Historic Beer Birthday: William S. Gossett

guinness-new
Today is the birthday of William Sealy Gosset (June 13, 1876–October 16, 1937). He “was an English statistician. He published under the pen name Student, and developed the Student’s t-distribution.” He also worked his entire career for Guinness Brewing, and was trained as a chemist, but it was his pioneering work in statstics, in which he was self-taught, that he is remembered today.

William_Sealy_Gosset

Here’s his biography, from Wikipedia:

Born in Canterbury, England to Agnes Sealy Vidal and Colonel Frederic Gosset, Gosset attended Winchester College before studying chemistry and mathematics at New College, Oxford. Upon graduating in 1899, he joined the brewery of Arthur Guinness & Son in Dublin, Ireland.

As an employee of Guinness, a progressive agro-chemical business, Gosset applied his statistical knowledge – both in the brewery and on the farm – to the selection of the best yielding varieties of barley. Gosset acquired that knowledge by study, by trial and error, and by spending two terms in 1906–1907 in the biometrical laboratory of Karl Pearson. Gosset and Pearson had a good relationship. Pearson helped Gosset with the mathematics of his papers, including the 1908 papers, but had little appreciation of their importance. The papers addressed the brewer’s concern with small samples; biometricians like Pearson, on the other hand, typically had hundreds of observations and saw no urgency in developing small-sample methods.

Another researcher at Guinness had previously published a paper containing trade secrets of the Guinness brewery. To prevent further disclosure of confidential information, Guinness prohibited its employees from publishing any papers regardless of the contained information. However, after pleading with the brewery and explaining that his mathematical and philosophical conclusions were of no possible practical use to competing brewers, he was allowed to publish them, but under a pseudonym (“Student”), to avoid difficulties with the rest of the staff. Thus his most noteworthy achievement is now called Student’s, rather than Gosset’s, t-distribution.

Gosset had almost all his papers including The probable error of a mean published in Pearson’s journal Biometrika under the pseudonym Student. It was, however, not Pearson but Ronald A. Fisher who appreciated the importance of Gosset’s small-sample work, after Gosset had written to him to say I am sending you a copy of Student’s Tables as you are the only man that’s ever likely to use them!. Fisher believed that Gosset had effected a “logical revolution”. Fisher introduced a new form of Student’s statistic, denoted t, in terms of which Gosset’s statistic was {\displaystyle z={\frac {t}{\sqrt {n-1}}}} z=\frac{t}{\sqrt{n-1}}. The t-form was adopted because it fit in with Fisher’s theory of degrees of freedom. Fisher was also responsible for applications of the t-distribution to regression analysis.

Although introduced by others, Studentized residuals are named in Student’s honour because, like the problem that led to Student’s t-distribution, the idea of adjusting for estimated standard deviations is central to that concept.

Gosset’s interest in the cultivation of barley led him to speculate that the design of experiments should aim not only at improving the average yield but also at breeding varieties whose yield was insensitive to variation in soil and climate, i.e. robust. This principle only appeared in the later thought of Ronald Fisher, and then in the work of Genichi Taguchi during the 1950s.

In 1935, Gosset left Dublin to take up the position of Head Brewer, in charge of the scientific side of production, at a new Guinness brewery at Park Royal in northwestern London. He died two years later in Beaconsfield, England, of a heart attack.

Gosset was a friend of both Pearson and Fisher, a noteworthy achievement, for each had a massive ego and a loathing for the other. He was a modest man who once cut short an admirer with the comment that “Fisher would have discovered it all anyway.”

t-test-slide

And this biography is from the MacTutor History of Mathematics archive:

William Sealey Gosset was born on June 13, 1876 in Canterbury, England where he was the oldest of five children. He died at the age of 61 in Beaconsfield, England on October 16, 1937. He attended the Royal Military Academy in Woolwich to b ecome an engineer before he was rejected because of poor eyesight. William Gosset was never employed as a statistician. In a world of quarrelsome statistics, but he got along with everyone. He was a very helpful, quiet, patient and loyal person.

