Mathematics And Numbers

Mathematics is a human invention and uses the other concept of numbers to describe the environment and its apparent physical characteristics. The fact that most things appear to work and some predictive occurrences seem to be correct supports the concept of mathematics as being an absolute and 'written in stone'. The numbers produced do not lie.

There are, however, some anomalies that have no known solution. The unit square (1 x 1) has a corner-to-corner diagonal of √2. The irrational number has no solution and theoretically has an infinite number of decimal places that progressively makes the non-solution just more and more accurate. The irresolvable problem with this is that a potentially infinite number of 'points' is constrained within boundaries. The paradox is that the problem can be visualised and easily drawn, yet the numerical answer can never be calculated. It's a philosophical issue concerning the 'virtual world' of numbers and so has no meaning in reality.

The question raised is:

"What else fails to be quantified
by using the accepted principles
of all mathematics?"

Some solutions cannot be found even in the local environment, so what confidence can there be in places that cannot be examined and can only be assumed to exist? It's almost a certainty that much in the realms of mathematics has yet to be discovered. Relationships exist that are, as yet, unknown and, perhaps, unknowable. It cannot be known if mathematics fails to enable solutions to be found and (as a consequence) will never be discovered. The path that mathematics explores may even be a dead-end. It seems to work at the moment, but...

The pyramids are thought to be more than 5000 years old. The Fibonacci relationship that mathematics uses to describe a spiral exists very visibly in the pyramid geometry. The relationship that describes the circumference of a circle is also found in the pyramid dimensions. These 'recent' discoveries post-date their appearance by some 4000 years (Fibonacci). The retrospective knowledge of π (pi) does not provide evidence that such a relationship seen in a circle was then known. It is possible that some other undiscovered relationship exists that links the pyramid and the circle. The irrational number pi (π) is still unquantifiable.

It's an odd 'fact' that the exactness
and precision of mathematics
seems to be destroyed by the
simple unit square (1 x 1)

Infinity

The concept of infinity explores the limitations of human thinking. It’s a paradox. To explore infinity by introducing limits and boundaries. Mathematics and numbers are a human concept and is by definition trapped inside a box. The box can even be imagined to be of infinite size.
   As an example, between two boundaries defined as +1 and +2 there exists potentially an infinite number of positions, though logically the boundaries conflict against the concept of an infinite number. The unbroken circle creates the boundary for an area that contains an infinite number of points of infinitely small size within two dimensions. Wherever the starting point in the closed circle may be, this starting point could never be identified when passing through or past it. Knowing when returning to the starting point would never be possible. The sphere describes three dimensions and a larger infinity. Logically, there must be a finite number if contained within any boundary.

Infinity defines no boundary

The movement between positive and negative is deemed to pass through nothing (zero), a ‘number’ that defines nothingness. Positive moves toward negative, though passing through nothing. A non-powered object moving upwards vertically (against) gravity will slow to a stop. The object will then fall downwards under the influence of gravity (whatever may cause it). At the highest point, the velocity is zero for necessarily a finite time that is potentially measurable. That moment must be real since the direction of motion is reversed and the velocity must have reached zero.
   Paradoxically, root 2 can never be defined mathematically though it can easily be drawn (diagonal of a 1 x unit square). There are clear boundaries though infinity has no boundary.
This type of argument goes nowhere, but can appear to prove ‘something’, literally making ‘something’ out of ‘nothing’. Almost a Big Bang scenario.