John Venn

Episode Transcript
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Speaker 1 (00:01):
Welcome to Stuff You Missed in History Class, a production
of iHeartRadio. Hello and welcome to the podcast. I'm Holly
Frye and I'm Tracy V. Wilson. I bet it's a
safe bet that most people listening have heard of a
Venn diagram. Seems likely, yeah, But the creator of the

(00:25):
concept of the Venn diagram, whose name was John Vin,
actually developed a much more complex set of relational diagrams
than the simplified ones that we often reference casually or
even see used in like, you know, newscasts or whatever,
but perhaps even more interesting. Although he is an important
figure in the fields of mathematics and logic, he eventually

(00:47):
left that work behind to write historical accounts of the
places and people that were important in his life. I
love this about him. He was also an inventor, not
of a lot of stuff, but of something really interesting.
So he's just a fun person to talk about. So
he is in the spotlight today. John Vin was born
on August fourth, eighteen thirty four, to parents the Reverend

(01:11):
Henry Vin and Martha Sykes Ven. He was their first child.
He was born at Kingston upon hull Port in the
East Riding of Yorkshire. In northeastern England. Martha died when
John was pretty young, and at the age of twelve
he attended Sir Roger Chumley's School in London, which is

(01:31):
known more commonly as the Highgate School. This was a
really interesting time to attend Highgate, as the headmaster at
the time, the Reverend John Bradley Dine, significantly expanded the
course offerings there to start, including mathematics and modern languages.
Since then would eventually become well known as a mathematician.

(01:51):
He seems to have benefited from this newer course of study.
John went to secondary school at City of London Academy, Islington.
Reverend Henry Ven, John's father, was rector of the Drypool
Parish when John was born, and he was also secretary
to the Society for Missions in Africa and the East.
And he was not the only activist Anglican priest in

(02:13):
the family. Henry's father, the Reverend John Vin, a lot
of John Ven's were trying to separate him out. Was
very influential in the church and had been the leader
of a group called the Clapham Sect which lobbied for
progressive causes and change within the church, as well as
without and the Clapham sect supported the abolition of slavery

(02:34):
and advocated for prison reform, among other causes. In John
Ven's obituary in the Royal Society's Proceedings publication, it was written, quote,
no one could have had a more uncompromisingly clerical ancestry
and upbringing than had Ven his five or six immediate ancestors,
whose lives he gave in his notable book The Annals

(02:55):
of a Clerical Family were vicars or rector's, occupying positions
of importance in the Church. When it was time to
move on to higher education, Ben attended Gonvillin Keys College
at the University of Cambridge, so often simply referred to
as Keyes. There he earned a degree in math and
ranked sixth among his fellow students in the final exam

(03:17):
in eighteen fifty seven, but it was just the beginning
of a long relationship with the school. Ben went on
to a fellowship at Keys, and when that was completed
in eighteen sixty two, he was hired as a lecturer.
But Ben wasn't only a mathematician. During that same time period,
he became ordained as a priest in the Church of England.

(03:39):
Just like his father and grandfather and forebears. Starting in
eighteen fifty nine. After becoming a clergyman, he worked for
a brief period exclusively in the church at Chesnent, Herstfordshire
and Mortlake, Surrey, but then he decided to go back
to keyes and mathematics, although he did retain his clergy status.
As a lecturer, Ben taught an the discipline known as

(04:01):
moral science, meaning he talked about logic and probability. This
led to him serving as an examiner for the Moral
History Tripos. Tripos Is are academic exams, and Cambridge is
often cited as the place this term started. The origin
of the word isn't known with certainty, but it might
have come from the tripod stool that examiners used sitting

(04:23):
on them during the test. Ven's own works would inform
these exams later, a guide for students preparing for exams
that was written in eighteen ninety one recommended reading several
of Ven's books for the logic and methodology section of
the test. But even when he was lecturing and serving
as examiner himself, he said to have shifted the tripos

