The Curse of the Presidents

William and Abraham and Franklin (and the Others)
Something To It After All?

Everyone knows about the Curse of the Presidents. That's the prediction that if presidents are elected in a year ending in zero, they will die in office. Sure, the curse hasn't always worked - which is good - but a lot of people still think there's something to it.

People who believe in the Curse have various explanations. Some say it's just happenstance. Others say it's because the way the planets line up. Of course, people also use the last argument to explain why the world came to an end in 1524, 1962, 1982, 2000, 2012, and 2017.

But probably the most popular story is the Curse was levied by the Native American leader, Tecumseh. Hence, the oft called "Curse of Tecumseh". As a few people know - a very few - in 1811 future President William Henry Harrison and his soldiers defeated Tecumseh and the Shawnee warriors at the Battle of Tippecanoe in Indiana (that was the Wild West back then). So we read that Chief Tecumseh was irritated and put a curse on the American presidents.

As you'd expect, Tecumseh started with William. But because Tecumseh was basically a nice guy, he only put the curse on presidents elected every twenty years. And then he decided after 1960, the presidents had been cursed enough.

Good story, yes. But is it true?

There is one undebatable and incontrovertible RULE for writing history. You have to have a source. Now there are some cultures where oral traditions are memorized by specialists, and these traditions can be valuable to the historian. But they must be viewed with caution, and certainly the best sources are original and contemporary documents: transcripts, letters, and diaries. And the general rule is that if you have a later account which disagrees with the contemporary record, you accept the contemporary record.

For instance, we all know the story where Patrick Henry stood up and began to trash the King of England. There were cries of "Treason!" from the other assemblymen but Patrick remained resolute and cried "If this be treason, make the most of it!"

This, too, is a great story.

But the only contemporary account comes from an eyewitness, a French visitor, who wrote in his diary how at the cries of "Treason!", Patrick said he begged pardon if in the heat of passions his speech had caused offense, and he would defend the King of England to his last drop of blood. So real historians do - and everyone else should - accept that Patrick begged pardon.

And the Curse of the Presidents?

Actually, the first documented record of the Curse of the Presidents is 120 years after the curse was (supposedly) levied. And that documentation was from a newspaper column written by none other than Robert Ripley. Yes, Robert "Believe it or Not" Ripley.

But no, Robert did not put any curse on American presidents. In fact, he didn't even say there was a curse. It's just that in his 1931 illustrated newspaper column, he pointed out there was this interesting twenty year pattern to five presidents who died in office:

President	Election Year
William Henry Harrison	1840
Abraham Lincoln	1860
James Garfield	1880
William McKinley	1900
Warren Harding	1920
?????	1940

He included the story in his compilation, Ripley's Big Book Believe It or Not which was published in 1934.

Now most people would have seen the curse as just an interesting coincidence except later Franklin Roosevelt - who was elected in 1940 - also died in office. Naturally Robert included Franklin in the chart in a 1946 update, and people began to wonder if there might be something to the Curse after all. Then when JFK was killed in Dallas, well, that seemed to settle the question. There was indeed a Curse of the Presidents.

President	Election Year
William Henry Harrison	1840
Abraham Lincoln	1860
James Garfield	1880
William McKinley	1900
Warren Harding	1920
Franklin Roosevelt	1940
John Kennedy	1960

Today many people take this curse quite seriously and they, the Curse Adherents, go into spittle-flinging diatribes about how the Curse Doubters - that is, (ptui) Skeptics - deride the Curse as a simple coincidence. What are the odds, the Adherents ask, that such a pattern could happen simply by coincidence?

Or look at it this way. American presidents have election years that end in 0, 2, 4, and 8. So the odd are 1 out of 4 that a president gets elected in a zero-ending year. That's 1/4 = 0.25 or 25%.

And for now we'll just look at Robert's original list. There were a total of 17 presidents filling in the years from 1840 to 1920, and six died in office. So the odds a president will die in office is 6/17 = 0.353 or 35.3 %.

Therefore the odds that a president will die in office and be elected in a zero-ending year from 1840 to 1920 is:

0.25 X 0.353 = 0.0882 or 8.82%.

So the odds that we will have five presidents elected in zero ending years and die in office are:

0.0882 X 0.0882 X 0.0882 X 0.0882 X 0.0882
= 0.00000534 or 0.000534 %

That ain't gonna happen just by chance.

Case closed, nicht wahr?

At this point the Curse Doubters or Skeptics - Rationalists, as some of them prefer - sadly shake their heads. Such arguments, they say, are totally irrelevant and are simply red herrings. A president dying in office is a rare event. And any combination of rare events - in a regular pattern or not - will give you exactly the same super-low probability. The presidents could have been elected in years 1840, 1852, 1868, 1876, and 1884, and you'll still get the 0.00000415 % probability of the presidents dying in those terms.

Instead, the Doubters claim that the "Curse" is nothing more than a lamentable combination of a horribly flawed belief, faulty reasoning, and profligate credulity. But what can you expect in a country where - quote - "educational television" - unquote - peppers its programming with invented documentaries about imaginary monsters and uses actors to play the part of professors from non-existent universities?

As for the Curse, the flaws are obvious.

First, claiming that Tecumseh put a curse on the presidents starting with William is absurd. Tecumseh never even knew that William became president, for crying out loud! William was elected in 1840 and Tecumseh died in 1813. Even if we skip Thomas Jefferson - who was elected in 1800 and left office hale and well - at least the Curse should have started with James Monroe who was elected in 1820. And James, like Tom, was very much alive when he stepped down and he lived until 1831. Blaming Tecumseh is just an anachronistic 20th century invention to explain why the Curse really doesn't work - not to mention it being horse hockey, bullshine, and poppycock.

And note, the Doubters snort, the Curse is worded so it can slide over any presidents who die in office, but are not elected in zero-ending years. For instance, Zachary Taylor died in office but was elected in the year 1848. The Curse Adherents should count this as a failed prediction but don't. They just ignore it.

There are also other cases that the Curse really fails but is said to succeed. Lincoln really died after his 1864 election. But since his first term was the election of 1860, the Adherents say Honest Abe was a victim of the Curse. This re-election-sleight-of-hand gives the Curse an extra chance to work.

