何有之鄉, 2.10

Posted on December 14, 2025 by rpflee

Where are you? | Utopia 2.10

選擇戀愛對象的原則，並不是找「理想伴侶」，而是找厭惡得來，仍然可以遷就到的人。反過來說，必須排除那些，「不可能遷就到」的可能對象。可以遷就到的，就是缺點；想遷就也遷就不到的，就為之人格問題。

不可能遷就到，而為了保命，必須立刻超光速逃離，或者𣊬間轉移的例子有：

……

十、不懂基礎語文。

即是同一句說話，重複很多次，也未必明白，即使該句說話，沒有任何常識以外的成份。

十一、不懂基礎數學。

例如，有人會以為：「0.12 大於 0.8，因為 12 大於 8。」

十二、記憶力比正常人差。

那將會是吵架之源，且源源不絕。

— Me@2025-12-14 11:11:14 AM

Chronological

Posted on December 11, 2025 by rpflee

To read a WordPress blog in chronological order, simply add ?order=asc to the end of URL.

— Me@2025-12-09 01:21:29 PM

4 Basis Fields, 2.2

Posted on December 7, 2025 by rpflee

Functional Differential Geometry

Why does d/dx appear in the book’s code (e.g. when defining a vector field like e0) before it is ever explicitly defined with a define, and why is it unbound until you run certain coordinate-system definitions?

In the FDG library (scmutils), the symbols d/dx, d/dy, d/dr, d/dθ, etc. are automatically created as literal vector-field basis objects the first time you define coordinates on a manifold using define-coordinates.

Specifically:

; rectangular coordinates
(define-coordinates (up x y) R2-rect)

does two things behind the scenes:

It creates coordinate functions x, y (or r, theta) that go from points → numbers.
It simultaneously creates the dual basis vector fields named d/dx, d/dy (or d/dr, d/dθ) that are literal vector fields on that coordinate system.

(for-each (lambda (name)
            (environment-define env
                                (string->symbol (string-append "d/d" (symbol->string name)))
                                (make-literal-vector-field name coord-sys)))
          coordinate-names)

These d/d… objects are not defined by a visible define in the user code; they are inserted into the global environment by the macro define-coordinates itself.

— Me@2025-10-12 10:49:20 AM

Classic Editor

Posted on December 6, 2025 by rpflee

If WordPress keeps opening the block editor instead of the Classic Editor, simply add

&classic-editor

to any edit URL such as

post.php?post=123&action=edit&classic-editor

and hit Enter to instantly open the Classic Editor.

— Me@2025-12-06 07:59:41 AM

Rediscovery 2

Posted on December 5, 2025 by rpflee

Good writers make readers think.

Great writers make readers feel.

Amazing writers make readers pause. All because you put their private thoughts and unspoken feelings into words they never could.

— Taylin John Simmonds

2025.12.05 Friday ACHK

好為人師 3.5

Posted on December 3, 2025 by rpflee

這段改編自 2023 年 6 月 23 日的對話。

教師和學生，並不是平等關係。那就可以導致，最終反目。原因是，雙方也會出於禮貌，即使在不同意對方時，也不會直斥其非、議事論事。既然不是開心見誠，無所顧忌，而是有所隱瞞，那就會導致誤會，日久累積加深。這情況在本人身上，發生不少次。有時是與學生反面，有時則是和教授，不相往來。

推而廣之，「講課」這個活動，本身是錯的——除非一些情況是，為了傳授你專業中的技術細節，予未有那些資料之人士。

「講課」的問題在於，講者會不自覺地，把自己神化；一旦高高在上，則會誤以為，自己講的必為正確。萬一聽眾聽不明白，就一定是他們的責任。

例如，電腦遊戲《最後生還者第II章》劣評如潮。作者的第一反應，不是虛心納諫，而是指責觀眾水平低。你是故事的創造神，不代表你在故事外也是。你還是要按現實世界的道理來行事。

