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Comment by tca | Hacker News Reader

You could invert the phrase and still make a lot of sense: 'Nature follows from the basic mathematical assumptions.'

But you are quite right: Philosophers know better, could know...

You could invert the phrase and still make a lot of sense: 'Nature follows from the basic mathematical assumptions.

It's not just that. It's also that a lot of physics can readily be explained and understood without mathematics. It's just that with mathematics, it's easier to demonstrate the consequences. It's important to remember that Einstein got at relativity by understanding the right assumption to be made.

Just to be clear on this: I fully agree that in advanced physics, you sometimes you have to blindly 'do the math' and can determine the physical interpretation of the result only afterwards. However, that doesn't mean that there is no physics without mathematics, it doesn't mean that there isn't a lot of physics that can be understood without mathematics and it certainly doesn't mean nature is mathematical in essence. Hell, it isn't even physical in essence, unless you can reduce our minds to physics.

The notion that 'nature is mathematical in essence' is not logically seperated from assumptions about the object/subject and mind/matter dualities (and about whether they are dualities in the first place) that I doubt most of the phycisists espousing these notions are willing to support, because they are rather incompatible with other parts of their worldview.

I like what you say, but I am conflicted. As I understood it, math is the language that physics uses for us to understand/manipulate reality. Just as one understand "coffee" without the word coffee, one can understand projectile motion without understanding derivatives -- however in the absence of a language to describe it, the concept remains difficult to build upon.

I do not understand about it not being logically separated from assumptions about dualities (Platonic forms?) and their respective worldview. Could you explain more please.

Some guy by the name of Hartry Field claims to have successfully generated a logical axiomitization of Newtonian mechanics, without using math, only qualitative concepts like "betweenness."[1] Math can extend this model and is consistent with it, but it's not necessary in principle. Of course, this does not mean that you don't need math in practice, in the same way that continuations are the only control structure you need in principle but in practice you use loops and function calls and switches or whatever. What it does mean, from a philosophical view, is that math isn't necessary the quintessential 'language of the universe' that we thought it was.

As far as advanced mathematical physics goes, our problem is that we stop being able to easily understand what the math represents when you go deep enough. A first derivative is understandable as velocity, the second as acceleration, and multiplying that by mass to get force has some intuitive notion. If you look in the middle of a bunch of scribblings, it's possible to put the equation into words and it will make sense and have a physical interpretation. Special relativity and the beginnings of quantum mechanics came about because we had intuitive concepts, and were able to fit math around them. In modern physics, the math has come first, and the intuition later or not at all. Quantum phenomena still have competing interpretations (probability fields, many-worlds), which may not even be mutually exclusive. Once we figure out what in the hell is going on, the math may prove to be unnecessary, but right now the math is all we have to go on, and we sort of have to treat it like a literal truth in order to get anything done.

[1] http://en.wikipedia.org/wiki/Philosophy_of_mathematics#Ficti...

Thanks. This is kinda difficult to wrap my head around though. I found this passage interesting:

"By this account, there are no metaphysical or epistemological problems special to mathematics. The only worries left are the general worries about non-mathematical physics, and about fiction in general. Field's approach has been very influential, but is widely rejected. This is in part because of the requirement of strong fragments of second-order logic to carry out his reduction, and because the statement of conservativity seems to require quantification over abstract models or deductions."

I will admit that I have a problem when fictionalism requires that we regard "2 + 2 = 4" as false (also from wikipedia). All in all an interesting idea.

> 'Nature follows from the basic mathematical assumptions.'

This statement is more treacherous than you give it credit for. If we understood all those mathematical assumptions, wouldn't that be the death of free will?

One might make the statement that mathematics is the act of discovering god's laws, but godel makes even that statement treacherous because he proves god's laws can never be consistent.

my understanding of the modern philisophical take on mathematics is that it's just the invention of useful tools for manipulating logical entities, which can seem rather pedestrian to the layman - but will never deter a true mathematician

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