He went to school at Winchester and was well educated before entering the New College in Oxford. Here he won a first degree in chemistry in 1899. After getting his degree as a chemist, he got a job at Guinness brewery in Dublin in 1899, where he did important work on statistics, but her was never hired at a statistician. It was his environment at Guinness’ that made him a statistician. The brewery was interested in how they could make the best beer.

In 1900, the Guinness Research Laboratory was opened, which was head by the most distinguished brewing chemist, Horace Brown. Horace Brown along with the other brews were wondering how to get the raw materials for brewing beer at the cheapest but getting the best. There were many factors that they had to take into account such as varieties of barley and hops, what conditions of dying, cultivation and maturing factors.

After a few years of research, given that they were given a free hand to explore the conditions of brewing. This gave Gosset a chance to work as a statistician. He was able to take the data from the different examples of brewing to help find out which way was the best. As the young brewers work together, it seemed natural for them to take the data to Gosset to solve the numerical problems.

Gosset, in 1903, could calculate standard errors. In 1904 he wrote on the brewing of beer. This report lead to Karl Pearson consulting Gosset. Gosset met Pearson in July of 1905 when they had long talk together. Pearson, in an hour and a half, m ade Gosset understand the theory of standard errors. Gosset went back to the brewery and practiced those method for the next year. The meeting was also successful in which Pearson got Gosset to take up the study of the law of error.

Gosset wrote paper in his spare time under the name “Student.” His paper were on the probability of error of the mean and of the correlation coefficient for publication. Gosset even managed to run cooperative experiments with Hunter a nd Bennett at Ballinacurra, Buffin at Cambridge, and Beaven at Warminster in the testing of seeds against other seeds. Gosset also work with R.A. Fisher. The funny part is that Fisher did not get along Pearson, but Gosset studied under Pearson and also got along with Fisher.

To quickly recap William Gosset, he was born in 1876 and died in 1937. He did mathematical research for beer brewing, but had the problem working with only a small sample size. He work on the concept of probable errror of a mean. He also analysi sed an extended and broad range of problems such as the counting with a haemacytometer, probable error of a correlation coefficient, cereals, agronomy and the Lanarkshire milk experiment.

A very personal friend, McMullen, said this about Gosset, “he was a very kindly and tolerant and absolutely devoid malice. He rarely spoke about personal matters but when his opinion was well worth listening to and not in the least superficia l.”

Pricenomics has a good overview of Gossett’s contributions to mathematics and statistics, entitled The Guinness Brewer Who Revolutionized Statistics.

Möbius Beer

mobius
Today is the birthday of mathematician August Ferdinand Möbius, for whom several mathematical items are named, although the most famous is certainly the Möbius Strip. Although the Möbius Strip was discovered by two different mathematicians around the same year, 1858, it bears his name and not fellow German colleague Johann Benedict Listing.

A Möbius Strip “is a surface with only one side and only one boundary,” so that it looks like it turns in on itself, but if you could walk around on top of one, you’d never come to the end. “The Möbius strip has the mathematical property of being non-orientable. It can be realized as a ruled surface.”

mobius-strip

I recalled seeing a famous beer label using a Möbius Strip, and a quick search revealed the one I was thinking of was Arizona Brewing’s flagship beer “A-1,” which used a multi-colored version.

A1-Label

Beer History has a good article about the brewery, A-1: The Western Way to Say Welcome
by Ed Sipos. The original A-1 label had an eagle on it, but by the 1950s Anheuser-Busch, which was spreading their tentacles nationally, decided to sue Arizona Brewing claiming the eagle on their label was too close to their own, and Arizona couldn’t afford to defend the lawsuit, and decided instead to simply change the label.

A-1-can
A can of A-1 from 1965-66.

And not too long ago, Tuscon-based Nimbus Brewery introduced a new version of A-1 Beer, though I’m not sure if it’s still being brewed.

Apparently there’s also a Mobius Infused Lager that looks like a gimmicky contract beer. It appears to be a generic lager “infused with taurine, ginseng, and caffeine.” Ugh, does that sound like a bad idea.

