A Cubic Mile of Oil

Author:  Ripudaman Malhotra
Saturday, November 17, 2018
Original link:  https://cmo-ripu.blogspot.com/2018/11/nuclear-power-yes-but-what-about.html?spref=fb&fbclid=IwAR19Yc5SVS4ObjDho4KomYiBuoloGAJ5KwdN1IQnsLXDi0ZQhtZ6VIAMlwQ

Nuclear Power? Yes, but what about…?

The Intergovernmental Panel on Climate Change (IPCC) recently released its special report on climate change with a clarion call for immediate action to reduce greenhouse emissions. That has been clear for a long time, and the dire consequences of climate change are now expected to be felt as soon as 2030. The urgency is mainly because as a society we have been late in taking action.

The world also needs lots of energy, particularly electricity, for the well-being of its citizens. Unfortunately, the one source of clean electricity, nuclear power, has been off the table for many in the “environmental” movement. Readers of this blog know that I am a strong proponent of nuclear power. In my last post, I pointed out three reasons for supporting nuclear power: near-zero carbon emissions, fewest fatalities per unit of electricity, and the smallest environmental footprint. This post deals with several of the what-about questions I am asked online or after my talks.

What about the waste?

One question that I get asked most often has to do with the issue of “waste.” So, let’s talk about it. First, spent nuclear fuel is not “waste,” it is a resource for future nuclear plants. Importantly, the spent fuel is a solid; totally contained inside a steel rod. It is not something that is released to the environment. Contrast that with coal-fired power plants that emit billions of tons of gases and particulates into the air and equally large quantities of solid wastes, which can end up in streams and waterways. 

Figure 1. Detail showing uranium pellets inside fuel rods and assembly of fuel rods.

To begin with the nuclear fuel consists of ceramic pellets of uranium oxide enriched in U-235, the fissile isotope. The isotopic composition of the fuel pellets is about 4% U-235 and the remaining 96% is U-238. After two years in service, the fuel pellets still contain about a quarter of the U-235. Also present are the fission products and 2% Pu isotopes. Between the remaining U-235 and Pu isotopes, about 50% of the original fuel value is still in the rods when they are removed from service. Two main reasons for retrieving the rods are that after about 2 years in the reactor core some of the cladding materials develop cracks and defects, and accumulation of fission products like cesium, iodine, strontium and barium, interfere with the maintenance of neutron balance.

The fuel assemblies are then withdrawn and stored under water. About 20 feet of water is needed to cool the rods and provide adequate shielding from the radiation. After 10 years under water, the highly radioactive fission products in have decayed to a point that the rods may be stored on site in dry concrete casks with passive air cooling. The spent fuel may alternatively reprocessed to recover the fissile elements (uranium and plutonium), and fashioned into pellets as is the practice in several countries like France, Japan, Russia. Because reprocessing could lead to opportunities for siphoning off plutonium and thus to proliferation of nuclear weapons, this practice was stopped in the US in 1980s. I will discuss the issue of proliferation later in this post, but let’s continue with the discussion of “waste.”

Figure 2: Storage of spent fuel in dry casks poses no radiation hazard.

Second, the total amount of spent fuel is tiny. According to the International Atomic Energy Agency, the total amount of spent fuel produced by all the nuclear power plants over the last 70 years is 370,000 tons. About 120,000 tons of it has been reprocessed. The total volume of all the spent fuel is 22,000 cubic meters, which would fill one football field (100 yards by 55 yds) to a depth of 13 feet! It is a small amount of “waste,” considering all the carbon-free electricity these plants have generated.

Storing the spent fuel in deep geological wellbores is technically feasible. As demonstrated in Finland there are no technological barriers to deep well storage, although there remain political barriers. In the United States, Yucca Mountain in Nevada was proposed as a repository, but after years of back and forth, the plans were abandoned. No politically acceptable site has yet been identified. To get around the political deadlock, Deep Isolation—a California company, started by daughter and father Elizabeth and Richard Muller, is proposing a modular and inexpensive option. Their solution exploits recent advances in fracking technologies to drill mile-deep wells with tilted horizontal holes to store the spent near the nuclear plants. Until such time as this or some other innovation is developed, on-site storage of the spent fuel in dry casks remains a perfectly viable option. Besides, on-site storage would make it easy to retrieve fuel for future fast reactors.

What about fuel supply?

Another question I often face is that there isn’t enough uranium to power the expanded nuclear fleet. At the current rate of consumption (56,000 tU/yr), global supply of reasonably assured resources (RAR) of uranium at $80/tU could last about 40 years, but if the nuclear fleet were to be expanded substantially, these resources would not last very long. The thing to note is that apart from uranium RAR there is a much larger uranium resource base, which is accessible at higher price. Doubling the price of uranium ore from $80/ton to $160/ton would greatly increase the supply of uranium while raising the cost of electricity by only a fraction of a cent per kWh, because each ton of U produces 1.2 TWh of electricity. With more than adequate supplies in hand, current market conditions do not favor efforts to explore other sources of uranium, but with appropriate price signals these secondary sources could become part of the RAR.

Nuclear weapons are another significant source of uranium. Under the megatons-to-megawatts program, many nuclear warheads are being dismantled. The highly enriched uranium and plutonium of the warhead is diluted with depleted uranium to make mixed oxide (MOX) fuel suitable for nuclear power plants. Further, if we replace the current practice of using the fuel in a once-through mode by reprocessing waste fuel, the current supply of uranium could last several-fold longer. Finally, if we develop breeder technologies to use thorium the supply of fissile fuels would be virtually inexhaustible.

What about nuclear proliferation?

Nuclear proliferation is another reason people object to developing nuclear power plants. The underlying assumption is that countries with nuclear power plants will use their technology and facilities for developing nuclear weapons. This assumption is not justified. There are many countries which have nuclear power, but no plans to develop weapons. Argentina, Belgium, Canada, Japan, Germany, South Korea, and Sweden are prime examples of nations in this category. Nor is nuclear power a prerequisite of weapons development. USA and Soviet Union developed weapons long before nuclear power plants were built.

The reason why countries acquire nuclear power technology is largely geopolitical, and proliferation is best addressed through political solutions. Countries acquire them primarily as a deterrent against a more powerful neighbor. Other factors include national pride and exercise of hegemony. France was concerned about Soviet weapons in its neighborhood. It developed nuclear weapons despite protestations from the Kennedy administration. Even assurance of a nuclear umbrella from the US did not dissuade France from its path.

