< Earlier Kibitzing · PAGE 271 OF 271 ·
|Jul-24-15|| ||al wazir: <beatgiant>: I spent a lot of time in a fruitless attempt to make something out of factoring the *difference*:|
ac - ab + (c - b) = (a + 1)(c - b) = 2^i - 2^j = 2^i[2^(j-i) - 1].
|Jul-25-15|| ||WannaBe: Well, now, moving on to the next Stumpers...
Shannon's Number, I'm quite sure many, if not all are familiar with it.
But, thanks to <DrDum>: https://www.youtube.com/watch?v=Km0... (12min+ clip)
|Jul-26-15|| ||Marmot PFL: The baseball pennant races are heating up, so I looked on the MLB site and found the probabilities for each team to make the playoffs (five spots are open in each league, three division winners and two wild cards).|
AL - KC 94.9, NYY 86.7, Houston 83.5, LAA, 78.9, Toronto 46.0, Minn 31.6 and so on
NL - StL 99.8, LAD 92.7, Pitt 77.0, Wash 76.2, SF 55.5, CHC 52.5, NYM 41.3
Is it possible for six teams to have a better than 50% chance of qualifying when only five spots are open? This seems wrong. After all if two teams were vying for one spot they both can't have better than a 50-50 chance.
I guess the site made a computation mistake, as scanning back over previous weeks there are no cases where more than 5 teams have a 50% chance.
|Jul-26-15|| ||WannaBe: <Marmot PFL> But it's <NOT> 2 teams fighting for one spot.|
SFG can win the west and LAD be the Wild Card (WC) or vice versa.
WAS or PIT can win their division or WC.
They (MLB.com or ESPN.com) run simulations of the remaining games of the season thousands of times, and then tally up the result.
Example: If they simulate the remaining games of the season 10,000 times 99.8 times StL made the playoff, but are they division champs or WC?
All we know, is that they made the it to the post-season. the 0.2 time, they collapsed and missed out.
|Jul-27-15|| ||al wazir: When MLB went over to the playoff format it devalued the World Series. Now even a mediocre team can -- and often does -- survive to compete for the "world" championship, so I no longer follow baseball closely.|
Here is a problem that I find more interesting, though I am not able to express it precisely. Suppose a tribe or race or species, not necessarily human, is living in isolation from all others of that species. (They can be the inhabitants of a remote island, or of a whole continent, or in principle even the entire world population.) Pick an individual at random living in that group today and another from n generations back. What is the probability that the later one is descended from the earlier one?
Some additional assumptions are needed. A "generation" is not a precise measure of time; two contemporaries may be descended from the same ancestor, but through different numbers of generations. I want to exclude highly structured mating patterns and extreme forms of social organization, e.g., (in the case of humans) an emperor who has a thousand concubines, leaving a single prostitute for all the other males. I also want to rule out exponential population growth and catastrophic population crashes such as a past volcanic eruption that killed all put a few individuals. However, I don't know how to formulate these restrictions.
But the basic idea is clear. I have two parents, four grandparents, eight great-grandparents, and 16 great-great-grandparents -- but only 30 great-great-great grandparents, because two of my greats were cousins. Under any reasonable assumptions, as n increases the number of ancestors falls further and further short of 2**n. In the limit as n approaches infinity the probability that a later individual is descended from *all* who lived n generations earlier (except those who had no progeny) approaches unity. But what is that probability as a function of n?
|Jul-27-15|| ||alexmagnus: Well, in case of humans they calculated the last common ancestor of the entire living (!) population at about 2500 years ago. And going another 2500 years back you get a world where everybody is either ancestor to everyone living today or has no living descendants today. Maybe from these numbers one can somehow get the probabilities in question.|
|Jul-27-15|| ||al wazir: : <alexmagnus: Well, in case of humans they calculated the last common ancestor of the entire living (!) population at about 2500 years ago.> I have to wonder how that was calculated. There are some Africans and some Pacific islanders and some "uncontacted" tribes in Amazonia, etc., that have been isolated for generations. I suppose the Africans are related to other Africans and the Pacific islanders are related to other islanders and the Indians are related to other Amerindians, but how can all those isolated groups, which have been separate from *each other* for millennia, be descended from a progenitor who lived as recently as 2500 years ago?|
That is a much more specific assertion than the *probability* I am asking for.
|Jul-27-15|| ||alexmagnus: <al wazir>. You miss what almost everybody misses here. Take Africa. Yes, prior to European colonization it took tens of thousands, sometimes even more, years to become related. But once Europeans came... They started sharing not only themselves as relatives, but also their entire ancestry. |
Say, Obama and Buffett ended up seventh cousins twice removed - with Obama's lineage going through his <father>.