Boolean Logic & Beer

boolean
Today would have been the 200th birthday of George Boole, the self-taught mathematician who came up with Boolean algebra and Boolean logic. He’s been called the “father of the information age” because his Boolean logic made possible modern computer science. “Boolean algebra has been fundamental in the development of digital electronics, and is provided for in all modern programming languages. It is also used in set theory and statistics.” Boolean logic is “a form of algebra in which all values are reduced to either TRUE or FALSE. Boolean logic is especially important for computer science because it fits nicely with the binary numbering system, in which each bit has a value of either 1 or 0.” How Stuff Works has a nice overview of How Boolean Logic Works.

So what does any of this have to do with beer? Practically nothing, except that Scientific American had an article yesterday about Boole to celebrate his 200th anniversary coming up today. In the piece, The Bicentennial of George Boole, the Man Who Laid the Foundations of the Digital Age, after writing about Boole’s life and contributions to the study of mathematics, the author turns to some examples of how his Boolean logic is applied in the real world in, for instance, Google searches:

Boolean algebra and Boolean logic are very well known today, and form the backbone of electrical engineering and computer science. Indeed anyone who even casually searches the Internet , say for “Michael Jackson” the late beer and whiskey expert rather than the singer and dancer of the same name, knows how to make judicious use of AND, OR and NOT.

It’s pretty cool that he picked Michael Jackson as the search topic, and it’s a good choice since it’s hard to get just beer-centric results when the more famous Michael Jackson usually tops the list unless you figure out how to filter out the king of pop. Michael used to joke that the singer was named after him, since he was older, but it must be a pain in neck for anyone who shares a name with a person more famous them themselves. Remember the character Michael Bolton in the wonderful film “Office Space?”

I reproduced the search, and got slightly different results, but pretty funny, and cool — at least from my point of view — is in both instances one of my posts was the third result.

boolean-Search2

It’s a lengthy post I did a couple of years ago, Know Your Beer Gods & Goddesses, in which I researched world cultures and created a list of gods and goddesses that had something to do with beer, discovering over 100 examples. I jokingly included an entry for Michael as the “God of Beer Writers,” so that’s why my post turns up in a search for Jackson’s name. So that made my day, nice to show up in Scientific American, however tangentially.

And just to round out the ephemeral post, I’ll leave you with a little Boolean humor:

three-logicians-walk-into-a-bar

Martin Gardner’s Beer Signs On The Highway

math
Today is the birthday of Martin Gardner, who was an American science and mathematics writer. For many years, beginning in 1957, he wrote a column that appeared in Scientific American. He helped popularize science, and especially math, creating hundreds of puzzles, often collected into books. He passed away in 2010, at age 95. My father-in-law was a huge fan and read most, of not all, of his books.

One of his brain teasers was called “Beer Signs on the Highway,” and originally appeared in Gardner’s column in Math Horizons, in the November 1995 issue. It was also included in the collection My Best Mathematical and Logic Puzzles and also New Mathematical Diversions.

my-best-mathematical-and-logic-puzzles new-diversions

So here it is:

beer-signs-on-highway

If you think you know the answer or have worked it out, leave your answer in the comments. I’ll post the answer in a couple of days. Good luck.

And the answer is? Drumroll, please:

drum_roll_please-Ringo

Could I get a proper drumroll, please?

drumroll

The Answer:

We can answer this without knowing the car’s speed. If x is the number of signs that the car passes in one minute, then the car will pass 60x signs in an hour. We’re told that the car is traveling at 10x miles per hour, so in 10x miles it will pass 60x signs, and in one mile it will pass 60x/10x signs, or 6. So the signs are 1/6 mile, or 880 feet, apart.

