One cannot say something is random in the system if he does not know what the system "is." The full number and types of dimensions are both unknown and unknowable. Likewise a particle or field which has no direct or indirect measurable effect cannot be said not to exist.
As used in science, the word "random" actually means "unpredictable."
As an example, if he did not know the origin of the string, a person looking at a series of numbers from the extension of Pi might conclude the numbers are random when they are in fact highly determined by calculating the ratio of a circle's circumference to its diameter.
Science has also misappropriated the word "information" which in mathematics (Shannon) means "the reduction of uncertainty in the receiver as it moves from a before state to an after state." As science has now misappropriated the term it basically means determinism.
Misappropriations such as these put the burden on the consumer to discover the actual meaning - but how few are willing to do the math!?
The language of mathematics is truly universal (Tegmark, Level IV etc.) and quite specific - it should not be misappropriated for reductionist investigations. e.g. by methodological naturalism.
The discipline of mathematics is rigorous. The most certain things we can declare about our observations are mathematical.
And the unreasonable effectiveness of mathematics in the natural sciences (Wigner) is like God's copyright notice on the cosmos.
What a wonderfully informative essay/post, dearest sister in Christ! Thank you oh so much for your penetrating insights!
I just loved this:
...if he did not know the origin of the string, a person looking at a series of numbers from the extension of Pi might conclude the numbers are random when they are in fact highly determined by calculating the ratio of a circle's circumference to its diameter.I confess I am truly fascinated by this mathematical crittur Pi, an irrational, transcendental number. It is strictly "determined" (by calculating the ratio of a circle's circumference to its diameter). Yet at the same time, we never can see the "end of the string" of the digits in its extension, because that extension is thought to be infinite.
Neither do we ever see the end of the string of digits in the extension of a rational number. But — since rational numbers are characterized as such on the basis of repeating behavior of some same sequence of digits, we feel we know what we need to know about rational numbers, their infinite extension regardless: They "resolve" for us within 4D spacetime reality.
But not so with Pi. Pi is an irrational number, exhibiting zero "patterning behavior" in its extension. Last time I checked, mathematicians had calculated Pi out to some 10 million digits of the extension and discovered no evidence of pattern, of repeating behavior. Pi is regarded as a transcendental number — because its extension runs out of our 4D spacetime reality altogether. I.e., it does not "resolve" within 4D spacetime.
Which insight leads me to believe that our ordinary 4D spacetime world exists as something embedded in a higher-dimensional reality. And as you truly say, "The full number and types of dimensions are both unknown and unknowable."
Also truly you say that "the discipline of mathematics is rigorous. The most certain things we can declare about our observations are mathematical."
And so I note with some bemusement that orthodox evolutionary biology has so far eschewed all representations of its theory and findings in precise mathematical terms. That should tell us something. Especially when the great evolutionary biologist Ernst Mayr seemed so pained by this discrepancy from standard scientific practice that he actually proposed that Biology ought to be regarded as an independent sovereign science on a par with physics, but not bound by the mathematical conventions of physics.
Jeepers, what the scientistic, materialist types have done to Shannon is a total disgrace. How his information theory can in any way be regarded as evidence of determination in Nature is beyond me.
Eugene Wigner's remark speaks truly to me: "The unreasonable effectiveness of mathematics in the natural sciences is like God's copyright notice on the cosmos."
Thank you ever so much, dearest sister in Christ, for your superb essay/post!
I was fairly certain I would trip your mathematic switch, AG.
So what’s the word/description Science is looking for when it says “random”? “Unpredictable”? Is there a better (more exact) description? And . . . to be “random,” must something first be designed to be random?
I get it when you explain that numbers that are an extension of Pi, taken out of context (the system), might be mistaken as “random.”
It strikes me that Science is sometimes even more confused than I.