《呂氏春秋‧慎行論》

察傳

夫得言不可以不察，數傳而白為黑，黑為白。故狗似玃，玃似母猴 ，母猴似人，人之與狗則遠矣。此愚者之所以大過也。聞而審則為福矣，聞而不審，不若無聞矣。

齊桓公聞管子於鮑叔，楚莊聞孫叔敖於沈尹筮，審之也，故國霸諸侯也。吳王聞越王句踐於太宰嚭，智伯聞趙襄子於張武，不審也，故國亡身死也。

凡聞言必熟論，其於人必驗之以理。魯哀公問於孔子曰：「樂正夔一足，信乎？」孔子曰：「昔者舜欲以樂傳教於天下，乃令重黎舉夔於草莽之中而進之，舜以為樂正。夔於是正六律，和五聲 ，以通八風，而天下大服。重黎又欲益求人，舜曰：『夫樂，天地之精也 ，得失之節也，故唯聖人為能和。樂之本也。夔能和之 ，以平天下 。若夔者一而足矣。』故曰夔一足，非一足也。」

宋之丁氏，家無井而出溉汲，常一人居外。及其家穿井，告人曰：「吾穿井得一人 。」有聞而傳之者曰：「丁氏穿井得一人 。」國人道之，聞之於宋君，宋君令人問之於丁氏，丁氏對曰：「得一人之使，非得一人於井中也。」求能之若此，不若無聞也。

子夏之晉，過衛，有讀史記者曰：「晉師三豕涉河。」子夏曰：「非也，是己亥也。夫『己』與『三』相近，『豕』與『亥』相似 。」至於晉而問之，則曰「晉師己亥涉河」也。辭多類非而是 ，多類是而非。是非之經，不可不分，此聖人之所慎也。然則何以慎？緣物之情及人之情以為所聞則得之矣。

古早的中國喜用『類比』來論事說理，難道這就是『科學』不興的原因嗎？李約瑟在其大著《中國的科學與文明》試圖解決這個今稱『李約瑟難題』之大哉問！終究還是百家爭鳴也？若是比喻的說︰一個孤立隔絕系統之演化，常因內部機制的折衝協調，周遭環境之影響相對的小很多。因此秦之『大一統』，歷代的『戰亂』頻起，能不達於『社會』之『平衡』的耶？？如此『主流價值』亦是已然確立成為『文化內涵』的吧！！所以『天不變』、『道不變』，人亦『不變』乎！！？？雖然李約瑟曾經明示『類比』── 關聯式 corelative thinking 思考 ── 難以建立完整的『邏輯體系』， 或是『科學』不興的理由耶？？！！如果『自然事物』之『邏輯推理』能形成系統『大樹』，那麼『類比關聯』將創造體系『森林』矣，豈可不『慎察』也。

類比（英語：Analogy，源自古希臘語：ἀναλογία，analogia，意為等比例的），或類推，是一種認知過程，將某個特定事物所附帶的訊息轉移到其他特定事物之上。類比通過比較兩件事情，清楚揭示二者之間的相似點，並將已知事物的特點，推衍到未知事物中，但兩者不一定有實質上的同源性，其類比也不見得「合理 」。在記憶、溝通與問題解決等過程中扮演重要角色；於不同學科中也有各自的定義。

舉例而言，原子中的原子核以及由電子組成的軌域，可類比成太陽系中行星環繞太陽的樣子。除此之外，修辭學中的譬喻法有時也是一種類比，例如將月亮比喻成銀幣。生物學中因趨同演化而形成的的同功或同型解剖構造，例如哺乳類、爬行類與鳥類的翅膀也是類似概念。

───

Analogy

Analogy (from Greek ἀναλογία, analogia, “proportion”^[1][2]) is a cognitive process of transferring information or meaning from a particular subject (the analogue or source) to another (the target), or a linguistic expression corresponding to such a process. In a narrower sense, analogy is an inference or an argument from one particular to another particular, as opposed to deduction, induction, and abduction, where at least one of the premises or the conclusion is general. The word analogy can also refer to the relation between the source and the target themselves, which is often, though not necessarily, a similarity, as in the biological notion of analogy.

Analogy plays a significant role in problem solving such as, decision making, perception, memory, creativity, emotion, explanation, and communication. It lies behind basic tasks such as the identification of places, objects and people, for example, in face perception and facial recognition systems. It has been argued that analogy is “the core of cognition”.^[3] Specific analogical language comprises exemplification, comparisons, metaphors, similes, allegories, and parables, but not metonymy. Phrases like and so on, and the like, as if, and the very word like also rely on an analogical understanding by the receiver of a message including them. Analogy is important not only in ordinary language and common sense (where proverbs and idioms give many examples of its application) but also in science, philosophy, and the humanities. The concepts of association, comparison, correspondence, mathematical and morphological homology, homomorphism, iconicity, isomorphism, metaphor, resemblance, and similarity are closely related to analogy. In cognitive linguistics, the notion of conceptual metaphor may be equivalent to that of analogy.

