Logs of Nature

In Mathematics by Brian Koberlein3 Comments

We generally think of numbers as a linear progression from 1 to 2 to 3, etc.  We also tend to measure things around us on a linear scale.  A ten hour road trip, for example, is very different from a one hour trip.  In the sciences, however, it is often more useful to look at things on a logarithmic scale.

A logarithm scale is one that focuses on the overall size, or  “order of magnitude” of objects.  For example, if something has a mass of 100 kilograms, then on a log scale it would be 2, since 100 = 10 x 10.  Likewise, 1,000 would be 3 on a log scale, since 1,000 = 10 x 10 x 10.  In general, you can base your log on any number you want.  The number 128 is 2 x 2 x 2 x 2 x 2 x 2 x 2, so you can say its log is 7 in “base 2.”  Perhaps the most common base in the physical sciences is the so-called natural log, which is a log of base e, where e is an irrational number about equal to 2.71818…

Log scales are so deeply rooted in physical phenomena that even our eyes and ears operate on a logarithmic scale.  This is why the loudness of sound is measured in the logarithmic decibel scale, and the brightness of stars is measured in apparent magnitude, which is a logarithmic scale of luminosity.   Even young children tend to perceive numbers on a logarithmic scale before we teach them linear counting.

Perhaps the most famous demonstration of a logarithmic scale is the short movie “Powers of Ten,” by Charles and Ray Eames.

While it’s a bit outdated, it shows how the universe can be viewed on a logarithmic scale, and how on such a scale humans exist roughly in the middle of the very large and the very small.

Comments

  1. my point is. that the exact dimensions is visually and metrically imposible to measure beacause it is gettin stretched up to its tension limits then snap back again to compress but like a rubbetband of a given weight eg. 1 kilo if rubber streched = 1,kilo unstreche rubbe. And why a galaxy loook flat is because of gravity. it is being compressed by the … actually its not a space.. that is why it looks like piizza or like making a dough whereas the baker is the grvity and the table is pushing upwards.

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