同因不同果

Posted on November 25, 2023 by rpflee

注定外外傳 2.3 | Can it be Otherwise? 3.3

而量子力學中的「疑似一個場境，多個可能結果」的原因是，「全同粒子」沒有客觀的身份，導致沒有辦法，定義到所謂的「同一個場境」。一個宏觀狀態，其實對應於，多個微觀狀態。

簡化來說，這次的宏觀狀態和上次相同，不代表微觀狀態和上次一樣。

詳細而言，「同一個微觀狀態」不只是「未有定義」，而是「不可能有，直接的定義」，因為，你試想想，我們怎麼分辨到，不同的「微觀狀態」呢？

只能透過對「宏觀狀態」的「觀察」或「量度」。

換句話說，你只能透過「宏觀狀態」，去定義各個「微觀狀態」。

所以，我們不可能，直接定義「同一個微觀狀態」。

要「同一個狀態」，最多只能定義「同一個宏觀狀態」。但那也只是簡稱，實情是「（其實對應於，多過一個微觀狀態的）同一個宏觀狀態」。

所謂的「宏觀狀態」，即是「物理現象」。所謂的「物理現象」，就是從「物理事件」中，可以「觀察」到的感覺，或「量度」到的數據。所謂的「微觀狀態」，即是「物理本體」。所謂的「物理本體」，就是指「物理事件」本身。例如，我看到一個杯子時，透過視覺接收到的杯子影像，就是「杯子現像」。而那些影像的原因來源，即是那個「杯子本身」，就是「杯子本體」。

同一個杯子，可以有不同的現象，例如，我在不用角度看那杯子，就會看在不同的影像。

又例如，即使我看到，一個彩色的杯子時，會接收到一個彩色影像，我的狗在看到那杯子時，只會看到黑白的版本，因為狗是色盲的。（那是簡化的講法，因為狗只是「紅綠色盲」，不是「全色盲」。）

「杯子本體」，可以視為「杯子全部」——有關杯子的全部事實。而「杯子現象」，則是「杯子部分」——有關杯子的部分事實。

留意，並沒有所謂的，「我看到杯子本身」和「我看到杯子現象」之分，因為，「我看到杯子」的意思，正正就是指：「我接收到，來自那杯子的影像訊息」。而「色即是空，空即是色」，就是這個意思。

「色」是「顏色影像」，即「現象」也。「空」則是「色」的因——有「顏色影像」之前，就存在的東西，即「本體」也。

正如，電腦「零件」，有分「硬件」和「軟件」。但沒有分「硬件模式」和「軟件模式」，因為，「軟件」正正是，硬件電子的排列模式；「軟件」這個字眼的定義，就是「硬件模式」。這裡，「硬件」對應「本體」，「軟件」對應「現象」。

另一個講法是，「杯子」就是「杯子本身」，而「看到杯子（的感覺）」，就是「杯子現象」。

我只是這個世界，小小的一個角落。這小小的一個角落，卻是我的全部世界。

—

既然，「我看到杯子本身」和「我看到杯子現象」沒有分別，我們為什麼還要分辨釐清，「杯子本身」和「杯子現象」呢？

亦即是話，為什麼「杯子本身」和「杯子現象」，卻會有分別呢？

那是為了提醒，還有其他的現象。

例如，剛才提及，同一個杯子，可以有不同的現象——即使我看到一個彩色的杯子時，會接收到一個彩色影像，我的狗在看到那杯子時，只會看到「沒有那麼彩色」的版本，因為，狗是「紅綠色盲」的。

又例如，同一個電腦遊戲，你用不同配備的電腦，會看到不同詳細程度的畫面。

再例如，同一板網頁，你用不同的電腦作業系統，會看到不同的字體。例如，這篇文章，如果你用 Linux 的話，呈現的是階書。但是，其他系統如果沒有該字體，則會顯示其他。

One of the most powerful illusions of the human experience is the illusion that we’re seeing objective reality through our own perceptions. We can only see what we see.

