Analogical models
Encyclopedia
Analogical models are a method of representing a phenomenon of the world, often called the ‘target system’ by another, more understandable or analysable system. They are also called dynamical analogies.
is the process of representing information about a particular subject (the analogue or source system) by another particular subject (the target system). A simple type of analogy is one that is based on shared properties (Stanford Encyclopedia of Philosophy). Analogical models, also called "analog" or "analogue" models, therefore seek the analog systems that share properties with the target system as a means of representing the world. It is often practicable to construct source systems that are smaller and/or faster than the target system so that one can deduce a priori
knowledge
of target system behaviour. Analog devices are therefore those in which may differ in substance or structure but share properties of dynamic behaviour (Truit and Rogers, p. 1-3).
(Olson 1958, p. 2).
For example, in analog electronic circuits, one can use voltage
to represent an arithmetic quantity; operational amplifier
s might then represent the arithmetic operations (addition, subtraction, multiplication, and division).Through the process of calibration
these smaller/bigger, slower/faster systems are scaled up or down so that they match the functioning of the target system, and are therefore called analogs of the target system. Once the calibration has taken place, modellers speak of a one-to-one correspondence in behaviour between the primary system and its analog. Thus the behaviour of two systems can be determined by experimenting with one.
.
published a book of dynamical
analogies that includes a table of equivalent elements in different systems such as electrical, acoustical, and mechanical systems. He claimed that the analogies presented would aid in solving various problems of dynamical systems and would help the analysis describing the performance of such systems.
of an electric circuit attempts to explain circuitry in terms of plumbing, where water represents the mobile sea of charge within metals, where pressure difference is analogy for Voltage
, and where water's flow rate is an analogy for Electric current
.
could also consist of gears and pulleys in calculation.
Examples are Vogel and Ewel who published 'An Electrical Analog of a Trophic Pyramid' (1972, Chpt 11, pp. 105–121), Elmore and Sands (1949) who published circuits devised for research in nuclear physics and the study of fast electrical transients done under the Manhattan Project (however no circuits having application to weapon technology were included for security reasons), and Howard T. Odum
(1994) who published circuits devised to analogically model ecological-economic systems at many scales of the geobiosphere.
Explanation
AnalogizingAnalogy
Analogy is a cognitive process of transferring information or meaning from a particular subject to another particular subject , and a linguistic expression corresponding to such a process...
is the process of representing information about a particular subject (the analogue or source system) by another particular subject (the target system). A simple type of analogy is one that is based on shared properties (Stanford Encyclopedia of Philosophy). Analogical models, also called "analog" or "analogue" models, therefore seek the analog systems that share properties with the target system as a means of representing the world. It is often practicable to construct source systems that are smaller and/or faster than the target system so that one can deduce a priori
A priori and a posteriori (philosophy)
The terms a priori and a posteriori are used in philosophy to distinguish two types of knowledge, justifications or arguments...
knowledge
Knowledge
Knowledge is a familiarity with someone or something unknown, which can include information, facts, descriptions, or skills acquired through experience or education. It can refer to the theoretical or practical understanding of a subject...
of target system behaviour. Analog devices are therefore those in which may differ in substance or structure but share properties of dynamic behaviour (Truit and Rogers, p. 1-3).
(Olson 1958, p. 2).
For example, in analog electronic circuits, one can use voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...
to represent an arithmetic quantity; operational amplifier
Operational amplifier
An operational amplifier is a DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output...
s might then represent the arithmetic operations (addition, subtraction, multiplication, and division).Through the process of calibration
Calibration
Calibration is a comparison between measurements – one of known magnitude or correctness made or set with one device and another measurement made in as similar a way as possible with a second device....
these smaller/bigger, slower/faster systems are scaled up or down so that they match the functioning of the target system, and are therefore called analogs of the target system. Once the calibration has taken place, modellers speak of a one-to-one correspondence in behaviour between the primary system and its analog. Thus the behaviour of two systems can be determined by experimenting with one.
Creating an analogical model
Many different instruments and systems can be used to create an analogical model. A mechanical device can be used to represent mathematical calculations. For instance, the Phillips Hydraulic Computer used the flow of water to model economic systems (the target system); electronic circuits can be used to represent both physiological and ecological systems. When a model is run on either an analog or digital computer this is known as the process of simulationSimulation
Simulation is the imitation of some real thing available, state of affairs, or process. The act of simulating something generally entails representing certain key characteristics or behaviours of a selected physical or abstract system....
