Monday, September 27, 2021

# Problematics: A barefoot walk on Kepler-452b

## Why Earth's twin is not an identical twin and magnifies life to larger than life

Kepler-452b is 60% larger than Earth in diameter; shouldn’t everything there be proportionately magnified? (Source: AP photograph)

Now that Kepler-452b has been discovered and discussed, the question is no longer “Is there life out there?” In Problematics, we take such things for granted. The question to explore is, therefore, “What forms of life exist on Kepler-452b?”

I propose human beings, for one. And big, hairy apes, besides bulldogs, stray dogs, cats and canaries. Add a few man-eating leopards, endangered tigers, extinct dodos, medicinal herbs, poisonous shrubs and harmful bacteria. In short, every life-form that is or was on Earth must also be on 452b.

Only larger. NASA says Kepler-452b’s diameter is 60% over and above Earth’s, so every object must be magnified, for the sake of proportion, 1.6 times in length units. The upper half of my illustration below has five possible  examples.

Take a gentleman, very tall even by the standards of 452b, standing 3m barefoot. Then send him on a carefully measured walk on the surface of his planet. He is under the illusion that he’s treading a straight line but, as every inhabitant of every round planet knows, he’s actually describing an arc of a circle. Let him complete that arc and come full circle to the starting point, however many years that takes him.

You know he’s just described the full circumference of his planet, which you can easily calculate with the help of Earth’s known diameter and the addition of 60% over and above. That is, however, only the distance his bare feet will have travelled, isn’t it? His head, 3m above his feet, must have described a slightly larger circle.

Puzzle#21A: How many more kilometres did the head travel than the feet did?

I adapted that puzzle from a chestnut, possibly of Soviet origin. The second puzzle is my own idea, built around data supplied by NASA and the late Isaac Asimov. In the lower half of the same illustration, the top two rows of the table ‘Planetary measurements’ contain numbers culled from the NASA website. The numbers in the bottom row, or ‘Mystery factor’, come from Asimov, although he obviously did not include Kepler-452b in those measurements.

“I don’t think that it (this collection of numbers) exists in this form anywhere else,” Asimov writes in ‘The Secret of the Universe’ (Oxford University Press). To know what the numbers mean, you will either need a copy of the book or have to work it out yourself.

Puzzle#21B: The numbers represent the relative values for a certain measurement. What is that measurement, what is the value for Kepler-452b, and what does 1 on this relative scale represent?

What you wrote

The crossword (solution above) looked like the easier of the two puzzles last week but it was the logic puzzle that drew the higher number of correct replies.

Dear Kabir, in Puzzle#20A, Mr Xylographer is the Accountant, Mr Yardmaster is the PRO, and Mr Zincographer is in Personnel. Mrs X earns in dollars, Mrs Y in pounds, and Mrs Z in rupees. The most knowledgeable woman should earn in rupees and is in hospital. That is Mrs Z as Mrs Y is in the gym and Mrs X earns in dollars. So, the women are determined. Mr Z cannot be the Accountant. Since Mr Y is PRO (as the person of this profession is married to Mrs Y), it leaves Mr X as Accountant. Thus Mr Z is in Personnel.
Sanjay Gupta (New Delhi)

Solved also by: Neha Awasthi (Goettingen, Germany), Rohan Jaikishen (IIM Kozhikode, batch of 2010), Lakshmi Swathi Gandham (Hyderabad), Biren Parmar (Texas A&M University), Vivek Jalan (founder, Customate Systems), Nitin Saraswat (Bank of America, Gurgaon), Sampath Kumar V (IIM Kozhikode alumnus), Anindita Basu (IBM India, Allahabad).