History 5

Posted on April 1, 2023 by rpflee

bambax on June 17, 2018

Not just music history, but history in general.

History told forwards is superstition: trying to show that what came after was inevitable, when in fact it was one future among an infinite number of different possible futures.

History told backwards makes sense: look for the seeds of post events, in the past.

However the human mind loves nothing more than causation; we see cause and effect everywhere even where it’s not, we like “stories”, we don’t understand, don’t believe in, and outright reject chance.

— We Should Teach Music History Backwards

— Hacker News

2023.04.01 Saturday ACHK

運動即速度；速度即所見

Posted on March 30, 2023 by rpflee

92-CE-PHY II – 4 前傳

— Me@2023-03-30 10:10:29 AM

Euler problem 12.1.1

Posted on March 27, 2023 by rpflee

(defmacro sq (x)
  `(* ,x ,x))

(defmacro last-item (lst)
  `(car (last ,lst)))

(defun good-reverse (lst)
  (labels ((rev (lst acc)
             (if (null lst)
                 acc
                 (rev
                  (cdr lst)
                  (cons (car lst) acc)))))
    (rev lst nil)))

(defun prime-sieve-a-list (input-lst)
  (labels ((sieve-iter (go-lst acc-list)
             (if (not go-lst) 
                 acc-list        
                 (if (> (sq (car go-lst))
                        (last-item go-lst))

                     (append (good-reverse acc-list)
                             go-lst)
                     
                     (sieve-iter
                      (remove-if #'(lambda (x)
                                     (=
                                      (mod x
                                           (car go-lst))
                                      0))
                                 (cdr go-lst))
                      (cons (car go-lst)
                            acc-list))))))

    (sieve-iter input-lst '())))

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

(defmacro prime-sieve (n)
  `(prime-sieve-a-list (cons 2
                             (range (1+ ,n)
                                    :min 3
                                    :step 2))))


(time (length (prime-sieve 20000000)))

;; Evaluation took:
;; 19.907 seconds of real time

What is the value of the first triangle number to have over five hundred divisors?

(defun factor-iter (n p-list acc-list)
  (if (NULL p-list)
      acc-list         
      (let* ((p (car p-list))                                   
             (ps (cdr p-list)))  
        (cond ((> (* p p) n)           
               (good-reverse (cons n
                                   acc-list)))
              ((eql (mod n p) 0)
               (factor-iter (floor n p)
                            p-list
                            (cons p acc-list)))   
              ('t
               (factor-iter n ps acc-list))))))

(defparameter *pm* 2000000)

(defparameter *psi* (prime-sieve *pm*))

(defun factor (n)
  (if (> n (expt *pm* 2))
      
      (let ((m (floor (sqrt n))))
        (factor-iter n (prime-sieve m) '()))
      
      (factor-iter n *psi* '())))

(defun group-factors (lst)
  (labels ((gf (acc lst)
             (if (NULL lst)
                 (good-reverse acc)
                 (let* ((p (car lst))
                        (ps (cdr lst))
                        (lp1 (list p 1)))
                   (if (NULL acc)                      
                       (gf (list lp1) ps)                      
                       (if (eql p (caar acc))
                           (gf (cons
                                (list p
                                      (+ 1
                                         (cadar acc)))
                                (cdr acc))
                               ps)                  
                           (gf (cons lp1 acc) ps)))))))    
    (gf '() lst)))

(defmacro sum (lst)
  `(reduce #'+ ,lst))

(defmacro product (lst)
  `(reduce #'* ,lst))

(defun nDiv (n)
  (product (mapcar #'(lambda (x) (1+ (cadr x)))
                   (group-factors (factor n)))))

(defun fm (m n)
  (labels ((tri-div (n)
             (if (evenp n)
                 (* (nDiv (/ n 2)) (nDiv (1+ n)))
                 (* (nDiv n) (nDiv (/ (1+ n) 2))))))    

    (if (> (tri-div n) m)
        (/  (* n (1+ n)) 2) 
        (fm m (+ 1 n)))))

;

(time (fm 500 1))

