Pastelland Forum

borys610 wrote:dualizm korpuskularno-falowy

częściowe zaburzenie ciągłości tkanki kostnej

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La
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http://www.youtube.com/watch?v=bjmgzLVuWLU

Mathematics of ancestral genealogy

You have two parents, four grandparents, eight greatgrandparents and sixteen greatgreatgrandparents.
For the n-th level of ancestral kinship, you have 2^n ancestors of that level. The zeroth level is yourself, as 2^0=1.
Your parents are the first level, so you have two of them, as 2^1=2. N can only be a natural number, zero included.
n
Ancestral kinship is henceforth defined as the set of all people who have directly worked in the past to ensure your (and your other ancestors') existence, in the biological meaning of the word [assuming no incest]. It is later abbreviated as a-kinship.
For n-th level of a-kinship, 2^n-1 ancestors are male, and the same number is female.
[For n>0 and n, as 2^0-1=0.5, and the number of people can only be an integer]
Therefore, f(n)=2^n where n is a natural number is a function visualizing the amount of a-kinship members.
For given number x of ancestors, their level is the number of x's non-distinct prime factors, or the logarithm of x to the base two.
The number of all the ancestors is the infinite sum of consecutive, natural powers of two: (2^0)+(2^1)+(2^2)+(2^3)+...

Construction of n-th level family names and their abbreviations

Zeroth, first and second levels of a-kinship have distinct names: you, parents, grandparents. Names for members of subsequent values of n are created by using the prefix great-, which is stackable - for n=5, for example, the name is greatgreatgrandparents.
Therefore, for n-th level of a-kinship, the name has n-3 great- prefixes; if that value is non-positive, a distinct name should be utilized.
Hence, k(n)=n-3 for n>3 is a function determining the number of naming prefixes.
With greater values of n, names like greatgreatgreatgreatgrandparents becaume tiresome to spell out, so they are shortened to great-m-parents, where m is the number of great- prefixes except for one, which is said at the beginning. For example, the members of the 10th level of a-kinship are great-6-parents [read as: great six parents], as m=(k(n))-1=n-4.
Hence, a great-1-parent is a greatgreatgrandparent, great-0-parent is a greatgrandparent, great-(-1)-parent is a grandparent, great-(-2)-parent is a regular parent, and great-(-3)-parent is yourself. These names can be subsituted for the regular ones.

Discrete names of given family members

Formulae given in the previous chapter do not, however, make discerning given, distinct family members possible. It is also inefficient and troubling to say, e.g., 'the mother of the mother of the father of the father of my mother'. Therefore, we propose a clear and efficient notation, called a v-name. A mother is depicted by an m, and a father by an f. The name of a given member is constructed by listing the genders of all the ancestors preceeding that person [in downward direction on a genealogy tree]. The aforementioned 'mother of the mother of the father of the father of my mother' is hence abbreviated as 'mffmm'. Reading this kind of abbreviations from left to right is like tracing the genealogy tree from down up - mother, father, father, mother, mother - so, the mother of the mother of the father of the father of the mother, as the English language approaches it from the opposite direction.
An abbreviated genealogy tree from n=4 to n=0 is given below.
Abbreviations in |brackets| mean marriages. The || line is the border between the mother's and the father's side. The |-| sign means a marriage between the mother's and the father's side, only present in n=1. Y stands for you.

| mmmm mmmf | mmfm mmff | mfmm mfmf | mffm mfff || fmmm fmmf | fmfm fmff | ffmm ffmf | fffm ffff |
| mmm mmf | mfm mff || fmm fmf | ffm fff|
| mm mf || fm ff |
| m |-| f |
y

Members whose v-names [abbreviated names] consist of only m's of f's are called border members. For a given n (bigger than 0) there are two border members, so they always make up 1/(2^n-1) of the family level members, and 2k/(2^n)+(2^n+1)+...+(2^k) of a given interval of a-member levels, where n is the smallest, and k the biggest value of the level number.
If in the v-name of an a-member more than one character comes up subsequently, it can be also shortened, such as mmmfmffm --> 3m-fm-2f-m.

Where the fuck is my Ph.D. right now.

(Next: time travel incest up in this bitch.)

^wha da fuk?

Did I ever told you Scientific thesis make me dizzy *_*

Vurn wrote:The number of all the ancestors is the infinite sum of consecutive, natural powers of two: (2^0)+(2^1)+(2^2)+(2^3)+...

Infinite?

Anyways I see a problem with this simplification, many of the ancestors you count as different are really the same; two ancestors of the 17th or 18th generation that are enough far apart in the tree are already very likely to be siblings. If your reasoning were true, around the 33th generation (log_2 of 7 billion) your ancestors alone would be more than all the people on Earth right now, and that's impossible, so in the long term it fails (in the short term it's a good approximation, though )

OnyxIonVortex wrote:

Vurn wrote:The number of all the ancestors is the infinite sum of consecutive, natural powers of two: (2^0)+(2^1)+(2^2)+(2^3)+...

Infinite?

Anyways I see a problem with this simplification, many of the ancestors you count as different are really the same; two ancestors of the 17th or 18th generation that are enough far apart in the tree are already very likely to be siblings. If your reasoning were true, around the 33th generation (log_2 of 7 billion) your ancestors alone would be more than all the people on Earth right now, and that's impossible, so in the long term it fails (in the short term it's a good approximation, though )

Because they are a lot of diferent factors that make it skeewed.

Submachine series FAKE ending

Lol, I hope not

Lol, I hope not

You noticed hidden "fake" word? If so, then your quote turns into 'Lol, I hope'. :P