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9. According to Albert Einstein the non mathematician, is seized by a mysterious shuddering when he hears of 'four-dimensional' things, he is seized by a feeling, which is very similar to the thoughts awakened by the occult. And at the same time the statement that the world in which we live is a four-dimensional space - time continuum is quite a common place statement.
This might lead to an argument regarding the use of the term ''commonplace'' by Einstein. Yet the difficulty lies more in the wording than the ideas. Einstein's concept of the universe as a four-dimensional space-time continuum becomes plain and clear, when what he means by ''continuum'' becomes clear. A continuum is something that is continuous, A ruler, for example, is a one-dimensional space continuum. Most rulers are divided into inches and fractions, scaled down to one-sixteenth of an inch.
Will it be possible to conceive a ruler, which is calibrated to a millionth or billionth of an inch. In theory there is no reason why the steps from point to point should not be even smaller. What distinguishes a continuum is the fact that the space between any two points can be sub-divided into an infinite number of smaller divisions.
A railroad track is a one-dimensional space continuum and on it the engineer of a train can describe his position at any time by citing a single co-ordinate point - i.e., a station or a milestone. A sea captain, however, has to worry about two dimensions. The surface of the sea is a two-dimensional continuum and the co-ordinate points by which sailor fixes his positions in his two dimensional continuum are latitude and longitude. An airplane pilot guides his plane through a three - dimensional continuum, hence he has to consider not only latitude and longitude, but also his height above the ground. The continuum of an airplane pilot constitutes space as we perceive it. In other words, the space of our world is a three-dimensional continuum.
Just indicating its position in space is not enough while describing any physical event, which involves motion. How position changes in time also needs to be mentioned. Thus to give an accurate picture of the operation of a New York - Chicago express, one must mention not only that it goes from New - York to Albany to Syracuse to Cleveland to Toledo to Chicago, but also the times at which it touches each of those points. This can be done either by means of a timetable or a visual chart. If the miles between New York and Chicago are plotted horizontally on a piece of ruled paper and the hours and minutes are plotted vertically, then a diagonal line properly drawn across the page illustrates the progress of the train in two - dimensional space - time continuum. This type of graphic representation is familiar to most newspaper readers; a stock market chart, for example, pictures financial events in a two - dimensional dollar - time continuum. Similarly for the best picturization of the flight of an airplane from New York to Los Angeles a four - dimensional space - time continuum is essential. The latitude, longitude and altitude will only make sense to the traffic manager of the airline if the time co - ordinate is also mentioned. Therefore time is the fourth dimension. If a flight has to be looked at, perceived as a whole, it wouldn't work if it is broken down into a series of disconnected take - offs, climbs, glides, and landing, it needs to be looked at and perceived as a continuous four - dimensional space - time continuum curve.
[i] In order to explain a difficult topic, the author use
(a) Simply phrased definition's
(b) An incessant metaphor
(c) A plain writing style
(d) Familiar images
(e) A quotation from Einstein
Ans : (d)
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