Technological Innovation as
an Evolutionary Process
Historical Perspective
5/1/2004
12:26 PM
Short “Systems AS-IS”
Paper
Short “Finding the Balance” Paper
Second note on patents
(biotechnology)
previous discussion on
“structural holonomy” -> .
We are struck by observations regarding the nature of categorical abstraction of multiple occurrences into one symbol, and the event chemistries that provide a set of associations rules for modeling how individual occurrences from several different categories fit together in situations. These observations are a bit ahead of our time, but potentially have great social value.
We have several problems. First, an element of non-rationality is present because of historical context. This non-rationality has lead to some confusion. By seeing the whole picture the cause of confusion can be explained.
Through an explicit recognition of the whole picture one can bring polylogics, schemalogics and categorical abstraction, etc into the market.
One can communicate an understanding to some small group of investors and they will understand how the beginnings of something new can occur with their assistance. The understanding is that history always surprises society, and the present moment is no exception. What we are looking to create is a clear view of what is next.
The elimination of confusion about issues related to computers and human knowledge will lead to a new production sector, where what is produced are many kinds of physical things whose production requires polylogics, schemalogics and categorical abstraction.
The whole picture comes from an historical perspective when combined with scholarship. This scholarship is presented clearly and with confidence.
The history of the development of computer science and Information Technology has introduced non-rationality in how computer technology has come to be.
1)
Computer
science has many challenges. But those
problems that can be solved by making the computer science complicated are
preferred by the nature of the specific drivers of economic compensation. These same market forces inhibit those
problems that can be solved by making computer science simpler. The reason why is because of the nature of
the current practices related to compensation for effort. The reason why does not speak directly to
the nature of computer science alone.
The difference between
the nature of computer science and the nature of living physical systems
becomes a critical factor.
2)
The
Artificial Intelligence (AI) confusion is maintained because AI advocates
claims that there is no essential difference between a computer and a human
brain.
3)
The
core of computer science is mathematics.
4)
Hilbert-type
mathematics is axiomatically closed and depends on deductive inference except
in the adoption of certain inductive steps (finite and infinite mathematical
induction) and the acceptance of a second category of axioms (Axiom of Choice
and the Well Ordering Principle) not defined initially as part of set
theory. The Peano axiom, which allows
one to build the set of integers, is a third category of axiom. Even with the introduction of additional
categories of axioms, one finds considerable weakness in the foundations of
mathematics.
5)
Our
society accepts the notion that the foundations of mathematics are the
foundation of a precise and exact science of natural systems. Most individuals are actually uncomfortable
with this notion, but are not equipped to lay out the issues, as I have. Then we have Godel’s work on completeness
and consistency and the use of the principle of proof by showing something is
inconsistent with previous truth.
In summary: applied computer science has largely ignored the formal difficulties found at the heart of Hilbert-type mathematics. Moreover the education of computer scientists has brought about an agreement that one need to bother about such things. This is where the confusion comes from.
Some additional discussion: Computer science education has consistently marginalized the literatures on Brower’s school of intuitionist mathematics, Godel’s work, and works by individuals like Robert Rosen {+}. For example, first order logics were believed by Russell and Whitehead to have a common simple foundation with set theory, and yet eventually their work on finding this common foundation was abandoned, largely but not only because of the work by Godel. But computer scientists do not learn this history.
An enigma exists. In spite of the importance, the difficulties of the Hilbert programme for the foundations of mathematics can be ignored. Why? It is because Hilbert mathematics has such great utility in engineering. If one assumes that the nature of life is reducible to engineering one has a perfect tool, as long as one avoids the consequences of occasional unexplained failures. Well, we have to be careful here. Living systems are not really fully simulated by any Hilbert type formalism. This was Penrose’s point.
One needs to look for something else other than a Hilbert type formalism to understand life. For example, one needs something more than first order logics to model the tipping points in manufacturing processes. Polylogics work within a set of other formalisms to provide a fine control over these tipping points, states in the manufacturing process where the process can easily be ruined or evolve into something having a greater value.
A proper understanding of natural linguistics tells us about the issues related to the control of symbol systems and their relationships to the real time natural world. The experiences from the failures of artificial intelligence set up the alternative.
We recognize that human reasoning is not reducible to logic and that the natural system is more complex that the formal systems that have so far been developed. So the functioning of the computer is to be understood by the average user. This means that if computer science can be simplified into a small set of first principles, these first principles will govern the nature of software.
Now that makes intuitive sense.
But this intuitive sense (Brower’s school of mathematical thought) is not re-enforced in our educational system. This is why the BCNGroup’s call for a National Project focuses on the development of a K-12 curriculum in the knowledge sciences.
Some additional comments: Educational renewal and the return to a Jeffersonian model of an agrarian society can be our future.
But in the present, computer scientists are confused because of two factors:
1)
As
a general condition of our economic system, the way that money is made by computer
scientists is bound up in making things hidden and proprietary
2)
The
problems in the foundations of mathematics and the philosophy of science have
not been properly addressed within our educational system. It is not even often understood by PhDs in
computer science. Or the understanding
that is taught is that these issues are simply un-important.
Why simpler? Why interoperable? Why should the organic (evolutionary) development of IT over the last decades produce a progressively simpler technology? Why should the organic (evolutionary) development of IT over the last decades produce a progressively more interoperable technology?
The first question has its answer in the reduction to first principles. Computer science is a subset of mathematics. If one accepts Hilbert’s programme for axiomatization and construction of a closed formalism having a fixed and known set of axioms, then computer science will simplify. A fixed set of axioms and the rules for construction of things like sets and ordered sets can be defined precisely based on the finite nature of things composed of bits.
Here is one of the first surprises of the knowledge age. Information technology will become free and unencumbered because the most powerful computer science is very simple. In this simplicity one also finds stability so that one learns once and then uses the same system for a very long time. From this simple and stable foundation, a science of complexity will develop that assists humans in learning about and controlling complex micro-ecological and micro-farming processes. The new production sector will be born.
If one accepts the Browser programme, then one realizes that a new computer science curriculum should be based on topic maps, polylogics, quasi-axiomatic theory, categorical abstraction, inductive informatics, and event chemistries. This computer science curriculum will see computer science as a subset of mathematics and the natural sciences as an application of mathematics. Mathematics itself will come to be understood in a more complete and reasonable way.
The computer science is an empowering technology and should be free to all to use so that money is made in producing physical things. The physical things will be cheap and well-understood nutraceuticals and pharmaceuticals, as well as many other kinds of wonderful things.