Michael at Vsauce, in his superb video on fixed points ( https://m.youtube.com/watch?v=csInNn6pfT4), asserts that the reason you eventually end up with 4 if you iterate the operation "spell the word and count the letters" is that 4 is the only fixed point of this map. This neglects the possibility of cycles. Can anyone find a language in which the spell-and-count map contains one or more cycles of length greater than 1? There is some ill-definedness of the spell-and-count map in English, and probably other languages too; e.g., 101 is both "one hundred one" and "one hundred and one". There's also the matter of the British billion vs. the American billion. All such variants are legitimate for purposes of my question. Jim Propp
trois cinq quatre six On 04-Oct-16 10:16, James Propp wrote:
Michael at Vsauce, in his superb video on fixed points ( https://m.youtube.com/watch?v=csInNn6pfT4), asserts that the reason you eventually end up with 4 if you iterate the operation "spell the word and count the letters" is that 4 is the only fixed point of this map. This neglects the possibility of cycles. Can anyone find a language in which the spell-and-count map contains one or more cycles of length greater than 1?
There is some ill-definedness of the spell-and-count map in English, and probably other languages too; e.g., 101 is both "one hundred one" and "one hundred and one". There's also the matter of the British billion vs. the American billion. All such variants are legitimate for purposes of my question.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Also. "cuatro seis" in Spanish. I suspect that all languages with advanced numeral systems have a threshold number, above which ever numeral has fewer letters than its value. I think this threshold in English is 4. On Tue, Oct 4, 2016 at 11:14 AM, Mike Speciner <ms@alum.mit.edu> wrote:
trois cinq quatre six
On 04-Oct-16 10:16, James Propp wrote:
Michael at Vsauce, in his superb video on fixed points ( https://m.youtube.com/watch?v=csInNn6pfT4), asserts that the reason you eventually end up with 4 if you iterate the operation "spell the word and count the letters" is that 4 is the only fixed point of this map. This neglects the possibility of cycles. Can anyone find a language in which the spell-and-count map contains one or more cycles of length greater than 1?
There is some ill-definedness of the spell-and-count map in English, and probably other languages too; e.g., 101 is both "one hundred one" and "one hundred and one". There's also the matter of the British billion vs. the American billion. All such variants are legitimate for purposes of my question.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Thanks, Mike! Jim On Tuesday, October 4, 2016, Mike Speciner <ms@alum.mit.edu> wrote:
trois cinq quatre six
On 04-Oct-16 10:16, James Propp wrote:
Michael at Vsauce, in his superb video on fixed points ( https://m.youtube.com/watch?v=csInNn6pfT4), asserts that the reason you eventually end up with 4 if you iterate the operation "spell the word and count the letters" is that 4 is the only fixed point of this map. This neglects the possibility of cycles. Can anyone find a language in which the spell-and-count map contains one or more cycles of length greater than 1?
There is some ill-definedness of the spell-and-count map in English, and probably other languages too; e.g., 101 is both "one hundred one" and "one hundred and one". There's also the matter of the British billion vs. the American billion. All such variants are legitimate for purposes of my question.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Latin: tribus-sex-tribus-sex... 3-6-3-6... É.
Le 4 oct. 2016 à 20:33, James Propp <jamespropp@gmail.com> a écrit :
Thanks, Mike!
Jim
On Tuesday, October 4, 2016, Mike Speciner <ms@alum.mit.edu> wrote:
trois cinq quatre six
On 04-Oct-16 10:16, James Propp wrote:
Michael at Vsauce, in his superb video on fixed points ( https://m.youtube.com/watch?v=csInNn6pfT4), asserts that the reason you eventually end up with 4 if you iterate the operation "spell the word and count the letters" is that 4 is the only fixed point of this map. This neglects the possibility of cycles. Can anyone find a language in which the spell-and-count map contains one or more cycles of length greater than 1?
There is some ill-definedness of the spell-and-count map in English, and probably other languages too; e.g., 101 is both "one hundred one" and "one hundred and one". There's also the matter of the British billion vs. the American billion. All such variants are legitimate for purposes of my question.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Portuguese: quatro-seis-quatro-seis... 4-6-4-6... É.
Le 4 oct. 2016 à 20:33, James Propp <jamespropp@gmail.com> a écrit :
Thanks, Mike!
Jim
On Tuesday, October 4, 2016, Mike Speciner <ms@alum.mit.edu> wrote:
trois cinq quatre six
On 04-Oct-16 10:16, James Propp wrote:
Michael at Vsauce, in his superb video on fixed points ( https://m.youtube.com/watch?v=csInNn6pfT4), asserts that the reason you eventually end up with 4 if you iterate the operation "spell the word and count the letters" is that 4 is the only fixed point of this map. This neglects the possibility of cycles. Can anyone find a language in which the spell-and-count map contains one or more cycles of length greater than 1?
There is some ill-definedness of the spell-and-count map in English, and probably other languages too; e.g., 101 is both "one hundred one" and "one hundred and one". There's also the matter of the British billion vs. the American billion. All such variants are legitimate for purposes of my question.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Icelandic: þrjú-fjórir-sex-þrjú-fjórir-sex... 3-4-6-3-4-6... É.
Le 4 oct. 2016 à 20:33, James Propp <jamespropp@gmail.com> a écrit :
Thanks, Mike!
Jim
On Tuesday, October 4, 2016, Mike Speciner <ms@alum.mit.edu> wrote:
trois cinq quatre six
On 04-Oct-16 10:16, James Propp wrote:
Michael at Vsauce, in his superb video on fixed points ( https://m.youtube.com/watch?v=csInNn6pfT4), asserts that the reason you eventually end up with 4 if you iterate the operation "spell the word and count the letters" is that 4 is the only fixed point of this map. This neglects the possibility of cycles. Can anyone find a language in which the spell-and-count map contains one or more cycles of length greater than 1?
There is some ill-definedness of the spell-and-count map in English, and probably other languages too; e.g., 101 is both "one hundred one" and "one hundred and one". There's also the matter of the British billion vs. the American billion. All such variants are legitimate for purposes of my question.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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participants (4)
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Allan Wechsler -
Eric Angelini -
James Propp -
Mike Speciner