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John Holbo - Editor
Scott Eric Kaufman - Editor
Aaron Bady
Adam Roberts
Amardeep Singh
Andrew Seal
Bill Benzon
Daniel Green
Jonathan Goodwin
Joseph Kugelmass
Lawrence LaRiviere White
Marc Bousquet
Matt Greenfield
Miriam Burstein
Ray Davis
Rohan Maitzen
Sean McCann
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Miriam Jones

Past Valve Book Events

cover of the book Theory's Empire

Event Archive

cover of the book The Literary Wittgenstein

Event Archive

cover of the book Graphs, Maps, Trees

Event Archive

cover of the book How Novels Think

Event Archive

cover of the book The Trouble With Diversity

Event Archive

cover of the book What's Liberal About the Liberal Arts?

Event Archive

cover of the book The Novel of Purpose

Event Archive

The Valve - Closed For Renovation

Happy Trails to You

What’s an Encyclopedia These Days?

Encyclopedia Britannica to Shut Down Print Operations

Intimate Enemies: What’s Opera, Doc?

Alphonso Lingis talks of various things, cameras and photos among them

Feynmann, John von Neumann, and Mental Models

Support Michael Sporn’s Film about Edgar Allen Poe

Philosophy, Ontics or Toothpaste for the Mind

Nazi Rules for Regulating Funk ‘n Freedom

The Early History of Modern Computing: A Brief Chronology

Computing Encounters Being, an Addendum

On the Origin of Objects (towards a philosophy of computation)

Symposium on Graeber’s Debt

The Nightmare of Digital Film Preservation

Richard Petti on Occupy Wall Street: America HAS a Ruling Class

Bill Benzon on Whatwhatwhatwhatwhatwhatwhat?

Nick J. on The Valve - Closed For Renovation

Bill Benzon on Encyclopedia Britannica to Shut Down Print Operations

Norma on Encyclopedia Britannica to Shut Down Print Operations

Bill Benzon on What’s an Object, Metaphysically Speaking?

john balwit on What’s an Object, Metaphysically Speaking?

William Ray on That Shakespeare Thing

Bill Benzon on That Shakespeare Thing

William Ray on That Shakespeare Thing

JoseAngel on That Shakespeare Thing

Bill Benzon on Objects and Graeber's Debt

Bill Benzon on A Dirty Dozen Sneaking up on the Apocalypse

JoseAngel on A Dirty Dozen Sneaking up on the Apocalypse

JoseAngel on Objects and Graeber's Debt

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Friday, August 25, 2006

Primum Mobile

Posted by Adam Roberts on 08/25/06 at 10:49 AM

[Note: In the first version of this post I got my sums stupidly and shamingly wrong; I’ve made the necessary corrections for a second edition.  Of course I’ve left my original errors in, so you can see them, and—quite properly—mock and deride me. Apologies.]

I was curious how fast the Primum Mobile moves, so I thought I’d do some sums.  First off, we need to know the dimensions of this particular sphere.  No problem: in The Discarded Image C S Lewis quotes a late medieval work called The South English Legendary:

We are there told that if a man could travel upwards at the rate of “forty mile and yet some del mo” a day, he still would not have reached the Stellatum (“the highest heven that ye alday seeth”) in 8000 years. [p.98]

The ‘stellatum’ is the sphere immediately inside the Primum Mobile rather than the Primum Mobile itself, but it gives us an idea of the distances involved.  A little more than 40 miles a day (say, 41) for 2,922,000 days (including leap years): that means the diameter radius of the Stellatum is 119,802,000 miles, or 192,802,630 km.

How much further the Primum Mobile is difficult to say.  We know that the Ptolomaic system, including the Primum Mobile, consisted of nine spheres:

Moon
Mercury
Venus
Sun
Mars
Jupiter
Saturn
Fixed Stars
Primum Mobile

Assuming these spheres to be equally spaced suggests that they are about 24 million kilometres apart (24,100,328.75 to be precise).  So, the Primum Mobile is a sphere with a diameter radius of 216,902,958.75 km, give or take a couple of thousand kms (for the diameter radius of the Earth).  This sphere rotates once a day, which means that it is travelling at a rate of [circumference = 1,362,841,483,500 metres, divided by the 86,400 seconds in a day] 2,511,000 15,773,628 m/sec.  This is pretty fast, but only a small fraction of the speed of light (which is more-or-less 300,000,000 m/sec).  At about one one-hundred-and-twenty-fifth five percent of c there should be no relativistic side-effects at that speed (relativistic alterations in size only start to be noticeable at about a tenth of the speed of light, apparently).

For comparison: the distorting mirror of modern science tells us that this distance (216,902,958.75 km) is about the distance between the Earth and the inner asteroid belt: further away from us than Mars but not as far as Jupiter.  (The distance between the earth and the Sun, the ‘A.U.’ or ‘Astronomical Unit’ beloved of astronomers, is 149,598,000 kilometers; Mars is about 1.5 A.U.s; the asteroids are between 2.3 and 3.3 A.U.s out).  If we started walking upwards from the Earth at the rate of 41 miles a day, in 8000 years we’d be well inside the asteroid belt.

