## Wednesday, September 24, 2014

### Science and lottery

Ask anyone who buys lottery tickets systematically, most of them will confirm they have a system. Most of them seem to be based on birthdays, although the days of the month are a serious limitation of the possibilities. Some play random numbers, which they withdraw from a bag (this is the best "system"), but most have a sort of a system.

I don't believe there is a winning system. People tried to convince me that numbers have their own life, and they are not quite random. "Laymen" tend to believe that if you toss a coin and you get head, next time are bigger chances to get tail. If you pay attention in US movies, you will see that almost every time a number appears, its digits are unique, for example 52490173, a permutation of a subset of 0123456789. Except of course for the phone numbers, which start with 555. This is because a number like 254377 seem too special. In fact such numbers which don't have unique digits are encountered more often in real life. So I don't buy the idea that lottery numbers are not random. Some try to convince me that because the balls are not perfect, they are biased, and some numbers are more likely to be extracted than others. Even if this is the case, I don't think you can actually use this to predict the numbers.

My opinion is that from lottery only the house wins, at least on average. This doesn't mean that if you play you will not win.

Now, since almost anyone who plays systematically has a system, and since the winner will be among these guys, most winners have a system. So, what happens when you win? You will believe that finally your system turned out to be correct. You may even write a book in which you explain the system, end get even richer by selling it. But you will definitely believe that you won because of your system. While I don't believe your system. You can tell me that your system turned out to be correct, even that it is science, because it made predictions, and it was confirmed by the most difficult test: actually playing and winning in real life! But I still don't believe in your system. Because anyone who wins has a system, and he won because sometimes people win, but not because of the system.

Now, imagine a world in which
• in order for a paper to be considered scientific, its basic hypotheses have to be falsifiable by experiments
• scientists have to publish lot of original papers, otherwise they will perish
This is pretty much our world, and I think that these two conditions lead to an avalanche of predictions. Whenever an experiment will be about to be performed, scientists will bet for various outcomes. And just like in betting, they will try to cover all possible outcomes.

So, after the experiment is performed, some will win the lottery, while some will lose it. Does this ensure that the winners really cracked the laws of Nature? Did they win because of their theory, because of their system? Or just because of pure luck, and they just tend to give credit to their system?

Doesn't this mean that something is wrong with the way we define science? Making predictions is easy. Suppose that there are 5 possible outcomes, and there are 5 theories predicting them, one for each outcome. Suppose that the experiment corroborates one of them, and falsifies the other four. Why where those 4 wrong in the first place? Just because after the experiment they turned out to be wrong? Why couldn't we see the reason why they are wrong before performing the experiment? What if the fifth, which was corroborated, is correct by a coincidence, for the wrong reason? What if there are 10 possible other explanations of the same result?

Yes, it is possible for a theory to be right for the wrong reason. Consider for example the following calculation:

The result is clearly correct, but the proof is wrong.

If a theory makes a correct prediction, this doesn't mean that it is correct. This is why we never consider a theory to be proved, or even confirmed. We just say that the experimental results corroborate it. Maybe later we will find a better theory, which will make the right predictions for the right reasons.

The problem is that, if we will find another theory which makes the same predictions, it will be considered inferior. The theory will be asked to come with new experimental proposals and its own predictions, which will contradict the predictions of the previous theories. If it will not be able to make new predictions, rather than being considered equal to the currently accepted one, it will be considered inferior. Because the current one made new predictions, but the new one made the same predictions.

This means that from two theories making the same predictions, the one that was proposed earlier will have some advantages over the one that was proposed at a later time. Even if the latter is conceptually superior, or simpler, or have other advantages.