There's no question about math's validity in solving purely
mathematical things.  Adding, subtracting, multiplying, dividing, etc.
- for those cases, our current form of mathematics is fine.  2 + 2
will always equal 4.

The problem arises when we use our current form of mathematics in an
attempt to model/describe/analyze the real, physical world.  The
system falls apart.

The main proof of mathematics being flawed in modeling physical things
is constants.  Planck's constant, the gravitational constant, the
speed of light, the gas constant, etc.  They are all fudge factors
because math isn't modeling the real world properly.  Each case is
different, but whenever a fudge factor (constant) is used, mathematics
has failed to accurately describe the scenario by a factor of X (X
being the constant).

From a website describing Planck's constant:

In 1900, Max Planck was working on the problem of how the radiation an
object emits is related to its temperature. He came up with a formula
that agreed very closely with experimental data, but the formula only
made sense if he assumed that the energy of a vibrating molecule was
quantized--that is, it could only take on certain values. The energy
would have to be proportional to the frequency of vibration, and it
seemed to come in little "chunks" of the frequency multiplied by a
certain constant. This constant came to be known as Planck's constant,
or h, and it has the value 6.626E-34 J-s.

I'm asking if there is (or could be) a better system than math - a
system without fudge factors - a system with a more pure understanding
of the real world.

I've done a little bit of research about String Theory, and my
proposed 'new system' sounds similar...  one governing equation
(system) that works for all scenarios.  A 100% completely descriptive
system that successfully models the real world without the need for
fudge factors i.e. constants.

Could something like this exist?  Would our minds be able to
comprehend it if we've been so 'brainwashed' by the current system of
mathematics?  Your thoughts...

---

Clarification of Question by azdoug-ga on 28 Dec 2005 06:56 PST

Here, this is what I'm talking about - The Theory of Everything.  I'm
guessing there is a Theory of Everything, but it's probably not based
in our current system of mathematics.

http://en.wikipedia.org/wiki/Theory_of_everything

The system falls apart? Science has been outstandingly successful in
modeling the physical world precisely because mathematics works so
well in describing nature. We can put a spacecraft in orbit around
Saturn with incredible precision using Newton's law. The constants you
refer to as fudge factors are an artifact of the historical system of
units we use. There is nothing fundamental about the second or the
meter, so we of course have to use a strange number (c ~ 2.998*10^8
meters/second) to give us the speed of light, the "fudge factor" in
equations like E=mc^2. The same is true of Planck's constant (h),
Newton's constant of gravitation (G), the charge of the electron (e),
etc. The only way to eliminate these fudge factors is to use a system
of units in which these constants are pure numbers like one or pi. A
goal of physics then is to calculate all the dimensionless ratios from
basic principles. For example, the fine structure constant
e^2/(2*pi*h*c) is approximately 1/137. A theory of everything would
explain why this number is pecisely what it is. It would also explain
why the ratio of the muon mass to the electron mass is about 207. This
goal is still far off, but is because we do not yet have a complete
theory, not because of any flaw in mathematics or its application to
the real world.

Azdoug,
Perhaps this text will help you:
http://www.pupress.princeton.edu/chapters/i7789.html

The Ancients consider mathematics to be an Art; it is entirely a human
development  (we think), and, of course, it does everything perfectly
that humans want it to do and even does a remarkably fine job of
handling many things in the real world: eliptic orbits, etc., etc.,
but not everything.
Kind of makes one accept IT or the Enlightment's concept of "the Great Clockmaker."
Maybe He added a few quirks to keep us in our place and not let us
have the godly knowledge of the theory of everything.

Math is perfect?  Explain a singularity.

The way I see it, math was invented by humans.  It doesn't occur
naturally in nature.  Humans aren't perfect, and can't they make a
system that perfectly describes nature.  If we had, there would be no
need for constants.