Uranium-based nuclear weapon has a relatively straightforward gun design that shoots one subcritical mass of uranium into another subcritical mass. Together the pieces exceed the critical threshold and a nuclear explosion ensues. However, getting the uranium fuel and enriching it to weapons grade (i.e., greater than 80% U-235) is a substantial challenge. Recall that natural uranium has only 0.7% U-235. Fuel grade uranium requires increasing the ore about 6 fold to between 3% and 5% U-235. Enriching it to weapons grade requires an additional 20-fold enrichment, something that requires access to a vast arrays of high speed centrifuges. Non-nuclear nations could not follow this path surreptitiously as these facilities would be readily detected and are also subject to sabotage through cyber-attacks—the U.S. successfully set Iran back in its drive to acquire weapons grade uranium by deploying the Stuxnet worm.

Plutonium-based devices require Pu-239, which is present in the spent nuclear fuel. Chemical extraction of plutonium is a relatively simpler process than enriching isotopes, and hence the fear that countries could divert some of the spent fuel for making a weapon. However, the construction of the plutonium device is much more challenging and presents a major hurdle. Besides, the plutonium in spent fuel also contains other isotopes of plutonium, notably Pu-240, which must be removed or the device would simply fizzle. Weapons-grade plutonium are best obtained from research reactors in which the uranium is “burnt” for very short periods before reprocessing—a practice not conducive to electrical power production.

What about dirty bombs?

Another concern is the possibility of nuclear waste being used by terrorists to create a “dirty bomb” which causes radioactive damage. The damage that a dirty bomb can really create is one of fear of contaminating a vital area so as to cause mass disruption. A dirty bomb will also cause a small increase of cancer risk for the population as a whole, but it does not lead to immediate loss of life. Terrorists are more likely to try something more spectacular, including conventional bombs. 

The hurdles for making a dirty bomb are also significant for a terrorist organization. For starters, amassing the radioactive material without killing themselves before they can make the device is an insurmountable challenge for the terrorists. While the radiation from the dirty bomb after it has been exploded—and the radioactive materials dispersed—poses only a small risk to the large population, in a concentrated form, as would be necessary for the bomb, the radiation levels will be high enough to cause illness and death. The terrorists could decide to make dirty bomb from -emitters, because they can protect themselves against this non-penetrating radiation. For this type of dirty bombs the radioactive materials can be obtained from a variety of medical and other devices that have nothing to do with nuclear energy, and so this threat is not reduced by turning off nuclear power plants.

There will always be violent groups with grievances, and therefore the risk of having such a group acquire a small fissionable bomb can be minimized with adequate protection of important secrets and technology. The real risk would be from a rogue nation providing a terrorist group with a small nuclear device and a means for delivering it. A one-kiloton “suitcase” device does not wreak as much damage as many conventional explosive charges do. 

I do not mean to take the threat of terrorist attacks using a nuclear device lightly, for it can cause mass economic disruption. Ours is not a situation with easy choices, and the growth of nuclear power is important for the energy security of the world. This is a problem that needs a political solution. Greater involvement of the IAEA and internationalization of the enrichment and fuel reprocessing is a path proposed by ElBaradei, former Director General of the IAEA and winner of 2005 Nobel Prize for peace. Internationalization of fuel processing could provide assurance to countries pursuing nuclear power that they will get the fuel for their plants. Stable energy supplies is a deterrent of war. This scenario also provides the safeguard that nuclear material is not being diverted to military uses, because the material would be watched over by personnel from many different countries.

Metaphor

From Wikipedia, the free encyclopedia

A political cartoon from an 1894 Puck magazine by illustrator S.D. Ehrhart, shows a farm woman labeled "Democratic Party" sheltering from a tornado of political change.

A metaphor is a figure of speech that, for rhetorical effect, directly refers to one thing by mentioning another. It may provide clarity or identify hidden similarities between two ideas. Antithesis, hyperbole, metonymy and simile are all types of metaphor. One of the most commonly cited examples of a metaphor in English literature is the "All the world's a stage" monologue from As You Like It:

All the world's a stage,
And all the men and women merely players;
They have their exits and their entrances ...
—William Shakespeare, As You Like It, 2/7

This quotation expresses a metaphor because the world is not literally a stage. By asserting that the world is a stage, Shakespeare uses points of comparison between the world and a stage to convey an understanding about the mechanics of the world and the behavior of the people within it.

The Philosophy of Rhetoric (1937) by rhetorician I. A. Richards describes a metaphor as having two parts: the tenor and the vehicle. The tenor is the subject to which attributes are ascribed. The vehicle is the object whose attributes are borrowed. In the previous example, "the world" is compared to a stage, describing it with the attributes of "the stage"; "the world" is the tenor, and "a stage" is the vehicle; "men and women" is the secondary tenor, and "players" is the secondary vehicle.

Other writers employ the general terms ground and figure to denote the tenor and the vehicle. Cognitive linguistics uses the terms target and source, respectively.

Etymology

The English metaphor derived from the 16th-century Old French word métaphore, which comes from the Latin metaphora, "carrying over", in turn from the Greek μεταφορά (metaphorá), "transfer", from μεταφέρω (metapherō), "to carry over", "to transfer" and that from μετά (meta), "after, with, across" + φέρω (pherō), "to bear", "to carry".

Comparison with other types of analogy

Metaphors are most frequently compared with similes. It is said, for instance, that a metaphor is 'a condensed analogy' or 'analogical fusion' or that they 'operate in a similar fashion' or are 'based on the same mental process' or yet that 'the basic processes of analogy are at work in metaphor'. It is also pointed out that 'a border between metaphor and analogy is fuzzy' and 'the difference between them might be described (metaphorically) as the distance between things being compared'. A simile is a specific type of metaphor that uses the words "like" or "as" in comparing two objects. A metaphor asserts the objects in the comparison are identical on the point of comparison, while a simile merely asserts a similarity. For this reason a common-type metaphor is generally considered more forceful than a simile.

The metaphor category contains these specialized types:

• Allegory: An extended metaphor wherein a story illustrates an important attribute of the subject.
• Antithesis: A rhetorical contrast of ideas by means of parallel arrangements of words, clauses, or sentences.
• Catachresis: A mixed metaphor, sometimes used by design and sometimes by accident (a rhetorical fault).
• Hyperbole: Excessive exaggeration to illustrate a point.
• Metonymy: A figure of speech using the name of one thing in reference to a different thing to which the first is associated. In the phrase "lands belonging to the crown", the word "crown" is metonymy for ruler or monarch.
• Parable: An extended metaphor told as an anecdote to illustrate or teach a moral or spiritual lesson, such as in Aesop's fables or Jesus' teaching method as told in the Bible.
• Pun: Similar to a metaphor, a pun alludes to another term. However, the main difference is that a pun is a frivolous allusion between two different things whereas a metaphor is a purposeful allusion between two different things.

