## Tuesday, April 8, 2014

### The Farthest Star is the Nearest Star

---Zeashan Zaidi

According to maths, the distance between the two points depends on the path which connects the points. For example, let A and B are the two cities. And there are three ways which connects A and B. The first way is hundred kilometers long while the second and third are sixty kilometers and eighty kilometers long respectively. So according to the first way the distance between A and B is hundred kilometers, while this distance is sixty kilometers and eighty kilometers respectively along with the second and third paths respectively. This rule is applicable to the entire universe. So it is clear that a thing could be near as well as far away from us at the same time.

Let us take another example. As we know that the earth is round. Let there are two cities within a country. If we make two routes between cities, one within the country and other around the earth, going in the opposite direction from one city to other; then first distance will be small while the other large. And thus the distance between the two cities at the same time will be too small and too large. As well as 'small' distance will be smaller, 'large' would be much larger. This is possible due to the roundedness of the earth. This distance also depends on the surface on which it is measured relatively.

Now let's talk about a branch of mathematics called Calculus of Variations. It was developed in the early 18th century by the famous mathematicians Leonhard Euler and Lagrange. This mathematics measures extreme values of heights, distances, time or energy etc.

So using calculus of variations we can find the minimum or maximum condition of something. But one drawback is that if we find maxima then we generally can’t find the minima or vice versa. In many cases we get only one extreme value (maxima or minima) and the second value comes either infinity or negative infinity.

But if we take the above assumption that as 'small' distance will be smaller, 'large' would be much larger we can say that the minima found will also be the maxima or vice versa.

For a closed surface (such as rounded ground) Maximum - Minimum be together is perfectly clear.

Now look at the second situation. Let we are interested in minimal distance between the two points. The distance between the points depends on the surface on which the points lie. If surface would be change, the minima will also change. The same shall also apply to the maximum. In this way we see that the distance between two locations in different situation will maximum and minimum in many ways.

This rule is applicable for not only the distance but also time, energy and other physical quantities.

So a star we see very far away, can be extremely near to us perhaps after changing the surface of space. Is this concept is similar to the concept of wormholes?