A Problem of Scale: Halfway in size between an atom and the universe

February 18, 2007 4:10 PM

"A human is halfway in size between an atom and the known universe"... This is a paraphrased quote I have come across several times. I like it. Who said it first? How true is it in the most literal sense? And, finally, what errors arrive in postulating a universe, or an atom, which can be measured AT ALL from our singular, relativistic, perspective?

I found this quote from Cosmic Evolution which further complicates the whole relative size issue:

"Roughly halfway in size between an atom and a human, the amoeba has poor awareness and coordination. It generally responds only at the point stimulated, communicating the information sluggishly through the rest of its body. Although amoebas have developed a crude nervous system, living things that aspire to be more agile—and smarter—surely need quicker internal reactions." - link

Kind of sets another stage from which to view this question.

I also found this quote from Holmes Rolston which further complicates things:

"The human world stands about midway between the infinitesimal and the immense. The size of our planet is near the geometric mean of the size of the known universe and the size of the atom. The mass of a human being is the geometric mean of the mass of the earth and the mass of a proton. A person contains about 10²⁸ atoms, more atoms than there are stars in the universe. Such considerations yield perhaps only a relative location. Still, questions of place and proportion arise." - link

Who first made this often used statement? My earlier questions still stand :-)

Thanks...

posted by 0bvious to Science & Nature (13 answers total)

Avogadro's Number is 6.022 * 10^23. That's the number of hydrogen atoms in a gram. If you figure the average atom in a human weighs about like nitrogen, about atomic number 14 (carbon and hydrogen lighter, oxygen and lots of stuff heavier), then an 80 Kg man contains maybe 3.5 * 10^27 atoms.

Nobody really knows how much mass there is in the universe. The estimates keep fluctuating up and down as cosmology keeps proceeding. But I read one time that number of hadrons in the universe was on the order of 10^73. Thus figuring on a logarithmic scale, that would put a human nearer to one third than one half.

Of course, that's mass. "size" could also mean "distance". The diameter of a proton is 8 * 10^-16 meters. A human is roughly 2 meters (give or take), so about 2.5 * 10^15 bigger.

Diameter of the universe? Well, in terms of General Relativity it's not even clear that's a meaningful concept. This page gives estimates on the order of 20 billion light years. A light year is just shy of 10^16 meters, so that would make the universe about 10^27 bigger than a human. We're closer to the middle, logarithmically speaking, but still not really at it.

Of course, if you evaluate it on a linear scale, then the atom is essentially zero, and half would be half the universe -- but that's no fun.
posted by Steven C. Den Beste at 4:38 PM on February 18, 2007

It appears to be from the start of a 1932 book by Sir Arthur Eddington, a British early twentieth century astrophysicist. According to JS Huxley in 1941, Eddington begins "his fascinating Stars and Atoms by pointing out that man is almost precisely halfway in size between an atom and a star."

I can't find an online reference that would work in the US but a Google book search brings up the result.
posted by TrashyRambo at 4:54 PM on February 18, 2007

You might enjoy the classic educational film Powers of Ten. They have a link to watch it at the official site but it didn't work for me. Here's a Google Video link.
posted by PercussivePaul at 5:01 PM on February 18, 2007

To follow up on what Steven C. Den Beste said, there's certainly ambiguity in how to define distance cosmologically, and there's also the question of where you put the edge of the universe you're measuring to.

For the latter, the cosmic microwave background is a good choice. If you do that then I think the comoving distance is about 20 billion light years, and that's the most sensible choice of distance measure for this question I think (the others differ by a factor of a thousand each way).

A back-of-the-envelope calculation I've just done puts the number of hadrons in that volume at nearer 10^79.
posted by edd at 5:19 PM on February 18, 2007

I was continuing to shrink, to become... what? The infinitesimal? What was I? Still a human being? Or was I the man of the future? If there were other bursts of radiation, other clouds drifting across seas and continents, would other beings follow me into this vast new world? So close - the infinitesimal and the infinite. But suddenly, I knew they were really the two ends of the same concept. The unbelievably small and the unbelievably vast eventually meet - like the closing of a gigantic circle. I looked up, as if somehow I would grasp the heavens. The universe, worlds beyond number, God's silver tapestry spread across the night. And in that moment, I knew the answer to the riddle of the infinite. I had thought in terms of man's own limited dimension. I had presumed upon nature. That existence begins and ends in man's conception, not nature's. And I felt my body dwindling, melting, becoming nothing. My fears melted away. And in their place came acceptance. All this vast majesty of creation, it had to mean something. And then I meant something, too. Yes, smaller than the smallest, I meant something, too. To God, there is no zero. I still exist! --- The Incredible Shrinking Man, by Richard Matheson.
posted by SPrintF at 5:24 PM on February 18, 2007

(I should add that 20 billion light years is the radius, not the diameter)
posted by edd at 5:29 PM on February 18, 2007

Just as a point of information, the geometric mean refers to the square root of the product of the two numbers. At least the statement about the relative lengths of the atom, the earth, and the universe is approximately correct.
posted by number9dream at 11:48 PM on February 18, 2007

In case it's not obvious, taking the geometric mean is identical to averaging the logs, as Steven C. Den Beste did.
posted by edd at 4:11 AM on February 19, 2007

It is a meaningless observation, really..

One might take it to mean that we have an about equal ability to look into the micro as the macro. That would say nothing about the nature of reality, of course, because it is still contingent on our understanding - necessarily incomplete. Even more though, the expected error in estimates of the size of the universe is measured in orders of magnitude.

In the most broad sense, if you aren't at an end point, you must be somewhere in the middle. If you lie at some point of an infinite line, then you are always in the middle, no matter where on the line you are!

Finally, if you ask yourself why estimates of the macro are so flawed, but estimates of the micro are precise, consider that More Is Different.
posted by Chuckles at 6:36 AM on February 19, 2007

The Powers of Ten video is still pretty cool though!
posted by Chuckles at 6:38 AM on February 19, 2007

The View from the Center of the Universe by Joel Primack & Nancy Abrams is a nice riff on how we are situated to observe the smallest and the largest, both size-wise and time-wise. If they're giving their talk near you, go! it's excellent. Their presentation has some great video that obviously can't fit in the book.
posted by anadem at 8:16 AM on February 19, 2007

"Size of an atom" also varies to some extent depending on how it's defined. The radius of a hydrogen atom (double it to get a diameter) is anywhere from 25 to 120 picometers, depending on how you're defining and measuring size. OTOH, when you're looking at a geometric mean between scales that large and that small, a 5-fold difference might not be a major issue.
posted by DevilsAdvocate at 9:26 AM on February 19, 2007

On a whim, I decided to look at what is at the geometric mean between a proton and the whole universe, and I came up with 400 miles, about the size of a smallish country. So perhaps a better question is not why humans are close to the geometric mean, but why human societies are scaled close to the geometric mean?
posted by edd at 9:52 AM on February 19, 2007