Base 10 logarithms are evil

On Mon, 1 Mar 2010 23:42:18 +0000, Dr J R Stockton wrote:

In sci.astro message , Mon,
1 Mar 2010 02:52:34, Matt posted:

This is what it means:
http://en.wikipedia.org/wiki/Resistor#Preferred_values
A logical scheme is to produce resistors in a range of values
which increase in a geometrical progression, so that each
value is greater than its predecessor by a fixed multiplier or
percentage, chosen to match the tolerance of the range. For
example, for a tolerance of ±20% it makes sense to have each
resistor about 1.5 times its predecessor, covering a decade in
6 values.

What? Not in ten values?! It seems that the electrical engineers
aren't tenth-dividing SI purists after all.


In SI, when it is appropriate to subdivide into parts of equal size,
then tenths, hundredths, etc., are used.

Ah. But when is it appropriate to divide real-world measurements into
tenths?

Don't most people find halves, quarters and thirds easier to estimate
than tenths? It was an acquired skill to read hundredths of a gram
(tenths of the smallest division provided on the scale) in chemistry
lab. Visually interpolating 0.3 and 0.7 did not come naturally to me.

Gasoline is sold by the tenth-gallon, but for whose convenience? I
usually think more in terms of half-a-tank than 7.3 gallons.


But, although the resistor values are expressed in SI, the choice of the
values is not governed by SI.

In the primitive days of electronics, it was found difficult and
unnecessary to make cheap exact-value resistors in bulk; hence the
common +-20% tolerance band for resistors. With such a tolerance,
values 1.0, 1.5, 2.2, 3.3, 4.7, 6.8, 10 cover the range 1 to 10. That
set of values, now standardised, is essentially a pragmatic, evolved
convention.

And there's the rub. SI is about conformity to fixed fractions of an
arbitrary measurement of length designed to be anti-imperial and
anti-everything else with which people were already familiar. It was
successful compromise: it made everyone unhappy. And threw away
centuries of pragmatic effort to measure things in ways that worked
well outside chemistry labs and other ivory towers.

The imperial foot may not be the best unit of length, and its division
into 12 inches can be computationally inconvenient, But it works
pretty well in everyday measurements by being easily divided into
halves, quarters and thirds without introducing non-terminating
decimal values.


Values half-way in between, and at the quarters, are also
standardised.

That is not a linear subdivision into equal differences; it is one of
equal ratios. Sometimes that is necessary - just consider a piano in
which each octave (factor of 2 in frequency) were divided into equal-
difference steps. Indeed, SI is an equal-ratio system for "units".

If we were starting again, we might choose ten subdovisions :
1.00 1.26 1.58 2.00 2.51 3.16 3.98 5.01 6.31 7.94 10.00 or
1.00 1.25 1.60 2.00 2.50 3.15 4.00 5.00 6.30 8.00 10.00 - and some of
those numbers are relatively common in electrical work.

Andrew Usher wrote:
Matt wrote:

Where do you find natural log paper?

What are the labels on the major divisions?
What? No links to sources of natural log paper? No links to scans of
graphs that you have made on natural log paper?

Who graphs on paper any more?

anybody who needs hard copy and doesn't have access to a computer
printer.

Would you really stop working if the computer broke?

snip

/BAH

On Mon, 1 Mar 2010 04:15:55 -0800 (PST), Andrew Usher wrote:

Matt wrote:

Where do you find natural log paper?

What are the labels on the major divisions?

What? No links to sources of natural log paper? No links to scans of
graphs that you have made on natural log paper?

Who graphs on paper any more? In any case, if you had to, you would
likely calculate the logs with a calculator (which all have log_e),
then graph them.

What benefit might there be from a plot created as suggested above by
taking logs with a calculator? The slope for an equation using 'e' is
simply rise/run on the graph; no need to convert from the slope
measured on a log10 plot.

What would be the cost of this convenience? It would be finding the LN
for each data point. I don't see any economy of effort.

During the centuries when there weren't calculators and countless very
smart people were invariably making graphs on paper, no one looked at
log10 paper and said, "We really need some LN paper instead?"

What might we infer from that?


How do you know you "would prefer to use natural logs even for
graphs?" Have you ever done it?

Yes, but on a computer, not on paper.

Then it shouldn't be difficult to produce a screen capture of such a
graph.

How did you label the major divisions on a log_e axis?

On Feb 19, 4:21*pm, Andrew Usher wrote:
The very first tables of logarithms were according to the natural base
e (essentially). Base 10 was only adopted because it is somewhat more
easy for calculation with the decimal system. Now that technology was
obliviated the need to use log table for calculating, there is no
further reason to use base 10 logarithms at all.

Yet, many fields of science continue to do so. Sometimes this creates
confusion, as in the fact that optical depths may be measured either
way, and it is not always specified which. There is no benefit to
thinking in base 10, conceptually, and there is the serious
disadvantages of always having to insert factors of log 10.

Using base 10 logs is another example (along with the metric system)
of ignorant decimal-philia.


The very first tables of logarithms and logarithmic rulers were
published/manufactured for engineers in order to help in multiplying
decimal numbers. They were in base 10.

On Mar 11, 1:33*am, "Ostap S. B. M. Bender Jr."
wrote:

The very first tables of logarithms and logarithmic rulers were
published/manufactured for engineers in order to help in multiplying
decimal numbers. They were in base 10.

Not so. http://17centurymaths.com/contents/napiercontents.html - no
base 10 there!

Andrew Usher