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I asked for an example of this taking place, not for a demonstration. To an onlooker listening to all sides....you giving an "example" of your position is in no way "trivial".

This is not a rational request for evidence. If me doing exactly what you are hypothesizing to be impossible isn't an adequate example, what is? You don't even grasp the obvious consequences to everything you think you know if what I asserted was wrong.

I will let you pick any source of randomness. It doesn't really matter as they will all produce any finite program in a finite amount of time. I can't believe that people are even arguing this point. It is ridiculous and founded in ignorance. People have done this at various times for decades (mostly at universities to prove a point), but it is a worthless proof because we can trivially prove it mathematically. So do you really question whether or not 2+2=4? How do you get on in the world? The mathematics of it is blatantly self-evident to me but apparently not to you. Perhaps you could take the time to read up on some elementary theorems of the subject we are talking about rather than insisting such things aren't so without the slightest clue one way or the other. Your mathematical position insists that no one can ever win the lottery, yet people do. The necessary consequence of the opposite of what I am asserting is that no one could ever win the lottery. By the exact same theorem.

"If me doing exactly what you are hypothesizing to be impossible isn't an adequate example, what is?"

First of all, your voicing magic perspectives about what I do or do not hypothesize smacks of "muddying the water".

Now...

I am not quite sure why you are failing to comprehend the difference between a "demonstration" and an "example" but please...

An example will suffice.

"I will let you pick any source of randomness. It doesn't really matter as they will all produce any finite program in a finite amount of time. I can't believe that people are even arguing this point. It is ridiculous and founded in ignorance. People have done this at various times for decades (mostly at universities to prove a point), but it is a worthless proof because we can trivially prove it mathematically. So do you really question whether or not 2+2=4? How do you get on in the world? The mathematics of it is blatantly self-evident to me but apparently not to you. Perhaps you could take the time to read up on some elementary theorems of the subject we are talking about rather than insisting such things aren't so without the slightest clue one way or the other. Your mathematical position insists that no one can ever win the lottery, yet people do."

That's incorrect. The reason that you can't show an example of a useful computer program self-forming in a random environment is because complex levels of organization can often be beyond what is possible for a random, chaotic system to create (we don't have infinite time, after all).

Likewise, your lottery example is flawed. A winning lottery ticket might be comprised of 6 two-digit numbers, yet 6 two-digit numbers is vastly insufficient for any modern, useful software program. Perhaps a simplified software program could be comprised of 20,000 two-digit numbers. A similar lottery would require hundreds of billions of years before a winner was ever found (i.e. far older than our existing universe).

Except, even when that winning number was hit in the random, chaotic, physical world of either DNA or computer programs, it would just be one organizational structure inside a mass of useless data in a place unable to to either execute (in the case of a computer program) or activate (i.e. abiogenesis) and survive (in the case of DNA), much less replicate, mutate, and form new generations of programs and life.

So no, you can't point to an example of a computer program self-forming from any chaotic, random environment (even though you absurdly pretend that such an exercise is "trivial")...