresses and expands Galton’s work somewhat, including another eighteen wonderful illustrations of similar images.

But the path back to Galton is not quite a straight one. Galton was initially concerned with imaging of numbers and numbers forms while people were performing mental calculations. Patrick on the other hand asked his subjects if they had associative images in their mind of numbers—formally, he asked them if the number series of 1-9 presented itself in a visual, representative way in their minds. In the second and third parts of his three-part inquiry, he asked the same question about letters and the alphabet, and then, thirdly, if they perceived any sense of color from letters and numbers, and what then what those exact relationships were.

It is interesting that in the studies of Galton and Patrick that over time in each of the subjects tested that (in Galton’s words) the images were “absolutely unchangeable except for a gradual development of complexity”. Since I (like Galton, which is probably the only time I will ever be able to associate myself with this man
in terms of familiar traits) have no such images in my head when I think about mathematics or numbers or letter or words in general, it is remarkable to me on the human scale that people who have these associations would have the same ones time after time. A movable feast, as it were. Of course it would make sense that this reference system would be constant—but for someone that doesn’t ‘see” these images at all, the fact that they are so flowing and lucid and unchanging is simply difficult for me to imagine. (In a few weeks I’ll return to this issue, looking at how some prodigiously gifted people “see” with their special attributes.)

Images below are from the Patrick paper:

Notes:
1. “The nine digits will ascend in a straight line before my mind’s eye, and the larger numbers will slant off at a queer angle”, Atlantic Monthly for February, 1873.
2. Nature, January 15, 1880. Follow the first link to a full reprint of the paper and a short article on it that appeared in this blog.
3. Full text of Galton’s work appears at Gutenberg: http://www.gutenberg.org/files/11562/11562-h/11562-h.htm#1noshow
4. Popular Science Monthly, February 1893 (pp 504-515). Full text of the article by Patrick here: https://en.wikisource.org/wiki/Popular_Science_Monthly/Volume_42/February_1893/Number_Forms I should also note that Patrick wrote a very early paper on the psychology of football in 1903, full article here: https://archive.org/stream/jstor-1412309/1412309_djvu.txt
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Anticipation, History of — Information, Quantitative Display of
Universal Spelling Board, 1889

JF Ptak Science Books Quick Post

I think that this would be fairly straightforward if not a little time-consuming to fabricate–of course the beautiful weariness and worn factor of such a thing would not survive a new version of itself:

[Found in The American Stationer, 17 October 1889, page 980.]

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Technology, History of
Kingdom of Dust: Dancing Dust and Vibrating Membranes

JF Ptak Science Books Quick Post

[Source, “Dust and Sand Figures on Membranes”, T. O’Connor Sloane, Ph.D, Scientific American, 1 April 1893, p 202.]

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Technology, History of
Two Dimensions to Three and Back Again (1588)–a Bit of an Optical Illusion

JF Ptak Science Books Quick Post

Luis Collado de Lebrija, the Royal Engineer of the Army of Lombardy and Piedmont, wrote his superior artillery manual Practica Manuale di Artegliteria and published it in 1588–he was one of the five leading military engineers of the late 16th century. The image below is an interesting one from that book, showing a large cannon bombarding what possibly might be a Turkish city. In any event, the trajectory of the very large shell seems to me to be a little odd at first, looking as though it was shot high and straight up, coming down to the right; but looking at it again, the trajectory is back on track going forward 1000 meters than going up and down. And then, again, another look, and the perspective seems flat again, and back and forth it seems to go if you let it.

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Militaria — Perception — Perspective — Technology, History of
WWI Project: German Poster Painters, 1917

JF Ptak Science Books Quick Post

This is an unusual image, a behind-the-scenes, behind-the-lines, everyday domestic front scene, something showing the war going on in the trenches (so to speak) at home. It shows two civilians working on popular posters for movies (“Die Silbernen Kugeln…”) and fund raising (“Die Deutsche Kriegs Anlehe”) for the German army. The image was found in the May 1917 issue of the (Leipzig) Illustrirte Zeitung:

No doubt there was a lot of this sort of activity going on, in wartime and not, but in my 30 years of travels through the history of illustration I don’t often see these images.

