1920s

Posted on October 26, 2022 by rpflee

Dear men,

If she won’t give you her 20s, don’t give her your 30s and 40s.

— Lovers’ Guide

— guideforlovers

Don’t give a woman your prime if she won’t give you hers.

A woman who spends her twenties sleeping around until her biological clock starts ticking isn’t worth a penny.

— ManlyConfidence

2022.10.26 Wednesday ACHK

Presentation 基本原理 1.2.2.5

Posted on October 26, 2022 by rpflee

這段改編自 2010 年 4 月 24 日的對話。

然後第三點會，補充第一點。剛才第一點說，一課應只有一個重點。定義何謂「一點」和何謂「一課」，正正是講者的職責。

第三點就是，宏觀而言，

說話要 in series（串聯），不要 in parallel（並聯）。你要說完一句說話，才開始下一句。你要講完一個 point（要點），才講下一個。

千萬不要企圖，在同一刻時間中，講超過一句說話。亦千萬不要企圖，在同一句說話中，包含超過一個要點（point）。

簡言之，說話要有條理。

— Me@2010.09.05

那就正正為什麼是「條理」，而不是「塊理」。思路是一「條」線，不是一「塊」面。

那就正正為什麼是「思路」，而不是「思面」。思路是一條「路」，不是一塊「面」。

那正正是，「安排」這個詞語的意思，把眾多想法要點，安放成一個排列。

情形就好像打字一樣。打字快的原因是，你打完一個英文字母，才打下一個；而不是在同一刻，打超過一個字母。

如果你企圖在同一刻，打超過一個字母，你會打錯字。字母次序錯了的話，時間得不償失。

— Me@2010.09.05

— Me@2022-10-25 02:58:36 PM

The Sixth Sense, 2.2

Posted on October 23, 2022 by rpflee

Euler problem 5.2 | Folding an infinite list, 2

f = foldr1 lcm [1..20]

Most problems on Project Euler can be solved in three ways:

with brute-force
with an algorithm that solves a more general problem
with a smart solution that requires pencil and paper at most

If you’re interested in a nice solution rather than fixing your code, try concentrating on the last approach …