But wait! Modern science now tells us that there are not seven but twelve planets: plus the moon and stellatum this gives us a new circumferential dimension of 361,504,931.25 1,865,322,636 km, and a speed of 4,184,000 21,589,382 m/sec: nearly twice as fast, half as fast again, but still small beer in cosmic terms.

In fact, I was am still surprised after doing my (now corrected) sums; not by how much the medievals underestimated the size of the cosmos (they made a pretty good fist, I’d say, at expressing hugeness in human terms; their problem was that, unbeknownst to them, the solar system is not spaced on a human scale at all) – but rather by how plausible this model was.  I’d thought that it was the unlikelihood of so vast crystal sphere rotating so rapidly as one-revolution-a-day; but two-and-a-half-million-metres-a-second isn’t impossibly, or even implausibly fast.  There are Pulsars that are star-sized and rotate with a period of milliseconds; much faster than the Primum.


Comments

. . . 24 million kilometres apart . . .

Um, err, make that c. 12 M km apart since they are arranged one inside the other about the same center point. While the orbits increase in diameter by 24 M km from one to the next, inside to out, the distance between one orbit and the next will only be half that.

On the number of planets, is Pluto in or out? (And what’s Disney say about it?)

By Bill Benzon on 08/25/06 at 03:36 PM | Permanent link to this comment

Um, err, make that c. 12 M km apart since they are arranged one inside the other about the same center point...

Err, um, but the measurements are radial, not diametrical.  The South English Legendary says you start in the middle (Earth) and walk outwards.  I appreciate, of course, that I muddy the waters by saying “the diameter of the Stellatum is ...” above; but I meant radius.  Ahem!

On the number of planets, is Pluto in or out? (And what’s Disney say about it?) My understanding is that we now have a solar system in which there are eight planets and three minor planets, Pluto being one of the latter.  I added in the inner asteroids as having a sphere of their own, just for the hell of it; hence twelve.

By Adam Roberts on 08/26/06 at 05:24 AM | Permanent link to this comment

Oops.  Bill’s query made me look at my sums again, and they were all kerplooey.  So I’ve redone them.  Not that I concede to his point; but pretty much everything else was wrong.

Gnaaaaraarrrrrrgh.

By Adam Roberts on 08/26/06 at 06:12 AM | Permanent link to this comment

Diameter? Radius? What’s the difference? It’s just math.

C. P. Snow’s giggling in his grave.

Bah! Science fictioneers, what do they know?

By Bill Benzon on 08/26/06 at 06:46 AM | Permanent link to this comment

It’s just math.

I think you mean maths.  It’s just maths.  Mathsss.

C. P. Snow’s giggling in his grave. The bastard!  Why doesn’t he come up here, where I can see him, and try that?  I’ll have him ...

By Adam Roberts on 08/26/06 at 12:53 PM | Permanent link to this comment

Johnny Mathis?

By Bill Benzon on 08/26/06 at 01:37 PM | Permanent link to this comment

Bah! Science balladeers, what do they know?

By Adam Roberts on 08/26/06 at 01:57 PM | Permanent link to this comment

Do you people call it “econs“ as well?

By Adam Kotsko on 08/26/06 at 04:48 PM | Permanent link to this comment

The Buddhist image for bigness is:

“If for every grain of sand in the Ganges River there were another Ganges River, and if for every grain of sand in any of these Ganges Rivers there was a whole universe full of precious jewels, would that be great wealth?”

[Answer: Yes, but it wouldn’t be enough wealth to buy liberation].

For long duration they skip the universe full of precious jewels and add:

“And if every thousand years a bird picked up one of these grains of sand......”

In Needham I read that there was a school of “Tantric mathematicians” who went wild with exponentiation. Note that these are not infinities, but “very large numbers”. I sat down and figured it out once, and ended up concluding that the Buddhist universe is actually older and larger than the actual physical universe.

Abstract objects can, in fact, lead to megalomania. Cf. Julian Simon’s claim that, since the points on a line are infinite, we can never run out of resources.

By John Emerson on 08/27/06 at 08:06 AM | Permanent link to this comment

...since the points on a line are infinite, we can never run out of resources.

Let them eat points, massless dimensionless points. They can live on ‘em too.

By Bill Benzon on 08/27/06 at 09:34 AM | Permanent link to this comment

"Let them eat points, massless dimensionless points.”

My friend makes a very good point.  No such thing as a dimensionless point.

My other friend makes a less good point:  “Do you people call it ‘econs‘ as well?” Well, no, no more than anybody I know calls economics ‘econ’.  Economics, unlike Mathematics, isn’t usually abbreviated ... surely!

