USING A BALLOON TO SPY OVER US

of the tiling problem formulated by Chinese American mathematician Hao Wang in 1961, is not solvable.

The task is to use a set of dominoes to cover an entire grid and, following the rules of most dominoes games, matching the number of pips on the ends of abutting dominoes. It turns out that there is no algorithm that can start with a set of dominoes and determine whether or not the set will completely cover the grid.

Keeping Problems Reasonable

A number of solvable problems can be solved by algorithms that halt in a reasonable amount of time. These “polynomial-time algorithms” are efficient algorithms, meaning it’s practical to use computers to solve instances of them.

Thousands of other solvable problems are not known to have polynomial-time algorithms, despite ongoing intensive efforts to find such algorithms. These include the Traveling Salesman Problem.

The Traveling Salesman Problem asks whether a set of points with some points directly connected, called a graph, has a path that starts from any point and goes through every other point exactly once, and comes back to the original point. Imagine that a salesman wants to find a route that passes all households in a neighborhood exactly once and returns to the starting point.

The Cost Of Knowing Exactly

The best-known algorithms for NP-complete problems are essentially searching for a solution from all possible answers. Traveling Salesman Problem on a graph of a few hundred points would take years to run on a supercomputer. Such algorithms are inefficient, meaning there are no math shortcuts.

Practical algorithms that address these problems in the real world can only offer approximations, though the approximations are improving. Whether there are efficient polynomial-time algorithms that can solve NPcomplete problems is among the seven millennium open problems posted by the Clay Mathematics Institute at the turn of 21st century, each carrying a prize of US$1 mn.

New Computation Form Beyond Turing

Could there be a new form of computation beyond Turing’s framework? In 1982, American physicist Richard Feynman, a Nobel laureate, put forward the idea of computation based on quantum mechanics.

In 1995, Peter Shor, an American applied mathematician, presented a quantum algorithm to factor integers in polynomial time. Mathematicians believe that this is unsolvable by polynomialtime algorithms in Turing’s framework. Factoring an integer means finding a smaller integer greater than 1 that can divide the integer. For example, the integer 688,826,081 is divisible by a smaller integer 25,253, because 688,826,081 = 25,253 x 27,277.

SOURCE: THE CONVERSATION

Exposing teachers to criminal prosecution for corporal punishment is definitely not a good idea for maintaining discipline in schools. That, however, does not allow short-tempered teachers to cross the line of reasonable degree to deal with errant pupils.

Spiritual Speak

This one is for all those times you made an excuse for not accomplishing your goals.

Bhagavad Gita

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A n innocuous-looking balloon hovering at a height of about 60,000 feet over American missile fields in Montana has led to a diplomatic row between the US and China. It has led to US Secretary of State Antony Blinken to abruptly call off his visit to Beijing. The high-level meeting was to take place after several years in an attempt to mend ties between the two countries. China reluctantly acknowledged that it was its balloon which had strayed into American airspace but said it was meant for monitoring weather and offered regret. American officials, including those from the Pentagon, insisted that it was meant for surveillance and

An innocuous-looking balloon hovering at a height of about 60,000 ft over American missile fields in Montana has led to a diplomatic row between the US and China. It has led to US Secy of State Antony Blinken to abruptly call off his visit to Beijing was equipped with the necessary equipment for the purpose. Blinken described the intrusion as “a violation of our sovereignty” and called it an “unacceptable as well as an irresponsible action”.

The spy balloon marks a new low in the ties between with Dr Murugan_MoS, Sh @TThenarasu, Sh TR Baalu & Dr @KanimozhiDMK.

China and the US. It also raises the question about a balloon’s use for spying when China, like several other countries, has advanced satellites to monitor activities in other countries. Use of balloons for surveillance is as old as World War-II. The Japanese used balloons to drop incendiary bombs over US targets. The Americans and Russians also used it during Cold War days. The problem with the Chinese balloon is that Americans are hesitant to shoot it down for fear of falling debris causing injuries to people. The Chinese incursion is being interpreted as a message about the extent Beijing is ready to go to show its strength. Talks, meanwhile, might take place at a later date.

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