Archive | April, 2012

The Art of Scientific Illustration

21 Apr

 One Picture is Worth Ten Thousand Words – Confucius.

Create, as if your life depends upon it – Jessie Shaw

There is hardly a more familiar artifact of modern life than the so-called scientific illustrations. That is, the diagram or picture in isometric or linear perspective with notations for scale and measurement which show how machines or houses or even human beings are put together and taken apart and how they work. Who, indeed, has never depended on such an illustration for assembling a Christmas bicycle or a Sears & Roebuch porch swing (not to mention for constructing an atomic reactor or preparing for open heart surgery)? So taken for granted is the ubiquitous scientific illustration that few scholars have ever sensed that it has any historical interest. – Samuel Y. Edgerton, Jr. [1]

Leonardo’s drawing of an ornithopter. He was inspired by the observation of birds flying, and this drawing is considered the first scientific illustration. Image credit: NASA/Photo Researchers, Inc.

The art of scientific drawing is an irreplaceable method for the better apprehension of ideas and a way to prepare the ground for new discoveries. All along the history of science, we know of great genius that relied on drawing to discover or better express his/her ideas.

The first men of science illustrating their writings were Leonardo da Vinci (see the ornithopter), Francis Bacon, Galileo, William Harvey, Descartes.

Leonardo was very eager to keep his secrets, not wanting they fall into the wrong hands. For this motive, he had a preferred left-hand writing in his notebooks (called ‘mirror writing’), while employing his hand-writing in conventional communication (in his letters). Movement specialist Grant Ramey [2] sustains that Da Vinci uses ‘mirror writing’ because he was passionate by symmetry and the human form in art and science. Apparently, Da Vinci wrote in his notebooks from right to left, with his left hand, in order to keep thinking (instead of to remain focused on his own writing), see here.

A scientific illustration is an important form of art, intending at the same time accurately transmit scientific knowledge. Interestingly, Goethe is quoted to have said that you really do not see a plant until you actually draw it…

Why we should start to draw figures in our intellectual and aesthetic activities? In order to understand the power of drawing, let us start to quote here another great man, Thomas H. Huxley, since it is with them that we learn: «[…] I should, in the first place, secure that training of the young in reading and writing, and in the habit of attention and observation, both to that which is told them, and that which they see, which everybody agrees to. But in addition to that, I should make it absolutely necessary for everybody, for a longer or shorter period, to learn to draw.»

In Meno, famous dialogue between Socrates and one of Meno’s slave (a boy), see Ref.[3] to read the complete dialogue, it is clear that by drawing and with the right questions, we may “recall” the knowledge we have in our minds. This famous dialogue depicts the problem of teaching science, in fact, a very old topic in philosophy of science, the problem of the “tacit knowledge” that we all may eventually possess.

We quote next to a short part of this important dialogue, led by Socrates while drawing on the ground.

«Meno: Yes, Socrates. But what do you mean by this, that we do not learn and what is called learning is recollection? Can you teach me that this is so? […]

Meno: Certainly. Step forward here.

Socrates: Now, is he Greek and speaks Greek?

Meno: Absolutely. He was born in the house.

Socrates: Then pay close attention to see whether he seems to recollect or to be learning from me.

M: I certainly will.

So: Tell me, boy, do you know that a square is like this? [Socrates draw a square on the ground, see 1]

Slave: I do.

So: And so a square has these lines, four of them, all equal? [see 2]

Slave: Of course.

So: And these ones going through the center are also equal? [see 3]

Slave: Yes.

So: And so there would be larger and smaller versions of this area? [see 4]

Slave: Certainly.

So: Now, if this side were two feet and this side two feet also, how many feet would the whole be? Look at it like this: if this one were two feet

but this one only one foot, wouldn’t the area have to be two feet taken once? [see 5]

Slave: Yes.

So: When this one is also two feet, there would be twice two?

Slave: There would.

So: An area of twice two feet?

Slave: Yes.

So: How much are twice two feet? Calculate and tell me. [see 6]

Slave: Four, Socrates. [see 7]

So: Couldn’t there be one different from this, doubled, but of the same kind, with all the lines equal, as in that one? [see 8]

Slave: Yes.

So: And how many feet in the area?

Slave: Eight.

So: Now could one draw another figure double the size of this, but similar, that is with all its sides equal like this one? [see 9]

Slave: Yes.

So: How many feet will its area be?

Slave: Eight.

So: Now then, try to tell me how long each of its sides will be. The present figure has a side of two feet. What will be the side

of the double-sized one?