— edited Oct 8, 2016 at 8:57

— huwr

— answered Dec 27, 2011 at 14:33

— Philip

— Stack Overflow

3.3 Electromagnetism in three dimensions

Posted on October 22, 2022 by rpflee

A First Course in String Theory

(a) Find the reduced Maxwell equations in three dimensions by starting with Maxwell’s equations and the force law in four dimensions, using the ansatz (3.11), and assuming that no field can depend on the $z$ direction.

~~~

$\displaystyle{\begin{aligned} \nabla \cdot \mathbf {E} &= \rho \\ \nabla \cdot \mathbf {B} &= 0 \\ \nabla \times \mathbf {E} &= - \frac{1}{c} {\frac {\partial \mathbf {B} }{\partial t}} \\ \nabla \times \mathbf {B} &= \frac{1}{c} \mathbf {J} + \frac{1}{c} {\frac {\partial \mathbf {E} }{\partial t}} \\ \end{aligned}}$

Eq. (3.11):

$\displaystyle{\begin{aligned} E_z &= 0 \\ B_x &= 0 \\ B_y &= 0 \\ \end{aligned}}$

$\displaystyle{\begin{aligned} \frac{\partial E_x}{\partial x} + \frac{\partial E_y}{\partial y} &= \rho \\ \frac{\partial B_z}{\partial z} &= 0 \\ \frac{\partial E_y}{\partial x} - \frac{\partial E_x}{\partial y} &= - \frac{1}{c} {\frac {\partial B_z }{\partial t}} \\ \nabla \times \mathbf {B} &= \frac{1}{c} \mathbf {J} + \frac{1}{c} {\frac {\partial \mathbf {E} }{\partial t}} \\ \end{aligned}}$

$\displaystyle{\begin{aligned} \frac{\partial B_z }{\partial y} - \frac{\partial B_y }{\partial z} &= \frac{1}{c} j_x + \frac{1}{c} {\frac {\partial E_x }{\partial t}} \\ \frac{\partial B_x }{\partial z} - \frac{\partial B_z }{\partial x} &= \frac{1}{c} j_y + \frac{1}{c} {\frac {\partial E_y }{\partial t}} \\ \frac{\partial B_y }{\partial x} - \frac{\partial B_x }{\partial y} &= \frac{1}{c} j_z + \frac{1}{c} {\frac {\partial E_z }{\partial t}} \\ \end{aligned}}$

$\displaystyle{\begin{aligned} \frac{\partial B_z }{\partial y} &= \frac{1}{c} j_x + \frac{1}{c} {\frac {\partial E_x }{\partial t}} \\ - \frac{\partial B_z }{\partial x} &= \frac{1}{c} j_y + \frac{1}{c} {\frac {\partial E_y }{\partial t}} \\ \end{aligned}}$

$\displaystyle{\begin{aligned} \frac{d \vec p}{dt} &= q \left( \vec E + \frac{\vec v}{c} \times \vec B \right) \\ \end{aligned}}$

$\displaystyle{\begin{aligned} \frac{d p_x}{dt} &= q \left( E_x + \frac{1}{c} (v_y B_z - v_z B_y) \right) \\ \frac{d p_y}{dt} &= q \left( E_y - \frac{1}{c} (v_x B_z - v_z B_x) \right) \\ \frac{d p_z}{dt} &= q \left( E_z + \frac{1}{c} (v_x B_y - v_y B_x) \right) \\ \end{aligned}}$

$\displaystyle{\begin{aligned} \frac{d p_x}{dt} &= q \left( E_x + \frac{1}{c} v_y B_z \right) \\ \frac{d p_y}{dt} &= q \left( E_y - \frac{1}{c} v_x B_z \right) \\ \frac{d p_z}{dt} &= 0 \\ \end{aligned}}$

— Me@2022-10-22 04:17:10 PM

Swampland

Posted on October 22, 2022 by rpflee

In physics, the term swampland refers to effective low-energy physical theories which are not compatible with string theory, in contrast to the so-called “string theory landscape” of compatible theories. In other words, the swampland is the set of consistent-looking theories with no consistent ultraviolet completion in string theory.

Developments in string theory suggest that the string theory landscape of false vacua is vast, so it is natural to ask if the landscape is as vast as allowed by consistent-looking effective field theories. Some authors, such as Cumrun Vafa, suggest that is not the case and that the swampland is in fact much larger than the string theory landscape.

— Wikipedia on Swampland (physics)

Recall that Vafa’s Swampland is a giant parameter space of effective field theories that cannot be realized within a consistent theory of quantum gravity i.e. within string/M-theory. Only a tiny island inside this Swampland, namely the stringy Landscape, is compatible with quantum gravity. String/M-theory makes lots of very strong predictions – namely that we don’t live in the Swampland. We have to live in the special hospitable Landscape.

— Vafa, quintessence vs Gross, Silverstein

— The Reference Frame

— Luboš Motl

2022.10.21 Friday ACHK

以原則為中心

Posted on October 20, 2022 by rpflee

自然定律 8

When your MindOS is aligned with PRINCIPLES, MAGIC expands.

— Me@2016-12-08 06:17:32 AM

PRINCIPLES

~ natural laws

— Me@2022-10-15 11:47:03 PM

排列組合 1.4

Posted on October 19, 2022 by rpflee

nCr, 0.4

— Me@2022-10-19 12:26:30 PM

Euler problem 5.1

Posted on October 17, 2022 by rpflee

1930s, 3

— meme creator

(defun range (max &key (min 0) (step 1))
  (loop :for n :from min :below max :by step
    collect n))

(defmacro lcm-lst (lst)
  `(apply #'lcm ,lst))

(lcm-lst (range 21 :min 2))

— palette fm

— Me@2022-10-17 05:21:23 PM

Ex 1.28 Kinetic energy contains terms that are linear

Posted on October 15, 2022 by rpflee

Structure and Interpretation of Classical Mechanics

An analogous result holds when the $f_\alpha$ ‘s depend explicitly on time.

a. Show that in this case the kinetic energy contains terms that are linear in the generalized velocities.