「講課」是錯，哪什麼是對呢？

「討論」——由你（或該領域經驗最深之人）所主導之討論。「討論」的特點是雙向；討論的結果未必會是，你原本的認知。

— Me@2025-12-02 11:45:33 PM

Euler problem 28.2

Posted on November 17, 2025 by rpflee

e28a :: Integer
e28a = 1 + sum [4*(n-2)^2 + 10*(n-1)
               | n <- [3, 5 .. 1001]]


e28b :: Integer
e28b = let n = 500
           sumSquares = n*(n+1)*(2*n+1) `div` 6
           sumLinear = n*(n+1) `div` 2
       in 16*sumSquares + 4*sumLinear + 4*n + 1

λ> :set +s
λ> e28a
669171001
(0.00 secs, 617,688 bytes)

λ> e28b
669171001
(0.00 secs, 82,400 bytes)
λ>

— Me@2025-11-17 12:00:22 AM

Paradigms of Artificial Intelligence Programming

Posted on October 13, 2025 by rpflee

You think you know when you learn, are more sure when you can write, even more when you can teach, but certain when you can program.

— Alan Perlis

2025.10.13 Monday ACHK

Digital physics, 0.2

Posted on July 29, 2025 by rpflee

The continuum (real number) is an algorithm.

— Me@2025-01-09 11:21:54 PM

But computers can manipulate and solve formulas describing real numbers using Symbolic computation, thus avoiding the need to approximate real numbers by using an infinite number of digits. Before symbolic computation, a number—in particular a real number, one with an infinite number of digits— was said to be computable if a Turing machine will continue to spit out digits endlessly. In other words, there is no “last digit”. But this sits uncomfortably with any proposal that the universe is the output of a virtual-reality exercise carried out in real time (or any plausible kind of time). Known physical laws (including quantum mechanics and its continuous spectra) are very much infused with real numbers and the mathematics of the continuum.

So ordinary computational descriptions do not have a cardinality of states and state space trajectories that is sufficient for them to map onto ordinary mathematical descriptions of natural systems. Thus, from the point of view of strict mathematical description, the thesis that everything is a computing system in this second sense cannot be supported.

Moreover, the universe seems to be able decide on their values in real time, moment by moment. As Richard Feynman put it:

It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do?

He then answered his own question as follows:

So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the checker board with all its apparent complexities. But this speculation is of the same nature as those other people make—'I like it,' 'I don't like it'—and it is not good to be prejudiced about these things.

— 12:29, 21 February 2011

— Wikipedia on Digital physics

The continuum, formed by real numbers, includes irrational numbers, which are not traditional numbers but algorithms.

— Me@2025-04-16 02:30:23 PM

Small big bang 7

Posted on July 21, 2025 by rpflee

Remember, your every action is a seed, a starting point of a causal chain, a small big bang.

— Me@2013-08-28 4:12 PM

馬和小孩, 2

Posted on June 28, 2025 by rpflee

這段改編自 2021 年 12 月 17 日的對話。

人的內置系統，即是先天而言，在愛情上是從一而終的。或者說，任何高等生物，都應該是那樣。

覺得「有外遇」沒有問題的人，是假設了雖然自己可以有外遇，但是太太卻不可以。

如果遊戲規則是，你有多少個外遇，太太亦會有多少個的話，大概沒有人會願意。

比喻說，如果有一個城市甲，政府考慮「應否把偷竊搶刧合法化」時，只給市民兩個選項：

要麼全民也可以偷搶，要麼全民也不可以。

那樣，大部人也會寧願，全民也不可以。

即使法津容許我，取他人之物，我也不可能持有，因為，他人也可以任意，偷搶我的東西。

— Me@2025-06-25 03:44:26 PM

Euler problem 28.1

Posted on June 15, 2025 by rpflee

(defun e-28 ()
  (+ 1 (loop :for n :from 3 :to 1001 :by 2
             :sum (+ (* 4 (expt (- n 2) 2))
                     (* 10 (- n 1))))))

CL-USER> (e-28)
669171001

— Me@2025-06-13 11:01:45 PM

Ex 1.33 Properties of E

Posted on June 3, 2025 by rpflee

Understanding the Euler-Lagrange Operator

Let $\displaystyle{F}$ and $\displaystyle{G}$ be two Lagrangian-like functions of a local tuple, $\displaystyle{C}$ be a local-tuple transformation function, and $\displaystyle{c}$ a constant.

