## January 7, 2008

### A Tiny Taste of the History of Mechanics

#### Posted by John Baez

This quarter I’m teaching a graduate math course on classical mechanics, focusing on Hamiltonian methods and symplectic geometry.

To get the course started, I’ll spend a class sketching the history of mechanics from Aristotle to Newton. It’s a hopeless task, but fun anyway… here are are my notes.

These are some incredibly sketchy notes, designed to convey just a tiny bit of the magnificent history of mechanics, from Aristotle to Newton. I’ve left out huge amounts of important and interesting stuff.

Aristotle

Aristotle wrote his Physics as lecture notes sometime around 350 BC. Some basic principles: All that moves is moved by something else. Action at a distance is inconceivable: the mover must always be connected to the moved.

What about falling bodies? These proved a bit embarrassing for Aristotle and his followers.

Aristotle’s physics is not truly quantitative, but at some points he seems to suggest that velocity is proportional to force divided by ‘resistance’: $v \propto F/R$ For falling bodies this might mean $v \propto m/R$ where $m$ is the body’s mass. This is actually true for a body falling at terminal velocity in air or some other medium with friction, but it doesn’t address the problem of how falling bodies accelerate

Aristotle seemed to believe that the stars and planets were made of a different substance than terrestrial matter (‘aether’, later called ‘quintessence’). So, it probably never occurred to him to find a unified theory of motion applying equally to a falling rock and the moon. This was Newton’s huge achievement.

Archimedes

Archimedes (287 BC - 212 BC) did amazing work on statics — and as we now know through recently discovered texts, he essentially invented the integral calculus.

Ptolemy

Ptolemy seems to have lived in Alexandria, 83 – 161 AD. In his Almagest he described a geocentric solar system with epicycles to compute the motions of the Sun, Moon, and 5 visible planets. It’s extremely accurate, and makes use of some very interesting mathematics. Most people who make fun of epicycles are idiots compared to Ptolemy.

Dark Ages

When the Romans took over Greece a long process of scientific decline began, nicely discussed in Lucio Russo’s The Forgotten Revolution: How Science Was Born in 300 BC and Why It Had to Be Reborn. Most Greek texts were lost completely; the ones that survived did so through a highly complex process of repeated translation, discussed in Scott Montgomery’s Science in Translation: Movements of Knowledge through Cultures and Time. A quote from the review by John Stachel:

Perhaps the best of the book’s many delightful challenges to conventional wisdom comes in the first section on the translations of Greek science. Here we learn why it is ridiculous to use a phrase like “the Renaissance recovery of the Greek classics”; that in fact the Renaissance recovered very little from the original Greek and that it was long before the Renaissance that Aristotle and Ptolemy, to name the two most important examples, were finally translated into Latin. What the Renaissance did was to create a myth by eliminating all the intermediate steps in the transmission. To assume that Greek was translated into Arabic “still essentially erases centuries of history” (p. 93). What was translated into Arabic was usually Syriac, and the translators were neither Arabs (as the great Muslim historian Ibn Khaldun admitted) nor Muslims. The real story involves Sanskrit compilers of ancient Babylonian astronomy, Nestorian Christian Syriac-speaking scholars of Greek in the Persian city of Jundishapur, and Arabic- and Pahlavi-speaking Muslim scholars of Syriac, including the Nestorian Hunayn Ibn Ishak (809-873) of Baghdad, “the greatest of all translators during this era” (p. 98).

So, it’s important to remember that the ‘Dark Ages’ were dark only in Western Europe (‘Christendom’), and that meantime Muslim scholars were making progress in astronomy, mathematics and so on. But, when the West finally got going, it did some wonderful things.

Etienne Tempier, Bishop of Paris

In the Middle Ages almost all Western European scholars were monks. The works of Aristotle were introduced around 1200 when they were imported via Arab sources, for example from Andalusia (now southern Spain). As they spread through Europe, they caused conflict with accepted views (a blend of Christian theology and Plato’s philosophy).

