[tortoise]

An ongoing point of contention between Wolfram and Chaitin (as I recall) is that Wolfram believes there is no such thing as a true random string, he would call all of them pseudo-random strings, even Chaitin's Omega. Again, as I recall, even Chaitin saw merit on the basis that every string is "caused."

For many types of system Wolfram is right, and I would even be willing to grant as a reasonable premise that it applies to the system we exist in.

The key point is this though: For any system in which Wolfram is correct, there can be deterministic processes that cannot be perceived as anything but random within that system. It is the nature of the beast. Some of the confusion is in that there are processes we cannot treat as anything but random pragmatically even if we know they are deterministic mathematically.

A recurring problem is that many people do not understand the limits of application of general mathematics. There are a great many premises and assumptions underlying many of the more well-known bits of math, and for application in specific instances one has to make sure that the mathematics is constrained to appropriate premises and assumptions if one wants to make a definitive assertion. This is a problem even among people who are nominally mathematically savvy. If I had a nickel for every time the Halting Problem was improperly invoked...

[Alamo-Girl]

Thank you so much for your post and your insight!

The key point is this though: For any system in which Wolfram is correct, there can be deterministic processes that cannot be perceived as anything but random within that system. It is the nature of the beast.

Exactly. That is a point I keep raising as well, particularly with regard to dimensionality. What we think we know is a matter of perception and we would be wise to be aware of our (artificial) limitations, IMHO...