A blog on US politics, Math, and Physics… with occasional bits of gaming

Orders of Magnitude

A common concept in physics is that of an “order of magnitude”. This is usually expressed as a power of ten with suitable dimensions, and a famous video from 1977 exhibits the idea for spatial scales. However, similar concepts can be applied to time, mass, numbers of people, wealth, or other quantities.

Enrico Fermi popularized using relatively straightforward assumptions to estimate unusual, or initially-hard-to-fathom quantities. The benefits of such estimates are being able to do a rough calculation relatively easily, thus providing some rough constraints on more-complex (and more time-consuming) precise techniques - which might otherwise hide significant errors. Order-of-magnitude estimates can also provide insight into how you would go about measuring or manipulating a given quantity, since those tools and techniques can vary widely as the same quantity varies in scale.

Conversely, trying to build detailed descriptions or understanding at unfamiliar orders of magnitude can lead you astray. For example, you’re familiar with changes and processes that span seconds to decades, but probably have much less intuition for history that has unfolded over millennia or longer - or the details of chemical reactions that may unfold in microseconds or less. You might also plan your free time based on a mix of chores and relaxation - but that mix and which items you prioritize would change heavily if your income changed by a factor of ten. Similarly, it’s challenging to extrapolate from what you and your family & friends can accomplish in a weekend to what larger organizations and nations can accomplish when working together.

Too often, oversimplified “common sense” arguments are used to deceive and to push false narratives & misunderstanding. Such disinformation & misinformation distribution can use misunderstandings about scale & orders of magnitude:

So when you here about unusual processes or extreme time scales, compare it to other things of the same order of magnitude. Or think about how your own everyday experiences might or might not relate to the scale of the problem.

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