FANTASTIC FIGURES

Evening Star, Issue 23325, 22 July 1939, Page 3

FANTASTIC FIGURES

(Written by Michael Lorant, for tho ‘ Evening Star.’)

Modern science, where very largo or very small numbers arc concerned, is constantly discovering new definitions, which enable us to carry our imaginations nearer to reality in this world almost unknown to laymen. in every language there is a favourite simile regarding excessively large numbers —namely, “ as countless as the stars in the sky.” This sounds very poetic, but does not cover tho truth. In tho year a.d. 130 Ptolemy registered 1,025 stars on tho oldest chart of tho skies, and this number is by no means “ countless;” Since then astronomers have constantly been discovering new stars, and to-Uay we know that there are nearly 4,000 stars which can be seen with the naked eye. Far more could! be expressed by the simile “ as innumerable as the sands of the desert,” as it is certain that no living creature could count them. Just after the war there was a time when the German, French, and other currencies ran into hundreds and thousands of millions. This was the so-called period of inflation, and at that time imagination simply ran riot in the contemplation of such vast numbers. It is a fact that there are very few people even amongst experts who have a clear idea as to the significance of one million. Mi Gordon Selfridge once tried to stage an exhibition whereby he might demonstrate to the public the value of £1,000,000. By placing diamonds worth that amount in a showcase, free rein was given to the imagination regarding the costliness of precious stones; but yet one had no clear conception of the actual unit, one million.

We shall try to give some idea of this almost unknown quantity from a (psychological and realistic point of view. The quickest pulse-beat ever experienced by man is about 200. Reckoning it at this rate, the pulse-beat would l , in the space of one hour,, amount to 12,000. This means 300,000 within a day and a night. Now, if anybody were able to calculate the beating of such a record pulse he would have to do so for four whole days and three whole nights in order to reach one million. Continuing in this manner, if the same man were to calculate for one year he would arrive at a result of about one hundred million, and so after 10 years’ calculation this remarkable pulse would be beating at the rate of one milliard (a thousand million). Science does not require the imagination to work with these huge numbers every day. But the figures with which wo deal in everyday life could, on occasion, increase to an amazing extent. We can realise that even a mile, which is 1,760 times longer than a yard, is a considerable length. That approximately it is the distance, for instance, from Oxford Circus to Trafalgar Square in London. On the roads we find the well-k,nown mile-stones. Anybody wfio can pass three of these in the space of one hour is a good hiker. If we multiply the distance of a mile, which wo can clearly imagine throughout everyday’s walk, by a thousand, we get an enormous distance. A thousand mile journey from London to the Continent would bring us to more than the middle or the latter. The longest distance on the earth is about 24,000 miles as the crow,flies, and that is the length of the Equator. A good hiker would only be able to accomplish this journey in the space of three years. Let us again multiply_ a thousand miles by a thousand. This gives us a million miles, which already brings us into void or nothingness. After completing a third of our imaginary journey, which consisted of more than 300,000 miles, we had already passed the moon, but we did not travel even a hundredth part of our way to the sun, which is nearly a hundred million miles away from the earth. Let us go a little further again and let us again multiply by a thousand, reaching this, way the enormous figure of one milliard. After traversing one milliard miles we reach our solar system, but after half a milliard miles we pass Jupiter. In spite of this we shall only reach Neptune after traversing three milliard miles. Let us go still further and multiply again by a thousand. The result is one billion. Well, after one billion miles we have left our solar system far behind, but we are still a great distance away from our nearest neighbour, the star Centaur. Thus we see how desolate is our void and each solar system is but a little oasis in it Our next measurement is a new one. The speed of light is nearly 200,000 miles per second, and in one year, therefore, it could travel nearly six billion miles. This is the measurement in astronomy. Let us go again a little further and multiply by a thousand. After about 600 billion miles we reach the Milky Way, and now wo can see that our* nearest neighbour in the void, Centaur, is as far from us as the distance which light could travel in 3J years. Multiplying again by a thousand and getting in the reach of our imagination the fantastic number, one trillion, we can say that after one trillion miles wc reach some new galaxies, and after three trillion miles, we reach tho Andromeda. Our most powerful astronomical telescope only covers this distance. This is the limit not only to our realisation, but also to our imagination of distance. Finally, after again multiplying a trillion miles by a thousand we pass every celestial body, and this numbeV, according to Professor Einstein, is the limit in mathematics. In thought and in theory we could multiply still further, hut in our own world and in tho void we cannot even imagine a distance measurable by any greater figure than that. We can imagine the void to be a, sphere and the limits or boundaries of this sphere are 600 trillion miles away from us Here wo must stop. Me cannot go any further even in our imagination. But we can take a ‘‘return ticket,” so to speak, and we can go to the other end of the scale —to that where infinitely small numbers prevail. Well, an inch is the, thirty-sixth part of a yard, and one-thirtieth of an inch is nearly equal to one millimetre, which is the thousandth part of a metre. It is really a very small measurement, but if one leg of our table is smaller by as much as a millimetre than the other three we should notice it. We try to bite something, or. rather, assuming that we do, and for some reason one of our teeth is slightly shorter than the others we should feel the tenth part of a millimetre. The tenth part of a millimetre is equal to the threehundredth part of an inch. This is the diameter of a point which we can see with the naked eye. Measurements after that can only be made with the aid of a microscope. Going a step further, wc shall examine the thousandth part of a millimetre, known in the metric system ns a mikvon. This is the thirty-thousandth part of au inch and is the measurement

of one of our body cells or bacteria. The wave lengths of light which can be seen with the naked eye are 1.8-1.4 mikrons, and this is the limit of the microscope. With the aid of an ultramicroscope we can go a little, but only a little, further. The thousandth part of a mikron is known in the metric system as a mikromikron, and this is equal! to the thirtymillionth part of an inch. This is how atoms are measured, and scentists also employ these measurements when dealing with Rontgen rays. There is ,iu existence a method of calculation ’employed recently by researchers to measure the diameter of an electron. It is the billionth part of an inch. The positive loaded proton which is running around the negative loaded electron is two thousand times smaller than this last figure. But it is the uttermost limit of the physical world which can be measured in Nauro, and we cannot even theoretically imagine a smaller unit. And now, having concluded our short essay, wo may ask ourselves of what use all this abstruse knowledge is in our practical lives. We can reply by saying that it is of very great use. It was only by means of these precise mathematics, for instance, that the modern “ molecular ” physics and chemistry were able to discover the Rontgen rays, the change of the elements, wireless telegraphy and wireless picture telegraphy. Medical science dealt in thp past only with cells, but to-day a new science has been built up based on the raolecuile. In this way physicians have already achieved great success in the modern therapy of diseases of the kidneys and heart and indigestion Without the help of these excessively largo and infinitely small figures we should he unable to obtain greater insight into the internal construction of our physical world, although it is true that even with their aid we are unable to soflve all the secrets of our existence and creation.