[sdiy] Is everything digital?

[Joe Franko]

You guys are making my brain hurt! This is one of the reasons I'm a
mathematician and not an engineer.

It seems to me that three things are probably true:

1. Fundamentally it's all statistics and at a fundamental level
probabilistic. So to speak in terms of analogue or digital is to want to pin
down something that can not be pinned down. Whether it is useful to see it
as analogue or digital only means we are asking which view gives us the best
approximations.

2. The map is not the territory. At the atomic and subatomic level we are
always talking about probabilistic phenomenon. I'm afraid that quarks,
strings, etc. are only useful mental constructs. We can not know with any
certainty the physical reality represented by these constructs. Our
understanding of group theory filled out our understanding of subatomic
particles. Group theory is a mathematical system that works particularly
well for describing subatomic particles. Group theory predicted reasonably
well the subatomic particles we had not yet discovered, but, as Einstein
said, it is a wonder that people confuse the math for the reality. Our
understanding of the atomic world is a mental construct, built on
mathematical laws and systems, subject to change as our mathematics changes,
as our probabilistic models change.

3. Godel's Theorem says to me that we may not ultimately know whether our
view of the universe is consistent. There will be parts of it that will
forever remain a part of the mysterium, the unknowable. Our desire for
certainty about the world is, Godel proved, doomed to failure. We must be
content with our probabilistic models, refining them as our mathematics gets
more creative. If viewing a particular phenomenon through an analogue lens
gives us good approximations, then that is a helpful way to see the world.
Doesn't matter "how it really is."

And now you know why engineers throw up their hands in despair with us pure
mathematicians.

(none of this may be "real" as I haven't had my morning coffee yet....)

Joe