The 'Chinese' Theory: For and Against

[Jorge_Stolfi]

This is ridiculous. In every case, for every person, there is a 100% chance of a 3 facing up when the die is rolled because that is the reality of the situation.

But you say that only because I told you that Uri Geller was there and intended to force a '3'.  And you believed that he could do it.

But what If I told you that Uri was a con artist who cheated all the way through the "scientific"  parapsychology tests that he was put to, but now is quite senile and believes that he really has psychokinetic powers but actually can't move one hair of a bacterium? 

If they were to test their probabilities by rolling the dice over and over, they would quickly be proved wrong, and would have to change their assumptions.

First: sure, if they had more information, the rational behavior would be to change their probabilities according to Bayes's formula.

Second: probability theory does not say that one can or should determine the probability of a future event from the outcomes of a series of "similar" experiments.  That deduction is based on a non-trivial reasoning, and may be rational for some people but not for others, even when looking at the same experiments. It depends on each person's knowledge and prior probabilities.

Consider again the scenario of my previous post, with Uri sane and powerful.  Let's say that Joe first tests the die by rolling 600 times, and sees that a '3' came out 113 times.  Then he would set his probability of a '3' on the next throw (for the bet) to 1/6 or 113/600 (depending on his prior faith on the maker's precision).  

But Uri would keep his probability at 99% -- because he just allowed the die to roll on its own during the test, but intended to force  the '3' outcome in next throw.  

The point here is that Joe's deduction of the probability of the next throw from the previous "113 out of 600" test was fundamentally flawed, because the next throw was not actually similar to the previous 600.  But 1/6 was a rational choice for him, because he did not know that.

In fact, the reason why 1/6 is the usual and rational choice for the probability of getting '3' on a fair die is that every one is equally ignorant about the reality of the situation.  No one (not even the person throwing it) knows the speed, position, and orientation of the die when it is released.  And even if they somehow obtained that data before the throw, no one would be capable of computing the die's trajectory from that data, accounting for all the minute irregularities of the table and imperfections of the die, until it got to rest.

And that brings up two more points: 

Third: your probabilities for the possible outcomes of some uncertain event will depend not only on the information that you have about that event, but also on your capacity to process that information.  

Scientists often compute probabilities by assuming that variables have a Gaussian distribution, even when that cannot be true, because the math becomes manageable that way.  For instance, in the C14 measurement of the VMS vellum, the technicians assumed that the actual ratio R of C14 to C12 atoms had a Gaussian distribution centered at the value that their instrument showed.  However, according that assumption, there was a small but positive probability that R could be negative, or greater than 1; which are physical impossibilities.

Quick, without looking: what is the probability that the 100th digit of pi is '3'?

If you memorized pi with 100 digits, your probability of that should be either 0 or 1.  But if you haven't,  the rational choice for you would be 1/10 -- because you would be unable to compute the 100th digit just like that, and you have no reason to think that any digit is more or lesslikely than any other.

Fourth: it does not make sense to assign a probability other than 0 or 1 to the outcome of an event that already happened and whose outcome you know.  Once a die, fair or not, has been thrown, and you saw that it stopped with '3' on top, your probability of that throw yielding '3' is 100% and that of any other digit is 0%.  

What may make sense is to compute the probability that someone (or you) would have assigned to the outcomes of that throw before knowing what the actual outcome was.  

Like: you tossed a coin 10 times and "heads" came up every time.  The probability of that run is 100% -- once you know that that is what happened.  But before you threw the coins, IF you had no reason to think that one side was more likely than the other, and IF you believed that each throw would start with different parameters, then you should have set your probability of 10 heads at 1/1024. 

Unless you are going to start claiming that we are all living in literally different realities

I am Platonist -- I do believe that there is a single "real reality", but each of us can have only incomplete and often different knowledge of it.  

The "incomplete" is why we must work with probabilities rather than with true-or-false logic; and the "different" is why each of us will often assign very different probabilities to uncertain events, even when confronted with the the same piece of evidence.

we must assume that everything being said has some underlying factual or logical basis that can be tested in some way

Unfortunately, at every moment we must make decisions before we can do those tests.  When you get out of the bed in the morning, do you first check whether the floor is still there, and will support your weight?

Your underlying assumptions about the VMS are either right or wrong (or a mix) because they are assertions about the properties of reality itself. ... The VMS is something. There do exist hypothetical correct assumptions about its nature.

 

Sure, either the SPS is a transcription of the SBJ, or it is not. (It could be some SBJ recipes mixed with other material, but I hope you will agree that this third possibility is much less likely that either of the other two.)  

So, if your underlying assumptions used to calculate your probabilities are wrong, your probabilities are likely correctly calculated, but wrong with regards to reality.

The probabilities that matter are those that follow from the assumption that the SPS is NOT the SBJ, but a completely unrelated text.  

We can count how many EVA letters there are in the relevant SPS text (about 41'000 in the single-star parags) and how many times each string of EVA letters occurs (232 times for daiin and 272 times for kaiin).  But, if the SPS is not the SBJ, the positions where each string occurs were determined by processes that we know nothing about (the contents of the text, the language, the orthography, etc.).  

Thus, because of that ignorance, it is reasonable to assume that the probability of parag f105v.32 containing N occurrences of daiin and M occurrences of kaiin is the number given by the appropriate probability theory formula for a "random" text of 361 letters generated by a Poisson-like process that spews about 5.6 daiin and 6.6 kaiin every 1000 letters, on the average.  That assumption also tells us the probability of that process generating seven daiin, in that parag, with specific distances between five of them.

And then we sould compute the probability of getting similar distance coincidences not only for the "red rooster" recipe but also for P other recipes and parag pairs with specific crib lists (like the "foxtail millet" and f107v.20 that I posted the other day).

Yes, I should write code to compute that probability with the proper combinatorial formula and string frequencies.  It is possible, but not trivial.  Meanwhile I must rely on crude approximations, like the "boxes with coins" model that I posted lat week.   The numbers I get have convinced me that the probability of the coincidences being due to mere chance is very small.  But I understand that your estimate can be different...

Because I know that many people are already firmly convinced that the text is a heavily encrypted European language, or random gibberish, or Bavarian or Greek or whatever with a non-standard spelling.

If you are convinced that that is the reason people have an issue with your methodology here, please reconsider. This almost feels like its getting tribal. I'm sure many of us here are discussing this in good faith and with an open mind.

That is not "bad faith".  It is just what Bayes's formula says.  If you have become quite convinced that X is true, you should dismiss any evidence for Y as "mere chance", even if the probability of it occurring by mere chance is (say) 0.1%. You should require a lot of evidence before changing your belief -- much more evidence than would suffice to convince someone with no prior opinion.

I am quite convinced that our brain is not capable of parapsichological feats like psychokinesis, clairvoyance, precognition, telepathy, etc.  That conviction resulted from my knowledge of physics and of how the brain works.   Thus, I dismiss offhand any report of such phenomena, even in supposedly "scientific" settings, as being due to fraud, bad protocols, faulty instruments, incorrect statistics, etc.  Without even bothering to read the details. It would take a very strong confirmation of many cases by many reputable scientists to change that  belief.

All the best, --stolfi