Demonstrate the following properties:

a. $\displaystyle{E[F + G] = E[F] + E[G]}$

…

d. $\displaystyle{\mathcal{E}[F \circ C] = D_t (DF \circ C) \partial_2 C + DF \circ C \mathcal{E}[C]}$

~~~

Eq. (1.167):

$\displaystyle{\bar \Gamma (\bar f) (t, q, v, \dots) = \bar f [\mathcal{O} (t,q,v, \dots)](t)}$

Eq. (1.174):

$\displaystyle{E[L] = D_t \partial_2 L - \partial_1 L}$

$\displaystyle{ \begin{aligned} E[L] &= D_t \partial_2 L - \partial_1 L \\ E[F+G] &= D_t \left( \partial_2 (F+G) \right) - \partial_1 (F+G) \\ &= D_t \left( \partial_2 F+\partial_2 G \right) - (\partial_1 F+ \partial_1 G) \\ &= D_t \partial_2 F+D_t \partial_2 G - (\partial_1 F+ \partial_1 G) \\ &= D_t \partial_2 F- \partial_1 F +D_t \partial_2 G - \partial_1 G \\ &= E[F] + E[G] \\ \end{aligned} }$

— Me@2025-05-30 03:40:41 PM

The Problem

$\displaystyle{ \begin{aligned} &E[F \circ C] (t,q,v,\dots) \\ &= (D_t \partial_2 (F \circ C) - \partial_1 (F \circ C)) (t,q,v,\dots)\\ &= (D_t \partial_2 (F (C(t,q,v,\dots))) - \partial_1 (F(C(t,q,v,\dots)))) \\ \end{aligned} }$

Prove that

$\displaystyle{\mathcal{E}[F \circ C] = D_t (DF \circ C) \partial_2 C + DF \circ C \mathcal{E}[C]}$

Key Terms Explained

Local Tuple: Think of this as a snapshot of a system’s state along a path. It includes:
- $\displaystyle{ t }$ : time,
- $\displaystyle{ q }$ : generalized coordinate (e.g., position),
- $\displaystyle{ v = \frac{dq}{dt} }$ : velocity,
- and possibly higher derivatives like acceleration. We’ll use $\displaystyle{ \eta = (t, q, v) }$ for simplicity.
Lagrangian-like Function $\displaystyle{ F }$ : A scalar function of the local tuple, such as $\displaystyle{ F(t, q, v) }$ , akin to a Lagrangian in mechanics.
Local-Tuple Transformation $\displaystyle{ C }$ : A function that maps one local tuple to another. For example, $\displaystyle{ C(\eta) = (t, C_q(t, q, v), C_v(t, q, v)) }$ , where $\displaystyle{ C_q }$ and $\displaystyle{ C_v }$ transform the coordinate and velocity.
Composition $\displaystyle{ F \circ C }$ : This is $\displaystyle{ F }$ evaluated at the transformed tuple: $\displaystyle{ (F \circ C)(\eta) = F(t, C_q(t, q, v), C_v(t, q, v)) }$ .
Euler-Lagrange Operator $\displaystyle{ E }$ : For a function $\displaystyle{ G(t, q, v) }$ , it’s defined as:
$\displaystyle{ E[G] = \frac{\partial G}{\partial q} - D_t \left( \frac{\partial G}{\partial v} \right) }$
This operator extracts the equations of motion when applied to a Lagrangian.
Total Time Derivative $\displaystyle{ D_t }$ : This accounts for how a function changes over time, considering all variables. For $\displaystyle{ h(t, q, v) }$ :
$\displaystyle{ D_t h = \frac{\partial h}{\partial t} + v \frac{\partial h}{\partial q} + a \frac{\partial h}{\partial v} }$
where $\displaystyle{ a = \frac{dv}{dt} }$ is acceleration.
Derivative $\displaystyle{ DF }$ : The derivative of $\displaystyle{ F }$ with respect to its spatial arguments, typically $\displaystyle{ DF = \left( \frac{\partial F}{\partial q}, \frac{\partial F}{\partial v} \right) }$ .

…

— Me@2025-05-31 01:32:05 PM

Deserve

Posted on May 29, 2025 by rpflee

You don’t attract what you want.

You attract what you believe you deserve.

— Tomas

2025.05.29 Thursday ACHK

有乜嘢會令你心花怒放

Posted on May 27, 2025 by rpflee

— Me@2025-05-27 10:55:48 PM

何有之鄉, 2.9

Posted on May 27, 2025 by rpflee

Where are you? 4 | Utopia 2.9

不可能遷就到，而為了保命，必須立刻超光速逃離，或者𣊬間轉移的例子有：

……

八、自我中心：

不會為他人著想，即不會從他人立場思考問題。

九、他我中心：

不會為自己考慮，即不懂維護自身權利。

那應該怎樣呢？

自己的世界，以自己為中心。

他人的世界，則以他人為中心。

每人也要為自己人生負責，不可推卸他人。

可以互相協助，不可互相推責。

— Me@2025-05-27 07:44:33 AM

xrandr, 2

Posted on April 20, 2025 by rpflee

xrandr -q

xrandr --output DisplayPort-3 --auto --primary --output HDMI-A-4 --auto --left-of DisplayPort-3

xrandr --output DisplayPort-3 --auto --primary --output HDMI-A-4 --off

— Me@2025-04-20 02:19:35 PM

13.1 Commutation relations for oscillators

Posted on April 18, 2025 by rpflee

A First Course in String Theory

(a) Use the lower-sign version of equation (13.28) and the appropriate mode expansion to verify explicitly that the unbarred commutation relations of (13.29) emerge.

