Everything Everywhere Daily: History, Science, Geography & More - Tau

Starting point is 00:00:00 For the last 250 years, there's been a problem in the world of mathematics. There is a good argument to be made that we've been doing it wrong. We've been teaching in a way that's been unnecessarily confusing and complicated, and we've been causing generations of students unnecessary headaches. Learn more about Tao and why it's better to use than Pi on this episode of Everything Everywhere Daily. What if your perceptions about the past were wrong? ThruLine is a podcast that takes you back in time to uncover the part parts of the story that may have gone unnoticed.

Starting point is 00:00:45 It effectively turned day into night. And how it shaped the world now. Time travel with us every week on the Thulein podcast from NPR. To understand what this episode is about and why there is a problem, we have to start with one of the simplest concepts in geometry, the circle. The circle is defined to be the set of all points in equal distance to a single point. Physically, you can make a circle with a compass by holding one end down on a single point and then swinging the rest of it around to make a circle. Likewise, you could take a piece of rope or string, fix it to a point, and then move it around to make a circle as well.

Starting point is 00:01:27 The point being, the defining characteristic of a circle is its radius, the distance from the center to the edge. No other two-dimensional shape has a radius. Just to hammer the point home, the radius is what makes a circle a circle. Every circle has a special ratio built into it regardless of how big or how small the circle is. Most of you know this ratio as the number pi. I've previously done an entire episode on Pi, but just to refresh your memory, pi is the ratio of the circumference of the circle to its diameter. And therein lies the problem.

Starting point is 00:02:04 There is almost nothing in mathematics that we use the diameter of a circle for. Why is it that when we define the most important ratio found inside every circle, we all of a sudden define it using the diameter rather than the radius. After all, it's the radius that defines the circle. You might be thinking that this really isn't that big of a deal. The diameter of a circle is just twice the radius. Just as every circle has a radius, so too does every circle have a diameter. That is true, but there's a problem.

Starting point is 00:02:35 While a circle is the only two-dimensional shape with a radius, it is not the only two-dimensional shape with a constant diameter. There is an entire class of shapes known as Raylu triangles that also have the same diameter in every direction going through a center point. A Rayu triangle basically looks like a triangle but with rounded sides. So if something has a fixed radius, it must be a circle. But if something has a fixed diameter, it is not necessarily a circle. So again, why do we calculate Pi using the diameter of a circle rather than the radius, which would seem to make much more sense? The calculation of the circle ratio goes back to antiquity.

Starting point is 00:03:16 In many histories of pie, you will hear of ancient mathematicians from Egypt, India, or China, who all calculated pie with various levels of accuracy. However, they were not always calculating the circumference divided by the diameter. Sometimes they were using the radius. The modern usage of the Greek letter pie to represent the ratio of the circumference to the diameter is attributed to the Swiss mathematician, Leonard Euler, one of the greatest mathematicians of all time. At the time he was writing in the first half of the 18th century, there was no standard symbol to

Starting point is 00:03:47 represent the circle constant. In 1727, in his paper essays explaining the properties of error, he used the Greek letter pi to represent the ratio of the circumference of the circle to its radius. In other words, how many times can the radius of a circle go around its circumference? The number he associated with the Greek letter pie in that paper was 6.28383183530. 07 going on to infinity. Or in other words, his original definition of pi was twice what we now consider pie because he was using the radius instead of the diameter. Had he ended there, I wouldn't be doing this episode.

Starting point is 00:04:28 Instead, he kept on writing and changed his definition of pie. In 1736, he started defining pi to be half the value he gave it originally. And what really cemented it into the world of mathematics was his 1748 book, Introduct, Introduction in analysis in infinitorum, where he said, quote, for the sake of brevity, we will write this number as pi. Thus, pie is equal to half the circumference of a circle of radius one. End quote. Euler wasn't dumb. He explicitly stated that pie was the constant that represented half a circle. Now, at this point, you might be thinking, who cares? When I first took trigonometry in high school, way back in the day, we were introduced to the concept of radians. Radians are a way of measuring

Starting point is 00:05:14 angles. One radian is just the angle measured by the arc of a circle with an arc length equal to the circle's radius. If you go all the way around a circle, in other words, 360 degrees, the total number of radius length that you've gone around the circumference is equal to two pi. When I was first learning this, I found this to be extremely confusing. Why? is one circle 2 pi? Why is half a circle pi and why is a quarter circle a half a pi? If you have a sine wave, it reaches its peak value at half pi. It's back to zero at pi, reaches its lowest point at 3-caves pi, and then finally completes