In 1277 the Bishop of Paris condemned a list of 219 theses, including some related to physics. Here are some of the condemned theses:

• 66. That God is unable to to impart rectilinear uniform motion to the heavens.
• 102. That nothing happens by chance, but everything comes about by necessity, and that all the things that will exist in the future will exist by necessity…

Also: if one thing affects another, the second must also affect the first!

William Occam

Occam (1288-1347) was a Franciscan friar famous for his ‘razor’; he also believed that in the absence of resistance motion would continue indefinitely.

Nicole Oresme

Oresme (1323-1382) was perhaps the first to draw graphs plotting the change of some quantity (or ‘form’) as a function of time — though not on a rectilinear grid as Descartes did. In his book Latitude of Forms, he considered various possibilities, including ‘uniformly difform’ quantities, i.e. those that change at a constant rate. He showed that an object whose speed was ‘uniformly difform’ would move a distance from time $t_1$ to time $t_2$ equal to $v_{mean}(t_2 - t_1)$ where $v_{mean}$ is the object’s speed at a time halfway between $t_1$ and $t_2$. In modern language: if the acceleration $\dot v(t) = a$ is constant, the change of position is $\int_{t_1}^{t_2} v(t) d t = \frac{1}{2} a (t_2 - t_1)^2$ Later people including (but not only) Galileo applied this idea to falling objects.

Oresme also proved the divergence of the harmonic series!

Nicolaus Copernicus

In 1543, in his De Revolutionibus, Copernicus rejected Ptolemy’s model of the solar system and reverted to an earlier Greek model in which the Earth goes around the Sun and all orbits are perfectly circular. This makes predictions much less accurate than Ptolemy’s!

Johannes Kepler

In 1596, Kepler published his Mysterium Cosmographicum which adopted a Copernican heliocentric cosmology and attempted to explain the radii of the planet’s orbits in terms of nested Platonic solids.

Later he spent years analyzing accurate data collected with his boss Tycho Brahe, and came up with a system where planets moved along circular orbits not quite centered at the Sun. (The off-center circle idea was already familiar to Ptolemy and called in Latin a punctum aequans.) However, he discovered slight discrepancies in the orbit of Mars (just 8 minutes, a minute being a 60th of a degree) which eventually led him to discard this system.

In the years that followed, he realized first that the planets could not move with constant speed around their orbits, and then that the orbits should be ellipses. In his 1609 book Astronomia Nova he formulated these laws:

1. Each planet moves along an ellipse with the Sun at one focus.
2. The vector from the Sun to the planet sweeps out equal areas in equal times.
3. The ratio of the squares of the periods of two planets is equal to the ratio of the cubes of their semimajor axes.

Perhaps even more importantly, we see in Kepler’s work these new features, listed by E. J. Dijksterhuis in his magnificent book The Mechanization of the World Picture: Pythagoras to Newton:

• Rejection of all arguments which are based solely on tradition and authority.
• Independence of scientific inquiry of all philosophical and theological tenets.
• Constant application of the mathematical mode of thought in the formulation and elaboration of hypothesis.
• Rigorous verification of the results deduced by the latter by means of an empiricism raised to the highest degree of accuracy.

Galileo Galilei

In 1632 Galileo wrote a book on Copernican astronomy versus Ptolemaic astronomy, Dialogue Concerning the Two Chief World Systems. Among other things, he formulated the principle of relativity of motion to explain why we wouldn’t fall off a moving Earth:

Shut yourself up with some friend in the main cabin below decks on some large ship, and have with you there some flies, butterflies, and other small flying animals. Have a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it. With the ship standing still, observe carefully how the little animals fly with equal speed to all sides of the cabin. The fish swim indifferently in all directions; the drops fall into the vessel beneath; and, in throwing something to your friend, you need throw it no more strongly in one direction than another, the distances being equal; jumping with your feet together, you pass equal spaces in every direction.

