Dimensionless doesn’t mean colorless
March 26, 2011 Leave a Comment
I got a message from Barbara Finer, a tech marketing guru ( her job is staying ahead of the curve). She mentioned that she was member # 284947 on LinkedIn which had recently topped 100,000,000 members. Barbara cleverly spins this as an early adopter cred’ and I guess so, since 99.75% of LinkedIn members (including me) joined after she did. Naturally, my focus is on some ridiculously obscure aspects of these numbers, but aspects that when applied to engineering data zoom, up from ridiculous to mission-critical.
We’ve written about the limitations of the SI unit system before. One kind of number units can’t touch are known as dimensionless numbers. A 45° angle, 27%, π, and yes, 284,947th member, are all dimensionless, but obviously not colorless, numbers. Mathematical physics says that they need to stay dimensionless, and that there is little that can be said about them unit-wise, because they are not lengths, times, or amounts of electrical current. But PayPal tells us instantly when a credit-card number we entered is not one, so why can’t we offer engineers a little help in telling an angle from a LinkedIn member? OK, an engineer will be more interested in distinguishing an angular velocity from a frequency, a common cause of confusion in engineering calculations.
In the dimensionless world, reckoning angles and counting members are pretty much the same as measuring angular velocity and frequency. As it happens, software can in fact help distinguish them (one has to be careful not to get physics mixed up in it or numerical hell beaks loose) and this approach to categorizing dimensionless quantities will be part of our upcoming truenumbers product release later this spring. We look forward to telling you more about it. We’re thinking about audaciously calling our approach to representing engineering numbers SI++. Let us know what you think, I hope NIST doesn’t mind!
