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Transgression and Science
Transgression

The concept of law is a restricted one with regards computers as with regards nature as in both it does not allow for the transgression of the law. That is, we have a law saying, that as pedestrians, we must not cross the street when there is a red light. But now suppose you see someone crossing the street, you could assume the light is green and start passing yourself. Sadly, many times you’d die as the light was red and the person was just passing before the car got there. The moral: seeing the symptom of a person crossing the street does not guarantee that he is abiding by the law, and so that the light is green.

Now this all seems simple and yet we do not comprehend it with regards nature. If there is a law, everything MUST abide by it. It is not that the lighter rock can decide to fall faster than the heavier rock. It is not that we can decide to levitate. No, these laws must be abided by, and by extension computer programs cannot just decide not to work as told, to all of a sudden run with no reason, but must constantly abide by the law.

You can say it is a different kind of law and I am mixing concepts, but I do not think so. You could say it is taken into account in Quantum physics where particles can in a sense jump and behave erratically, similarly to a glass all of a sudden jumping, as quantum physics is a theory based on probability. That is an important point, and seems to answer our question, but it really doesn’t, I think. On the contrary even.

Quantum mechanics does say that a glass can all of a sudden just jump, but then it incorporates the transgression into the theory in a way so that the glass can not transgress the law but will have to follow it. Whatever it does, it follows the law, and again we are in the safe ground where the law cannot be broken. But moreover, if one thinks about this, and why this case exists in the theory it actually tells us that glasses can, with no reason, all of a sudden jump, hover, go to the left or right, depending on nothing. Or, perhaps, depending on what we could call their own will. This would certainly seem to say that they can break the law, the old law which would say that it must stay still unless there is a power on it. Thus the theory actually says that the glass can not adhere to the old laws when it feels like, and the new law simply takes that into account, to form a new law to which, again, it must abide. It must abide it, as to transgress it, is in a sense, impossible; again.

And so, all Quantum mechanics actually shows us, if we accept it, is that even in nature elements can simply decide to not follow the law! To act irrationally, or unlawfully. But then, learning from the symptom, learning not from the origin but the symptom, seeing other people cross the street, doesn’t tell us anything about whether the light is red or green, simply a probabilistic answer, which, moreover, as we don’t know the probability of following the law, doesn’t tell us much. This renders all physical experiments, or rather their use in constructing and checking theories, rather pointless as most work not by looking at the traffic light but by checking if people cross the street.

Well then, science doesn’t seem to be on very firm grounds here. But this is not about science, but on our incapability of actually comprehending the possibility of transgression in nature. Of nature not always following its laws. And this my friends is an important thing to comprehend.

To summarize, the classical view of the world as operating by laws which science simply needs to find, and then everything MUST operate by them might simply be false. This is not a call to drop science as we have no other recourse, but, rather, to comprehend the possibility of transgression in nature. Something which in our current logic seems incomprehensible.
These sorts of questions about probability are very tricky ...

You might think of a quantum mechanics "law" as a sort of practical advice.  It says, "the glass might jump up in the air, but don't bet on it."  Suppose you run a department store that sells glasses.  They are sitting on shelves, ready to be purchased by customers.  Now, if you believe that the glasses will jump up in the air, you should tie the glasses to the shelves with rubber bands, to make sure they don't smash themselves when they jump.  But this would be an unwise course of action.  It would be expensive, time consuming, and would probably not pay off.

Of course, now I have reduced a simple question about probability, to a messier one about "practical advice."  What is "practical advice"?  You may not be satisfied with this sort of reduction.

In any event, I would disagree with the statement that "this renders all physical experiments, or rather their use in constructing and checking theories, rather pointless."  In the case of the traffic light law, you could measure the number of traffic light violations over a very long period of time, say 1,000,000 crossings of the streets.

Of course, you could still develop a wrong theory if you are unlucky, for instance if the people crossing the street behave very differently than the actual underlying probability would suggest.  Suppose you flip a coin 1,000,000 times, and you get 900,000 heads.  It's an ordinary coin, and the flips were purely by chance.  Then you might suggest a "90% heads" theory, which would be very wrong.

But again, the practical advice is that you should exclude theories which produce the observed data with very small probabilities.  That is, if something works 90% of the time, you should assume that the correct probability is in the vicinity of 90%.  (The theory of statistics will give you an idea of how close your estimate might be.)