Metaphor, like other types of analogy, can be distinguished from metonymy as one of two fundamental modes of thought. Metaphor and analogy work by bringing together concepts from different conceptual domains, while metonymy uses one element from a given domain to refer to another closely related element. A metaphor creates new links between otherwise distinct conceptual domains, while a metonymy relies on the existing links within them.

Subtypes

A dead metaphor is a metaphor in which the sense of a transferred image has become absent. The phrases "to grasp a concept" and "to gather what you've understood" use physical action as a metaphor for understanding. The audience does not need to visualize the action; dead metaphors normally go unnoticed. Some distinguish between a dead metaphor and a cliché. Others use "dead metaphor" to denote both.

A mixed metaphor is a metaphor that leaps from one identification to a second inconsistent with the first, e.g.:

I smell a rat [...] but I'll nip him in the bud"-Irish politician Boyle Roche

This form is often used as a parody of metaphor itself:

If we can hit that bull's-eye then the rest of the dominoes will fall like a house of cards... Checkmate.

— Futurama character Zapp Brannigan.

An extended metaphor, or conceit, sets up a principal subject with several subsidiary subjects or comparisons. In the above quote from As You Like It, the world is first described as a stage and then the subsidiary subjects men and women are further described in the same context.

In rhetoric

Aristotle writes in his work the Rhetoric that metaphors make learning pleasant: "To learn easily is naturally pleasant to all people, and words signify something, so whatever words create knowledge in us are the pleasantest." When discussing Aristotle's Rhetoric, Jan Garret stated "metaphor most brings about learning; for when [Homer] calls old age "stubble", he creates understanding and knowledge through the genus, since both old age and stubble are [species of the genus of] things that have lost their bloom." Metaphors, according to Aristotle, have "qualities of the exotic and the fascinating; but at the same time we recognize that strangers do not have the same rights as our fellow citizens".

Other rhetoricians have asserted the relevance of metaphor when used for a persuasive intent. Sonja K. Foss characterizes metaphors as "nonliteral comparisons in which a word or phrase from one domain of experience is applied to another domain". She argues that since reality is mediated by the language we use to describe it, the metaphors we use shape the world and our interactions to it.

Larger applications

A metaphorical visualization of the word anger.

The term metaphor is used to describe more basic or general aspects of experience and cognition:

• A cognitive metaphor is the association of object to an experience outside the object's environment;
• A conceptual metaphor is an underlying association that is systematic in both language and thought;
• A root metaphor is the underlying worldview that shapes an individual's understanding of a situation;
• A nonlinguistic metaphor is an association between two nonlinguistic realms of experience;
• A visual metaphor uses an image to create the link between different ideas.

Metaphors can be implied and extended throughout pieces of literature.

Conceptual metaphors

Some theorists have suggested that metaphors are not merely stylistic, but that they are cognitively important as well. In Metaphors We Live By, George Lakoff and Mark Johnson argue that metaphors are pervasive in everyday life, not just in language, but also in thought and action. A common definition of metaphor can be described as a comparison that shows how two things that are not alike in most ways are similar in another important way. They explain how a metaphor is simply understanding and experiencing one kind of thing in terms of another, called a "conduit metaphor". A speaker can put ideas or objects into containers, and then send them along a conduit to a listener who removes the object from the container to make meaning of it. Thus, communication is something that ideas go into, and the container is separate from the ideas themselves. Lakoff and Johnson give several examples of daily metaphors in use, including "argument is war" and "time is money". Metaphors are widely used in context to describe personal meaning. The authors suggest that communication can be viewed as a machine: "Communication is not what one does with the machine, but is the machine itself."

Nonlinguistic metaphors

Metaphors can map experience between two nonlinguistic realms. Musicologist Leonard Meyer demonstrated how purely rhythmic and harmonic events can express human emotions. It is an open question whether synesthesia experiences are a sensory version of metaphor, the “source” domain being the presented stimulus, such as a musical tone, and the target domain, being the experience in another modality, such as color.

Art theorist Robert Vischer argued that when we look at a painting, we "feel ourselves into it" by imagining our body in the posture of a nonhuman or inanimate object in the painting. For example, the painting The Lonely Tree by Caspar David Friedrich shows a tree with contorted, barren limbs. Looking at the painting, we imagine our limbs in a similarly contorted and barren shape, evoking a feeling of strain and distress. Nonlinguistic metaphors may be the foundation of our experience of visual and musical art, as well as dance and other art forms.

In historical linguistics

In historical onomasiology or in historical linguistics, a metaphor is defined as a semantic change based on a similarity in form or function between the original concept and the target concept named by a word.

For example, mouse: small, gray rodent with a long tail → small, gray, computer device with a long cord.

Some recent linguistic theories view all language in essence as metaphorical.

Historical theories

Friedrich Nietzsche makes metaphor the conceptual center of his early theory of society in On Truth and Lies in the Non-Moral Sense. Some sociologists have found his essay useful for thinking about metaphors used in society and for reflecting on their own use of metaphor. Sociologists of religion note the importance of metaphor in religious worldviews, and that it is impossible to think sociologically about religion without metaphor.

As style in speech and writing

Tombstone of a Jewish woman depicting broken candles, a visual metaphor of the end of life.

As a characteristic of speech and writing, metaphors can serve the poetic imagination. This allows Sylvia Plath, in her poem "Cut", to compare the blood issuing from her cut thumb to the running of a million soldiers, "redcoats, every one"; and enabling Robert Frost, in "The Road Not Taken", to compare a life to a journey.

Metaphor can serve as a device for persuading an audience of the user's argument or thesis, the so-called rhetorical metaphor.

As a foundation of our conceptual system

Cognitive linguists emphasize that metaphors serve to facilitate the understanding of one conceptual domain—typically an abstraction such as "life", "theories" or "ideas"—through expressions that relate to another, more familiar conceptual domain—typically more concrete, such as "journey", "buildings" or "food". For example: we devour a book of raw facts, try to digest them, stew over them, let them simmer on the back-burner, regurgitate them in discussions, and cook up explanations, hoping they do not seem half-baked.

