Hold Your Horses

Shortly after the death of Blaise Pascal in 1662 at the age of 39, a servant was sorting through Pascal’s clothes and noticed something sewn into a coat that Pascal had often worn.  Out of curiosity the servant cut open the cloth and found a parchment, inside of which was a faded piece of paper.  The parchment and the paper both contained, in Pascal’s handwriting, nearly the same words.  Evidently the paper was the original draft and the parchment was a carefully prepared copy.  In addition to the text, both the paper copy and the parchment contained hand-drawn crosses.  The words written on the original piece of paper (from an English translation given in Marvin O’Connell’s book “Blaise Pascal, Reasons of the Heart”) were

The year of grace 1654.

Monday, 23 November, feast of St. Clement,

pope and martyr and others in the martyrology.

The eve of Saint Chrysogonus martyr and others.

From about half-past ten in the evening

        until about half-past midnight.

Fire.

The God of Abraham, the God of Isaac, the God of Jacob.

Not of the philosophers and intellectuals.

Certitude, certitude, feeling, joy, peace.

The God of Jesus Christ.

My God and your God [in Latin, accusative case].

Your God will be my God.

Forgetfulness of the world and of everything except God.

One finds oneself only by way of the directions taught

        in the gospel.

The grandeur of the human soul.

Oh just Father, the world has not known you,

       but I have known you.

Joy, joy,,, joy, tears of joy.

I have separated myself from him.______________

They have abandoned me, the fountain of living water [in Latin].

My God, will you leave me?

May I not be separated from him eternally.

This is eternal life, that they know you the one true God

       and J.C. whom you have sent.

Jesus Christ.____________________

Jesus Christ.______________

I have separated myself from him. I have run away from him,

        renounced him, crucified him.

May I never be separated from him._______________

One preserves oneself only by way of the lessons taught

         in the gospel.

Renunciation total and sweet.

And so forth.

In the parchment, the concluding phrase “and so forth” was replaced with the lines

Total submission to Jesus Christ and to my director.

Eternally in bliss, in exchange for a day of hard training

     in this world.

May I never forget your words [in Latin].

The parchment contained several other changes as well, and also noted biblical references for most of the lines.  For example, the line “My God and your God” refers to John 20:17

Touch me not, for I am not yet ascended to my Father, but go to my brethren and say unto them, I ascend unto my Father, and your Father; and to my God, and your God.

The next line in the paper version of Pascal’s memorial is “Your God will be my God”, and beside this he wrote simply “Ruth”, presumably referring to the passage in the book of Ruth (1:16) where, following the death of her husband, Ruth tells her mother in law

Intreat me not to leave thee, or to return from following after thee: for whither thou goest, I will go; and where thou lodgest, I will lodge: they people shall be my people, and thy God my God.

In any case, November of 1654 was certainly a turning point in Pascal’s life, because this is when he finally renounced his “self-serving” activities (including mathematics and physics) and resolved to devote the remainder of his life to the worship and service of God.  He retired to the monastery at Port Royal and employed his talents in writing polemics supporting the Jansenists against the Jesuits.  On the subject of his former pass-times he wrote

Reason has its own sphere, mathematics and the natural sciences… but the truths which it is really important for man to know, his nature and his supernatural destiny, these cannot be discovered by the philosopher or the scientist.  I passed a long time in the study of the abstract sciences, but the scant communication which one can have in them (that is, the comparative fewness of the people with whom one shares these studies and with whom one can communicate) disgusted me. When I began the study of man, I saw that these abstract sciences are not proper to man....

Despite the significance of his conversion, according to most accounts he never once mentioned his “night of fire” to anyone, which is remarkable considering all his passionate devotional writing.  He kept those scraps of paper next to his heart for the rest of his life to remind him of his experience on the night of November 23, 1654, and yet he never breathed a word of it. 

Or did he?  Some authors claim a third copy of the Memorial was made by a close friend of Pascal’s, but it isn’t clear if this third copy was made prior to Pascal’s death.  If it was, it would seem to contradict the claim that Pascal never mentioned his “night of fire” to anyone.  Some authors even suggest that the Memorial was included in drafts of Pascal’s Penses, whereas others insist that the only source for this writing is the copy found in Pascal’s coat.  There are also inconsistencies as to whether Pascal’s coat contained just the parchment, or the original draft paper copy as well.