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World War I
A Simpler Explanation in a Complicated Print
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I have long enjoyed Marie Boas (Hall) The Scientific Renaissance , 1450-1630–it is a very fine book that covers a lot of ground and material and time. Skimming through it tonight I came upon an image of the wood engraving of the great pump designed by Jacques Besson (1540? – 1573, an inventor, mathematician, philosopher) that appeared in his Theatres des Instruments, published in 1579. Interestingly Boas writes in the description of the fabulous device that “the elaborate machinery seems unnecessarily complicated for the simple domestic task shown, and suggests the imaginative elements in many Renaissance engineering books”. Which is true–except that I think there is another, simpler explanation for the “simple task” shown: it is what fit on the page. The image is already filled with the machine, with little space left for anything else. So, the simple display; the intention of the illustration is to show the mechanism, and not the result of its employment. I think. Far be it for me to criticize Boas, which I don’t think I’m actually doing–I just think that the display of such a simple result was an outcome of paper and ink.

(http://www.sil.si.edu/DigitalCollections/HST/Besson/besson-toc.htm)

Other excellent works by Boas Hall include:
- Robert Boyle and Seventeenth-Century Chemistry. Cambridge: Cambridge University Press, 1958.
- Robert Boyle on Natural Philosophy: An Essay, with Selections from His Writings. Bloomington: Indiana University Press, 1965.
- Nature and Nature’s Laws. Documents of the Scientific Revolution. London: Macmillan, 1970.
- The Mechanical Philosophy. New York: Arno Press, 1981.
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Prints–looking HARD/deeply at — Technology, History of
The History of Sleep: Tough Going in the Trenches, 1916

JF Ptak Science Books Quick Post

“What hath night to do with sleep?” John Milton, Paradise Lost

Sleeping during front line duty in WWI was a mixed affair, at best–there could be weeks of tedium (even in the Spring) while a soldier’s front line tour extended over four to eight weeks (with about the same amount of time in the other lines of battlefield defense), followed by days or weeks of firing and fighting. In the bad times sleep would come when available, and convenience didn’t necessarily have anything to do with it, as we can tell in this photograph. Here the soldiers are crammed into any little indentation in the walls of the trench, any little bit that would keep them from being underfoot should anyone need to walk the trench line. It was not only the sound of battle and the struggle to stay alive–sleep was assaulted by many other things, even in times of the space-in-between-the-fighting: there was a significant rat issue, there was a potential cascading problem of what to do with human waste, bugs, the wet, the cold (and the wet and the cold), the heat, stench, humidity, and then just general discomfort.

Needless to say that in general, sleep was difficult on the front.

Source: Imperial War Museum. “Soldiers of ‘A’ Company, 11th Battalion, the Cheshire Regiment, occupy a captured German trench. Q 3990 This photograph shows an infantryman on sentry duty, whilst some of his comrades snatch a few moments of sleep behind him. They are in what was previously a German trench at Ovillers-la-Boisselle on the Somme, July 1916.”

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World War I
The Sum of All Dreams–(The Caloric Capacity of Every Dream That Has Ever Been Dreamt)

JF Ptak Science Books Quick Post An entry in the series A History of Blank, Empty, and Missing Things

[From Rex Knight’s odd aether-waves work, Wake Up and Sleep!, 1938]

The good estimate of the number of people who have lived on the Earth is about 100 billion.

I wonder about the resting results in their lives, of their sleeping adventures, of their dreams.

If the average age of all people who have ever lived is, say, 30 years, that makes 3 trillion years of living, or about 1 quadrillion hours.

Let’s say that everybody got six hours of sleep for about 165 trillion hours; and let’s say that people dream, say, five times per not, that makes, again, about a quadrillion dreams.

If we in general burn 50 calories a dream, that translates to about 50 quadrillion calories holding up the dreams of mankind.

I wonder where all those dreams have gone?