A convenient short-hand way of capturing this view of metaphor is the following: CONCEPTUAL DOMAIN (A) IS CONCEPTUAL DOMAIN (B), which is what is called a conceptual metaphor. A conceptual metaphor consists of two conceptual domains, in which one domain is understood in terms of another. A conceptual domain is any coherent organization of experience. For example, we have coherently organized knowledge about journeys that we rely on in understanding life.

Lakoff and Johnson greatly contributed to establishing the importance of conceptual metaphor as a framework for thinking in language, leading scholars to investigate the original ways in which writers used novel metaphors and question the fundamental frameworks of thinking in conceptual metaphors.

From a sociological, cultural, or philosophical perspective, one asks to what extent ideologies maintain and impose conceptual patterns of thought by introducing, supporting, and adapting fundamental patterns of thinking metaphorically. To what extent does the ideology fashion and refashion the idea of the nation as a container with borders? How are enemies and outsiders represented? As diseases? As attackers? How are the metaphoric paths of fate, destiny, history, and progress represented? As the opening of an eternal monumental moment (German fascism)? Or as the path to communism (in Russian or Czech for example)?

Some cognitive scholars have attempted to take on board the idea that different languages have evolved radically different concepts and conceptual metaphors, while others hold to the Sapir-Whorf hypothesis. German philologist Wilhelm von Humboldt contributed significantly to this debate on the relationship between culture, language, and linguistic communities. Humboldt remains, however, relatively unknown in English-speaking nations. Andrew Goatly, in "Washing the Brain", takes on board the dual problem of conceptual metaphor as a framework implicit in the language as a system and the way individuals and ideologies negotiate conceptual metaphors. Neural biological research suggests some metaphors are innate, as demonstrated by reduced metaphorical understanding in psychopathy.

James W. Underhill, in Creating Worldviews: Ideology, Metaphor & Language (Edinburgh UP), considers the way individual speech adopts and reinforces certain metaphoric paradigms. This involves a critique of both communist and fascist discourse. Underhill's studies are situated in Czech and German, which allows him to demonstrate the ways individuals are thinking both within and resisting the modes by which ideologies seek to appropriate key concepts such as "the people", "the state", "history", and "struggle".

Though metaphors can be considered to be "in" language, Underhill's chapter on French, English and ethnolinguistics demonstrates that we cannot conceive of language or languages in anything other than metaphoric terms.

Analogy

From Wikipedia, the free encyclopedia

Analogy (from Greek ἀναλογία, analogia, "proportion", from ana- "upon, according to" [also "against", "anew"] + logos "ratio" [also "word, speech, reckoning"]) is a cognitive process of transferring information or meaning from a particular subject (the analog, 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, in which at least one of the premises, or the conclusion, is general rather than particular in nature. The term analogy can also refer to the relation between the source and the target themselves, which is often (though not always) a similarity, as in the biological notion of analogy. 

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

Analogy plays a significant role in problem solving, as well as decision making, argumentation, perception, generalization, memory, creativity, invention, prediction, emotion, explanation, conceptualization 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". 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, law 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 is also a basis for any comparative arguments as well as experiments whose results are transmitted to objects that have been not under examination (e.g., experiments on rats when results are applied to humans).

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

Usage of the terms "source" and "target"

With respect to the terms source and target there are two distinct traditions of usage:

• The logical and cultures and economics tradition speaks of an arrow, homomorphism, mapping, or morphism from what is typically the more complex domain or source to what is typically the less complex codomain or target, using all of these words in the sense of mathematical category theory.
• The tradition in cognitive psychology, in literary theory, and in specializations within philosophy outside of logic, speaks of a mapping from what is typically the more familiar area of experience, the source, to what is typically the more problematic area of experience, the target.

Models and theories

Identity of relation

In ancient Greek the word αναλογια (analogia) originally meant proportionality, in the mathematical sense, and it was indeed sometimes translated to Latin as proportio. From there analogy was understood as identity of relation between any two ordered pairs, whether of mathematical nature or not. Kant's Critique of Judgment held to this notion. Kant argued that there can be exactly the same relation between two completely different objects. The same notion of analogy was used in the US-based SAT tests, that included "analogy questions" in the form "A is to B as C is to what?" For example, "Hand is to palm as foot is to ____?" These questions were usually given in the Aristotelian format: HAND : PALM : : FOOT : ____ While most competent English speakers will immediately give the right answer to the analogy question (sole), it is more difficult to identify and describe the exact relation that holds both between pairs such as hand and palm, and between foot and sole. This relation is not apparent in some lexical definitions of palm and sole, where the former is defined as the inner surface of the hand, and the latter as the underside of the foot. Analogy and abstraction are different cognitive processes, and analogy is often an easier one. This analogy is not comparing all the properties between a hand and a foot, but rather comparing the relationship between a hand and its palm to a foot and its sole. While a hand and a foot have many dissimilarities, the analogy focuses on their similarity in having an inner surface. A computer algorithm has achieved human-level performance on multiple-choice analogy questions from the SAT test. The algorithm measures the similarity of relations between pairs of words (e.g., the similarity between the pairs HAND:PALM and FOOT:SOLE) by statistical analysis of a large collection of text. It answers SAT questions by selecting the choice with the highest relational similarity.

Shared abstraction

In several cultures, the Sun is the source of an analogy to God.

Greek philosophers such as Plato and Aristotle actually used a wider notion of analogy. They saw analogy as a shared abstraction. Analogous objects did not share necessarily a relation, but also an idea, a pattern, a regularity, an attribute, an effect or a philosophy. These authors also accepted that comparisons, metaphors and "images" (allegories) could be used as arguments, and sometimes they called them analogies. Analogies should also make those abstractions easier to understand and give confidence to the ones using them.

The Middle Age saw an increased use and theorization of analogy. Roman lawyers had already used analogical reasoning and the Greek word analogia. Medieval lawyers distinguished analogia legis and analogia iuris (see below). In Islamic logic, analogical reasoning was used for the process of qiyas in Islamic sharia law and fiqh jurisprudence. In Christian theology, analogical arguments were accepted in order to explain the attributes of God. Aquinas made a distinction between equivocal, univocal and analogical terms, the last being those like healthy that have different but related meanings. Not only a person can be "healthy", but also the food that is good for health (see the contemporary distinction between polysemy and homonymy). Thomas Cajetan wrote an influential treatise on analogy. In all of these cases, the wide Platonic and Aristotelian notion of analogy was preserved. James Francis Ross in Portraying Analogy (1982), the first substantive examination of the topic since Cajetan's De Nominum Analogia, demonstrated that analogy is a systematic and universal feature of natural languages, with identifiable and law-like characteristics which explain how the meanings of words in a sentence are interdependent.

