On the myth that probability depends on knowledge

Darken-Sol

if i created a device to drop a coin the same exact way each time, and i put the coin in heads up each time, the first drop would presumably be the only drop with a probability of 50-50. it seems the knowledge of that outcome would effect the probability of every other drop. please help me out if my thinking is flawed.

DaleSpam

Now you want to take a semantic debate about the word "probability" and add a semantic debate about the word " definition".

The point is that it is perfectly well-accepted to consider probability to depend on knowledge. It is not a myth. Your continued refusal to recognize this obvious fact makes you seem irrational and biased. How can anyone reason or debate with someone who won't even acknowledge commonly accepted meanings of terms?

A. Neumaier

If your device were deterministic, and you were able to replicate things with infinite precision, the later outcomes would be the same as the first one. But neither of these assumptions can be realized.

A. Neumaier

You seem to imply that semantics is irrelevant for meaning.

I never saw anyone before equating interpretation with definition. They are worlds apart.

And about the semantics of myth:

from http://en.wikipedia.org/wiki/Myth :
from http://en.wikipedia.org/wiki/National_myth :
Thus something may be well accepted and still be a myth.

Darken-Sol

i'm just using a cheap chute and a pencil. 9 out of ten times its heads, so far. that one tails, does that set the odds back to 50-50? even though the results say 90% heads. would an observer with no knowledge have a 50-50 chance?

A. Neumaier

It depends on whether you think in terms of subjective or objective probability.

The objective probability is independent of how much an observer knows, and can be determined approximately from sufficiently many experiments. To someone who knows none or only few experimental outcomes, the objective probability will be unknown rather than 50-50.

The subjective probability depends on the prejudice an observer has (encoded in the prior) and the amount of data (which modify the prior), so it may well be 50-50 for an observer with no knowledge.

DaleSpam

You are clearly not a reasonable person to discuss with. No progress can be made in such a conversation.

Darken-Sol

your saying there was only one outcome objectively, even though i couldnt be certain. so subjectively i had 2 choices, and then one choice for each successive drop?

A. Neumaier

Objectively, the odds seem to be close to 90-10, according to your description, though I don't know whether your sample was large enough to draw this conclusion with some confidence.

Subjectively, it depends on what you are willing to substitute for your ignorance.

If _I_ were the subject and had no knowledge, I'd defer judgment rather than assert an arbitrary probability. This is the scientifically sound way to proceed.

Darken-Sol

the knowledge has no effect on the probability of the outcome, just probable correct answers. i think i got it. i guess i agree with you then.

kaonyx

Quantum mechanics has demonstrated that what we do not know can arise from what we cannot know. Information that parts of a system can have about other parts of a system is not really separate from the systems themselves. We have to stop pretending to be omniscient.

harrylin

I have just now been introduced to probability theory by Jaynes, and the way he described probability (as a tool for prediction), it definitely depends on information. I suppose that what you call "probability", is what he might have called statistical "frequency".

Thus it is "just" a matter of words and definition, but, as I just discovered, it's an important one and you are right to bring it up!

Jaynes argues, or in fact he shows, that quite some paradoxes (incl. in QM such as Bell's) result from confusions between, on the one hand:
- our probabilistic inferences and predictions based on the information that we have,
and on the other hand:
- the effects and statistics of physical measurements that allow to verify those predictions.

Harald

A. Neumaier

Jaynes propbabilities are subjective, then the dependence on knowledge is appropriate.
When he applies it to statistical mechanics, though, he gets the right results only if he assumes the right sort of knowledge, namely those of the additive conserved quantities. Would someone apply his max entropy principle using onlz knowledge about the expectation of the square of H, say, he would get very wrong formulas.

Thus one needs to know the correct formulas to know which sort of information one may use as input to his subjective approach....

For a detailed discussion, see Sections 10.6 and 10.7 of my book

Arnold Neumaier and Dennis Westra,
Classical and Quantum Mechanics via Lie algebras,
2008, 2011. http://lanl.arxiv.org/abs/0810.1019

harrylin

It appears to me that what you call "subjective" is what he called "objective"; and of course any prediction is based on certain assumptions (theories that are based on human knowledge). Anyway, thanks for the link - and if you want to call a prediction based on QM, "subjective", then that's fine to me.