1 Cat: Meow! Meow!
2 Isaac Newton: That darn cat. I shall have to invent some apparatus to allow it to enter and leave as it desires without my intervention.
3 Isaac Newton: Some sort of cunning flap arrangement in the door, through which the cat may effect its own ingress and egress.
4 Cat: {thinking} This guy is a much better owner than Schrödinger.

Isaac Newton did indeed invent the cat flap. Or at least popular legend has it - the true inventor is probably lost to history.

Although given how clever Newton was, it certainly isn't terribly far-fetched.

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2024-07-13 Rerun commentary: There is written evidence of cat doors as far back as Chaucer in the 14th century. In The Canterbury Tales, Chaucer wrote as part of "The Miller's Tale" (331-334):

But al for noghte, he herde nat a word.
An hole he foond, ful lowe upon a bord,
Ther as the cat was wont in for to crepe,
And at that hole he looked in ful depe,

And there are extant doors with cat holes dating back to the 15th century, such as this one.

One may reasonably expect that the idea of cat doors was around much earlier though.

A reader writes that the French word for "cat door", chatière, is attested in text as far back as 1269-1278, providing this etymology.