— Christopher Nolan

以下其中三句同義：

1. 小世界，不是大世界。

2. 你的世界，只是你的世界。

3. 你的世界，只是主觀世界，不是客觀世界。

4. 你對客觀世界的感官和認知，只是客觀世界的部分，不是客觀世界的全部。

5. 你的世界，只是世界的現像，不是世界的本體。

其實，五句也同義。

愚蠢的人以為，自己的主觀世界，就是客觀世界；所以，他們不知道，自己的愚蠢。

聰明的人知道，自己的主觀世界，只是客觀世界的，一小部分；所以，他們可以真切感受到，自己的愚蠢。

— Me@2009.09.17

— Me@2023-11-13 12:56:32 PM

— Me@2023-11-24 11:12:39 AM

Quicklisp error

Posted on November 23, 2023 by rpflee

Common Lisp calculator, 2

1. To run the following code, you have to install the Quicklisp library manager by following the steps in my blog post titled cmu-infix.

2.1 To enable the library, in the Common Lisp REPL, run the code:

(ql:quickload :cmu-infix)

(named-readtables:in-readtable cmu-infix:syntax)

2.2 If you encounter the error message:

Lisp connection closed unexpectedly: connection broken by remote peer

2.2.1 empty the cache folder:

~/.cache/common-lisp/

2.2.2 Restart the Common Lisp REPL.

2.2.3 Reload the library.

3.1 The goal of the following code is to create our own REPL.

(defmacro infix-string-eval (a-string)
  `(eval (read-from-string
          (concatenate 'string
                       "#I (" ,a-string ")"))))

(defun read-repl-all ()
  (loop (print (write-to-string (read)))))

(defun my-repl ()
  (loop
    (let ((a-string (write-to-string (read))))
      (if (or (string-equal "(exit)" a-string)
              (string-equal "exit" a-string))
          (return)            
          (print
           (infix-string-eval
            (string-trim "|()" a-string)))))))

3.2 In the Common Lisp REPL, run the code:

(my-repl)

— Me@2022-12-26 01:10:34 PM

The symbol

is the bitwise exclusive OR.

To create an exponentiation, we use

^^

— Me@2023-09-09 12:51:46 PM

— Me@2023-11-22 12:56:00 PM

3 Vector Fields and One-Form Fields, 2

Posted on November 20, 2023 by rpflee

Functional Differential Geometry

p. 21

1.1

$\displaystyle{(Df(x)) \Delta x}$ is the directional derivative of $\displaystyle{f}$ at $\displaystyle{x}$ with respect to $\displaystyle{\Delta x}$ , which is a vector in terms of a coordinate component tuple.

1.2

Note that $\displaystyle{\Delta x}$ is not actually coordinates, but a change of coordinates. Instead, $\displaystyle{x}$ is the coordinate tuple.

Moreover, $\displaystyle{x}$ and $\displaystyle{\Delta x}$ are independent of each other.

1.3

Instead of being a function of position $\displaystyle{x}$ only, $\displaystyle{(Df(x)) \Delta x}$ depends also on $\displaystyle{\Delta x}$ . So $\displaystyle{(Df(x)) \Delta x}$ is NOT a vector field.

2.1

$\displaystyle{(Df(x)) b(x) \ne (Df(x)) \Delta x}$

Instead, $\displaystyle{(Df(x)) b(x)}$ is a generalization of $\displaystyle{(Df(x)) \Delta x}$ .

2.2

Note that $\displaystyle{b(x)}$ is a function chosen by you.

2.3

Since $\displaystyle{(Df(x)) b(x)}$ is a function of position $\displaystyle{x}$ only, it is a vector field.

