although I think logically and easily accepted at least the principles of symbolic logic when studying philosophy, I cannot perform mental arithmetic - the simplest calculation requires pen and paper;
my school education was seriously deficient because we never even heard of calculus - I understand the phrase, "mathematical study of continuous change," but lose the thread as soon as "functions" are mentioned.
However, it makes sense to be told that the position of a planet is a function of the time. There are two quantities, one dependent on the other. I have had to formulate this basic principle of calculus for myself when thinking about the nature of time and the concept of time travel. People say that they move along time at the rate of sixty seconds per minute yet sixty seconds and one minute are a single quantity. The Time Traveler does not accelerate along time but experiences time dilation which is described as a slowing down, not as a speeding up. Time Patrol timecycles do not move through time but disappear at one set of spatial coordinates and appear at another.
See Space and Time and The Logic of Time Travel: Part I.
6 comments:
Kaor, Paul!
I'm not much better than you when it comes to arithmetic and mathematics! Anything more complex than the simplest calculations and I have to use paper and pen.
And think of how HARD it was for arithmeticians to do any kind of mathematical calculations before Hindu numbers spread from India. That alone must have been what made possible the vast developments of mathematics seen in the West.
Sean
Kaor, Paul!
Another thing to keep in mind about "The Three-Cornered Wheel" is how impressed both Martin Schuster and David Falkayn were by the INTELLIGENCE of the Ivanhoans. Really, it's a pity we don't see them again after "The Season of Forgiveness."
Sean
I'm terrible at math myself. I have no problem with the -concepts-. I can comprehend time-dilation intuitively, for instance. But mastering algebra was an awful struggle for me.
Dear Mr. Stirling,
Even so, you did better than I did! (Smiles)
Sean
"I cannot perform mental arithmetic - the simplest calculation requires pen and paper"
It's a matter of degree.
I can do arithmetic and even basic algebra in my head.
I tend to visualize the symbols on an imaginary piece of paper.
However, I can only keep track of a very modest number of symbols at once.
So eg: I can only handle so many digit numbers in arithmetic, or so many variables in algebra.
Then I have to start writing the calculation. The paper provides a much greater working memory than my brain.
Kaor, Jim!
Even so you are still doing better than too many of the rest of us! Hard, rote drilling in the arithmetic tables is a necessary basic.
Ad astra! Sean
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