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After receiving a "brain," the Scarecrow in The Wizard of Oz famously says the following:

“The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side!”

Which as generations of know-it-alls have noted, is incorrect. That's a right triangle, you idiot!

Over the years I have a number of conflicting explanations for the mistake, all treated as the real reason. Among them:

  • this was intentional, and is intended to show the scarecrow is in fact as dim as always
  • this was intentional, because the filmmakers thought the word isosceles sounded "smarter"
  • this was mistake on the part of the actor, and the script said "right triangle."
  • this was a mistake on the part of the filmmakers

Is there any firm evidence or statements from those involved about which explanation is correct?

TenthJustice
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3 Answers3

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There is a version of the script that had more to say to make it obvious that it was intentional, according to:

Hollywood Science: The Next Generation, From Spaceships to Microchips

(ISBN 331954215X, 9783319542157; Kevin R. Grazier, Stephen Cass; Springer, 2017)

So I went back to the scripts I’ve got here, and we can specially credit Noel Langley with that part of the script. I’ve got a draft dated April 18, 1938 and these are changes to a script he already did.

           SCARECROW
The sum of the square roots of any 
two sides of an isosceles triangle
 is equal to the square root of the
 remaining side: H-2-O plus H-2-S-
O-4 equals H-2-S-O-3 using pi-r
 squared as a common denominator. 
Oh joy! Oh rapture! What a brain!

—perhaps the blend of chemistry with geometry in that manner was too obvious. That line does, however, remove much of the doubt that the Scarecrow’s faulty exposition on the nature of the isosceles triangle is intentional on the part of the writers, and it also makes it clear that, in essence, the Wizard did very little.

blobbymcblobby
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Seem pretty obvious that the Wizard, being a fake himself, could only give fake gifts -- he sort of says this. The scarecrow obviously did have brains and perhaps armed with a belief in his own abilities would eventually become genuinely educated. Of course the Tin Man had a heart or he would not have wanted one. The Cowardly Lion just, like the others, needed to believe in himself.

Dorothy was given a real magical gift because the witches of Oz were magical. Why they put up with the Wizard I'll never know; perhaps the Good Witch was just being kind or needed someone to rule Oz although she would step in if necessary as she indeed did in Dorothy's case.

releseabe
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    this answer is more to the point of the story. The wizard is a fraud and what people needed was confidence. This particularly fits the written work behind the film, which I believe was a commentary against the gold standard for US currency (the gold road to the house of green is a hollow fake, use confidence = fiat trust instead) – Mike M Sep 27 '22 at 14:46
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    @MikeM The monetary policy thesis is a really interesting theory, and one I hadn't read before, but it doesn't seem to be a mainstream or confirmed interpretation. – Jeff Bowman Sep 27 '22 at 17:54
  • So the Scarecrow may be the first cinematic example of the Dunning-Kruger effect! – Cristobol Polychronopolis Sep 27 '22 at 18:14
  • @JeffBowman: I never found the monetary thing compelling but maybe someone who lived in those days would have. Or even Baum was subconsciously affected by what seems to me now to be a quaint controversy given how far away we are from silver and gold-backed money. There are of course plenty of people who still want gold-backed currency -- very complex issues, out of scope for here and way too complex for me. One thing: no matter how much gold is worth per ounce, physically holding it and moving it is a big expense. When US bought AK, tons of gold were sent to Russia. – releseabe Sep 27 '22 at 22:14
  • In that case, "tons" was literal: The payment was $7.2 million, with the price of gold being set at $27.86 per troy ounce, so that works out to 258 435 ounces, or 8.038 metric tons, of gold. – dan04 Sep 28 '22 at 00:18
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    @dan04: yup: it had to stored, transported and guarded and then stored again. Probably had to be counted and authenticated (at least weighed in those less sophisticated days). I bet the total cost was easily 1 percent of value. – releseabe Sep 28 '22 at 00:29
  • I went back and read the corresponding chapters from the original Frank L. Baum novel. It doesn't have a similar quote, but it's quite clear that the wizard knows he's a fraud, and that he believes that all the scarecrow needs is to believe in himself. He already can think, but lacks experience, which he is gaining every day. The scarecrow spends the next few days thinking thoughts that he doesn't share because he knows no one will understand them. – user1629060 Sep 28 '22 at 13:27
  • WRT why the witches put up with him: In the book, the Wizard says that the good witches tolerated him because they were good and he was trying to be a good ruler of the Emerald City. The evil witches left him alone because they thought he was more powerful than them, which is why it was important for him to maintain the fraud of being a Wizard, even though he was really a humbug. – user1629060 Sep 28 '22 at 13:31
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    thanks, @JeffBowman -- that, in the link, does sound like what I learned a long time ago and I see it may have been more clever than well-supported – Mike M Sep 28 '22 at 18:07
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    To back up that that it was well known the wizard was a fraud, the lyrics to America's "Tin Man" from the 1970's has the line, "But Oz never did give nothing to the Tin Man; That he didn't, didn't already have." – JS. Sep 29 '22 at 01:44
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    Just an aside: There remain, according to IMDB, at least a couple cast members from the movie. Both were kids in crowd scenes, villagers and/or Munchkins and both are over 90. I think one cast member from Gone With the Wind and probably some other surprises. – releseabe Sep 30 '22 at 14:14
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I don't think it's a invalidation of the scarecrow. I think it's saying in fantasy land that math is fantasy too. Or it's being not serious about math, when the moral of the story was the part that was supposed to shine.

Alex
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    perhaps, but the other answers make a good point: it's meant to invalidate the Wizard's powers. – Luciano Sep 28 '22 at 08:27