When you have observed all these things carefully (though doubtless when the ship is standing still everything must happen in this way), have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still.

He also argued that discounting wind resistance, a falling object would fall at a constant acceleration independent of its mass. Using the same geometrical argument as Oresme and others, he saw that this meant it would fall a distance proportional to $t^2$.

Isaac Newton

Isaac Newton unified the work of Galileo and others on ‘terrestrial mechanics’ (falling bodies) with the work of Kepler and others on ‘celestial mechanics’ (the motion of planets). In his Philosophiae Naturalis Principia Mathematica, published in 1687 after enormous delays, he formulated three laws of motion:

• Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.
Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.
• Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.
The rate of change of momentum of a body is proportional to the resultant force acting on the body and is in the same direction.
• Lex III: Actioni contrariam semper et aequalem esse reactionem: sive corporum duorum actiones in se mutuo semper esse aequales et in partes contrarias dirigi.
All forces occur in pairs, and these two forces are equal in magnitude and opposite in direction.

Note the third law is one of the doctrines condemned by the Bishop of Paris.

Oversimplifying enormously, one can say that a key step here was going from a first-order differential equation (trying to explain velocity) to a second-order one (trying to explain acceleration). Newton’s second law can be formulated as a differential equation $F = m a$ or $F = m\frac{d^2 q}{d t^2}$ where $m$ is the body’s mass, $q : \mathbb{R} \to \mathbb{R}^3$ is its position as a function of time, and $F$ is the force upon it, typically some function of $q$, ${d q\over d t}$, and perhaps $t$ as well. This formulation is anachronistic since Newton didn’t use vectors — but he did invent the differential and integral calculus. (So did Leibniz: Newton would write $\dot q$ while Leibniz wrote $\frac{d q}{d t}$.)

Newton’s colleague Robert Hooke suggested had that the gravitational force exerted by one body on another was inversely proportional to the square of the distance between them. Superficially, at least, this violates Aristotle’s principle of ‘no action at a distance’. In an amazing tour de force, Newton was able to derive Kepler’s three laws from the inverse square force law. You will derive the first one in a guided homework exercise. That should teach you how smart Newton was!

Posted at January 7, 2008 12:47 AM UTC

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### Re: A Tiny Taste of the History of Mechanics

If I recall correctly, Copernicus still used epicycles.

It’s also been suggested that the “Prutenic Tables”, calculated by Erasmus Reinhold following the Copernican model, predicted a 1563 conjunction between Jupiter and Saturn more accurately than the alternatives, helping to spread interest in Copernicus and his work.

Posted by: Blake Stacey on January 7, 2008 2:09 AM | Permalink | Reply to this

### Re: A Tiny Taste of the History of Mechanics

Hmm, interesting! I’ll have to check that out.

I’d welcome any other little-known tidbits on the history of mechanics that people happen to know. I probably won’t be able to use them all in class, but I can send the students here. I’m trying to give them a sense of history a wee bit deeper than the usual “People stupidly believed Aristotle until the Renaissance; then Galileo Kepler and Newton straightened everything out.”

Posted by: John Baez on January 7, 2008 4:48 AM | Permalink | Reply to this

### Re: A Tiny Taste of the History of Mechanics

Well, you mentioned Oresme, which is a good beginning. I seem to recall that Leonardo da Vinci also made some observations which are typically forgotten or neglected: he noticed that cannonballs followed curving trajectories, for example, and tried to figure out a numerical law for falling bodies (the task which Galileo did successfully). Recalling where I saw that is going to tax my brain… it might well’ve been the second episode of The Mechanical Universe (see The Google).

I believe a fellow named Benedetti did experiments similar to those Galileo did later on falling bodies (drop a heavy and a light rock from a tower at the same time, etc.). He, and possibly Alberti, advanced conceptual arguments for why Artistotle’s idea of falling was mistaken.