.
Mechanical analogies
Electrical phenomena can be mapped to mechanical phenomena in two different ways. See http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Analogs/ElectricalMechanicalAnalogs.htmlHydraulic analogy
- In an hydraulic analogy, a water integratorWater integratorThe Water Integrator was an early analog computer built in the Soviet Union in 1928. It functioned by careful manipulation of water through a room full of interconnected pipes and pumps. The water level in various chambers represented stored numbers, and the rate of flow between them represented...
might be used to perform the mathematical operation of integrationIntegralIntegration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...
.
Physiological analogies
- Francis CrickFrancis CrickFrancis Harry Compton Crick OM FRS was an English molecular biologist, biophysicist, and neuroscientist, and most noted for being one of two co-discoverers of the structure of the DNA molecule in 1953, together with James D. Watson...
used the study of the visual systemVisual systemThe visual system is the part of the central nervous system which enables organisms to process visual detail, as well as enabling several non-image forming photoresponse functions. It interprets information from visible light to build a representation of the surrounding world...
as a proxy for the study of awarenessAwarenessAwareness is the state or ability to perceive, to feel, or to be conscious of events, objects or sensory patterns. In this level of consciousness, sense data can be confirmed by an observer without necessarily implying understanding. More broadly, it is the state or quality of being aware of...
.
Formal analogies
- "The same equationEquationAn equation is a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing the expressions on either side of an equals sign , for examplex + 3 = 5\,asserts that x+3 is equal to 5...
s have the same solutionSolutionIn chemistry, a solution is a homogeneous mixture composed of only one phase. In such a mixture, a solute is dissolved in another substance, known as a solvent. The solvent does the dissolving.- Types of solutions :...
s." -- Richard FeynmanRichard FeynmanRichard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...
- For example, the inverse-square laws of gravitationGravitationGravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...
and electromagnetismElectromagnetismElectromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
can be described by analogous equations on a geometrical basis, almost without regard to the physical details about massMassMass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
es and chargesCharge (physics)In physics, a charge may refer to one of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. Charges are associated with conserved quantum numbers.-Formal definition:...
.
- For example, the inverse-square laws of gravitation
- RecursionRecursionRecursion is the process of repeating items in a self-similar way. For instance, when the surfaces of two mirrors are exactly parallel with each other the nested images that occur are a form of infinite recursion. The term has a variety of meanings specific to a variety of disciplines ranging from...
requires a similarity within a situation; for example, ArchimedesArchimedesArchimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an...
used the myriadMyriadMyriad , "numberlesscountless, infinite", is a classical Greek word for the number 10,000. In modern English, the word refers to an unspecified large quantity.-History and usage:...
to count the number of grains of sand on a beachThe Sand ReckonerThe Sand Reckoner is a work by Archimedes in which he set out to determine an upper bound for the number of grains of sand that fit into the universe. In order to do this, he had to estimate the size of the universe according to the then-current model, and invent a way to talk about extremely...
by using the concept of myriad myriads.
Dynamical analogies
Arising from his pioneering work in the field of acoustical engineering research, in 1958 (pp. 27–29) Dr. Harry F. OlsonHarry F. Olson
Harry Ferdinand Olson was a prominent engineer at RCA Victor.Harry F. Olson, a pioneer in the field of 20th century acoustical engineering, was born in Mount Pleasant, Iowa to Swedish immigrant parents...
published a book of dynamical
Dynamics (mechanics)
In the field of physics, the study of the causes of motion and changes in motion is dynamics. In other words the study of forces and why objects are in motion. Dynamics includes the study of the effect of torques on motion...
analogies that includes a table of equivalent elements in different systems such as electrical, acoustical, and mechanical systems. He claimed that the analogies presented would aid in solving various problems of dynamical systems and would help the analysis describing the performance of such systems.
Table of equivalents
| Electrical | Mechanical Rectilineal | Mechanical Rotational | Acoustical | Economic | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Quantity | Symbol | Dimension | Quantity | Symbol | Dimension | Quantity | Symbol | Dimension | ||
| Current | i | Linear velocity | | | |||||||
| emf | e |  |
||||||||
| Electrical resistance | re | Mechanical resistance | |Resistance to consume | |||||||
| Electrical Capacitance | CE | t2/L | Compliance | Savings(Credit) | ||||||
| Energy | WE | Lq2t-2, | . | Output | ||||||
| Power | PE | Power | |Production(Consumption) | |||||||
Hydraulic Analog
A fluid or Hydraulic analogyHydraulic analogy
The electronic–hydraulic analogy 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...
of an electric circuit attempts to explain circuitry in terms of plumbing, where water represents the mobile sea of charge within metals, where pressure difference is analogy for Voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...