Slave: It will be double, Socrates, obviously.

So: You see, Meno, that I am not teaching him anything, only asking. Now he thinks he knows the length of the side of the

eight-feet square.

MENO: Yes.

So: But does he?

Meno: Certainly not.

So: He thinks it is twice the length of the other.

MENO: Yes.

So: Now watch how he recollects things in order — the proper way to recollect.

Archimedes was also known to write in whatever surfaces he had at hand, on the sawdust-covered floors, on the sand, drawing geometric shapes on the extinguished fires. That ‘s why the majority of Archimedes drawings are forever lost. He spent hours, sited on the floor, like most geometers at his time did, since it was too expensive to scribbled on a papyrus and then thrown it away.

Galileo Galilei with the help of his telescope (invented by him) also made the first drawing of the moon. The consequences were controversial since the Catholic Church saw in his drawings, his sketches of the moon, irregular surface, full of craters, a proof that the heavenly bodies were not perfect, as supposed before. But the dialectical fight between science and religion was just beginning {5}. the old war between the Catholic Church and science made the popes suspicious of the scientific findings and induce them to create the Vatican Observatory with headquarters at the papal summer residence in Castel Gandolfo, Italy, outside Rome. Quite surprisingly, they also have a research center, the Vatican Observatory Research Group, hosted by Steward Observatory at the University of Arizona, Tucson, USA. Located at the Mount Graham International Observatory, in southeastern Arizona, the Vatican possesses the 1.8m Alice P. Lennon Telescope with its Thomas J. Bannan Astrophysics Facility, known together as the Vatican Advanced Technology Telescope. Vatican astronomers said recently that it is okay that people believe in ET’s [5].

Hiero II calling Archimedes to fortify Syracuse. Archimedes was considered at the time a great mind in matters of military strategy. Painting by Sebastiano Ricci. Image credit:

Galileo first drawing of the Moon.

Remark that by drawing you may understand the Pythagoras theorem (see also here).

We must not lose sight that analytical equations represent spatial structures. Our mind must deal with this “hidden” aspect of the mathematical formalism. This is most important for people working in visual science, like computers programming {2}.

Researches were done by Professor Shaaron Ainsworth of the University of Nottingham’s School of Psychology, and colleagues from La Trobe and Deakin Universities in Australia, have shown that students learn better when they are endowed to draw, a method which helps students in visualizing abstract concepts, to recall and to more easily engage in communicating with each other. Teachers at school should endeavor to teach and encourage students to draw what they have learned since this is a powerful method to apprehend any subject, and a powerful process when aiming to transmit ideas to other people {4}. According to Horst Bredekamp [6], it was the ability to draw shown by Galileo that allowed him to better understand Nature; due to their artistic abilities, he could see better than others not gifted in the arts of illustration.


[1] Samuel Y. Edgerton, Jr., in “The Renaissance Development of the Scientific Illustration”

[2] Science and Education, Thomas H. Huxley

[3] Meno, by Platon

[4] Scientific Illustrations, by John L. Ridgway

[5] Vatican Astronomers says its okay to believe in ET, by Nancy Atkinson

[6] Galileo in Context, (p. 180) Edited by Jürgen Renn


{1} The Craft of Scientific Illustrations [contains important advice on how to draw a scientific illustration] []

{2} The importance of drawing

{3} Drawing pictures key to learn science

{4} Drawing and doodling can help you learn science

{5} Catholic Church and Science

Spinoza and the Tractatus Theologico-Politicus

5 Apr

We choose our joys and sorrows long before we experience them. – Kahlil Gibran [1]

Konstatiert ist es, das der Lebenswandel des Spinoza frei von allem Tadel war,und rein und makellos wie das Leben seines gbttlichen Vetters, Jesu Christi. Auch wie Dieser litt er fiir seine Lehre wie Dieser trug er die Dornenkrone. Ueberall, wo ein grosser Geist seine Gedenken ausspricht, ist Golgotha. – Heinrich Heine

Scientists face every day the problem of the origin of being. From where all things came from? But due to the frugality of information we possess, of our knowledge and experiences in this world, the temptation to believe that there is a God at the source of all that exists is enormous. We do not intend here to quest this possibility since we cannot “prove” it. That is a question of faith. In my humble opinion, we are too far away to really understand what is God (we do not even know who we are, human beings, and the proof is the lack of respect we submit to the other human fellows permanently around the globe). Hence, in the West, our temptation resides in to see God as an old man, sat above the clouds (this is the image that, we, Catholics, we learn at school) and which in my viewpoint not even minimally respectable it is.