(04:45):
in developing the exam to reflect developing concepts in probability theory.
He eventually stepped aside as examiner because he wanted to
focus on studying and writing about the school's history. He
also wrote about his own res boots in genealogy, publishing
that previously mentioned book Annals of a Clerical Family, which
traced the Ven family history to Devin, with a likely

(05:08):
earlier origin in Somerset. In his writing, John noted that
the name Ben had first been spelled with an F
instead of a V, but had changed at some point,
and that the change was most likely to align more
closely with the common pronunciation that was used in the
West Country. A few years into his career teaching at Keys,
Ben published a book titled The Logic of Chance that

(05:31):
was in eighteen sixty six. Economist John Maynard Keynes is
often quoted as praising Ben's book, saying it was quote
strikingly original and considerably influenced the development of the theory
of statistics. The book sought to shift the way people
looked at probability, specifically by incorporating the idea of frequency

(05:53):
into mathematical prediction models, meaning how often a thing might happen.
He worked against the assay based probability interpretations that presumed
causality when looking at effects, which was why he felt
that longer runs of observation would offer greater insight. He
also made the case that the margin of error on

(06:14):
probabilities had to shift in proportion to the data set.
Smaller data sets would have larger margins of error, and
vice versa. These concepts were applied to scenarios like gambling
and birth outcomes. In the book, The Logic of Chance
became an important text in probability, and it had three
editions printed between its original eighteen sixty six published date

(06:37):
and eighteen eighty eight. This was a paradigm shift in
its time. We know that, of course having more data
means you have better models of probability, but prior to
Ven's book, most of probability theory was based on the
idea that the right formulas would be accurate predictors regardless
of the data set, but that of course led to

(06:57):
unpredictable outcomes. Then approach came to be known as frequentism.
And in addition to being a big statement about how
logic and probability should be applied, Then made another interesting
statement with the book right out of the gate, because
he said in the preface that he wanted the information
in it to be accessible. Writing of probability quote, I
am convinced moreover that it can and ought to be

(07:20):
rendered both interesting and intelligible to ordinary readers who have
any taste for philosophy. The year after The Logic of
Chance was released, John Ven got married to Susannah Carnegie Edmondstone.
Susannah was born in Marlborough in eighteen forty three, and
like John, she was the child of an Anglican priest

(07:41):
that was the Reverend Charles welland Edmondstone. After the two
of them got married, they settled into married life in Cambridge.
They eventually had a child named John Archibald, but that
wasn't until sixteen years into the marriage, so Susannah would
have been about forty at the time that she gave birth,
which is an unusual situation for the time. Susannah is

(08:02):
interesting in her own right because she was hardly idle
in her time as a wife. Before John Archibald was born.
She was in fact a novelist. As her husband was
publishing books on probability, she was penning titles like The
Gwillians of Bryn Gwillian, which was published in eighteen seventy six,
and that told the story of a family of children
who are raised by their father and governess after their

(08:24):
mother dies. She wrote several more novels, and she also
worked with John on some of his historical writing. All
of her novels except the last, were initially published anonymously.
Her last work of fiction, The Husband of One Wife,
came out in eighteen ninety four, and that book tells
the story that seems to mirror Susannah's own life. It's

(08:45):
about a young woman who gets married and moves to
Cambridge to live with her husband. We're about to get
to the diagrams, but before we do, we will pause
for a sponsor break. In eighteen eighty one, John Ven

(09:07):
published another book, this one titled Symbolic Logic, and it
was in this work that he introduced the concept of
ven diagrams as part of set theory. Ven diagrams, as
many listeners already know, often use overlapping circles to represent
sets of data. The region that overlaps represents a commonality
among those sets of data. This is the most basic

(09:29):
way this concept is used in casual conversation, although it's
really a visual way to parse information and figure out
logic problems, and some ven diagrams can be much more complex,
but all of them show the way that sets intersect
and join together. For example, you might be given the
information that out of a group of people, five are

(09:52):
tall and three have green eyes, two are tall and
also have green eyes, and five members of the group
are neither tall nor have green eyes. Using a Venn
diagram with two overlapping circles, you could assign the number
two to the overlap section and label each of the
circles remaining areas one for the tall people, one for