But in any case, the Doubters shout,

THERE IS NO PATTERN TO THE DEATHS OF THE PRESIDENTS!

Instead, look what the Curse does. It takes the years the presidents died in office - which has no particular pattern - and reassigns them to election terms which by definition occur in equally spaced years - and of which 25 % end in zero!

President	Year Died	Reassigned Year
W. H. Harrison	1841	1840
Taylor	1850	Ignored
Lincoln	1865	1860
Garfield	1881	1880
McKinley	1901	1900
Harding	1923	1920
Roosevelt	1945	1940
Kennedy	1963	1960

In other words, the Doubters say

THE CURSE IS AN ARTIFICIAL CONSTRUCT!

Such artificially devised patterns, they sneer, is a well-known ploy of pseudo-scientific numerological nattering nabobs of negativism and can easily be recognized as a farce by people skilled in true data analysis. Claiming an event is of low probability don't mean diddly if the event is contrived and artificial. Instead what we are seeing is simply a rather pathetic example of how you can combine data mining with data massaging.

Yes, the Doubters say, the case is indeed closed.

Let's Massage Down in the Mines

But Doubters aren't through yet. Data mining, they point out, is a very sinister practice to be eschewed by fair minded scientists. With data mining you can easily fool yourself into thinking you've found some amazing scientific - or mystical - principle when all you've done is found nothing more unusual than patterns in tea leaves or figures in clouds.

To see a simple example of order-hidden-in-randomness, look at the digits of the number pi (π). Without rehashing tedious details, we can say that the digits of pi have all the characteristics of a random sequence. But you can find all sorts of patterns if you look long enough. You can even claim that π predicts the future!

For instance, look through π until you reach digit 197,454,808. Then we find the sequence 07041776.

That is, the date July 4, 1776!

So π predicts the Declaration of Independence!

Or at digit 110,584,175 we find the sequence 04201889. That date - April 20, 1889 - is Hitler's Birthday!

So π predicts Hitler!

Then at position 19,822,679 we find the sequence 11221963. That is, November 22, 1963.

So in one swoop π predicts the deaths of John Kennedy, C. S. Lewis, and Aldous Huxley - and the birthday of John Nance Garner, the American Vice-President and friend of famed lawman Pat Garrett!

That's all the Curse of the Presidents is, say the Doubters. Fiddle with numbers, look for patterns, and eventually you get whatever you want. Childish, superstitious, claptrap.

But hold on yourself, Pilgrim, the Adherents say. Data mining is far from sinister. It's the basis for the natural sciences where obtaining controlled laboratory data isn't possible. We're talking geology, astronomy, epidemiology, climatology. Practitioners of these sciences have to look for patterns amidst tons of random information.

That's science!

As far as "massaging" data, legitimate scientists do that all the time. For instance, creating a histogram is grouping data and assigning the values to a rounded-off number. That's exactly what we do in the Curse of the Presidents. So don't give us any garbáge about artificial constructs. That's what data analysis is.

So the Curse of the Presidents is fully d'accord with what scientists do every day.

So there.

The Generalized Curse of the Presidents

Besides, the Adherents say, the Doubters haven't answered our original question. Even with massaged data, the odds of the Curse arising by chance is nigh on vanishingly small. Yes, there was one exception - Zachary Taylor - but predictions don't have to be perfect. A scientific prediction simply has to be better than chance.

And OK, we'll stick just with Robert's original observations, and we'll include re-elections. That is, from 1840 to 1920 we have a total of 21 terms, and there are eight terms held by presidents who died in office. So the odds that a term was held by a president who died in office is 8/21 = 0.38 or 38 %.

And to have five of these all occur on specific zero-ending elections years is low. In fact, the odds of this happening are:

0.38 X 0.38 X 0.38 X 0.38 X 0.38 = 0.00792 or 0.792%

We repeat. How can you say this "curse" is simply chance?

Easy, the Doubters sneer. You've just proven the point that the Curse is nonsense. All you are doing is using one of the most famous fallacies of logic. This is the Golfball in the Fairway Fallacy.

Suppose a famous golfer like Patty Berg is at the starting tee on Hole 1. In front of her is a fairway of 10,000,000,000 blades of grass. She hits the ball, and when it lands, it lands on a blade of grass.

Look at the odds against that happening! Why with 10,000,000,000 blades of grass and one getting hit, the odds of the golf ball hitting that one blade of grass is 10 billion to 1!

It's a miracle!

Of course, anyone can see such a claim is absurd. Yes, hitting any particular blade of grass is of low probability, but it's ridiculous to claim this is anything out of the ordinary.

And that, the Doubters say, is exactly what the Adherents are doing.

In other words, the Curse of the Presidents is only one particular pattern out of a number of other patterns. And if any of those other patterns had occurred, the Adherents would have claimed it as a mystical Curse.

Or look at it like this. Suppose starting with 1840, each of the five successive presidents had died in office. That is, we would have had:

President	Election Year	Died in Office
W. H. Harrison	1840	Yes
Polk	1844	Yes
Taylor	1848	Yes
Fillmore	1852	Yes
Pierce	1856	Yes

Certainly this pattern would have been called the Curse of the Presidents.

But what if it turns out that the five presidents elected in alternate terms had died in office?

President	Election Year	Died in Office
W. H. Harrison	1840	Yes
Polk	1844	No
Taylor	1848	Yes
Fillmore	1852	No
Pierce	1856	Yes
Buchanan	1860	No
Lincoln	1864	Yes
Grant	1868	No
Hayes	1872	Yes

Yep. That, too, would have been a "Curse of the Presidents". In fact, any regularly spaced sequence of terms of office would have been claimed to have been a Curse of the Presidents.

Now it's true that any one of these patterns has a low probability - 0.79%. So the actually observed curse - the election years spaced 20 years apart beginning with 1840 - is only one specific instance of a number of low probability events.

Yes, a Golfball in the Fairway Fallacy!. That's all the Curse is.

Of course, the Adherents don't buy it. There are - to quote Carl Sagan - billions and billions of blades of grass in a golf course. But how many regularly spaced patterns are there in the terms of the presidents?

