Monthly Archives: October 2023

朋友同事 6.4

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這段改編自 2010 年 4 月 24 日的對話。

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You cannot change the people around you, but you can change the people you choose to be around.

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大部分情況下，你不能改變別人，你只能更換別人。例如，你不能期望，不守時的人，會變成守時。你要朋友守時，就直接找守時的人做朋友。

— Me@2023-05-29 02:37:56 PM

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「如果介意缺點的話，大概沒有任何朋友」這個想法，大錯特錯，因為，即使「任何人必有缺點」，缺點其實可分成，「被動缺點」和「主動缺點」。「被動缺點」可以避開；「主動缺點」則會主動攻擊你。

主動缺點，亦稱「人格問題」。其大鑊之處在於，你想相處，也相處不來，甚至相處不到。例如遲到失約，你想見他也見不到。

公事有關的，就是「主動缺點」。可以無關的，為之「被動缺點」。

人格，即是「系統程式」加「公用程式」。人格問題，就是「系統程式」或「公用程式」的毛病。其他缺點，則是「應用程式」的問題。

一個文書程式，不能用來繪圖，只是「被動缺點」。繪圖程式不能繪圖，則是「主動缺點」。那有兩種情況：

1. 繪圖程式因本身未完成，而未能繪圖。

2. 電腦的系統程式出現問題，導致原本設計，用來繪圖的程式，不能再繪圖。這就是為何「主動缺點」，亦稱為「人格問題」。

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當然，如果有一個人，「人格有問題但企圖去改」的話，他是人類有的少數。你可以暫時標籤他為，「人格沒有問題」，繼續與其相處，因為，你可以協助他改正。如果在合理時間內，也未改正完成，才疏遠絕交之。例如，有些人在我提供了，守時的方法後，仍然接連失約。

Sometimes you have to give up on people; not because you don’t care, but because they don’t.

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— Me@2023-09-18 11:12:31 AM

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2023.10.29 Sunday (c) All rights reserved by ACHK

Euler problem 17.1

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(defun remove-char (lst string)
  (cond ((not lst) string)
        ('t (remove-char (cdr lst)
                         (remove (car lst)
                                 string)))))

(defmacro english-reduced (n)
  `(length (remove-char (list #\- #\space)
                        (format nil "~r" ,n))))

(defmacro english-and (n)
  `(cond
     ((= (mod n 100) 0) (english-reduced ,n))
     ((> ,n 100) (+ 3 (english-reduced ,n)))
     ('t (english-reduced ,n))))

(defun e17 ()
  (labels ((e17-iter (n acc)
             (cond ((<= n 0) acc)
                   ('t (e17-iter (- n 1)
                                 (+ acc
                                    (english-and n)))
                       ))))
    (e17-iter 1000 0)))


CL-USER> (e17)
21124

— Me@2023-10-26 06:36:38 PM

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2023.10.26 Thursday (c) All rights reserved by ACHK

1.8.4 Noether’s Theorem

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1. …

2. However, there are more general symmetries that no coordinate system can fully express. For example, motion in a central potential is spherically symmetric … , but the expression of the Lagrangian for the system in spherical coordinates exhibits symmetry around only one axis.

3. …

4. A continuous symmetry is a parametric family of symmetries. Noether proved that for any continuous symmetry there is a conserved quantity.

— Structure and Interpretation of Classical Mechanics

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2023.10.23 Monday ACHK

Ideal clock 6.1

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How to check the accuracy of a clock in the real world?

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For that particular clock model, buy another exact copy. If the 2 copies keep in sync, then they are accurate, since the probability of their random errors match is extremely low.

How about systematic errors?

— Me@2015-09-14 09:15:35 AM

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Compare that clock with another with a different model.

Even if the other model’s clock may be with lower accuracy, it can help you to find the systematic errors of your clock model.

— Me@2015-09-14 10:00:56 AM

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2023.10.23 Monday (c) All rights reserved by ACHK

Split-brain, 2.2

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zeta0134 on May 13, 2018 | next [–]

I spent two years living with a man, then my lover, who refused to seek medical help but almost certainly had something like disassociative identity. He had learned to cope with it by giving his voices distinct names, and adopting their personas over times, often in response to external stimuli. As an outside observer with no such symptoms of my own, I found this completely fascinating.

He’s very spiritual, one of his inner voices would often come out and sage the house, offer prayers, and perform personal rituals which he kept secret. Otherwise though, I found that his personas largely reflected his current emotional state. One persona would almost always be “out” when he was upset with a friend, or struggling with some stress. Another was more childlike and playful. He described them as always there, and even though he appeared to allow one of them to be “in charge” as he put it, he said the voices were always in the back of his mind, directing his thoughts.

The experience has opened my eyes, and allowed me to see these disorders in a more positive light. I never told him what I thought of his diagnosis and never felt the need; while his condition lent itself to occasional mood swings, he made a point of respecting his voices, allowed them to become a part of him, and I feel had largely learned to cope. He could even switch his behaviors off for a while when needed, usually for work or when he felt the need to be professional.

I don’t think medication would have helped, not that he would have taken it. He had figured himself out for better or worse, and I just learned to accept him as he was.