In this text, I am concerned about a man who thought about this fundamental quest, Benedict de Spinoza. His family were natives from Portugal, as I am, and this condition allows me to draw some conclusions, since, in my viewpoint, the actual mentality pervading all our activities in the actuality is not much different from the one that Spinoza felt, when he lived in the bosom of the Portuguese Jewish Community of Amsterdam. His parents bestowed on his only son (they had also two girls), the best education at the Jewish High School, with the guidance of a learned Talmudist, Morteira. He was introduced to the learning of the Hebrews, the mysteries of the Cabala and the Talmud, the Old Testament, commented by Ibn Ezra and Maimonides. He had knowledge of Portuguese, Spanish, French, Italian, and German. He wrote in Dutch with difficulty, which is quite surprising. He studied Latin by himself {FN2}, and after with Francis Van den Ende, a physician, with whom he gained knowledge of physical sciences, «which so largely leavened his philosophy» (in the Introduction of Ref. [3]).

But his thoughts collided with the wall of incomprehension. As referred by R. H. M. Elwes, one of the best scholars on Spinoza, “[…] hence with curious irony his works, which few read and still fewer understood, became associated with notions of monstrous impiety, and their author, who loved virtue with single-hearted and saintly devotion, was brand as a railer against God and a subverter of morality, whom it was a shame even to speak of.» [3]

The grinding lathe for optical lenses. Spinoza’s house in Rijnsberg near Leiden, Netherlands. Spinoza (1632-1677) lived in Rijnsberg between 1660 and 1663. Image credit:

The Jewish doctors tried to retain him in their community, even offering to him a yearly pension of 1,000 florins,, but Spinoza rejected. It is told that Spinoza’s life was threatened, one day when he was coming out of the Portuguese synagogue. Finally, he was then excommunicated [2].

He then had no reason to stay in Amsterdam, and he leaves this city to work manually polishing glasses and studying with his mind in an acquaintance house, in a place situated in the road that links Amsterdam to Auwerkerke. When he finishes his polishing, his friend takes care of them, sell them and remit the money to him [2]. Spinoza engages in the activities of trade in order to provide means for life’s necessities. Trade is a basic aspect of human’s life.

One episode shows a characteristic of his personality. On the death of his father, his sisters wanted to deprive him of the inheritance (sustaining that he was a heretic). Spinoza claim his rights on the court of law, he gained the process, but at the end he gave back all the inheritance to his sisters, only retaining one bed…

Interior of the Portuguese Synagogue of Amsterdam.

The best biography of this great thinker is probably the one of Johannes Colerus, The Life of Benedict de Spinoza [2].

Coleridge expressed the opinion that Ethics, the Novum Organum, and the Critique of Pure Reason were “the three greatest works written since the introduction of Christianity [1]. Despite the rigorous character of his writings, recurring to a kind of geometric exposition (influence of Euclid), numerous poets and imaginative writers embraced his philosophical exposition and study him deeply. Among them, we may refer Goethe, Novalis (who celebrated him as “the man intoxicated with Deity”) [4], Lessing, Lord Byron, Heine, Auerbach, Coleridge, Shelley, George Eliot.

Benedict de Spinoza. Image credit: Wikipedia.

In the preface, Benedict de Spinoza immediately starts to situate the problem with a fact we already know: «Men would never be superstitious, if they could govern all their circumstances by set rules, or if they were always favoured by fortune: but being frequently driven into straits where rules are useless, and being often kept fluctuating pitiably between hope and fear by the uncertainty of fortune’s greedily coveted favors, they are consequently, for the most part, very prone to credulity. The human mind is readily swayed this way or that in times of doubt, especially when hope and fear are struggling for the mastery, though usually, it is boastful, over-confident, and vain.» [3]

He also gave a clarified example: «Superstition, then, is engendered, preserved, and fostered by fear. If anyone desires an example, let him take Alexander, who only began superstitiously to seek guidance from seers when he first learned to fear fortune in the passes of Sysis; whereas after he had conquered Darius he consulted prophets no more, till a second time frightened by reverses. When the Scythians were provoking a battle, the Bactrians had deserted, and he himself was lying sick of his wounds, “he once more turned to superstition, the mockery of human wisdom, and bade Aristander, to whom he confided his credulity, inquire the issue of affairs with sacrificed victims.” [Note 1]. Very numerous examples of a like nature might be cited, clearly showing the fact, that only while under the dominion of fear do men fall a prey to superstition; that all portents ever invested with the reverence of misguided religion are mere phantoms of dejected and fearful minds; and lastly, that prophets have most power among the people, and are most formidable rulers, precisely at those times when the state is in most peril. I think this is sufficiently plain to all, and will, therefore, say no more on the subject”. »

