Understanding

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Understanding is a psychological process related to an abstract or physical object, such as a person, situation, or message whereby one is able to think about it and use concepts to deal adequately with that object. Understanding is a relation between the knower and an object of understanding. Understanding implies abilities and dispositions with respect to an object of knowledge that are sufficient to support intelligent behaviour. [1]

A person is a being that has certain capacities or attributes such as reason, morality, consciousness or self-consciousness, and being a part of a culturally established form of social relations such as kinship, ownership of property, or legal responsibility. The defining features of personhood and consequently what makes a person count as a person differ widely among cultures and contexts.

Message discrete unit of communication intended by the source for consumption by some recipient or group of recipients

A message is a discrete unit of communication intended by the source for consumption by some recipient or group of recipients. A message may be delivered by various means, including courier, telegraphy, carrier pigeon and electronic bus. A message can be the content of a broadcast. An interactive exchange of messages forms a conversation.

Concept mental representation or an abstract object or an ability

Concepts are mental representations, abstract objects or abilities that make up the fundamental building blocks of thoughts and beliefs. They play an important role in all aspects of cognition.

Contents

Understanding is often, though not always, related to learning concepts, and sometimes also the theory or theories associated with those concepts. However, a person may have a good ability to predict the behaviour of an object, animal or system—and therefore may, in some sense, understand it—without necessarily being familiar with the concepts or theories associated with that object, animal or system in their culture. They may have developed their own distinct concepts and theories, which may be equivalent, better or worse than the recognised standard concepts and theories of their culture. Thus, understanding is correlated with the ability to make inferences.

Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word infer means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in Europe dates at least to Aristotle. Deduction is inference deriving logical conclusions from premises known or assumed to be true, with the laws of valid inference being studied in logic. Induction is inference from particular premises to a universal conclusion. A third type of inference is sometimes distinguished, notably by Charles Sanders Peirce, distinguishing abduction from induction, where abduction is inference to the best explanation.

Examples

  1. One understands the weather if one is able to predict (e.g. if it is very cloudy, it may rain) and/or give an explanation of some of its features, etc.
  2. A psychiatrist understands another person's anxieties if he/she knows that person's anxieties, their causes, and can give useful advice on how to cope with the anxiety.
  3. One understands a piece of reasoning or an argument if one can consciously reproduce the information content conveyed by the message.
  4. One understands a language to the extent that one can reproduce the information content conveyed by a broad range of spoken utterances or written messages in that language.

Shallow and deep

Someone who has a more sophisticated understanding, more predictively accurate understanding, and/or an understanding that allows them to make explanations that others commonly judge to be better, of something, is said to understand that thing "deeply". Conversely, someone who has a more limited understanding of a thing is said to have a "shallow" understanding. However, the depth of understanding required to usefully participate in an occupation or activity may vary greatly.

For example, consider multiplication of integers. Starting from the most shallow level of understanding, we have (at least) the following possibilities:

Multiplication mathematical operation and Multiply, Product, By, Times, Lots Of

Multiplication is one of the four elementary mathematical operations of arithmetic; with the others being addition, subtraction and division.

Integer Number in {..., –2, –1, 0, 1, 2, ...}

An integer is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5 1/2, and 2 are not.

