"I know it will be called blasphemy by some, but I believe that pi is wrong."
That's the opening line of a watershed essay written in 2001 by mathematician Bob Palais of the University of Utah. In "Pi is Wrong!" Palais argued that, for thousands of years, humans have been focusing their attention and adulation on the wrong mathematical constant.
Two times pi, not pi itself, is the truly sacred number of the circle, Palais contended. We should be celebrating and symbolizing the value that is equal to approximately 6.28 — the ratio of a circle's circumference to its radius — and not to the 3.14'ish ratio of its circumference to its diameter (a largely irrelevant property in geometry).
Last year, Palais' followers gave the new constant, 2pi, a name: tau. Since then, the tau movement has steadily grown, with its members hoping to replace pi as it appears in textbooks and calculators with tau, the true idol of math. Yesterday — 6/28 — they even celebrated Tau Day in math events worldwide.
But is pi really "wrong"? And if it is, why is tau better?
The mathematicians aren't saying that pi has been wrongly calculated. Its value is still approximately 3.14, as it always was. Rather they argue that 3.14 isn't the value that matters most when it comes to circles. Palais originally argued that pi should be changed to equal 6.28 while others prefer giving that number a new name altogether.
Kevin Houston, a mathematician at the University of Leeds in the U.K. who has made a YouTube video to explain all the advantages of tau over pi, said the most compelling argument for tau is that it is a much more natural number to use in the fields of math involving circles, like geometry, trigonometry and even advanced calculus.
"When measuring angles, mathematicians don't use degrees, they use radians," Houston enthusiastically told Life's Little Mysteries, a sister site to LiveScience. "There are 2pi radians in a circle. This means one quarter of a circle corresponds to half of pi. That is, one quarter corresponds to a half. That's crazy. Similarly, three quarters of a circle is three halves of pi. Three quarters corresponds to three halves!" [A Real Pie Chart: America's Favorite Pies]
"Let's now use tau," he continued. "One quarter of a circle is one quarter of tau. One quarter corresponds to one quarter! Isn't that sensible and easy to remember? Similarly, three quarters of a circle is three quarters of tau." Making tau equal to the full angular turn through a circle, he said, is "so easy and would prevent math, physics and engineering students from making silly errors."
A better teaching tool
Aside from preventing errors, as Palais put it in his article, "The opportunity to impress students with a beautiful and natural simplification has turned into an absurd exercise in memorization and dogma."
Indeed, other tau advocates have said they've noticed a significant improvement in the ability of students to learn math, especially geometry and trigonometry where factors of 2pi show up the most, when the students learn with tau rather than pi.
Though 2pi appears much more often in calculations than does pi by itself (in fact, mathematicians often accidentally drop or ad that extra factor of 2 in their calculations), "there is no need for pi to be eradicated," Houston said. "You might say I'm not anti-pi, I'm pro-tau. Hence, anyone could use pi when they had a calculation involving half of tau."
Tau, the 19th letter of the Greek alphabet, was chosen independently as the symbol for 2pi by Michael Hartl, physicist and mathematician and author of "The Tau Manifesto," and Peter Harremoës, a Danish information theorist. In an email, Houston explained their choice: "It looks a bit like pi and is the Greek 't,' so fits well with the idea of turn. (Since tau is used in angles you can talk about one quarter turn and so on.)"
Pi is too ingrained in our culture and our math to succumb to tau overnight, but the movement pushes ever onward. "Change will be incremental," Houston said.
This article was provided by Life's Little Mysteries, a sister site to LiveScience. Follow us on Twitter @llmysteries, then join us on Facebook. Follow Natalie Wolchover on Twitter @nattyover.
Sunday, July 03, 2011
Saturday, September 04, 2010
Imagine Stephen Hawking is reincarnated, and this time round his father is a philosopher. One day, when little Stephen is about five years old, they're sitting in the summer house with Fido, their pet dog. And Stephen asks one of those questions children love to repeat.
Daddy. Yes Stephen? Why is Fido? Well, Stephen, Fido had a mummy and daddy like you.
Yeah but, why is Fido? Err, you mean why is he a dog? That's because his parents were dogs, and his parent's parents were dogs too. They belong to what we call the same species. (Stephen is precocious in this life too.)
But why is Fido? Well, we know that Fido's parent's parent's parent's parents – a long way back – were not dogs, but were wolves. That was before human beings made them pets.