Well, if you sit down and do all the counting, you can find a total of 45 individual patterns of equally spaced terms - all of which would have been cited as a Curse of the Presidents. We'll ignore Zachary and so we have 7 terms out of 21 of presidents who died office. That's 7/21 = 0.33 or 33 %.

Remember, though, we are looking at only five terms that end in zero. So the probability of five presidents dying in those terms is:

0.33 X 0.33 X 0.33 X 0.33 X 0.33 = 0.004115 or 0.4%.

But then we also have 45 equivalent patterns. So the probability that we would have some Curse of the Presidents is:

0.004115 X 45 = 0.185 or 18.5 %

Now you may think 18.5% is pretty low to claim as a chance occurrence. Actually, as we'll explain below it isn't and is well within the bounds of probability.

For those who may think we have been confusticating the issues, there is a another tack. Using a computer method known as resampling statistics and using 20,000 replicates, we have a value of 18.7% ± 0.2 %. What we got with our simple probabilistic calculation.

What we've found then is that, yes, any one Curse of the Presidents is rare, but finding some Curse of the President is no big deal.

Again, the Curse of the Presidents is nothing more than the Golfball in the Fairway Fallacy.

When is a Prediction Not a Prediction?

The Adherents, though, have one more ace up their sleeve. And it's that Curse of the Presidents that follows the tenants of a proper scientific theory.

Ha?, ask the Doubters (quoting Shakespeare). How is that possible?

Laughing behind their hands, the Adherents point out that one of the fundamental properties of a valid theory is that it is predictive. That is, it reliably predicts future events observed after the theory is first formulated.

And that, the Adherents tell their Doubting friends, is exactly what the Curse did.

But first a bit about what we mean by prediction.

There are many old writings which are supposed to be able to predict the future. For instance, the famous French writer Michel de Nostredame - better known as Nostradamus - wrote in in the 16th century. Michel's fans tell us he predicted the Kennedys, Napoleon, and Hitler and a lot of more recent stuff.

But note that we never know what Michel predicted until after the event happens. In other words, something happened, then someone goes back and riffles through Michel's otherwise incomprehensible writings, and lo and behold!, we find something Michel wrote that seems to sort of fit what what has happened.

Sound familiar?

Yes, what we're seeing is data mining.

That is, the readers of Michel are mining his writings for words and phrases and then correlating them with other words and phrases that describe some event that has already happened.

But (and pardon us if we shout) CORRELATION IS NOT PREDICTION!

Correlation by itself proves nothing, particularly when combined with data mining and data massaging. All it means is you've mined your data and found or created a pattern.

To determine if you have a bonafide scientific theory, you have to prove it has (and again pardon) TRUE PREDICTIVE POWER. And this is something we'd like to learn to test.

I thought you would, as Captain Mephisto said to Sidney Brand. It's very simple really - with just a few guidelines.

	To predict something, the event cannot yet have happened.
	The prediction must be clearly stated, and it must be easily recognized if it happens.
	The event's occurrence must be beyond the scope of reasonable chance.

As always a few examples are in order. Or rather a few examples of what are not real predictions are in order.

Suppose you predict there will be earthquakes. Then all you're doing is "predicting" something that happens hundreds of times a day. Even major earthquakes happen several times a month. So predicting earthquakes will happen is not really predicting.

In other words, a meaningful prediction cannot be about a common or frequent event.

But it can't be predicting that a rare event won't happen, either. If you predict there will not be a major earthquake in Omaha, Nebraska, Central Standard Time on that does not mean you can predict the future with 99.99999999% accuracy.

We repeat. Predicting that a rare event will not happen is not predicting.

In a similar vein, there are also what we can call "Waiting for Godot" predictions. These are predictions which people keep making but they never happen. All apocalyptic predictions (so far) have fallen into this class.

For instance if you sternly warned your college roommate in 1974 that the "world will end this generation", you may think you've made a prediction. However, you might notice that after half a century you're still making the same prediction to your kids who don't believe you either. True, eventually the prediction will come true. After all, if you keep making the prediction for another for 5 billion years, the sun will expand to a red giant and burn up the Earth "this generation". But you still aren't really predicting anything.

There is, though, an easy way out so your predictions always come true. Just change your definitions when you're wrong. In the 1970's, some people - including a Nobel Prize winner who really should have known better - had stated that "civilization as we had known it" would come to an end in the 1980's. But as of the world has kept moving along fine, thank you.

So what to do? Admit the predictions were wrong? Heaven forfend!

Instead you simply change your definitions. For instance, "civilization as we had known it" in the 1970's was before the computer and Internet revolution. And with the rise of the Information Age, communication - which was slow, expensive, and tortuous - became cheap and instantaneous. So you can say that in 1980's - quote - "civilization as we had known it" - unquote - had indeed come to an end.

But that still ain't predicting anything!

When a Prediction IS a Prediction

So to test if a theory - or someone - has true predictive power, we have to make sure that

1. The event hasn't already happened.
   
   
2. What is predicted is clearly stated and specific.
   
   
3. A successful prediction isn't just a lucky guess.

Tough criteria, yes, but if you really want to play the game, that's the way it is.

So does the Curse of the Presidents really predict?

We'll accept that data mining and massaging is OK. And so we'll hypothesize that there is some - as yet undiscovered - principle that has caused the presidents who were elected in the years ending in zero to have died in office.

And we'll treat it as a real scientific theory.

The Theory of the Presidents

Now we must point out there is one fundamental and absolutely unshakable rule in creating and testing a viable, scientific, and real theory. And once more we shout:

THE DATA USED TO CREATE A THEORY
CANNOT BE USED TO
TEST THE THEORY!

What was that again?

THE DATA USED TO CREATE A THEORY
CANNOT BE USED TO
TEST THE THEORY!

And, you ask querulously, why not?

Remember data mining? If you formulate a theory, you've been data mining, massaging, and correlating. That means you're virtually guaranteed to find something that looks like an amazing low-probability prediction when really it might easily be due to chance.

The test, though, is what it predicts for the future. Now if your theory is simply good luck, then future observations will not be likely to agree with the theory.

