{ "export": { "source": "https://urth.darkrealm.vip/thread/urth/5085", "note": "Exported from an unofficial mirror of a public mailing list. Copyright in each message remains with the person who wrote it. Email addresses are obscured as `user at host`, the form the original archive published. This file was rebuilt from parsed fields rather than retained headers, so it is faithful in content but not byte-exact.", "addresses": "obscured as 'user at host'" }, "archive": "urth", "thread": { "id": 5085, "subject": "Whorl arithmetic -- Fibonacci sequence", "messages": 4, "voices": 3, "first": "2008-07-03T20:43:31+00:00", "last": "2008-07-04T13:20:39+00:00" }, "messages": [ { "message_id": "<1bf4dd40807031343s37b07578w6b671774db006c0c@mail.gmail.com>", "from": { "name": "Dave Tallman", "address": "davetallman at msn.com" }, "date": "2008-07-03T20:43:31+00:00", "subject": "(urth) Whorl arithmetic -- Fibonacci sequence", "in_reply_to": null, "reply_link": null, "blocks": [ { "kind": "text", "depth": 0, "text": "In CotLS chapter 5, Maytera Marble/Rose thinks \"... as predictably as the\nsixth term in a Fibonacci series of ten was an eleventh of the whole.\"\n\nThis is peculiar, because the Fibonacci series is:\n1. 1\n2. 1\n3. 2\n4. 3\n5. 5\n6. 8\n7. 13\n8. 21\n9. 34\n10. 55\n\nThe sum of the first ten terms is 143 = 11*13, so it's the seventh term that\nis the eleventh of the whole, not the sixth.\nThe sum of the first nine terms is 88 = 11*8, which means the sixth term is\nthe eleventh of the whole, as stated.\n\nIn base 9, our nine is represented as 10. To make the statement correct, we\nhave to translate the \"series of ten\" in base-9 arithmetic and the\n\"eleventh\" in the decimal system.\n\nDid the Maytera make a mistake, or did Wolfe, or should we revive the old\nbase-9 controversy about Whorl arithmetic? There's another passage where the\nchildren seemingly make trvial arithmetic mistakes, as pointed out by\nBorski.\n\nIn _Nightside the Long Sun_, on p. 29, Wolfe has Maytera Marble presiding" }, { "kind": "quote", "depth": 1, "text": "over a mathematics lesson, \"watching the children take nineteen from\ntwenty-nine and get nine, add seven and seventeen and get twenty-three.\"\nThis, however, is only possible in a base 9 numbering system, and a strange\none at that, since a conventional base 9 system would only include the\ndigits 0 to 8 (there should thus no 9, 19, or 29)." }, { "kind": "text", "depth": 0, "text": " Both statements could be correct if done in base 9, provided we solved the\n\"9\" representation problem and allow mixed translations:\n (28+1)(base 9) - (18+1)(base 9) = 9 (decimal)\n 7(base 9) + 17(base 9) = 23 (decimal)\n\nThere might be some more clues involving costs with cards and bits, if we\nlook for them." } ] }, { "message_id": "<978305.88928.qm@web83702.mail.sp1.yahoo.com>", "from": { "name": "John Smith", "address": "jsmith2627 at att.net" }, "date": "2008-07-03T20:57:46+00:00", "subject": "(urth) Whorl arithmetic -- Fibonacci sequence", "in_reply_to": "<1bf4dd40807031343s37b07578w6b671774db006c0c@mail.gmail.com>", "reply_link": "header", "blocks": [ { "kind": "text", "depth": 0, "text": "I thought that this was just a joke. The teacher is\ngetting old and making mistakes." }, { "kind": "quote", "depth": 1, "text": "--- Dave Tallman wrote:\nIn CotLS chapter 5, Maytera Marble/Rose thinks \"...\nas predictably as the\nsixth term in a Fibonacci series of ten was an\neleventh of the whole.\"\n\nThis is peculiar, because the Fibonacci series is:\n1. 1\n2. 1\n3. 2\n4. 3\n5. 5\n6. 8\n7. 13\n8. 21\n9. 34\n10. 55\n\nThe sum of the first ten terms is 143 = 11*13, so\nit's the seventh term that\nis the eleventh of the whole, not the sixth.\nThe sum of the first nine terms is 88 = 11*8, which\nmeans the sixth term is\nthe eleventh of the whole, as stated.\n\nIn base 9, our nine is represented as 10. To make\nthe statement correct, we\nhave to translate the \"series of ten\" in base-9\narithmetic and the\n\"eleventh\" in the decimal system.\n\nDid the Maytera make a mistake, or did Wolfe, or\nshould we revive the old\nbase-9 controversy about Whorl arithmetic? There's\nanother passage where the\nchildren seemingly make trvial arithmetic mistakes,\nas pointed out by\nBorski.\n\nIn _Nightside the Long Sun_, on p. 29, Wolfe has\nMaytera Marble presiding\nover a mathematics lesson, \"watching the children\ntake nineteen from\ntwenty-nine and get nine, add seven and seventeen\nand get twenty-three.