One of my old physics professors said something similar - there are only three numbers in the world - 0, 1, and infinity. No wait, zero is just one divided by infinity, so there are only two numbers, zero and one. So if the answer is not zero, it must be one. (ie, how to justify dimensional analysis and ignore any dimensionaless constant).
Hysterical, especially for the fact that he quotes 'two' and 'three' in the sentence itself.
Another one would be philosophy: there’s nothing, something and everything. Or logic: ∃, ¬∃ and ∀. Just rambling here, but seems like universal concepts across fields.
Chiming in from theoretical linguistics: it is impossible for natural languages to "count", i.e. make reference to numbers other than 0, 1 or infinity.
As an example, there are languages where prenominal genitives are impossible (0).
Then, there are languages, such as German, where only one prenominal genitive is possible (1):
> Annas Haus
> *Annas Hunds Haus
Finally, there are languages, such as English, where an infinite number of prenominal genitives are possible (infinity).
> Anna's house
> Anna's dog's house
> Anna's mother's dog's house
> Anna's mother's sister's ... dog's house
But there are no languages where only two or three prenominal genitives are possible.
This property is taken to be part of Universal Grammar, i.e. the genetic/biological/mental system that makes human language possible.
As a German speaker, the claim "more than one prenominal genitive is impossible" seems interesting but perhaps not entirely accurate. As a non-linguist I probably misunderstand the meaning of prenominal genitive and might be missing your argument's point. For the overarching discussion we should note though the great variety of refering to "more than one element" in German.
> Anna's mother's sister's dog's house
> Das Haus des Hundes der Schwester der Mutter von Anna.
It's difficult to parse though. We only get to know about Anna at the end of the sentence. Consequently, we avoid such sentences or use workarounds.
> Von Annas Mutters Schwester dem Hund sein Haus.
If you ever use such a construction German speakers will correct your bad language but they will perfectly understand the sentence's meaning.
He already got rid of "three" and just needed a little help to get rid of "two." Since we already have 0 and (almost) everything else can just be "one more" than something else, we only need 0 and one more ... or 1.
As a physicist? When we did physics at school, and we were solving problems, the answer was always a number together with its unit. pi² might be 10 because it is a pure number, but g can never be 10, because it is an acceleration, a physical quantity, so it must be 10 of some unit.
Not if you define g as the real number before m/s^2, in the expression '10 m/s^2'.
In middle school physics lessons this makes teachers to hate you (it's their job to ensure that you do not do this), but after that, this has advantages time to time.
.. I remember hearing an anecdote that ancient Greeks did not know that numbers can be dimensionless, and when they tried to solve cubic equations, they always made sure that they add and substract cubic things. E.g. they didn't do x^3 - x, but only things like x^3 - 2*3*x. I don't think this is true (especially since terms can be padded with a bunch of 1s), but maybe it has some truth in it. It is plausible that they thought about numbers different ways than we do now, and they had different soft rules that what they can do with them.
According to the Banach–Tarski paradox, if you accept the Axiom of Choice, you can disassemble a spherical cow and put the parts back together such that you end up with two cows of the original size. How exactly this affects Cow Economics is not well-understood.
I think it was Gauss who proved that any convex cow would work equally well. But we need to assume an infinitesimally thin and infinitely long tail as boundary condition.
1) it isn't circular, although just barely (it's an ellipse)
2) the length of the day is not really related to the length of a year, and the second was defined as 1 / (24 * 60 * 60) = 1 / 86400 of the mean solar day length
So this is really just a coincidence, there is no mathematical or physical reason why this relationship (the year being close to an even power of 10 times pi seconds) would exist.
But from the fact that an Earth year happens to be roughly pi*10^7 seconds long, it follows that in 10^7 seconds Earth travels about two radians, or one orbital diameter, and equivalently that the diameter of Earth's orbit is roughly 10^7 seconds times Earth's orbital speed.
Not sure why everyone is surprised.
Ah, and a year is pi*10e9 seconds (IIRC)