, and where water's flow rate is an analogy for Electric current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...
.
Analogue computers
Electronic circuits were used to model and simulate engineering systems such as aeroplanes and nuclear power plants before digital computers became widely available with fast enough turn over times to be practically useful. Electronic circuit instruments called analog computers were used to speed up circuit construction time. However analog computers like the norden bombsightNorden bombsight
The Norden bombsight was a tachometric bombsight used by the United States Army Air Forces and the United States Navy during World War II, and the United States Air Force in the Korean and the Vietnam Wars to aid the crew of bomber aircraft in dropping bombs accurately...
could also consist of gears and pulleys in calculation.
Examples are Vogel and Ewel who published 'An Electrical Analog of a Trophic Pyramid' (1972, Chpt 11, pp. 105–121), Elmore and Sands (1949) who published circuits devised for research in nuclear physics and the study of fast electrical transients done under the Manhattan Project (however no circuits having application to weapon technology were included for security reasons), and Howard T. Odum
Howard T. Odum
Howard Thomas Odum was an American ecologist...
(1994) who published circuits devised to analogically model ecological-economic systems at many scales of the geobiosphere.
Philosophical conundrum
The process of analogical modelling has philosophical difficulties. As noted in the Stanford Encyclopedia of Philosophy, there is the question of how the physical/biological laws of the target system relate to the analogical models created by humans to represent the target system. We seem to assume that the process of constructing analogical models gives us access to the fundamental laws governing the target system. However strictly speaking we only have empirical knowledge of the laws that hold true for the analogical system, and if the time constant for the target system is larger than the life cycle of human being (as in the case of the geobiosphere) it is therefore very difficult for any single human to empirically verify the validity of the extension of the laws of their model to the target system in their lifetime.Quotation
- "Good mathematicians see analogies. Great mathematicians see analogies between analogies." --Stefan BanachStefan BanachStefan Banach was a Polish mathematician who worked in interwar Poland and in Soviet Ukraine. He is generally considered to have been one of the 20th century's most important and influential mathematicians....
, as quoted by Stan Ulam.
See also
- AnalogyAnalogyAnalogy is a cognitive process of transferring information or meaning from a particular subject to another particular subject , and a linguistic expression corresponding to such a process...
- Conceptual metaphorConceptual metaphorIn cognitive linguistics, conceptual metaphor, or cognitive metaphor, refers to the understanding of one idea, or conceptual domain, in terms of another, for example, understanding quantity in terms of directionality . A conceptual domain can be any coherent organization of human experience...
- HomomorphismHomomorphismIn abstract algebra, a homomorphism is a structure-preserving map between two algebraic structures . The word homomorphism comes from the Greek language: ὁμός meaning "same" and μορφή meaning "shape".- Definition :The definition of homomorphism depends on the type of algebraic structure under...
- InquiryInquiryAn inquiry is any process that has the aim of augmenting knowledge, resolving doubt, or solving a problem. A theory of inquiry is an account of the various types of inquiry and a treatment of the ways that each type of inquiry achieves its aim.-Deduction:...
- MetaphorMetaphorA metaphor is a literary figure of speech that uses an image, story or tangible thing to represent a less tangible thing or some intangible quality or idea; e.g., "Her eyes were glistening jewels." Metaphor may also be used for any rhetorical figures of speech that achieve their effects via...
- MONIAC
- Model
- MorphismMorphismIn mathematics, a morphism is an abstraction derived from structure-preserving mappings between two mathematical structures. The notion of morphism recurs in much of contemporary mathematics...
- ParadigmParadigmThe word paradigm has been used in science to describe distinct concepts. It comes from Greek "παράδειγμα" , "pattern, example, sample" from the verb "παραδείκνυμι" , "exhibit, represent, expose" and that from "παρά" , "beside, beyond" + "δείκνυμι" , "to show, to point out".The original Greek...
- wind tunnelWind tunnelA wind tunnel is a research tool used in aerodynamic research to study the effects of air moving past solid objects.-Theory of operation:Wind tunnels were first proposed as a means of studying vehicles in free flight...