Posted by: Blake Stacey on January 7, 2008 6:13 AM | Permalink | Reply to this

### Re: A Tiny Taste of the History of Mechanics

…not on a rectilinear grid as Descartes did.

Are you sure Descartes’ axes were rectilinear? I have a recollection they weren’t. Here it presents a picture of Descartes’ treatment of Pappus’ problem which suggest otherwise, and it claims Fermat was prior in any case.

Posted by: David Corfield on January 7, 2008 12:31 PM | Permalink | Reply to this

### Re: A Tiny Taste of the History of Mechanics

See the current Notices AMS for a review of a new book about Descartes

Posted by: jim stasheff on January 7, 2008 1:38 PM | Permalink | Reply to this

### Re: A Tiny Taste of the History of Mechanics

Here’s a link to Michael Serfati’s review of Desmond Clarke’s Descartes: A Biography (2006).

Posted by: Blake Stacey on January 7, 2008 2:25 PM | Permalink | Reply to this

### Re: A Tiny Taste of the History of Mechanics

Good. There in Figure 2 of the communication by Michel Serfati is an image of Descartes’ diagram. It’s accompanied by some commentary.

Posted by: David Corfield on January 7, 2008 2:32 PM | Permalink | Reply to this

### Re: A Tiny Taste of the History of Mechanics

I found Guillemin, Sternbergs book on these issues very interesting.

Posted by: Thomas Riepe on January 7, 2008 1:32 PM | Permalink | Reply to this

### Re: A Tiny Taste of the History of Mechanics

I think Aristotle’s model of the solar system was based on that of Callipus so you could mention him. Do you mention Aristarchus who advocated heliocentric motion?

Also, Empedocles said that light travels at finite speed. Aristotle said light travels at infinite speed because when the sun first starts to rise at the eastern horizon, the western mountains are illuminated instantly. The fact that light travels at finite speed was rediscovered when people were studying the moons of Jupiter. The reason they were doing that is because they hoped the moons of Jupiter could be used as a clock so they could use that to solve the “longitude problem”, and win the huge prize money.

Jeffery Winkler

http://www.geocities.com/jefferywinkler

Posted by: Jeffery Winkler on January 7, 2008 7:13 PM | Permalink | Reply to this

### Re: A Tiny Taste of the History of Mechanics

This is supposed to be a 1½-hour review of the history of mechanics from Aristotle to Newton, so I won’t have time to say much — but that’s why I’ll direct the students to this blog entry to read more!

But yes, I should mention Aristarchus, just to dispel the misimpression that a Sun-centered solar system was an idea new to Copernicus!

Here’s a nice quote by Archimedes:

You King Gelon are aware the ‘universe’ is the name given by most astronomers to the sphere the centre of which is the centre of the earth, while its radius is equal to the straight line between the centre of the sun and the centre of the earth. This is the common account as you have heard from astronomers. But Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the universe is many times greater than the ‘universe’ just mentioned. His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun on the circumference of a circle, the sun lying in the middle of the orbit, and that the sphere of fixed stars, situated about the same centre as the sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the centre of the sphere bears to its surface.

I bet Aristarchus’ argument was simple and convincing: the ‘fixed stars’ must be much farther than the Sun, since we can’t easily see their parallax as the Earth moves around the Sun. (One ‘parallax second’ or ‘parsec’ is 3.26 light years.)

But, I’m not sure I understand that last proportionality statement. Our distance to fixed stars is to the radius of the Earth’s orbit as what is to what???

If I understood the statement I’d like to use it to compute how far away Aristarchus thought the stars were. His estimate of the distance to the Sun was not too terrible — off by an order of magnitude, in part because for some bizzaro reason he estimated the angle subtended by the sun to be 2 degrees, while anyone can easily tell it’s about a quarter of that.