But if the theory is real, then it should continue to accurately predict specific future events.

Therefore to test a theory you must:

1. Gather data and form your theory. This data is called the correlation set.
   
   
2. Then gather absolutely new data to test your theory. This data is the validation set.

Now the "Theory of the Presidents" was actually created, as we saw, by Robert Ripley in the 1930's. And what made it seem like it had predictive power was, by golly, it did predict the fate of the presidents who were elected in 1940 and 1960.

So from our data gathered from 1840 to 1920, we have formulated the hypothesis:

There is some as yet undetermined principle that causes presidents elected in zero ending years to die in office.

And we found out

Using data from 1840 to 1920, the theory perfectly predicted the outcome of the elections of 1940 and 1960.

So we've proved the theory is right?

Right?

Well, there is, remember, that other rule:

The predictions must be unlikely to have arisen by chance.

And how, you ask, do we test this?

Surprisingly it's pretty easy. Because our validation data set - the years from 1924 go 1960 - is fairly small, we can use what fancy pants data analysts call exact statistical analysis. In exact statistical analysis we simply list all possible rearrangements of the presidential terms from 1924 to 1960 and count how often the years 1940 and 1960 simultaneously coincide with a term of a president who died in office. Doing so is not particularly difficult as there are freely available on-line resources to generate and count the rearrangements.

A small sample of the permutations is shown in the table below and you can see how to tote up the probabilities. You can see all of the permutations in a new window if you just click here.

Permutations	1924	1928	1932	1936	1940	1944	1948	1952	1956	1960	Agrees with "Theory"
Historical Sequence	C	H	R	R	R	R	T	E	E	K
Permutation 1	R	R	R	R	H	K	T	E	E	C	No
Permutation 2	T	K	H	C	E	E	R	R	R	R	No
Permutation 3	H	R	R	R	R	T	E	E	C	K	Yes
	:	:	:	:	:	:	:	:	:	:
Permutation 720	R	R	R	R	K	E	E	C	T	H	No
C: Coolidge   H: Hoover   R: Roosevelt   T: Truman   E: Eisenhower   K: Kennedy

Notice that what we're doing is what hot-shot number crunchers call taking permutations without repetitions. We rearrange the terms but don't repeat presidents getting elected more or less often than they really did.

Now often having unlimited repetitions is OK. That allows you to consider unlikely scenarios that nevertheless could happen. But we don't think Calvin Coolidge could have been elected in every term from 1924 to 1960. Not only would Calvin be starting his last term at 88 years old, but after World War II, presidential terms were limited to two.

In any case we want to test the effect of how the actual re-elections really affected the likelihood that the president died in office. So we are also sticking with the re-elections as they happened. That is, when taking our permutations, we don't split up the terms of Franklin Roosevelt or Dwight Eisenhower. We keep those terms together.

Now if we use the elections from 1924 to 1960 and keep the re-election terms together, we find there are 720 distinct rearrangements. Of these there are 90 where an election of Kennedy and Roosevelt - who died in office - both fell on the years ending in zero. So the probability that the historical observations occurred by chance is 90/720 or 12.5 %.

Well, that settles it say the Adherents. That means we have an 87.5% probably that the curse is not due to chance.

That's almost 90%! The Curse is indeed real!

Case closed again!

Not so fast, say the Doubters.

A probability of 12.5 % may seem low, they say, but only to those poorly versed in probability. For instance, if you were pitching pennies, and on the first three tosses one of the players ended up getting 3 heads in a row, would you accuse him of using some new scientific principle or invoking some mystical power?

Of course not. Three heads occur by chance all the time. And yet the probability of getting three heads in a row is:

0.5 X 0.5 X 0.5 = 0.125 or 12.5%

Exactly the same as for our Curse!

But what values of probability - called the significance - should we use to decide some event isn't due to luck?

Well four heads in a row you might begin to wonder, but probably would still wait for more information. And four heads in a row is 6.25 % probability.

But what if you got five heads in a row - which has a 3.25 % probability. Well, then you'd be justified in thinking - not necessarily that there was some mystical intervention - but that the fellow was controlling the tosses some way (which skilled coin tossers can do). Certainly you would be justified in thinking the repeated heads was caused by something other than chance.

So data analysts and statisticians have decided that to label an event as deterministic it must be somewhere getting between four heads in a row (6.25%) and five heads in a row (3.25 %). So a good value is 5%. Or as it's sometimes put, there must be 95 % confidence the event is not due to chance.

Size Matters After All

We see, then, that even though the elections from 1924 to 1960 agreed perfectly with our theory, there wasn't enough data for a proper validation. Simply put, the sample size was too small.

So yes, we need more data beyond the elections of 1940 to 1960.

Which eventually we got.

The extra data, of course, was the presidential elections of 1980 and 2000. And both presidents - Ronald Reagan and George W. Bush - left the office alive and well.

And the theory?

Well, it worked half the time - 1940 and 1960 - and failed the other half - 1980 and 2000. So our Theory of the Presidents was no better than a flip of the coin.

In the end, then, the Curse Doubters tell us that the Curse of the Presidents is an interesting example of forming a theory where there is an initial (and somewhat contrived) high correlation and so merited further exploration. But by the time we got enough data to test the theory properly, we found our theory had no predictive power. Ergo, the theory is no good, and there isn't any Curse.

The (Revised) Theory of the President

The Adherents, of course, don't accept this gobbledygook any more than Albert Einstein ever accepted quantum mechanics. All the extra data means is that the theory needs a bit of tweaking. After all, Newton's theory of gravitation doesn't explain everything - like bending of light as it passes the Sun or the fact that the planet Mercury circles the Sun a bit strangely. The tweaking was done by Albert in his Theory of Relativity.

And there's nothing wrong with tweaking. Scientists revise their theories all the time when they get new data. And we need only a minor revision. Remember, Ronald Reagan was seriously wounded in an assassination attempt. And George W. Bush survived a planned attack on the White House.

So our revised theory is that presidents elected in years ending with zero will be subject to some danger.

Unfortunately, this new theory - as we can put it - generalizes to non-testability. We can see what this means if we list the presidents and their various health issues and dangers they encountered.