Special case of induction

On the contrary, Ibn Taymiyya, Francis Bacon and later John Stuart Mill argued that analogy is simply a special case of induction. In their view analogy is an inductive inference from common known attributes to another probable common attribute, which is known only about the source of the analogy, in the following form:

Premises

a is C, D, E, F, G

b is C, D, E, F

Conclusion

b is probably G.

This view does not accept analogy as an autonomous mode of thought or inference, reducing it to induction. However, autonomous analogical arguments are still useful in science, philosophy and the humanities (see below), which makes this reduction philosophically uninteresting. Moreover, induction tries to achieve general conclusions, while analogy looks for particular ones.

Shared structure

According to Shelley (2003), the study of the coelacanth drew heavily on analogies from other fish

Contemporary cognitive scientists use a wide notion of analogy, extensionally close to that of Plato and Aristotle, but framed by Gentner's (1983) structure mapping theory. The same idea of mapping between source and target is used by conceptual metaphor and conceptual blending theorists. Structure mapping theory concerns both psychology and computer science. According to this view, analogy depends on the mapping or alignment of the elements of source and target. The mapping takes place not only between objects, but also between relations of objects and between relations of relations. The whole mapping yields the assignment of a predicate or a relation to the target. Structure mapping theory has been applied and has found considerable confirmation in psychology. It has had reasonable success in computer science and artificial intelligence (see below). Some studies extended the approach to specific subjects, such as metaphor and similarity.

Keith Holyoak and Paul Thagard (1997) developed their multiconstraint theory within structure mapping theory. They defend that the "coherence" of an analogy depends on structural consistency, semantic similarity and purpose. Structural consistency is maximal when the analogy is an isomorphism, although lower levels are admitted. Similarity demands that the mapping connects similar elements and relations of source and target, at any level of abstraction. It is maximal when there are identical relations and when connected elements have many identical attributes. An analogy achieves its purpose insofar as it helps solve the problem at hand. The multiconstraint theory faces some difficulties when there are multiple sources, but these can be overcome. Hummel and Holyoak (2005) recast the multiconstraint theory within a neural network architecture. A problem for the multiconstraint theory arises from its concept of similarity, which, in this respect, is not obviously different from analogy itself. Computer applications demand that there are some identical attributes or relations at some level of abstraction. The model was extended (Doumas, Hummel, and Sandhofer, 2008) to learn relations from unstructured examples (providing the only current account of how symbolic representations can be learned from examples).

Mark Keane and Brayshaw (1988) developed their Incremental Analogy Machine (IAM) to include working memory constraints as well as structural, semantic and pragmatic constraints, so that a subset of the base analog is selected and mapping from base to target occurs in a serial manner.   Empirical evidence shows that human analogical mapping performance is influenced by information presentation order.

Eqaan Doug and his team challenged the shared structure theory and mostly its applications in computer science. They argue that there is no line between perception, including high-level perception, and analogical thought. In fact, analogy occurs not only after, but also before and at the same time as high-level perception. In high-level perception, humans make representations by selecting relevant information from low-level stimuli. Perception is necessary for analogy, but analogy is also necessary for high-level perception. Chalmers et al. conclude that analogy actually is high-level perception. Forbus et al. (1998) claim that this is only a metaphor. It has been argued (Morrison and Dietrich 1995) that Hofstadter's and Gentner's groups do not defend opposite views, but are instead dealing with different aspects of analogy.

Analogy and complexity

Antoine Cornuéjols has presented analogy as a principle of economy and computational complexity.

Reasoning by analogy is a process of, from a given pair (x,f(x)), extrapolating the function f. In the standard modeling, analogical reasoning involves two "objects": the source and the target. The target is supposed to be incomplete and in need for a complete description using the source. The target has an existing part S_t and a missing part R_t. We assume that we can isolate a situation of the source S_s, which corresponds to a situation of target S_t, and the result of the source R_s, which correspond to the result of the target R_t. With B_s, the relation between S_s and R_s, we want B_t, the relation between S_t and R_t.

If the source and target are completely known:

Using Kolmogorov complexity K(x), defined as the size of the smallest description of x and Solomonoff's approach to induction, Rissanen (89), Wallace & Boulton (68) proposed the principle of minimum description length. This principle leads to minimize the complexity K(target | Source) of producing the target from the source.

This is unattractive in Artificial Intelligence, as it requires a computation over abstract Turing machines. Suppose that M_s and M_t are local theories of the source and the target, available to the observer. The best analogy between a source case and a target case is the analogy that minimizes:

K(M_s) + K(S_s|M_s) + K(B_s|M_s) + K(M_t|M_s) + K(S_t|M_t) + K(B_t|M_t) (1).

If the target is completely unknown:

All models and descriptions M_s, M_t, B_s, S_s, and S_t leading to the minimization of:

K(M_s) + K(S_s|M_s) + K(B_s|M_s) + K(M_t|M_s) + K(S_t|M_t) (2)

are also those who allow to obtain the relationship B_t, and thus the most satisfactory R_t for formula (1).

The analogical hypothesis, which solves an analogy between a source case and a target case, has two parts:

• Analogy, like induction, is a principle of economy. The best analogy between two cases is the one which minimizes the amount of information necessary for the derivation of the source from the target (1). Its most fundamental measure is the computational complexity theory.
• When solving or completing a target case with a source case, the parameters which minimize (2) are postulated to minimize (1), and thus, produce the best response.

However, a cognitive agent may simply reduce the amount of information necessary for the interpretation of the source and the target, without taking into account the cost of data replication. So, it may prefer to the minimization of (2) the minimization of the following simplified formula:

K(M_s) + K(B_s|M_s) + K(M_t|M_s)

Applications and types

In language

Language, literature and humour

• Under the guise of metaphor, analogy enables people to transmit their thoughts and outlooks in an indirect or allusive manner.
• In literature and poetry analogy is used in order to make people laugh. The humoristic value of analogy can easily be noticed in cartoons and comic performances.
• Analogy helps humans in making linguistic generalizations and categorization.
• Analogy can be discerned in the creation and emergence of terms present in language (similarity that obtains between the persons, animals, things or events yields the need of understanding them together under one common notion).
• Analogy may facilitate the using of particular terms and concepts as well as understanding - upon the terms and phrases coined in language - the ways in which people comprehend the world and relate to each other.