(10:14):
the green eyed people. You've also accounted for two of
the tall people in the overlap, so you know there
are three more tall people, and the number goes into
the circle labeled tall. We've accounted for two green eyed people,
and you know that there's three, so a one goes
into the circle labeled green eyes. The number five, representing

(10:35):
the five people who have neither attribute, sits outside those
two circles. To figure out how many people there are
in total in the group, you'd add each of the
numbers you'd written down together. So the two people who
are tall and green eyed, plus the three people who
are only tall, plus the one person who only has
green eyes, plus the five people who have neither of

(10:57):
those attributes, so you know there are eleven people total.
There can also be ven diagrams with three circles, and
those are used to represent syllogisms. Those are logic arguments
in which two premises are a given and then a
conclusion is reached using deductive reasoning. A simple example would
be to say, all sneakers are shoes. That's premis ie.

(11:19):
Premise two is that some sneakers are blue. Therefore, your
deductive reasoning leads you to some shoes are blue. The
three circles overlap in a way that a central section
of the diagram is simultaneously part of all three circles.
Those are the some blue shoes. Syllogisms were not new
to John Ven. They go all the way back to Aristotle,

(11:41):
and though his writings about them do not contain diagrams,
some logicians over the years have suspected that he may
have used them to work his ideas out. So the
Ven diagram is a way to visually represent the existence
and non existence of variables within sets. But this isn't
really something that he came up with out of nowhere.

(12:04):
Gottfried Wilhelm Leibnitz of Leipzig, Germany lived in the seventeenth
and early eighteenth centuries, and he studied the use and
viability of diagrams to solve logic queries. He thought that
Aristotle's concepts on the matter needed some more work, but
to be clear, he was drawn to that work because
he thought Aristotle's concept was compelling, writing quote, I hold

(12:27):
that the invention of the form of syllogisms is a
most beautiful of the human spirit. Leibnus's work started to
include the use of circles and linear progression to work
through syllogistic concepts, which when you look at them, are
very clearly a precursor of the ven diagram. Leibniz did

(12:48):
eventually favor using lines that created boxes as part of
their logical grouping. Yeah, he got away from circles, but
circles were favored by another logician, Leonard Euler, who was
born in Basel, Switzerland in seventeen oh seven. Although he
favored using circles to work out logic puzzles, he was
very clear that the shape was not the important thing,

(13:10):
noting in writing quote these circles, or rather these spaces,
for it is of no importance what figure they are of,
are extremely commodious for facilitating our reflections on this subject,
and for unfolding all the boasted mysteries of logic which
that art finds it so difficult to explain. Whereas by
means of these signs, the whole is rendered sensible to

(13:30):
the eye. We may employ, then spaces formed at pleasure
to represent every general notion. And Euler's diagrams were well
known in his time, although he wasn't applying mathematics or
specifically algebra to them the way that then eventually would.
They were just ways of grouping ideas. There were other
mathematicians and logicians who worked in the manipulation of visual

(13:55):
diagrams to work out logic, both numerical and theoretical, but
John Ben's criticism of those who had come before led
him to work out his approach. He wrote, for example,
of Uller's work that it wasn't robust enough, stating quote,
any system which merely exhibits the mutual relations of two

(14:15):
classes to one another is not general enough. We must
provide a place and a notation for the various combinations
which arise from considering three, four or more classes. In fact,
we must be prepared for a complete generalization. Ben also
created way more complex diagrams than just two and three

(14:36):
circle ones, and some of those are developing ideas put
forth by the other two men we just talked about.
Ben's book Symbolic Logic was also a defense and expansion
of the work of George Boole, who had died twelve
years earlier at the age of forty nine, and specifically
his approach to algebraic mathematical logic. Boolean algebra represents relationships

(15:00):
tween objects or ideas, so it works differently than ordinary algebra.
For example, it doesn't require numeric quantities, but it can
operate with variables like truth or falsehood. Boolean algebra is
important because it's the foundation of things like probability and
geometry of sets, but perhaps mostly so because in modern
daily life it has impacted the way computer circuits are designed.

