## General Discussion > Ratio of Ratios

How do you relate your concept of "ratio of ratios" to the concept of "cross-ratio" yielded by the search URL above?

Doug wrote:
"If we express this same relationship in terms of the ratio of the number of SUDR units (2) and and the number of TUDR units (1), instead of in terms of the space and time units that make them up, we get a different number altogether, even though they are both expressing the same value. The new number is a ratio of ratios"

Regards,
Horace

August 4, 2007 | Horace

The cross ratio is a concept of projective geometry. I remember researching it a little last year, but I would have to go back to refresh my memory about it, before I could say much about it.

However, the ratio of ratios is simply a mathematical concept and it means exactly what it says it does:

a|b:c|d

Doug

August 4, 2007 | Doug

Their "ratio of ratios" seems to have the same origins as yours.

In projective geometry tutorial is writen:
"As mentioned before, projective geometry preserves neither distances nor ratios of distances. However, the cross ratio, which is a ratio of ratios of distances, is preserved and is therefore a useful concept"

In that context "cross ratio" is synonymous with "ratio of ratios" and in Bruce's publication, cross ratio applies not only to distances but pairs of units of motion as well. Just like your gear ratios of SURDS an TURDS.

August 4, 2007 | Horace

LOL. You mean space unit-displacement ratios (SUDRs) and time unit-displacement ratios (TUDRs). I'll look into it as soon as I can. I have my hands full with ISUS stuff at the moment.

Doug

August 6, 2007 | Doug

Doug wrote on rstheory.com:

"The markers were not very fresh and I didn't have my glasses, so I missed a lot of the details, but as I listened I realized that Bruce's work is not incompatible with mine. In fact, they're complimentary to a great extent..."

I am so glad you had a talk with Bruce and the other guys. I felt you were ignored far too long, and was afraid that after the ad hominem flame wars on the ISUS site, you'll never work together again.

I always thought that your work had a lot in common (as evidenced by the previous posts in this thread). I hope that my words of encouragement played a small role in leading up to the opening onto each other's concepts.

Did anyone mention me during your meeting even once ?

Horace

January 28, 2008 | Horace