In the current Staff Report, Dex addresses the old joke about 2+2=5 “for large values of 2”. While the explanation he gives might be the relevant one for mathematicians, statisticians, and accountants, there’s another possible interpretation for physicists.
Physicists often relate various models with different domains by “changing” the values of fundamental constants. Thus, for instance, one might say that relativity becomes Newtonian mechanics in the limit where c goes to infinity, or that quantum mechanics does the same in the limit where hbar goes to zero. The joke could also be a reference to this practice, because these things are actually fundamental constants, just as much so as 2, and can no more be changed than 2 can.
Of course, when we say things like “as c goes to infinity”, or “as hbar goes to zero”, we don’t really mean that literally. It’s actually just a verbal shorthand for saying that all of the velocities in a problem are very small, or that all actions and angular momenta are very large. But that’s not as funny.
In audio engineering sometimes 2 + 2 = 2.828… Non-correlated audio voltages add by the root-mean-square method, so Vtotal = sqrt(V1^2 + V2^2). So put in 2V of voice and 2V of guitar, and the result witll be approximately sqrt of 4+4, or sqrt of 8, or 2.828427125… Noise voltages add the same way.
I’m just glad thesehorriblethreads aren’t getting rehashed. Or someone hasn’t worked this into the calculations involved in understanding a jet airplane on a treadmill.
I actually wonder if 2 + 2 could equal five for extremely small values of 2.
If the value of 2 was tiny enough, we could have quantum effects happen, and occasionally, a virtual 1 would suddenly appear and push 2 + 2 into equaling five.
2 + 2 certainly equals many superimposed values all at once, until you actually do the arithmetic and observe an answer, which has a high probability of being 4.
But now here’s a question: If many people do this same arithmetic, does each case constitute a new instance of the phenomenon? That is (using the language of the “many worlds” model) does the universe branch out into several new universes each time someone does this arithmetic and observes a solution, with each universe displaying a different one of the originally superimposed solutions?
Or, given that 2 is a constant, does the sum of 2 + 2 behave like an observation that is done only one time, once and for all no matter how many individual people do this sum to make the observation? Under this model, there would exist separate universes in which each of the possible sums is observed, but not a whole new set of separate universes each time someone does the arithmetic.
Could anyone speculate on what the “reality” is? (We’re talking about quantum reality, folks. Make what you will of that.) Or is this just philosophizing at a level beyond that which we could ever resolve by experiments?
Ah, I hadn’t noticed that this Staff Report was a repeat. I knew I had posted on the topic before, but had forgotten that it was in response to Dex’s report. So I guess this was a bit unnecessary, then.
In a related field, 3-phase electrical does some funky math that way as well, related to RMS wave math… 120v+120v=208v and the amperage is calculated with RMS…