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홍차넷
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티타임
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- 다양한 주제에 대해 자유롭게 글을 작성하는 게시판입니다.
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전체기타일상/생각꿀팁/강좌방송/연예도서/문학영화의료/건강문화/예술경제생활체육과학/기술철학/종교정치요리/음식역사여행육아/가정IT/컴퓨터음악창작게임스포츠사회오프모임
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| Date |
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| Name | 다시갑시다 |
| Link #1 | http://redtea.kr/?b=12&n=412 |
| Link #2 | https://phys.org/news/2017-04-anumeric-people-language-words.html |
| Subject | 자연수의 자연스러움 |
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최근에 추게에도 올라간 글 [음수x음수는 왜 양수인가요?] (링크: https://new.redtea.kr/?b=12&n=412) 에서 제가 와인하우스님의 대댓글에 대한 답으로 숫자의 본질에 대한 드립을 던졌었습니다 (링크: https://new.redtea.kr/?b=12&n=412&c=9580). 그런데 이 드립이 순수하게 드립은 아니였어요. 적어도 인간이라는 동물에게 숫자는 자연스러운 개념은 아니라고 합니다. 전에 이야기를 들어보았고 가끔씩 생각하는 개념인데 마침 오늘 이런 글을 읽어서 짧게 써봅니다: https://phys.org/news/2017-04-anumeric-people-language-words.html 숫자가 자연스러운 개념인지 아닌지를 확인하는 방법으로는 숫자의 개념을 사람들이 어떻게 이해하느냐를 비교해봐야할겁니다. 그리고 이중에서 가장 흥미로운 케이스들은 숫자의 개념이 희미한 사람들이겠죠. 숫자의 개념이 희미한것을 어떻게 아냐고요? 그 사람들이 사용하는 언어를 보면 알수가있다고합니다. 현재 주류 언어중에 숫자가 없는 언어들은 찾기 힘들지만, 아직도 아마존 깊은곳에서 사는 소수부족등 몇몇 언어들은 숫자체계가 전무하거나 (anumeric), 거의 전무한 (nearly anumeric) 경우가 있다고합니다. 그리고 이 사람들과의 교류를 통해서 인류와 숫자간의 관계를 유추해보는거죠. 이렇게 수체계가 없다시피한 생활을 해온 사람들은 대체로 1,2,3 이상의 숫자를 이해하는것 자체에 어려움을 느낀다고합니다. 과일 4개, 5개, 6개의 구분이 애매모호함은 물론이요, 과일 4개가 정확히 무엇을 뜻하는지조차 햇갈려한다는거죠. 예를 들어서 과일 4개를 보여주고 그게 눈에서 보이지 않게 바구니로 덮은후에, "바구니에서 과일을 하나씩 뺄테니, 바구니안에 과일이 없어질때 나에게 알려달라"라는 간단한 실험도 힘들어한다고합니다. 다큰 성인이 말이죠. 그렇다고 이 사람들이 지적장애가있거나 하다고 볼수는 없습니다. 자신들의 주생활터전인 아마존의 생태계의 변화와 이해 같은면에서는 굉장히 해박하고 논리정연한 모습을 보여준다고하니까요. 다만 숫자를 세는데에있어서 '어려움'을 겪는것이죠. 그리고 이렇게 3보다 큰수에 대한 햇갈림은 아직 언어를 완전히 습득하지 못한 어린아이들 사이에서도 흔히발견할수있다고합니다. 저 아마존의 부족들도 그렇고 아이들도 그렇고 수가 커진다고 수의 개념이 없어지는건 아니라고합니다. 예를 들어서 8개랑 16개중에 뭐가 더 많냐, 그러면 16개가 더 많다는 자각은 할수있지만 16개가 8개보다 8[개]라는 정확한 측정단위만큼 크다는 개념을 형성시키는데에 어려움을 겪는다는거죠. 보통 아이들이 3보다 큰수를 처음 배우는 방법은 그저 [사, 오, 육, 칠, 팔, 구, 십...]등 단어가 같이 이어지기 때문에 그런게있다는것을 그냥 받아들이고서 점차 실생활에서 숫자의 사용을 접하면서 숫자가 무엇인지를 이해하기 시작한다고합니다. 그 과정을 우리사회의 99.99999%의 일원들이 비슷한 시기에 받아들이기에 자연스럽다고 느낄뿐이죠. 그리고 다행히도? 우리가 사용하는 십진법은 최초이자 가장 보편적인 도구인 손가락10개와 맞물려있죠. 우리 숫자의 언어체계도 이에 기반해있고요 (십일, 열둘, twenty/two-ten three, 등등). 그렇기에 아이들이 숫자를 처음 배울때 10개 이상의 개념을 이해하는데 한번 걸림돌이 생기는건 전혀 이상한일이 아닌것일수도있다는거죠. 손가락으로만 숫자를 새는 아이들에게 아직 숫자란 개념이 자리잡은게 아니라 그저 자신의 손가락을 관측하고있는것이라고 볼수있으니까요. 그보다 큰수를 이해시키기 위해서 주위 사람들의 손가락이나 본인의 발가락 등을 소환시켜야만하는것도 다 이유가있는거죠. 이런 생각을해보면 좀 더 나이가 들어서 맞닥트리는 수학적 고민들에 대해서 다시 생각해볼 기회가 생기지 않나 싶습니다. 캡틴아메리카님의 글에서 나온 음수의 이해, 댓글에서 언급된 허수의 이해, 그리고 더 나아가서 수학이 어려운 이유. 수학은 흔히 '자연의 언어'와 같이 대원리적 불변의 법칙과 같은류의 언어로 표현되죠. 그리고 많은 사람들이 그렇게 이해를하고있다고 느낍니다. 예를 들어서 우리가 어린나이부터 지적능력이 굉장히 뛰어나다고 판단하는 친구들 중에 수학을 잘하는 친구들이 많다고 느끼는데, 그런 선입견이 영향을 끼치는게 아닌가...하는 생각이죠. 우리가 사용하는 숫자의 (실수에 양수인 자연수) 태반이 사람에게 자연적으로 이해가되는게 아니라 반복된 사용과 훈련에 의해서 사회인들 대부분이 동의하는 의미를 지니고있는 개념이라면, 음수나 허수와 같은 좀 더 복잡한 숫자에 대한 이해, 수학에 대한 이해와 교육에 대한 접근도 그걸 인지해야한다고 느낍니다. 하지만 보통 저정도 시점에서 "자연적으로 수학을 잘하는 사람/못하는 사람"으로 나뉘게 되죠. 아쉬워요, 수학을 애초에 태어날때부터 이해한다고 할만한 사람은 거의 없는것이고, 원래 수학이란 학문을 그때까지 얼마나 반복적이고 체계적으로 경험해보았냐가 '수학적 재능'의 실체일수도있다는거니까요. 조금 더 나아가보면 수학과 숫자의 이해라는것이 얼마나 자연적이고 절대적인지에 대해서 생각해볼 기회 정도는 있어야한다고 믿습니다. 수학은 우리가 알고있는 자연의 패턴과 논리를 설명하는 최고의 방법이지만 그 자체가 자연과 동일시될수있는지 말이죠. Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 133 Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 146 Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 161 7
이 게시판에 등록된 다시갑시다님의 최근 게시물
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Warning: Use of undefined constant level - assumed 'level' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 577
Warning: Use of undefined constant grant_delete - assumed 'grant_delete' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 577
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 425
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 429
Warning: Use of undefined constant use_formmail - assumed 'use_formmail' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 605
Warning: Use of undefined constant name - assumed 'name' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 599
Warning: Use of undefined constant name - assumed 'name' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 599
Warning: Use of undefined constant name - assumed 'name' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 600
Warning: Use of undefined constant name - assumed 'name' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 600
Warning: Use of undefined constant is_admin - assumed 'is_admin' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 605