~~~

$\displaystyle{\begin{aligned} \mathbf{v_\alpha} &= \partial_0 f_\alpha (t,q) + \partial_1 f_\alpha (t,q) v \\ T(t,q,v) &= \frac{1}{2} \sum_\alpha m_\alpha v^2_\alpha \\ v_\alpha &= |\mathbf{v}_\alpha| \\ v &= \text{generalized velocity} \\ \mathbf{v}_\alpha &= \text{rectangular velocity} \\ \end{aligned}}$

$\displaystyle{\begin{aligned} &T(t,q,v) \\ &= \frac{1}{2} \sum_\alpha m_\alpha |\partial_0 f_\alpha (t,q) + \partial_1 f_\alpha (t,q) v|^2 \\ &= \frac{1}{2} \sum_\alpha m_\alpha \left \{ [\partial_0 f_\alpha (t,q)]^2 + 2 \partial_0 f_\alpha (t,q) \partial_1 f_\alpha (t,q) v + [\partial_1 f_\alpha (t,q) v]^2 \right \} \\ \end{aligned}}$

— Me@2022-10-15 11:17:59 AM

Computing Note

Posted on October 13, 2022 by rpflee

21122002 not mine but quotation

Yet, in principle, computers cannot be asked to discover proofs, except in very restricted areas of mathematics–such as elementary Euclidean geometry–where the set of theorems happens to be recursive, as was proved by Tarski.

… the prime number theorem was first suggested as the result of extensive hand calculations on the prime numbers up to 3,000,000 by the Swiss mathematician Leonhard Euler (1707-83), a process that would have been greatly facilitated by the availability of a modern computer.

Thus Godel was able to assert that the set of theorems of mathematics is recursively enumerable, and, more recently, the American linguist Noam Chomsky (b. 1928) could say that the set of grammatical sentences of a natural language, such as English, is recursively enumerable.

Godel’s incompleteness theorem is that the consistency of mathematics can be proved only in a language which is stronger than the language of mathematics itself. Yet, formalism is not dead- …

— Encyclopædia Britannica

2022.10.13 Thursday ACHK

2003 AI Quantum Mechanics

Posted on October 12, 2022 by rpflee

2004 AI MSc Physics/Teacher/Programmer 

2005 Physics M.Phil. 

2003to2008

~ Me@2002

This history has unfolded with 70% accuracy.

— Me@2022-10-12 05:45:41 PM

眾害取其輕 10.2

Posted on October 12, 2022 by rpflee

The least of all evils, 10.2

這段改編自 2021 年 12 月 15 日的對話。

…

「眾害之最輕」有時可以零，有時不可以零。你只能客觀面對，不能主觀判斷。換句話說，「眾害之最輕」不一定「可以零」，亦不一定「不可以零」。

記住，主觀意願不成理據。任何人在，沒有足夠理據的情況下，認為某事選擇的「眾害之最輕」必為零，或者認為「眾害之最輕」必不為零，都是狂妄；要麼是蠢，要麼是壞，通常又蠢又壞。

不可為零的眾害之最輕，簡稱「必要之惡」。

愚善的人往往認為，任何情況下，任何人的任何痛苦，都可以驅除，或應該驅除。他們移除「必要之惡」時，引發「不必要之惡」，帶來更大的痛苦。例如，移除工作之痛，卻換來捱餓之苦。

又例如，任何學問，必有必須背誦的地方。但是，竟然有人提倡「背誦是苦，所以應該只需要理解，而毋須背誦」。我年輕時錯信這點，誤了學業。正確的取向是：

1. 理解後背誦

2. 有用的東西就背

3. 無用的東西就不背

愚賤之人的邪惡，則是另一個極端。他們認為，任何情況下，痛苦都無可避免。以「眾害取其輕」為名，把「不必要之惡」標籤為「必要之惡」，讓自己及他人承受著大量，不必要的痛苦。

例如，有一科目的考試，有大量零碎，而沒有用的東西要背誦。我向講師反映時，他卻說：「這科的性質是這樣的。」

我當時心想，這科考試考什麼，其實全由他設計；他有絕對權力，在那科之中，選擇有用的內容來出題。

又例如，工作固然是苦，但卻可分成，有用之苦（必要之惡）和無用之苦（額外之惡）。

天作孽猶可恕，自作孽不可活。

辭職的原因往往不是，工作本質困難到，你承受不到；而是上司緣於個人的喜好或誤解，僭建了很多不相干的工序環節。而跟他反映時，他卻會覺得，工作有困難在所難免，年青人不要怕吃苦。

他不知道，那其實並非「必要之苦」，而是他在自製的災難。

— Me@2022-10-11 11:39:33 PM

Euler problem 4.2

Posted on October 11, 2022 by rpflee

Find the largest palindrome made from the product of two 3-digit numbers.

