Daily Archives: March 2, 2013

Learning physics online?

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事業愛情觀 3

   
It always makes me laugh when people hope they can learn physics online. Yeah, sure you can, just as you can learn languages online but you’re not going to be articulate compared to someone that is on a full time course. They live physics for years with like minded people, day in, day out. If you want to learn physics the same way someone learns a foreign language by carrying around a translation dictionary because they lack the effort required, then go right ahead. Just don’t delude yourself in believing you can know what a graduate physicist knows.

Let me put it another way:

A physicist on a full time course might spend at least 50 hours a week learning about physics. How much time do you have to spare?

   
— answered May 25 ’11 at 22:16

— Larry Harson

2013.03.02 Saturday ACHK

Marriage

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Process, not a state, 8

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Marriage is not a single event. Marriage is a lifelong process.

“Married” is not a state, but a process.

— Me@2010.12.24

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2013.03.02 Saturday (c) All rights reserved by ACHK

微積分 6.1

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無限年 3.1

這段改編自 2010 年 4 月 3 日的對話。

簡便起見，你可以視「無限份之一」等如「零」。

1/infinity = 0

不過，那只是輔助記憶的密碼，而不是正確合法的數學符號，因為，「無限」並不是一個數字，你不可以用「無限」來運算，或者表達任何數量。正確的寫法是，

\left( \lim_{x \to \infty} \frac{1}{x} \right) = 0

而它的真正意思是：

如果 x 越來越大，1/x 會越來越接近零。

（安：那為什麼不直接那樣說，而要用複雜的數學符號來誤導人？）

因為那句說話冗長，但在數學中又要時常使用。沒有「簡稱」的話，會十分不便。正如，當我們教一個小朋友，「爺爺」是「爸爸的爸爸」的簡稱時，他同樣可以質疑，為什麼不直接說「爸爸的爸爸」，而要用複雜難寫的文字來誤導人？

「爺爺」=「爸爸的爸爸」

「」= 「如果 x 越來越大，1/x 會越來越接近零。」

還有，這一句仍然只是「簡稱」，還未精確到可以視為數學句子。完整的版本詳盡很多。

— Me@2013.03.01

2013.03.02 Saturday (c) All rights reserved by ACHK