Data for the Revised Theory of the Presidents

First Election	President	Birth	Death	Age at Death	Dangers During Office	Cause of Death
1788	Washington	1732	1799	67	Surgery from Leg Infection, Near Fatal Pneumonia or Influenza	Acute Epiglotitis
1796	Adams	1735	1826	90	Obesity, Tobacco Addiction (Smoking and Chewing)	Heart Failure, Pneumonia
1800	Jefferson	1743	1826	83	Severe and Potentially Fatal Jaw Infection	Old Age, Multiple Diseases
1808	Madison	1751	1836	85	Potentially Fatal Malarial Attacks	Old Age, Multiple Diseases
1816	Monroe	1758	1831	73	Bedridden with Malaria	Heart Failure, Tuberculosis
1924	J. Q. Adams	1767	1848	80	No Serious Problems	Stroke
1828	Jackson	1767	1845	78	Effects of Old Bullet Wounds Requiring Surgery, Assassination Attempt	Old Age, Multiple Diseases
1836	Van Buren	1782	1862	79	Dyspepsia	Heart Failure, Pneumonia
1840	W. H. Harrison	1773	1841	68	Died in Office	Pneumonia
1844	Polk	1795	1849	53	Bedridden with Undiagnosed Illness, Possibly Malaria	Cholera
1848	Taylor	1784	1850	65	Died in Office	Food Poisoning
1848	Fillmore	1800	1874	74	Obesity	Stroke
1852	Pierce	1804	1869	66	Alcoholism, Possibly Tuberculosis	Stroke
1856	Buchanan	1791	1868	77	Potentially Fatal Dysentery, Heavy Drinking	Pneumonia, Pericarditis
1860	Lincoln	1809	1865	56	Assassinated	Assassination
1864	Johnson	1808	1875	66	Malaria, Dysentery	Stroke
1868	Grant	1822	1885	63	Eight to Ten Cigars a Day, Rumored High Alcohol Consumption	Throat Cancer
1876	Hayes	1822	1893	70	No Serious Problems	Heart Attack
1880	Garfield	1831	1881	49	Assassinated	Assassination
1880	Arthur	1829	1886	56	Serious Kidney Diseases, Hypertensive Cardiovasclar Disease	Chronic Renal Failure, Stroke
1884	Cleveland	1837	1908	71	Oral Cancer Requiring Surgery	Multiple Diseases
1888	B. Harrison	1833	1901	67	No Serious Problems	Pneumonia
1896	McKinley	1843	1901	58	Assassinated	Assassination
1900	T. Roosevelt	1858	1919	61	Temporarily Confined to Wheelchair After Serious Carriage Accident	Heart Attack
1908	Taft	1857	1930	72	Severe Obesity, Assassination Attempt	Cardiovascular Disease
1912	Wilson	1856	1924	67	Debilitating Stroke	Multiple Cardiovascular Problems
1920	Harding	1865	1923	57	Died in Office	Heart Attack
1924	Coolidge	1872	1933	60	Heavy Cigar Smoking, Possibly Major Psychological Problems	Heart Attack
1928	Hoover	1874	1964	90	Assassination Plot	Old Age, Internal Bleeding
1932	F. Roosevelt	1882	1945	63	Died in Office	Cerebral Hemmorage
1948	Truman	1884	1972	88	Assassination Attempt	Old Age, Multisystem Failure
1952	Eisenhower	1890	1969	78	Heart Attack	Congestive Heart Failure
1960	Kennedy	1917	1963	46	Assassinated	Assassination
1964	Johnson	1908	1973	64	Gall Bladder Attack, Cancer (Both Requiring Surgery), Pneumonia	Heart Attack
1968	Nixon	1913	1994	81	Potentially Fatal Phlebitis ( Blood Clot in Legs), Assassination Plot	Stroke
1976	Carter	1924			No Serious Problems
1980	Reagan	1911	2004	93	Assassination Attempt	Old Age, Altzheimers
1988	G. H. Bush	1924			Atrial Fibrillation from Hyperthyroidism (Graves' Disease), Assassination Plot
1992	Clinton	1946			Assassination Plots
2000	G. W. Bush	1946			Assassination Attempts
2008	Obama	1961			Assassination Plots

Note that many of the health issues are not necessarily serious today, but they were then. George Washington had a leg infection that required surgery - in a day without antiseptics and anesthesia - and also contracted influenza so virulent that it apparently developed into pneumonia. His friends and family thought he might die.

When he was president, Andrew Jackson's had to have surgery to remove a old bullet received during a duel. The operation was - again without anesthetic and antiseptics - quite serious by the standards of the day. Grover Cleveland had cancer which required surgery (both the illness and procedure were kept from the public). Theodore Roosevelt was involved in a carriage/street car collision which killed a Secret Service agent and put him temporarily in a wheelchair. A number of presidents, including Taft, Truman, Ford, and the younger Bush survived assassination attempts and plots (President Ford, as John Tyler, is not listed because neither was ever elected as president). Woodrow Wilson suffered a debilitating stroke and had the 25th Amendment been in effect, the Vice President would have taken over.

We see, then, that so many presidents fit the new theory that any agreement with the data will easily be due to chance. But at some point revision of a theory becomes self-defeating - and you just have to admit your theory is wrong.

But in any case revising a theory uses all of the data currently in hand. That is, our old validation set becomes part of the new correlation set. Therefore to properly test the new theory, an entirely new validation set is needed. So we will have to wait quite a while to find out if any new "Theory of the Presidents" can ever be properly validated.

The Real Curse of the Presidents?

At this point the Adherents will probably be venting their spleens that once more we have some (ptui) skeptic just digging through the rubbish until they find ways to trash the theory.

The author and illustrator of CooperToons denies such an accusation. Au contraire (as Shakespeare would have said), the CooperToons policy is to abhor blind skepticism and is indeed proud to boast of credulity that is second to none.

Un Skeptique? Qui? Moi? C'nest pas possible!

Instead the open-minded, intelligent, educated, and above all, modest scholar will consider all possibilities and deny none. Certainly, a seeker of wisdom will recognize that beneath myths, legends,and superstitions, there is often a glimmer of truth. And we can finally see that there was at least some kind of Curse of the Presidents.

