為了清楚說明 M♪o 之『學習』『遞迴觀』，也許簡單的辦法是用她自身的『學習』歷程來詮釋︰

 

山高侵昊  天，時  厲，難與行。何德能嘉遯？志固執用黃牛革。傲來有石  猴，獨尊是佛陀，如來血脈一滴傳，因而敢登唯我峰。臨 事心踟躕，意緒無處寄

《晚晴》李商隱

深居俯夾城，春去夏猶清。
天意憐幽草，人間重晚晴。
並添高閣迥，微注小窗明。
越鳥巢乾後，歸飛體更輕。

，總是時到時擔當。

派︰突然停課，吹嚮了《加百利之號角！！》︰

這樣的一個學習者將會如何建造自己知識之金字塔的呢？他會不會用『想像的實驗』去釐清『基本概念』之糾葛的呢？還是用『推導歸謬』的邏輯，去探測一個『自明假設』之深遠結論的呢？又或者會將在大自然中發現的方程式求解，然後『畫圖』與『演示』這個解之意義的呢？……

如果從人類的創造發明史來看，那樣的學習者終將使用當時之最好的『學習工具』，打造自己的『學習工具箱』，甚至會創新『既有之工具』。就現今來講，除了使用電腦的一般應用軟體之外 ── 比方說文書處理等等 ──，最重要的就是能掌握 『程式語言』與『數學語言』的工具。或許這正是樹莓派基金會一開始打造樹莓派時所想的重要原因，讓學習者能有學習的工具！！
……

─── 引自《 M♪o 之學習筆記本《辰》組元︰【䷠】黃牛之革》

 

這是一條經『生澀』過『熟巧』的道路。或許因此可以知『經驗』之『粹練』如何型塑了一個人的『理解』︰

……

， 真真是，夏日午後雷雨多，把我們當『鴨子』，叫我們『聽雷』的哩！雖是這麼想，那裡頭還彷彿真有『名堂』的ㄟ，即使聽無，就當是異地觀光！！

☆ 編者言

自『卯』的首篇 ䷁ 起， M♪o 學習筆記之篇章序次，改成了『十二爻辰』， 或許是因應課綱變了，不宜再用『五行序』。十二爻辰又稱作『十二消息卦』，是一年四季流轉，天地給予『消息』。所謂『八月有凶』，蓋指『臨』䷒ 經過『泰』䷊ ，而後『否』䷋ ，再到『觀』 ䷓ ，中有八個月。由『臨』月始一，八月入『否』。此篇可苦了編者，九天九地，收尋《庫文》《網文》以應其《 》數。

 

生︰同學們，要深入理解『入出針』，必須確實明白『取樣原理』， 《  》技講︰

Sampling (signal processing)

In signal processing, sampling is the reduction of a continuous signal to a discrete signal. A common example is the conversion of a sound wave (a continuous signal) to a sequence of samples (a discrete-time signal).

A sample is a value or set of values at a point in time and/or space.

A sampler is a subsystem or operation that extracts samples from a continuous signal.

A theoretical ideal sampler produces samples equivalent to the instantaneous value of the continuous signal at the desired points.

Theory

Sampling can be done for functions varying in space, time, or any other dimension, and similar results are obtained in two or more dimensions.

For functions that vary with time, let s(t) be a continuous function (or “signal”) to be sampled, and let sampling be performed by measuring the value of the continuous function every T seconds, which is called the sampling interval.^[1]  Then the sampled function is given by the sequence:

s(nT),   for integer values of n.

The sampling frequency or sampling rate, f_s, is the average number of samples obtained in one second (samples per second), thus f_s = 1/T.

Reconstructing a continuous function from samples is done by interpolation algorithms. The Whittaker–Shannon interpolation formula is mathematically equivalent to an ideal lowpass filter whose input is a sequence of Dirac delta functions that are modulated (multiplied) by the sample values. When the time interval between adjacent samples is a constant (T), the sequence of delta functions is called a Dirac comb. Mathematically, the modulated Dirac comb is equivalent to the product of the comb function with s(t). That purely mathematical abstraction is sometimes referred to as impulse sampling.^[2]

