In the “Does 2 + 2 = 5 for very large values of 2?” column, Dex regards this joke as being related to rounding and estimating. For example, he gives a 0-decimal rounding of 2.48+2.47=4.95 => 2+2+5.
I’d like to mention this is one of my favorite math jokes. It was, in fact, hanged on my wall for a while. But I always considered it an approximation-related thing.
For example, you can really say that 2x~=2x+1 for very large values of x (where the unit size “1” is negligible in comparison to the very large 2x). Thus, for approximation sake, 2001 can be treaded as 2000 to simplify calculation (x=1000).
The joke relies on replacing x with the small value “2”, but keeping the “very large value”.
Am I way off in this?
Note: Maybe this was done before. “2+2=5” is not easy to search.
PS: There’s also a beautiful stroll down mathematics history lanes around the “2+2=5” theme. It’s too long to post here, but if anyone is interested, I will post it somewhere else.
I think that the “2x ~ 2x + 1 for large values of x” and then require the substitution x = 2 to get “4 ~ 5” and then replace 4 with 2 + 2 … is way too complicated for a joke, even a mathematical one.
The statement referring to “large values of 2” is pretty clearly values like 2.8, seems to me.
If you’ve got something amusing, I’m assuming it’s copyrighted, in which case the best bet is to find an online source (that has copyright rights) and provide a link. I’d be curious, for one.
I can also add a couple of comments on that from another website I frequent (no copyright):
[regarding Gauss’s arithmetic]
I must point out that this arithmetic was also independently developed by Johann Boylai and by Nicolai Ivanovitch Lobachevsky. Although Gauss was almost certainly the first to conceive of it, he feared to contradict the deeply rooted sentiment that 2 + 2 = 4. Even those who were willing to consider 2 + 2 = 5 would laugh at the idea of a smaller value! So Gauss never published his ideas, despite his already sterling reputation. But when the younger and still unknown Boylai proved braver as well, publishing his work, Gauss attempted to take credit for the discovery. Unbeknownst to both of them, Lobachevsky had already published in Russia 6 years earlier.
Thus it is more properly Lobachevsky’s arithmetic, not Gauss’s.
[second note]
Perhaps it should also include the truth and fuller implications of Kurt Gödel proof, which may have been the reason for his ‘retirement’ from mathematics. The dilemma of mathematics remaining incomplete by not admitting inconsistencies is challenged. The result, 2+2=4, which is accepted as true, yet clearly unproved, presents us with the disturbing fact that mathematics does not just remain incomplete, but also uncertain.
Thanks, Puzzler, I’ll have that link added to the bottom of the Staff Report.
However, I suspect that any proof by Nicolai Ivanovitch Lobachevsky would beat Gauss by a matter of weeks (or months, perhaps) but not years… at least, according to Tom Lehrer’s take.
Dex makes a good point about precision in measurement at the end of the article. But I always thought the humour in the joke was merely based on the absurdism of the phrase “for large values of 2”
Perhaps it’s just because I’m a physicist, but I have a different take. Folks will sometimes say things like “Quantum mechanics reduces to classical mechanics, for low values of [del]h[/del]”, or “Relativity reduces to Newtonian kinematics, for large values of c”, when of course, [del]h[/del] and c are fundamental constants, which can no more have “large values” than 2 can.
Your error is in perceiving that the only definition for “2” is the integer value meaning 1 + 1, where “1” is the unit integer. Obviously, “2” can mean more than that.
IANA physicist, but isn’t c specified as the speed of light in a vacuum? The speed of light in a different medium - e.g. a cloud of sodium vapor - can be significantly lower, but it doesn’t change the lightspeed constant.
c ought to be renamed “Einstein’s Constant” because it is a constant, as it is the speed of light in a perfect vacuum. If you measure how fast light goes in any other medium, you get a number less than c (assuming you don’t screw up your units and your measuring apparatus is accurate enough).
