No, it wouldn't average out, but its effects would be minimized by it being short w/resp to the window width.

Yes that minimization must occur if the rapid changes are impulsive in nature, or similar to a delta function. That is, some event causes support for a candidate to change quickly , and then that event tends to lose control, and support returns to its previous level.

But is that the right model? A very different model would use a step function. This model says that some event changes the support for a candidate, and that change tends to "stick". But then other events happen, and they can make changes of different magnitude and direction. And then the effects of these multiple events tend to cancel out over the length of the poll window, or perhaps over a much longer time.

The advantage of the step function model is that it can explain long term trends. The step functions of one sign tend to be bigger or more frequent on average than those with the other sign, and so support tends to move in one direction on average.

The disadvantage of the impulsive or delta function model is that it does not explain trends. You need to add something else to the model, a different kind of event.

Yes, a one dimensional random walk, that is, confined to a line. A "directed" walk would go a distance ns, where n is the number of steps, and s is the step size. A random walk would be expected to go about the square root of n times s. If n is large, the distance of the random walk is much less than the directed walk. That is, the drunk walker does not stay where he is, but does not get very far, either.

Thanks, I read the article you linked to and I think you quoted the most interesting part. I disagree with his statement that you cannot claim a trend in a day and a half. If a change is unusually large, then it is unlikely to be canceled by another change in the next day and a half, and therefore you do have significance in a short time. Determination of significance should be based on both time and magnitude.

Yes, for example, we go about our lives in a universe apparently controlled by the deterministic laws of classical physics without even a thought that quantum mechanics is a better description. We just do not need it at our level.

Thank you. And I can say: We must teach more philosophy...We must teach more philosophy... It is all important!

Let us suppose that you are the batter in a baseball game. The pitch comes, and your job is to track the ball: determine exactly where it is and where it is going before it gets to you so that you can hit it. You do not do your job perfectly in general, and your are likely to say "This is not easy, I am not good enough to do this perfectly." You are not likely to say (and would be incorrect if you said) "The universe will not let me do my job."

However, if you tried to track really small things, you would find through careful experimentation and analysis that the universe really is the problem in this case. There are limitations to how accurately you can know simultaneously where something is and where it is going. Here are two extreme views of this situation:

1. Everything does have a precise location and speed, even on a very small scale. But we cannot communicate the information accurately.

2. Simultaneous knowledge of position and velocity is a concept we have because it is so close to correct on our natural scale of things that it works essentially perfectly for baseball. But the concept need have no meaning outside its realm of verified applicability, and it is up to us to figure out how the world really works.

View 1 is dead wrong; it took a few decades to really show this, but that question was settled some time ago. View 2 is reasonable for most things. But I would hesitate to say it is perfectly true. Physics does not really provide us with mental pictures of how things work; it allows us to predict the results of observations.

There is a lot more that could be said, but this is enough for now.

And before you post again, please go back and read the article again, maybe twice. I think your reading comprehension is a bit weak. Might not hurt to take a second look at some of the comments, also. You might be surprised at what you are missing.

GG:Is there anyone who could make a list of all of the pros and cons from our invasion of Iraq and -- while including the hundreds of thousands of innocent dead human beings and the 4 million who are displaced -- argue that it was worth it? What kind of moral depravity would allow that argument to be made?

Proximity Warning will be along to take a crack at it soon, in his own way. How much effort should go into countering his statements? Is it better to ignore him completely?

Those are all legitimate questions. Why not look for the answers? Let me ask you one: What are you willing to sacrifice to give up our dependence on foreign oil?

Those are mostly rhetorical questions. Can you show that our ships are protecting the oil flow from, well, what? Pirates? And that that is their major function there?

And there is not a single UN speed boat inspector left in Iran. Proof that sanctions have failed, and we must invade at once.

Did you forget that we are dealing with religious fundamentalists, who are not rational actors?

Do you actually know anybody outside of your own neighborhood? Most Iranians are more rational than you.