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<html><body>&#272;&acirc;y l&agrave; m&#7897;t c&acirc;u tr&#7843; l&#7901;i cho c&acirc;u h&#7887;i <a href="https://www.quora.com/What-are-the-basic-math-skills-that-everyone-should-know">&#272;&acirc;u l&agrave; nh&#7919;ng k&#297; n&#259;ng to&aacute;n h&#7885;c c&#417; b&#7843;n nh&#7845;t m&agrave; m&#7885;i ng&#432;&#7901;i n&ecirc;n bi&#7871;t?</a>. Kh&aacute; l&agrave; th&uacute; v&#7883; n&ecirc;n m&igrave;nh tr&iacute;ch d&#7851;n l&#7841;i.H&#7887;i: &#272;&acirc;u l&agrave; nh&#7919;ng k&#297; n&#259;ng to&aacute;n h&#7885;c c&#417; b&#7843;n nh&#7845;t m&agrave; m&#7885;i ng&#432;&#7901;i c&#7847;n ph&#7843;i bi&#7871;t?&#272;&aacute;p: Trong giai &#273;o&#7841;n cao tr&agrave;o c&#7911;a cu&#7897;c Chi&#7871;n tranh th&#7871; gi&#7899;i l&#7847;n th&#7913; II, r&#7845;t nhi&#7873;u chi&#7871;n &#273;&#7845;u c&#417; c&#7911;a M&#7929; quay tr&#7903; v&#7873; t&#7915; chi&#7871;n tr&#432;&#7901;ng mang theo h&agrave;ng &#273;&#7889;ng v&#7871;t &#273;&#7841;n b&#7855;n chi ch&iacute;t tr&ecirc;n m&igrave;nh.V&#7883; tr&iacute; c&aacute;c v&#7871;t &#273;&#7841;n ph&acirc;n b&#7889; t&#7853;p trung v&agrave;o c&aacute;c v&ugrave;ng kh&aacute;c nhau tr&ecirc;n m&aacute;y bay, ch&#7911; y&#7871;u l&agrave; &#273;&#7897;ng c&#417;, th&acirc;n, c&aacute;nh, &#273;u&ocirc;i,...<figure class="image"><img src="https://thefullsnack.com/posts/img/rifle-shot-down-2.png" alt=""></figure>Qu&acirc;n &#273;&#7897;i (Hoa K&#7923;) nh&#7853;n ra r&#7857;ng h&#7885; c&oacute; th&#7875; kh&#7843;o s&aacute;t v&#7883; tr&iacute; c&aacute;c v&#7871;t &#273;&#7841;n b&#7855;n tr&ecirc;n c&aacute;c m&aacute;y bay tr&#7903; v&#7873;, t&#7915; &#273;&oacute; h&#7885; c&oacute; th&#7875; gia c&#7889; nh&#7919;ng v&ugrave;ng n&agrave;o m&agrave; th&#432;&#7901;ng xuy&ecirc;n b&#7883; b&#7855;n tr&uacute;ng nh&#7845;t, t&#7915; &#273;&oacute; th&igrave; h&#7885; c&oacute; th&#7875; gi&#7843;m &#273;&#432;&#7907;c t&#7889;i &#273;a s&#7889; m&aacute;y bay b&#7883; b&#7855;n h&#7841;.H&#7885; t&igrave;m &#273;&#7871;n <a href="https://en.wikipedia.org/wiki/Abraham_Wald">Abraham Wald</a> v&agrave; m&#7897;t v&agrave;i nh&agrave; nghi&ecirc;n c&#7913;u th&#7889;ng k&ecirc; &#273;&#7847;u ng&agrave;nh th&#7901;i &#273;&oacute;, v&#7899;i d&#7919; li&#7879;u h&#7885; &#273;&#432;a ra nh&#432; sau:<figure class="table"><table><thead><tr><th>V&ugrave;ng tr&ecirc;n m&aacute;y bay</th><th>T&#7881; l&#7879; l&#7895; &#273;&#7841;n tr&ecirc;n m&#7897;t feet vu&ocirc;ng</th></tr></thead><tbody><tr><td>&#272;&#7897;ng c&#417;</td><td>1.11</td></tr><tr><td>Th&acirc;n</td><td>1.73</td></tr><tr><td>H&#7879; th&#7889;ng d&#7851;n nhi&ecirc;n li&#7879;u</td><td>1.55</td></tr><tr><td>C&aacute;c ph&#7847;n kh&aacute;c</td><td>1.8</td></tr></tbody></table></figure>D&#7921;a v&agrave;o s&#7889; li&#7879;u n&agrave;y, b&#7841;n ngh&#297; qu&acirc;n &#273;&#7897;i c&#7847;n gia c&#7889; ph&#7847;n n&agrave;o?