Vsauce! Kevin here. And I’m about to bust the greatest female tycoon of the 19th century using
FORENSIC MATH -- I just need skim milk, an amputated leg, and a family of nerds to do
it. Millions of dollars were at stake -- and it all came down to handwriting.
I’ve told some stories about how math has perverted the pursuit of justice
and destroyed lives -- but when one of America’s richest women tried to steal even more money,
math detected her fraud.
Hetty Green was bred to make money -- and she was the best at it.
At 6 years old, Hetty was reading financial newspapers to her father,
who owned a whaling firm in Massachusetts. She tracked stock prices with her grandfather, and by
age 13 was the family bookkeeper. In the 1850’s, the family had MILLIONS -- which in today’s
money is TENS of millions. But Hetty needed more. And when her aunt died, she saw dollar signs.
First, you need to understand Hetty. Her entire LIFE was all about money -- and
she racked up a fortune that would be valued well into the BILLIONS today.
She was known as the “Witch of Wall Street” -- but she was famously miserly. She was just
as obsessed with making money as she was with never spending ANY of it.
Here are some examples.
She spent so long trying to find a free clinic to treat her son’s leg injury that she waited
too long and it had to be amputated. She refused to use hot water because fuel to heat it felt like
a waste of money. She wore one black dress and a single set of underwear that she only changed when
they wore out. When she bailed out the New York City government by writing a check to cover its
budgetary shortfalls, she was living in boarding houses -- because she wanted to. She said, “Just
because I dress plainly and do not spend a fortune on my gowns, they say I am cranky or insane.”
Hetty Green wasn’t insane -- but she was a criminal. And that’s where the math comes in.
When her aunt Sylvia died in 1865,
her will stipulated that about $1 million would go to charities. That’s about $15 million today.
The other $1 million would be put in a trust for Hetty. So half for charity. Half for Hetty.
Here’s what happened next...
Hetty remarkably produced an earlier copy of the will stating that 100%
of her aunt’s fortune would go directly to her… which seemed pretty convenient. It also had a page
attached that invalidated any future wills, which seemed… really convenient. The estate’s executor,
Thomas Mandell, saw it and was like, “I don’t think so.”
So what did Hetty do? She sued the estate -- and that’s when nerds came to the rescue.
Charles Sanders Peirce was a literal genius -- by age 23, he had 3 degrees from Harvard. He
eventually became one of America’s greatest logicians, including realizing in 1886 that
electrical circuits could carry out logical operations. That resulted in the digital computer
decades later, but in 1865, he entered a courtroom in Boston to analyze Aunt Sylvia’s handwriting.
Charles compared 42 samples of Sylvia’s signature and concluded
that it had 30 downstrokes -- in graphonomics, a “ballistic stroke” that conveys a distinct
change in the absolute velocity of the pen. My signature has 18 -- 8 in Kevin, 10 in Lieber.
Here’s a question. How consistent is a signature? How much did Sylvia’s vary
from sample to sample? How much does MINE vary?
LET’S FIND OUT. Right after this.
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Okay. I signed my name, and then I made 42 more signatures -- and tried to make them match.
Then I judged each sample against the original signature to find out how many of the 18
downstrokes in my name were the same -- I looked at size, length, and angle to determine whether
each stroke was substantially similar. They followed a normal distribution, and the result was
an average of 7.405 matches out of a possible 18 -- so only 41% the same. And I was really trying
to make them the same! Sylvia’s 42 signatures were probably done over a period of years.
But the interesting thing is the variance -- my signatures have a standard deviation of 1.326,
which means that 99.73% of my signatures should fall between 3.427
and 11.383 -- that’s a range of plus and minus 3 sigma. The Z-score of each sample
indicates how many standard deviations that sample is from the mean -- basically,
how much of an outlier it is. My most deviant sample was 10 matches, for a Z-score of 1.957.
I actually did one more set of comparisons just to make sure.
I compared signature #21 to all the others. The mean was 6.810 matches
and the standard deviation was 1.418. The highest Z score was still only 2.249.
Based on my 42 samples, how deviant would a perfect 18-for-18 match
actually be? It would have a Z-score of 7.989 -- nearly 8 standard deviations from the mean.
The odds of a signature being seven standard deviations from the mean
are about 1 in 390 billion -- the odds of 7.989? Uhhh. Figure it out and tell me in the comments.
Back to Hetty.
Charles Peirce found that Sylvia’s 42 samples had an average of 6 downward strokes matching
the will’s signature -- so about 20% -- and conformed to a binomial distribution
just like mine. And probably YOURS.
When Charles compared the signature on the first page of the will to the signature on
the attached second page, he found that all 30 downstrokes were a perfect match. A 100% perfect
match. His father Benjamin Peirce was a Harvard mathematician -- he testified
that the probability of Sylvia’s second signature being a perfect
30 for 30 match was 2.666 x 10^21 -- or 1 in 2 sextillion, 666 quintillion. So yeah.
Benjamin Peirce said, “Such evanescent shadows of probability cannot belong
to actual life.” Which is an amazing quote. Uhhh yeah, Hetty traced Aunt Sylvia’s signature.
She lost the case and fled with her husband to London when the family threatened to have
her indicted for fraud. But… she didn’t really lose. After 5 years in court,
she was awarded $600,000 from the estate -- less than the original legitimate will gave her, but
still $12 million in today’s money. And the state never brought criminal charges against... the
wealthiest woman living in it. The following year, Hetty had a daughter -- who she named Sylvia.
Hetty Green died during a heated argument with her maid about the benefits of skim milk. Today her
estate would be valued at $5 billion. She really was America’s first female business tycoon -- and
she wasn’t all bad. She became an anonymous philanthropist and served as a nurse to care for
friends and family. In 1951, Sylvia Green died, leaving over 99% of the family fortune to charity.
I’ve made videos about the crazy odds of two people having the same name -- and having weirdly
similar fingerprints -- and having rare tragedies strike twice in the same family. I’ve shown that
math alone is a terrible basis for convicting someone of a crime -- and insane odds can still
mean innocence. With Sylvia Ann Howland’s will, we have to consider the totality of
the circumstances: Hetty’s motive, her obsessive greed, her miraculous production of a will that
just happened to be entirely in her favor -- all combined with truly astronomical signature odds.
Knowing when not to believe in coincidences is just as crucial as accepting them.
1 in a billion? Okay -- if 1 in a billion people won a lottery,
that means about 8 people alive right now would hit the jackpot. It’s
not impossible. A mountain of evidence plus 1 in 2.6 sextillion? Yeah. I don’t think so, Hetty.
Hetty Green spent a lifetime accumulating money,
power, and influence -- and she could never get enough of any of it. But in the end,
all of Hetty’s precious millions couldn’t compete with the Peirce family’s sextillions.
And as always, thanks for watching.