Comments for The Renaissance Mathematicus

Comment on The Starry Messenger What it Said and What that Really Meant! by Online Kredit

Online Kredit — Tue, 21 May 2013 17:20:10 +0000

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Comment on Hans Peter from Langendorf by A maths book from a painter | The Renaissance Mathematicus

A maths book from a painter | The Renaissance Mathematicus — Tue, 21 May 2013 15:32:58 +0000

[…] writing master Johannes Neudörfer (1497 – 1563) brother in law of the printer publisher Johannes Petreius. The typeface is a fraktur script and although this was not the first fraktur typeface, all fraktur […]

Comment on The Phlogiston Theory is not equivalent to the Aquatic Ape Hypothesis. by Michael Weiss

Michael Weiss — Tue, 21 May 2013 12:53:06 +0000

I meant the Tychonic system modified to use Kepler’s first two laws. In other words, kinematically it is equivalent to Kepler’s system, but physically it still has a motionless earth.

Comment on A maths book from a painter by Thingumbob (@Thingumbobesq)

Thingumbob (@Thingumbobesq) — Tue, 21 May 2013 12:50:59 +0000

Thanks for the post. The constructive geometry Dürer advanced puts me in mind of another seminal figure in that department Jakob Steiner, whose method was a closely guarded military secret once upon a time.

Comment on A maths book from a painter by Megan

Megan — Tue, 21 May 2013 07:24:10 +0000

Are there any pictures of the book, so we can see the typeface? That’s pretty neat.

Comment on The Phlogiston Theory is not equivalent to the Aquatic Ape Hypothesis. by Ian Paul Wragg

Ian Paul Wragg — Tue, 21 May 2013 06:32:04 +0000

” I believe many astronomers preferred a geo-helio-centric version of Kepler to the real thing,”

Michael, I take it you mean “Tycho Brahe” rather than Kepler?

Comment on The Phlogiston Theory is not equivalent to the Aquatic Ape Hypothesis. by Michael Weiss

Michael Weiss — Tue, 21 May 2013 00:10:40 +0000

As I understand it, the key issue was whether the heavenly spheres really existed, or whether you just had a geometrical scheme to "save the phenomena". It's easy to see how the Eudoxean scheme accomodates actual spheres, not so obvious with the Ptolemaic system as presented in the Almagest. Peuerbach's Theoricae Novae Planetarum has been translated by E.J.Aiton (Osiris, 2nd Series, Vol. 3 (1987), pp. 4-43), but I've only skimmed it; I need to reread it more carefully. Here's how Aiton describes it in his intro: Peurbach's Theoricae novae planetarum introduces the reader to the Ptolemaic geometrical models as embodied in the physical realizations described by Ptolemy in his Planetary Hypotheses. It's clear from the figure on the opening page that the Theoricae wasn't strictly homocentric, but employed eccentric spheres as well. Ptolemy "swept away" by Copernicus? I don't think so. An adequate discussion would also have to include geo-helio-centric (Tychonic) models; I believe many astronomers preferred a geo-helio-centric version of Kepler to the real thing, once the Rudolphine tables had shown that ellipses were here to stay.

Comment on The Phlogiston Theory is not equivalent to the Aquatic Ape Hypothesis. by Tim O'Neill

Tim O'Neill — Mon, 20 May 2013 22:50:38 +0000

Wikipedia says this about Purbach’s model:
“Purbach is also noted for his great attempt to reconcile the opposing theories of the universe, the so-called homocentric spheres of Eudoxus of Cnidus and Aristotle, with Ptolemy’s epicyclic trains. This work, Theoricæ novæ planetarum, had an enormous success and remained the basis of academic instruction in astronomy until years after Nicolaus Copernicus had swept away all these hypotheses.”

So “swept away” by Copernicus?

Comment on The Phlogiston Theory is not equivalent to the Aquatic Ape Hypothesis. by Michael Weiss

Michael Weiss — Mon, 20 May 2013 19:16:35 +0000

Hmm, I see you omitted the previous paragraph from Ben Richmond’s piece, which was even worse:

Pseudoscientists love to fashion themselves as modern Copernicuses whose ground-breaking, paradigm-shifting discoveries are being oppressed by the “priests” of the age, just as the Church covered up the Renaissance astronomer’s theory of the Sun in the center of the solar system with the Earth revolving around it. [emphasis added]

Comment on The Phlogiston Theory is not equivalent to the Aquatic Ape Hypothesis. by Michael Weiss

Michael Weiss — Mon, 20 May 2013 16:29:23 +0000

Phlogiston theory was also Kuhn’s standard example of so-called “Kuhn loss”, where a new theory loses some explanatory power possessed by its predecessor. Phlogiston theory explained “why metals had so many more properties in common than did their ores” (Structure, p.99), which Lavoisier’s theory failed to do.

As for Ptolemaic astronomy, I’m starting to wonder if Peuerbach actually did simplify Ptolemy. I state this diffidently, as I have a lot more reading to do here. I have not yet been able to come up with an “epicycle count” over 32 for the Syntaxis (that’s epicyles plus deferents plus equants …) Peuerbach adds spheres to make it a mechanical rather than a purely geometrical description — at least that’s how it looks to me at first perusal. (Apparently Ptolemy already proposed this in another work.) Wikipedia says that the oft-quoted figure of 80 epicycles referred to a descendent of the Eudoxian homocentric spheres, a very different beast.

As for the rant, I hope it felt good to write it — it felt good to read it! You don’t believe this sort of lazy journalistic shorthand (phlogiston=crazy-think, etc.) can be stamped out, do you?