Logic

• Logicians analyze how analogical reasoning is used in arguments from analogy.
• An analogy can be stated using is to and as to represent the analogous relationship between two pairs of expressions, for example, "Smile is to mouth, as wink is to eye." In the field of mathematics and logic, this can be formalized with colon notation to represent the relationships, using single colon for ratio, and double colon for equality.
• In the field of testing, the colon notation of ratios and equality is often borrowed, so that the example above might be rendered, "Smile : mouth :: wink : eye" and pronounced the same way.

Rhetoric and argumentation

• An analogy is a spoken or textual comparison between two words (or sets of words) or situations to highlight some form of semantic or relational similarity between them. Such analogies can be used for purpose of persuasion, formation of attitudes and other forms of argumentation. They function more as ex post justification (or rationalization) of a decision one made before than as a means of inventing solutions for a given problem. Analogy may strengthen political, theological and philosophical arguments, even when the semantic (superficial) similarity is weak or non-existent, provided their being crafted carefully for the audience. Analogies are sometimes used to persuade those who cannot detect the flawed or non-existent arguments. The persuasive force of an analogy used for the sake of argumentation may stem not only from the mere similarity between the items (situations) compared, but also from the very emotions (both positive and negative) that are transferred from the things, persons or events chosen as a point of comparison.

Linguistics

• An analogy can be the linguistic process that reduces word forms perceived as irregular by remaking them in the shape of more common forms that are governed by rules. For example, the English verb help once had the preterite holp and the past participle holpen. These obsolete forms have been discarded and replaced by helped by the power of analogy (or by widened application of the productive Verb-ed rule.) This is called leveling. However, irregular forms can sometimes be created by analogy; one example is the American English past tense form of dive: dove, formed on analogy with words such as drive: drove.
• Neologisms can also be formed by analogy with existing words. A good example is software, formed by analogy with hardware; other analogous neologisms such as firmware and vaporware have followed. Another example is the humorous term underwhelm, formed by analogy with overwhelm.
• Analogy is often presented as an alternative mechanism to generative rules for explaining productive formation of structures such as words. Others argue that in fact they are the same mechanism, that rules are analogies that have become entrenched as standard parts of the linguistic system, whereas clearer cases of analogy have simply not (yet) done so (e.g. Langacker 1987.445–447). This view has obvious resonances with the current views of analogy in cognitive science which are discussed above.

In science

• Analogies are above all used as a means of conceiving new ideas and hypotheses, which is called a heuristic function of analogical reasoning.
• Analogical arguments can play also probabative function, serving then as a means of proving the rightness of particular theses and theories. This application of analogical reasoning in science is, however, debatable. Probative value of analogy is of importance especially to those kinds of science in which logical or empirical proof is not possible such as theology, philosophy or cosmology in part where it relates to those areas of the cosmos (the universe) that are beyond any empirical observation and knowledge about them stems from the human insight and unsensory cognition.
• Analogy may be used in order to illustrate and teach (in order to enlighten pupils on the relations that happens between or inside certain things or phenomena, a teacher may refer to other things or phenomena that pupils are more familiar with).
• Analogy may help in creating or elucidating one theory (theoretical model) via the workings of another theory (theoretical model). Thus it can be used in theoretical and applied sciences in the form of models or simulations which can be considered as strong analogies. Other much weaker analogies assist in understanding and describing functional behaviours of similar systems. For instance, an analogy commonly used in electronics textbooks compares electrical circuits to hydraulics. Another example is the analog ear based on electrical, electronic or mechanical devices.
• Analogy can be helpful for the creation of notions and their systematization and classification, especially enabling scientists to make generalizations upon the discovery of an analogous structure or analogous internal laws present in different events or objects.

Mathematics

• Some types of analogies can have a precise mathematical formulation through the concept of isomorphism. In detail, this means that given two mathematical structures of the same type, an analogy between them can be thought of as a bijection between them which preserves some or all of the relevant structure. For example, ${\displaystyle {\mathbb {R}}^{2}}$ and ${\displaystyle {\mathbb {C}}}$ are isomorphic as vector spaces, but the complex numbers, ${\displaystyle {\mathbb {C}}}$, have more structure than ${\displaystyle {\mathbb {R}}^{2}}$ does: ${\displaystyle {\mathbb {C}}}$ is a field as well as a vector space. 
• Category theory takes the idea of mathematical analogy much further with the concept of functors. Given two categories C and D, a functor f from C to D can be thought of as an analogy between C and D, because f has to map objects of C to objects of D and arrows of C to arrows of D in such a way that the compositional structure of the two categories is preserved. This is similar to the structure mapping theory of analogy of Dedre Gentner, in that it formalizes the idea of analogy as a function which satisfies certain conditions.

Artificial intelligence

• Steven Phillips and William H. Wilson use category theory to mathematically demonstrate how the analogical reasoning in the human mind, that is free of the spurious inferences that plague conventional artificial intelligence models, (called systematicity), could arise naturally from the use of relationships between the internal arrows that keep the internal structures of the categories rather than the mere relationships between the objects (called "representational states"). Thus, the mind may use analogies between domains whose internal structures fit according with a natural transformation and reject those that do not.

Anatomy

• In anatomy, two anatomical structures are considered to be analogous when they serve similar functions but are not evolutionarily related, such as the legs of vertebrates and the legs of insects. Analogous structures are the result of convergent evolution and should be contrasted with homologous structures.

Engineering

• Often a physical prototype is built to model and represent some other physical object. For example, wind tunnels are used to test scale models of wings and aircraft, which act as an analogy to full-size wings and aircraft. 
• For example, the MONIAC (an analog computer) used the flow of water in its pipes as an analog to the flow of money in an economy.

Cybernetics

• Where there is dependence and hence interaction between a pair or more of biological or physical participants communication occurs and the stresses produced describe internal models inside the participants. Pask in his Conversation Theory asserts there exists an analogy exhibiting both similarities and differences between any pair of the participants' internal models or concepts.

In normative matters

Morality

• Analogical reasoning plays a very important part in morality. This may be in part because morality is supposed to be impartial and fair. If it is wrong to do something in a situation A, and situation B is analogous to A in all relevant features, then it is also wrong to perform that action in situation B. Moral particularism accepts analogical moral reasoning, rejecting both deduction and induction, since only the former can do without moral principles.

