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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Replying to @MathPrinceps @WriterobinRS
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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Replying to @MathPrinceps @WriterobinRS
And indeed some of the meaning in a number may be best appreciated by "seeing it," rather than by representing it by symbols of any kind.
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Replying to @MathPrinceps @WriterobinRS
Some of the meaning of a word comes from its sound when pronounced -- and some of the meaning in a number comes from its visible "shape."
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Replying to @MathPrinceps @WriterobinRS
I've stressed that numbers are like words, and the metaphor continues: mathematics is like language, its masterpieces like great narratives.
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Replying to @MathPrinceps @WriterobinRS
Unfortunately, mathematics education aims to teach the written language of mathematics before its students have learned the spoken language.
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Replying to @MathPrinceps @WriterobinRS
Learning a new abstract system of symbolic representation in order to write the words of a language you do not speak is naturally very hard.
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We wait until children have extensive experience of spoken language before we try to teach them to read and write. By then, they're eager.
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Replying to @MathPrinceps @WriterobinRS
To a child of five or six, reading and writing are like magical superpowers. The desire to wield them independently of adults is tremendous.
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Replying to @MathPrinceps @WriterobinRS
The desire to master an abstract symbolic system of representation must spring from a vivid, personal appreciation of its power and utility.
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