The students left exactly after an hour. The wall exactly opposite to this house has been painted white. The door has been painted black. I replaced the chair in verandah.
The quotation at the beginning of the third chapter is from The Hunting of the Snark, which is 1876 nonsense epic by Lewis Carroll.
“What’s the good of Mercator’s North Poles and Equators,
Tropics, Zones, and Meridian Lines?”
So the Bellman would cry: and the crew would reply
“They are merely conventional signs!”
I think the chapter is about finding out coordinates for addresses. At least in the beginning.
[ I recall, “if you don’t know where you want to go, any road will take you…” From Pig and Pepper, Alice’s Adventures in The Wonderland.]

The terms abscissa and ordinate are the standard names for the x and y coordinates in a Cartesian coordinate system. Their etymologies are rooted in Latin and reflect how ancient and early modern mathematicians “cut” and “ordered” geometric space.
1. Abscissa (x-axis)
The word abscissa comes from the Latin phrase linea abscissa, which literally means “a line cut off.”
* Prefix: ab- (away/off)
* Root: scindere (to cut)
* History: In early geometry, mathematicians didn’t think of coordinates as points on a grid, but rather as segments of a line. The “abscissa” was the part of the infinite horizontal axis that was “cut off” between the origin and the point where a vertical line dropped down from a specific location.
* Standardization: While used in various forms by Apollonius of Perga in Ancient Greece, the term was popularized in Latin by Gottfried Wilhelm Leibniz in the late 17th century.
2. Ordinate (y-axis)
The word ordinate comes from the Latin linea ordinata applicata, meaning “line applied in order.”
* Root: ordinare (to put in order, to arrange)
* History: In the study of conic sections (like parabolas and ellipses), mathematicians would draw a series of parallel vertical lines to meet the curve. Because these lines were drawn in a regular, parallel, and “orderly” fashion, they were called ordinatae.
* Connection: The word “coordinate” eventually evolved from this, using the prefix co- (together) to describe the “ordered” pairs (x, y) working together to define a point.
Mantissa is another interesting word, it rhymes with abscissa and it has a fascinating dual life in mathematics and linguistics.
Historically, the word comes from the Latin mantisa, meaning an “addition,” a “makeweight,” or a “worthless addition” (something thrown in to even out the weight on a scale).
Today, you will mostly encounter it in two mathematical contexts:
1. Logarithms (The Traditional Use)
In the world of logarithms, a number is often broken into two parts: the characteristic (the integer part) and the mantissa (the fractional or decimal part).
For example, in the common logarithm \log_{10}(200) \approx 2.3010:
* The 2 is the characteristic.
* The .3010 is the mantissa.
2. Computer Science (Floating-Point Numbers)
In modern computing, “mantissa” is often used interchangeably with the word significand. When a computer stores a number in scientific notation (like 1.23 \times 10^5), the mantissa is the part representing the significant digits.
In the number 1.23 \times 10^5:
* 1.23 is the mantissa (significand).
* 5 is the exponent.
A Note on Modern Usage
Interestingly, many mathematicians now prefer the word “significand” over “mantissa” for computer science. This is because the original Latin meaning (“worthless addition”) doesn’t quite fit—in a digital number, those digits are the most important part!
Is it still used elsewhere?
Outside of math, it is extremely rare. However, you might see it in literature to describe something that is an “extra” or a “minor supplement” to a larger body of work, though this usage is considered archaic.
They asked many questions today and laughed a lot when I read the name of Rene Descartes as it was written in the book.
Rene Descartes used to stay in his bed for a long time in morning. Once he was thinking about how to locate a point. It was a classical problem at that time. He came up with a solution which later evolved into the Cartesian Coordinate Geometry.
I told them the importance of his work. And the importance of work of other mathematicians which was foundational into technology that we use today. Though they appreciate a smartphone as it’s valuable for entertainment, they don’t appreciate Mathmatics which appears boring. The elder asks me which is bigger : 1 lakh or 1 crore?
I note down numbers with zeroes after one. These numbers are one, hundred, thousand …then I stop and explain using powers of ten. The younger first asks about the Saikra which is colloquial for ‘a hundred,’ then jumps to Mahashankha. A very large number. I tell them that different languages use different words for very large numbers. I tell them about Googol:
A googol is the number 1 followed by 100 zeros.
In scientific notation, it is written as 10^{100}. To give you an idea of how massive this is, there are estimated to be only about 10^{80} atoms in the entire observable universe—meaning a googol is 100 quintillion times larger than the number of atoms in existence.
