-Carl Sagan

This sounds like a made up story. I didn’t believe it myself. Urban legends about politicians, Science and mathematics are very common. But this one isn't a legend. The state of Indiana really did come close to legally changing the value of pi. The idea of such a story is hilarious. The reality of such a story is horrific. In 1897 a man named Edward Goodwin thought the accepted value of pi couldn’t be correct. I’ve done a video on the subject of pi, but the important facts are as follows: If you draw a circle, you’ll find the circumference is longer than the diameter. Specifically, it's just over three times longer. No matter how big you draw it, the circumference will always be three, one tenth, four hundredths, five thousandths, nine ten-thousandths...bigger than the diameter. Or, to write that number in numerals: 3.14159…times bigger. This number, 3.14159… is what we call an “irrational” number, meaning you can’t translate it into a fraction. For example, the number 1.75 can be translated as 7/4. The infinitely long number 0.33333... can be written as 1/3 and so on. But pi is not like that. Pi cannot be written as a fraction or in any other simple form. It goes on forever (as far as we can tell) and there is no pattern to it (as far as we can tell). It is irrational. To be honest, pi is a hideous, inconvenient and awkward number. It goes on forever at random which means we can never know its accurate value (it doesn't have one). So, in order to deal with this monstrosity, we call it "pi" for short and represent it with the famous stone-henge symbol. Incredibly useful in pretty much all of modern Physics, not to mention engineering, statistics and a whole host of other stuff. Pi is an important part of the modern world and yes, it's a shame it's such a horrible number. Enter an Indiana gentleman by the name of Edward Goodwin; an amateur mathematician who didn’t agree with this value of pi. His reasoning was that a circle couldn’t possibly have an irrational number built into it. The world has a perfect design so the idea of circles having this ugly number hidden inside them wasn’t to be tolerated. So he set about trying to prove that pi wasn’t 3.14159... According to the mathematician David Singmaster, Goodwin produced nine completely new values of pi, each using a different method (all wrong) six of which he decided showed real promise. Among these six values were 3.2, 3.23 and even 4. Now, whereas most people might get other mathematicians to check their work, Goodwin did something else. He tried to get a law passed which would make pi legally one of his values. He tried to ban the concept of 3.14159... The proposed bill was submitted to the Indiana Committee on Education as House Bill #246 (Indiana House of Representatives, 1897) and, instead of considering him a crackpot, the representatives actually decided to take a vote on pi and Goodwin’s bill was approved by 67 votes to nil. That’s right. 67 actual human beings decided that pi was not 3.14159… but one of Goodwin’s values. Following approval, the bill was then submitted to the state Senate where it successfully made it past the first reading. Fortunately, on the second reading, a member of the legislature showed it to his mathematician friend, Clarence Waldo. Waldo made sure the bill was shot down and the value of pi was allowed to remain as it was. Crisis was averted and Goodwin was largely forgotten by history. To this day, nobody knows what he looks like. A photograph of Waldo does survive on the other hand, but he's in the middle of a crowd somewhere and it's really hard to find him.
The fact that Edward Goodwin disagreed with pi is not a problem. Honestly it’s not. If someone says something strange (and pi is strange), you’re allowed to question them and suggest alternatives (provided you're willing to accept the strange idea if it still turns out to be better than yours). In fact, challenging accepted ideas is one of the reasons we make progress as a species. Think where we’d be if nobody challenged the ideas of Earth being flat and sitting at the centre of the Universe. Goodwin made a mistake and guess what, getting things wrong in Maths and Science is absolutely fine! True, he should have got his ideas peer-reviewed by other mathematicians, rather than going straight to government, but I find it hard to be angry at this guy. I kind of like him. I mean, it shows weirdly passionate dedication to come up with nine different values for pi. No, Goodwin’s actions aren’t the major issue here. I don’t even have a problem with 67 politicians not understanding what pi is. Most politicians have backgrounds in business and law, not mathematics. For what it’s worth, I would like to see more Scientifically and mathematically educated people in government (obviously) but the fact remains that most politicians have expertise in...well....politics rather than STEM.It’s understandable that a room of non-mathematicians got confused by the technical language of Goodwin’s bill, so it’s forgivable none of them realised how outrageous his claims were. Failing to understand something is not a crime either. The real problem is that these senators decided to take a vote on it anyway. They thought they could determine truth by popular vote and that's not how we figure things out. Did they think circles all over the country would suddenly develop points in order to validate the new law? Governments have to make decisions on ethical conduct, economics, trade and welfare of its citizens. Their function is to protect and serve the population of their country. They do not get to make decisions about objective truth. Natural law does not have to conform to governmental law and if we say pi is legally 9, that doesn't make it so, Reality don’t work like that guv. The fact is you can’t decide truth by committee or by vote or by authority. You decide it by investigating and considering the evidence. Nature is not a democracy. She's a dictator. Whatever she says, goes. You certainly aren't allowed to reject a fact because you don’t like it or make parts of reality illegal. If nature is ugly, then she’s ugly. Deal with it. I, for instance, find it very difficult to accept the existence of the movie Flashdance. I mean, the main character is a welder who moonlights as a cabaret dancer?? It’s a film which tries to fuse gritty crime-drama and psychological angst with ballet and 80s disco. How is that a thing which the Universe permitted? My point is, Flashdance is not a part of nature I’m comfortable with. But I can’t just vote it out of existence and pretend it never happened. Flashdance is a part of the world and I have to make peace with that. What a feeling.Likewise, pi is the value it is. If you find this aspect of nature strange and unattractive…well…too bad. That's how circles are. The ratio between their outside and their middle is an unpleasant number. You can go out and check it by measuring the circle yourself, that's the whole point of finding out truth. You can find it out! Nature’s laws are not always what we’d like them to be. Sometimes unusual, sometimes overly complicated and even, in the case of pi, messy. But, like it or not, you don’t get to say how the world is. You can only discover and accept it. If you don't like our Universe then find another one. And take the movie Flashdance with you.
4 Comments
John Stones
9/4/2016 04:52:05 am
"It goes on forever (as far as we can tell) and there is no pattern to it (as far as we can tell). It is irrational."
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tim
9/4/2016 05:07:06 am
Fair point. What I meant was that pi is irrational as far as we can tell.
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John Stones
9/4/2016 11:08:24 am
And I would further argue that since we can prove that Pi is irrational, e.g. Niven's proof (my favourite) that pi is irrational with mathematical certainty, not as far as we can tell.
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tim
9/5/2016 12:22:57 pm
Now we're cooking with gas!
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