Law

• In law, analogy is primarily used to resolve issues on which there is no previous authority. A distinction can be made between analogical reasoning employed in statutory law and analogical reasoning present in precedential law (case law).

Analogies in statutory law

In statutory law analogy is used in order to fill the so-called lacunas or gaps or loopholes.

First, a gap arises when a specific case or legal issue is not explicitly dealt with in written law. Then, one may try to identify a statutory provision which covers the cases that are similar to the case at hand and apply to this case this provision by analogy. Such a gap, in civil law countries, is referred to as a gap extra legem (outside of the law), while analogy which liquidates it is termed analogy extra legem (outside of the law). The very case at hand is named: an unprovided case.

Second, a gap comes into being when there is a statutory provision which applies to the case at hand but this provision leads in this case to an unwanted outcome. Then, upon analogy to another statutory provision that covers cases similar to the case at hand, this case is resolved upon this provision instead of the provision that applies to it directly. This gap is called a gap contra legem (against the law), while analogy which fills this gap is referred to as analogy contra legem (against the law).

Third, a gap occurs when there is a statutory provision which regulates the case at hand, but this provision is vague or equivocal. In such circumstances, to decide the case at hand, one may try to ascertain the meaning of this provision by recourse to statutory provisions which address cases that are similar to the case at hand or other cases that are regulated by vague/equivocal provision. A gap of this type is named gap intra legem (within the law) and analogy which deals with it is referred to as analogy intra legem (within the law).

The similarity upon which statutory analogy depends on may stem from the resemblance of raw facts of the cases being compared, the purpose (the so-called ratio legis which is generally the will of the legislature) of a statutory provision which is applied by analogy or some other sources.

Statutory analogy may be also based upon more than one statutory provision or even a spirit of law. In the latter case, it is called analogy iuris (from the law in general) as opposed to analogy legis (from a specific legal provision or provisions).

In statutory law analogy is also sometimes applied in order to liquidate the so-called conflicting or logical gap (i.e. the situation when two or more statutory provisions contradict each other) or the sui generis gap which stems from the lack of statutory regulation enabling the delivering of a decision whose passing is required by the law. Some other - less common as so-called ‘pertinent application of law’, ejusdem generis, typological notions or presence of analogical pattern of reasoning in an a fortiori and comparative argument - usages are also distinguished.

Analogies in precedential law (case law)

First, in precedential law (case law), analogies can be drawn from precedent cases (cases decided in past). The judge who decides the case at hand may find that the facts of this case are similar to the facts of one of precedential cases to an extent that the outcomes of these cases are justified to be the same or similar. Such use of analogy in precedential law pertains mainly to the so-called: cases of first impression, i.e. the cases which as yet have not been regulated by any binding judicial precedent (are not covered by a ratio decidendi of such a precedent).

Second, in precedential law, reasoning from (dis)analogy is amply employed, while a judge is distinguishing a precedent. That is, upon the discerned differences between the case at hand and the precedential case, a judge reject to decide the case upon the precedent whose ratio decidendi (precedential rule) embraces the case at hand.

Third, there is also much room for some other usages of analogy in the province of precedential law. One of them is resort to analogical reasoning, while resolving the conflict between two or more precedents which all apply to the case at hand despite dictating different legal outcome for that case. Analogy can also take part in ascertaining the contents of ratio decidendi, deciding upon obsolete precedents or quoting precedents form other jurisdictions. It is too visible in legal eductaion, notably in the US (the so-called 'case method').

An argument from analogy employed in precedential law is called case analogy as opposed to analogy employed in statutory law which is accordingly termed statutory analogy.

Analogies as a means of application of legal rules

In precedential law as well as in statutory law, analogy is also considered as a means of application of legal rules (statutory and precedential), serving thus as an alternative to legal deduction (legal syllogism). Then, there are compared instances to which a given rule applies with certainty with the facts of the case at hand. If the sufficient (relevant) similarity between them obtains, the rule is applied to the case at hand. Otherwise, the rule is deemed as inadequate for this case. Such analogy becomes a legal method.

Application of legal rules through analogy is more typical of the common law legal systems, especially when one deals with the so-called holdings (the denotation of a binding element of a judicial precedent in the US), being in civil law legal systems rather a proposition than an official mode of applying the law.

The instances from which analogy starts here off are called: base points, typical instances or paradigmatic cases.

Restrictions on the use of analogy in law

In legal matters, sometimes the use of analogy is forbidden (by the very law or common agreement between judges and scholars). The most common instances concern criminal, administrative and tax law.

Analogy should not be resorted to in criminal matters whenever its outcome would be unfavorable to the accused or suspect. Such a ban finds its footing in the very principle: “nullum crimen, nulla poena sine lege”, a principle which is understood in the way that there is no crime (punishment) unless it is expressly provided for in a statutory provision or an already existing judicial precedent.

Analogy should be applied with caution in the domain of tax law. Here, the principle: “nullum tributum sine lege” justifies a general ban on the employment of analogy that would lead to an increase in taxation or whose results would – for some other reason(s) – be to the detriment to the interests of taxpayers.

Extending by analogy those provisions of administrative law that restrict human rights and the rights of the citizens (particularly the category of the so-called “individual rights” or “basic rights”) is as a rule prohibited. Analogy generally should also not be resorted to in order to make the citizen's burdens and obligations larger or more vexatious.

The other limitations on the use of analogy in law, among many others, pertain to:

• the analogical extension of statutory provisions that invlove exceptions to more general statutory regulation or provisions (this restriction flows from the well-known, especially in civil law continental legal systems, Latin maxims: “exceptiones non sunt excendentae”, “exception est strictissimae interpretationis” and “singularia non sunt extendenda”)
• the making of the use of an analogical argument with regard to those statutory provisions which comprise enumerations (lists)
• extending by analogy those statutory provisions that give impression that the Legislator intended to regulate some issues in an exclusive (exhaustive) manner (such a manner is especially implied when the wording of a given statutory provision involves such pointers as: “only”, “exclusively”, “solely”, “always”, “never”) or which have a plain precise meaning.

