Talk:Two New Sciences

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What is this page for? What is the formula for Galileo's ramp?

(William M. Connolley 20:35, 23 Mar 2005 (UTC)) That is a strange comment. Here is (I hope) a better one: the page says:

• Galileo's experimental setup to measure the literal flow of time (see above), in order to describe the motion of a ball, was palpable enough and persuasive enough for Isaac Newton to state: I do not define time, space, place and motion, as being well known to all.
• Even Einstein would state...

The quotes are accurate but I do not see anything to attribute Newtons or Einsteins statements back to Galileo.

The section is titled reactions by commentators. The fundamental nature of Galileo's experimental setup obviously affected the conception of time for the physicists who came after him: Newton, for sure, and even Einstein's conception of a clock in Special Relativity (but he went past this concept in GRT). Perhaps that needs to be stated, but that is a separate article that belongs to twentieth century physics. Ancheta Wis 01:17, 25 Mar 2005 (UTC)

The Time in physics article does not cite Galileo's conception of time, not even his discovery of the constant period of the pendulum. But his philosophical concept of time obviously influenced Newton's concept: "...time, of itself, and from its own nature flows equably without regard to anything external..."

There is a quine here. Galileo's conception of time was abstracted for part of the basis for Universal gravitation (meaning the use of derivatives with respect to time, and the integrals over time -- Newton's fluxions and fluents); but the flow of water under the influence of gravitation, as a water clock would cease to "flow equably" if water clocks A and B were to be accelerated or jerked. For example, close to Earth, on the International Space Station, the water clocks would cease to "flow equably".

In other words, Newton's gravitation was formulated using a conception of time which exploited gravitation. ("...time, of itself, and from its own nature...") The definitions seem to be resting on something which is self-referential, or an indirect self-reference.

Ancheta Wis 10:17, 25 Mar 2005 (UTC)

(William M. Connolley 11:33, 25 Mar 2005 (UTC)) The section is called reactions by commentators. But neither Newton or Einstein are commentators on Galileo. I don't think that section is appropriate.

Not trying for a disagreement here. The commentary is on Galileo's conception of time, not on the man or his attitude. It is not an accident that Stephen Hawking included them all in the same book. Ancheta Wis 11:51, 25 Mar 2005 (UTC)

If you are saying that the flow of time could be a separate article, I do not disagree. But it all rests on that water clock used by Galileo. Ancheta Wis 11:51, 25 Mar 2005 (UTC)

"So great a contribution to physics was Two New Sciences that scholars have long maintained that the book anticipated Isaac Newton's laws of motion." --Stephen Hawking, ed. p. 397, On the Shoulders of Giants. Ancheta Wis 12:13, 25 Mar 2005 (UTC)

"Galileo ... is the father of modern physics -- indeed of modern science" -- Albert Einstein. --Stephen Hawking, ed. p. 398, On the Shoulders of Giants. Ancheta Wis 12:18, 25 Mar 2005 (UTC)

(William M. Connolley 12:22, 25 Mar 2005 (UTC)) OK, I've read OTSOG too. But saying that Newton got his absolute time, as known to everyone, from Galileo, is over-interpreting. Its also a bit odd to attribute exactly the opposite - Einsteins rejection of absolute time - to the same source.

Now we're getting to one of my favorite topics, Newton's use of functions called fluxions and fluents. His use of the term mathematical time bespeaks that he obviously had a feeling for the flow of time. If you are saying that he didn't get it from Galileo, then where did he get it? Newton must have included Galileo as one of the Giants upon whose shoulders he was standing. Ancheta Wis 12:36, 25 Mar 2005 (UTC).

[edit] "What is this page for? What is the formula for Galileo's ramp?"

To answer the original question on the talk page, Galileo was able to "slow down" the rate of acceleration by inclining his wooden molding by some angle θ. Horizontal would be θ = 0 degrees, and vertical would be θ = 90 degrees. By taking ratios of the elapsed times and angles, he was able to determine that the acceleration of gravity was constant. But by rolling the hard bronze ball down the ramp at angle θ he was able to "slow down" the acceleration by a factor of sin(θ)

I see that the sine article uses radians; 90 degrees = π/2 radians.

Ancheta Wis 11:20, 25 Mar 2005 (UTC)

[edit] Stillman Drake

It should be noted that the initial contributor to this article, Wikipedian User:Dandrake is the son of this noted authority on Galileo. Note to Dan: WMC forced me to re-examine Newton's relationship to Galileo; hence the flow of time which I attribute to Galileo, and its provenance to Galileo is called into question. What I found from Westfall is that Galileo's Dialog was part of Newton's study (but no evidence of Discorso). Hence I was forced to find a new home for the flow of time text, which concept I still maintain originated from the Giant, Galileo. One uncomfortable note is that Stephen Hawking's reprint of the 5 Giants called it Dialog on Two New Sciences. Now I could have just used Hawking to parry the call, but it is probably just as well to have moved the Newton and Einstein reactions to the New Sciences to a new home. Ancheta Wis 16:34, 25 Mar 2005 (UTC) I should probably start filling in the red link to Stillman Drake. Would that be alright with you?

[edit] Galilean Transformations

Can some tell me if Galileo actually published his Galilean transformation in this book, or did he just explain the concept of relativity via the "cabin below decks in a sailing ship" example? What I am wondering is whether the Galilean transformations are a Newtonian interpretation of Galilean relativity, since I know Newton was big on absolute time. --Michael C. Price ^talk 20:59, 5 July 2006 (UTC)

It seems the sailing ship example comes from Galileo's 1632 Dialogue Concerning the Two Chief World Systems. It looks compatible with specicial relativity. Haven't tracked down the first appearance of the Galilean transformation yet. --Michael C. Price ^talk 06:01, 6 July 2006 (UTC)