2.4

Let

$\displaystyle{ \begin{aligned} D_b(f)(x) &= ((Df(x)) b(x) \\ \end{aligned} }$

2.5

$\displaystyle{ \begin{aligned} \textbf{v}(\text{f})(\textbf{m}) &\ne D_b(f)(x) \\ \end{aligned} }$

Instead, $\displaystyle{ \textbf{v}(\text{f})(\textbf{m})}$ is a further generalization of $\displaystyle{ D_b(f)(x)}$ .

2.6

While $\displaystyle{ x }$ is the tuple of coordinate components of a point, $\displaystyle{ \textbf{m} }$ is the abstract point itself.

— Me@2023-11-19 11:40:49 AM

Ideal clock 6.2

Posted on November 18, 2023 by rpflee

How do we find the accuracy of atomic clocks?

The nearest we have to a standard is International Atomic Time. This is:

TAI as a time scale is a weighted average of the time kept by over 200 atomic clocks in over 50 national laboratories worldwide.

The errors in individual clocks can be assessed by comparing them to the weighted average.

— answered Dec 18, 2014 at 18:06

— John Rennie

We measure multiple clocks against each other and compare the statistical errors. This assumes that the clocks do not have the same systematic errors, of course. In practice this is controlled by using different technologies with different systematic errors and by having multiple clocks of the same technology built and operated by different groups of people in different locations of the world. In addition we are also comparing against precision clocks provided by nature, like pulsars. While those are not quite as accurate as our atomic clocks, they are guaranteed to be independent of us. – CuriousOne Dec 18, 2014 at 14:31

— Physics StackExchange

2023.11.18 Saturday ACHK

Warranty

Posted on November 14, 2023 by rpflee

Extend Your Handheld Coverage (Available in U.S. only)

Protect your Palm handheld with Palm Care plan and receive up to two years of additional support.

With Palm Care Plan:
Extend your handheld coverage by 12 months. Covers your Palm handheld against defects in workmanship and material.

Extend technical telephone support to two years. Call toll free and get a prompt response to your problem.

Receive a one-time, FREE screen replacement (not covered under the original warranty).

Express replacement and no additional shipping charges. Get a replacement handheld within 1-3 business days at no extra charge during the length of your contract (not covered under the original warranty).

Visit …com/warranty to find out more.

Excludes certain damage caused by misuse, neglect, improper installation or testing, unauthorized attempts to open, repair, or modify the product, or any other cause beyond the range of normal use. Available in the U.S. only. See the above website for complete details.

2023.11.15 Wednesday ACHK

注定外外傳 2.2

Posted on November 13, 2023 by rpflee

Eternal return, 3.2 | Can it be Otherwise? 3.2

「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？

自由命定問題，不可能答的主要原因是，並沒有兩個，百分百相同的情境，因為，邏輯上(即是根據定義)，「百分百相同的情境」就會有「百分百相同的結果」。「自由命定」(Can it be otherwise?) 這問題，再也沒有意思。

還有，即使你宣稱，第二個情境和第一個「百分百相同」，它們至少時間上不同。如果連時間都相同，那所謂的「第二個情境」，根本是第一個情境，即是從來沒有「第二個情境」。

而量子力學中的「疑似一個場境，多個可能結果」的原因是，「全同粒子」沒有客觀的身份，導致沒有辦法，定義到所謂的「同一個場境」，因為，一個宏觀狀態，其實對應於多個微觀狀態。

簡化來說，這次的宏觀狀態和上次相同，不代表微觀狀態和上次一樣。詳細而言，「同一個微觀狀態」不只是「未有定義」，而是「不可能有，直接的定義」，因為，你試想想，我們怎麼分辨到，不同的「微觀狀態」呢？

只能透過對「宏觀狀態」的「觀察」或「量度」。換句話說，你只能透過「宏觀狀態」，去定義各個「微觀狀態」。所以，我們不可能去，直接定義「同一個微觀狀態」。要「同一個狀態」，最多只能定義「同一個宏觀狀態」。但那也只是簡稱，實情是「（其實對應於，多過一個微觀狀態的）同一個宏觀狀態」。