  1. A small child may not understand what multiplication is, but may understand that it is a type of mathematics that they will learn when they are older at school. This is "understanding of context"; being able to put an as-yet not-understood concept into some kind of context. Even understanding that a concept is not part of one's current knowledge is, in itself, a type of understanding (see the Dunning–Kruger effect, which is about people who do not have a good understanding of what they do not know).
  2. A slightly older child may understand that multiplication of two integers can be done, at least when the numbers are between 1 and 12, by looking up the two numbers in a times table. They may also be able to memorise and recall the relevant times table in order to answer a multiplication question such as "2 times 4 is what?". This is a simple form of operational understanding; understanding a question well enough to be able to do the operations necessary to be able to find an answer.
  3. A yet older child may understand that multiplication of larger numbers can be done using a different method, such as long multiplication, or using a calculator. This is a more advanced form of operational understanding because it supports answering a wider range of questions of the same type.
  4. A teenager may understand that multiplication is repeated addition, but not understand the broader implications of this. For example, when their teacher refers to multiplying 6 by 3 as "adding 6 to itself 3 times", they may understand that the teacher is talking about two entirely equivalent things. However, they might not understand how to apply this knowledge to implement multiplication as an algorithm on a computer using only addition and looping as basic constructs. This level of understanding is "understanding a definition" (or "understanding the definition" when a concept only has one definition).
  5. A teenager may also understand the mathematical idea of abstracting over individual whole numbers as variables, and how to efficiently (i.e. not via trial-and-error) solve algebraic equations involving multiplication by such variables, such as . This is "relational understanding"; understanding how multiplication relates to division.
  6. An undergraduate studying mathematics may come to learn that "the integers equipped with multiplication" is merely one example of a range of mathematical structures called monoids, and that theorems about monoids apply equally well to multiplication and other types of monoids.

For the purpose of operating a cash register at McDonald's, a person does not need a very deep understanding of the multiplication involved in calculating the total price of two Big Macs. However, for the purpose of contributing to number theory research, a person would need to have a relatively deep understanding of multiplication — along with other relevant arithmetical concepts such as division and prime numbers.

Cash register mechanical or electronic device for registering and calculating transactions at a point of sale

A cash register, also referred to as a till in the United Kingdom and other Commonwealth countries, is a mechanical or electronic device for registering and calculating transactions at a point of sale. It is usually attached to a drawer for storing cash and other valuables. The cash register is also usually attached to a printer, that can print out receipts for record keeping purposes.

McDonalds American fast food restaurant chain

McDonald's is an American fast food company, founded in 1940 as a restaurant operated by Richard and Maurice McDonald, in San Bernardino, California, United States. They rechristened their business as a hamburger stand, and later turned the company into a franchise, with the Golden Arches logo being introduced in 1953 at a location in Phoenix, Arizona. In 1955, Ray Kroc, a businessman, joined the company as a franchise agent and proceeded to purchase the chain from the McDonald brothers. McDonald's had its original headquarters in Oak Brook, Illinois, but moved its global headquarters to Chicago in early 2018.

Big Mac a hamburger sold by McDonalds

The Big Mac is a hamburger sold by international fast food restaurant chain McDonald's. It was introduced in the Greater Pittsburgh area, United States, in 1967 and nationwide in 1968. It is one of the company's flagship products.

Assessment

It is possible for a person, or a piece of "intelligent" software, that in reality only has a shallow understanding of a topic, to appear to have a deeper understanding than they actually do, when the right questions are asked of it. The most obvious way this can happen is by memorization of correct answers to known questions, but there are other, more subtle ways that a person or computer can (intentionally or otherwise) deceive somebody about their level of understanding, too. This is particularly a risk with artificial intelligence, in which the ability of a piece of artificial intelligence software to very quickly try out millions of possibilities (attempted solutions, theories, etc.) could create a misleading impression of the real depth of its understanding. Supposed AI software could in fact come up with impressive answers to questions that were difficult for unaided humans to answer, without really understanding the concepts at all, simply by dumbly applying rules very quickly. (However, see the Chinese room argument for a controversial philosophical extension of this argument.)

Memorization

Memorization is the process of committing something to memory. Mental process undertaken in order to store in memory for later recall items such as experiences, names, appointments, addresses, telephone numbers, lists, stories, poems, pictures, maps, diagrams, facts, music or other visual, auditory, or tactical information.

In computer science, artificial intelligence (AI), sometimes called machine intelligence, is intelligence demonstrated by machines, in contrast to the natural intelligence displayed by humans and other animals. Computer science defines AI research as the study of "intelligent agents": any device that perceives its environment and takes actions that maximize its chance of successfully achieving its goals. More specifically, Kaplan and Haenlein define AI as “a system’s ability to correctly interpret external data, to learn from such data, and to use those learnings to achieve specific goals and tasks through flexible adaptation”. Colloquially, the term "artificial intelligence" is used to describe machines that mimic "cognitive" functions that humans associate with other human minds, such as "learning" and "problem solving".