Starting point is 00:05:55 the wave at 2 pi. The cosine function is similar. In fact, you find 2 pi popping up all over the place in mathematics and physics. In quantum physics, the plon constant is calculated using. 2 pi. In statistics, normal distribution is calculated using 2 pi. 4EA transformations, the Rhyman Zeta function, Koshi's integral formula, and a host of advanced mathematical functions all use 2 pi. So, if 2 times pi is everywhere, shouldn't that be the constant that we use? After all, 2 pi is just the common sense ratio of the circumference to the radius. Well, there are mathematicians

Starting point is 00:06:35 who think exactly that. In 2001, right? Robert Pallet, a mathematician from the University of Utah, published a paper titled, Pye is Wrong. In it, he argued for changing how we think of circles and angles. Saying that a full circle is two pi is like saying a complete trip somewhere is twice half the distance. Technically correct, but confusing. It would be much easier to say that a circle is one turn. That is common language that everyone can understand.

Starting point is 00:07:05 A turn would be equal to 360 degrees. Half a circle is half a turn. Three quarters of a circle is three quarters of a turn. He suggested replacing the pie symbol with a new symbol that had three legs instead of two. His idea for a new symbol didn't catch on, but the idea of using a single constant to represent two pi did. In 2010, the physicist Michael Hartle wrote a blog post where he proposed a new symbol for the constant. The Greek letter, tau. The Greek letter tau visually sort of looks like pi with only one leg. It also kind of looks like the letter T in the Latin alphabet.

Starting point is 00:07:43 It would also represent the concept of a turn. One turn would equal one tau number of radii along the circumference. Tao would simplify many mathematical formulas and would make certain things like angles in trigonometry a whole lot easier to understand. In theory, tau is a pretty good idea. and personally I think it makes sense. Using the radius instead of the diameter of a circle is more intuitive, and if we were to be sent some mathematical message by aliens,

Starting point is 00:08:13 I would be willing to bet that they would be more likely to use tau than pie. Since 2010, there has been a movement for the adoption of tau amongst mathematicians. Probably the biggest thing has been the adoption of Tao Day. In the American system of dates, March 14th is written as 314, which are the first several digits of Pi. Hence, March 14th is Pi Day. As Tao is just two times Pi, Tao enthusiasts have adopted June 28th, 628 as International Tao Day.

Starting point is 00:08:44 It is an excuse to talk about Tao and to do crazy things like record podcasts on the subject. While there has been a vocal community of Tao advocates, getting people to actually switch from using Pi has proven extremely difficult. There have been some programming languages which have adopted Tao as a value, which is pretty easy to do considering it's just two times pi. These include Python, Java, Rust, and dot net. The online education platform Khan Academy now accepts answers using Tao instead of Pi. And there has been at least one academic paper that has used Tao instead of Pi.

Starting point is 00:09:17 However, that isn't a whole lot to point to since Robert Palais wrote the original Pi is wrong article over two decades ago. There is over 250 years worth of mathematical papers and textbooks out there that use Pi. Everyone who studied mathematics, even at a cursory level, knows about Pi and has become accustomed to using it. There are literally buttons hardwired into most calculators just for Pi. Change will be difficult, if not completely impossible. If the United States can't convert to the metric system, getting the entire world to change from Pi to Tao might just be a bridge too far. Nonetheless, the Tao advocates make a very good point. Mathematics would be simpler and easier to understand.

Starting point is 00:10:00 understand if tau had originally been adopted as the circle constant rather than pie. And we owe all of that to an 18th century mathematical genius who changed his mind about what he wanted the Greek symbol pie to represent. The executive producer of Everything Everywhere Daily is Charles Daniel. The associate producers are Thor Thompson and Peter Bennett. Today's review comes from listener Mack O'Dale on Apple Podcasts in the United States. They write, extremely interesting podcast. I love finding out about things I never even knew.

Starting point is 00:10:33 existed. This podcast really brings a lot of interesting topics to light. I've always said, it's not what you don't know that's important. It's what you don't know that you don't know. Thanks to everything everywhere daily, there are far less things I don't know. Keep up the good work. Thanks, Matt O'Dale. As I've mentioned before, even if you change unknown unknowns to known unknowns, in other words, going from being totally ignorant about a subject to at least being aware you don't know something about a subject, you've made substantial progress. Remember, if you leave a review or send me a boostagram. You two can have it read on the show.

Everything Everywhere Daily: History, Science, Geography & More - Tau

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