Re: OT: Converting miles/km

Jeff Barnett <jbb@notatt.com> wrote:

On 9/25/2024 2:46 PM, J. J. Lodder wrote:

Jeff Barnett <jbb@notatt.com> wrote:
 

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.

 
He didn't win the nobel for this book.
(or for his peculiar philosophy of sciece)
It is one of those books that many know exists,
but few will actually have seen it, let alone read any of it.
(don't worry, no loss)
You will need a good old university library to find it,
or you may find a very rare antiquarian copy,
or an almost as rare and by now also antiquarian reprint.
 

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.

 
All completely trivial.
What's more, the subject matter has been almost completely forgotten.
All that remains is elementary high school knowledge
of the -conventional- systems of dimensions
that is nowadays associated with the SI.
Few people even know anymore that other systems of dimensions
are possible.
The misconception that a 'dimension' is somehow a property
of a physical quantity is shared nearly universally.
 

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.

 
You may crash Mars landers through non-matching units,
never by non-matching dimensions.
 

The cherry on the cake is discovery of new physical laws via
dimensional analysis.

 
Not really. At best it allows you to guess at the form.
The book codifies the obvious.
Dimensional analysis was already well known and understood
through the works of the 19th century greats, such as Kelvin
and Rayleigh.
The use of the so called 'dimensionless numbers',
such as Reynolds', or Froude's number was already well established.
 

If you can obtain access to a copy of this book, I recommend taking a
spin through it.

 
A waste of time and perhaps also money, if you don't mind me saying so.
 

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.

 
Already then, Bridgman was belabouring the obvious,

 
Let me start by pointing out that I don't believe I implied that his
Noble Prize was for this book; I know it wasn't. I'm assuming from the
above that you haven't read the book. There is material in it that you
must have skipped or don't remember if you had.

That is quite possible. I have held a copy in my hands long ago,
and glanced at some of the pages. Enough of them to justify my opinion
expressed here that he is belabouring the obvious with to many examples,
while not expression the general idea of 'dimension' clearly enough.
It may have been a first edition.

By the way, much to my
surprise new paperback copies are available from Amazon for a modest
price. The copy I have was made on a xerox machine 50+ years ago and is
torture to read - every page has a different slant.
 
It's mostly true that unit mistakes can cause mayhem but so can
dimensional mistakes. I remember helping track down a calculation that
would not balance on Apollo because a newbie engineer didn't realize
that "knots" measured speed, not distance. No harm was done, just a big
waste of time. This is all apropos of the discussion in this thread.

Certainly, no need to inform me about the such problems.
I have wasted some time correcting someone who had used old data,
assuming that 'statvolt' is just an oldfashioned name for 'volt'.
(this is both a unit error and a dimension error)
 

There were other similar mistakes that were common - I suppose these
events (as well as greed) were responsible for the huge people and
project redundancies on Apollo.
 
Later on in a different world, I invented some unit and dimension
software for the Symbolics Lisp Machines. Dimensions had the status of
data types and units were presentation types. So if you wanted to input,
say an energy, the mouse would highlight and retrieve both erg and joule
values but not numbers that represented forces. The developer could
define the system (e.g. mks or fps) by preferred units as well as the
electrostatic system in play. Conversions were automatic and, assuming
the programmer didn't bitch things up, neither could his users. I
mentioned this stuff to a physicist and was told to go read his copy of
Bridgman.

I know.
This is automating those crazy American engineering formulae like:

X/[unit of X] = [strange dimensioned constant] times [A / unit of A to
be used] times [B / unit for B] .....  divided by [F/ unit of F]

The book is chuck full of examples that show world class physicist
making unit and dimension errors. It also shows some techniques to avoid
them. And as I said above some new physics was discovered using the
described techniques.

Possibly, but I wouldn't know an example of new physics -derived- in
this way.
All I know about are swindles, rederiving what you know already. [1]

Once again, I remind you the book is 100 years
old. The above discussion shows that folks in the arts and sciences are
still making elementary mistakes of the sorts described.

Of course, there is no end to the mistakes people will make.
By Murphy, the best remedy is not correction afterwards,
but using sane systems beforehand
that makes most of those errors impossible to make.

Jan

--
"Don't tell me what is wrong with the works of others. Do something good
yourself!" (a grumpy old professor I knew long ago)

[1] Typical example: It is sometimes claimed that you can -derive-
the period of a pendulum using dimensional arguments,
as depending on length of the pendulum and small g only.
(and hence independent of amplitude)
This is a typical example of assuming what needs to be shown.