~~~

Eq. (13.28):

$[(\dot X^I - X^{I'}) (\tau, \sigma), (\dot X^J - X^{J'})(\tau, \sigma')] = - 4 \pi \alpha' i \eta^{IJ} \frac{d}{d \sigma} \delta(\sigma - \sigma')$

Eq. (13.29):

$\left[ \alpha_m^I, \alpha_n^J \right] = m \delta_{m+n, 0} \eta^{IJ}$

Eq. (13.24):

$\displaystyle{X^\mu (\tau, \sigma) = x_0^\mu + \sqrt{2 \alpha'} \alpha_0^\mu \tau + i \sqrt{\frac{\alpha'}{2}} \sum_{n \neq 0} \frac{e^{-i n \tau}}{n} (\alpha_n^\mu e^{i n \sigma} + \bar \alpha_n^\mu e^{-in \sigma})}$

$\displaystyle{\dot{X}^\mu(\tau, \sigma) = \sqrt{2 \alpha'} \alpha_0^\mu + \sqrt{\frac{\alpha'}{2}} \sum_{n \neq 0} e^{-i n \tau} \left( \alpha_n^\mu e^{i n \sigma} + \bar{\alpha}_n^\mu e^{-i n \sigma} \right)}$

$\displaystyle{X^{\mu'}(\tau, \sigma) = \sqrt{\frac{\alpha'}{2}} \sum_{n \neq 0} e^{-i n \tau} \left( \bar{\alpha}_n^\mu e^{-i n \sigma} - \alpha_n^\mu e^{i n \sigma} \right)}$

$\displaystyle{\begin{aligned} &\int_0^{2 \pi} f(\sigma) d \sigma\frac{d}{d \sigma} \delta(\sigma - \sigma') \\ &= \int_0^{2 \pi} f(\sigma) d \delta(\sigma - \sigma') \\ &= f(2 \pi) \delta(2 \pi - \sigma') - f(0) \delta(0 - \sigma') - \int_0^{2 \pi} \delta(\sigma - \sigma') \frac{df(\sigma)}{d \sigma} d \sigma \\ \end{aligned}}$

Eq. (13.26):

