Zipf's Law

What if I told you that just by using a simple formula, I can calculate the number of times any word comes in this article, or in a book, or even across the entire internet…?
Zipf’s Law allows you to do exactly that with math that even a second grader can understand.

The law states that “Given some corpus of natural language utterances, the frequency of any word is inversely proportional to its rank in the frequency table.”
Now what this essentially means is any word which is the nth most common word will occur x times where

Formula

X= Number of times the most common word is used
N

This extremely overpowered. This is mainly because in any language, English, German, French and even the ones which we have not been able to decipher yet follow a peculiar system.

The most used word is used almost two times more than the second most used word, three times more than the third most common word, four times as common as the fourth most common word and so on and so forth.

In the case of English, “The” happens to be the most common word, “of” comes in the second place, “and” in the third.

Now “the” accounts for about 7% of the total words.
So going by the above formula, “of” would account for about 7/2% = 3.5% of the total words and this actually holds true!

“And” accounts for about 7/3% =2.3% of the total words and this also comes out to be correct.

Numerically, “the” comes 69,971 times, “of” comes 36,411 times, “and” comes 28,852 times. These are out of a net total of about million words.

Go ahead do the math, verify it for yourself!
(All the above readings are from the Brown Corpus of American English text)

Now comes the really fun part,

GRAPHS!

The graph below shows the number of occurrences of the 7 most popular words in the Brown Corpus.

Notice the curve!

Also for anybody who knows log, it gets even more interesting

The graph below is a log-log chart.

It depicts practically the same thing just with a log graph.

Moreover, this law does not only limit itself to languages, it is even true for
• Page hits to Popularity rank of the web page
• Population ranks of cities to City size
•  Corporation Sizes to corporation ranking
•  Income ranking to net income
•  Popularity of TV channel to its TRP

It is like this law is everywhere as if it has been built into the human brains and psychology.

The law is among the most mysterious and there is no specific reason as to why this happens. There are a bunch of theories all over the internet but none do justice to the law and hence have not been included in this article.

This law does not end here, just as any other principle or law in math it is connected to many others and some of the ones are

1.       Benford’s LawPareto principle

All of those will be covered in the posts that follow. Zipf’s law does not end here…
PS- For the above content:
“The” comes 48 times out of 527 words (approx. 9%)
“Of” comes 24 times (Exactly Half!= 4.5%)
“And” comes 15 times (approx. 1/3 = 3%)

While the sample size is very small the law still holds true.
Need I justify this law any further?

Enjoy your high school with - High School Pedia : www.highschoolpedia.com

Anode Ray Experiment

→Anode ray experiment was conducted by E Goldstein. →These rays are also known as canal rays. →This experiment helped in the discovery of the proton. Apparatus Used A discharge tube  was taken in which there were 2 electrodes i.e. Anode(+ve) and the cathode (-ve). The tube was filled with an inert gas. A perforated or porous cathode was used. A layer of zinc sulphide was placed at the back of the cathode. There was a vacuum pump in the tube. High voltage (5000v-10000v) was allowed to flow through the system. It was observed that when the gas was at 1atm(atmospheric pressure ) no change was seen in the tube.  When the   pressure   was decreased inside the tube, a glow could be seen at the back side of the cathode.

Levitation 2

LEVITATION II To be completely honest I was going to start this with a pun. I did think of one but it doesn’t float… I am sorry I just had to. Anyway, this is the second part to the article on super cool ways of making things levitate. Go check the first part out if you haven’t already. Actually, the first part may have become repulsive with all the magnets and stuff, but I promise this will be more attractive. Get it? No? I’ll stop now. I am just going to jump straight into it. 1.    Electrostatic Levitation I know you are probably sick and tired of magnets but they are the best way you know… This method is somewhat similar. You remember that cool science experiment you did with two straws attracting or repulsing each other based on their charge? So basically using the same principle we can make a charged object levitate. But before you try it, let me tell you it won’t be easy. Even impossible according to our Mr. Earnshaw. He even made a law (the law is

Animal and Plant Cells

Cells Cells are the basic functional, biological and structural unit of life. The word cell is a Latin word meaning ‘small room’. Cells are also known as building blocks of life.  The branch of science that deals with the form, structure, and composition of a cell is known as Cytology. All organisms around us are made up of cells. Bacteria, ameba, paramecium, algae, fungi, plants and animals are made up of cells.  Cells together form tissues. And tissue together makes an organ. History Of Cell The cell was discovered by Robert Hooke in 1665. He assembled a simple microscope and observed a very thin slice of cork under his primitive microscope. The cork was obtained from the outer covering of a tree called bark. Robert Hooke observed many little-partitioned boxes or compartments in the cork slice. These boxes appeared like a honey-comb. He termed these boxes as the cell. He also noticed that one box was separated from another by a wall. What Ho

Isotopes, Isobars and Isotones

Isotopes These are elements which have the same atomic number but different atomic mass . They have the same atomic number because the number of protons that are inside their nuclei remains the same. But, they have different atomic mass because the number of neutrons that are also inside their nuclei is different. As the number of protons inside nuclei remains same, therefore the overall charge of the elements also remains same as in isotopes: no of protons = no of electrons . Hence, as isotopes overall charge remains neutral, therefore their chemical properties will also remain identical.   Therefore, Isotopes are chemically same but physically different.