Ernố Rubik
I heard a story about Ernố Rubik that was not entirely true, shall we say! In 1990 he became President of the Hungarian Engineering Academy.
At 3 minutes 42 seconds on the ability to recognise which situation the cube is in, see A General Strategy for Solving Problems by Analysis of Situational Logic. This is what I call abstraction. The nature of abstraction is essentially linguistic, and is easier to understand if you study simple formal languages such as the lambda calculus. In such formal languages, the idea of abstraction is captured by the notion of a bound variable, which is a way of associating a name to part of a more complex expression where the name is essentially a place-holder for some as yet unspecified part of the whole expression. So in the case of the Rubik's cube abstraction of an algorithm to, say, rotate one edge cube so that the colours are swapped, can be specified regardless of which of the twelve edges contains the cube being rotated, and regardless of which particular pair of colours are on that cube. In a sense, this tells you what an algorithm is, because without this ability to abstract from the concrete instance of the problem, there would be no need to speak of any general algorithm, there would just be billions of special rules that each applied in only particular circumstances. So I think this was probably what led many to feel that unscrambling a Rubik's cube was impossible. Now that ought to make some people think about entropy and the second law of thermodynamics, which, as we all know, is what stops time from running backwards! This linguistic nature of abstraction is not in itself abstract, it has very real psychological effects! See John Searle on Philosophy of Language and, for some of the pathological consequences, see John Searle on Intention and Meaning.
Rubik himself didn't have much to do with most of the Rubik's cubes made, but the company is still not doing too badly. Their new puzzle scares the crap out of me though!!
Those of you who are brave enough might want to go on an archaeological dig with my professor. Indiana Jade on Information and Representation I'll just stay at home, ... don't worry about breakfast, ...
If you are interested to know how that new cube will be designed, then you need to think of all the operations that you can perform on an ordinary Rubik's cube as abstract permutations. The global solution algorithm that results from combining elementary operations based on pattern-matching can be thought of as a polymorphic type. See this description of Hindley-Milner type inference.
Sarah who was also in Budapest in June 1990 knows this gypsy dance:
... I'm self-isolating, ... got some zombies coming around for a maths lesson: AcTVism Munich on Collateral Murder and Technology. See Why is Telecommunications Security Important?
At 3 minutes 42 seconds on the ability to recognise which situation the cube is in, see A General Strategy for Solving Problems by Analysis of Situational Logic. This is what I call abstraction. The nature of abstraction is essentially linguistic, and is easier to understand if you study simple formal languages such as the lambda calculus. In such formal languages, the idea of abstraction is captured by the notion of a bound variable, which is a way of associating a name to part of a more complex expression where the name is essentially a place-holder for some as yet unspecified part of the whole expression. So in the case of the Rubik's cube abstraction of an algorithm to, say, rotate one edge cube so that the colours are swapped, can be specified regardless of which of the twelve edges contains the cube being rotated, and regardless of which particular pair of colours are on that cube. In a sense, this tells you what an algorithm is, because without this ability to abstract from the concrete instance of the problem, there would be no need to speak of any general algorithm, there would just be billions of special rules that each applied in only particular circumstances. So I think this was probably what led many to feel that unscrambling a Rubik's cube was impossible. Now that ought to make some people think about entropy and the second law of thermodynamics, which, as we all know, is what stops time from running backwards! This linguistic nature of abstraction is not in itself abstract, it has very real psychological effects! See John Searle on Philosophy of Language and, for some of the pathological consequences, see John Searle on Intention and Meaning.
Rubik himself didn't have much to do with most of the Rubik's cubes made, but the company is still not doing too badly. Their new puzzle scares the crap out of me though!!
Those of you who are brave enough might want to go on an archaeological dig with my professor. Indiana Jade on Information and Representation I'll just stay at home, ... don't worry about breakfast, ...
If you are interested to know how that new cube will be designed, then you need to think of all the operations that you can perform on an ordinary Rubik's cube as abstract permutations. The global solution algorithm that results from combining elementary operations based on pattern-matching can be thought of as a polymorphic type. See this description of Hindley-Milner type inference.
Sarah who was also in Budapest in June 1990 knows this gypsy dance:
... I'm self-isolating, ... got some zombies coming around for a maths lesson: AcTVism Munich on Collateral Murder and Technology. See Why is Telecommunications Security Important?
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