— The Sound of Madness

— Hacker News

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2023.10.18 Wednesday ACHK

未來騙局, 4

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這段改編自 2023 年 06 月 20 日的對話。

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產品有「五年保養」的意思，並不是指五年內不會壞，而是指如果五年內有壞，會有修理或更換。「產品保養」即使是那樣，寬鬆版本的定義，有時都是騙局，雖然有時不是。

例子一，冷氣機三年保養，但是，有壞時，平常人是沒有能力，搬它下來，再運送去製造商。

例子二，幾百元以內的小型電器，或者電腦產品，如果壞了，即使在保養期內，你會特意請假一天，拿它去廠商修理，然後待修理完成後，再請另一天假去取回嗎？

你拿去修理再取回，交通費用和時間成本，遠高於立刻去零售商店，重新買一個。

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「產品保養」有用的，只是一些特定情況：

1. 該保養包括了「七日有壞的話，可以於零售商一換一」。重點是「於零售商」和「毋須等待修理」。

2. 電器電腦價值數千，遠高於交通和時間的代價。

3. 保障零售商。如果某個型號的產品，有大量次貨的話，零售商可以追究批發商，要求更換。

— Me@2023-06-22 11:49:37 AM

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2023.10.15 Sunday (c) All rights reserved by ACHK

Picasa

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This is a file from the Wikimedia Commons.

Picasa was a cross-platform image organizer and image viewer for organizing and editing digital photos, integrated with a now defunct photo-sharing website, originally created by a company named Lifescape (which at that time was incubated by Idealab) in 2002.

— Wikipedia on Picasa

— Me@2023-10-10 08:09:55 PM

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2023.10.10 Tuesday (c) All rights reserved by ACHK

3.6 Analytic continuation for gamma function, 2

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A First Course in String Theory

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…

\displaystyle{ \begin{aligned} \Gamma (z) &= \int_{0}^{1}t^{z-1}e^{-t}dt + \int_{1}^{\infty}t^{z-1}e^{-t}dt \\\\ \end{aligned} \\ }

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Prove that \displaystyle{\int_{1}^{\infty}t^{z-1}e^{-t}dt} converges.

Since \displaystyle{ \begin{aligned} e^t &= \sum_{s=0}^\infty \frac{t^s}{s!} \\ \end{aligned} \\ },

for any integer r \ge 0 and any real t > 0,

\displaystyle{ \begin{aligned} e^t &\ge \frac{t^r}{r!} \\ \end{aligned}~~~}

Then

\displaystyle{ \begin{aligned} e^{-t} &\le \frac{1}{\frac{t^r}{r!}} \\ \end{aligned} \\ }

Let \displaystyle{ \begin{aligned} x &= \Re(z) \\ \end{aligned} \\ }:

\displaystyle{ \begin{aligned} t^{x-1}e^{-t} &\le \frac{t^{x-1}}{\frac{t^r}{r!}} \\ t^{x-1}e^{-t} &\le r! t^{x - r - 1} \\ \end{aligned} \\ }

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By choosing an r such that r \ge 1 and r \ge \Re(z) + 1,

for any t \ge 1,

\displaystyle{ \begin{aligned} t^{x-1}e^{-t} &\le r! t^{x - (x+1) - 1} \\ t^{x-1}e^{-t} &\le r! t^{-2} \\ \end{aligned} \\ }

Therefore,

\displaystyle{ \begin{aligned} \int_1^\infty t^{x-1}e^{-t} dt &\le r! \int_1^\infty t^{-2} dt = - r! [ t^{-1} ]_1^\infty = r! \\ \end{aligned} \\ }

In other words, for any complex z ,

\displaystyle{ \begin{aligned} \left| \int_1^\infty t^{z-1} e^{-t} dt \right| &\le r! \\ \end{aligned} \\ }

for some r such that r \ge 1 and r \ge \Re(z) + 1.

So

\displaystyle{ \begin{aligned} \left| \int_1^\infty t^{z-1} e^{-t} dt \right| &\le r! \\ \end{aligned} \\ }

converges for any z .

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Prove that \displaystyle{\int_{0}^{1}t^{z-1}e^{-t}dt} converges.

…

— Me@2023-09-07 07:38:17 PM

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2023.10.08 Sunday (c) All rights reserved by ACHK

注定外外傳 2

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Eternal return, 3 | Can it be Otherwise? 3

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Eternal recurrence is not a useful concept.

If two periods of time are identical in all details, they are actually the same period, not two periods. If two periods of time are not identical in all details, the second period is not an “eternal return” of the first period.

— Me@2013-06-04 01:30:16 AM

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「自由命定問題」的意思是問：

同一個輸入，會否只有唯一的輸出？

簡化地問：

同因是否必同果？

詳細地問：

如果第二次實驗的，所有初始設定，和第一次的完全相同的話，第二次實驗的結果，會不會和第一次的，完全相同呢？

— Me@2023-09-14 12:43:41 AM

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2023.10.07 Saturday (c) All rights reserved by ACHK

反情感勒索 2.3

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這段改編自 2021 年 12 月 16 日的對話。

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大部分情況下，你做的任何決定，都總會令到一些人不高興。既然那樣，為何不選擇做，自己喜歡的事情？

比喻說：

你行左的話，便令到右邊的人不開心。

你行右的話，就令到左邊的人不快樂。

你走中間路線呢？則左右也得罪。

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行左失右

行右失左

行中皆失

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不要輕易發脾氣，但亦不要害怕發脾氣；

不要輕易得罪人，但亦不要害怕得罪人。

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客觀對錯的事情，就選擇正確合理之道。

主觀喜好的事情，則揀取心懷熱誠之路。

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大事選理性

小事選感情

— Me@2023-10-05 11:19:18 PM

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2023.10.06 Friday (c) All rights reserved by ACHK