(15:24):
In eighteen eighty three, Ben decided to resign from his
position as an Anglican clergyman. He'd come to the decision
that Anglicanism didn't really align with his beliefs anymore, although
he did continue to be a part of the Church.
According to an account written by his son Quote, it
had long ceased to be regarded as an anomaly for

(15:44):
a clergyman to preach the then circumscribed evangelical creed and,
at the same time, without the slightest insincerity, to devote
himself actively to philosophical studies, yet finding himself still less
in sympathy with the orthodox clerical outlook, then availed himself
of the clerical disabilities Act of a naturally speculative frame

(16:09):
of mind. He was wont to say later that, owing
to subsequent change and accepted opinion regarding the thirty nine articles,
he could consistently have retained his orders. He remained, indeed
throughout his life a man of sincere religious conviction. That
same year, also eighteen eighty three, John Vin was elected

(16:29):
to the Royal Society, and he received his science doctorate
from Cambridge. Six years after these events, in eighteen eighty nine,
he published The Principles of Empirical or Inductive Logic, and
the opening of the Principles makes clear that ven has
been troubled by the way concepts of logic have been
poorly defined in communication about them, and that not practicing

(16:51):
clear establishing rules regarding logic arguments have hurt the field overall.
This kind of a long quote, but I want to
include it because it gives you grit insight into the
way he thinks about things. Quote. Since logic, as conceived
and expounded in this work is not an ultimate science
in the sense of being concerned directly with really first
principles of any kind, we find ourselves obliged, on a

(17:14):
general survey of our province, to take for granted that
a great deal has already been decided for us in
various directions. In other words, we have to demand a
variety of postulates, drawn partly from the region of metaphysics,
partly from those of psychology, physical science, grammar, and so forth.
Some of these postulates will be readily accepted. Others will

(17:35):
be admitted by those who have had any philosophic training.
Some might take it have hardly yet been duly appreciated
or even recognized. This being so, it would seem convenient
that the more important of these postulates should be prominently
and definitely stated at the outset. For one reason or another, however,
such a course seems seldom adopted, and the result has

(17:57):
been disadvantageous in more ways than one. This neglect to
state the postulates has, for instance, brought down upon the
logician charges of inconsistency and shortsightedness, which might as fairly
be brought against the representatives of most other sciences, but
which sounded damaging when he had to meet them alone.
It has also tended, as I shall trust to show

(18:19):
in the sequel, to encourage mistaken views as to the
functions and province of the science. Whilst the general objections
to such an emission on the grounds of method are
too obvious to need reinforcement. In a moment, we'll discuss
how Ven seemed to sort of turn on a dime
in terms of his interests and projects in the late

(18:39):
eighteen eighties. First, though, we'll hear from the sponsors that
keep the show going. So before the break, we mentioned
that in eighteen eighty nine John Ven published The Principles
of Empirical or Inductive Life, and even before that in

(19:02):
eighteen eighty eight, as he was working on the book,
then seemed to have decided that it was going to
be his last work in logic and probability theory, because
he donated all of his personal Library on those subjects
to the Cambridge University Library and after that then ventured
into publishing non mathematical works at the end of the
nineteenth century, although they were books related to his work

(19:24):
in education. He published The Biographical History of Gonville and
Keys College thirteen forty nine to eighteen ninety seven in
eighteen ninety seven. This was a four volume project and
it included portraits of various people related to the school's history,
as well as additional illustrations. He also wrote an entry
for the Cambridge College series titled Simply Gonvillin Keys College.