\"" }, { "kind": "quote", "depth": 2, "text": "This, however, is only possible in a base 9\nnumbering system, and a strange\none at that, since a conventional base 9 system\nwould only include the\ndigits 0 to 8 (there should thus no 9, 19, or 29)." }, { "kind": "quote", "depth": 1, "text": " Both statements could be correct if done in base 9,\nprovided we solved the\n\"9\" representation problem and allow mixed\ntranslations:\n (28+1)(base 9) - (18+1)(base 9) = 9 (decimal)\n 7(base 9) + 17(base 9) = 23 (decimal)\n\nThere might be some more clues involving costs with\ncards and bits, if we\nlook for them." }, { "kind": "quote", "depth": 2, "text": "_______________________________________________" } ] }, { "message_id": "<486DA316.8040402@lpthe.jussieu.fr>", "from": { "name": "Paul Zinn-Justin", "address": "pzinn at lpthe.jussieu.fr" }, "date": "2008-07-04T04:12:06+00:00", "subject": "(urth) Whorl arithmetic -- Fibonacci sequence", "in_reply_to": "<1bf4dd40807031343s37b07578w6b671774db006c0c@mail.gmail.com>", "reply_link": "header", "blocks": [ { "kind": "text", "depth": 0, "text": "Hi,\nFirst post here, as a mathematician I felt compelled to respond...\nUnfortunately your base 9 theory does not work.\nThe reason is, note that in your quote it is never mentioned that one\nshould consider only the *first* terms of the Fibonacci series.\nIn fact, the correct property is\n\"the 7th term in any sequence of 10 successive numbers from the\nFibonacci series is the eleventh of the sum of the sequence\"\nhowever, if you replace 10 with 9 and 7 with 6, the property is no more\ntrue. (in other words, the equality you mention with 88 is a coincidence).\n\nPaul" }, { "kind": "quote", "depth": 1, "text": "Dave Tallman wrote:\nIn CotLS chapter 5, Maytera Marble/Rose thinks \"... as predictably as \nthe sixth term in a Fibonacci series of ten was an eleventh of the whole.\"\n\nThis is peculiar, because the Fibonacci series is:\n1. 1\n2. 1\n3. 2\n4. 3\n5. 5\n6. 8\n7. 13\n8. 21\n9. 34\n10. 55\n\nThe sum of the first ten terms is 143 = 11*13, so it's the seventh \nterm that is the eleventh of the whole, not the sixth.\nThe sum of the first nine terms is 88 = 11*8, which means the sixth \nterm is the eleventh of the whole, as stated.\n\nIn base 9, our nine is represented as 10. To make the statement \ncorrect, we have to translate the \"series of ten\" in base-9 arithmetic \nand the \"eleventh\" in the decimal system.\n\nDid the Maytera make a mistake, or did Wolfe, or should we revive the \nold base-9 controversy about Whorl arithmetic? There's another passage \nwhere the children seemingly make trvial arithmetic mistakes, as \npointed out by Borski.\n\n In _Nightside the Long Sun_, on p. 29, Wolfe has Maytera Marble presiding\n over a mathematics lesson, \"watching the children take nineteen from\n\n twenty-nine and get nine, add seven and seventeen and get twenty-three.\"\n This, however, is only possible in a base 9 numbering system, and a strange\n one at that, since a conventional base 9 system would only include the\n\n digits 0 to 8 (there should thus no 9, 19, or 29).\n\n\n Both statements could be correct if done in base 9, provided we \nsolved the \"9\" representation problem and allow mixed translations:\n (28+1)(base 9) - (18+1)(base 9) = 9 (decimal)\n 7(base 9) + 17(base 9) = 23 (decimal)\n\nThere might be some more clues involving costs with cards and bits, if \nwe look for them.\n\n\n------------------------------------------------------------------------\n\n_______________________________________________" } ] }, { "message_id": "<486E23A7.3020608@gmail.com>", "from": { "name": "Dave Tallman", "address": "davetallman at msn.com" }, "date": "2008-07-04T13:20:39+00:00", "subject": "(urth) Whorl arithmetic -- Fibonacci sequence", "in_reply_to": "<486DA316.8040402@lpthe.jussieu.fr>", "reply_link": "header", "blocks": [ { "kind": "quote", "depth": 1, "text": "Paul Zinn-Justin wrote:\nHi,\nFirst post here, as a mathematician I felt compelled to respond...\nUnfortunately your base 9 theory does not work.\nThe reason is, note that in your quote it is never mentioned that one\nshould consider only the *first* terms of the Fibonacci series.\nIn fact, the correct property is\n\"the 7th term in any sequence of 10 successive numbers from the\nFibonacci series is the eleventh of the sum of the sequence\"\nhowever, if you replace 10 with 9 and 7 with 6, the property is no more\ntrue. (in other words, the equality you mention with 88 is a coincidence).\n " }, { "kind": "text", "depth": 0, "text": "Hi Paul, thanks for posting. I can see how it works when I write it out \nsymbolically (a, b, a+b, a+2b,...).\n\nIt looks like Maytera Marble's mistake -- possibly from her aging memory \nor from confusion after her merge with Rose.\n\nIt's still an open question if another base might be used. I think not. \nThere's a place where Marble compares her strength to another chem and \nsays it is 4.25 times stronger than she is. That's a nice fraction in \nbase 10, but not in base 9.\n\nThe number of bits to a card might be 9, though. They are \"small squares \nsheared from so many cards\" (Lake 2). If cards themselves are square \nthen the number of bits per card should be a square number too. They \nwouldn't want to waste the precious card material, and they can't make \ntoo many cuts per card." } ] } ] }