As for isolated tribes, IMO most if them isolated just relatively recently, after getting rumors about the horrors of contact (deadly diseases f.x.). Note that most "isolated" tribes have languages somehow related to "non-isolated" ones. The only people I can imagine having been isolated for millennia as for now is the population of North Sentinel Island - not only are they hostile to any invaders, the island itself is nicely protected from an invasion by a reef.
|Jul-27-15|| ||Diademas: <alexmagnus: Well, in case of humans they calculated the last common ancestor of the entire living (!) population at about 2500 years ago.>|
Thats just not correct. Our last common female ancester (Mithocondrial Eve) lived aprox. 100.000-200.000 years ago. https://en.m.wikipedia.org/wiki/Mit...
<< In human genetics, Mitochondrial Eve is the matrilineal most recent common ancestor (MRCA), in a direct, unbroken, maternal line, of all currently living humans, who is estimated to have lived approximately 100,000–200,000 years ago. This is the most recent woman from whom all living humans today descend, in an unbroken line, on their mother’s side, and through the mothers of those mothers, and so on, back until all lines converge on one person. >>
Regarding our last common male ancester (Y-cromosom Adam), thats more up to debate, but its a far cry from 2500 years.
<< In 2013, Francalacci et al. reported the sequencing of male-specific single-nucleotide Y-chromosome polymorphisms (MSY-SNPs) from 1204 Sardinian men, which indicated an estimate of 180,000 to 200,000 years for the common origin of all humans through paternal lineage.>>
|Jul-27-15|| ||alexmagnus: <Didema> Another common misconception. You and your maternal grandfather are separated by just two generations, but it may take all of the 70.000 years to find your common ancestor on a male-only line.|
|Jul-27-15|| ||alexmagnus: <Diademas>, pardon for badly mistyping your handle, dyac ))|
|Jul-27-15|| ||Diademas: Ok. Since the Indigenous Australians has been isolated for more than 40.000 years. How does that fit in?|
|Jul-27-15|| ||alexmagnus: Same as with Obama and Buffet. A common ancestor through someone less isolated whose ancestor had an affair with a colonizer. That is - in 1770 someone of James Cook's crew fathered a child with an aboriginal woman - whoops, now all of descendants of Cook's ancestors are related to all of descendants of that woman's ancestors.|
|Jul-27-15|| ||Diademas: Now your grasping for straws 😏
Prior to 1961 (and some places later) interracial contact in Australia was at best restricted. Mostly even banned.
<<Victoria’s Aborigines Protection Act 1869 (Vic) gave the Board for the
Protection of Aborigines the power to refuse marriage applications from
Indigenous Victorians.4 In Queensland, the Aboriginals Protection and
Restriction of the Sale of Opium Act 1897 (Qld) prohibited Indigenous
woman from marrying anyone other than an Indigenous man without the
permission of an Aboriginal Protector.5
2.9 In the Northern Territory, which was governed by Commonwealth law,
the Aboriginals Ordinance 1918 restricted marriages between Indigenous
women and non-Indigenous men. For example, the marriage of
Indigenous or half-caste women to non-Indigenous men required legal
permission.>> Interracial connections were discouraged and frawned upon from voth sides. I would guess a fair portion of aboriginees has no european ancesters.
Btw. Do you have a source for your claim of 2500 years?
|Jul-27-15|| ||alexmagnus: There are many papers on this topic. One example: http://steveolson.com/uploads/2009/...|
As for restriction: if sufficiently long ago in time, <one> violation of such a restriction can produce a whole population of related people through two separate groups ))
|Jul-27-15|| ||Diademas: Very interesting reading. I need some time to go thoroughly through it, but it seems much less conclusive than your claim. For instance: <<The dynamics of human subpopulations are much more complex
than those in the simple graph model discussed above. Although
these complexities make theoretical analysis difficult, a computer
model incorporating more complicated forms of population sub-
structure and migration allows the demographic history of human
populations to be simulated. The Supplementary Information
contains more details on the model and computations; here we
briefly outline some of the main points.>>|
|Jul-27-15|| ||Marmot PFL: <<alexmagnus: Well, in case of humans they calculated the last common ancestor of the entire living (!) population at about 2500 years ago.> |
Must be a young earth creationist to believe in that.
|Jul-27-15|| ||alexmagnus: <Marmot> No, I am not. But see, if the male-only line is some 70-100k years old, the "universal" line cannot be too old. It must be in any case <much> younger (see the "maternal grandfather" example). |
By the way, in a model without any isolates, the most recent common ancestor of population of n lives binary logarithm of n generations ago. For humans, that would be just 33 generations. http://www.stat.yale.edu/~jtc5/pape...
|Jul-27-15|| ||Diademas: Ive gonne through the paper and there are some issues. Both methological and in presentation.