When I was younger, I used to tell my brothers the following theory.  The world is populated not only by humans, but also by little elves, about one foot tall.  They move around, going about their business.  And it so happens that you have never been fortunate enough to see them, because they are always standing behind your back.  This is just your bad luck.  Other people see the elves all the time.  Maybe some day soon you will see one.  Also, discussion of the elves is taboo, and no one tells you about them until you are older. 

Now, my brothers had an observation to the effect that there were no elves.  Do you feel that this observation was "rather pointless", and that they should have believed my story?
Hi William,
I'm sorry but there was a misunderstanding, no doubt arising from my post being not so well written.

My point was that currently science operates under the strict assumption that everything in nature abides by certain laws. Science does not accept the idea of a transgression of the law.
When things weren't behaving as planned, statistics came into play in order to eliminate even the possibility of a transgression of the law, of a breaking of a law.

Let's look at your coin example. If out of 10000 times the coin comes out 10000 times heads, it is still ok statistically. There is a very small chance that it will happen, but the chance exists nonetheless. Even if you throw the coin 10 million billion times and it still comes up heads every time, well that's the statistical curve for you. (Some sharp people might assume the coin is not a completely equal one.) But what if it wasn't statistics but that simply the coin feels like breaking the law. Feels like always coming up head? It can't break the law no matter how hard it tries.

Science assumes the world operates according to rules, but that assumption could be false, or more interestingly, could be sometimes false. Sometimes, the world might just choose to break the law, like the pedestrian choosing to cross the street when the light is red, even if they know they shouldn't.
I mentioned quantum mechanics to show how science incorporated into itself that very possibility, and thus actually not allowing for the possibility of breaking the law.


[Photo: stroboscopic coin toss by Andrew Davidhazy]
Hi Hugh,

Good to talk to you again!

Let me just confirm a few things that I think we agree on.  You say, "it can't break the law no matter how hard it tries."  Here, you are talking about a kind of "absolute transgression", with a certain binary dualism of "unlawful" vs. "lawful."  This dualism exists in Newtonian mechanics.  In Newtonian mechanics, a physical event can have a probability of 0, in which case it is unlawful, or 1, in which case it is mandatory.  ("Everything not forbidden is compulsory" as the communist ants say in T. H. White.) Thus, in Newtonian mechanics, if a glass were to jump in the air for no reason, it would be transgressing the physical law.  But the transgression is only hypothetical.  I will call it "hypothetical" because according to Newton, it never occurs.

This dualism does not exist in a probabilistic theory.  In quantum mechanics, an event can have a probability of 1/2, 1/10, 1/100000, etc.  So the idea of "transgression" does not apply here, at least not in the absolute sense.  So I agree that "it can't break the law no matter how hard it tries" meaning "for coin flips, there is no event of probability 0."  So far, I think we are in agreement about all of these things. 

Now, you are saying that we must give up absolute, hypothetical transgression -- laws which could be transgressed, but never are.  Either we must develop a theory in which the transgression is relative (i.e probabilistic), or a theory in which it is actual (i.e. transgressions actually do occur.)  Quantum mechanics allows probabilistic transgression.  But you want to consider the latter type of theory.

The first thing that comes to mind is a "rule of thumb."  Such theories already exist and are very useful.  For instance, in biology, I could have a theory like "all animals have the same lifespan, if the time is measured in the animal's own heartbeats."  (That's an actual biophysical law, I believe.)  Now obviously, many animals do deviate from this law.  But the law is approximately correct in many cases.

In quantum chemistry, there are all sorts of laws that describe how the electron shells fill up, how the spins align, etc.  Some of these laws are transgressed by one chemical or another.  But this is only because they are rules of thumb, and are not derived in a rigorous manner from the Schrodinger equation. 

QM is so successful at predicting how nature behaves, that at present it is treated as an exact law.  (Or at least probabilistically exact.)  Perhaps someday QM, too will turn out to be a rule of thumb, which can be transgressed.  Just as Newton's theory was transgressed by QM.

"Transgressions of physical laws" also makes me think of religion and miracles.

By the way, regarding quantum cops and traffic violations:
http://www.galactanet.com/comic/view.php?strip=89

Sorry if I am still not understanding.  Let me know.
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