能知過去未來, 2

Posted on June 28, 2024 by rpflee

我能知過去未來，偏偏不掌握現在。

— Me@2011.09.02

— Me@2024-06-28

無拍之拖 3.2

Posted on June 27, 2024 by rpflee

眾害取其輕 | The least of all evils, 13.2 | 友情演義 2.2 | 相聚零刻 3.2 | 原來是你 4.2

這段改編自 2023 年 6 月 20 日的對話。

…

維持「曖昧時期」，不是健康的關係，因為，如果一邊覺得只是友情，而另一邊卻覺得不是的話，即引起極大誤會，所以我視「曖昧時期」為「害」。

但那是「必要之惡」，因為人不會未卜先知；你總不能，亦總不會，在從來未相處暸解過，就喜歡別人，向她示愛。

但是，那並不代表，你沒有任何責任，去盡快盡量減輕，那「必要之惡」。亦即是話，「曖昧時期」一但有結果，就應立即終止。

「結果」就是，愛情或友情。「終止」就是，要麼進化成情侶，要麼退化成朋友。

— Me@2024-06-26 04:05:21 PM

Batman: Return of the Joker

Posted on June 26, 2024 by rpflee

Euler problem 20.1

Find the sum of the digits in the number $\displaystyle{100!}$ .

(reduce #'+
        (map 'list #'digit-char-p
             (write-to-string
              (reduce #'* (loop for i
                                from 1 to 100
                                collect i)))))

CL-USER> 
648

— Me@2024-06-25 08:26:22 PM

1.9 Abstraction of Path Functions, 2

Posted on June 15, 2024 by rpflee

Structure and Interpretation of Classical Mechanics

Let $\displaystyle{\bar \Gamma}$ be a function such that

$\displaystyle{\begin{aligned} f &= \bar \Gamma (\bar f) \\ \end{aligned}}$

So, to get a value of $\displaystyle{\begin{aligned} f \end{aligned}}$ , we input a local tuple:

$\displaystyle{\begin{aligned} f (t, q(t), v(t), \cdots, q^{(n)}(t)) &= f (t, q, v, \cdots, q^{(n)})(t) \\ &= f(\Gamma[q])(t) \\ &= f \circ \Gamma[q](t) \\ &= \bar f [q](t) \\ \bar \Gamma (\bar f) (t, q(t), v(t), \cdots, q^{(n)}(t)) &= \bar f [q](t) \\ \end{aligned}}$

(define ((Gamma-bar f-bar) path-q-local-tuple)
  (let* ((tqva path-q-local-tuple)
         (t (time tqva))         
         (O-tqva (osculating-path tqva)))   
    ((f-bar O-tqva) t)))

The procedure osculating-path takes a number of local components and returns a path with these components; it is implemented as a power series.

In scmutils, you can use the pp function to get the definition of a function. For example, the code

(pp osculating-path)

results

(define ((osculating-path state0) t)
  (let ((t0 (time state0))
        (q0 (coordinate state0))
        (k (vector-length state0)))
    (let ((dt (- t t0)))
      (let loop ((n 2) (sum q0) (dt^n/n! dt))
        (if (fix:= n k)
            sum
            (loop (+ n 1)
                  (+ sum
                     (* (vector-ref state0 n)
                        dt^n/n!))
                  (/ (* dt^n/n! dt) n)))))))

$\displaystyle{\begin{aligned} q(t) &= q_0 + v_0 (t-t_0) + \frac{1}{2} a_0 (t-t_0)^2 + ... +\frac{1}{n!} q^{(n)}_0 (t-t_0)^n \\ &= q_0 + v_0 (dt) + \frac{1}{2} a_0 (dt)^2 + ... +\frac{1}{n!} q^{(n)}_0 (dt)^n \\ \end{aligned}}$

Note that for the function in the program, $\displaystyle{\bar \Gamma (\bar f)}$ , the input is actually not $\displaystyle{(t, q, v, \cdots, q^{(n)})}$ but $\displaystyle{(t, q(t), v(t), \cdots, q^{(n)}(t))}$ .

$\displaystyle{\begin{aligned} \bar \Gamma (\bar f) (t, q(t), v(t), \cdots) &= \bar f[O(t, q, v, \cdots)](t) \\ \end{aligned}}$

(define (F->C F)
  (define (f-bar q-prime)
    (define q
      (compose F (Gamma q-prime)))
    (Gamma q))
  (Gamma-bar f-bar))

(show-expression 
 ((F->C p->r)
  (->local 't
           (up 'r 'theta)
           (up 'rdot 'thetadot))))

— Me@2023-12-19 08:16:40 PM

Philosophical Investigations, 2

Posted on June 12, 2024 by rpflee

According to Wittgenstein, philosophical problems arise when language is forced from its proper home into a metaphysical environment, where all the familiar and necessary landmarks and contextual clues are removed. He describes this metaphysical environment as like being on frictionless ice: where the conditions are apparently perfect for a philosophically and logically perfect language, all philosophical problems can be solved without the muddying effects of everyday contexts; but where, precisely because of the lack of friction, language can in fact do no work at all. Wittgenstein argues that philosophers must leave the frictionless ice and return to the “rough ground” of ordinary language in use. Much of the Investigations consists of examples of how the first false steps can be avoided, so that philosophical problems are dissolved, rather than solved: “The clarity we are aiming at is indeed complete clarity. But this simply means that the philosophical problems should completely disappear.”

— Wikipedia on Ludwig Wittgenstein

2024.06.12 Wednesday ACHK

天使與傻瓜 3

Posted on June 10, 2024 by rpflee

自己的世界，以自己為中心，並不是「自我中心」；

要求別人的世界，也以你自己為中心，才是「自我中心」。

而「他我中心」，則是自己的世界，以他人為中心。

不要自我中心；

不要他我中心，

因其兩者皆錯。

— Me@2023-09-13 09:33:19 PM

所有第一次

Posted on June 6, 2024 by rpflee

這段改編自 2021 年 12 月 15 日的對話。

《我的第一次》這是我給學生訂的作文題目，批閱作文的時候，忽然憶起自己重要的第一次。我第一次真正愛上國文課，是因為來了一位姓盛的老師。我第一次暗戀，對象是一位同班同學，她叫陳文靖，就坐在我前面。每天上課時，我總會間歇嗅到，她髮鬢的爽身粉香味。我第一次感到自己重要，是在你出生的那天。嬰兒床上的你，臉上滿是皺紋，口中嗚嗚地發出，小貓般微弱哭叫。我抱起你，有點不知所措，但是一種奇妙感覺，同時洶湧而來，世界變得溫柔，我也從此變得重要。一晃眼，小貓不再是小貓，早已出發尋找，他自己的第一次去了，在一個靜靜的角落裡，尚有一個全新的『第一次』在等著他。

–《男人四十》

拍拖，不要只為互相陪伴。拍拖，應以結婚有目的。肯定不是你未來太太的人，應立刻中止當時（或潛在）的戀愛關係。

與女子第一次看星空；第一次看煙花；第一次討論人生大計；第一次討論廣義相對論；第一次討論羅馬帝園衰亡史；等等，都應全部留給，唯一的真正未來太太，盡量。

— Me@2024-06-04 12:11:17 PM

Physics Town

continues

Monthly Archives: June 2024