Theme: Science

https://www.quantamagazine.org/20160524-mathematicians-bridge-finite-infinite-divide/WHY OPERATIONALISM MATTERS IN MATHEMATICS: DEMYSTIFYING AND EXPLAINING THE ART OF DEDUCTION OF DETERMINISTIC PHENOMENON WITH DECREASTING AMOUTS OF INFORMATION.

This subject is interesting if for no other reason than mathematical language developed out of a form of mysticism(platonism), and has retained some of those characteristics across over two thousand years.

The intuitionists failed to create the reformation that would have made these subjects quite simple to understand.

We have reformed physics from the Aristotelian “first mover” category of language. We have reformed morality to be expressed in economic language. but we have not reformed the language of mathematics, thereby reducing mathematical platonism to operational (existential and computable) axioms.

If we do so, the discipline of mathematics has evolved as much by eliminating axioms of correspondence (or asserting axioms of non-correspondence), then leaving mathematicians to attempt to find methods of deduction with fewer and fewer properties to work with.

From this perspective, mathematical reasoning has been an exercise in the exploration of deduction of deterministic systems of correspondence (pairs) using decreasing information because of decreasing axioms (rules) of correspondence.

Or more simply said, mathematics evolved from the pairing of stones while counting sheep, then giving names to the stones, then positional names to larger quantities of stones. then to sets of stones. Then to ratios of stones. Then space, then time. Then deductions from stones, space, and time.

So we have merely increased the properties (axioms) and removed the properties (axioms) of correspondence with reality and explored how to perform deductions with more or fewer properties (axioms) of correspondence.

That we have not reformed the philosophy and language mathematics as we have in other fields is due to the fact that the intuitionists in all fields (Bridgman/physics, Mises in economics, Brouwer/mathematics, and various authors in Psychology) possessed different incentives and different threats to their credibility. Interestingly, psychology has reformed through the use of ‘operationism’, the physical sciences have reformed in large part, economics has not reformed, and mathematics has not. And the answer why is interesting: psychology was under threat of classification as a pseudoscience threatening incomes. Economists currently fight that battle, but the political utility of models plus the extensive time that passes (a generation or more) before policy makes itself visible, provides convenient escape from criticism. Mathematics has not in large part because unlike psychology, economics, or the physical sciences **it’s external consequences are irrelevant**. Meaning that there is no pressure to reform, because mathematicians outside of the sciences have no feedback mechanism to force them to.

There is nothing magical or mysterious about mathematics. What’s interesting is how we add and subtract properties of reality in order to created models that retain determinism and allow us to perform deductions with decreasing information, about scale independent patterns.

The only reason it’s even vaguely interesting is because the human mind is so easily overwhelmed with but a few short term memory facts, and a few axis of causality. Almost all mathematical operations (transformations) are determined by the capacity of our minds, and greater minds might not need symbols and operators of similar simplicity in order to see deductions or relations of far greater complexity.

So, mathematics is trivial really. But if you talk about it in magic words, it’s going to sound magical. When really, it’s just a matter of not being able to sense relations with our mind, the same way we cannot sense distant objects in the heavens with our eyes, the same way we cannot hear distant sounds with our ears or feel subtle vibrations with our feet.

We use tools of all forms to increase the power of our senses, and mathematics consists of states and operations that humans can operate and sense in complex deterministic models what we cannot sense and perceive without states and operations to assist us.

The moment you add or remove an axiom (command, or fact) the results are deterministic. The interesting part is only that we are developing the art of deduction for increasingly informationally sparse relations.

Curt Doolittle

The Propertarian Institute

Kiev, Ukraine