understanding probability

[Paul King]

> On Fri, Aug 9, 2013 at 5:40 AM, Christopher Browne wrote:

> The harder one is that "physics is wrong."  I note that the place that
> we get new bits of physics is by coming to the conclusion that the
> model that we have doesn't correctly express reality.  You need to
> modify Newtonian physics (which are *mostly* nicely expressive of the
> phenomena we tend to see) when at certain edges one needs to take
> Relativity into account.  Now, there's a pretty big burden of proof
> required to establish that *everyone* has been getting things wrong and
> that the deep models need to be changed.

Actually, the way I teach physics is to say that Quantum Mechanics is the 
"correct" theory, while still saying that Newtonian mechanics works well
at the macroscopic level. That is, classical mechanics needs no 
modification for what it does. We can still use it to build our bridges
and skyscrapers. It just wouldn't be used to explain what goes on inside a
silicon chip. Or most of the most useful reaction mechanisms of biochemistry
would also not have good explanations.

So, technically, Newtonian Physics, in its promise to explain the world,
couldn't do it unless you excluded those things beyond the fringes of our 
sense of reality, like black holes and atoms. Since it failed to do so, 
quantum mechanics claims to cover everything this time. But using its 
equations to build bridges or skyscrapers is unnecessarily complicated, 
so the simpler equations of classical mechanics serve just nicely.

> 
> The easier one is more about the local interpretation.  For the fissile
> mass, if I see way too many atoms decaying, more than my model of the
> object would account for, then it seems quite reasonable to think that
> maybe my model of the particular object is wrong.  Perhaps I didn't
> account for a nearby chunk of Polonium, or something of the sort.  I'm
> not talking about saying "theories of radioactivity are wrong," rather,
> I *thought* that the situation involved one thing, with one rate of
> radioactive decay, but reality is somewhere else.
> 

It could be that your conjecture is wrong, but Quantum mechanics is a 
probabilistic model, so there is nothing saying that in the next 60 seconds,

the small percentage of radioactive isotopes in your body of Carbon, 
Hydrogen, Oxygen, Phosphorus, Nitrogen and so on will not all emit a beta 
particles in that time. That likelihood is extremely remote, but it
still stands as a likelihood. A probability. Like the probability of 100 
monkeys typing out a Shakespearean sonnet by hacking the letters at random.
Might not happen, but it could.

Four aces dealt once would only surprise me, but if it happened two or more 
times in a row, that might make me suspicious.

> 
> But the pundits originally thought that MD5 was pretty good, and there
> has indeed been this sort of shift to thinking that it isn't wise to
> use MD5 for cryptographically-important tasks anymore because it has
> some flaws.  That sure seems like a precedent of the same sort of
> thing.
> 
> Based on the history of hashing algorithms thus far, it seems pretty
> reasonable to imagine it quite possible that 10 years from now someone
> may discover significant flaws in SHA-1.  That doesn't imply that *my*
> collision represents a flaw in SHA-1.
> 
> But I would be careful not to be *too* self-satisfiedly certain that a
> collision indicates identical data; I'd want to at least consider
> checking.
> --
> When confronted by a difficult problem, solve it by reducing it to the
> question, "How would the Lone Ranger handle this?"
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