## Phil Plait gets it wrong

See A (very) smart kid and a solid theory

But when you start to approach the speed of light, or deal with masses that are very large, Newton’s math breaks down. It doesn’t work.

This is wrong, completely so. Newton’s math works just fine – it simply doesn’t give the correct answers, because Newton’s laws don’t hold over those domains. Newton couldn’t have *known* that – his theories were correct to the limits of measurement of his day – but he was, in fact, incorrect about how the world works.

Relativity may also be shown to be wrong. That would be quite impressive. But not through merely manipulating mathematics. It’s conceivable that a better mathematical description could be found, one that would clear up the problems of unifying General Relativity and quantum mechanics, for example. Every time we make an observation we admit the possibility that the resulting evidence may overturn existing ideas, though, and Einstein’s great work is not spare this standard.

It has been said that scientists must sacrifice their children if the evidence demands it. It’s not talking about human sacrifice, of course, but a very human sacrifice. As much as I love ol’ Albert, if the evidence shows his ideas don’t work in some domain, out they go!

April, 2011 at 1:29 am

It seems to me that Phil Plait is almost certainly aware of the distinction you’re trying to draw here, and that the quoted statement is not COMPLETELY wrong since it is completely correct if you substitute “Newton’s Law” for “Newton’s math”. At most it’s wrong in as far as the meaning of “Newton’s math” is ambiguous — and it’s debatable as to whether it actually is, in the original context.

April, 2011 at 7:20 pm

I think you’re probably right about that.

IF.

As the statement stands, it’s wrong – and wrong conceptually, not merely in the way an equation might be if you reverse a sign by accident. Sure, it can be made correct, but that misses the point.

Plait is possessed of sufficient expertise that I don’t feel we should cut him any slack when it comes to mistakes of this nature and import.

April, 2011 at 10:50 pm

From a mathematical perspective, an equation is not by itself either right or wrong. These judgments can only be made after first asserting some kind of association between the equation and some other entity. This might be the preceding equation, where the association is that (1) implies (2), or some conceptual binding of the symbols to either theoretical or observational entities.

The first case is syntactic “wrongness”: we believe there to be no formal derivation of (2) from (1).

The second case is semantic “wrongness”: the symbols’ conceptual associates (which we have but the equation does not) do not actually satisfy the asserted relationship.

Newton’s equations are correct in the first sense but not in the second.

A change of sign can make an equation wrong in either sense, but usually OUR error is syntactic and not semantic. We often lose track of some signs in a lengthy derivation, but we don’t often accidentally associate mass or displacement with a negative quantity.

It probably warrants some discussion as to whether one of these kinds of “wrongness” is a special case of the other. Thinking about that a bit may be a good way to flesh out your meta-mathematical philosophy (although, having just thought about it a bit, I’m still as confused as ever when it comes to that).

Anyway, that all is not *exactly* relevant to the post. Your sign error analogy was very good food for thought though, for as well as relating to “Why is it wrong to say Newton’s math is wrong?”, it also raised the question “Why is it wrong to reverse a sign in an equation?”

Actually, what immediately came to mind was this — in what way can an equation possibly be “wrong”, except conceptually?

April, 2011 at 6:59 pm

6 x 8 = 42

Hmmmm….

April, 2011 at 7:53 pm

Right upon associating each numeric token with its congruence class modulo 2, and the (x) operator as multiplication of congruence classes.

Wrong under the “usual” associations.

That wasn’t even a stretch! It’s strictly by convention, and for the clarity of the human reader, that mathematicians write a ~ b (mod m) as opposed to just a = b, with the understanding in the latter case that the equality is now among congruence classes and not integers.

I’m confident though that you could come up with another example which would require me to do something more artificial — but I wouldn’t be doing anything that isn’t, in principle, in accordance with the usual treatment of equations.

For example, the characteristic polynomial of a square real matrix is expressed using addition and multiplication of real numbers — something like p(x) = 2x^2+ 3, for instance.

Now, the Cayley-Hamilton theorem states that every square matrix A satisfies its own characteristic polynomial — in our case this means p(A) = 2*A^2 + 3 = 0. Now multiplication is both associated with matrix multiplication AND matrix scaling, the (+) is interpreted as matrix addition, that 3 means the matrix whose only non-zero entries are 3s along the diagonal, and 0 is the zero matrix.

Which is a lot more complicated than what needs to be done to make sense of 6 x 8 = 42.

April, 2011 at 5:33 pm

See how easy intellectual dishonesty is?

April, 2011 at 3:52 am

Sometimes it’s as simple as criticizing others for what you fail to do yourself.

April, 2011 at 4:17 pm

You know, no matter how much time I spend on the Internet, the extent of human stupidity never fails to amaze me.

April, 2011 at 7:35 pm

Our insulting each other isn’t exactly a way to raise the bar. Would you say something substantive here — about whatever part of this is actually controversial/stupid?

You wrote 6 x 8 = 42 and MEANT for me to understand this as an identity among integers. And the moment you tried to make the equation MEAN something, it no longer stood on its own, it had an interpretation and yes it was wrong.

It’s basic mathematical logic that truth depends only on the interpretation of non-logical symbols (such as constants and functions). I’m not making this shit up.

April, 2011 at 8:40 pm

If you recognize the collection of activated pixels as symbols, then they take on possible meaning in the act of recognition.

I could spew out a random sequence of letters and claim that, given the right interpretative system, it would constitute a meaningful reply to your comments. But that would be insolence, and you would respond to it as such.

A configuration can’t be wrong. An equation, which requires that a set of configurations constitute language, can be – and according to the grammatical and semantic structures of that language, the vast majority of equations will be wrong.

Strip away that inherent context, and it’s not wrong any longer. But it’s also not an equation any longer, either.