Brent,

excuse the bartender as interlocutor:
  > they are inconsistent in their assignment of probabilities.<
do you really 'believe' in (math?) probability?
If I choose a domainful of cases, compare them and find 51% of a
variant, does that mean anything in projection within the not chosen
cases?
Don't even exceed the domain, just do not 'order' the cases in the
counting. Only in our intimidated mind do we find it natural that x,
y, z, will be distributed in some humanly orderly fashion.

Relations can upset all regularity. Qualitative aspects can overturn
the quanti expectations. The world is not a math-test with controlled
setup.
Anticipation is fine, but dangerous.

Similarly: statistical results depend on the sampling, the boundary of
the counting area. Choose a different domain and your statistics (of
the same title) will turn out differently.
Our logic (wish?) does not control nature.

Probability and statistics is human logic. It works in many human
cases (situations) and so we generalize them for quali-totality.
So is the law of the big numbers. Big for whom?

Then we run into catastrophes and paradoxes.

John M



On Mon, Sep 22, 2008 at 2:10 PM, Brent Meeker <[EMAIL PROTECTED]> wrote:
>
> [EMAIL PROTECTED] wrote:
>> Let the algorithm that represents the brain of a typical new-born baby
>> be denoted as B1.
>>
>> Now surely we can agree that the brain of a new-born baby does not
>> have sophisticated Bayesian machinary built into it?  Yes, there must
>> be *some* intrinsic built-in reasoning structure, but everything we
>> know suggests that the intrinsic reasoning mechanisms of the human
>> brain must be quite weak and simple.
>>
>> Let the algorithm which represents the brain of the baby B1 which grew
>> up into a 20-year old with a PhD in Bayesian math be denoted as B2.
>>
>> Now somehow, the algorithm B1 was able to 'optimze' its original
>> reasoning mechanisms by a smooth transformation into B2. (assume there
>> was 'brain surgery', no 'hand coding').
>>
>> The environment! you may shout.  The baby got all its information from
>> human culture (Reading math books, learning from math professors), you
>> might try to argue, that's how B1 (baby) was able to transform into B2
>> (PhD in Bayes)
>>
>> But this cant be correct.  Since, humans existed long before Bayesian
>> math was developed.  Every single Bayesian technique had to be
>> developed by a human in the past, without being told.  So in theory,
>> B1 could have grown into B2 entirely on its own, without being told
>> anything by anyone  about Bayesian math.
>
> I don't think it likely that one individual could have gone from B1 to B2
> without being told anything about probability, preference ordering, logic and
> mathematics.  Just because there is a chain of maybe a few hundred individuals
> who did it or contributed to it, it doesn't follow that one person could do 
> it.
>
> However, I recommend William S. Cooper's little book, "The Evolution of 
> Reason"
> which takes your idea of development of modern forms of reasoning from simpler
> forms seriously and fills out details and also suggests further advances.
>
>>
>> The conclusion:
>>
>> *There exists a very simple algorithm which is only a very weak
>> approximation to PhD Bayesian reasoning, which is perfectly capable of
>> recursive self-improvement to the PhD level!  No hand coding of
>> advanced Bayesian math is needed.
>>
>> Or to simply rephrase:
>>
>> Humans could reason before they discovered Bayes.
>
> But they commonly violate the rationality standards of Bayesian inference, 
> i.e.
> they are inconsistent in their assignment of probabilities.
>
> Brent Meeker
>
> >
>

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