Expressiveness

In my opinion, it is not sufficient to simply “model” time using a time-less notation. The concept of “time” needs to be built into the notation itself as a first-class principle. What do I mean by that? I don’t know, but, I do strongly believe that the first part of solving a problem is to clearly state what the problem is. Maybe this discussion will cause lightbulbs to fire over other peoples’ heads.

The concept of expressiveness is orthogonal to the concept of helpful. Expressiveness is the property of simply being able to express a concept in some notation, regardless of how contorted the expression becomes (see, for example, our complicated concepts of concurrency in modern function-based programming languages). Helpful notations allow us to free our minds and to think about concepts without being hindered by too much unrelated complexity. For example, electronic LRC circuits are cheap and easy to invent for handling continuous waveforms neatly, whereas the attempt to reduce these same waveforms into discrete forms takes textbooks and years of University training.

Note that, in the above, I am not advocating getting rid of unrelated complexity, only eliding complexity to allow one to think about certain aspects without getting tangled up with details that are unrelated to the aspects being considered. Physicists call this kind of thing a “simplifying assumption”. On the other hand physicists - real physicists - remember what the simplifications are and switch notations when those simplifications are no longer valid nor helpful. For example, Feynman used diagrams (Feynman diagrams) to explore and express certain concepts and did not feel wedded to using only functional notation. Likewise, Polyani could not have made advances in his thinking by sticking to purely functional expression.

It is true that expressing our understanding in terms of equations can lead to new “discoveries” about the properties of the aspects being considered, but, this technique is only valid for interpolating information, and becomes dangerous (religious, blinding) when over-used to extrapolate information.

We must remember that our notations must be used to describe Reality, not to dictate what Reality is.

Sticking to one, and only one, notation leads to notation worship and the belief that the notation is reality.

For example, it is commonly believed that Maxwell’s Equations describe all electrical phenomena. This is not true. Maxwell’s Equations include simplifying assumptions that make it easier to think about certain aspects of electricity and can be used to Engineer electrical devices. Maxwell’s Equations leave out an aspect of electrical phenomena - self induction - that need to be considered as we develop further detailed thinking about electricity and want to invent new kinds of electrical devices.

Expressiveness

Expressiveness

See Also

Blogs

Videos

Books

Discord

Twitter

Mastodon