Re: OT: Converting miles/km

On 9/19/2024 5:12 PM, Christian Weisgerber wrote:

I'm sorry, I don't know where to post this.  I'm crossposting to
alt.usage.english, because statute miles as a unit mostly afflict
the English-speaking world.
 So you want to convert between miles and kilometers.  The conversion
factor is... uh...  A 40-year-old calculator book provides a useful
tip:  Unless you're designing a space probe, you can use ln(5).
 WHAT?
 Yes, the natural logrithm of 5 approximates the conversion factor
between miles and kilometers; specifically one mile is about ln(5)
kilometers.  It's accurate to four digits.
 If nothing else, it's faster to type on a calculator.
 I think that's hysterical.
 

After glancing at the discussion that follows this post, I thought it appropriate to point out the book "Dimensional Analysis" New Haven: Yale University Press (1922) by the Nobel Prize winning physicist Percy Williams Bridgman. It essentially describes and defines physical dimensions such as distance, speed, energy, force, etc. as well as units that are defined within a dimension such as meters, feet, and microns as distances. It shows that dimensions MUST match on both sides of an equation and, if not, there must be multiplicative constants that have appropriate dimensions to restore balance. You may define base dimensions and the others in terms of the base. For example, length, mass, and time to do mechanics.
Within an equation, you must use the same units everyplace for quantities in a specific dimension or dimensionless units of conversion such as 12 inches per foot. It even shows how to determine when physics equations express nonsense because of unit disparity or non matching dimensions. The cherry on the cake is discovery of new physical laws via dimensional analysis.
If you can obtain access to a copy of this book, I recommend taking a spin through it. A hundred years ago it was novel and educated some very bright individuals who hadn't quite caught on to what your current discussion is all about. It wasn't all that obvious way back when. Of course it was as soon as the subject was systematically presented.
--
Jeff Barnett