Analogy has been studied and discussed since classical antiquity by philosophers, scientists, and lawyers. The last few decades have shown a renewed interest in analogy, most notably in cognitive science.

Rutherford’s model of the atom (modified by Niels Bohr) made an analogy between the atom and the solar system.

………

 

植種大樹，走入森林，方知

縱使宇宙萬有同源，萬象表現實在是錯綜複雜耶！！方了

世間書籍雖然汗牛充棟，原創概念往往卻沒有幾個？？

─ 《W!O+ 的《小伶鼬工坊演義》︰神經網絡【轉折點】四中》

 

如何了解『電容器』之『充』、『放』電呢？

維基百科詞條如是說︰

DC circuits

See also: RC circuit

A simple resistor-capacitor circuit demonstrates charging of a capacitor.

A series circuit containing only a resistor, a capacitor, a switch and a constant DC source of voltage V₀ is known as a charging circuit.^[26] If the capacitor is initially uncharged while the switch is open, and the switch is closed at t₀, it follows from Kirchhoff’s voltage law that

Taking the derivative and multiplying by C, gives a first-order differential equation:

At t = 0, the voltage across the capacitor is zero and the voltage across the resistor is V₀. The initial current is then I(0) =V₀/R. With this assumption, solving the differential equation yields

where τ₀ = RC, the time constant of the system. As the capacitor reaches equilibrium with the source voltage, the voltages across the resistor and the current through the entire circuit decay exponentially. In the case of a discharging capacitor, the capacitor’s initial voltage (V_Ci) replaces V₀. The equations become

 

lcapy 軟體這麼講︰

Simple transient analysis

Let’s consider a series R-C network in series with a DC voltage source

>>> from lcapy import *
>>> n = Vstep(20) + R(5) + C(10, 0)
>>> n
Vstep(20) + R(5) + C(10, 0)
>>> Voc = n.Voc(s)
>>> Voc
20
──
s
>>> n.Isc(s)
   4
────────
s + 1/50
>>> isc = n.Isc.transient_response()
>>> isc
⎧   -t
⎪   ───
⎨    50
⎪4⋅ℯ     for t ≥ 0

 

Here n is network formed by the components in series, and n.Voc(s) is the open-circuit s-domain voltage across the network. Note, this is the same as the s-domain value of the voltage source. n.Isc(s) is the short-circuit s-domain voltage through the network. The method transient_response converts this to the time-domain. Note, since the capacitor has the initial value specified, this network is analysed as an initial value problem and thus the result is not known for  . If the initial capacitor voltage is not specified, the network cannot be analysed.

Of course, the previous example can be performed symbolically,

>>> from lcapy import *
>>> n = Vstep('V_1') + R('R_1') + C('C_1', 0)
>>> n
Vstep(V₁) + R(R₁) + C(C₁, 0)
>>> Voc = n.Voc(s)
>>> Voc
V₁
──
s
>>> n.Isc(s)
      V₁
──────────────
   ⎛      1  ⎞
R₁⋅⎜s + ─────⎟
   ⎝    C₁⋅R₁⎠
>>> isc = n.Isc.transient_response()
>>> isc
⎧     -t
⎪    ─────
⎪    C₁⋅R₁
⎨V₁⋅ℯ
⎪─────────  for t ≥ 0
⎪    R₁
⎩

 

※ 參考

 

內容十分一致。

若問那個 RC 電路是『直流電路』嗎？

lcapy 『電路分析』 

Circuit Analysis

>>> cct1 = (Vstep(10) + R(1)) | C(2)

>>> cct2 = Circuit()
>>> cct2.add('V 1 0 step 10')
>>> cct2.add('R 1 2 1')
>>> cct2.add('C 2 0 2')

The two approaches have many attributes and methods in common. For example,

>>> cct1.is_causal
True
>>> cct2.is_causal
True
>>> cct1.is_dc
False
>>> cct2.is_dc
False

However, there are subtle differences. For example,

>>> cct1.Voc.s
   5
──────
 2   s
s  + ─
     2

>>> cct2.Voc(2, 0).s
   5
──────
 2   s
s  + ─
     2

Notice, the second example requires specific nodes to determine the open-circuit voltage across.

……

Laplace analysis

The response due to a transient excitation from an independent source can be analysed using Laplace analysis. Since the unilateral transform is not unique (it ignores the circuit behaviour for  , the response can only be determined for  .

If the independent sources are known to be causal (a causal signal is zero for  analogous to a causal impulse response) and the initial conditions (i.e., the voltages across capacitors and currents through inductors) are zero, then the response is 0 for  . Thus in this case, the response can be specified for all  .