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Blank and Empty Things; A History of
The Square in Tintin, Mondrian, & Malevich (1916-1930)

JF Ptak Science Books Post 2584

There are no doubt squares in the general outline of the comic book panels of Tintin–what I had in mind was a very special square that occurs in Tintin’s adventures in the Soviet Union. This was the first adventure of Tintin, and appeared in a serialized form in 1929-1930. We are introduced to the young and intrepid journalist/adventurer here in glorious black and white (this would be the only one of the Tintin adventures that was never rendered in color at one time or another), being sent off to the newish (since 1922) Soviet Union. At the time it was Stalin’s USSR, and things were not–shall we say–going well for the people of the Soviet Union. Tintin’s creator, Georges Remi (“Herge”) was working an anti-Marxist angle for his conservative publisher, and he had no difficulty in supplying story lines to fulfill that need–some of these were exaggerated overall, and some were exaggerated but proved correct over time. The adventures there were difficult, occasionally brutal, and overall not brutal enough.

Herge depicted an unpleasant Soviet Union, working out from the “stinking slum” of Moscow out to the farms that were being destroyed in the countryside. He insinuated threats of violence in voting, death by firing squads, the starving of the peasants, and much else. The deal is that by the time the strip reached its conclusion in 1930 Stalin was already underway in his loudly quiet way in instituting the Great Famine/Holodomor in the Ukraine, and by the end of this created famine–a reverse nuclear weapon of food withdrawal–something on the order of 7 million people would be starved to death by 1934. Then of course came the Great Terror of 1936-8, and the rest of it. Herge may have exaggerated some stuff in 1929/30, but few people could have imagined (even when it was happening) the scale of Stalin’s great evil.

That said, I wanted really to just talk about one square in the Tintin adventure. This is where Herge goes black (Soprano’s style)–he leaves an entire panel black to depict violence. Entirely black. I’m not a comic book/graphic novel guy, but I’ve seen my fair share of them (most <1970) and I have to say that seeing the black panel was extremely surprising. In my experience, it just didn’t happen.

And what that did was call to mind other squares–notably of course Kasimir Malevich’s (1878-1935) great construction, the Black Square (beginning in 1915):

Then of course there’s the Cubists…but what comes next to mind re the square (and the black one at that) are the later works by Piet Mondrian. Mondrian had gone through a tremendous period of change int he decades from 1905-1935, though it seems to me that even as early as 1909 squares began to appear in the skies (and other places) in his pre-Cubist representational paintings ( as in Sea Toward Sunset, 1909, and Church in Zeeland, 1909/1910), the geometry taking hold for good by 1916. A good example is Composition with Large Red Plane, Yellow, Black, Grey and Blue, 1921:

[Image source: http://www.abstractcritical.com/article/malevich-and-mondrian/index.html This illustrates an interesting article, “Malevich and Mondrian” by David Evison.]

And so we could wind our way through the history of black squares, but we’ll stop there. Oh, one more: the great squares of Oliver Byrne who in his gorgeous 1847 work replaced numbers with colors in presenting the first six books of Euclid:

[Source: https://historyofideasblog.com/thesciencebookstore/2008/05/jf-ptak-scien-1.html I wrote a little about this in the first few months of this blog back in 2008 in “Dismantling Reality–Euclid, Mondrian, Malevich, Lobachevsky and the Appearance and Disappearance of Form Through Geometry”, which I admit is a big title for a thousand-word blog, but so it goes.]

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Anticipation, History of — Art History — History of Lines
On Taking Someone to Task for Not Acknowledging Having Used Someone Else’s Work (1875)

JF Ptak Science Books Quick Post

The brilliant and versatile W. Stanley Jevons–logician, economist, computer pioneer–was a very busy man who packed a lot into his 46 years. Some of published output included numerous journal articles, and some of those contributions included book reviews, including this one, on Theo. Ribot’s Heredity, a Psychological Study of it Phenomena, Laws, Causes, and Consequences, which was published in 1875, with the review appearing in the April 29, 1875 issue of Nature. This one popped into view not so much for its broad consideration, but for the zinger at the end, prodding Ribot for not having included an acknowledgment to Sir Francis Galton, whose work he quotes from and relies upon in his book–it is a fairly soft rebuke but not without its spikes:

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History of Memory