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This question at the Movies and TV Stack Exchange seems to be off topic since they don't do story identification questions.

Is there an episode in the genre of the Twilight Zone or Outerlimits where a scientist was asked to make a pegasus? He was trying to explain to his physics-naive client that he could give a horse wings, but it would be to large and heavy to fly.

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I believe this may be the episode "Jerry Was A Man" from the series "Masters of Science Fiction," an adaptation of a story by Robert A. Heinlein.

The short story includes a conversation just like what you describe:

"Siddown, young man!" Cargrew ordered. "Take your trade to those thumb-fingered idiots if you wish—but I warn you they couldn’t grow wings on a grasshopper. First you listen to me."

"We can grow anything and make it live. I can make you a living thing—I won't call it an animal—the size and shape of that table over there. It wouldn’t be good for anything, but it would be alive. It would ingest food, use chemical energy, give off excretions, and display irritability. But it would be a silly piece of manipulation. Mechanically a table and an animal are two different things. Their functions are different, so their shapes are different. Now I can make you a winged horse—"

"You just said you couldn’t."

"Don’t interrupt. I can make a winged horse that will look just like the pictures in the fairy stories. If you want to pay for it; we’ll make it—we’re in business. But it won’t be able to fly."

"Why not?"

"Because it’s not built for flying. The ancient who dreamed up that myth knew nothing about aerodynamics and still less about biology. He stuck wings on a horse, just stuck them on, thumb tacks and glue. But that doesn’t make a flying machine. Remember, son, that an animal is a machine, primarily a heat engine with a control system to operate levers and hydraulic systems, according to definite engineering laws. You savvy to aerodynamics?"

"Well, I’m a pilot."

"Hummph! Well, try to understand this. A horse hasn’t got the heat engine for flight. He’s a hayburner and that’s not efficient. We might mess around with a horse’s insides so that he could live on a diet of nothing but sugar and then he might have enough energy to fly short distances. But he still would not look like the mythical Pegasus. To anchor his flying muscles he would need a breast bone maybe ten feet long. He might have to have as much as eighty feet wing spread. Folded, his wings would cover him like a tent. You’re up against the cube-square disadvantage."

This summary of the TV episode seems to indicate that scene was indeed included:

The Von Vogels recount being in their club and getting into an argument with another member about his dog, which he claims is a “plasto-biological hybrid,” custom-made to have six legs. Jealous, the Von Vogels want to get back at him by purchasing a “designer animal” more “impressive” than his, and decide that they can accomplish this with a creature made in the image of the mythological Pegasus. Instead, Cargrew produces a miniature adult elephant barely a foot high, which he has dubbed “Napoleon,” able to both read and write. However, Cargrew keeps refusing their request for a Pegasus, explaining that while he could make a horse with wings, it would be unable to fly. Cargrew laments aloud that he is wasting his talents on supplying rich people with genetically-engineered curiosities instead of curing diseases or improving the world in any meaningful way.

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The discussion of the plausibility of creating a living Pegasus reminds me of the classic Robert A. Heinlein science fiction story "Jerry Was a Man", Thrilling Wonder Stories, October, 1947, which I remember did appear as an episode of a science fiction anthology television series.

Here is a link to a list of all the publications of "Jerry Was A Man".

And this Wikipedia page identifies the televisions adaptation of "Jerry Was a Man" as the August 18, 2007 episode of Masters of Science Fiction.

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