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Newton’s Cats |
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I have set my life upon a cast, |
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And I will stand the hazard of the die: |
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I think there be six Richmonds in the field; |
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Five have I slain to-day instead of him. |
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A horse! a horse! my kingdom for a horse! |
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Shakespeare |
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The most famous cat in theoretical physics is Schrodinger’s, but there is also a cat story associated with another great physicist, Isaac Newton. As the story was told to me by my high school physics teacher, Newton cut a small hole in his door for his cat to go in and out as it pleased. Later the cat had a litter of three kittens, so Newton cut three more holes in the door, so they could all go in and out freely. |
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I’ve subsequently learned that this version of the story is non-standard. According to the standard version, Newton cut just one additional door, smaller than the first, for the kittens. On this account, Newton’s conceptual mistake is that he failed to realize a smaller cat didn’t need a smaller door, since it could obviously fit through the larger door. But this seems to miss the main point (or what should be the main point) of the story, which is that additional cats don’t need any additional doors at all, because they can pass through sequentially, rather than all at once. |
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Newtonian physics was predicated on the idea that we reside in three-dimensional space. Time was not regarded as another dimension. After learning special relativity I assumed that the story about Newton’s cats had been intended to illustrate the fact that, even though the single cat door is a single point in space, it occupies a range of events in spacetime. Thus Newton’s conceptual mistake is failing to recognize that the time dimension enables the cats to pass through the same point in space at different times, i.e., different events in four-dimensional spacetime. |
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Surprisingly, none of the commentators on this (obviously apocryphal) story has ever mentioned that it illustrates a point about physics. The story is always presented purely as just an absurdly stupid thing done by a supposedly brilliant man. |
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There’s no contemporary evidence that Newton ever owned a cat, and in fact some of his biographers stated explicitly that he never owned any pet in his adult life. (He spent some time on a farm as a boy, but was so day-dreamy and listless that he was deemed unsuitable for agricultural work. His uncle declared that Isaac was “fit for nothin but the versity”, so he was sent off to school.) The earliest known account of the cat-door story was apparently 1827, exactly a hundred years after Newton’s death, and even this source mentions the doubtful authenticity (although claiming that the door of Newton’s lodging at Trinity college actually did contain two cat-sized holes). |
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Another famous – and equally doubtful – story about Newton and his alleged pets relates to the notorious fire of the early 1690s that supposedly destroyed Newton’s papers and notes for experiments conducted over many decades. In romantic imagination these papers contained great discoveries that were lost to mankind forever. According to some accounts, the fire was started when Newton’s dog, Diamond, knocked over a candle. When Newton surveyed what had been lost, he allegedly declared “O Diamond, Diamond, thou little knowest the mischief thou hast done." |
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Most historians agree that there could well have been a fire in Newton’s residence around 1693, since some of Newton’s surviving papers from that time period are charred, but there’s no contemporary evidence that he ever owned a dog, let alone that it started a fire. |
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Once, when traveling in England, an old airplane mechanic pointed out to me that we were passing Bosworth Field, where Richard III was defeated in 1485, and the mechanic said this reminded him of a story: A man was passing by a large flat field and noticed several men out in the middle of the field holding a tall ladder vertically while one man with a tape measure tried to climb to the top of the ladder. The climber would get part way up, but then the ladder would tip and tumble to the ground. They tried this repeatedly. Finally, curiosity got the better of the passer by, so he approached the men and asked what they were doing. They said they were trying to measure how tall the ladder was. He asked why they didn’t just lay the ladder on the ground and measure it horizontally. They said “Oh, we already know how long it is, we’re trying to measure how tall it is”. |
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This story is similar to the story about Newton’s cats, in the sense that it could be seen as just an example of stupidity, whereas it actually illustrates an important physical principle, in this case the isotropy of space. To make the relevance even more clear, the men might be running with the horizontal ladder at high speed past a stationary tape measure, to determine the length of the ladder when it is in motion, as distinct from the length of the ladder when it is stationary. Prior to the advent of special relativity this distinction would have seemed absurd, but in fact there is a difference. Indeed, in Minkowski spacetime, the transformation to a moving frame is formally identical to a rotation in space. |
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Newton’s Principia is almost perfectly abstract and mathematical, presented in an austere and impersonal tone… with one exception. To convey the meaning of his “third law of motion” (to every action there is always opposed an equal and opposite reaction), he draws on an image that he might have remembered from his childhood days on the farm: “If a horse draws a stone tied to a rope, the horse (if I may so say) will be equally drawn back towards the stone.” |
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