Re: Order of Magnitude

[Ben Kovitz <bkovitz -at- nethere -dot- com>]

Steve Goldberg wrote:

> I think 'order of magnitude' is a relatively new use of jargon and am
> grappling with how best to word it.
> My application increases speed by 2 to 3 times; so do I say:
> 
> * We increase speed by an order of magnitude of 2-3 times;
> 
> * Speed is increased by 2-3 orders of magnitude(s);
> 
> * Speed is increased (order of magnitude x 2)

Excellent question!  It's a testament to your integrity to understand
the meaning of the jargon before using it.  There are indeed a lot of
people who will be justifiably ticked off if you use this term
unconventionally.

"Order of magnitude" is well established in science and engineering. 
I wouldn't be surprised if it has 100 years of usage.

It means "the range of quantitative variation expressible by varying
the first digit of a measurement".  Increased by an order of magnitude
means "increased by a factor of 10".  Increased by two orders of
magnitude means "increased by a factor of 100".  Increased by five
orders of magnitude means "increased by a factor of 100,000".

The term comes up in fields where there are enormous variations
between the quantities involved--so enormous that it's not always
obvious what range of uncertainty you're talking about when you make a
rough estimate.  Normally when you make a rough estimate, you say, or
imply, "give or take 2 or 3" or something like that.  For example, you
might say, "the bookcase was roughly 4 feet tall," and people know
that you mean, "give or take a few inches," not "give or take a few
hundred thousand miles."  In fields like astronomy, though, there is
such huge range of quantities that you need to specify the number of
digits in the estimate you're making.  Specifying an order of
magnitude is like telling which ballpark you mean when you make a
ballpark estimate.  For example, the distance from the Earth to the
Moon is roughly 238,000 miles, and the distance from the Earth to the
Sun is roughly 93,000,000 miles.  Being off by "a little bit" in the
case of the Moon means one thing; being off by "a little bit" in the
case of the Sun means a much wider range of uncertainty.  That's
because the Earth-Sun distance is two orders of magnitude up from the
Earth-Moon distance.

To go to a different "order of magnitude" means to go beyond the range
expressible by changing just one digit.  For many rough, practical
purposes in fields with huge quantitative variation, all you need to
know is the range within a factor of ten--that is, how many digits are
in the measurement.

So I would recommend saying, "my application increases speed by 2 to 3
times" and leave "order of magnitude" out of it altogether.  The
element of "specifying how many digits it takes to describe the range
of variation" just doesn't enter into it.

Here are a couple relevant web pages:

http://www.wsu.edu:8080/~brians/errors/orders.html
http://whatis.techtarget.com/definition/0,,sid9_gci527311,00.html


Ben Kovitz
Author, Practical Software Requirements: A Manual of Content & Style
http://www.amazon.com/exec/obidos/ASIN/1884777597
http://www.manning.com/Kovitz

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