Posted by: John Baez on January 7, 2008 10:22 PM | Permalink | Reply to this

### Re: A Tiny Taste of the History of Mechanics

Terry Tao’s Cosmic Distance Ladder slides tell all.

Posted by: David Corfield on January 7, 2008 10:39 PM | Permalink | Reply to this

### Re: A Tiny Taste of the History of Mechanics

One of the difficulties they had was the need to intellectually separate the concepts of momentum, force, and kinetic energy.

p = mv

F = ma = m dv/dt

k = 1/2 mv^2

Notice each of these is mass multiplied by some form of velocity, either just velocity, or velocity squared, or the derivative of velocity with respect to time. They knew that mass times some form of velocity had some significance. It was only through careful experiments that they separated these into three different things.

Jeffery Winkler

http://www.geocities.com/jefferywinkler

Posted by: Jeffery Winkler on January 7, 2008 7:33 PM | Permalink | Reply to this

### Re: A Tiny Taste of the History of Mechanics

I think I once read a hilarious piece by Leibniz where he was criticizing Descartes on the issue of whether $m v$ or $m v^2$ is conserved in an elastic collision.

It’s hilarious not mainly because of the problem — which requires some understanding of vectors versus scalars to straighten out. It’s hilarious because it reminds me a bit of the flame wars one sees on the internet today! Leibniz don’t call Descartes names, but he uses a lot of subtle digs to suggest that Descartes must be sort of a dope.

From the Stanford Encyclopedia of Philosophy:

Given the controversy that erupted in the wake of Leibniz’s argument, it may be worthwhile to make two brief remarks in connection with the conservation principles of Newtonian mechanics. First, the Cartesian quantity of motion is not a vector quantity – it doesn’t take account of the direction of the moving body – and therefore it must be distinguished from the Newtonian notion of momentum ($m v$). In fact, Leibniz accepts the conservation of momentum and thus must be understood only to be arguing against the non-vectorial quantity of motion. Second, although kinetic energy ($1/2 mv^2$) is conserved only in elastic collisions, Leibniz maintains that, at root, all fundamental collisions are elastic, and that inelastic collisions must therefore be analyzed as collisions of composite, and ultimately elastic, bodies.

Posted by: John Baez on January 7, 2008 10:34 PM | Permalink | Reply to this

### Re: A Tiny Taste of the History of Mechanics

Perhaps some students may find it interesting that Laplace’s cosmology had a huge impact on the Zeitgeist. E.g. on Blanqui, a french revolutionaire after whom Verne modeled the figure of Nemo and whose essay was regarded by Walter Benjamin as a keytext to the mentality of the 19th century.

Posted by: Thomas Riepe on January 8, 2008 8:31 PM | Permalink | Reply to this

### Re: A Tiny Taste of the History of Mechanics

Just a few notes, picked up from my reading over the years:

I don’t think Aristotle knew that falling bodies accelerate. On the other hand, he seems to have been the first person to think seriously about friction and how it affected motion.

His ideas on motion also seem to have been heavily influenced by the idea of motion as always being bounded at both ends—going from a starting point to a goal.

He did think that the heavens were made of a fundamentally different substance from the earth. In fact, this idea was part of a long tradition. This tradition was partly religious (a natural human tendency to think of heaven as more perfect than earth), and partly based on observation: heavenly bodies seem to continue forever unchanging, moving in stately, simple circles, endlessly repeating, while things on earth move in straight lines or complicated, irregular paths, and come to a halt, and generally suffer change and decay. (Of course, these observations then play back into religious ideas.)

There seem to have been two traditions in mechanics. One was based more on practical machine-building, and runs from the very early, simple ideas of people like Archytas of Tarentum though Biton, Philo of Byzantium and Ctesibius, while the other is very mathematical and runs from Euclid through Archimedes (and has had better luck in the survival of its texts). Hero of Alexandria, though he belongs mainly to the first tradition, also includes elements of the second, and they seem to have merged in Islamic science.