The Chinese room argument holds that a program cannot give a computer a "mind", "understanding" or "consciousness", regardless of how intelligently or human-like the program may make the computer behave. The argument was first presented by philosopher John Searle in his paper, "Minds, Brains, and Programs", published in Behavioral and Brain Sciences in 1980. It has been widely discussed in the years since. The central point of the argument is a thought experiment known as the Chinese room.

Examinations are designed to assess students' understanding (and sometimes also other things such as knowledge and writing abilities) without falling prey to these risks. They do this partly by asking multiple different questions about a topic to reduce the risk of measurement error, and partly by forbidding access to reference works and the outside world to reduce the risk of someone else's understanding being passed off as one's own. Because of the faster and more accurate computation and memorization abilities of computers, such tests would arguably often have to be modified if they were to be used to accurately assess the understanding of an artificial intelligence.

Test (assessment) Procedure for measuring a subjects knowledge, skill, aptitude, physical fitness, or other characteristics

A test or examination is an assessment intended to measure a test-taker's knowledge, skill, aptitude, physical fitness, or classification in many other topics. A test may be administered verbally, on paper, on a computer, or in a predetermined area that requires a test taker to demonstrate or perform a set of skills. Tests vary in style, rigor and requirements. For example, in a closed book test, a test taker is usually required to rely upon memory to respond to specific items whereas in an open book test, a test taker may use one or more supplementary tools such as a reference book or calculator when responding. A test may be administered formally or informally. An example of an informal test would be a reading test administered by a parent to a child. A formal test might be a final examination administered by a teacher in a classroom or an I.Q. test administered by a psychologist in a clinic. Formal testing often results in a grade or a test score. A test score may be interpreted with regards to a norm or criterion, or occasionally both. The norm may be established independently, or by statistical analysis of a large number of participants. An exam is meant to test a persons knowledge or willingness to give time to manipulate that subject.

Conversely, it is even easier for a person or artificial intelligence to fake a shallower level of understanding than they actually have; they simply need to respond with the same kind of answers that someone with a more limited understanding, or no understanding, would respond with — such as "I don't know", or obviously wrong answers. This is relevant for judges in Turing tests; it is unlikely to be effective to simply ask the respondents to mentally calculate the answer to a very difficult arithmetical question, because the computer is likely to simply dumb itself down and pretend not to know the answer.

As a model

Gregory Chaitin, a noted computer scientist, propounds a view that comprehension is a kind of data compression. [2] In his essay "The Limits of Reason", he argues that understanding something means being able to figure out a simple set of rules that explains it. For example, we understand why day and night exist because we have a simple model—the rotation of the earth—that explains a tremendous amount of data—changes in brightness, temperature, and atmospheric composition of the earth. We have compressed a large amount of information by using a simple model that predicts it. Similarly, we understand the number 0.33333... by thinking of it as one-third. The first way of representing the number requires five concepts ("0", "decimal point", "3", "infinity", "infinity of 3"); but the second way can produce all the data of the first representation, but uses only three concepts ("1", "division", "3"). Chaitin argues that comprehension is this ability to compress data.

Components

Cognition and affect

Cognition is the process by which sensory inputs are transformed. Affect refers to the experience of feelings or emotions. Cognition and affect constitute understanding.

Religious perspectives

In Catholicism and Anglicanism, understanding is one of the Seven gifts of the Holy Spirit.

See also

Related Research Articles

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Division (mathematics) arithmetic operation; one of the four basic operations of arithmetic (others being addition, subtraction, multiplication).The division of two natural numbers is the process of calculating the number of times one number is contained within one another

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Addition arithmetic operation of adding (augend+addend=summand+summand=sum, total). (Add, Sum, Plus, Increase, Total)

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References

  1. Bereiter, Carl. "Education and mind in the Knowledge Age". Archived from the original on 2006-02-25.
  2. Chaitin, Gregory (2006), The Limits Of Reason (PDF), archived from the original (PDF) on 2016-03-04