I don’t remember if “c+c=c” shows up in the paper, but one of the things shown was that the speed of light is constant, hence “c”.

It could well be that " 2+2 =4" is true for all humans, if not " universally true", whatever that would mean. Such relations are just presupposed in our reasoning, a core component in the lens through which we view the world a la Kant.

It doesn’t.

Under both currently understood physical law, and the logical law of identity, c + c = c is unintelligible.

If you don’t already have it, see http://www.fourmilab.ch/etexts/einstein/specrel/www/

I guess “c+c=c” is nonsense as a logical string.

Thanks. I will read that later.

2 + 2 can equal 0,1,2,3 or 4 in modular arithmetic. If each 2 has the dimension of decibel sound measurements, the total number of decibels is 5ish. Whether 2+2=4 depends on the context. But if you supply the context 'the natural number 2 + the natural number 2 is the natural number 4 in the usual systems of arithmetic', it is definitely true.

Do you have a maths degree or are you self-taught?

I've got a maths degree and a good chunk of it was self taught due to course structure. Currently doing a PhD in it too, and I've been employed as a research assistant in applied statistics a couple of times. /CV :)

You should really post more often. :up:

I've got 1.8k of the damn things, I should probably post less.

Naw. I would ask you to lead a reading group on a symbolic logic text, but you’re probably already too busy. Perhaps @andrewk?

If you are standing on a train platform and the train is travelling at 20km/h according to your reference frame, and the driver switches the headlamp on and emits light at the speed c, then in your reference frame you will measure the light as travelling at c, and not at c + 20km/hr. — Crazy Diamond

Yes.

That was the puzzling observed phenomenon in the Michelson-Morley experiment that led to Special Relativity in the first place. If something is travelling at the speed of light and it emits light, everyone will measure that light as travelling at exactly the speed of light, whatever their reference frame. No standard addition ever works with light. c + c = c, and that's the observation that led to the equation. I don't see how and why it can be dismissed as only a superficial feature of different reference frames. Please enlighten me! (Pun intended...) — Crazy Diamond

OK, think of the reference frame as an implicit aspect of the velocity that must be factored in to any calculation. The train is travelling at 20km/h in my reference frame (on the train platform) but is at rest in its own reference frame. That is, there is only ever a velocity relative to a reference frame. Just adding the velocities assumes that the reference frame information can be ignored, whereas the formula factors them in. That is, the formula calculates the velocity of the emitted light in my reference frame given the train's velocity in my reference frame (20km/h) and the velocity of the emitted light (c) in the train's reference frame. Which is (20 + c) / (1 + (20 * c) / c^2) = c.

It's like calculating the amount of US dollars given 20 US dollars and 100 Australian dollars. 20 + 100 = 120, but the answer to the actual question is 20 + (100 * 0.70) = 90 US dollars (assuming the exchange rate is 1AUD = 0.70USD). If we ignore the currency rates, and it so happened that they were the same, then just adding the dollar amounts would give the correct answer. Similarly, if we ignore the reference frames and it so happened that there was no maximum velocity across all reference frames, then just adding the velocities would give the correct answer.

Some models satisfy it, others do not quite do so. If I have one rock in a cup, and out another rock in that cup, now I have 2 rocks in that cup. But if I have 1 drop of water, and put it together with another drop of water, I still have 1 drop water. Albeit, a bigger droplet.

Isn't 2+2=4 just an instance of the law of identity, A=A? Any something is itself. How could it be that anything in actual physical reality could be not itself? — petrichor

That's not the law of identity... And besides which, there's some evidence that quantum objects are individuated so there is metaphysical leeway here.

That's not the law of identity. — MindForged

You're right. It isn't. I am not claiming that "2+2=4" is actually the law of identity itself as traditionally given. The law of identity says that "A = A". "A" is identical with itself. What I am suggesting is that "2+2=4" or any other correct mathematical expression like it where two expressions on opposite sides of an equals sign are in fact equal is perhaps regardable as an instance of this law. The law itself is more abstract and covers all possible cases.

"2+2=4" is just another way of saying "4=4".

"2+2" and "4" are just different ways of expressing the same thing.

There is a reason it works to replace one expression with an equivalent one in an algebraic operation. You could replace "2+2" with "4" or "8/2" or "1+1+1+1" or "2*2" or "sqrt(16)" or "12-8". You get the idea.

And besides which, there's some evidence that quantum objects are individuated so there is metaphysical leeway here.

You're going to have to explain that to me. And if quantum objects are individuated as you say, what does that mean for pure mathematical quantities like "4"?

What I am suggesting is that "2+2=4" or any other correct mathematical expression like it where two expressions on opposite sides of an equals sign are in fact equal is perhaps regardable as an instance of this law. — petrichor

I think the question at issue is whether it is a fact. As others have explained, it doesn't have to be. It depends on your starting assumptions.

This has been investigated and found to be true. — Crazy Diamond

Can you provide a link or citation for this? Cause I was curious to read more, but I can't find anything. Thanks!

Can you provide a link or citation for this? Cause I was curious to read more, but I can't find anything. Thanks! — NKBJ

The formula for adding velocities in relativistic physics is
$u = \frac{v + u'}{1+\frac{vu'}{c^2}}$

It is described here. Like any other formula in physics, it depends on the ordinary truths of arithmetic.

There's no need to go al relativistic. One raindrop plus one raindrop makes one raindrop.

It's universal given a standard definition for arithmetic and natural numbers. And seeing as how useful arithmetic is, we can assume any intelligent beings out there in the cosmos will agree that 2 + 2 = 4.