;; Evaluation took:
;; 0.007 seconds of real time

;; 76576500

— Me@2023-03-25 07:51:18 PM

3.4 Electric fields and potentials of point charges

Posted on March 18, 2023 by rpflee

A First Course in String Theory

(a) Show that for time-independent fields, the Maxwell equation $\displaystyle{T_{0ij}=0}$ implies that $\displaystyle{\partial_i E_j - \partial_j E_i = 0}$ . Explain why this condition is satisfied by the ansatz $\displaystyle{\vec E = - \nabla \Phi}$ .

~~~

Eq. (3.23):

$\displaystyle{ \begin{aligned} T_{\mu \lambda \nu} &= \partial_\lambda F_{\mu \nu} + \partial_\mu F_{\nu \lambda} + \partial_\nu F_{\lambda \mu} \\ \end{aligned}}$

…

$\displaystyle{ \begin{aligned} &\vec E \\ &= - \nabla \Phi \\ &= - \left( \partial_x, \partial_y, \partial_z \right) \Phi \\ \end{aligned}}$

$\displaystyle{ \begin{aligned} &\partial_i E_j - \partial_j E_i \\ &= \partial_i \partial_j \Phi - \partial_j \partial_i \Phi \\ \end{aligned}}$

— Me@2023-03-18 11:08:24 AM

Debugging quantum concepts

Posted on March 17, 2023 by rpflee

Reality is a superposition of eigenstates. Even if we use the pilot-wave formalism, in which a particle has definite position or momentum, the pilot wave itself is in a superposition.

— Me@2012-04-16 2:27:20 PM

Physics reality is NOT a superposition of eigenstates. If physics reality was a superposition of eigenstates, there would have never been any interference patterns.

For an experimental setup, what is in a superposition is the quantum state, which is a tool for deducing probabilities of different potential measurement results.

“A quantum state is a superposition of eigenstates” just means nothing more than that we need to use individual probabilities of the eigenstates to calculate the probabilities.

A quantum state, which is represented by a wave function, is logical, mathematical, conceptual, and linguistic in nature. A quantum state is NOT physical. A quantum state is NOT reality. A quantum state is NOT directly corresponding to a physical reality (aka observable events, measurement results, etc.)

A quantum state is NOT even corresponding to a probability directly. (If a quantum state was a probability, there would have never been the phenomenon of interference.) Instead, a quantum state is corresponding to a probability amplitude, which is used for calculating probabilities.

— Me@2023-03-16 09:57:07 AM

Computing Note, 5

Posted on March 15, 2023 by rpflee

21[.]07[.]2002 

From Personal Computer[s] to Personal Robots 

27[.]07[.]2002 

optical fibers

In the beginning of the optical fiber research, 
there were a lot of difficulties. But I thought if 
[I succeeded], the research payoff would be huge, 
because it could create a whole new world. 
"Mingpao Monthly"

        By the Father of Optical Fibers 

19[.]08[.]2002

Make Robot as inexpensive and as useful as 
Personal Computer -- Personal Robot

Corsair Vengeance RGB Pro

Posted on March 13, 2023 by rpflee

你有「婚前性」的話，一定不會從一而終。

如果你宣稱，你的「婚前性」對象，由始至現在至未來，只有一位，亦只會有一位的話，那樣，你在一開始時，為何不先與其結婚？

第二，數字不是零或一的話，就不知是多少。

第三，可以前的話，就可以外。

— Me@2023-03-12 10:28:29 AM

MangoHud

Posted on March 7, 2023 by rpflee

A Vulkan and OpenGL overlay for monitoring FPS, temperatures, CPU/GPU load and more.

vram
ram
swap
gpu_temp
cpu_temp
gpu_power
cpu_power

— Me@2023-03-07 09:14:51 AM

Ex 2.1-2 Particle in a Box

Posted on March 5, 2023 by rpflee

Quantum Methods with Mathematica

Reproduce Figure 2.1-1 …

~~~

phi[n_, x_] := Sin[n Pi x]

p[n_] := Plot[phi[n,x],{x,0,1}]

GraphicsColumn[{p[1], p[2], p[3]}]

— Me@2023-03-03 01:30:46 PM

Intermediate states

Posted on March 2, 2023 by rpflee

What happens in the interval between the initial and final states of the interaction process?

What happens in between is everything and nothing. There is no privileged clearcut answer what happened that would be physically meaningful. It’s really the very basic point of quantum mechanics that only results of measurements are physically meaningful facts or observables; all other data are fictitious or uncertain. By the very definition of your problem, no measurement took place in the intermediate states which means that no sharp answers to any questions were generated, no answers or values became real or privileged or facts.

…

But unlike classical physics, quantum mechanics says that not only the probabilities of each history matter. All the relative phases matter, too.

— answered Jan 9, 2021 at 16:10

— Luboš Motl

— Physics StackExchange

2023.03.02 Thursday ACHK

Copyleft 7

Posted on March 1, 2023 by rpflee

What stands in the way becomes the way.

— Marcus Aurelius

capitalize on

~ 用之以謀利

~ 利用

copyleft

~ 敵為己用

~ 幽默利用

~ 反利用

~ 草船借箭

— Me@2023-03-01 01:22:15 PM

人生 Presentation, 2.3

Posted on February 28, 2023 by rpflee

這段改編自 2010 年 4 月 24 日的對話。

…

那是 Paul Buchheit 講過的，我現在轉述成：

在第一個版本中，最重要賣點以外的優點，都只是雜音。

這個原理翻譯成教學版本的話，就是：

在教授新課題時，應只聚焦核心思想，用不同的字眼言辭去覆術它，而斬釘截鐵地，省略其他一切細節，暫時。

主題以外的有趣內容，一律視為敵人，暫時。

這和之前那一點「每課只講一點」的分別是：

你不單止要「只講一點」，還要有「主動放棄其他」的心態。

為什麼兩人開始情投意合時，不立刻結婚呢？

因為相愛容易，相處很難。

相愛時，你可以選擇只接受，對方優點中，最好的一點。

相處時，你不可以選擇不接受，對方缺點中，最差的一點。

所以，即使開始情投意合，兩人也應先作朋友，不作情侶。

可以作朋友的，不一定適合，作情侶。

同理，可以作情侶的，不一定適合作夫妻。

所以，當發覺必定，終不成夫妻時，應立刻終止情侶關係。

這和之前那一點「一生只愛一人」的分別是：

你不單止要「只愛一人」，還要有「主動放棄其他」的心態。

未來妻子以外的女子，（！）現在（！）就要疏遠，無論她有多好，你有多喜歡。

— Me@2023-02-28 11:16:42 AM

Euler problem 10.2

Posted on February 26, 2023 by rpflee

Find the sum of all the primes below two million.