g = [(y, z, y*z) | y<-[100..999], z<-[y..999], f==y*z]
    where
      f = maximum [x | y<-[100..999], z<-[y..999],
                   let x=y*z, let s=show x, s==reverse s]

— based on Haskell offical

— Me@2022-10-10 10:09:53 PM

Ex 1.1: Motion on a Sphere

Posted on October 9, 2022 by rpflee

Functional Differential Geometry

The metric for a unit sphere, expressed in colatitude $\displaystyle{\theta}$ and longitude $\displaystyle{\phi}$ , is

$\displaystyle{g(u,v) = d\theta(u) d \theta(v) + (\sin \theta)^2 d \phi (u) d \phi (v)}$

Compute the Lagrange equations for motion of a free particle on the sphere and convince yourself that they describe great circles. For example, consider the motion on the equator $\displaystyle{\theta = \pi/2}$ and motion on a line of longitude ( $\displaystyle{\phi}$ is constant).

~~~

(define ((Lfree mass) state)
  (* 1/2 mass (square (velocity state))))

(define ((sphere->R3 R) state)
  (let ((q (coordinate state)))
    (let ((theta (ref q 0)) (phi (ref q 1)))
      (up (* R (sin theta) (cos phi))
          (* R (sin theta) (sin phi))
          (* R (cos theta))))))

(define ((F->C F) local)
  (up (time local)
      (F local)
      (+ (((partial 0) F) local)
         (* (((partial 1) F) local)
            (velocity local)))))

(define (Lsphere m R)
  (compose (Lfree m) (F->C (sphere->R3 R))))

(show-expression
 ((Lsphere 'm 'R)
  (up 't
      (up 'theta 'phi)
      (up 'thetadot 'phidot))))

(show-expression
 (((Lagrange-equations
    (Lsphere 'm 'R))
   (up
    (literal-function 'theta)
    (literal-function 'phi)))
  't))

$\displaystyle{ \begin{aligned} - \sin \theta (D \phi)^2 \cos \theta + D^2 \theta &= 0 \\ 2 \sin \theta D \theta D \phi \cos \theta + D^2 \phi (\sin \theta)^2 &= 0 \\ \\ D^2 \theta &= (D \phi)^2 \cos \theta \sin \theta \\ D( D \phi (\sin \theta)^2) &= 0 \\ \\ \end{aligned}}$

$\displaystyle{ \begin{aligned} D \phi (\sin \theta)^2 &\equiv C \\ \\ \end{aligned}}$

for some constant $C$ .

Since $\displaystyle{ \begin{aligned} D \phi (\sin \theta)^2 &= 0 \\ \\ \end{aligned}}$ for some $\theta$ ,

$\displaystyle{ \begin{aligned} D \phi (\sin \theta)^2 &\equiv 0 \\ \\ \end{aligned}}$

This is equivalent to setting up the coordinate system such that the initial value of $\theta$ equals zero.

Also, since $\displaystyle{ \begin{aligned} (\sin \theta)^2 &\ne 0 \\ \\ \end{aligned}}$ for some $\theta$ ,

$\displaystyle{ \begin{aligned} D \phi &\equiv 0 \\ \\ \end{aligned}}$

— Me@2022-10-08 04:56:27 PM

Visualize, 2

Posted on October 7, 2022 by rpflee

visual

~ spatial

~ global

~ parallel

Since our retinas are 2D, what we see are actually only 2D.

— Me@2016-08-20 03:11:13 PM

The point is not to eliminate risk,

Posted on October 7, 2022 by rpflee

but to minimize risk

~ take the best kind of risk

~ aka FAITH.

— Me@2017-01-04 11:03:09 PM

What is a leader? 2

Posted on October 6, 2022 by rpflee

Presentation 基本原理 1.2.2.4

這段改編自 2010 年 4 月 24 日的對話。

When You’re Teaching a Subject, Don’t Think About That Subject: Think About Teaching – don’t focus on subtleties that interest you; focus on your audience.

— How to Teach Stuff

— John Baez

第二個重點教學原則是：

Focus on teaching, not the subtleties that interest you.

即是聚焦於教學成果，而不是你最有興趣的細節。

亦即是話，重點不是「你」，亦不是「觀眾」；重點是「教學」本身。

教學時候，你應該說的，既不是你想說的，亦不是觀眾想聽的。

（安：難道什麼也不說嗎？）

不是這個意思。

教學時候，你應該說的是，既不是你想說的，亦不是觀眾想聽的，而是觀眾需要的。

假想你是醫生，你想說給病人的，就是光顧最昂貴的療程；病人想聽的，就是他其實沒有大礙，什麼針藥也不需。但是，它們兩者，也不是你應該講的。

不是以你為中心，亦不是以觀眾為中心，而是以原則為中心。

「以原則為中心」對我來說，是新知識。我以前一直以為，不以自己為中心，不自說自話，改為講「觀眾想聽」的，就已經正確。但是，我漸漸地發現，只講「觀眾想聽」的，又好似有些問題。

（安：教學就是令人，愚蠢變聰明。原本愚蠢的人，很難會知道當刻學什麼，對智力最有利。）

A good leader tells you not what he wants to say, not what you want to hear, but what you need to know.

— Me@2022-10-05 10:23:24 AM

Euler problem 4.1

Posted on October 3, 2022 by rpflee

(describe #'elt)

(defun palindromep (seq)
  (let ((end (1- (length seq))))
    (or (< end 1)
        (and (eql (elt seq 0) (elt seq end))
             (palindromep (subseq seq 1 end))))))

(defun euler-4 ()
  (loop for a from 1 to 999
      maximize
      (loop for b from 1 to 999
            when (palindromep
                    (prin1-to-string (* a b)))
              maximize (* a b) into best
            finally (return (or best 0)))))

— skeeto/euler-cl

— Me@2022.10.03 03:03:30 PM

3.2 Maxwell equations in four dimensions, 2

Posted on October 2, 2022 by rpflee

A First Course in String Theory

(b) Show explicitly that the Maxwell equations with sources emerge from (3.34).