First, we'll do away with any artificial constructs. Let's just look at the data for crying out loud! Out of 44 presidents (we count Grover Cleveland twice), all seven presidents who died in office occupied 13 terms. And these terms were squeezed in the years from 1840 to 1960 or 33 terms.

What is the likelihood that will happen by chance?

Of course we want to avoid a Golfball in the Fairway Fallacy. So we ask what is the likelihood that 13 terms of the presidents who died in office will be squeezed into any single block of no more than 33 consecutive terms?

Now you can use simple combinatorial methods of the type taught to all middle school students for this problem. It's pretty simple. You must take the formula:

33 X 32 X 31 X 30 X 29 X 28 X 27 X 26 X 25 X 24 X 23 X 22 X 21
= 3,569,119,343,741,952,000

which is how many ways you can cram 13 terms into 33 terms.

But this distinguishes the sequences based on order. So we divide this number by:

13 X 12 X 11 X 10 X 9 X 8 X 7 X 6 X 5 X 4 X 2 X 1
=2,075,673,600

So we have

Combinations = 3,569,119,343,741,952,000 ÷ 2,075,673,600
=1,719,499,320

And as far as cramming the 13 terms into all 59 terms is:

Permutations = 59 X 58 X 57 X 56 X 55 X 54 X 53 X 52 X 51 X 50 X 49 X 48 X 47
= 25,203,096,726,965,853,696,000

And so the combinations are:

Combinations = 25,203,096,726,965,853,696,000 ÷ 2,075,673,600
= 12,142,129,054,860

So the probability of packing the 13 terms sequentially into the 33 terms:

Probability = 1,719,499,320 ÷ 12,142,129,054,860
= 0.000142 or 0.0142%

On the other hand, there are 27 equivalent 13 consecutive terms in a series of 59 terms. So the total probability of squeezing our terms is:

0.00014 X 27 = 0.0037 or 0.37%

Way below the 5% needed for a chance occurrence.

We can therefore confidently, honestly, and scientifically claim that having our presidents die from 1840 to 1960 - or any similar block of terms - is indeed unusual - or at least something beyond random chance.

So even though there may not be the Curse of the Presidents, there is certainly some Curse of the Presidents.

"Nikita! What's going on?"
   -   Laventry Beria to Nikita Khrushchev,
       June 26, 1953

So what, as Laventry asked Nikita, is going on?

Well, first it's always good to get more data.

The presidents who were elected in 1788 to 1836 - George Washington to Andrew Jackson - lived an average of a remarkable 79.3 years. True, George died relatively young - age 67 - but that was because he caught a then inevitably fatal disease, acute epiglottitis, after riding in the snow and sleet (the story that he jumped into snowbank to escape being nabbed in flagrante is apocryphal).

And surprisingly, the average age to which presidents have lived after 1960 was exactly the same - 79.3 years.

And in the years from 1840 to 1960? Well, there is a difference. The average lifespan was only 65.8 years. Even removing the presidents who fell by an assassin's hand, the average age was 68.6. You can see the data best in a graph.

Presidential Longevity

Hm. It seems that the presidents in the "curse years" lacked a robustness of the earlier and later presidents.

So why is presidential health better at the extremities but not in the middle?

That the later presidents lived - and are living - long lives isn't unusual. They get the best health care possible. They have no waiting lists in case they need a medical procedure and it's all paid for by their government funded pensions.

And the longevity of the early presidents isn't hard to understand, either. Presidents from George Washington to Andrew Jackson lived remarkably clean lives. Yes, they drank but not to excess, and usually wine (with some beer). Red wines in moderation - quite popular with the Founding Fathers - has been linked with good cardiovascular health.

Of course, man doth not live on booze alone, and our Founding Presidents, although men who liked a good meal and fine food, did not pork away. But more importantly they exercised. Washington and Jackson were quite the outdoorsmen and even John Adams - "His Rotundancy" - walked about six miles a day specifically for exercise. In his old age when long treks did get a bit much, he took up horseback riding. After he left office he continued to work on his farm, and Abigail remembers him working in the fields while swearing at the way Thomas Jefferson was running the country. John's son, Quincy and the sixth president, was also a vigorous walker and went swimming regularly - in the buff the story goes. That these men should live long healthy lives is not, in hindsight, that odd.

So what was the problem that started around 1840?

First we have to find whether with the presidents we're seeing is out of the ordinary. That is, we'll ask just how long did your average Joe Blow live during those apparently perilous times. And to avoid the problem of infant mortality throwing us off, we'll look at the longevity of white males who made it to 20 years of age. And what we see isn't what we expect.

American Longevity
(White Males After Age 20)

Yep, for more than half a century from the time of George Washington's administration life expectancy for adult males actually dropped - and considerably. And it didn't rise much for the rest of the century.

The graph is a distillation of data from various sources, but the first part - up to 1900 - is based on data gathered by a college professor who has studied mortality rates during the 19th century. His conclusion was the drop in longevity was tied with the growth of American cities and shift in population to urban areas. In cities you had crowding and with it poorer sanitation and therefore more disease. Other studies have found that - quote - "primitive cultures" - unquote - who lived in sparsely populated rural areas have longer life spans than citizens of cities in developing countries.

True, we can't say that the presidents lived in squalor but they certainly lived next door to it. Washington, D. C. in the mid-19th century was a mess - "a swampy pig sty" is accurate both metaphorically and literally. And indeed, Zachary Taylor, the second president to die in office, likely fell from food poisoning aggravated by the unhealthy D. C. environment. Specifically Zachary developed a "bloody flux" after he had eaten chilled fruit and drank cold drinks - all cooled with ice which may have been made from contaminated water.

Of course, in olden days lifetimes were cut short by disease far more often than now. Although surgery made strides particularly after the Civil War, what we now call internal medicine was a joke. Not just a joke but often deadly. As late as the early 20th century, one textbook prescribed a remedy for spasms, nervous irritability, severe vomiting, diarrhea, spasmodic coughs, asthma, hysteria, chorea, dyspepsia, diseases of the skin, the cough of consumptives, cardiac palpitations, hypertrophy of the heart, angina, difficulty in breathing, and congestive headache. The "remedy" was nothing more than a common and highly deadly poison which we will not name. To be fair, the textbook warned there were possible side effects with this "remedy" - like death. But we see that even into the early 20th century doctors were prescribing deadly poisons which had no medicinal value at all.