&#272;a s&#7889; m&#7885;i ng&#432;&#7901;i cho r&#7857;ng n&ecirc;n gia c&#7889; th&acirc;n m&aacute;y bay (v&igrave; c&oacute; t&#7881; l&#7879; &#259;n &#273;&#7841;n cao nh&#7845;t), v&agrave; t&#7845;t c&#7843; &#273;&#7873;u sai.C&acirc;u tr&#7843; l&#7901;i ch&iacute;nh x&aacute;c ph&#7843;i l&agrave; &#273;&#7897;ng c&#417;.Wald nh&#7853;n ra m&#7897;t &#273;i&#7873;u l&agrave;, d&#7919; li&#7879;u m&agrave; ph&iacute;a qu&acirc;n &#273;&#7897;i cung c&#7845;p cho &ocirc;ng kh&ocirc;ng n&oacute;i l&ecirc;n &#273;&#432;&#7907;c v&#7845;n &#273;&#7873;. L&yacute; do m&agrave; t&#7881; l&#7879; b&#7855;n tr&uacute;ng &#273;&#7897;ng c&#417; tr&ecirc;n b&#7843;ng s&#7889; li&#7879;u tr&ecirc;n th&#7845;p r&#7845;t &#273;&#417;n gi&#7843;n. &#272;&oacute; l&agrave; c&aacute;c m&aacute;y bay &#259;n &#273;&#7841;n v&agrave;o &#273;&#7897;ng c&#417; th&#432;&#7901;ng kh&ocirc;ng c&ograve;n quay v&#7873; &#273;&#432;&#7907;c n&#7919;a (vcl).<figure class="image"><img src="https://thefullsnack.com/posts/img/rifle-shot-down.png" alt=""></figure>V&agrave; th&#7921;c t&#7871; l&agrave; ph&#7847;n l&#7899;n c&aacute;c m&aacute;y bay tr&#7903; v&#7873; c&oacute; t&#7881; l&#7879; &#259;n &#273;&#7841;n v&agrave;o th&acirc;n cao h&#417;n n&oacute;i l&ecirc;n m&#7897;t &#273;i&#7873;u l&agrave; th&acirc;n m&aacute;y bay d&ugrave; c&oacute; &#259;n nhi&#7873;u &#273;&#7841;n th&igrave; v&#7851;n c&oacute; kh&#7843; n&#259;ng ch&#7883;u &#273;&#7921;ng cao h&#417;n l&agrave; c&aacute;c b&#7897; ph&#7853;n kh&aacute;c.Wald cho r&#7857;ng ch&#7881; c&oacute; 2 c&aacute;ch gi&#7843;i th&iacute;ch cho s&#7889; li&#7879;u m&agrave; &ocirc;ng &#273;&#432;&#7907;c cung c&#7845;p:<ol><li>M&#7845;y vi&ecirc;n &#273;&#7841;n th&#432;&#7901;ng &#273;&#432;&#7907;c b&#7855;n tr&uacute;ng c&aacute;c ph&#7847;n kh&aacute;c nhi&#7873;u h&#417;n l&agrave; b&#7855;n v&agrave;o &#273;&#7897;ng c&#417;</li><li>&#272;&#7897;ng c&#417; l&agrave; t&#7917; huy&#7879;t c&#7911;a m&aacute;y bay</li></ol>V&agrave; kh&ocirc;ng c&#7847;n ph&#7843;i l&agrave; thi&ecirc;n t&agrave;i th&igrave; m&#7899;i nh&#7853;n ra ngay, c&aacute;ch th&#7913; 2 m&#7899;i l&agrave; c&aacute;ch gi&#7843;i th&iacute;ch ch&iacute;nh x&aacute;c v&#7845;n &#273;&#7873; n&agrave;y. V&agrave; qu&acirc;n &#273;&#7897;i &#273;&atilde; nghe theo l&#7901;i c&#7911;a Wald &#273;&#7875; gia c&#7889; ph&#7847;n &#273;&#7897;ng c&#417;, hi&#7879;u qu&#7843; th&#7845;y