(19:48):
Ben wrote several books that mentioned Keys, including Early Collegiate Life,
which walked through some accounts of what it was like
in its early days, laid out as narrative sketches. The
published lists of students who had been admitted to the
college in the fifteen hundreds and sixteen hundreds. Then worked
with his son John Archibald to assemble a list of

(20:09):
Cambridge alumni, which was also published as Alumni Cantabrigenses. This
included biographies of students and graduates, and it chronicle things
like students who had held offices in various organizations. An
unnamed colleague was quoted in Ven's obituary as saying, quote,
it is difficult for anyone who has not seen the

(20:31):
work in its making to realize the immense amount of
research involved in this great undertaking. Apparently, Ven's research for
this book involved going through the archives and records of
not just the school, but also various churches to correctly
list all of the available details of each alumnus's life.
Like he would go to an alumnus's hometown church and

(20:54):
go through all of their records and do that for
all of these people on this list. It was like
he must have loved research. An obituary for Ben that
appeared in the British Medical Journal described his output about
Keys this way quote. The works which he wrote about
the college are somewhat voluminous and are characterized by thoroughness,

(21:17):
but are for the most part full of human interest.
As a rule, they are pleasant reading, though in parts
they are necessarily statistical statistics. Asie, he clearly had a
deep love for the school, where he had been both
a student and a teacher, and his dedication was recognized.
He was made president of Gonville and Keys College in

(21:38):
nineteen oh three. In nineteen oh nine, there is this
wonderful and curious moment in Ven's life story, and we're
going to talk about it kind of to a disproportionate
amount because it is one of those things that is
both charming and surprising, but it also shows how broad
the interests of his life were. He invented a bowling machine,

(21:58):
not in the sense of the sport of bowling that
we know it today in the US, but bowling as
it relates to cricket. So for our listeners who are
more familiar with baseball, bowling is similar to pitching. I'm
sorry for any cricket officionados who are like, it's much
more complex and nuanced than that. We're just going for
wide strokes here. According to the saffron Walden Weekly News

(22:20):
from June eleventh, nineteen oh nine, quote, the preliminary of
what promises to be a sensation in the cricket world
took place on Fenners on Thursday week. Doctor Vin, president
of Keyes College, who is a Fellow of the Royal
Society and a Doctor of Science, has, in conjunction with
his son mister Javen, invented and patented a bowling machine

(22:41):
which in all probability will supersede the drudgery of bowling
at the practice nets. At the event mentioned in the article,
a number of cricketers visiting from Australia were able to
observe and test this machine, and they found it to
be quite impressive. The write up continues, quote the mission
can bowl any kind of ball at any variation of

(23:03):
pace or length, and can produce a deadly break either
from the leg or off side of the wicket. Batsman
wishing to practice any particular kind of stroke or perfect
himself in dealing with any kind of ball, may set
the machine up at one end of the pitch and
practice to his heart's content. And the Australians found it

(23:24):
to be formidable. Apparently it got the better of one
of their star players. Yes, some descriptions of this suggest
that this was kind of a feather in the cap
of England in terms of cricket reputation, to have vested
the Australians with a machine made by an Englishman. This
article describes the machine's design, noting that quote it is

(23:47):
not beautiful to look at, but its utility seems to
be undeniable, and it notes quote above, an ungainly base
equipped with strong springs and cords towers a gaunt iron
arm having at its summit a grip of four fingers
which rotate in either direction. The article also mentions that
people had been trying to invent a bowling machine for

(24:08):
cricket practice for quite a while, but no one had
been able to create one that could consistently deliver the
wide array of pitches that a human could until the
VENs did it. And they had, according to the paper,
patented this machine in England, the US and Australia. So
it seemed like they might be on the verge of
a huge business opportunity, but that didn't happen. We're going

(24:30):
to loop back to this machine in just a bit.
Van wrote a biography of the school's second founder, titled
John Keyes, which was published in nineteen ten for Keys's
four hundredth birthday. John ven died on April fourth, nineteen
twenty three, at the age of eighty nine. He had
served as president of Gonville and Keys College right up

(24:51):
until his death. To his last day, he had, according
to the British Medical Journal obituary we mentioned earlier quote,
retained to the full his clearness of mind and much
of his activity of body. He was always willing to
place his great store of knowledge at the disposal of others.
His Royal Society obituary described then in his last years