This is an interesting (albeit confusing) story.  If true, we know about Pascal’s night of fire only because of a very alert servant.  It’s easy to imagine Pascal’s old coat being tossed into a furnace like the sled at the end of Citizen Kane, with the parchment undiscovered.  But in many popular books on famous mathematicians the story of Pascal’s final religious conversion is even more melodramatic.  One of the best known such books, originally published in 1893 and followed by several later editions, is W.W Rouse Ball’s “A Short Account of the History of Mathematics”.  According to Rouse Ball

[Pascal] was driving a four-in-hand on November 23, 1654, when the horses ran away; the two leaders dashed over the parapet of the bridge at Neuilly, and Pascal was saved only by the traces breaking. Always somewhat of a mystic, he considered this a special summons to abandon the world. He wrote an account of the accident on a small piece of parchment, which for the rest of his life he wore next to his heart, to perpetually remind him of his covenant…

This is very strange, because nothing in Pascal’s amulet can be described as “an account of the accident”.  In fact, as far as I know, there is no indication at all of any accident with horses and the bridge at Neuilly in any of Pascal’s writings, nor does this incident appear in any of the biographies of Pascal that I’ve read.  What was the source of Rouse Ball’s story, and how could he have been so misinformed as to the contents of Pascal’s famous memorial? 

The story about the horses and Pascal’s narrow escape from death has been picked up by countless subsequent authors, usually citing either Rouse Ball or E.T. Bell’s “Men of Mathematics” as their source.  Bell seems to have taken Rouse Ball’s lurid account and embellished it still further, so it reads like this:

On the day of his conversion [Pascal] was driving a four-in-hand when the horses bolted. The leaders plunged over the parapet of the bridge at Neuilly, but the traces broke, and Pascal remained on the road.  To a man of Pascal's mystical temperament this lucky escape from a violent death was a direct warning from Heaven to pull himself up sharply on the brink of the moral precipice over which he, the victim of his morbid self-analysis, imagined he was about to plunge. He took a small piece of parchment, inscribed on it some obscure sentiments of mystical devotion, and thenceforth wore it next to his heart as an amulet to protect him from temptation and remind him of the goodness of God which had snatched him, a miserable sinner, from the very mouth of hell.

To his credit, Bell seems to know that the parchment doesn’t contain an account of “the accident”, but he still presents the horse and bridge incident as the proximate cause of Pascal writing the document, something which we can’t possibly know to be the case if Pascal never even mentioned the parchment or his “night of fire” to anyone.  Also, as previously mentioned, we have no indication that an accident involving horses even took place, let alone that it prompted Pascal’s religious conversion.

Next we come to Stuart Hollingdale’s “Makers of Mathematics”, published in 1989.  The account given by Hollingdale is obviously taken directly from Rouse Ball and Bell, right down to the “miserable sinner” at “the very mouth of hell”:

In November 1654, Pascal experienced another conversion; this time it was for life. The story is that he was driving a four-in-hand when the two leading horses plunged over the parapet of the bridge at Neuilly. Fortunately the traces broke and Pascal survived unhurt. He took the incident as a divine warning of the danger of plunging over the moral precipice, a fear that had haunted his morbid imagination for years. He was indeed a miserable sinner who had been snatched from the very mouth of hell.

Out of curiosity I searched around for other descriptions of Pascal’s conversion.  Many authors just repeat the descriptions of Rouse Ball or E. T. Bell nearly verbatim, but sometimes they add their own embellishments.  It’s interesting how this single story (of dubious authenticity) is re-told and re-worded.  A brief sampling of the descriptions I have found is given below.

On this day, November 23, 1654, Pascal's horses bolted and plunged off a bridge. Pascal was thrown into the roadway. He saw this as a warning directly from God. That night he experienced a Christian conversion that would cause his outstanding scientific work to take second place in his pursuits. Light flooded his room. He recognized Jesus, the Word. For the rest of his life Pascal carried around a piece of parchment sewn into his coat--a parchment inscribed with ecstatic phrases…

Pascal attended parties where gambling was being conducted, and unfortunately became distracted by this lifestyle. However, Pascal had a narrow escape from death in 1654, when the horses pulling his carriage bolted. The horses were killed, but Pascal was unhurt. Convinced that it was God who had saved him, he reassessed how he was living.

One day, when Pascal was driving his carriage, his horses got scared and jumped over the wall of a bridge. The horses plunged to their deaths, but because the leather straps that connected the carriage to the horses broke, Pascal was saved. This event so impressed Pascal that he decided that this was an act of God and became a true believer.

Following an accident at the Neuilly bridge where the horses plunged over the parapet but the carriage miraculously survived in 1654, Pascal abandoned mathematics and physics for philosophy and theology.

On November 23, 1654 Pascal had a dramatic near death experience during a lighting storm while crossing a bridge in Paris; he wrote about it [in a document] eventually called the Memorial, which he sowed on the inside label of his coat.