removeIf :: (a -> Bool) -> [a] -> [a]
removeIf p = filter (not . p)

sieveIter :: Integral a => [a] -> [a] -> [a]
sieveIter [] (x:xs) = x:xs
sieveIter (x:xs) acc
  | x^2 > last (x:xs) = reverse acc++(x:xs)
  | otherwise = sieveIter xss (x:acc)
  where
    xss = removeIf (\n -> n `mod` x == 0) xs

primeList :: Integral a => [a] -> [a]
primeList xs = sieveIter xs []

pL :: [Integer]
pL = primeList [2..2000000]

f :: Integer
f = sum (takeWhile (< 2000000) pL)

— colorized by palette fm

— Me@2023-02-25 12:35:57 PM

Zsh, 2

Posted on February 24, 2023 by rpflee

To install the Z shell (Zsh):

1. Read my blog post “Zsh” to follow the instructions point 1 and point 2.

2. In the Bash terminal, run

zsh

once, in order to get the config file generated.

3. Return to my blog post “Zsh” to follow the remaining steps.

— Me@2023-01-19 12:41:56 PM

— Me@2023-02-24 05:19:38 PM

Looper, 6

Posted on February 24, 2023 by rpflee

Causal diamonds in time travel, 3

Time travel in the absolute sense is logically impossible.

If time travel was logically possible, it still could be logically consistent from the time traveller’s point of view, as long as he cannot see from the perspective of the meta time.

— Me@2016-06-01 07:10:51 AM

— Me@2023-02-23 12:13:20 PM

When physics meets biology

Posted on February 23, 2023 by rpflee

oli5679 on May 15, 2018

There was a really good chapter on his time in a biology lab in his book, “Surely you’re joking Mr. Feynman”. I have always remembered this quote:

When it came time for me to give my talk on the subject, I started off by drawing an outline of the cat and began to name the various muscles.

The other students in the class interrupt me: “We know all that!”

“Oh,” I say, “you do? Then no wonder I can catch up with you so fast after you’ve had four years of biology.” They had wasted all their time memorizing stuff like that, when it could be looked up in fifteen minutes.

sykh on May 15, 2018

Feynman was wrong on his view. The same thing could have been said of him and physicists. Oh, you spent your time memorizing formulas when it could be looked up in 15 minutes.

This is a nonsensical point of view for two reasons. [1] People in areas of their expertise tend to know a lot in that area off the top of their head because they have encountered this stuff so much that it has become memorized. That memorized knowledge comes from experience not a memorization exercise. [2] It’s also nonsensical because if you didn’t have a core set of knowledge memorized in your area of expertise and instead relied on spending 15 minutes looking up each fact necessary to understand a given situation you’d end up wasting your whole day just trying to understand the meaning of the problem.

— Hacker News

2023.02.22 Wednesday ACHK

分數版 nCr

Posted on February 22, 2023 by rpflee

nCr, 0.10

Euler problem 10.1

Posted on February 21, 2023 by rpflee

Find the sum of all the primes below two million.

(defmacro sq (x)
  `(* ,x ,x))

(defmacro last-item (lst)
  `(car (last ,lst)))

(defun good-reverse (lst)
  (labels ((rev (lst acc)
         (if (null lst)
         acc
         (rev
          (cdr lst)
          (cons (car lst) acc)))))
    (rev lst nil)))

(defun prime-sieve-a-list (input-lst)
  (labels ((sieve-iter (go-lst acc-list)
         (if (not go-lst) 
         acc-list        
         (if (> (sq (car go-lst))
            (last-item go-lst))

             (append (good-reverse acc-list)
                 go-lst)
             
             (sieve-iter
              (remove-if #'(lambda (x)
                     (=
                      (mod x (car go-lst))
                      0))
                 (cdr go-lst))
              (cons (car go-lst)
                acc-list))))))

    (sieve-iter input-lst '())))

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

(defmacro prime-sieve (n)
  `(prime-sieve-a-list (cons 2 (range (1+ ,n)
                      :min 3
                      :step 2))))

(defun sum (lst)
  (reduce #'+ lst))

(sum (prime-sieve 2000000))

(time (sum (prime-sieve 2000000)))

— Me@2023-02-16 11:34:49 PM

G40-70

Posted on February 15, 2023 by rpflee

If you are using SSD, you should turn off the swap file:

1. In command line, run

swapoff --all

2. Backup the file

/etc/fstab

3. Then, in that file, comment out any lines that contain the word “swap”.

— Me@2023-02-14 05:00:26 PM

Causal diamonds in time travel, 2

Posted on February 13, 2023 by rpflee