As I indicated in yesterday's post, I was disappointed by Ratcliffe's book, The Static Universe: exploding the myth of cosmic expansion (2010).
He fails to make his case, even to a will-to-believer like me, and he mixes up his case with a polemic against all of modern geometry, going back as far as Carl Friedrich Gauss. [Gauss is the rightwardmost figure in the photo above, a still of the afterlife of great mathematicians as represented in the stage show Fermat's Last Tango.]
The wrongness of the paths followed by modern cosmology, then, has its origin prior to the mid-point of the 19th century, when Gauss started working on non-Euclidean space.
As some of my readers may have learned at school, Euclid's geometry rests in large part upon the following axiom: "If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet...."
This is known as the "parallel postulate." It was stated in much simpler terms by a Scottish mathematician named John Playfair, roughly a generation before Gauss began looking into the matter. Playfair said, "There is at most one line that can be drawn through another line at an external point."
Sometimes popularizers summarize this all as "parallel lines don't meet," but that is misleading. It may sound more like a tautology than an axiom.. If we understand parallel lines as any pair of lines that both pass through a common third line at 90 degree angle, though, then this is an accurate inference from the fifth axiom.
At any rate, one key thing about Euclid's fifth axiom is: There is no proof of it. That's why it has to be taken as an axiom! Another key thing to remember: it doesn't sound necessary. It never did. The other four axioms in Euclid seem unassailable in a way this one does not. For example: Euclid posits that it is possible in principle to draw a straight line from any point to any other point. That is the postulate that space is continuous. Another one: all right angles are equal to each other. Now, that one sounds like a tautology. Every right angle is a right angle.
But the fifth axiom, either as Euclid stated it or in Playfair's reworking, looks like something tacked on to make the system work.
This situation (as Ratcliffe sees things) is what induced Gauss to make trouble, which led ultimately to the idea of a Big Bang and an expanding cosmos. Ratcliffe seems to be saying that real space is Euclidean space, and that any other view, even the possibility of any other view, involves over-thinking things, letting our abstractions run away from us.
"Carl Friedrich Gauss (1777 - 1855) is remembered as the Prince of Mathematicians," he writes at one point, "and it is he who holds a close second place in my adulation, after Euclid."
Don't mess with number one, though. As we read further, we find that "simple life" reference amplified. It seems that Gauss earns our author's admiration due to the nature of the life he led, the fact that he was a good teacher whose students "revered him for his even temper and generous spirit," and so forth: not due to his researches, especially not due to his contributions to geometry.
I've gone on a bit long. I'll finish this line of thought tomorrow.
He fails to make his case, even to a will-to-believer like me, and he mixes up his case with a polemic against all of modern geometry, going back as far as Carl Friedrich Gauss. [Gauss is the rightwardmost figure in the photo above, a still of the afterlife of great mathematicians as represented in the stage show Fermat's Last Tango.]
The wrongness of the paths followed by modern cosmology, then, has its origin prior to the mid-point of the 19th century, when Gauss started working on non-Euclidean space.
As some of my readers may have learned at school, Euclid's geometry rests in large part upon the following axiom: "If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet...."
This is known as the "parallel postulate." It was stated in much simpler terms by a Scottish mathematician named John Playfair, roughly a generation before Gauss began looking into the matter. Playfair said, "There is at most one line that can be drawn through another line at an external point."
Sometimes popularizers summarize this all as "parallel lines don't meet," but that is misleading. It may sound more like a tautology than an axiom.. If we understand parallel lines as any pair of lines that both pass through a common third line at 90 degree angle, though, then this is an accurate inference from the fifth axiom.
At any rate, one key thing about Euclid's fifth axiom is: There is no proof of it. That's why it has to be taken as an axiom! Another key thing to remember: it doesn't sound necessary. It never did. The other four axioms in Euclid seem unassailable in a way this one does not. For example: Euclid posits that it is possible in principle to draw a straight line from any point to any other point. That is the postulate that space is continuous. Another one: all right angles are equal to each other. Now, that one sounds like a tautology. Every right angle is a right angle.
But the fifth axiom, either as Euclid stated it or in Playfair's reworking, looks like something tacked on to make the system work.
This situation (as Ratcliffe sees things) is what induced Gauss to make trouble, which led ultimately to the idea of a Big Bang and an expanding cosmos. Ratcliffe seems to be saying that real space is Euclidean space, and that any other view, even the possibility of any other view, involves over-thinking things, letting our abstractions run away from us.
"Carl Friedrich Gauss (1777 - 1855) is remembered as the Prince of Mathematicians," he writes at one point, "and it is he who holds a close second place in my adulation, after Euclid."
Don't mess with number one, though. As we read further, we find that "simple life" reference amplified. It seems that Gauss earns our author's admiration due to the nature of the life he led, the fact that he was a good teacher whose students "revered him for his even temper and generous spirit," and so forth: not due to his researches, especially not due to his contributions to geometry.
I've gone on a bit long. I'll finish this line of thought tomorrow.
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