— Me@2015-09-08 04:04:48 PM

— Me@2023-09-13 11:41:57 PM

— Me@2023-11-13 12:56:32 PM

Euler problem 17.2

Posted on November 8, 2023 by rpflee

import Data.Char ( digitToInt )

one :: [String]
one =
  [ "one",
    "two",
    "three",
    "four",
    "five",
    "six",
    "seven",
    "eight",
    "nine",
    "ten",
    "eleven",
    "twelve",
    "thirteen",
    "fourteen",
    "fifteen",
    "sixteen",
    "seventeen",
    "eighteen",
    "nineteen"
  ]

ty :: [String]
ty =
  [ "twenty",
    "thirty",
    "forty",
    "fifty",
    "sixty",
    "seventy",
    "eighty",
    "ninety"
  ]

english :: Int -> [Char]
english x
  | x == 0 = []
  | x < 20 = one !! (x - 1)
  | x >= 20 && x < 100 =
      ty !! (firstDigit x - 2)
        ++ " "
        ++ english (x - firstDigit x * 10)
        
  | x < 1000 && x `mod` 100 == 0 =
      one !! (firstDigit x - 1)
        ++ " hundred"
      
  | x > 100 && x <= 999 =
      one !! (firstDigit x - 1)
        ++ " hundred and "
        ++ english (x - firstDigit x * 100)
        
  | x == 1000 = "one thousand"
  | otherwise = "error"
  where
    firstDigit = digitToInt . head . show

removeSpace :: [Char] -> [Char]
removeSpace = filter (`notElem` " ")

engCat :: [Int] -> [Char]
engCat = concatMap english

e17 :: Int
e17 = length . removeSpace $ engCat [1..1000]

— based on Haskell official

λ> e17
21124

— colorized by palette fm

— Me@2023-11-07 11:24:03 PM

KDE Wifi

Posted on November 6, 2023 by rpflee

Sometimes, KDE Plasma keeps turning off wifi during every startup. To solve this problem:

1. Type this command to the terminal:

sudo emacs \ 
/etc/systemd/system/unb-wifi.service

1.1 If you like, you can replace

emacs

with your favourite editor’s name in this command.

1.2 The goal of this command is to create the new text file

unb-wifi.service

2.1 Copy and paste the following code to the text file.

[Unit]
Description=Unblock WiFi Devices

[Service]
Type=oneshot
ExecStart=/usr/sbin/rfkill unblock wifi
ExecStart=/usr/bin/nmcli radio wifi on
ExecStop=
RemainAfterExit=yes

[Install]
WantedBy=multi-user.target

2.2 Save the file and exit the editor.

3.1 Execute this command in bash terminal:

sudo systemctl enable \ 
unb-wifi.service

If you get any errors, try this instead:

sudo systemctl enable \ 
/etc/systemd/system/unb-wifi.service

3.2 Then, execute also:

sudo systemctl start \ 
unb-wifi.service

If you get any errors, try this instead:

sudo systemctl start \ 
/etc/systemd/system/unb-wifi.service

3.3 If you still get errors, restart your computer.

Check if the wifi is already on.

— Me@2023-11-05 12:56:05 PM

時光起源, 2

Posted on November 3, 2023 by rpflee

The Origin of Time, 2

In general, on average, a large object moves slower than a small object, because each one’s speed is constrained by its slowest component particle and the large object consists of more particles.

In other words, if the two objects have identical particle components and identical particle densities, the large object has a bigger inertia than the small one.

“Being constrained by other component particles” is the exact cause of the existence of mass of an object. Even when all the particles within the object travel at the speed of light, some may be travelling in different directions. So the object as a whole cannot travel at the speed of light.

— Me@2023-10-22 07:37:01 AM

Physics Town

continues

Monthly Archives: November 2023