Throughout our early history, one thing that doctor's did prescribe was alcohol. Even during Prohibition, doctor's were allowed to "buy, sell, and transport" alcohol for medicinal purposes. Naturally that included the doctors of the American presidents.

Prohibition notwithstanding, Americans have always drunk a lot, but more in the earlier days. In the Colonial Era, after an age of 15 the consumption of alcohol was about 2 ounces of alcohol a day. Quite a bit more than the average consumption today which is less than an ounce per diem per capita.

Of course, water was often contaminated and so drinking alcoholic beverages was safer. And since beer, wine, or cider were staples, drinking tended to be spread out over the day - a dram here, a dram there. The effect of 2 ounces spread out over a whole day was fairly minimal and people could function more or less normally.

As the nineteenth century progressed drinking water became safer and more people began to give up alcohol. But oddly enough, the total amount consumed did not. Quite the contrary. By 1830 the average American was drinking over 7 gallons a year of alcohol - a full gallon more per year than their Colonial forebears. Much of the increase came from easier availability. Rum, originally the hard spirit of choice for the Founding Fathers, was replaced by the cheaper domestic whiskey.

However, it was not only the amount of the drinking but drinking habits that changed. As the Temperance Movement began to make strides in the 1830's, drinking in the morning became frowned on and eventually even a tot before five was taken as a sign of moral failing. That meant those who did drink were drinking more, and they were concentrating their drinking into the after-work and social hours.

As a result people tended to drink more in a shorter span and in binges. There was also more of the hard stuff and by the late 19th century the mixed drink was the new rage (the painter Henri Toulouse-Lautrec loved to mix cocktails for himself and his friends). Eventually it became standard operating procedure for Dad to get home and have his drink before dinner. Then you had a few after-dinner drinks and before retiring, a couple of nightcaps.

To get an idea of how much people drank up to the mid-20th century, look at the American writer, Ernest Hemingway. In the mid-1950's he was recovering from injuries received in a plane crash in Africa. While in Spain he visited an old friend, Dr. Madinoveitia, who was one of Madrid's most prominent physicians. After seeing Ernest. Dr. Madinoveitia insisted on giving him a physical and when it was over, the doctor prescribed a rigid diet. That included - get this - no more than one glass of wine per meal and no more than five ounces of whiskey a day.

Yes, in the 1950's a diet that was considered particularly healthful and that drastically curtailed alcohol still permitted seven drinks a day.

Such a massive rate of alcohol consumption didn't drop in later years and in fact may have increased. One party handbook from the 1960's said that for an evening's entertainment, you should expect the guests each to drink about half a bottle of hard liquor the first two hours and three quarters of a bottle every two hours after that. So in a typical evening's entertainment, you'd pack away about 30 ounces of hard liquor. Not surprisingly, this was also the era when over 50,000 Americans were dying each year in automobile accidents.

Americans only began reducing their drinking in the 1980's and then because of the crackdown on drinking and driving as well as the implementation of mandatory drug and alcohol tests in the workplace. Although liberals, civil libertarians, and boozers, may decry the practice, it did at least improve our health.

There is one rather touchy subject we have to mention but which is certainly relevant to the era when the presidents died. Before the Civil War, the idea of assassination was absurd. Presidents were elected with the will of the people (albiet filtered through the Electoral College) and - rare by today's standards - the public admired their politicians. Security was non-existant mainly because no one thought it was necessary.

Even with the Civil War, presidential security remained virtually nil. Despite warnings from his friends, Lincoln would ride from the White House to the Old Soldiers' Home - a place to take a welcome break - without a guard. But eventually Lincoln began to heed the advice and agreed to have a guard or policeman accompany him when he moved about. But in the end it didn't do much good. Contrary to what you read, there was a guard at the door of Ford's Theater. It was probably Charles Forbes, the presidential messenger. When John Wilkes Booth walked up, he handed Charles his calling card. Charles took the card, went into the box, and apparently with Lincoln's permission, admitted the famous actor.

From 1865 to 1901, all of the presidents who died in office were felled by assassins. Still, security remained lax, and the presidents went about with minimal security. Secret Service protection began only with Grover Cleveland and then only part time and informally. Security stepped up after McKinley was killed, but even the presidential protection was not required by law.

Actually in the day before some political candidates and their supporters seemingly sanction violence against their opponents, Americans saw lack of security as a benefit of democracy. Kings required regiments of soldiers to protect them, but the American president needed no protection. Any citizen could walk up to him and say hello and be greeted in return.

It wasn't until 1951 that a law was passed for the Secret Service to protect the president and his family. Then Harry Truman, president from 1945 to 1952, would take his morning walks accompanied by four agents, although the agent assigned to walk ahead would sometimes get lost if the president made an unexpected turn. Truman would also greet passers-by and shake their hands and talk to reporters. Only after a president died in office on November 22, 1963 was security changed to where contact with the public was tightly choreographed. Restricted contact with crowds has certainly been a factor in that for over a century only one president has been killed in office, even though there have been close shaves.

Finally, there's the topic that at first glance may seem unimportant regarding the presidents. Lighting up.

Many of the long-lived presidents smoked. But before the 1840's most people - men and women - puffed on pipes and Andrew Jackson was supposedly fond of having a bowl or two. But cigars also became popular early on, and John Adams, James Madison, and James Monroe all toked up on stogies.

Despite an odor that makes strong men quail and lesser men barf, after the 1850's it became quite fashionable to offer a cigar to a friend. Calvin Coolidge would offer cheap cigars to his visitors and smoked the better ones - or at least the more expensive - himself. Since it's been shown that heavy tobacco use of any kind reduces longevity, the longer-lived but cigar smoking presidents must have puffed less frequently than those who succumbed earlier. Calvin was a heavy smoker of cigars but did so in a rather surreptitious manner. Yes, he smoked only 4 cigars a day but these were twelve inchers. He died at age 60.

