Saturated with Knowledge

What was and still is

Dateline, 1850 and Now...  We have arrived at the point where professionals have a large amount of knowledge about particularly narrowing topics. The narrowing has constricted now for a couple of centuries.  As in the past, investigators become saturated.  For ancient geometers, this occurred a couple of  centuries BCE. They can know little more, and little more was contributed.  Until...  a new idea emerges, it becomes the hammer to resolve all questions. Older outmoded techniques are diminished, deprecated, and eventually forgotten. This is the model of scientific investigations and other objective disciplines.  When the new is judged as more powerful and more predictive, the old is discarded.

All this is according to Thomas Kuhn.  Advance of knowledge is not linear, it is not even monotone.

What are new ideas and from where do they come?  A number of forms seem obvious.

• Technique
• Innovation
• Enhanced precision
• Increased dimension
• Discretization
•  Scale transformation

There evolves the understanding of an innate and bounded capacity for active options.  For example, given that a person can resolve a question using a dozen novel (and personal) options.   Each problem is then resolved within novel information and a base knowledge. A problem that cannot be resolved within the  dozen is nonetheless solved within the dozen.  This creates impossible situations.  

How can knowledge advance and techniques for advancing knowledge evolve?  The first answer is fresh blood.  Required is the activation and involvement of new people brought into the assembly.  Centuries of new graduate students have furnished this critical resource.  Without graduate students or other fresh blood, knowledge would simply not advance.  It would remain in a stasis, with unsolved problems elevated to a canonical level of non-understanding and imperfect, incorrect solutions.  The spiral loop will sustain forever.  We may call this is the fossilization of knowledge.  Graduate students or interns, furnish the fresh and new ideas that range beyond the dozen, that disregard the dozen learned in their normal educational process. In other worlds, business for example, this could account for the new group mentality of problem solving together, brainstorming. We can't hire new people, but the same people with possibly differing solution methods may produce something new.  This is called innovation, a topic worshipped in the business world. 

New options must then be codified and absorbed into standard procedure. But there is a natural limit.  Mostly we examine only within our personal context. Our personal limits, regardless of how vast, are simply finite and finite of low dimensionality. Using the language of logistics, we call this one's carrying capacity.  Most investigators have the same dozen, and the better ones use them to more successful ends.  The natural limit is what makes some problems intractable - not impossible but beyond personal and even group capacity.  The body of solvers use only their knowledge and methods, which for serious problems simply do not suffice. It could be one reason to explain the vast migration of talent from company to company, campus to campus.

All this said, it will happen that the grad student fix will fail.  And all the other types will fail.  A total saturation will envelop all thinking. 

Enter the computer

Always preferring to begin exactly there, we mention just a few aspects of knowledge that we could never know without these electronic beasts.  Consider just three – without much detail.  You may add your own examples.  Many involve massive data; many involve simulation, visualization, data compression, and pattern recognition. 

·         DNA – we could never know about specific DNA characteristics without sequencing algorithms

·         CHAOS, FRACTALS – we could never have detailed knowledge of chaos, synchronization of multiple oscillators, and fractals without computers

·         BIG DATA – we could never achieve the benefits afforded to us from the analysis of massive data resources.

From just a few examples, the answer is clear.  Computers are a key part of the contemporary investigative infrastructure.  Yet, they are constrained to specific tasks.  They are not free to explore.  So we ask…

How can computers help this increasingly dysfunctional process?  First of all, computers have vast resources of information about any subject, and unlimited computing cycles.  Second, they are tireless but stupid.   They need help.  Techniques of coding may not yet be there beyond mere word searches and the like.  But this will come.  Problems need to be coded and the solutions, as well.  Moreover, the accepted specific logic needs for the specific subject.  In some cases, for example, a multi-valued logic is quite appropriate.  

The day will come when some new idea can be codified and then integrated into the codex of all relevant ideas to resolve questions of consistency and compatibility, to propose problem availability, and ultimately problem solvability.  One question is where we mortals will figure into this mix?