Friday, July 31, 2015


3 is the only prime number that is 1 less than a perfect square.

Saturday, July 18, 2015


Why is a baker’s dozen 13 and not 12?

There are three main theories for why a baker’s dozen is 13 instead of 12, but most think it has its origins in the fact that many societies throughout history have had extremely strict laws concerning baker’s wares, due to the fact that it is fairly easy for bakers to cheat patrons and sell them less than what they think they are getting.
These societies took this very seriously as bread was a primary food source for many people.  For example, in ancient Egypt, should a baker be found to cheat someone, they would have their ear nailed to the door of their bakery. In Babylon, if a baker was found to have sold a “light loaf” to someone, the baker would have his hand chopped off.
Another example was in Britain in the mid-13th century with the establishment of the Assize of Bread and Ale statute, which was in effect all the way up to the 19th century before being repealed by the Statute Law Revision Act of 1863.  The Assize of Bread and Ale statute set the price of ale and what weight a farthing loaf of bread should be.   Specifically it stated:
By the consent of the whole realm of England, the measure of the king was made; that is to say: that an English penny, called a sterling round, and without any clipping, shall weigh thirty-two wheat corns in the midst of the ear, and twenty-pence do make an ounce, and twelve ounces one pound, and eight pounds do make a gallon of wine, and eight gallons of wine do make a London bushel, which is the eighth part of a quarter.
So basically, in terms of bread, setting the relationship between the price of wheat and what the subsequent price of a loaf of bread from a certain quantity of wheat should be.
Even though this statute was enacted at the request of bakers, it still posed a problem for them.  If they happened to accidentally cheat a customer by giving them less than what they were supposed to as outlined by the statute, they were subject to extremely severe fines and punishment, which varied depending on where the lawbreaker lived, but could include, like the Babylonians’ punishment, losing a hand.
As it wasn’t that hard to accidentally cheat a customer, given making a loaf of bread with exacting attributes is nearly impossible by hand without modern day tools, bakers began giving more than what the statute outlined to make sure they went over and never under.  Specifically, in terms of the “baker’s dozen”, if a vendor or other customer were to order a dozen or several dozen loaves of bread from a baker, the baker would give them 13 for every dozen they ordered.  Likewise, when selling quantities of anything, they’d give 13 measures when only 12 were purchased.
This practice eventually made its way into the Worshipful Company of Bakers (London) guild code.  This guild was actually started in the 12th century and had a large part in formulating the rules on the Assize of Bread and Ale statute.
Though the above is generally thought to be the correct origins for a baker’s dozen, there are two alternate theories put forth that are somewhat plausible, though lacking in hard historical evidence and visible progression.  The first is that bakers would sell 13 loaves to vendors, while only charging them for 12 which allowed the vendor to then sell all 13 at full price; thus, they’d earn a 7.7% profit per loaf.  So in this case, vendors were being given a sort of wholesale price, but without breaking the laws outlined in the Assize of Bread and Ale which had no exceptions for allowing a cheaper price to vendors.  This theory has some holes in it, but is quite plausible on the whole.
Yet another theory is that it was simply a product of the way bakers bake bread.  Baking trays tend to have a 3:2 aspect ratio.  The most efficient two-dimensional arrangement then of loaves/biscuits/whatever on such a tray results in 13 items with a 4+5+4 hexagonal arrangement, which avoids corners.  It was important to avoid the corners because the corners of a baking tray will heat up and cool off faster than the edges and the interior, which would result in not cooking anything on the corner evenly with the rest.  This theory doesn’t explain why they’d sell them in batches 13 for the price of 12, but at least explains why they may have commonly made them in batches of 13 in the first place and is still a possible source, or at least contributor, to the “baker’s dozen” if it was fairly universal that baker’s baked things in groups of 13, as is suggested by the theory.

Friday, July 17, 2015

Thursday, July 16, 2015


Ashkenazi Jews descend from 350 people, study finds

‘Bottleneck’ dates back 600 to 800 years, genome analysis shows; researcher says among population ‘everyone is a 30th cousin’

The study, published in the Nature Communications journal Tuesday, was authored by Shai Carmi, a computer science professor at Columbia University, and more than 20 medical researchers from Yale, Columbia, Yeshiva University’s Albert Einstein College of Medicine, Memorial Sloan-Kettering Cancer Center, Hebrew University of Jerusalem and other institutions.

Researchers analyzed the genomes of 128 Ashkenazi Jews and compared them to those of non-Jewish Europeans in order to determine which genetic markers are unique to Ashkenazi Jews. They found that the Ashkenazi Jews’ genetic similarities were so acute that one of the study’s researchers, Columbia professor Itsik Pe’er, told the Live Science website that among Ashkenazi Jews, “everyone is a 30th cousin.”

for more information: 

Saturday, July 4, 2015


About the 56 men who signed the Declaration of Independence:

Five signers were captured by the British as traitors, and tortured before they died.
Twelve had their homes ransacked and burned.
Two lost their sons serving in the Revolutionary Army; another had two sons captured.
Nine of the 56 fought and died from wounds or hardships of the Revolutionary War.

What kind of men were they?
Twenty-four were lawyers and jurists.
Eleven were merchants,
nine were farmers and large plantation owners;

men of means, well educated, but they signed the Declaration of Independence knowing full well that the penalty would be death if they were captured.

Carter Braxton of Virginia, a wealthy planter and trader, saw his ships swept from the seas by the British Navy. He sold his home and properties to pay his debts, and died in rags.

Thomas McKeam was so hounded by the British that he was forced to move his family almost constantly. He served in the Congress without pay, and his family was kept in hiding. His possessions were taken from him, and poverty was his reward.

Vandals or soldiers looted the properties of Dillery, Hall, Clymer, Walton , Gwinnett, Heyward, Ruttledge, and Middleton.

At the battle of Yorktown, ThomasNelson, Jr., noted that the British General Cornwallis had taken over the Nelson home for his headquarters. He quietly urged General George Washington to open fire. The home was destroyed, and Nelson died bankrupt.

Francis Lewis had his home and properties destroyed. The enemy jailed his wife, and she died within a few months.

John Hart was driven from his wife's bedside as she was dying. Their 13 children fled for their lives. His fields and his gristmill were laid to waste. For more than a year he lived in forests and caves, returning home to find his wife dead and his children vanished.

Thursday, July 2, 2015


Samuel Reshevsky, age 8, defeating several chess masters at once in France, 1920