Then came cigarettes.

Cigarettes were primarily a Turkish invention and it was the soldiers returning to England from the Crimean War that started the craze. By 1850, cigarettes were commonplace and by 1870 most men were puffing away. Although still not considered quite proper for a lady, the fairer sex found that they could sneak ciggies a lot easier than pipes or cigars. Cigarettes were more compact and if you got together with your friends while hubby was away you could indulge in the wicked pleasure.

By 1930, about half of the adult population smoked and for adult males the figure was more like 70%. This certainly kept lifetimes short and even today the life expectancy of smokers is about 64 years - not much lower than what it was for the Presidents from 1840 to 1960.

But how did cigarettes effect the presidents if they mostly smoked cigars?

Part of the problem is that the presidents have been a bit secretive about their bad habits. We don't know how much or how many cigarettes they consumed. The historical record is also being confused since cigarettes are sometimes airbrushed out of photographs of famous celebrities.

But for those who we know who smoked cigarettes, it's instructive to flag them on the previous graph.

Presidential Longevity and Ciggies

So we see that it isn't really just that the heaviest cigarette smoker - FDR - was one of the presidents who died in office. But the 20th century presidents who smoked cigarettes during or after their tenure fit with the cluster of the unhealthy 19th century presidents. Warren Harding smoked cigars and cigarettes and apparently had a real tobacco addiciton. He would even chew cigarettes if he couldn't conveniently light up. He died in office at age 57, most likely of a heart attack.

LBJ was a heavy smoker who quit in 1955 after a heart attack. But once he left the White House he again took up cigarettes with élan. He died at age 64.

And finally we'll contrast FDR, Warren, and LBJ with Dwight Eisenhower. Ike quit his four pack a day habit before the election and never took it up again. Ike lived into his late seventies - very near the age of the early and latest presidents and a quite respectable age for the time.

So now we know the real Curse of the Presidents!

References

Ripley's Big Book Believe it or Not, Robert Ripley, Simon and Schuster, 1934.

The Pi-Search Page, http://www.angio.net/pi/. Beware of some pages which actually display the digits of Pi. They may freeze up your browsers. This page, though, allows you to search for patterns in Pi without having to display all the digits up to that point.

The Health of the Presidents: The 41 United States Presidents Through 1993 from a Physician's Point of View, John Bumgarner, 1994. A good reference albeit not error free. The book states Teddy Roosevelt was wounded while president which wasn't true. He had left office but was running for president on the Bull Moose Party.

"Medical History of American Presidents", http://www.doctorzebra.com/prez/. A nice compilation involving review of the literature (including primary sources) by a licensed medical doctor. The book by John Bumgarner is a major reference.

"Decennial Life Tables for the White Population of the United States, 1790 - 1900", J. David Hacker, Historical Methods, Vol. 43, Issue 2, pp. 45-79, 2010.

"1900-2000: Changes in Life Expectancy in the United States", Elder Web. Web. A number of Internet sites list life expecancy with more or less degrees of clarity. This site shows data in a fairly simple and intelligible manner. For inclusion in the above graph, the values were adjusted by interpolation to correct removal of the effects of childhood mortality. The exact manner of the interpolation is left, as the textbooks say, as an exercise for the reader.

"Table 22. Life Expectancy at Birth, at 65 Years of Age, and at 75 Years of Age, by Race and Sex: United States, Selected Years 1900 - 2000", Center for Disease Control, http://www.cdc.gov/nchs/data/hus/2010/022.pdf. This table is kind of hard to find if you go the CDS website itself. But you can find it and similar tables if you go to the National Center for Health Statistics home page (http://www.cdc.gov/nchs/) and do a search.

"Truman and the Secret Service", National Park Service, https://www.nps.gov/hstr/planyourvisit/upload/secret-service.pdf

"The Incredible Walking President", Harry Truman's Excellent Adventure, www.trumanroadtrip.com/articles/article/6829750/120407.htm.

"Smoking's Many Myths Examined", Christopher Wanjek, Live Science, November 18, 2008. Web. Actually a good article and it is not - as you might think - a pro-smoker site.

We Saw Lincoln Shot: One Hundred Eyewitness Accounts, Timothy Good, University Press of Mississippi, Jackson, Mississippi, 1995. Despite variant accounts and the stories starting in the 1930's, there is no mystery how John Wilkes Booth got into the box at Ford's Theater. According to eyewitness accounts, Wilkes walked up to the guard at the door, probably the Presidential Messenger, Charles Forbes, spoke to him, and was granted admittance. At least one witness even said he saw Wilkes had over his card. Charles then took the card into the box and returned shortly afterwards and admitted Wilkes, no doubt with Lincoln's permission. That one of the most famous actors in America was allowed to meet the president would not have been unusual. There is also a story that when attending another play where Wilkes starred, Lincoln had actually requested to meet the actor.

Papa Hemingway, A.E. Hotchner, Random House 1966. This gives us the "reduced drinking" diet of Ernest which allowed him to have seven drinks a day. Another diet was calves liver and Scotch whiskey in unlimited amounts. Hotch said he wasn't sure if this later diet was doctor prescribed or not.

Daily Life in the Colonial City, Keith Krawczynski, Greenwood, 2013.

Spirited Republic: Alcohol's Evolving Role in US History, Bruce Bustard, National Archives, 2014.

Action Cookbook: Len Deighton's Guide to Eating, Len Deighton, Jonathan Cape, 1965.

The Supersizers Go Seventies, Giles Coren and Sue Perkins (Presenters), BBC, 2008. Toward the end of the episode, Giles and Sue throw a 1970's party. Giles said when he read the amounts of liquor recommended he was so flabbergasted that he had to re-read the part nine times to be sure.

Health and Disease , Rene Dubos and Maya Pines, Time-Life, Life Science Library, 1969.

"The Science of Substance Abuse: When Presidents Smoke", Dirk Hanson, Addiction Inbox. November 9, 2010. Web.

"The George Washington Scandals", John Fitzpatrick, Schribner's Magazine, pp. 389-394, 1927.