(25:12):
this way and it's quite charming, and the way I
would love to be described one day quote A good
field botanist, a bit of a mountaineer, a craftsman, and
with a gift of dry humor. Then lived his long
life to the full. Age treated him kindly, an active
spare man. He retained his sprightly walk and his interest
in work and play until the end. John's wife, Susannah,

(25:34):
died eight years after him. John Archibald Ben continued publishing
updates to the Cambridge Alumnilist after his father died for
another thirty one years. The younger Van also followed in
his father's footsteps in terms of academic leadership roles. He
became president of Queen's College in nineteen thirty two, and

(25:55):
like his father, worked until his death. In twenty seventeen,
Hull Drypool Bridge got a makeover inspired by its famous
logician historian. This was a pricey public art project. It
cost or reported three hundred twenty five thousand pounds. Artist
Sarah Daniels designed the artwork that adorns the bridge, which

(26:15):
features interlocking circles in shades of yellow that repeat in
a large scale pattern. Two reference, of course ven diagrams,
and recently. That bowling machine was in the news in
June of twenty twenty four, so just a little more
than a month ago if you're listening to this. Around
the time it's published, a whole slew of articles ran

(26:36):
about a project headed up by Hugh Hunt, professor of Engineering,
Dynamics and Vibration at Cambridge. Hunt was driven by the
idea of showing what he called John Ven's quirky side,
and by the desire to show students that mathematics and
fun can absolutely mix. Hunt and his colleagues had only
a photograph from when the machine was originally built in

(26:57):
the early nineteen hundreds and a patent application to work
from the head of Design at the Cambridge Engineering Department,
Thomas Glenday led a group of engineers through the process
of figuring out exactly how this machine worked and building
it at one fifth scale to see if they had
the details right. Since patent applications in their diagrams they're

(27:19):
all about the concept rather than the technicality. The team
had to do a lot of work to just re
engineer this bowler, but they did. They tweaked the elements
that weren't working on this miniature version before they built
a full scale one, and that one works. Yeah. As
of last month, I know there was at least one
event where it was. I think it was at the

(27:40):
Essex County Cricket Club where they were doing a presentation
about it. I hope it gets put on display somewhere
because it's a really cool idea to build an invention
that somebody else made and that you have to figure
out how it actually worked. So that is our discussion
on John Benn, which I love because he's so much
more than the diagrams, and even the diagrams are so

(28:02):
much more than the way we usually hear or know
about them. So yeah, I always like a little expansion
of knowledge. I have a very very cute listener mail
from our listener Don. The cute part is the picture.
Don writes, good day, Holly and Tracy. I just finished
listening to your episode on historical roads and Highways. I

(28:24):
was fortunate enough to go to Italy in twenty nineteen
with my mother and my sister. We drove the Autostrata,
both to Florence and again to Storo, where we have family.
I couldn't believe how large the rest stops were, with
gas stations on both sides that often had a bridge
across the highway to access the auto grill on either side.
So convenient when you're driving either direction and need to

(28:45):
stop for gas and food. The Church of the Autostrata
seems so out of place, but knowing its history, it
is in the perfect location. The toll system is not
something I'd dealt with before, and we always held onto
any change we got when shopping so we'd have enough
on hand for the toll boosts that are throughout the Audustrata.
I have attached a picture of my daughter's dog, Leo.

(29:06):
He is very attached to me and I'm not sure
what I will do when my daughter is ready to
move out. Thank you for your wonderful work done. This
dog is so cute. He's a little terrier. It looks
like maybe a Yorkie maybe a little Yorky mix, and
it's just one of those pictures where you just know
he is curled up right next to her and just
wants love and attention, and he's very cute. Those eyes

(29:29):
Man dogs get me every time. I know all of
this talk of the autostrata makes me want to go
back to Italy sooner rather than later, So let's do that.
You can write us if you have any email thoughts
you'd like to share at History Podcast at iHeartRadio dot com.
And if you'd like to subscribe and you haven't gotten

(29:49):
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(30:09):
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