Comments on Number and Numbers.

Richard Sansom.

 

When I studied mathematics at the university, there were two *schools:* pure and applied math.  As the names imply, pure math was not concerned with the utility or meaning of an expression, but only its form, and applied math was only concerned with the practical utility of an expression. 

 

 

A quadratic equation can be solved simply to solve it, or to solve it for some practical purpose. 

But at the most fundamental level, numbers are the naming of aggregates, period; they have been so from the start and remain so today.  Pythagoras aside, originally, numbers had no mystical meaning and certainly no ontological reality - Penrose aside. 

 

The way in which numbers are constructed, sans application to anything real, is nothing more than following consistent axioms or rules that have been invented by the human mind to frame how one deals with numbers.  Contrary to the opinion of many, there is no analog between such rules and observed nature. 

 

 

However, many eyebrows are raised when a mathematical expression seems to describe some aspect of nature, and this often convinces one that such a correspondence is an amazing reality, proving that the expression is embedded in some natural process. 

Examples abound: the Fibbonaci series, seemingly describing the growth arrangement of leaves on certain plants, being one; or the shape of certain sea shells being described by the formulae for various kinds of spirals.  Regarding the Fibonacci spirals, one scientist says:

 

"Patterns that evolve naturally are generally an optimized configuration for an assembly of elements under an interaction," Cao explained to PhysOrg.com.   "We conjecture that the Fibonacci spirals are the configuration of least elastic energy. Our experimental results provide a vivid demonstration of this energy principle. This is the best support for this energy principle of phyllotaxis (or *leaf arrangement,* often credited to D'Arcy Thompson) before a rigorous mathematical proof is available."

 

So, what does this mean - that nature has the equation for a spiral embedded in its genes and mathematicians have been clever enough to discern the apparent internal formula? 

No, it means that the human brain is capable of seeing connections that have no meaning other than verisimilitude. This tends to reinforce a Platonic world view - i.e. that numbers and equations are ontologically real, as in the opinion of Penrose and Plato. 

 

Numbers do not exist.  Fibonacci series do not exist.  The nautilus shell and sunflower seeds do.