Friday, September 12, 2014

Google number


The internet Search engine goggle is the name of a hundred zero number. The term was coined in 1938 by a nephew of an American mathematician Edward Kasner. Kasner was inspired to publish the concept in 1940 titled "Mathematics and the Imagination".

In order to appreciate this number think of one multiplied by 10 a hundred times. That is, one multiplied by ten is ten. Ten multiplied by ten is a  hundred, a hundred multiplied ten, is a thousand, a thousand multiplied by ten, is ten thousand, ten thousand multiplied ten is a hundred thousand, a hundred thousand multiplied ten is a is a million, a million multiplied by ten is ten million, ten million multiplied by ten is a hundred million, a hundred million multiplied by ten is is a thousand million and that is only one multiplied by ten nine times.

 In other words the number one has no zeros, one zero, two zeros, three zeros, four, five, and six zeros for a million respectively. There is no reason why not an indefinite number of zeros. One multiplied no times is one, multiplied by ten is once, multiplied ten twice, three four five six and so on and one multiplied by ten six times is a million. In other words a seven digit number one and six zeros.

If we continue with multiplying seven times is ten million and so on. A zero is added every time we multiply by ten. Ten million is one multiplied by ten, seven times and a hundred million is one multiplied by ten eight times respectively. In some calculators, our computers and mobile phones with calculators we can enter ten then tap the multiply key twice toggling the equals key (  = ) many times that keeps adding zeros as many as the device allows.

Two dollar calculators has only a maximum of seven  zeros which will be one and an eight digit number one and seven zeros. Bulky desk top calculators can go high as a thirteen digit number ( One and twelve zeros ). We need a lot more than that for a goggle.  Beyond a thirteen digit number we need scientific notation called powers used in scientific calculators. A power for one for example is one multiplied by zero that as one has no zeros.

If we do our arithmetic a one with a a zero is one zero. A hundred is one with two zeros. A thousand is one with three zeros ten thousand is one with with four, a hundred thousand is one with five and a million is one with six zeros respectively.  One and seven zeros is ten million, one and eight zeros is a a hundred million and one with nine zeros is a thousand million and so on.

If we keep adding zeros one and ten zeros is ten thousand million, one and eleven is a hundred thousand million and a billion is one and twelve zeros and so on. As google has a hundred zeros there will be eighty eight to go giving a grand total of one multiplied by ten a hundred times giving us a hundred and one digit number.

Using scientific calculators we press what is called the exponent key ( EXP ) by first pressing one entering the key pressing a number. For example entering one pressing the exponent  Key then entering five pressing the equals key ( = ) displays a six digit one and five zero number for a hundred thousand. Five thousand million for example is entering one entering the EXP key entering fourteen entering the equals key. It is essentially five zeros of five hundred thousand and plus the nine zeros of  a thousand million.

In print these are a ten with a little razed number just to right. A million is ten with a little razed six a seven digit number one with six zeros and a billion is a thirteen digit number one with twelve zeros ten with a littler razed twelve and so on. Ten thousand is a billion a fourteen digit number one with thirteen zeros, a thousand billion billion, a fifteen digit number one with fourteen just to the right of the ten. Ten to the fifteen is a sixteen digit number one with fifteen zeros a million billion. A trillion is a nineteen digit number one with eighteen zeros ten with a little razed eighteen respectively.

Ten to the power of nineteen is just a mere ten trillion no where near goggle. A twentieth power is only a hundred trillion. The twenty-first at  is a only a mere thousand  trillion. The twenty-second power only a mere hundred thousand trillion. The twenty third power is only a a hundred thousand trillion. The twenty-third  power is only a million trillion and the twenty-fourth power is only ten million trillion respectively.

So far that's only quarter way to a hundred zeros  another twenty-five or multiplied by twenty-five more times to go to tot he power of a a hundred which is only half way to goggle.

Ten to the fifty. It still leaves fifty zeros short to be a  goggle ten to the hundred successively multiplied by ten hundred times. Normally a number as big as this has no particular significance in ordinary math's. Not when it comes to atomic particle physics and the vast distance of the universe it's not.

All in all Edward Kasner had illustrated goggle demonstrated ultimate of big numbers doesn't stop there. If we multiply the hundred zeros in goggle by ten we have a thousand and one digit number number, one and a thousand zeros. It is even possible to multiply goggle by itself called Google squared resulting in a ten thousand and one digit number one a ndd ten thousand zeros called a googolplex.

Kasner went on to demonstrate there is no reason why not we can have, more ten thousand digit numbers, ten to the million, ten to the billion ten to the billion, or ten to the trillion goggle's which is indecently is no where near infinite in doing so achieved an excellent illustration numbers can project a number is possible number of stars in the universe for the cliché "there are more stars in the universe than all the grains of sand (including the worlds deserts) in the worlds beaches"  let a lone all the atoms in every star.

Mathematics tells us a reciprocal is the same number but as a fraction. For example the reciprocal of ten is a tenth which is one divided by ten equals zero point zero one. Or the reciprocal of a thousand is four decimal zeros and  divided by ten three times. In other words if we take a million transposing the zeros to the right of one gives us a millionth. We can apply the same with hundreds of millions of trillion zero number. These are called minus powers where there is a little razed take away sign just to the left of the little razed power.

Positive powers is the one on the "right" of the zeros and minus powers is the one on the right of the same number of zeros. A number like five hundred and fifty four is a positive five hundred and fifty, and in the minus the same number one divided by ten five times equals three decimal zeros on the right of a hundred and fifty four a six digit number. The reciprocal brings us back to the same number. So 0.0000554 and 554 are reciprocals of each other.

The law of mathematics tells us five hundred and fifty four multiplied by the minus version gives us one respectively. In other words five hundred and fifty four in the positive the same number in the minus five hundred and fifty fourth of one. Operating on the principle finding the reciprocal of any number is simple. 1 divide what ever number weather a whole positive or decimal fraction. In some calculators we can toggle back and fourth the minus key the same numbers.

This makes it all possible to use basic arithmetic in a branch of science of the sub atomic particles of the atom called Quantum physics, known as quantum or temporal mechanics.

In 1900 a German Physicist Max Planck announced he had figured out a mathematical unit for matter, length, time and energy as the smallest units in the universe. This number is six point two, six times ten to minus forty three named after him expressed as a Plank constant. In other words six point two six is divided by ten forty-three times giving a forty three decimal value, six two six on the right of forty zeros. In other words a Planck constant is the length of ten to the minus forty three of a meter, a second, a joule of energy or of a kilogram of matter.

As the reciprocal tells us the forty-three zeros on the right of six, two, six transposed to the left gives the same constant only in the positive value. The molecules that make up matter are as tiny as ten to the minus fifteen. The atoms that make up the molecules are as tiny as ten to the minus twenty-five. The particles that make up the atom are smaller still. The particles that make up the particles of the atom yet again smaller. Think of the reciprocal of a trillion.

If this seem a bit mind boggling think of it this way. Typical school rulers measure the thickness of a common news paper page in the standard metric system prefix unit micro for a millionth called a micrometer. A micrometer is ten to the minus six of a meter. Microscopes see our body cells in nanometers ten to the minus nine of a meter.  

The reciprocal of ten to the minus forty three  is ten to the power of forty-three. For example ten to the power of forty three in the positive value Planck seconds equals a second. In other words a second is divided into ten to the forty three units, As you can see ten to the forty third  power is no where near ten to the hundred of a goggle.

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