Warning: Use of undefined constant is_admin - assumed 'is_admin' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 605
Warning: Use of undefined constant is_admin - assumed 'is_admin' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 609
Warning: Use of undefined constant is_admin - assumed 'is_admin' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 609
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 614
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 616
Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 618
Warning: Use of undefined constant name - assumed 'name' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 618
Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 612
Warning: Use of undefined constant name - assumed 'name' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 612
Warning: Use of undefined constant reg_date - assumed 'reg_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 620
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 628
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 628
Warning: Use of undefined constant HTTP_HOST - assumed 'HTTP_HOST' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 640
Warning: Use of undefined constant name - assumed 'name' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 644
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 646
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/view.php on line 646
Warning: Use of undefined constant HTTP_HOST - assumed 'HTTP_HOST' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/cmt_replace.php on line 3
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 6
Warning: Use of undefined constant file_name - assumed 'file_name' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 28
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 65
80595 class="iamcmt" style="display:none;"> Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 66
80595 class='vcm '>
Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 70
Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 71
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 76
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 117
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 118
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 119
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 120
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 121
80595'> 유리소년
Warning: Use of undefined constant mod_date - assumed 'mod_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 133
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 140
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 140
Warning: Use of undefined constant reg_date - assumed 'reg_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 142
17/04/27 01:52
80595>삭제 주소복사
Warning: Use of undefined constant level - assumed 'level' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 150
수학은 학부만 전공하고 때려치운 허섭입니다만
<자연수>의 정의가 <자연을 묘사하는 데 흔히 사용되는 수>라면
양의 정수에 한정하는 건 맞지 않죠. 복소수까지를 그렇게 부르는 게 맞을 겁니다.
수학자들 사이에서 <셈수counting number>라고 이름을 바꿔버리자는 논의가 진지하게 있었죠.
어휘의 유사성으로 인해 countable 개념과 헷갈릴 수 있다는 이유로 폐기되었습니다만.
Warning: Use of undefined constant level - assumed 'level' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 158
Warning: Use of undefined constant password - assumed 'password' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 166
Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 171
Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 172
Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 172
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 173
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 173
Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 173
<자연수>의 정의가 <자연을 묘사하는 데 흔히 사용되는 수>라면
양의 정수에 한정하는 건 맞지 않죠. 복소수까지를 그렇게 부르는 게 맞을 겁니다.
수학자들 사이에서 <셈수counting number>라고 이름을 바꿔버리자는 논의가 진지하게 있었죠.
어휘의 유사성으로 인해 countable 개념과 헷갈릴 수 있다는 이유로 폐기되었습니다만.
Warning: Use of undefined constant level - assumed 'level' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 158
Warning: Use of undefined constant password - assumed 'password' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 166
Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 171
Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 172
Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 172
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 173
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 173
Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 173
80595>
80595>
