# Meaning of “one order of magnitude improvement”

There is no single development, in either technology or management technique, which by itself promises even one order of magnitude improvement in productivity, in reliability, in simplicity.

What exactly is the message trying to say? What exactly does it mean by one order of magnitude improvement?

• Link to context please? – simchona Aug 8 '11 at 18:31
• This is from "No Silver Bullet" by Fred Brooks. He is saying that we have Moore's Law for computer hardware, promising frequent doubling of computational power, but there is no equivalent for software engineering methodologies. – alexg Aug 8 '11 at 18:44

An order of magnitude is:

the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. In its most common usage, the amount being scaled is 10 and the scale is the (base 10) exponent being applied to this amount (therefore, to be an order of magnitude greater is to be 10 times as large). Such differences in order of magnitude can be measured on the logarithmic scale in "decades" (i.e. factors of ten).

To start, let's simplify the excerpt:

There is no development that promises an improvement of even one order of magnitude.

Since an "order of magnitude" is used to mean a major improvement, we can say that there is no development that gives a major improvement.

• Note that many scientist take an order of magnitude (in base N) to run from sqrt(10) ~= 3.16 through 31.6 (or sqrt(N) through N*sqrt(N)). That is the range is geometric (because it is a multiplicative measure) and centered on 10 (N), but the implied precision is pretty low. – dmckee --- ex-moderator kitten Aug 8 '11 at 20:34
• 100 is an order of magnitude larger than 10. (10^2 > 10^1) – Andrew Lewis Aug 9 '11 at 4:39

An order of magnitude is 10 times.

One order of magnitude is ten times greater, two orders of magnitude is 100 times greater, etc.

The phrase can be used literally to mean something that is ten times faster, better, or the like, but can also be used figuratively to mean something that is vastly different than before.

It can be used both positively and negatively:

The computer was orders of magnitude better than the abacus.
Last night's hangover was an order of magnitude worse than the one I had after your bachelor party last year.

In the context of this phrase, there are no breakthrough developments that will really significantly increase productivity, reliability, or simplicity.

Looks like somebody trying to add spurious precision to his argument. Improving reliability from 99% to 99.9% (or 50% to 95%) would, mathematically, be "a one order of magnitude improvement", but productivity probably can't be measured this way, and simplicity?!?

• These would be order of magnitude reductions of [downtime|inefficiency|losses], but would not be order of magnitude gains. – dmckee --- ex-moderator kitten Aug 8 '11 at 20:30
• @dmckee: Mathematically, I can't argue with you. But as a matter of English usage: are you really saying that nothing can ever be improved by an order of magnitude if it (say reliability) is above 10%? – Tim Lymington Aug 8 '11 at 20:43
• Tim, the number of burgers served can be improved by an order of magnitude, as can the range of a battery powered car (hopefully!); but no, you can not improve your fraction of the electorate by an order of magnitude once you have a significant portion on your side. – dmckee --- ex-moderator kitten Aug 8 '11 at 20:51