Most sampled signals are not simply stored and reconstructed. But the fidelity of a theoretical reconstruction is a customary measure of the effectiveness of sampling. That fidelity is reduced when s(t) contains frequency components whose periodicity is smaller than 2 samples; or equivalently the ratio of cycles to samples exceeds ½ (see Aliasing). The quantity ½ cycles/sample × f_s samples/sec = f_s/2 cycles/sec (hertz) is known as the Nyquist frequency of the sampler. Therefore s(t) is usually the output of a lowpass filter, functionally known as an anti-aliasing filter. Without an anti-aliasing filter, frequencies higher than the Nyquist frequency will influence the samples in a way that is misinterpreted by the interpolation process.^[3]
……

ㄚ˙ㄏㄚˋ，AHHA 過去本不是『白老鼠』，焉知 ── 莊子 ──，焉不知 ── 惠施 ──『魚出游』的『感覺』？！

果然然，『拔茅茹，以其夤，』但求『征吉。』？？

碼︰研 習。 今天時候晚了，不實作，就研習一點什麼是『取樣』之概念。何謂『平』與『陂』的呢？如果從螞蟻和大象的『觀點』來看，能夠一樣嗎？？光以『相對大小』來 講，大象以為『平』的，對螞蟻來說，可以『陂』陡的不得了。再說螞蟻的一步『小』，大象的足距『大』，要是用幾何上的『曲線』比喻，螞蟻『沿』著曲線走， 大象一『踏』就一段。如此螞蟻的『足跡』即使是『離散』也較『符合』那條『曲線』，大象『疏闊』之『步履』恐不存那條『曲線』之形的了。此《 》

的精義，就是表達開關『兩態取值』之『取樣』觀。不同的取樣『速度』 ── 頻率 ──，所讀到的『情況』可以不同。『高』頻的似『螞蟻』，『低』頻的如『大象』。若是忽略了『彈跳』的暫態現象，恐會引發『開』或『關』狀態之『誤判』，不可不慎。

同學們可以參考下面程式

pi@raspberrypi ~ $ sudo -s
root@raspberrypi:/home/pi# python3
Python 3.2.3 (default, Mar  1 2013, 11:53:50) 
[GCC 4.6.3] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> import RPi.GPIO as GPIO
>>> from time import sleep
>>> GPIO.setmode(GPIO.BCM)
>>> 
>>> 按鍵一 = 23
>>> 頻率 = 100
>>> 數據列 = []
>>> 
>>> def 等入高針按鍵取值(針碼, 取值列, 頻率=100, 資料=100):
...     GPIO.setup(針碼, GPIO.IN, pull_up_down = GPIO.PUD_UP)
...     while True:
...         if GPIO.input(針碼) == 0:
...             for i in range(資料):
...                 取值列.append(GPIO.input(針碼))
...                 sleep(1.0/頻率)
...             break
... 
>>> 等入高針按鍵取值(按鍵一, 數據列)
>>> 數據列
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
>>> len(數據列)
100
>>> 測試列=[]
>>> 等入高針按鍵取值(按鍵一, 測試列, 頻率=500, 資料=500)
>>> len(測試列)
500
>>> 數據列
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
>>>

，試著探討『彈跳現象』。

☿ 行︰豈可『妄自菲薄』，定要『發憤圖強』。☿

訊︰☿ 今方知所謂『無平不陂』矣。

─── 引自《 M♪o 之學習筆記本《卯》基件︰【䷊】無平不陂》

 

所以可以將 M♪o 之『學習』『遞迴觀』詮釋為萬事萬物『理解』的『定點』，一再『回歸地』『認識』那個『事物』，終至能達該個『事物』之『理解』。這是『過程』與『結果』間『契合』的共鳴﹐可能也是『理解』之可以『理解』，『生命』『認知』不假外求的『絕待』。然後明白了解，現象『認知學習』之環境的『主旨』就是『生命』之『理解』的『途徑』罷了！！

 

【 JACK 環境安裝】

sudo apt-get install jaaa jack-capture jack-keyboard jack-mixer jack-rack jack-stdio jack-tools jackeq jnoise meterbridge freqtweak 

sudo apt-get install lilypond rosegarden kmidimon

sudo apt-get install qjackctl qsynth

sudo apt-get install puredata

sudo apt-get install brp-pacu japa

sudo apt-get install x42-plugins

sudo apt-get install alsaplayer-gtk alsaplayer-jack alsaplayer-text

sudo pip3 install JACK-Client