$\displaystyle{\begin{aligned} \left[(\dot X^I - X^{I'}) (\tau, \sigma), (\dot X^J - X^{J'})(\tau, \sigma')\right] &= - 4 \pi \alpha' i \eta^{IJ} \frac{d}{d \sigma} \delta(\sigma - \sigma') \\ \left[ \sqrt{2 \alpha'} \sum_{m \in \mathbb{Z}} \alpha_m^I e^{-i m (\tau - \sigma)}, \sqrt{2 \alpha'} \sum_{n \in \mathbb{Z}} \alpha_n^J e^{-i n (\tau - \sigma')} \right] &= - 4 \pi \alpha' i \eta^{IJ} \frac{d}{d \sigma} \delta(\sigma - \sigma') \\ \sum_{m \in \mathbb{Z}} \sum_{n \in \mathbb{Z}} e^{-i m (\tau - \sigma)} e^{-i n (\tau - \sigma')} \left[ \alpha_m^I , \alpha_n^J \right] &= - 2 \pi i \eta^{IJ} \frac{d}{d \sigma} \delta(\sigma - \sigma') \\ \end{aligned}}$

$\displaystyle{\begin{aligned} \frac{1}{2 \pi} \int_0^{2 \pi} d \sigma e^{iq\sigma} \sum_{m \in \mathbb{Z}} \sum_{n \in \mathbb{Z}} e^{-i (m+n) \tau} e^{i m \sigma} e^{i n \sigma'} \left[ \alpha_m^I , \alpha_n^J \right] &= - 2 \pi i \eta^{IJ} \frac{1}{2 \pi} \int_0^{2 \pi} d \sigma e^{iq\sigma} \frac{d}{d \sigma} \delta(\sigma - \sigma') \\ \end{aligned}}$

$\displaystyle{\begin{aligned} \sum_{n \in \mathbb{Z}} e^{-i (-q+n) \tau} e^{i n \sigma'} \left[ \alpha_{-q}^I , \alpha_n^J \right] &= - i \eta^{IJ} \left[ \delta(2 \pi - \sigma') - \delta(0 - \sigma') - iq \int_0^{2 \pi} \delta (\sigma - \sigma') e^{i q \sigma} d\sigma \right] \\ \sum_{n \in \mathbb{Z}} e^{-i (-q+n) \tau} e^{i n \sigma'} \left[ \alpha_{-q}^I , \alpha_n^J \right]&= - i \eta^{IJ} \left[ \delta(2 \pi - \sigma') - \delta(0 - \sigma') - iq e^{i q \sigma'} \right] \\ \end{aligned}}$

$\displaystyle{\begin{aligned} \frac{1}{2 \pi} \int_0^{2 \pi} d \sigma' e^{ip\sigma'} \sum_{n \in \mathbb{Z}} e^{-i (-q+n) \tau} e^{i n \sigma'} \left[ \alpha_{-q}^I , \alpha_n^J \right]&= - i \eta^{IJ} \frac{1}{2 \pi} \int_0^{2 \pi} d \sigma' e^{ip\sigma'} \left[ \delta(2 \pi - \sigma') - \delta(0 - \sigma') - iq e^{i q \sigma'} \right] \\ \end{aligned}}$

$\displaystyle{\begin{aligned} e^{i (p+q) \tau} \left[ \alpha_{-q}^I , \alpha_{-p}^J \right]&= - \eta^{IJ} \frac{1}{2 \pi} q \int_0^{2 \pi} d \sigma' e^{ip\sigma'} e^{i q \sigma'} \\ e^{i (p+q) \tau} \left[ \alpha_{-q}^I , \alpha_{-p}^J \right]&= - \eta^{IJ} q \delta_{p+q,0} \\ \\ \\ e^{i (m+n) \tau} \left[ \alpha_{-n}^I , \alpha_{-m}^J \right]&= - n \delta_{m+n,0} \eta^{IJ} \\ \end{aligned}}$

— Me@2025-04-17 12:26:46 PM

Digital physics, 0.1

Posted on April 16, 2025 by rpflee