Sometime around [1654] he nearly lost his life in an accident. The horses pulling his carriage bolted and the carriage was left hanging over a bridge above the river Seine. Although he was rescued without any physical injury, it does appear that he was much affected psychologically. Not long after he underwent another religious experience, on 23 November 1654, and he pledged his life to Christianity.

It’s interesting to learn that “light flooded his room” at the moment of Pascal’s conversion (this is especially valuable information since Pascal himself never mentioned the incident to anyone), and that there was a lightning storm, and that his horses “got scared and jumped over the wall”.  It’s also worth noting that some authors say the horse incident actually occurred on November 23, the date of the memorial, whereas others imply that the incident occurred some time prior to Pascal’s night of fire. 

One of the most informative descriptions I’ve found is from the 1911 edition of the Encyclopedia Britannica:

Jacqueline represents the retirement as the final result of a long course of dissatisfaction with mundane life. But there are certain anecdotic embellishments of the act which are too famous to be passed over, though they are in part apocryphal. It seems that Pascal in driving to Neuilly was run away with by the horses, and would have been plunged in the river but that the traces fortunately broke. To this, which seems authentic, is usually added the tradition (due to the abb Boileau) that afterwards he used at times to see an imaginary precipice by his bedside, or at the foot of the chair on which he was sitting. Further, from the 23rd of November 1654 dates the singular document usually known as Pascal’s amulet, a parchment slip which he wore constantly about him, and which bears the date followed by some lines of incoherent and strongly mystical devotion.

According to this account, the basic facts are that Pascal was dissatisfied with his life, and experienced a conversion.  All the rest is described as “anecdotic embellishment”, although the article does say the horse story “seems authentic”.  Does this mean there is external evidence to support the story, or does it just mean that the story seems intrinsically plausible?  On another point, the characterization of Pascal’s memorial as “incoherent” seems a bit harsh.

Herbert Westren Turnbull (who was a student of Rouse Ball in college) tells the story of Pascal’s conversion in “The Great Mathematicians” (1940) this way

A … conversion took place … arising from a narrow escape in a carriage accident.  Henceforth Pascal led a life of self-denial and charity, rarely equaled and still more rarely surpassed.

This is fairly subdued in its description of the horse accident, but Turnbull’s appraisal of Pascal’s selflessness following his conversion seems grossly over-stated.  By all accounts Pascal spent most of the rest of his life writing anti-Jesuit polemics and defending the Jansenists.  Are these considered to have been charitable works?  Also, it must be admitted that Pascal lapsed back into mathematics for a brief period in 1658 and 1659, supposedly prompted by a toothache.  According to Carl Boyer

One night in 1658 a toothache or illness prevented him from falling asleep, and as a distraction from the pain he turned to the study of the cycloid.  Miraculously, the pain eased, and Pascal took this as a sign from God that the study of mathematics was not displeasing to Him.

One of the things that Pascal had found reprehensible about the life of the scientist was the competitive aspect, the desire for reputation, so after his conversion he chose to write anonymously using pseudonyms.  For example, his Lettres provincinciales was written under the pseudonym Louis de Montalte.  He was so proud of his results on the cycloid that he issued two challenge problems as a contest for other mathematicians, then decided none of the entries was deserving of a prize, and published his own solutions, under the pseudonym Amos Dettonville (which is an anagram of Louis de Montalte with u = v).  During several months from 1658 and 1659 Pascal wrote on other mathematical topics, mostly related to the cycloid, including A Treatise on the Sines of a Quadrant of a Circle, in which he gave a method for determining the area under a circular arc.  It’s hard to imagine that anyone was ever in doubt as to the author’s identity, so Turnbull’s claim that Pascal, after his conversion, led a life of self-denial and charity “rarely equaled and still more rarely surpassed” seems like an exaggeration.  The cycloid controversy made Pascal realize that he hadn’t yet freed himself from competitiveness and the love of fame, so he resolved once again to have no more scientific discourse.  He died three years later.

Incidentally, speaking of revelations, about ten years after Pascal’s death, Leibniz was reading Pascal’s 1659 paper on the area under a circular arc, and “a light suddenly burst upon him”.  At this moment, looking at Pascal’s diagram, Leibniz realized that the tangent (derivative) was determined by dividing by the difference between the ordinates, and the quadrature (integral) was determined by multiplying by that same difference, and that, therefore, these two operations were the reciprocals of each other, i.e., the fundamental theorem of calculus. 

It was right there in the diagram, but apparently Pascal didn’t see it.  Leibniz wrote to James Bernoulli that “sometimes Pascal seemed to have had a bandage over his eyes”.

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