The response due to a general non-causal excitation is hard to determine using Laplace analysis. One strategy is to use circuit analysis techniques to determine the response for  , compute the pre-initial conditions, and then use Laplace analysis to determine the response for  . Note, the pre-initial conditions at  are required. These differ from the initial conditions at  whenever a Dirac delta (or its derivative) excitation is considered. Determining the initial conditions is not straightforward for arbitrary excitations and at the moment Lcapy expects you to do this!

The use of pre-initial conditions also allows switching circuits to be considered (see Switching analysis). In this case the independent sources are ignored for  and the result is only known for  .

Note if any of the pre-initial conditions are non-zero and the independent sources are causal then either we have an initial value problem or a mistake has been made. Lcapy assumes that if any of the inductors and capacitors have explicit initial conditions, then the circuit is to be analysed as an initial value problem with the independent sources ignored for  . In this case a DC source is not DC since it is considered to switch on at  .

………

Switching analysis

Whenever a circuit has a switch it is time variant. The opening or closing of switch changes the circuit and can produce transients. While a switch violates the LTI requirements for linear circuit analysis, the circuit prior to the switch changing can be analysed and Vnoiused to determine the initial conditions for the circuit after the switched changed. Lcapy requires that you do this! The independent sources are ignored for  and the result is only known for  .

───

 

範例

※ 註

28.3. pdb — The Python Debugger

Source code: Lib/pdb.py

---

The module pdb defines an interactive source code debugger for Python programs. It supports setting (conditional) breakpoints and single stepping at the source line level, inspection of stack frames, source code listing, and evaluation of arbitrary Python code in the context of any stack frame. It also supports post-mortem debugging and can be called under program control.

The debugger is extensible – it is actually defined as the class Pdb. This is currently undocumented but easily understood by reading the source. The extension interface uses the modules bdb and cmd.

The debugger’s prompt is (Pdb). Typical usage to run a program under control of the debugger is:

>>> import pdb
>>> import mymodule
>>> pdb.run('mymodule.test()')
> <string>(0)?()
(Pdb) continue
> <string>(1)?()
(Pdb) continue
NameError: 'spam'
> <string>(1)?()
(Pdb)

 

裡有答案︰不是！

 

但是讀過『直流』

Direct current

Direct Current (red line). The vertical axis shows current or voltage and the horizontal ‘t’ axis measures time and shows the zero value.

Direct current (DC) is the unidirectional flow of electric charge. A battery is a good example of a DC power supply. Direct current may flow in a conductor such as a wire, but can also flow through semiconductors,insulators, or even through a vacuum as in electron or ion beams. The electric current flows in a constant direction, distinguishing it from alternating current (AC). A term formerly used for this type of current was galvanic current.^[1]

The abbreviations AC and DC are often used to mean simply alternating and direct, as when they modify current or voltage.^[2][3]

Direct current may be obtained from an alternating current supply by use of a rectifier, which contains electronic elements (usually) or electromechanical elements (historically) that allow current to flow only in one direction. Direct current may be converted into alternating current with an inverter or a motor-generator set.

Direct current is used to charge batteries and as power supply for electronic systems. Very large quantities of direct-current power are used in production of aluminum and other electrochemical processes. It is also used for some railways, especially in urban areas. High-voltage direct current is used to transmit large amounts of power from remote generation sites or to interconnect alternating current power grids.

……

Various definitions

Types of direct current

The term DC is used to refer to power systems that use only one polarity of voltage or current, and to refer to the constant, zero-frequency, or slowly varying local mean value of a voltage or current.^[9] For example, the voltage across a DC voltage source is constant as is the current through a DC current source. The DC solution of an electric circuit is the solution where all voltages and currents are constant. It can be shown that any stationary voltage or current waveform can be decomposed into a sum of a DC component and a zero-mean time-varying component; the DC component is defined to be the expected value, or the average value of the voltage or current over all time.

Although DC stands for “direct current”, DC often refers to “constant polarity”. Under this definition, DC voltages can vary in time, as seen in the raw output of a rectifier or the fluctuating voice signal on a telephone line.

Some forms of DC (such as that produced by a voltage regulator) have almost no variations in voltage, but may still have variations in output power and current.

Circuits

A direct current circuit is an electrical circuit that consists of any combination of constant voltage sources, constant current sources, and resistors. In this case, the circuit voltages and currents are independent of time. A particular circuit voltage or current does not depend on the past value of any circuit voltage or current. This implies that the system of equations that represent a DC circuit do not involve integrals or derivatives with respect to time.

If a capacitor or inductor is added to a DC circuit, the resulting circuit is not, strictly speaking, a DC circuit. However, most such circuits have a DC solution. This solution gives the circuit voltages and currents when the circuit is in DC steady state. Such a circuit is represented by a system of differential equations. The solution to these equations usually contain a time varying or transient part as well as constant or steady state part. It is this steady state part that is the DC solution. There are some circuits that do not have a DC solution. Two simple examples are a constant current source connected to a capacitor and a constant voltage source connected to an inductor.