In regards to the methological issues most of them are in regards to the weight put on the computer simulation. Some of them might be inavoidable and the authors rightly makes reservations.|
A worse problem is the selection of data and presentation. For instance: They use the Aboriginal Tasmane populatian as an example of isolated populations beeing mixed up with imigrants. This population went extinct in the 1870s. They dont adress the elephant in the room, namely the Australien Aboriginees. In a 1933 census, the last time this was seen as political correct, over 60.000 people was labeled "full blood Aboriginees".
That number might be wrong, but not as wrong as the number now should be zero.
I would go so far as to say that <It is a high probarbility that two random people on earth has at least one common ancester in the last 3000 years.>
That might seem dull and cautious compared to <Well, in case of humans they calculated the last common ancestor of the entire living (!) population at about 2500 years ago.>
But I think its more accurate.
|Jul-27-15|| ||alexmagnus: <Diademas>, I doubt many Aborigines in 1931 knew whether some of their ancestors in 1700s (Cook's time) had an indirect (through some uncle) contact with a non-Aborigine. |
It's not a random reason I bring Cook as an example. James Cook's logbooks show clear dissatisfaction with the sexual behaviour of his crewmates, who made it with as many women of each place they visited as they possibly could get without raping them (rape happened too, but Cook severely punished it). So, in places Cook visited, quite many people carry the genes of his crew - and I doubt even 1% of them knows it.
|Jul-27-15|| ||Marmot PFL: Didn't have time to read it yet, but the usual estimates I had seen before were 50,000-100,000 years.|
|Jul-27-15|| ||alexmagnus: By they, in my own family... I know it only to the sixth generation, but already there I encounter five different ethnicities (Russians, Ukrainians, Turks, Georgians and Jews). With some really bizarre plots - the Turk-Georgian case, f.x., was a Turkish man kidnapping a Georgian women somewhere in the 19th century. Don't remember how they ended up in Ukraine (where the rest of the list came from), but somehow they did. |
By the way migration. We know virtually nothing about the aborigine's history, due to simple lack of written material. But in Europe's history, extreme migrational waves were not uncommon. Actually, I doubt <any> ethnic group in Europe still lives on the same geographical spot it lived 2000 years ago - the group is either extinct or have moved.
|Jul-27-15|| ||alexmagnus: <Didn't have time to read it yet, but the usual estimates I had seen before were 50,000-100,000 years.>|
That's for one-gender lineages. That is, counting only fathers (typical number here is 75k, some think it has to do with the Toba eruption) or only mothers (150-300k). But what if we take both? The extreme example of maternal grandfather shows how much difference it can make.
|Jul-27-15|| ||Diademas: <<It's not a random reason I bring Cook as an example. James Cook's logbooks show clear dissatisfaction with the sexual behaviour of his crewmates, who made it with as many women of each place they visited as they possibly could get without raping them (rape happened too, but Cook severely punished it). So, in places Cook visited, quite many people carry the genes of his crew>>|
Cooks first encounter with Aboriginees were in Botany Bay April 29th 1770 with a tribe called Gweagal. The meeting was hostile and at an helthy distance. They later had interactions with the natives in what is known today as Cooktown after a collision with the Great Barrier Reef. By all accounts the crew's encounters with the local Aboriginal people were mainly peaceable.
I find no signs any large scale raping or sexual contact.
A short search on the net dont realy give your claim any support. That is if we dont count the nutcase David Icke... 😎
|Jul-27-15|| ||al wazir: <Diademas> and <alexmagnus>: Thanks for your links and your comments. I see that my question was extremely naive. It misses both the more interesting (from a genetic point of view) aspects of the subject and the enormous amount of work that has already been done on it.|
I have a couple of comments:
1. No contradiction is inherent in the enormous disparity between the two dates given (2500 years ago for the MRCA and 100,000–200,000 years ago for Matrilineal Eve). They are answers to two entirely different questions.
2. I think the work of Rohde et al. (the Nature paper on the MRCA) is a good rough cut of a much more realistic model. It would take a lot of work, but the connections between "continents," "countries," and "towns" could be made more realistic by using better empirical data. In particular, a more refined model could be used to test the sensitivity of the results on the various assumptions. For example, what are the implications of possible interbreeding between Norsemen and Amerindians ca. 1000 AD or between Europeans and Australian aborigines after 1700 AD, or their absence? What are the consequences of various assumed dates for Asian peoples' migrations to North America, the Indo-European migrations in Eurasia, and Phoenician, Greek, Roman, etc., settlements in Africa?
3. I still don't see any way to answer my question or even to formulate it precisely.
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