Thanks for the insightful comment.

Rhett

Maybe you should spend time brushing up on your English instead of wasting your obvious Physics talent with blogs like this…

Suppose you have a certain amount of information which you want to remember exactly, so you make a digital record of it with n bits. However, every minute, each bit of information has some small chance p of being flipped randomly. Over a long time, you accumulate errors and your record evolves into completely random mush.

Now imagine you foresaw the previous disaster, so you decided to build three records of information. They begin identically. Again, every minute, each bit has some small probability p of being flipped. So, at the end of each minute, you compare all three records. If a bit flipped, you’ll have one record that disagrees with the other two. That way, you catch the mistake, and can manually flip it back.

Unfortunately, after some extremely long period of time, you will have a case where the very same bit flips in two different records in the same minute. When you do the comparison at the end of the minute, the record with the correct bit will be outvoted, and you’ll lose some of your information for the first time. But if this happens once, give it long enough, and it will happen again and again. So after many ages, you’ll again have mush for data.

Assuming the rate of random errors is fixed, you can slow the degradation of your data by 1) making more copies 2) checking more frequently Say you make c copies of your data and check on it with a frequency f. The sad news is that for any given probability P that no degradations have taken place, we can find some function t(c,f,n,p,P) that gives a time t such that if you wait for t minutes, the probability that you will lose some of your data exceeds P.

In other words, if you want things to remain exactly the same for infinitely long, even an infinite supply of free energy won’t save you. Eventually, you’ll have to forget.

However, there could be a way around this. What you need to do is continually increase the number of copies of data you have as a function of time (or continually increase the frequency of your checks as a function of time). If you continually make more copies of your data as time goes on, you may be able to get your probability of an error to converge to some value less than one as t -> infinity. However, to implement this strategy, the number of copies of the data you’re capable of storing would have to be unbounded (or the frequency with which you conduct checks on your data would have to be likewise unbounded.)

I think Professor Jones’s trip in the refrigerator (in Indiana Jones 4) is a more egregious example of that kind of bad movie physics. Or maybe I’m just saying that because I liked Iron Man more.

http://home.roadrunner.com/~tadhurst/DWFTTW.htm

-tad

If you can believe string theory has 10^(10^5) acceptable vacuum solutions you can hardly criticize a mere 126 minutes of gadget porn. Ask yourself, “how did Iron Man take a whiz?” Now we shall see if the movie is true to itself - “They say the best weapon is one you never have to fire. I prefer the weapon you only need to fire once.”