Ptolemy was the end of a long tradition in mathematical astronomy. Other important names are Apollonius of Perga and Hipparchus. Epicycles were invented in the Alexandrian period, centuries before Ptolemy.

One of the nice things about Ptolemy’s system is that you can see, in retrospect, how his various devices account for various real features of planetary motion. The epicycles mainly serve to handle the fact that the apparently motion of the planets includes the annual motion of the earth (though he used them for other things too). The eccentric and equant, between them, account for both the fact that the centres of the planetary orbits don’t coincide with the sun (the main observational consequence of Kepler’s first law) and for Kepler’s second law.

The eccentric and equant garnered a lot of criticism over the centuries for violating the principle of uniform circular motion (which seemed to be mandated by the physics—e.g. observations of flywheels: why would a spinning object adapt its speed to to the distance between a point on its rim and some other point near but not at its centre?) Both devices can be replaced by using extra epicycles, and this was one of the things Copernicus “cleaned up” in the Ptolemaic system.

One of the important developments in Islamic astronomy was a spectacular improvement in numerical methods. Ptolemy was, in effect, working with 3-digit trig tables. A few hundred years later, Muslim astronomers were able to work with (the equivalent of) 8-digit trig tables. (I think the tables themselves were optimised for streamlining astronomical calculations, as well.) Observational instruments also improved. People don’t often mention the stupendous amount of very tedious calculation that astronomers have always had to do, and the huge importance of improvements in algorithms (which continues to this day).

The mechanical tradition came into the Latin west from Islam in the late 13th century, via Jordanus Nemorarius, Gerard of Brussels and probably a few others. From these, there developed an English tradition in kinetics (the “Oxford Calculators”, e.g. Thomas Bradwardine), and from that developed a Parisian tradition in dynamics, first by Jean Buridan and then by Oresme, his pupil. These ended up merging the mechanical tradition with Aristotle’s ideas on force and motion.

(These men were also important for other reasons. Bradwardine was a major theologian, while Buridan was not only an important philosopher, but was also said to have seduced the Queen of France, and only narrowly escaped execution.)

One interesting effect of the edicts of Bishop Tempier was to prevent Aristotle gaining a stranglehold on all thinking about dynamics, cosmology and many other areas. So, by emphasising God’s unlimited power to do all sorts of weird and unexpected things, it paradoxically encouraged people to think freely about various ways that motion, space and force might in principle work. So long as natural philosophers couched their ideas as hypothetical debating points, they were relatively free to discuss idea in physics (which seldom seemed likely to undermine the temporal power of the Church, and so were seen as much less of a threat than unorthodox ideas on the Eucharist or on translating the Bible into the vernacular).

The traditions of astronomy and mechanics remained quite separate, even though astronomers sometimes thought about the dynamics of the heavens and people in the mechanical tradition thought about cosmology. Astronomers liked to make careful observations and build complicated models, then do huge calculations, while natural philosophers generally liked simple, conceptual models and broad-brush arguments (although they sometimes did serious mathematics as well). Even at the end of the 16th century, it’s clear that Galileo basically belongs to the mechanical tradition while Kepler belongs to the astronomical tradition, even though Kepler thought a lot about dynamics and Galileo thought a lot about astronomy.

Between Galileo and Newton is Descartes, whose system of the world was hugely influential, particularly in France where it was only slowly ousted by the Newtonian system in the first half of the eighteenth century. (After which, the French became more Newtonian than the British, and stuck to point-to-point action-at-a-distance models in electromagnetism through much of the 19th century, while some British physicists were trying to build field models, or at least models that eventually evolved into field models.)

