Re: Introduction to Doug's RSt (3)
Doug
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Thanks for your question Sun. Sorry it has taken so long to respond. The reversals are definitely a philosophical challenge, but assuming them, we derive the natural numbers from the integers and a whole slew of other things.
Starting with a unit ratio of space/time change (s/t = 1/1), the first possibility is 1/2 and 2/1, depending upon which aspect is reversing. These two ratios equate or resolve to -1 and +1 respectively and the combinations of them can be used to arrive at any natural number.
These fundamental units of motion were called time and space “displacements” in Larson’s works.
At the LRC, we call them SUDRs and TUDRs, denoting them with upper case S and T. A combination of them is denoted S|T.
Combining 1/2 and 2/1 on a calculator generates a sum of 2.5, but this is due to the underlying assumption that reciprocals of positive integers should be treated as fractions of a whole- instead of reciprocal integers.
As far as frequencies go, there is one cycle of reversal per two units of time (space). Summing frequencies, however, is trickier than summing displacements. As you probably know, combining two radio frequencies produces both the sum and difference frequencies, but the frequency of 2/1 is four times the frequency of 1/2.
Moreover, the absolute value of the space over time frequency (1/2) is equal to that of the time over space frequency (2/1). Taking this seeming contradiction into account requires us to think about it a little differently, which I’ll try to explain directly.
Starting with a unit ratio of space/time change (s/t = 1/1), the first possibility is 1/2 and 2/1, depending upon which aspect is reversing. These two ratios equate or resolve to -1 and +1 respectively and the combinations of them can be used to arrive at any natural number.
These fundamental units of motion were called time and space “displacements” in Larson’s works.
At the LRC, we call them SUDRs and TUDRs, denoting them with upper case S and T. A combination of them is denoted S|T.
Combining 1/2 and 2/1 on a calculator generates a sum of 2.5, but this is due to the underlying assumption that reciprocals of positive integers should be treated as fractions of a whole- instead of reciprocal integers.
As far as frequencies go, there is one cycle of reversal per two units of time (space). Summing frequencies, however, is trickier than summing displacements. As you probably know, combining two radio frequencies produces both the sum and difference frequencies, but the frequency of 2/1 is four times the frequency of 1/2.
Moreover, the absolute value of the space over time frequency (1/2) is equal to that of the time over space frequency (2/1). Taking this seeming contradiction into account requires us to think about it a little differently, which I’ll try to explain directly.
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