Is Time Irrational

Hurry up, rush because you need to get somewhere quickly and there is no time to waste, no time to consider other options, basically no time to think about anything.  As the rabbit said before he disappeared down a large hole, ‘I’m late, I’m late for a very important date.’  In the hustle and bustle of our daily lives, we never slow down to smell the roses, or appreciate the precious little things that life has to offer.  We want to be productive, so we try to cram as much as we can into the hours of the day in which we are awake.  Even when it is not the holiday rush, people are constantly pushing themselves, racing against the clock, anxiously hoping to complete a task, before they hear another tick tock.

People need to embrace the present, because that is where we live and if you spend your whole life rushing around, then aren’t you just rushing into your grave?  Time is valuable, but it is a renewable resource, so you should always be able to make time.  What is your time worth?  Do you have an hourly rate that you charge?  Would you spend more money to reach your destination faster?  Let’s say you paid $25 extra to catch an earlier plane and then that plane ended up crashing and then taking another viewpoint let’s say that you gave up your seat on an over booked plane and were rewarded with $350 and while you were waiting you met the love of your life.  It seems like time was on the side of the person that was willing to wait.

Any number that is not classified as being rational is considered to be irrational.  Irrational numbers are a bit weird, as they cannot be represented as a simple fraction and they do not terminate or repeat.  This is where I usually tell my students the story of Hippasus of Metapontum.  About 10 years after Pythagoras (the Greek guy who the formula is named after) founded his mathematics school, a student named Hippasus made a forbidden discovery that was so staggering, he felt compelled to tell the other students.  The Pythagorean Theorem works with right triangles and it says the two shorter sides (referred to as adjacent and opposite sides) when squared and added together will be equal the longer side (referred to as the hypotenuse) when it is squared.  This is usually expressed with the formula a2 + b2 = c2.  One day Hippasus started working with a triangle where both the short sides were equal to 1 unit of length, thus a = b = 1.  Hippasus tried to use his teacher’s famous theorem to find the length of the diagonal of a unit square and he was able to prove that there were no numbers p, q such that c = p/q that could satisfy the Pythagorean theorem for this triangle.

Pythagoras was in love with numbers, he thought they were totally awesome and he saw this numerical harmony was contained in numbers as being a logical means of explaining an entire cosmology of life around him.  Numbers were reality because they expressed the true nature of things.  Pythagoras’ school was a community or society based on religion and science and it was called the semicircle.  This school had many followers, they were all obsessed with the significance of whole numbers and their ratios, they believed that everything was related to mathematics and the most distinctive of the Pythagorean doctrines is the principle that number is the essence and basis of all things.  The motto, “All is number” was carved above the entrance to this school.

Why would truth be considered to be a crime?  Hippasus accidentally discovered that this length could not be expressed as the ratio of two integers, so the school considered it to be a dangerous ratio that must be kept secret.  There is no real proof of the murder of Hippasus, so it is just a legend, but the secret of irrational numbers was real, and it was thought that a square’s sides being incommensurable with its diagonal for this triangle was dangerous.  This seemingly harmless discovery would cost Hippasus his life.  One stormy day poor Hippasus was taken out for a boat ride in the Mediterranean Sea by the students who were horrified of his new idea.  When the boat reached the open water they all grabbed hold of Hippasus and heaved his body overboard where he would die, thus preventing this secret from being revealed to the rest of the world.  The code of silence enforced by these students caused Hippasus to become shark bait offered up to the god Poseidon.

Computers have been programmed to try to resolve pi (an irrational number) and although they have gone out to numerous decimal places, so far a solution of its exact value has never been found and it has not repeated.  The only way to show that a decimal expansion of a number will neither end nor repeat is to show that it cannot be written as a fraction.  Just like the Energizer Bunny, irrational numbers go on and on forever and forever.  So my point is that since time keeps going on, does that make time irrational?

Taking a picture or making a film captures moments in time that can be replayed over and over and the movie Groundhog Day showed how things can keep repeating.  It is often said that history repeats itself, but history is a series of events and it is not actually time.  Time does not repeat even though certain moments can be saved and repeated.  Many people experience what the French term ‘Déjà vu’, which literally means ‘already seen’, and this is a phenomenon which occurs involving a strong sensation that an event or experience currently being experienced has already been experienced in the past.

Time and tide wait for no man and eventually my existence here on Earth will end, but time will keep marching forward.  Even when our Earth stops turning and way after that, when our universe goes into the big freeze and all the energy is gone from the Big Bang, there will be nothing that can stop time.  Hypothetically speaking, time can be stopped, but in reality, it is a technological barrier that must follow the laws of nature.  It is theorized that time cannot exist inside of a black hole, however we actually do not totally understand these mysterious objects at least well enough to know if that statement is correct.  If you had the ability to stop time, would you even want to do that?

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