I have discovered that I am related to someone specific who lived in 1066.  How likely is this? In other words, the answer could be “No big deal. When you go back that many generations,the math shows that you are X percent likely to be related to anyone, where X is large - say 50-90% - because you have so many ancestors and the population then was so small.” Or the answer could be “WOW, that’s significant. Because the likelihood of that is small, where X is low.” So maybe the general question is “What is the likelihood that Person A, living now, is related to Person B, living in 1066?” And to specify even more narrowly, let’s constrain to the European/ Scandinavian/ Finnish populations that existed then.
I was thinking about something the other day (that is probably stupid), and thought this would be a good place to talk about it.  If someone wanted to draw its family tree over the last 1000 years, he'd write a binary tree with a depth of about 40 (counting 25 years on average between each generations). This tree would have 240 leaves, or about 1012 ancestors on the deeper level. That is obviously much more than the total world population and a stupid figure when you think about it.  The only explanation that I can think of is that a real genealogy tree must have "linked" branches at several levels that change the actual number of ancestors. Anyway, for an average person, how many ancestors would that make? Could one assume that all or nearly all of the persons that lived in its country or world region a 1000 years ago would be part of its ancestors?
/A problem from the 2012 MIT Integration Bee is $$ \int_0^1\frac{x^7-1}{\log(x)}\mathrm dx $$ The answer is $\log(8)$. Wolfram Alpha gives an indefinite form in terms of the logarithmic integral function, but times out doing the computation. Is there a way to do it by hand? It seems pretty straightforward to dual boot those versions of Windows when the newest is installed after Windows XP. But the inverse isn't happening on my machine. I tried even editing the BOOT.INI file, but the boot just freezes or displays that a file is missing when I try to boot another partition.  Currently I'm stuck with Windows XP, and I need to boot my Windows 7 instead.  What is the solution? Is the gravitational constant $G$ a fundamental universal constant? I am being prompted with the following error while using \pagestyle{headings} on a book class LaTeX document:  Overfull \hbox (240.44835pt too wide) has occurred while \output is active \OT1/cmr/m/sl/12 CHAPTER 1. THE CITY OF CARTHAGE WAS THE CENTRE OF THE ANCIENT CARTHAGINIAN CIVILIZATION \OT1/cmr/m/n/12 2   The following is the offending code:  \documentclass[12pt,letterpaper,oneside]{book}  \pagestyle{headings}   \begin{document}  \pagenumbering{arabic}  \chapter{The city of Carthage was the centre of the ancient Carthaginian civilization} The city of Carthage was the centre of the ancient Carthaginian civilization. The city developed from a Phoenician colony of the 1st millennium BC into the capital of an ancient empire.[2] The area of Carthage was before inhabited by Berber people who also became the bulk of Carthage's population and constituted a significant part of its army, economy and administration. Native Berbers and settling Phoenicians in Carthage mixed in different ways including religion and language, creating the Punic language and culture.  The name of Carthage, Latin: Carthago or Karthago,  meaning "New City"   The first civilization that developed within the city's sphere of influence is referred to as Punic (a form of the word "Phoenician") or Carthaginian. The city of Carthage is located on the eastern side of Lake Tunis across from the centre of Tunis. According to Greek historians, Carthage was founded by Canaanite-speaking Phoenician colonists from Tyre (in modern Lebanon) under the leadership of Queen Elissa or Dido. It became a large and rich city and thus a major power in the Mediterranean. The resulting rivalry with Syracuse, Numidia, and Rome was accompanied by several wars with respective invasions of each other's homeland.  Hannibal's invasion of Italy in the Second Punic War culminated in the Carthaginian victory at Cannae and led to a serious threat to the continuation of Roman rule over Italy; however, the Romans gained the upper hand by invading Africa and defeating Carthage at the Battle of Zama in 202 BC. Following the Third Punic War, the city was destroyed by the Romans in 146 BC. However, the Romans refounded Carthage, which became the empire's fourth most important city and the second most important city in the Latin West. It later became the capital of the short-lived Vandal kingdom. It remained one of the most important Roman cities until the Muslim conquest, when it was destroyed a second time in 698.  The ancient Greek philosopher Aristotle wrote extensively on Carthaginian politics, and he considered the city to have one of the best governing institutions in the world, along with those of the Greek states of Sparta and Crete.[5][6]  \section{Topography} Carthage was built on a promontory with sea inlets to the north and the south. The city's location made it master of the Mediterranean's maritime trade. All ships crossing the sea had to pass between Sicily and the coast of Tunisia, where Carthage was built, affording it great power and influence.  \end{document}    The \hbox refers to:      How can I solve this issue using \pagestyle{myheadings}? Or how can I solve this issue keeping the book class heading format? #!/bin/bash  SUBJECT="WARNING CPU USAGE HIGH" TO=gmail id MESSAGE=/tmp/messages echo "#######################" &gt; $MESSAGE echo "CPU statistics as follows.." &gt;&gt; $MESSAGE mpstat &gt;&gt; $MESSAGE echo "#######################" &gt;&gt; $MESSAGE CPU_USAGE=$(top -b -n1 | awk '/^Cpu/ {print $2}' | cut -d. -f1) [ $CPU_USAGE -gt 85 ] &amp;&amp; mail -s "$SUBJECT" "$TO" &lt; $MESSAGE`   ./cpu.sh: line 11: [: -gt: unary operator expected What might be the reason I am trying to build a computer, placing an  in a custom .  The case is an extra small form factor which can accommodate the Mini ITX board, but it requires an external power supply, similar to the power-bricks that laptops use.  I am looking at different power supplies and like , but I cannot figure out whether/how to power this system, because they provide a 24-pin connector, but the motherboard has a 4-pin connector as well.  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On these settings most of the memory usage was taken up by sqlservr.exe and the server would eventually need to be restarted every day or two. It would run normally at first but within a day start to timeout on simple operations like looking up a record using the primary key.   I have changed min=4,096 and max=6,144. This results in only 1.4GB memory usage. However now all four cpus are running at 50-60% cpu usage constantly. Tasks are taking roughly 1/3rd longer to execute, although the server is much more stable. Why is document.write considered a "bad practice"? I've done a clean install of 18.04 and I can't open desktop folders, not even the desktop trash can. Anybody else had this issue? I click on the desktop folders (double click) and nothing happens.  Strange enough, I can open  them when using Nautilus and going to home\stackinator\desktop\ or whatever the path is (can't remember at this point). 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