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How information is represented can greatly affect how easy it is to do different things with it" (David Marr, Vision, 1982, p.21)  Questions: 1) show and explain this phenomenon (give an example as well) 2) For the study of mental representations, Is there any lesson learned from this phenomenon?

How information is represented can greatly affect how easy it is to do different things with it" (David Marr, Vision, 1982, p.21)  Questions: 1) show and explain this phenomenon (give an example as well) 2) For the study of mental representations, Is there any lesson learned from this phenomenon?

Ciccarelli: Psychology_5 (5th Edition)
Ciccarelli: Psychology_5 (5th Edition)
5th Edition
ISBN:9780134477961
Author:Saundra K. Ciccarelli, J. Noland White
Publisher:Saundra K. Ciccarelli, J. Noland White
Chapter1: The Science Of Psychology
Section: Chapter Questions
Problem 1TY
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"How information is represented can greatly affect how easy it is to do different things

with it" (David Marr, Vision, 1982, p.21) 

Questions:

1) show and explain this phenomenon (give an example as well)

2) For the study of mental representations, Is there any lesson learned from this phenomenon?

of words, and so forih. The phrase "formal scheme" is critical to the defi- nition, but the reader should not be frightened by it. The reason is simply that we are dealing with information-processing machines, and the way such machines work is by using symbols to stand for things-to represent things, in our terminology. To say that something is a formal scheme means only that it is a set of symbols with rules for putting them together-no more and no less. A representation, therefore, is not a foreign idea at all-we all use representations all the time. However, the notion that one can capture some aspect of reality by making a description of it using a symbol and that to do so can be useful seems to me a fascinating and powerful idea But even the simple examples we have discussed introduce some rather general and important issues that arise whenever one chooses to use one particular representation. For example, if one chooses the Arabic numeral representation, it is easy to discover whether a number is a power of 10 but difficult to discover whether it is a power of 2. If one chooses the binary representation, the situation is reversed Thus, there is a trade-of, particular representation makes certain information explicit at the expense of information that is pushed into the background and may be quite hard to recover. This issue is important, because how information is represented can greatly affect how easy it is to do different things with it. This is evident even from our numbers example: It is easy to add, to subtract, and even to multiply if the Arabic or binary representations are used, but it is not at all casy to do these things-especially multiplication-with Roman numerals. This is a key reason why the Roman culture failed to develop mathematics in the way the earlier Arabic cultures had. An anakogous problem faces computer engineers today Electronic technology is much more suited to a binary number system than to the comentional base 10 system, yet humans supply their data and require the results in base 10. The design decision facing the engineer, therefore, is. Should one pay the cost of conversion into base 2, carry out the arithmetic in a binary representation, and then comvert back into decimal mumbers on output; or should one sacrifice efficiency of circuitry to carry out oper- ations directly in a decimal representation? On the whole, business com puters and pocket calculators take the second approach, and general pur- pose computers take the first. But even though one is not restricted to using Rust one representation system for a given rype of informaxion, the choice of which to use is important and cannot be taken lightly It deter- mines what information is made explicit and hence what is pushed further into the hackground, and it has a far-reaching effect on the ease and
Transcribed Image Text:of words, and so forih. The phrase "formal scheme" is critical to the defi- nition, but the reader should not be frightened by it. The reason is simply that we are dealing with information-processing machines, and the way such machines work is by using symbols to stand for things-to represent things, in our terminology. To say that something is a formal scheme means only that it is a set of symbols with rules for putting them together-no more and no less. A representation, therefore, is not a foreign idea at all-we all use representations all the time. However, the notion that one can capture some aspect of reality by making a description of it using a symbol and that to do so can be useful seems to me a fascinating and powerful idea But even the simple examples we have discussed introduce some rather general and important issues that arise whenever one chooses to use one particular representation. For example, if one chooses the Arabic numeral representation, it is easy to discover whether a number is a power of 10 but difficult to discover whether it is a power of 2. If one chooses the binary representation, the situation is reversed Thus, there is a trade-of, particular representation makes certain information explicit at the expense of information that is pushed into the background and may be quite hard to recover. This issue is important, because how information is represented can greatly affect how easy it is to do different things with it. This is evident even from our numbers example: It is easy to add, to subtract, and even to multiply if the Arabic or binary representations are used, but it is not at all casy to do these things-especially multiplication-with Roman numerals. This is a key reason why the Roman culture failed to develop mathematics in the way the earlier Arabic cultures had. An anakogous problem faces computer engineers today Electronic technology is much more suited to a binary number system than to the comentional base 10 system, yet humans supply their data and require the results in base 10. The design decision facing the engineer, therefore, is. Should one pay the cost of conversion into base 2, carry out the arithmetic in a binary representation, and then comvert back into decimal mumbers on output; or should one sacrifice efficiency of circuitry to carry out oper- ations directly in a decimal representation? On the whole, business com puters and pocket calculators take the second approach, and general pur- pose computers take the first. But even though one is not restricted to using Rust one representation system for a given rype of informaxion, the choice of which to use is important and cannot be taken lightly It deter- mines what information is made explicit and hence what is pushed further into the hackground, and it has a far-reaching effect on the ease and
Representation and Description A representation is a formal sysem for making explicit certain entities or types of information, together with a specification of how the system does this. And I shafl call the result of using a representation to describe a given entity a description of the entity in that representation (Marr and Nishihara, 1978). For example, the Arabic, Roman, and binary numeral systems are all formal systems for representing numbers. The Arabic representation con- sists of a string of symbols drawn from the set (0, 1, 2, 3. 4, 5, 6, 7, 8, 9), and the rule for constructing the description of a particular integer n is that one decomposes n into a sum of multiples of powers of 10 and unites these multiples into a string with the largest powers on the left and the smallest on the right. Thus, thirty-seven equals 3 x 10' + 7x 10", which becomes 37, the Arabic numeral systems description of the number. What this description makes explicit is the numher's decomposition into powers of 10. The binary numeral system's description of the number thirty-seven is 100101, and this description makes explicit the number's decomposition into powers of 2. In the Roman numeral system, thirty seven is represented as XXXVII. This definitton of a representation is quite general. For example, a representation for shape would be a formal scheme for describing some aspects of shape, together with rules that specify how the scheme is applied to any particular shape. A musical score provides a way of representing a symphony; the alphabet allows the construction of a written representation
Transcribed Image Text:Representation and Description A representation is a formal sysem for making explicit certain entities or types of information, together with a specification of how the system does this. And I shafl call the result of using a representation to describe a given entity a description of the entity in that representation (Marr and Nishihara, 1978). For example, the Arabic, Roman, and binary numeral systems are all formal systems for representing numbers. The Arabic representation con- sists of a string of symbols drawn from the set (0, 1, 2, 3. 4, 5, 6, 7, 8, 9), and the rule for constructing the description of a particular integer n is that one decomposes n into a sum of multiples of powers of 10 and unites these multiples into a string with the largest powers on the left and the smallest on the right. Thus, thirty-seven equals 3 x 10' + 7x 10", which becomes 37, the Arabic numeral systems description of the number. What this description makes explicit is the numher's decomposition into powers of 10. The binary numeral system's description of the number thirty-seven is 100101, and this description makes explicit the number's decomposition into powers of 2. In the Roman numeral system, thirty seven is represented as XXXVII. This definitton of a representation is quite general. For example, a representation for shape would be a formal scheme for describing some aspects of shape, together with rules that specify how the scheme is applied to any particular shape. A musical score provides a way of representing a symphony; the alphabet allows the construction of a written representation
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