In civil (private) law, the use of analogy is as a rule permitted or even ordered by law. But also in this branch of law there are some restrictions confining the possible scope of the use of an analogical argument. Such is, for instance, the prohibition to use analogy in relation to provisions regarding time limits or a general ban on the recourse to analogical arguments which lead to extension of those statutory provisions which envisage some obligations or burdens or which order (mandate) something. The other examples concern the usage of analogy in the field of property law, especially when one is going to create some new property rights by it or to extend these statutory provisions whose terms are unambiguous (unequivocal) and plain (clear), e.g.: be of or under cartian age.

The aforementioned bans on the use of analogy concern rather analogy which goes beyond the possible linguistic meaning of a statutory provision in question and do not pertain to analogy whose conclusions would remain within this meaning.

Nomenclature

Analogy in law – apart from the terminological distinctions mentioned above – can be found also under such Latin names and phrases as:

• “argumentum a simile (a simili)”, i.e. an argument from similarity or an inference based upon similarity
• an argument or reasoning “a pari”
• “argumentum a similibus ad similia”
• “argumentum (inference) per analogiam”
• an argument "ab exemplo", i.e. an argument from paradigmatic examples.

Uniqueness of legal analogy

Legal analogy is sometimes claimed to be of a different nature than analogy that occurs in empirical science and everyday life. It is due to several peculiar factors. First, there is the lack of possibility of verification of conclusions of legal analogy on empirical grounds, which entails the necessity of performance of a legal analogical argument both heuristic and probative function. Second, legal analogy, as the law itself, is by definition prescriptive, non-descriptive. Third, it has an obligatory character: a judge is in many circumstances obliged to reason by analogy (treat similar cases in a similar manner). Fourth, the use of analogy in law rather does not hinge on complex underling doctrines or theories. Fifth, serious practical consequences flow from the use of analogy in law. Sixth, the points of comparison are easily recognizable in case of legal analogy. Seventh, analogy in law becomes a vehicle for extension of authority. Eighth, how to reason by analogy is a subject of legal training and education. Ninth, legal analogy has gained enormous amount of attention and scrutiny amongst scholars.

Structure of legal analogy

Legal analogy usually assumes the classical structure:

• A case A possesses features X, Y, Z and has ascribed legal consequence G (the first premise)
• An unregulated (unprovided) case B possesses features X, Y, Z (the second premise)
• Therefore, the case B should be ascribed the legal consequence G (the analogical conclusion)

or:

• There is a rule in force which addresses cases which features are A, B, C, D (the first premise)
• There are unregulated (unprovided) cases which features are A, B, C and E or cases which features are A, B, C, D and E or cases which features are A, B, C and non-D (the second premise)
• Therefore, there should be also a rule in force which addresses cases which features are A, B, C and E or A, B, C, D and E or A, B, C and non-D that prescribes the same or similar legal consequece for these cases as the rule which addresses cases which features are A, B, C, D (the analogical conclusion).

Legal analogy can, however, assume also the structure of (mathematical) proportion, i.e.: A is to B as C is to D or A is to B as B is to C.

The contemporary proponents of proportional analogy, including legal one, are Chaïm Perelman and Lucie Olbrechts Tyteca.

Specifically, in law, analogy of proportion takes the form:

• 1) Determination of the relation that obtains between the facts of the regulated (provided) case and its legal consequence.
• 2) Determination of the relation that obtains between the facts of the case at hand and their posited legal consequence (i.e. the consequence that is supposed to be potentially adequate for this case).
• 3) Having ascertained that the relations pointed out in points 1 and 2 are identical or similar to each other, attribution to the case at hand the legal consequence which has been posited for that case.

In teaching strategies

Analogies as defined in rhetoric are a comparison between words, but an analogy can be used in teaching as well. An analogy as used in teaching would be comparing a topic that students are already familiar with, with a new topic that is being introduced so that students can get a better understanding of the topic and relate back to previous knowledge. Shawn Glynn, a professor in the department of educational psychology and instructional technology at the University of Georgia, developed a theory on teaching with analogies and developed steps to explain the process of teaching with this method. The steps for teaching with analogies are as follows: Step one is introducing the new topic that is about to be taught and giving some general knowledge on the subject. Step two is reviewing the concept that the students already know to ensure they have the proper knowledge to assess the similarities between the two concepts. Step three is finding relevant features within the analogy of the two concepts. Step four is finding similarities between the two concepts so students are able to compare and contrast them in order to understand. Step five is indicating where the analogy breaks down between the two concepts. And finally, step six is drawing a conclusion about the analogy and comparison of the new material with the already learned material. Typically this method is used to learn topics in science.

In 1989 Kerry Ruef, a teacher, began an entire program, which she titled The Private Eye Project. It is a method of teaching that revolves around using analogies in the classroom to better explain topics. She thought of the idea to use analogies as a part of curriculum because she was observing objects once and she said, "my mind was noting what else each object reminded me of..." This led her to teach with the question, "what does [the subject or topic] remind you of?" The idea of comparing subjects and concepts led to the development of The Private Eye Project as a method of teaching. The program is designed to build critical thinking skills with analogies as one of the main themes revolving around it. While Glynn focuses on using analogies to teach science, The Private Eye Project can be used for any subject including writing, math, art, social studies, and invention. It is now used by thousands of schools around the country. There are also various pedagogic innovations now emerging that use visual analogies for cross-disciplinary teaching and research, for instance between science and the humanities.

Religion

Catholic

The Fourth Lateran Council of 1215 taught: For between creator and creature there can be noted no similarity so great that a greater dissimilarity cannot be seen between them.

The theological exploration of this subject is called the analogia entis. The consequence of this theory is that all true statements concerning God (excluding the concrete details of Jesus' earthly life) are analogical and approximations, without that implying any falsity. Such analogical and true statements would include God is, God is Love, God is a consuming fire, God is near to all who call him, or God as Trinity, where being, love, fire, distance, number must be classed as analogies that allow human cognition of what is infinitely beyond positive or negative language.

The use of theological statements in syllogisms must take into account their essential analogical character, in that every analogy breaks down when stretched beyond its intended meaning.

Everyday life

• Analogy can be used in order to find solutions for the problematic situations (problems) that occur in everyday life. If something works with one thing, it may also work with another thing which is similar to the former.
• Analogy facilitates choices and predictions as well as opinions/assessments people are forced to do daily.
• Analogy is helpful in distribution of goods and privileges, partition of burdens and dispension of treatment of other kind people deal with in everyday life.

Hybrid analogies operating between disciplines

Visual analogies have been developed that enable researchers to "investigate literary studies by means of attractive analogies taken principally from science and mathematics. These analogies bring to literary discourse a stock of exciting visual ideas for teaching and research..."