If the early mathematicians had taken a different route, what system
would we be using today?  It wouldn't be mathematics as we currently
know it.  It would be something else...

This 'something else' might do a better job modeling the physical world.

Surely, if it were true that "math was invented by humans," pi would
be precisely equal to three.

We define Pi as the relationship of a circle's diameter to it's
circumference.  Pi = C/d.  For any given circle, C and d are
measureable quantities.  Draw any circle, measure it's C and d, divide
the two, and you get Pi.  whoop-de-doo.  Humans did this.

Same for radians.  We define a radian as the ratio between a circle's
arc length and it's radius.  If the two measureable quantities are the
same, the angle creating that arc is 1 radian.  Once again,
whoop-de-doo.  Humans did this also.

My point is the "WE DEFINE" part.  We chose to interpret naturally
occurring things in certain ways.  We chose to divide C by d - we
chose to compare the arc length with a radius - we chose to measure
gravity - Max Planck chose to derive "a formula that agreed very
closely with experimental data, but the formula only made sense if he
assumed that the energy of a vibrating molecule was quantized--that
is, it could only take on certain values."

I'm thinking there are 2 possible reasons why we don't have a
successful "LAW of Everything".  1. From the very beginning, we chose
the wrong units for any given measureable thing.  2. From the very
beginning, we erroneously tried to use man-made mathematics to
model/describe/analyze God-made nature.

Or maybe it's a little of both.  The use of constants prove #1 is a
correct statement, and singularities prove #2 is also a correct
statement.

Regarding "We define Pi as the relationship of a circle's diameter to it's
circumference.  Pi = C/d.  For any given circle, C and d are
measureable quantities.  Draw any circle, measure it's C and d, divide
the two, and you get Pi.  whoop-de-doo.  Humans did this."

But if we define pi as C*d or C+d or C-d or d-C, we don't get a
constant. (Of course, there's d/C, which is also a constant.). We
(except mathematicians and programmers) don't have freedom to define
whatever we please as a constant; we are limited by what's out there
already.

Well, I've found what I need.

Planck Units (God's Units) are an attempt to find the 'real' units of
length, time, force, power, temperature, density, etc.  When
incorporated into various equations and formulas, these units negate
the need for constants.  Essentially, all the previously used
constants become 1 because we're using the right units - the real
units of time, length, temperature, etc...

Here's some more info about Plank Units:
http://en.wikipedia.org/wiki/Planck_units

Fascinating stuff!

Hey, that is great, Azdoug!  Glad you found it.  I wonder if anyone
has found a way to use "God's units" in practice  - software that
digests those equations.

If anyone was questioning my claim that Mathematics is perfect  - as a
human "art" - I meant that it works for problems defined by humans  -
which are defined by the constraints of the art of mathematics.  That
is (the Greek word escapes me) circular  - except for those darned
circles and pi, which Planck Units seem to have to deal with.  But,
again, the perfect circle is a human concept ...

Cheers, Myoarin

The so called "Planck's Units" are just one of the many possible ways
to do as I mentioned above, i.e. work in a system of units in which
each of the fundamental constants is a pure number, conveniently
chosen to be 1 or pi or something similar. For example, systems like
this universally set the speed of light to be one, but there are
choices about the others. None of this matters. The equations are
simpler because we eliminate the constants. So, for example, the
equivalence of mass and energy is written E=m instead of E=mc^2, since
c is equal to 1. Again, the only thing that matters is the values of
the dimensionless ratios (numbers without units). For example, the
fine structure constant that I mentioned earlier is a measure of the
strength of the electromagnetic interaction between particles with a
single electric charge. It is approximately equal to 1/137. The
similar dimensionless constant for the gravitational interaction of
particles the mass of the proton is many-many orders of magnitude
smaller. It doesn't matter whether you consider this to be that the
gravitational constant G is very small or that the mass of the proton
is very small. You are free to choose units in which the mass of the
proton is one or G is one, the physics is the same.