1. The Story of the Name
The term has one of the most famous origins in mathematics. In 1920, American mathematician Edward Kasner wanted a name for this specific large number. He asked his nine-year-old nephew, Milton Sirotta, to come up with a word. Milton suggested “googol,” and the name stuck.
2. Googol vs. Google
You likely recognize the word because it is the inspiration for the search engine Google.
* The Intent: The founders, Larry Page and Sergey Brin, originally wanted to name the company “Googol” to represent their mission to organize an “infinite” amount of information.
* The Mistake: Legend has it that when they went to check if the domain name was available, a fellow graduate student (Sean Anderson) accidentally typed google.com instead of https://www.google.com/search?q=googol.com. Larry Page liked the misspelled version better, and the rest is history.
3. The Even Bigger “Googolplex”
Milton Sirotta didn’t stop at the googol. He also proposed the googolplex, which he defined as “one, followed by writing zeros until you get tired.”
Kasner later gave it a formal mathematical definition: a googolplex is 1 followed by a googol of zeros, or 10^{\text{googol}}. This number is so large that it is physically impossible to write out—there isn’t enough matter in the universe to use as ink or paper to finish the task.
Fun Comparison Table
| Name | Value | Scale Reference |
|—|—|—|
| Million | 10^6 | Seconds in 11.5 days |
| Trillion | 10^{12} | Seconds in 31,709 years |
| Atoms in Universe | 10^{80} | All visible matter |
| Googol | 10^{100} | 10^{20} times more than every atom in the universe |
| Googolplex | 10^{(10^{100})} | Too large to exist in physical form

Descartes’ surname sounded like Hindi word “dakaar” ( belching) to them. It made them laugh for a while. Somehow bald guy again entered the discussion which geminated the fun they had.
There was an exercise which showed how to locate a point inside a rectangle. I described the practical importance of knowing it. Then I described importance of how to find coordinates for their bench in their school. A structure with rows and columns was given. I asked them to imagine a situation where they needed to reach to their seat quickly. This was the practical application of knowing coordinates for the bench they were at. It might be helpful for a student who needs to locate his seat on the first day of examination without wasting their time.
Their printed time table was inside the mathematics book. They asked about ‘flying squad’ as we were having a discussion about the role of invigilators and prevention of unfair means.
I gave them Addition and Subtraction problems in assignment. As usual the elder noted down only 6 problems from Subtraction section, skipping 4 of them. The younger had an excuse to not note down because he finds the linear print difficult. He’s accustomed to doing them by writing numbers in separate rows. I asked his elder brother to help him with his notebook at home.
They kept quarreling. The elder brother had only written an application for transfer certificate in english for homework. This he did in school. The younger attempted nothing. He was flying kites.
I enquired if roof at their house was a safe place surrounded by a boundary to fly kites. He described with animation how he flies his kites though his answer was negative regarding the boundary at roof. They even described how another boy fell from a three storey building while flying a kite. A tragic accident. He showed me his hands with marks made by the string ( known as maanjha).
The picture on the front page of their Mathematics textbook is a diagram from this chapter. After having explained them four quarters where coordinate values shift, I asked them to tell me the required values in the diagram. The elder grasped it clearly whereas the younger struggled. He came up with only one coordinate.
His narcissism might be a cover for his deficits. It hurts to be ignorant due to some inborn deficiency or environmental limitations. It’s covered by being prophetic. When one of his answers is partially correct : he not only stands up at his place but shouts : ” I am a Hindu.” Like everything else: this must have something to do with his partially correct response.
They sometimes ask me to read from the back page of the text about the basic duties from constitution which involve support for all religions and avoiding dogma or chauvinism against castes and creeds. Younger doesn’t understand it at all. Elder might have learned to behave better.
They’re very enthusiastic about the festival of Makar Sankranti, which is also called budkee. It’s colloquial for ‘dip.’ Dip in holy waters. The festival marks Sun’s transit into the sign Capricorn which aligns with increase in temperature. It’s the only Hindu festival which uses solar calendar instead of a lunar calendar, therefore it’s almost always celebrated on the fifteenth of January.
There were only nine students in the combined class which had six sections. Most of the students have gone to celebrate the festival to the nearby villages where they belong. Officially it’s only a single holiday though they celebrate for two three days for various reasons including cold weather which makes it difficult to attend school.