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What if Elephants did Math?

By Craig Dwyer

Reflection on

“Philosophical Problems of Mathematics in the Light of Evolutionary Epistemology” by YEHUDA

RAV

The way we think, our cognitive apparatus, is the result of millions of 

years of human evolution. These apparatus were chosen by natural selection

because they provided a world picture that must have been appropriate for

dealing with world in which we were grounded. Otherwise, survival would not

have been possible.

Humans are bipedal animals. We have eyes set in the front of the head

giving us 3D vision. Our hands have four fingers and a supporting thumb. Our

brain takes up close to 20% of the energy our bodies produce. I could go on.

This physical set-up, which is at the genetic level, evolved from countless

other potential possibilities. It has given us a perspective and way of viewing

the world which is fundamentally different from other animals. An Elephant

for instance, with its four legs, eyes on opposite sides of its head, inflexible body,

and extremely sensitive trunk, would experience the world much differently

than we do. If Elephants did mathematics, it would certainly look and feel

different. This thought goes against the Platonic worldview that mathematics

in out there waiting to be discovered. Rather, it suggests that mathematics is an

embodied experience, resulting from our physical apparatus, and shaped by

our sense of perception of the world around us.

Our coordination system and the way in which we move to survive andlive (when you fall, your hands automatically shoot forward to soften the

impact to your head, thus preserving the body part that is vital, the brain, for

one that is expendable, the hands and arms), are at the root of our logical

thinking. Along with our physical apparatus, humankind has evolved a sense

of cultural thinking as well. By banding together and living in complex groups

(a survival mechanism) we have developed a continuous process of growth in

terms of social and cultural needs.

Mathematics can be viewed in the same two-tiered web. The

logico-operational level is based on adaptive cognitive mechanisms. Theseschema are fixed by our physical reality, or how we experience the world (they

are fixed on our sense of nowness, as evolution works on a timescale that

humans are unable to experience, even though we may indeed be evolving

physically, there is no way to determine where those adaptations will lead, as

evolution is opportunistic). The thematic level is determined by our diverse

cultures and social needs. This level is dynamic, changing, and continually

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evolving.

These two levels can inform an age old question presented by Socrates;

“ How to explain that, as often happens, mathematicians living far apart from

each other and having no contact, independently discover the same truth? I

never heard of two poets writing the same poem”. They discover the same

truth (I use this word loosely) because they are both human, and they exist in

the same bodies that have the same physical perception of the world. They

share the logico-operational level of human mathematics. At the same time

that they discovered the same truth working in different axiomatic languages

and systems of math. These systems would be informed by the thematic web of 

mathematics, or their embodied culture.

A Thought Experiment

What if Elephants did math? What would their logico-operational level

entail? What would their thematic level entail? How would these two levels

coexist to bring forth a mathematics that is completely embodied in their

experience of being an Elephant?