~~~

Eq. (3.34):

$\displaystyle{\begin{aligned} \frac{\partial F^{\mu \nu}}{\partial x^\nu} &= \frac{1}{c} j^\mu \\ \end{aligned}}$

$\displaystyle{\begin{aligned} \frac{\partial F^{\mu 0}}{\partial x^0} + \frac{\partial F^{\mu 1}}{\partial x^1} + \frac{\partial F^{\mu 2}}{\partial x^2} + \frac{\partial F^{\mu 3}}{\partial x^3} &= \frac{1}{c} j^\mu \\ \\ \end{aligned}}$

$\displaystyle{\begin{aligned} \frac{\partial F^{0 0}}{\partial x^0} + \frac{\partial F^{0 1}}{\partial x^1} + \frac{\partial F^{0 2}}{\partial x^2} + \frac{\partial F^{0 3}}{\partial x^3} &= \frac{1}{c} j^0 \\ \frac{\partial E_x}{\partial x^1} + \frac{\partial E_y}{\partial x^2} + \frac{\partial E_z}{\partial x^3} &= \rho \\ \nabla \cdot \mathbf{E} &= \rho \\ \\ \end{aligned}}$

$\displaystyle{\begin{aligned} \frac{\partial F^{1 0}}{\partial x^0} + \frac{\partial F^{1 1}}{\partial x^1} + \frac{\partial F^{1 2}}{\partial x^2} + \frac{\partial F^{1 3}}{\partial x^3} &= \frac{1}{c} j^1 \\ - \frac{\partial E_x}{\partial x^0} + \frac{\partial 0}{\partial x^1} + \frac{\partial B_z}{\partial x^2} - \frac{\partial B_y}{\partial x^3} &= \frac{1}{c} j^1 \\ \frac{\partial B_z}{\partial y} - \frac{\partial B_y}{\partial z} &= \frac{1}{c} j^1 + \frac{\partial E_x}{\partial x^0} \\ \end{aligned}}$

— Me@2022.10.02 11:49:59 AM

For all, 10

Posted on October 1, 2022 by rpflee

No observer can observe and get all the information of the current state of the whole universe.

Since the definition of the “universe” is “everything”, any observer must be part of the universe. Also, in the universe, any observer has at least one thing it cannot observe directly—itself.

Therefore, no observer can observe the whole universe in all details.

— Me@2022.09.30 07:57:46 PM

Can a part of a painting represent all the information of the whole?

No.

(Kn: Yes, if excluding itself.)

That is exactly my point.

“Yes only if that part does not contain that part itself” is equivalent to “no”.

— Me@2016-08-20 03:30:26 PM

Physics Town

continues