Alexandre the Great. Image credit:

Superstition and fear makes people dependent on charlatans, and their freedom, life and well-being is seriously menaced, as you can infer from the video here, showing a bishop from the Church “Igreja do Reino de Deus”, teaching other acolyte how to rob people with the easy talk about “religion”, not Religion, a way for Man to get in touch with higher qualities of Nature. And he becomes a very wealthy man…Nowadays, it is easy to find people with such a greed everywhere, as the financial crisis has shown to everyone.

One aspect of his system of philosophy stays in the spirit of the times when people believed that truth was something definite and relatively simple to grasp with a thinking brain, diligence, and a sound method. In times we can read works with a tone of confidence, that nowadays is fade away since Kurt Gödel and others have shown to us, how fragile are our systems of thought. Spinoza chooses a system of geometric presentation, in the way of Euclides, believing to get rid of error. “It is the part of a wise man, not to bewail nor to deride, but to understand”. Descartes is also present in his system of philosophy.

Einstein’s had a great admiration for his philosophy, and he told to Rabbi Herbert Goldstein when inquired about God: “I believe in Spinoza’s God who reveals himself in the orderly harmony of what exists, not in a God who concerns himself with fates and actions of human beings.”{FN3}. Also, Richard P. Feynman, one of the best minds of the last century, also intended to clarify the idea of God, a major purpose in the work and life of Spinoza {FN4}, as it is clear on this video below, sustaining that “our Gods are too provincial”. Feynman stresses too, in one of his talks, that science can’t prove if flying saucers exist, but science can tell us if they likely or unlikely exist…

The work of Spinoza benefited from science method of thinking, his thoughts are organized in a kind of geometric way. He inherited from the Hebrews the taste of freedom (conquered through science, magic, and knowledge), as it is understood by the writings of the Old Testament, which runs through the whole struggle of the Israelites – actually an amalgam of tribes, – the liberation from bondage, as it is clearly transmitted in the Exodus, an important part of the Bible. His life gives us examples which can be an inspiration for all of us in the actuality, in the actuality of this immensely beautiful, but miserable world, too. Anybody who understood Baruch Spinoza, that really understood his message, knows that we all must strive to be free…


[1] Kahlil Gibrain

[2] Joannes Colerus, The Life of Benedict de Spinoza

[3] Benedict de Spinoza, Tractatus Thelogicus-Politicus

[4] Novalis, This Life, Thoughts and works, edited and translated by M. J. Hope


{FN1} Here, Spinoza, apparently cites Curtius, Vol. 4, see also p.4 of Ref. [3] by yourself.

{FN2} Interestingly, we can read in a footnote of p.xi: «A translator has special opportunities for observing the extent of Spinoza’s knowledge of Latin. His sentences are grammatical and his meaning almost always clear. But his vocabulary is restricted; his style is wanting in flexibility, and seldom idiomatic; in fact, the niceties of scholarship are wanting. He reminds one of a clever workman who accomplishes much with simple tools.»

{FN3} This answer was given to the Rabbi Herbert Goldstein of the Institutional Synagogue, New York, April 24, 1921, published in the New York Times, April 25, 1929; from Einstein: The Life and Times, Ronald W. Clark, New York: World Publishing Co., 1971, p. 413; also cited as a telegram to a Jewish newspaper, 1929, Einstein Archive 33-272, from Alice Calaprice, ed., The Expanded Quotable Einstein, Princeton, NJ: Princeton University Press, 2000, p. 204. THIS REFERENCE WAS OBTAINED IN THE SITE OF STEPHEN JAY GOLD.

{FN4} Here I thank M. Garber for calling my attention to the opinion that Feynman had about Spinoza:

“My son is taking a course in philosophy, and last night we were looking at something by Spinoza and there was the most childish reasoning! There were all these attributes, and Substances, and all this meaningless chewing around, and we started to laugh. Now how could we do that? Here’s this great Dutch philosopher, and we’re laughing at him. It’s because there’s no excuse for it! In the same period there was Newton, there was Harvey studying the circulation of the blood, there were people with methods of analysis by which progress was being made! You can take every one of Spinoza’s propositions, and take the contrary propositions, and look at the world and you can’t tell which is right.”

Richard P. Feynman, The Pleasure of Finding Things Out


(1) the Jewish Virtual Library


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