ngay, r&#7845;t nhi&#7873;u m&aacute;y bay M&#7929; &#273;&atilde; s&#7889;ng s&oacute;t tr&#7903; v&#7873; sau &#273;&oacute;.M&#7897;t trong nh&#7919;ng k&#297; n&#259;ng to&aacute;n h&#7885;c b&#7883; coi nh&#7865; nh&#7845;t &#273;&oacute; ch&iacute;nh l&agrave; kh&#7843; n&#259;ng th&#7845;u hi&#7875;u &#273;&#432;&#7907;c v&#7845;n &#273;&#7873; &#7849;n gi&#7845;u &#273;&#7857;ng sau nh&#7919;ng ph&#7887;ng &#273;o&aacute;n do c&aacute;c con s&#7889; &#273;&#432;a ra. Abraham Wald &#273;&atilde; gi&#7843;i quy&#7871;t &#273;&#432;&#7907;c v&#7845;n &#273;&#7873; m&aacute;y bay b&#7903;i v&igrave; &ocirc;ng &#7845;y nh&#7853;n ra qu&acirc;n &#273;&#7897;i M&#7929; &#273;&atilde; m&#7855;c sai l&#7847;m khi ph&#7887;ng &#273;o&aacute;n r&#7857;ng d&#7919; li&#7879;u tr&ecirc;n &#273;&#7841;i di&#7879;n cho to&agrave;n b&#7897; t&#7845;t c&#7843; c&aacute;c chi&#7871;n &#273;&#7845;u c&#417;, thay v&igrave; ch&iacute;nh x&aacute;c ph&#7843;i l&agrave; c&aacute;c chi&#7871;n &#273;&#7845;u c&#417; quay tr&#7903; v&#7873; &#273;&#432;&#7907;c.Ng&agrave;y nay, c&oacute; r&#7845;t nhi&#7873;u nh&#7919;ng con s&#7889; &#273;&#432;&#7907;c tr&#432;ng ra tr&ecirc;n truy&#7873;n th&ocirc;ng, ch&#7881; nh&#7857;m m&#7897;t m&#7909;c &#273;&iacute;ch duy nh&#7845;t l&agrave; &#273;&aacute;nh l&#7915;a ng&#432;&#7901;i &#273;&#7885;c &#273;&#7875; h&#7885; ph&#7843;i tin v&agrave;o nh&#7919;ng g&igrave; h&#7885; mu&#7889;n nghe, nh&#432;ng m&agrave; b&#7841;n c&#7847;n ph&#7843;i t&#7881;nh t&aacute;o &#273;&#7875; nh&#7853;n ra c&aacute;i n&agrave;o l&agrave; bullshit v&agrave; c&aacute;i n&agrave;o l&agrave; &#273;&uacute;ng, nh&#7853;n ra c&aacute;i n&agrave;o l&agrave; nh&#7919;ng s&#7921; ph&#7887;ng &#273;o&aacute;n, b&#7883; &#273;&aacute;nh l&#7915;a b&#7903;i nh&#7919;ng con s&#7889;.<figure class="image"><img src="https://thefullsnack.com/posts/img/rifle-shot-down-3.png" alt=""></figure>N&#7871;u b&#7841;n mu&#7889;n xem th&ecirc;m nhi&#7873;u v&iacute; d&#7909; ki&#7875;u n&agrave;y n&#7919;a, t&ocirc;i r&#7845;t khuy&#7871;n kh&iacute;ch &#273;&#7885;c quy&#7875;n s&aacute;ch <a href="https://www.amazon.com/How-Not-Be-Wrong-Mathematical/dp/0143127535">How Not to Be Wrong: The Power of Mathematical Thinking</a> c&#7911;a Jordan Ellenberg, trong cu&#7889;n n&agrave;y gi&#7843;i th&iacute;ch r&#7845;t hay v&iacute; d&#7909; v&#7873; Wald v&agrave; r&#7845;t nhi&#7873;u v&iacute; d&#7909; kh&aacute;c v&#7873; chuy&#7879;n b&#7883; d&#7919; li&#7879;u &#273;&aacute;nh l&#7915;a d&#7851;n &#273;&#7871;n nh&#7919;ng k&#7871;t lu&#7853;n ng&#7899; ng&#7849;n n&#7919;a.Ngu&#7891;n: thefullsnack</body></html>

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