There are a bunch of other interesting people around during the Scientific Revolution, such as William Gilbert, whose careful studies of magnetism were admired by Kepler and influenced people’s thinking about gravity; and Robert Boyle and Robert Hooke and Christopher Wren and Christiaan Huygens and the Bernouillis and Leibniz … who all studied force and motion (pendulums, air pressure, collision mechanics, the concepts of impetus, vis viva and vis mortua which preceded momentum and kinetic and potential energy, and so on and so forth … )

Don’t know if any of this is of any use …

Posted by: Tim Silverman on January 24, 2008 8:15 PM | Permalink | Reply to this

### Re: A Tiny Taste of the History of Mechanics

Buridan was not only an important philosopher, but was also said to have seduced the Queen of France, and only narrowly escaped execution.

Buridan’s name is most famously associated with “Buridan’s ass”, which placed squarely in the middle between two equally inviting piles of hay, is unable to choose between them and starves. He (I mean Jean Buridan, not the ass) is also said to have founded the University of Vienna.

I was curious about this story about seducing the queen of France, so I looked it up. But apparently all of it is apocryphal. “Buridan’s ass” was made famous by Spinoza, but appears nowhere in Buridan’s writings. The University of Vienna was founded in the year 1237, well before his birth. And the tale of his amorous adventures with a queen apparently comes from a poem, La Testament, by one Francois Villon.

Oh well.

Posted by: Todd Trimble on January 24, 2008 9:10 PM | Permalink | Reply to this

### Re: A Tiny Taste of the History of Mechanics

Poor Buridan. A great philosopher, friends with the Queen of France… but all she cared about was his ass.

Still, it’s better than getting the word “dunce” named after you.

Posted by: John Baez on January 24, 2008 9:45 PM | Permalink | Reply to this

### Re: A Tiny Taste of the History of Mechanics

Thus violating the Commandment, “Thou shalt not covet thy neighbor’s ass.”

<ducking for cover>

Posted by: Todd Trimble on January 24, 2008 10:13 PM | Permalink | Reply to this

### Re: A Tiny Taste of the History of Mechanics

conc. “Islamic astronomy”, here a very nice article with lots of interesting links, found by Mike H.

Posted by: Thomas on March 16, 2009 12:41 AM | Permalink | Reply to this

### Re: A Tiny Taste of the History of Mechanics

Here an article on Newtons math and precursers.

Posted by: Thomas Riepe on April 5, 2008 5:57 PM | Permalink | Reply to this

### Leibniz; Re: A Tiny Taste of the History of Mechanics

Th article seems to be in German. This would anger Newton, who’d suspect a dirty trick by his Continental arch-rival Gottfried Wilhelm Leibniz (also Leibnitz or von Leibniz [1 July (June 21 Old Style) 1646 – 14 November 1716]

Of course, to be fair, Leibniz wrote primarily in Latin and French.

Posted by: Jonathan Vos Post on April 6, 2008 6:27 PM | Permalink | Reply to this

### Re: A Tiny Taste of the History of Mechanics

Here’s news on the “Antikythera mechanism”:
http://tinyurl.com/6bplha

Posted by: Thomas Riepe on July 31, 2008 8:23 AM | Permalink | Reply to this

### Re: A Tiny Taste of the History of Mechanics

Cool! Sometime I need to do a This Week’s Finds on what is perhaps the world’s first analogue computer.

Posted by: John Baez on July 31, 2008 9:03 AM | Permalink | Reply to this

### Lost Technology; Re: A Tiny Taste of the History of Mechanics

The problem with decoding the faint words on the device’s Olympics dial was that the Greek translators didn’t know Chinese?

Yes, a column on this would be cool. The Scientific American article captivated me years ago, and the iterated news since is startling.

Babylonian’s wet-cell batteries for electroplating the king’s jewelry. Egyptian brain surgery.

What else did the ancients have working that we don’t know about? I had a long discussion once with Prof. Geoffrey Landis and Dr. George Hockney on whether the Mayans could have had spark-gap radio transmitters and receivers, but that all their gold wire and silver apparatus was long since melted down by conquistadors.

Posted by: Jonathan Vos Post on July 31, 2008 5:13 PM | Permalink | Reply to this

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