Oh. Why is Fido? Before there were wolves there was another species out of which wolves grow. We call it evolution, Stephen, and it's a very important process in the natural world.
Ev-o-lu-tion. (Stephen likes the feel of that word.) But why is Fido? Before that species, there was another, and another, and another, all the way back to tiny animals we call cells.
Why IS Fido? You're asking about biochemistry now. Err, roughly you can say that when the stuff of which everything is made is put together in a very complicated way – like a fantastic lego puzzle – then it takes on this very special property we call life.
WHY IS FIDO? Before life, there was just stuff – matter. It hung around for many billions of years on planet earth.
But why is FIDO? Before the earth, there were stars, and galaxies, subatomic particles and strange things like black holes. (Stephen has the very strange feeling that he knows all about black holes, even though he's only five.)
Yeah but, why is Fido? Scientists think it all started with a big bang, Stephen, a kind of spontaneous eruption out of which everything came.
Wow! Why is Fido? The big bang must have happened because of the laws of physics.
BUT WHY IS FIDO?
(At this point Stephen's father pauses. Being a philosopher, he realises that Stephen is now asking a very different question to all the ones he's asked before. You see, before, his questions could be answered with reference to some preceding state of affairs, out of which Fido can be said to have come. Now, though, he is asking about where everything came from, and being everything, there is no antecedent reality to refer to. To start to talk of nothing, not even abstract laws of nature, let alone wildly compressed energy, is to try to put everything in the context of nothing. But nothing is precisely that: not a quantum field fluctuating in the vacuum, not one universe springing out of a multiverse. Nothing is more radical than that. It is nothing. It's impossible to conceive of, in fact. It's no wonder Stephen's father pauses.)
I'm not sure we can ask that question, Stephen. It makes no sense.
But I want to know: why is Fido?
Well, some say the universe just is. There's a famous philosopher from about 100 years ago, Bertrand Russell, and he thought that.
(Stephen harrumphs.) But why is Fido?
There is another answer.
Yes? (Stephen sits up.)
Well, it's not exactly an answer.
More like a mystery.
I like mysteries.
But I'm not sure you're going to like this one.
Well, there was another philosopher who was a friend of Bertrand Russell, in fact. He was called Ludwig Wittgenstein, and he said, "Not how the world is, but that it is, is the mystery."
And the mystery is sometimes given a name.
What's the name?
It's called God.
(With thanks to Herbert McCabe)
Monday, December 29, 2008
"Science brings men nearer to God" - Louis Pasteur
"The FOOL hath said in his heart, there is no God".- Psalms 14:1
Atheists, please stop making claims without support or scientific evidence. Also, please stop asking questions which were already answered in this video. EX. "Who created God?" Again, the 1st law confirms energy is eternal. Before the universe began, there must have existed an ORIGINAL, initial, energy source which has ALWAYS existed. This initial, original, energy source IS God. ( GOD IS THE CREATOR WHO IS UNCREATED)
Atheists may say " Well, all of the energy in the universe could have derived itself from multiple energy sources, not just a single one".That maybe true, but it still poses a serious problem. Multiple or single unintelligent energy source(s) would most likely result in chaos and disorder.
(cont) Because they can't regulate their outflow of energy thus, dispersing uncontrolled and violent emissions of energy without organization or order unlike an intelligent energy source (GOD).
Every example of DUMB energy source(s) that we can observe are volatile and destructive by nature and will NEVER create organization . Examples : the sun, tornadoes, hurricanes, earthquakes. Sure tornadoes or hurricanes may APPEAR organized but, they will never CREATE organization.
You can still hope that all of the energy in the universe originated from an unconscious, dumb, energy source or multiple ones, but it defies common sense and reasoning. We can clearly observe complexity, design, and order throughout the universe. The possibility of a single all powerful, intelligent, energy source (God) still remains ( This is more logical).
Atheists may also say " Well, based on the 2nd law of thermodynamics God may eventually disorganize and deteriorate overtime if he is composed of energy". God is composed of energy but not entirely energy. The God I serve is composed of INFINITE INTELLIGENCE as well.
(cont.) He can certainly be intelligent enough to break the boundaries of the 2nd law and find a way to harness his energy infinitely and NEVER result in disorder. If you can't agree with this explanation, you're putting limits on God which is simply IDIOTIC.