In electronics, it is common to refer to a circuit that is powered by a DC voltage source such as a battery or the output of a DC power supply as a DC circuit even though what is meant is that the circuit is DC powered.

 

詞條的人，又會怎麼判斷呢？？

因此藉『類比』想象者，能不慎察『異同』也！！

Hydraulic analogy

The electronic–hydraulic analogy (derisively referred to as the drain-pipe theory by Oliver Lodge) ^[1] is the most widely used analogy for “electron fluid” in a metal conductor. Since electric current is invisible and the processes at play in electronics are often difficult to demonstrate, the various electronic components are represented by hydraulic equivalents. Electricity (as well as heat) was originally understood to be a kind of fluid, and the names of certain electric quantities (such as current) are derived from hydraulic equivalents. As with all analogies, it demands an intuitive and competent understanding of the baseline paradigms (electronics and hydraulics).

Analogy between a hydraulic circuit (left) and an electronic circuit (right).

Limits to the analogy

If taken too far, the water analogy can create misconceptions. For it to be useful, one must remain aware of the regions where electricity and water behave very differently.

Fields (Maxwell equations, Inductance): Electrons can push or pull other distant electrons via their fields, while water molecules experience forces only from direct contact with other molecules. For this reason, waves in water travel at the speed of sound, but waves in a sea of charge will travel much faster as the forces from one electron are applied to many distant electrons and not to only the neighbors in direct contact. In a hydraulic transmission line, the energy flows as mechanical waves through the water, but in an electric transmission line the energy flows as fields in the space surrounding the wires, and does not flow inside the metal. Also, an accelerating electron will drag its neighbors along while attracting them, both because of magnetic forces.

Charge: Unlike water, movable charge carriers can be positive or negative, and conductors can exhibit an overall positive or negative net charge. The mobile carriers in electric currents are usually electrons, but sometimes they are charged positively, such as the positive ions in an electrolyte, the H⁺ ions in proton conductors or holes in p-type semiconductors and some (very rare) conductors.

Leaking pipes: The electric charge of an electrical circuit and its elements is usually almost equal to zero, hence it is (almost) constant. This is formalized in Kirchhoff’s current law, which does not have an analogy to hydraulic systems, where amount of the liquid is not usually constant. Even with incompressible liquid the system may contain such elements as pistons and open pools, so the volume of liquid contained in a part of the system can change. For this reason, continuing electric currents require closed loops rather than hydraulics’ open source/sink resembling spigots and buckets.

Fluid velocity and resistance of metals: As with water hoses, the carrier drift velocity in conductors is directly proportional to current. However, water only experiences drag via the pipes’ inner surface, while charges are slowed at all points within a metal, as with water forced through a filter. Also, typical velocity of charge carriers within a conductor is less than centimeters per minute, and the “electrical friction” is extremely high. If charges ever flowed as fast as water can flow in pipes, the electric current would be immense, and the conductors would become incandescently hot and perhaps vaporize. To model the resistance and the charge-velocity of metals, perhaps a pipe packed with sponge, or a narrow straw filled with syrup, would be a better analogy than a large-diameter water pipe. Resistance in most electrical conductors is a linear function: as current increases, voltage drop increases proportionally (Ohm’s Law). Liquid resistance in pipes is not linear with volume, varying as the square of volumetric flow (see Darcy–Weisbach equation).

Quantum Mechanics: Solid conductors and insulators contain charges at more than one discrete level of atomic orbit energy, while the water in one region of a pipe can only have a single value of pressure. For this reason there is no hydraulic explanation for such things as a battery‘s charge pumping ability, a diode‘s depletion layer and voltage drop, solar cell functions, Peltier effect, etc., however equivalent devices can be designed which exhibit similar responses, although some of the mechanisms would only serve to regulate the flow curves rather than to contribute to the component’s primary function.

In order for the model to be useful, the reader or student must have a substantial understanding of the model (hydraulic) system’s principles. It also requires that the principles can be transferred to the target (electrical) system. Hydraulic systems are deceptively simple: the phenomenon of pump cavitation is a known, complex problem that few people outside of the fluid power or irrigation industries would understand. For those who do, the hydraulic analogy is amusing, as no “cavitation” equivalent exists in electrical engineering. The hydraulic analogy can give a mistaken sense of understanding that will be exposed once a detailed description of electrical circuit theory is required.

One must also consider the difficulties in trying to make an analogy match reality completely. The above “electrical friction” example, where the hydraulic analog is a pipe filled with sponge material, illustrates the problem: the model must be increased in complexity beyond any realistic scenario.