Is the Mind the Fundamental Link Between Mathematics and Physics?

[Loren Booda]

What comprises the transition from math to physics? alexander has said that physics is math. John Archibald Wheeler has wondered how equations "fly" (take on a physical character). I believe that math and physics are interchangable, that both can be shown to transform into the other. We could not appreciate mathematics without reference to physics, as physics so familiarly founds itself upon mathematics.

Is there a process intermediate to these two sciences? Perhaps psychophysical modeling, where the symbols of math meet the sensation of physics. As dreams are psychological representations of the physical world, they attempt to apply logic to fit experience. The idea that the cognition be the connection between math and physics is anathema to those studies, since the first is inexact and subjective, but the latter two pride themselves on being the epitome of precision and objectivity.

Could the mind hold the fundamental link between mathematics and physics?

 

[enigma]

Mathematics is a tool.

Physics is the application of that tool to real life.

In case you couldn't tell, I'm not that metaphysical

 

[brum]

If you look at something in the physical world, let's say, a rolling ball, you will not find an equation somewhere in it that it physically follows.

You cannot find equations somewhere in clouds by which the clouds follow to determine their next move in the air.

You don't see equations in bouncing balls that tells it, for example, to bounce up a certain height.


We can, however, predict things in the physical universe with mathematics, simply because it works, not that the various equations can somehow be "found" in objects.

 

[Loren Booda]

brum

We can, however, predict things in the physical universe with mathematics, simply because it works, not that the various equations can somehow be "found" in objects

Not found physically, but intimately related to physics through mental logic. A subset of the most basic mathematics exists as symbolic imagery corresponding simultaneously to the set of physical perceptions. I guarantee that each of us reduces unconsciously our physical experience to balance with the pure mathematics inherent to the brain.

 

[m_ridsdale]

Could the mind hold the fundamental link between mathematics and physics?

Quite possibly. I can recommend a book called Where Mathematics Comes From, by cognitive scientists George Lakoff and Rafael Núñez. They use the tools of cognitive science to analyse some of the most common concepts in mathematics (such as negative numbers, infinity, derivatives... ), and try to show how these are metaphorical extensions of concepts which are directly grounded in our brains.

Example: from an age of no more than a few months, we all show an ability to "subitise" a group of objectswe are shown, that is, to instantly see whether there are 1, 2, 3 or some other small number of objects. The upper limit of numbers we can subitise is debatable, but clearly we cannot go very high. Lakoff and Núñez argue that this is the basis of our concept of a positive integer, but that to go from subitising to reasoning about numbers like 100 or a googol requires us to metaphorically extend our natural subitising ability.

If I haven't explained this very well it's because I probably haven't fully grasped their argument; I find thinking about thinking can get you stuck in an infinite loop and tie you up in knots, I'd really like to read the book again before I'm sure of my opinion of it.

You can get a flavour of the book by looking at http://www.edge.org/q2002/q_lakoff.html, scroll down to where Lakoff gives his answer to the question "How can we understand the fact that such complex and precise mathematical relations inhere in nature?"

 

[Loren Booda]

All mathematical (and thus physical) concepts would eventually be founded on the most primitive math, counting, and its intuitive ideational mechanical representations.

 

[STAii]

It very possible to make some physical observations, and studies without the reffer to mathematics.
(Like studying the fact that a car with a bigger mass will have a bigger effect on a wall (when colission between them happens) then a less massive one).
But those observations will be very simple, and far from accurate.
But still this prooves that physics is not completely dependent on mathematics.
On the other hand the use of mathematics will make the results more elegant, more accurate, and more profounded (in some fields).
Also notice that methmatics alone (when not related to any other science), can serve nothing.
Therefore i like to believe (as enigma said) that Math is the tool, and Physics is the science .

 

[quantumdude]

Originally posted by Loren Booda
I believe that math and physics are interchangable, that both can be shown to transform into the other.

While The Unreasonable Effectiveness of Mathematics in the Physical Sciences is undeniable, I do not think the converse is true. In other words, while it certainly seems like all physics can be described mathematically, it does not seem like all mathematics corresponds to something physical.

Mathematics is as rich as the mathematician's imagination, and I can only conclude that the reason is that the origin of mathematics is the mathematician's imagination.

 

[rutwig]

Originally posted by Tom
In other words, while it certainly seems like all physics can be described mathematically, it does not seem like all mathematics corresponds to something physical.
[/i]. [/B]

Well, under certain circumstances the mathematical tools does not suffice to describe physics, see e.g. the spontaneous symmetry breaking. Also in characterizing the states by representations, you can easily loose states if they correspond to eigenvalues of certain distributions, which cannot be deduced from the symmetry analysis of the system.
And of course not any mathematical tools has a physical interpretation (at least not yet).

 

[suffian]

In my own opinion, mathematics has its own inherent beauty. Even if math were severed from its practical applications, it represents some of the purest logic people have come up with. Using mathematical logic, one can deduce a statement to a degree of certainty beyond that which can be achieved in almost any other subject. In addition, unlike physics, almost all the pieces of mathematics fit together like a well-constructed jigsaw puzzle. In physics, theories often conflict, but because of their domain of practicality, most of them are retained (if only for a lower course). In contrast, mathematics laws don't become superseded by later laws (yes, the area of a circle will always be pi r squared). Not that I don't appreciate physics; I just think we don't need physics to justify math.

 

[drag]

Greetings !

Hmm...
( If any of you read my PoE thread in Phil. forum,
my response may be easier to understand. )
The Universe is a system. That is, it has a minimum
of two componenets of some sort - hence
numbers can be applied to the Universe.
The only basic given in math as far as I know are
numbers. Everything in math is made of numbers.
So, combining these two facts together we arrive at
the conclusion that math can "fit" to the Universe
so well because it has only that one thing
"in common" with it.

What about all the rest ?

Simple, all the rest are NOT things in common,
but descriptions of patterns between numbers.
That is, math takes these basic givens called
numbers and explores all the possible patterns
that may result from them. Of course, ussualy the
patterns being explored are connected to the real
world because they are invented to explain
physical phenomena (like interactions of "basic"
componenets called particles for example).

"Does dice play God ?"

Live long and prosper.