We have devised a system of writing numbers, using numerals. But being able to write a large number is very different from understanding it.
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Replying to @MathPrinceps @WriterobinRS
Just as we may be able to spell a word we can't define, we may string together numerals to "spell" a number whose meaning we don't know.
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Replying to @MathPrinceps @WriterobinRS
The secret to the meaning of numbers is the same as the secret to the meaning of words: context. Story. Narrative. Numbers act and interact.
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Replying to @MathPrinceps @WriterobinRS
Understanding a number is like knowing a person. Extensive experience of the way numbers behave confers understanding. Nothing else does.
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Replying to @MathPrinceps @WriterobinRS
One thing especially deserves emphasis: numbers are beautiful. Their beauty is obscured by the usual way of representing them symbolically.
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Replying to @WriterobinRS
Ah, now this is something I may be able to convey best with a picture. Take a look at this number, for example.pic.twitter.com/NNNbnJodbE
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Replying to @MathPrinceps @WriterobinRS
This is a beautiful, classical number. Pierre de Fermat, one of the first great students of number, was enchanted by it.
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Replying to @MathPrinceps @WriterobinRS
Most people never realize that this number has this fascinating, multifaceted, 7-based structure. They know it only as 400.
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Replying to @MathPrinceps @WriterobinRS
But to refer to this marvelous creature merely as 400 is to miss all its meaning and magic and poetry. No real mathematician would do this.
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It takes specialized training and extensive experience to recognize the beauty in its conventional representation, as 7^0 + 7^1 + 7^2 + 7^3.
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Replying to @MathPrinceps @WriterobinRS
It is easier to see it in the picture I have shown you. But symbolic representations are powerful. Just as written language is powerful.
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Replying to @MathPrinceps @WriterobinRS
No symbolic representations are needed, though, to appreciate the wonder of this number, which, like the best words, has multiple meanings.
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