The 'Chinese' Theory: For and Against

[Jorge_Stolfi]

 there is no such thing as "the" probability, either.  The probability of a statement is a numeric expression of our belief is true. Therefore "my" probability is different from "your" probability which is different from that other guy's probability.  Because the probability is determined by the totality of what one knows and how one reasons.

What? Either the probability of your matches being coincidence are based on some actual mathematical foundation, or they aren't. Otherwise, what is to stop you from saying "I found 1 word that matches once, therefore it is proven to be a match".  There has to be some kind of standard of proof here, or everyone will just claim anything without any proof at all. 

That is unfortunately a common misconception: that probabilities are "physical" properties like temperatures or latitudes, that can be measured or calculated in an objective way.

But the truth is like I stated above.  

Probabilities cannot be measured by some "You are not allowed to view links. Register or Login to view. (p.37)".   

Probability theory cannot produce any specific probability, not even the popular 50% for heads in a coin toss. It only gives math formulas that tell how to keep one's probabilities consistent: like "your probability of heads plus your probability of tails cannot exceed 1.0, and the difference must be your probability of all other outcomes combined, including the coin falling on its edge or being snatched by a magpie in mid-air."  But ultimately all your probabilities will depend on some key probabilities that you can and must choose without a mathematical justification.

Joe throws a die, and his probability of it showing '3' is 1/6 is because he believes that there is only one '3' on that die, and has no reason tho give one side of the cube more probability than any other, and he knows that the probabilities must add to 1.

His grandma Jane is sitting at his side, but her probability of a '3' is 80% because she had a vivid dream where her great-great-grandfather appeared and told her to bet on '3'.  

My probability of a '3' is 50% because I used my parlor magician skills to replace Joe's die by one that has '3' on three of the sides.  Thus I bet $12 on '3' against his $24 on any other number.  Probability theory then tells me that my expected win is 0.5 x $24 - 0.5 x $12 = $12; while the same theory tells him that his expected win is 5/6 x $12 - 1/6 x $24 = $6.

But I did not notice that Penn and Teller are sitting next to me, that they saw my swindle, and that they counteracted it by replacing the die with another one that is heavily loaded on the '4' side. Based on a few test throws they did previosly with that die, their probability of a '3' is only 5%.

But none of us realized that the elderly gentleman sitting next to Joe was his uncle Uri Geller, who proceeded to use his psychokinetic abilities to make sure that the die always came to rest with the '3' side up.  (While bending everyone's car keys as an unintentional side effect.) So his probability of a '3' is 100%.

And all six of us are correct according to probability theory.

Can you honestly say that if you were reading this thread (written by someone else), that you would consider this theory as being proven?

Obviously I cannot give an impartial answer.  

But yes: if I started with no opinion on the matter, after looking at the data provided, quickly checking the statistics of 主 and daiin and doing some rough estimates of the probability of the coincidences being due to mere chance, I should set my probability of the claim SPS=SBJ being true to something like 90% or more.

Why are you convinced of something that you do not think people will be convinced by?

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. 

A very important tool of probability theory is Bayes's formula, that tells how you should change your probabilities when you learn new relevant data.  It is totally deterministic and mathematical -- but it says that your probability of X after seeing the data D depends on your probability of X before seeing the data, and your probability of the data D coming up depending on whether X is true or false.  

In particular, if your probability for X before seeing some evidence D was 0.01%, and D could be remotely the result of chance, the formula says that you should rather believe that D is almost certainly due to chance, and raise your probability of X to only (say) 0.02%.  

If that is your case, it will take a lot of evidence to raise your probability of X above 50%.

To me, this seems like the theory version of many imagery comparison threads, where someone goes "look, these two diagams look similar, they must be related. What are the chances that these things match up perfectly?".

Yes, it is fundamentally the same situation: getting people to revise their probabilities of Y ("the VMS author had a microscope") by presenting some evidence E (the image of a diatom next to page f69r).  

The difference is just the numerical values of the probabilities involved and how much they change after seeing E.  For me, the probability of the similarity I can see in E being due to mere chance is very high, because in my view the image of a chariot wheel or open umbrella or any of a thousand other objects would look just as similar to You are not allowed to view links. Register or Login to view. as the diatom.  Thus seeing E has hardly any effect on my probability of Y.

Whereas, by my estimates, the probability of the length histograms match and the coincidences in gap sizes of 主 and daiin being due to mere chance is so low that it raised my probability of SPS=SBJ to near 100% from the previous value of (say) 1%. That is where it was when I was already quite convinced that the text was in some unencripted East Asian language, but I did not know which books, if any, it was transcribed from.

All the best, --stolfi