April 25, 1997

If it were a star, then the immutable heavens had changed, and the basic contrast between the superlunary region and the corruptible earth was in question. If it were a star, the earth might more easily be conceived as a planet, for the transitory character of terrestrial affairs would now have been discovered in the heavens as well. Brahe and the best of his contemporaries did conclude that the visitor was a star. Observations like the one illustrated in figure 39 indicated that it could not be located below the sphere of the moon or even close to the sublunary region. Probably it was among the stars for it was observed to move with them. Another cause for cosmological upheaval had been discovered.

The Copernican Revolution, Thomas Kuhn p. 206-207.

The new star of 1572 was a super nova.
What were the arguments about it the 16th Century?

The class now breaks into groups with large paper to draw a picture of how the parallax would be used to decide this question. The pictures will be posted during discussion.

Discussion Questions:

• a. Assuming the nova is near the earth, is it closer, in your picture, or farther from polaris as you go north?

• b. A small variation (one degree for example) in angle produces a bigger error in distance if the star is close or far? How does Galileo turn this to his advantage?

  Discussion of data: on what basis does Galileo criticize the data of the "anti-Tycho"?
  How does Sagredo argue? Would you believe the 12 data points or the 5 data points? Do you think Galileo is using math properly in this case? Considerations of error and geometry supersede any amount of data, don't they?

  What is Galileo saying in the quote below? Do you agree? How does Galileo's idea relate to Dee. Where does this kind of thinking come from? (Pythagorean, mystics). Are there mathematicians who think like this today?

  Of such are the mathematical sciences alone; that is, geometry and arithmetic, in which the Divine intellect indeed know infinitely more proposition, since it knows all. But with regard to those few which the human intellect does understand, I believe its knowledge equals the Divine in objective certainty, for here it succeeds in understanding necessity, beyond which there can be no greater sureness.
  

  Dialogue Concerning the Two Chief World Systems, "The First Day," Galileo Galilei, page 23.

  Ulam's unreasonable effectiveness of math.

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