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From: Jeff Barnett <jbb@notatt.com>
Newsgroups: sci.lang,alt.usage.english
Subject: Re: OT: Converting miles/km
Date: Wed, 25 Sep 2024 10:06:07 -0600
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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