by John Q on April 7, 2006

Following up Kieran’s post quoting Douglas Adams’ line that “You may think it’s a long way down the street to the Chemist’s, but that’s just peanuts to space” I thought I’d try to work out the scale of comparison that is, in some sense directly available to us and compare it to the scale of the universe. (I’m bound to make a mistake here, but what are comments threads for if not to fix these things).

The distances directly available to us range from around 0.1 mm (roughly, a hair’s breadth) to perhaps 10 million km, the distance a regular world traveller might cover in a lifetime. That’s from 10^-4^ m to 10^10^ m, or fourteen orders of magnitude. If I have it right, the potentially observable universe includes distances up to about 10 billion light years, or 10^27^ m, which is seventeen orders of magnitude greater than the maximum human-range distance.

Going the other way, the diameter of the electron is around 10^-18^ m (fourteen orders of magnitude smaller than the minimal human scale) and the Planck length is 10^-35^ m, another seventeen orders of magnitude smaller again.

So, in log terms, the range we can experience directly covers about a quarter of the range from the Planck length to the size of the universe. I suspect you could do something similar for time, taking the human range from tenths of a second to the centuries reachable with two or three handshakes.

Note: (Of course, there are no original ideas. After I wrote this, I found this handy scale at Wikipedia). Still, it’s done now.

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04.12.06 at 10:20 pm



Richard 04.07.06 at 4:27 am

Nice post. I guess it’s like sound or light – we poor humans only get to experience the bits in the middle of the scale…


Doug 04.07.06 at 5:25 am

Alas, there are no original comments either.


Simstim 04.07.06 at 6:23 am

Surely this is a bit closer to the spirit of that Adams quote?


Sirocco 04.07.06 at 6:50 am

Here is a scale reduction I like: if observable space is compressed by a factor of 10 billion, Earth is the size of a 1.3 millimeter grain of sand and the Sun that of a 14 centimeter orange 15 meters away. On this scale the distance to the nearest star, Proxima Centauri, is 4,300 kilometers — roughly that of Oslo to the Canary Islands.

Add the estimate that observable space contains more stars than there are grains of sand in the Sahara, or on all the planet’s beaches combined, and one may begin to feel slightly provincial.


Charly 04.07.06 at 7:21 am

10-18 is the diameter of a proton. Electron is much smaller than that if it even has a diameter


Nada 04.07.06 at 8:15 am

A whole QUARTER? Does anyone else find that astonishingly large? I feel like I live comfortably in the universe now, in addition to occupying a vanishingly small portion of it.


Santorum's Little Helper 04.07.06 at 9:12 am

Somewhat related:
At the University of Colorado they have a to scale model of the solar system. I consider myself somewhat numerate, but is a very different sense you get walking around the model and observing the scaled size and distances in lengths and sizes we understand at such an intuitive level.


Santorum's Little Helper 04.07.06 at 9:19 am

Here is some more info, if you are interested.

Excerpt from the link:
Some interesting facts illustrated in the model
The Sun is roughly the size of a grapefruit (14 cm diameter), while the planets range in size from dust-speck-size Pluto to marble-size Jupiter. Earth is about the size of a pinhead (1.3 mm diameter).

The inner planets (Mercury, Venus, Earth, Mars) are all located within a couple dozen steps of the sun, with the Earth located 15 meters from the Sun. The outer planets (Jupiter, Saturn, Uranus, Neptune, Pluto) are spread much farther apart with Pluto located about 600 meters (just over 1/3 mile) from the Sun. Walking the full length of the model would take about ten minutes, not including stops.

You can fit the Earth and the entire orbit of the Moon in the palm of your hand — which represents the farthest humans have ever traveled.

On this same scale, the nearest stars besides the Sun are more than 4,000 kilometers (2,500 miles) away — roughly the distance from Boulder to the Panama Canal.


joel turnipseed 04.07.06 at 9:41 am

The American Museum of Natural History has a fantastic exhibit on this.

Of course, as Thoreau said: “I have traveled a great deal in Concord.” With our imaginative abilities to do things like put together the Rose Center exhibit (or this post), not to mention to do the kind of roaming into other lives we do with the various arts–no need to feel entirely cooped up (or small).


Martin James 04.07.06 at 9:51 am

But how big is an idea?

Its curious to me how many people don’t believe ideas exist in space and time and that the few that do believe they must exist in space and time haven’t figured out a way to measure them.


Matt Austern 04.07.06 at 11:16 am

You do know the book and film Powers of Ten, right?


Brett Bellmore 04.07.06 at 11:55 am

A whole quarter on a logirithmic scale. On a linear scale, an infintesimal fraction.


Kenny Easwaran 04.07.06 at 3:25 pm

12 – the point is, that in some sense logarithmic scales are what’s relevant for comparisons like this. There are basically only four non-overalpping ranges possible for beings with a range of experience like ours. I was also quite impressed at seeing just how much of the universe we might comprehend that way. Of course, this still means that there’s three whole ranges from as big to as small as we can really comprehend, which are beyond our possibility of understanding in this physical sense at all.


John Quiggin 04.07.06 at 10:59 pm

“You do know the book and film Powers of Ten, right?”

Well, I do now. The whole point of posts like this is to get pointed to stuff like that. Thanks v much, Matt, I’ll chase it up.


emmineb 04.08.06 at 6:51 am

You can watch the “Powers movie of ten” movie at YouTube.
I saw it lying on the floor at my friend’s, who has a 102 inches projector. Definetely the best way to see it. Or any movie for that matter.
Then you have the double slit experiment cartoon; quantum mechanics made as simple yet as fantastic as kids’ magic.


p m 04.08.06 at 8:16 am

here you go.

also: this.


marek 04.09.06 at 2:10 pm

And this is the whole solar system at a scale of one pixel to about 10,000 km. That makes for the widest GIF you will ever have seen, but really does bring home the relative scale.

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