By Adam Roberts on 08/27/06 at 01:25 PM | Permanent link to this comment

Everyone calls it econ.

By on 08/27/06 at 02:42 PM | Permanent link to this comment

Math.
Econ.
Psych.
Soc (pron. “sosh”, studies the soce the way psych studies the psyche.)
PE or Phys Ed.
Poli Sci.
Chem.
Bio.
Physics, “Phys” only in combination.
Phil.

Almost everything has a short form.

By John Emerson on 08/27/06 at 03:21 PM | Permanent link to this comment

"Almost everything has a short form.

Well, I can only say: not in England.  The only thing that has a short form in England is ‘the names of a certain class of celebrity’, and they’re usually abbreviated to ‘[x]-vowel-zza’.  Gazza.  Shezza.  Prezza.  And so on.

Honestly: do people in the States say ‘this semester I’m studing Polly Sigh’?  And nobody laughs at them?

By Adam Roberts on 08/27/06 at 03:28 PM | Permanent link to this comment

Sometimes Pol sci, I think.

England always tends to be behind the curve.

By John Emerson on 08/27/06 at 03:38 PM | Permanent link to this comment

"England always tends to be behind the curve.”

It’s because we’re such a new country.  Relative to America.

By Adam Roberts on 08/27/06 at 03:44 PM | Permanent link to this comment

I have only ever heard Polly Sigh.

By Adam Kotsko on 08/27/06 at 03:47 PM | Permanent link to this comment

All phreaks know the real break with the symmetrical ptolemaic system was not via Copernicus, but via Kepler, who demonstrated the assymmetry of the galaxy: planets move in elliptical orbits. For this the Cat. and lutheran churches ex-communciated him.  (And you are on a imperfect sphere which moves at approx. 66,600 mph past El Sol.........)

(heh heh, Paddy Chester)

By on 08/27/06 at 04:38 PM | Permanent link to this comment

I think the Ptolemaic system had some 80+ cycles and epicycles to account for the movements of planetary bodies. By shifting the center of the whole shebang to the sun Copernicus cut that number in half. He was still using circles as the curve of choice and so needed a small pile of epicycles to make the data fit the model. It was still a pretty clumsy system.

When Kepler realized that the orbits were elliptical, that cut the number of curves down to the number of planetary bodies. Now, along comes Newton who explains the shape and size of the orbits through gravitational attraction. That, in turn, allowed later astronomers to predict the existence of further planets on the basis of observed perturbations in the orbits of existing planets.

By Bill Benzon on 08/27/06 at 06:15 PM | Permanent link to this comment

"predict the existence of further planets” S/B “predict the existence of further sun-orbiting bodies of a sub-planetary type.”

By John Emerson on 08/27/06 at 07:34 PM | Permanent link to this comment

Well, Neptune and Uranus are planets and they were discovered after Newton, no?

By Bill Benzon on 08/27/06 at 07:41 PM | Permanent link to this comment

I think that Pluto was the one discovered by looking at perturbations of the orbits of other planets. Hopefully someone who knows for sure what they’re talking about will adjudicate this.

By John Emerson on 08/27/06 at 08:02 PM | Permanent link to this comment

From the Wikipedia:

Discovered on September 23, 1846, Neptune is notable for being the only planet discovered based on mathematical prediction rather than regular observations. Perturbations in the orbit of Uranus led astronomers to deduce Neptune’s existence.

By Bill Benzon on 08/27/06 at 09:17 PM | Permanent link to this comment

I stand corrected.

By John Emerson on 08/27/06 at 09:43 PM | Permanent link to this comment

Scientists postulated Pluto to explain perturbations in the orbit of Neptune, but it turned out that the perturbations didn’t really exist (better observation and calculation made the perturbation go away), and Pluto is much too small to cause perturbations in Neptune’s orbit, anyway.

When I first went to college, it took me three months to figure out what “poli sci” meant.  At first, I thought it some kind of multiple-science major, like a physics-chemistry double major.

By on 08/28/06 at 02:27 PM | Permanent link to this comment

Adam, here’s an interesting commentary on Pluto:

<CENTER><object width="425" height="350"><param name="movie" value="http://www.youtube.com/v/0w0hpyNenjM"></param><embed src="http://www.youtube.com/v/0w0hpyNenjM" type="application/x-shockwave-flash" width="425" height="350"></embed></object></CENTER>

By Bill Benzon on 09/10/06 at 09:42 AM | Permanent link to this comment

Thanks Bill.  That is one scary, plasticated, robotoid, virtual-reality impression of a woman, on that clip.

By Adam Roberts on 09/11/06 at 11:43 AM | Permanent link to this comment

LOL!  That’s what a lot of people at YouTube have concluded, and it turns out they’re right. But this isn’t the place for that discussion. Scan down to the bottom of this discussion if you’re interested.

By Bill Benzon on 09/11/06 at 12:52 PM | Permanent link to this comment

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