response to why math works
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8/13/2019 Response to Why Math Works
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Sourabh Das
Response to why Math Works
There are many interesting concepts discussed by the physicist. There are obvious examples of human
invention such as formulas for physics with quantities and units such as time in seconds, length in meters
etc... However these are defined by people as to the actual lengthof 1 meter or the temperature of 1C.
These are obviously human inventions.
Then comes the examples of natural math existing in the world. The relationship between a radius andcircumference of a circle is undeniably a derived solution of. In the natural world, in a flat plane, the value
of cannot be changed. Other such values such as eare a very fundamental and natural value that is
undeniably discoveredin many different applications of math, with no human manipulation.
These obvious examples suggest that math is both an invented set of tools, and a discovery from nature.
However, taking a broader consideration into minda different and alien situation, where all the
intelligences, works and discoveries by men, were owned by a jellyfish like entity in the Pacific Ocean,
floating about. How would the math discovered and the math invented compare with math as we know it
today? Would natural numbers exist? Forget integers, forget fractions...would actual numerical quantities
exist at all? If we ignore the inspiration part of the entity and assume that it has developed math to define itssurrounding, would it use numbers or numerical like values? I believe the answer is yes. Even if it did not
have anything to count, the concept of value would develop to compare things in an absolute scale. The idea
of integers would possibly be more complex in this entitys- world then it is for us, but it would exist. It would
then naturally have to define the actual quantity of each unit (how long is 1 second exactly?) but that is only
the next logical step. However this does not necessarily restrict mathematical development in other fields.
For example, it may develop a non-numerical, abstract-for-us concept for calculus to easily define curves.
In an even more abstract environment, such as space, space-time curves may change the way geometry
works, and change its axioms such that our Euclidian methods are incorrect in that nature. In this world,
everything we have learnt and everything we are used to, will be useless.
From a more terrestrial standpoint, our aim is to try and reach that absolute level of understanding, and
define similar things in different ways to explore and discover the relations in the natural world. For example,
there are different methods of defining points in a graph: position of x & y, and vectors & magnitude. Though
we attempt to correctly represent the reality of nature through math, we often fail to see the greater
underlying mechanisms, as our terrestrial boundaries lead us to only think in a relatively closed-minded
fashion.
I believe that real math is the actualnature of things. The math as we know it is just a tool developed by us
a language that crudely defines this nature, to allow us to communicate the nature of things. It is constantly
being refined to be as accurate as possible. New concepts are being discovered, experimented on andcalculated with, and we can never know if we truly understand the nature of things. Until we discover all the
secrets of the universe, we can never know if the methods we are using are correct. For all we know we
may be using the right methods perfectly for solving and calculating what we need, or we may be terribly
flawed in our logic and everything we have discovered so far only fits together with each other but not the
true nature of things. In other words, it is exceedingly difficult to know if our development of math is just an
outcome of our circumstances, or an inevitable chain of discoveries leading us to the point we are now.
Either way, until we discover all the secrets of the universe, we can never know if our math is developed or
discovered.