The assumption of knowing

About probability is a reference to where I first considered this subject. In the picture the blue square is the visible indicators possible. The brown square are the whole conditions. The green are the possible associated sets. The problem is stated as "What is the probability that if I have a son, that I will have another son if everybody has two children.".In this case it is NOT 2/3 likely for the same gender.

In a random distribution there will not be a skewed association. By creating sets that make false assumptions about the underlying set it would seem to be true. The set of pairs contains BB BG GB GG and so the set of observations for B is BB BB BG BG and conversely. It is true that a set which is skewed can be created if the starting set is BB BG GG, which has an even distribution of B and G, however it is not a representation of the actual distribution that would exist.

It is of interest because it can be the source of some confusion in genetic recombination of dominant and recessive genes. The human or animal mind is not always the naturally best tool for understanding. A person has to be aware that the wetware has some nasty edge conditions that are far worse than integer overflow, loss of precision in floating point, and type casting losses. At least it doesn't have a divide by zero fault or SIGSEGV. One would have to suppose that results are skewed to avoid type 2 results. By "type 2" I mean that a failure to choose something in a case that leads to death is a fatal error like SIGSEGV and so a brain only gets to make that mistake once.

The best way to predict the future is to create it.

Language of thought

I am considering Markov models and how they can be used to devise the causal and dependent relationships in any number of applications. The tools to display and manipulate those relationships exist, but a simple interface is lacking. I hope to create a simple framework that I can expand and extend to correlate relationships as well as data. It has many applications.
This course in applied probability at MIT has quite a bit of data on the subject.
The graph is gnuplot with a set of sample data using "pm3d at b".
This is another area where symbols and definitions interact.Symbols ∩ (&cap; ) and ∪ (&cup; ) describe set relationships and it does seem that if I am to ever use all of this in one single context that I must either make new symbols or use something more complex that is context sensitive. I could say set.intersect and use ∩ to display it when in that context and use my own symbol when dealing with it myself. It isn't to hide what I am doing, it is just too confusing to see the same symbols applied in too many places. In linear algebra the symbol Ax=b has a vastly different meaning and P(A) means probability of A in that context and if I were programming it would be function P with parameter A. Even within this sentence the concept of AND is used while describing the symbol ∩ ∧ ∪ ( &and; is also a symbol for and). If a person confines activity to a single specialty it is fine, but when a person tries to take advantage of the fact that these methods resolve to the same action in new terms, it gets odd. It isn't just i and j as it goes way farther than that when I do Python or C and deal with an array. [i][j] and then there is <i>italic</i>. I think I ( meaning me and not the Identity matrix or i the imaginary axis or i the italic or even i the common C iterator ) will make an extended symbol set for myself because it is like trying to write every word as a sequence of 0s and 1s because the language is not complex enough to express all the possibilities. It just gets worse in the future. I think that English is a stone age language. A vast majority of what is new was never known and as a result the language grows in the same way that it was created, like some bizarre multiply emergent mess. It is bad enough that virtually every nation on the planet has their own language, but to start having sub-languages for every science is too much. AFAIK IMHO srsly!