Cosmologists commonly note how small we are as humans in relation to the size of the universe, so this post has the goal of making you feel just a *little* bit better. It all relates to (1) how you count, and (2) as compared to what? Graphed my way, here is your new place in the universe:

The left-most scale is size in meters, but a logarithmic measure of in *powers of 10 meters* (e.g., E+04 is 10 to the 4th meters, or 10 kilometers), or in other words, in “orders of magnitude.” The horizontal scale represents each fourteen “places in the universe” listed below, ranging from the *“really small”* to the *“really big.” *You and your kind clock in at number 6, on the low end of the range between one and 10 meters in length (ten to the zero and ten to the first powers, respectively).

The negative powers of 10 at the bottom of the chart translate to the number of digits to the right of a decimal point, so the average human hair is about 0.0001 meters in width. That single water molecule requires nine zeroes to the right of the decimal point to measure its width in meters.

If we were to instead use a *linear scale* in Excel for this data, we would get a nearly-flat line all the way up through #13 if the size of the *observed* universe is used at the top value. *Everything else*, including our own Milky Way Galaxy, is insignificant in comparison, let alone us humans:

I have noted in earlier posts that although humans count things in integer, linear units, nature instead tends to “do math” logarithmically. In other words, “stuff grows” proportionally in exponential math, whether it be bacteria counts in an infected cut, nautilus shells, or even whole cities of people. The ball you drop falls to the ground at a rate that increases exponentially, about 9.8 meters per second squared (there’s the exponential). Gravity “counts” distances logarithmically. [2]

**Okay, so where am I and what does it matter?**

What that top graph is saying is that your place in the universe is just under half the way up the “complexity scale” that we can observe, if physical size can be considered a “proxy” for complexity and we count in powers of 10.

Single atoms define the elements, and they combine into molecules like water’s mix of hydrogen and oxygen. Carbon atoms are particularly “promiscuous” and combine in multiple and complex ways with oxygen, nitrogen and several other elements to create “organic molecules” of numerous types, including the amino acids and DNA that make up the cells of your body.

The cells of your body plus the millions of bacteria in your gut biome combine to make “you” and other humans. All of us together plus the rest of living and non-living things around us make up Earth. Add together lots of “earths” in orbit around stars and you get galaxies. Combine billions of galaxies and you get the Universe.

And you are reading this because “something happens” at this one-to-ten-meter span of complexity in which we humans occupy our small place in the universe. This “something happening” is that our organism type is able to observe “its own place” in that universe. Not only that, but we can both look all the way down to the atomic level and all the way up to galaxies formed back in time close to the “Big Bang” that created this dispensation of the universe.

And so, in this sense, we are “in the middle of the universe,” and we can observe it both up and down the scale from us. Quite the feat!

Notes:

- All sizes are approximate and many depend on how you measure them, but they are all close enough for the horseshoes (powers of 10) of this exercise. A picometer is one trillionth of a meter. One angstrom is 100 picometers. A micrometer is one millionth of a meter. A light year is 9.46 trillion kilometers, give or take.
- “Exponential” and “logarithmic” are two sides of the same mathematical coin. For instance, an investment growing at 10% “compounded” over three years would grow by an exponential function of
**(1+0.10)**, or 1.331 times its original value. The same function could be expressed as^{3}**3 times log(1.10) = log(1.331)**. The use of the logarithm turns a messy exponential function into a much simpler multiplication. The latter is likely how your calculator is actually doing that first calculation, and what you would have done using a slide rule fifty years ago. “Common” logs use a base of 10, but computers and physicists use a base of Euler’s number, or*e**,*which has a value of 2.71828… (like**pi**, never resolving) because of its special properties.

Tony BroughInteresting perspective on relative size.

Very, very few people understand the significance of logarithmic metrics. Even most educated people probably won’t understand that. It doesn’t change the significance of your message, but may cause many to misunderstand the true immensity of the universe. Your linear plot helps explain.

I recall in college the best example our professors used to explain the significance of logarithmic metrics was the scale of audible sound. For every decade of an increase, a doubling of volume… or something like that anyway.

@rklindgrenPost authorYes, this is the Weber-Fechner Law, and it applies to volume, pitch, perceived light intensity, touch, and bunches of other biological functions, all where we perceive linearity, but the differences are really logarithmic. One theory is that we evolved this sense because you can cram a much broader range of information in a much smaller space. In fact you can see this in the graph of the post, where one scale covers the breadth of our known universe from atoms to galaxies. All with a click of an Excel function switching from linear to log.