Never Drink And Derive

humor
No that’s not a typo. Today’s Friday frivolity is a nice mix of drinking and math. Remember people, don’t try to figure out the quadratic formula while operating heavy machinery. Once you start deriving, it’s hard to stop. I assume this will resonate with the illiterate and math-challenged among the neo-prohibitionists.

never-drink-and-derive

Three Logicians Walk Into A Bar …

logic-brain
While I had a logic class in college, and dabbled in debate, I’ve probably forgotten more than I ever learned. But I still love the notion of breaking down the thought process. My son, who’s 11 and autistic, often has trouble understanding humor. As a result, I increasingly find myself trying to explain the punchline of a joke — why it’s funny — and I’ll break it down for him. What invariably happens, of course, is that in that process, the joke is stripped of its humor and is no longer funny. For some reason, that never deters me. I’ve always had a thing for jokes and thinking about why they’re funny. If I wasn’t so damn shy I would have loved to have tried my hand at stand-up comedy back when I was a younger man. I think that’s why I loved The Aristocrats so much. Ninety minutes breaking down and re-telling one joke. What’s not to love?

So check out the comic strip below. It’s mildly amusing, at least to me. You most likely won’t laugh out loud, but you may smile, at least. But from the point of view of logic, it’s also quite correct, and instructional. It was originally posted by Spiked Math Comics, who admits he doesn’t know the strip’s original creator.

three-logicians

But here’s where it veers headlong into geekdom. It was picked up by a Danish University linguistics student, Emil Kirkegaard, who posted Three Logicians Walk Into a Bar: A Formal Explanation, a breakdown and analysis of the joke, complete with formulas, and explanation of the logic principles behind it.

Here’s one expressing the root problem: E↔(Wa∧Wb∧Wc)

The whole explanation is just as funny as the original strip, to me at least, in its own right and certainly does explain the joke, although if you didn’t think it was funny to begin with, this probably isn’t going to help. But us geeks have to stick together, no matter what geekworld we belong to.

Ancient Egypt, Math & Beer

egyptian-dudes
Thanks to Pete Slosberg — he of the formerly wicked persuasion — for passing this along. It’s not strictly about beer, so feel free to ignore it if math and history isn’t your cup of beer. Today’s New York Times Science has a fun article, Math Puzzles’ Oldest Ancestors Took Form on Egyptian Papyrus, about how the Rhind Mathematical Papyrus contains several clever math puzzles, including some thought to be more modern and also having to do with beer.

AN00569564_002.jpg

For example, some of the puzzles “involve a pefsu, a unit measuring the strength or weakness of beer or bread based on how much grain is used to make it,” such as this one:

One problem calculates whether it’s right to exchange 100 loaves of 20-pefsu bread for 10 jugs of 4-pefsu malt-date beer. After a series of steps, the papyrus proclaims, according to one translation: “Behold! The beer quantity is found to be correct.”

Fun stuff. I wonder what “pefsu” is compared to say a.b.v.?

The Math Behind Beer Goggles

math
This isn’t exactly news, the effect known as “beer goggles” — where after a few pints people appear more attractive — was confirmed in 2002 and the mathematical formula was announced in 2005. Whether Matt Damon wrote it out on a hallway blackboard one late night is still not known. But How Stuff Works (under the TLC Cooking imprimatur) has a nice summary of the formula.

The first study I recall seeing was in 2002, and was conducted by the University of Glasgow. Both the BBC and the Daily Collegian had the story. Then, in 2005, researchers at the University of Manchester stumbled upon the formula for how it all works. They also discovered that “alcohol is not really the only factor affecting the drunken perception of beauty. Other factors, according to their research, include:

  • How brightly lit the area is
  • The observer’s eye-sight quality
  • The amount of smoke in the air
  • The distance of the observer from the observed

The formula is laid out below.

goggles-formula

Here’s how to decode the formula:

  • An is the number of servings of alcohol
  • d is the distance between the observer and the observed, measured in meters
  • S is the smokiness of the area on a scale of 0 – 10
  • L is the lighting level of the area, measured in candelas per square meter, in which 150 is normal room lightning
  • Vo is Snellen visual acuity, in which 6/6 is normal and 6/12 is the lower limit at which someone is able to drive

The formula works out a “beer goggle” score ranging from 1 to 100+. When ø = 1, the observer is perceiving the same degree of beauty he or she would perceive in a sober state. At 100+, everybody in the room is a perfect 10.

And one last odd finding of the second study. “A nearsighted, sober person who isn’t wearing his or her glasses can experience a beer-goggle effect equivalent to drinking eight pints of beer.”