The problem of probability

[liamconnor]

I have often struggled with the concept ( and more so, the application) of probability. It is often treated as though it told us something about the universe: as if it can tell us about the weather or the result of coin flipping. The more I think about it, the more convinced I am that it tells us nothing more than our ability to predict what is happening. This is not semantics. The one asserts something about reality; the other asserts something about our guess about reality.

Take an example: if I flip a coin, probability says there is a 50/50 chance for heads and tales. But surely, if the conditions.......and I mean ALL the conditions (the coin, the weather, the placement of the coin upon the precise contours of my fingerprint; the velocity of the flip, etc.) then the result will be the same, every time.

Thus it seems to me that the 50/50 chance of a coin toss says more about our ability to guess the outcome than the actual outcome. The outcome is 100%. We simply can't know what that 100% means.



Question for debate: What does the principle of probability really tell us?

[marco]

We are not gods, but we are getting there. Probability theory relies on the predictability of the world we live in for much of its information.

However, it does not predict specific events, but rather establishes a range of variability within which one can expect the majority of a large number of events to fall. The problem with your assertion regarding us getting there, is that the goal is not static. If the standard is human perception, I would suggest that some of the ancients would consider us deities already. However, since we understand what we do, for the most part, we consider those things to be quite mundane. So, the goal of becoming a deity is equivalent to chasing the horizon. However, if one were able to establish a static goal at which one would know conclusively that one was a deity, such a goal would have to be so far, that all human accomplishments to date would amount to less than a snails pace to the edge of the universe. Even presuming a logarithmic scale, that would still constitute a rather insignificant advancement.

As a child I may have imagined deification a desideratum, bluethread, but when one is floored by a simple virus or left to feel foolish at a miscalculation one has a good grasp of one's human imperfections. Nice people aim to make the world nicer. I was speaking exuberantly of man's proximity to heaven but as the poet, Thomas Hood, said in his lovely I Remember poem- it offers little joy to know one is further off from heaven in adulthood than in boyhood.

Anyway, probability, used properly, provides us with answers. It is sometimes better to have approximate answers rather than exact theoretical ones. In mathematics we use numerical methods to give a workable number and often put aside the exact calculation from a theoretical formula. Probability provides us with results on which we can make informed decisions. But since we are not gods, we cannot guarantee perfection from probable but feasible answers. I don't see that as a problem.

[bluethread]

Probability provides us with results on which we can make informed decisions. But since we are not gods, we cannot guarantee perfection from probable but feasible answers. I don't see that as a problem.

I think that sums up the utility of probabilities in regard to individual behavior. They are like Zephod Bebblebrox's glasses that turn black whenever danger approaches. They give us an assurance that, even if we are desperately wrong, we are at least no more wrong than a given percentage, plus or minus a standard deviation, of the rest of the population.

[marco]

I think that sums up the utility of probabilities in regard to individual behavior. They are like Zephod Bebblebrox's glasses that turn black whenever danger approaches. They give us an assurance that, even if we are desperately wrong, we are at least no more wrong than a given percentage, plus or minus a standard deviation, of the rest of the population.

Probability theory is widely used, even in medicine. We can reduce the margin of doubt to as small as we want, as has already been explained. In gambling situations we can accurately evaluate our chances of success or failure and people make a lot of money on the accuracy of probability theory. There's an amusing example of how we can always win in a gambling situation where we have to choose between red or black, say. We gamble $1 on red; we lose so we next gamble $2 always on red and lose so we next gamble $4 again on red; and so on. Records will tell us what the longest run of red might be. In the end we will eventually win $1 provided we are allowed to continue indefinitely.

Throwing dice and coins is just the outskirts of what is involved. We use calculus in working with probability.

[bluethread]

. . . provided we are allowed to continue indefinitely.

That is the key. Probability favors large numbers. That is why casinos are so profitable. As a business plan, it is also reasonable for a doctor to practice statistical medicine, because he has a large number of patients. However, for the specific patient, it might be deadly.

[marco]

. . . provided we are allowed to continue indefinitely.

That is the key. Probability favors large numbers. That is why casinos are so profitable. As a business plan, it is also reasonable for a doctor to practice statistical medicine, because he has a large number of patients. However, for the specific patient, it might be deadly.

Employing probability theory AVOIDS danger to a great extent. For thousands of people who take a tablet, one might suffer ill effects. Administering a drug may prevent clotting; on the other hand it might cause some secondary problem. There is no right or wrong answer, but probability does help in making a decision. It is far better than simple guesswork or try it and see.

I have no problem with the proper use of probability in whatever field.

[bluethread]

I have no problem with the proper use of probability in whatever field.

Again, another coveat, with which I agree. In a well balanced decision process, that takes externalities into consideation, statistics can be helpful. That is why I favor private agency over public, or even professional subservience.