"2 is the rarest number in nature"

I remember reading a quote some time ago to the effect that two is the rarest number in nature, because if something can happen more than once, then it will probably happen many times, not just twice. This idea came up in a conversation yesterday, but I haven’t been able to find the exact quote anywhere. Unfortunately I don’t recall the exact quote or the person who originally said it, and googling hasn’t turned up anything. Anyone know the source of this idea?

Whoah…this new layout if funky.

Aaaanyway… I dont know if he’s the source, but Dr Asimov used the theory as part of the resolution of his novel The Gods Themselves. (On a much grander scale…heh.)

In that novel, after it’s discovered that they were causing problems for the inahbitants of an alternate universe, they sought an uninhabited universe to damage instead. The reasoning for even bothering was that the most likely case was that something like the creation of a universe won’t happen at all. It happening exactly once is also high probability. But if 2 is possible, the chances are that it’s happened many, many times.

… It makes a lot more sense when he’s explaining it.

Taking a look around, most of the animal life (including me :wink: ) posess bilateral symmetry…a geometry based on two.

Then wouldn’t three be just as rare a number in nature as two, and wouldn’t seven be also, and six? Is something happening exactly four times that much more common than twice? It all just seems so arbitrary. Meanwhile, I look on my front lawn, and there they are–two dogs humping. Duality abounds in our world at least, especially as regards reproduction of nearly all the vertebrates and even some invertebrates.

And it’s easy to say that a universe being created once is a ‘very high probability’–now that we have one. I don’t see it as all that likely in absolute terms, though…the most likely thing would have been for there to be nothing at all. To overcome that vast likelihood must quite reasonably have taken what some might call “supernatural” power. But I digress.

If the Creator can create one universe, He could just as well have created two, just to have a spare in case something went awry. If you believe Scientific American (cover story from late last year), there are actually an INFINITE number of universes in our “multiverse”. So there are thus by definition also an infinite number of universes exactly like this one–including all the same galaxies and all the people at the exact same ages they are now, sporting identical DNA and bearing the same names, having the same experiences at the same precise moment, walking the same dogs, etc. The old “we all have a twin somewhere” idea. And they supply some advanced math & physics that supposedly prove there is roughly a 100% probability of this being the case. Of course, this would also mean there are an infinite number of universes where everything and everyone are exactly the same as this one except for ONE person who’s named Bob Johnson in this universe being named Joe McTeague in the other…and an infinite number where TWO or THREE people have different names and different cars but everything else is the same, and so on, ad infinitum (literally). To my finite intellect, this is little more than an absurdist exercise that adds nothing to our collective knowledge base or to or understanding of even our lonely, single universe. However, if true, this would also mean, of course, that somewhere in “nature” there is a universe where there are exactly TWO of everything. So the OP’s assumption is cast in the shadow of some doubt.

I’m not familiar with the quote, but the idea is sound. A better way to put it might be “Either a thing is unique, or it is not. If it is not unique, then there is a greater chance of there being multiple other instances than just one other instance.”

Enola, bilateral symmetry is an example of 2 being a rare number, since many Earthly lifeforms are bilaterally symmetrical. Bilateral symmetry is not unique to one lifeform, nor is it rare. In nature, there is generally a lot more than one instance of any organism, therefore, there just two is rare.

We live on one planet, among many; in one solar system, among many; in one galaxy, among many; in one universe…is it unique or not? If not, it is more likely that there are many other universes than just one other.

From The Jargon File:

Zero-One-Infinity Rule: prov.

“Allow none of foo, one of foo, or any number of foo.” A rule of thumb for software design, which instructs one to not place random limits on the number of instances of a given entity (such as: windows in a window system, letters in an OS’s filenames, etc.). Specifically, one should either disallow the entity entirely, allow exactly one instance (an “exception”), or allow as many as the user wants — address space and memory permitting.

The logic behind this rule is that there are often situations where it makes clear sense to allow one of something instead of none. However, if one decides to go further and allow N (for N > 1), then why not N+1? And if N+1, then why not N+2, and so on? Once above 1, there’s no excuse not to allow any N; hence, infinity.

Many hackers recall in this connection Isaac Asimov’s SF novel The Gods Themselves in which a character announces that the number 2 is impossible — if you’re going to believe in more than one universe, you might as well believe in an infinite number of them.

Hmmm…

H[sub]2[/sub] is pretty common

Thanks for the replies everyone, most of you stated the idea better than I did in bringing it up :). Zero/one/infinity and unique/not unique are probably more clear ways to put it.

Cillasi explained it the way I was thinking. For example, Earth is the only planet we know of with life, and some people would argue that we’re the only one that exists anywhere. If we find another planet with life, it would be harder to argue that there’re only those two planets with life; more likely there are many more.

And hyjyljyj is right that if two is unlikely, then so is 3, 4, a million, etc. In fact it’s probably true that 3 is less likely than 2, and 4 less likely than 3, so the phrasing I used may have been exactly wrong :).

Aren’t binary stars quite common too?

…but 2 is the only even prime number.

Tlaking about rarity of numbers than certainly huge numbers like 10^(10^(10^10)) must be astoundlingly rare. I can think of no physical object that would possess the quality of this number.

On the other hand all rational numbers are exceedingly rare. If you were to pick a random number from a bag containing all of the numbers in the universe than you would never pick a rational number.