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"Alas, some scientists cannot resist stepping into areas requiring a different discipline and making observations without delineating the difference."

Not scientists we know, I hope... '-)

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That, btw, is my peeve about the abuse of the word "random." Randomness originates as a Mathematics term. It has a specific meaning, to wit one cannot say something is random in the system when he doesn't know what the system "is."

So -- we're back to "randomness" again. (Hope I don't get "shouted down" again...)

I agree the term has mathematical rigor -- but what term would you use to determine and describe the directions and energies of gas molecules in an "ideal gas" closed system?

How about an arbitrary, "open" system such as the room (part of a set of interconnected rooms) in which you find yourself? Describe the air molecule motion there...

Example: if the molecules in your room moved "non-'random'ly", (PChem term) and headed in a single direction , one wall (or more) would disappear explosively. (And, if we could create and direct that "non-'random'ness", we could make some extremely efficient internal combustion engines...)

Why can we expect a tire to remain uniformly inflated, if not due to "random" molecular motion? Chaos?

"PV=NkT" has mathematical (and physical meaning. Upon what assumption of molecular motion (other than elasticity and non-reactivity) does it depend?

IOW, what form of molecular motion makes the Ideal Gas 'Law' work -- every time it's tested? What about real-world gases & mixtures thereof in non-closed systems?

Or, to move closer to the "creation" aspects of this conversation, it would appear to me that, unlike the gases in which we are now immersed, the motion of "stuff" at (or shortly after) the instant of "creation" had something definitely "non-random" imposed upon it:

Please, Dear Sister, share your preferred term, so that we "mere" scientists don't profane your love of "random" mathematical perfection -- even within our own minds... AND, so that we can discuss the above (the closest we've yet come to examining the conditions at "time=zero" so far) without offending your "peeve"... '-)

Imagine for a moment that you are a 2D spatial being, living on a sheet of glass. All around you are imprints of iron filings (imprints being the 2D locations where particles of 3D filings are located). Suddenly you perceive the filings to be moving, collecting into a single imprint, which by you calculation does not added up to the total of the dispersed imprints before the motion began. You would not know that a 3D spatial being is passing a magnet under the glass that is your plane of existence, causing the filings to gather in a heap.

I'm sure you can figure out the point of the imaginary scene. The 2D being does not have the complete knowledge of the entire system at work in order to understand that the filing imprints did not randomly collect into a single imprint.

There is growing evidence that branes other than our 4D brane exist and effect our 4D brane. It is sort of like the analogy offered above. The crystallography photos of non-stick coatings appear to be showing how another brane is influencing the disposition of the coating crystals, as one example of the growing body of data regarding 'other' branes which effect our 4D brane. [You can read about this topic in Lisa Randall's recent book: pp 18 – 19, Warped Passages, Harper Collins, 2005] It is currently being tossed around theoretical circles that gravity in our 4D brane is a sort of shadow effect leaking into our brane from a higher dimensional brane.

Not sure what the disagreement is here, but I'd say "random" is a perfectly fine word when used in proper context.
Outside the purity of mathematics, "random" is a general term used to describe unpredictable events -- the flip of a coin, motions of air molecules, etc. -- but what it really means in those cases is: we can't take the time and effort to measure precisely every force influencing the results, and so we'll just pretend those actions are "random".

That's "random" from a human point of view.
But if you will permit me to speculate -- from an omniscient "G*d's eye" point of view, nothing but nothing is "random", since, first, G*d does precisely know every force and factor influencing a particular outcome, and second, since all was planned out by G*d from the beginning, nothing is a surprise to Him.

No, I'm not talking about predestination, because we don't know anything about that -- that's G*d's realm, not ours.
Our role is to do the best we can, hope for the best, and keep the faith that all will be for the best, even when things look worst.

Nobody could say that better than this:

"Take therefore no thought for the morrow: for the morrow shall take thought for the things of itself. Sufficient unto the day is the evil thereof."

So "random" is a human idea, sufficient unto the day... ;-)

Thank you so much for sharing your insights and concerns, dear brother in Christ!

LOLOL!

BroJoeK's answer works for me; namely:

"Outside the purity of mathematics, "random" is a general term used to describe unpredictable events -- the flip of a coin, motions of air molecules, etc. -- but what it really means in those cases is: we can't take the time and effort to measure precisely every force influencing the results, and so we'll just pretend those actions are "random".

More specifically, the motion of gas molecules is isotropic meaning it has the same value regardless of direction (not relative) whereas the cosmic microwave background is anistropic meaning it has different values in different directions (relative.)

For Lurkers, metals are examples of isotropic materials - they have the same strength in every direction - whereas woods have different strengths in different directions, e.g. against the grain versus with the grain.

Neither isotropy nor anistropy are "random" in the meaning of mathematics. Rather, they are pseudo-random because they are the effects of prior deterministic events.

Statistical randomness (the property being described in the physical sciences with the use 'random' - the unpredictability) is not the same as algorithmic randomness. Under Kolmogrov complexity, for instance, a numeric sequence must be incompressible to be considered random. Indeed most views in algorithmic randomness would insist on that property as well as the inability to make money betting on it (Martin-Löf–Chaitin Thesis et al).

... it would appear to me that, unlike the gases in which we are now immersed, the motion of "stuff" at (or shortly after) the instant of "creation" had something definitely "non-random" imposed upon it....

"A picture is worth a thousand words!"

It seems clear to me that "picture" of the CMB at close to the initial state of the universe is not of an isotropic ("random") distribution.

As Sir Fred Hoyle put it, it very much looks as if some "superintellect has monkeyed with physics."

I do not see how the numerous universal physical constants which appear to be the "initial conditions" of an evolving material universe compossible with life and mind can have arisen from randomness, chaos. No more than the beauty of the world can have arisen randomly. Or even the physical laws themselves.

Thank you so very much, dear brother in Christ, for your splendid essay/post!