"Deluded or not, supporters of superstition and pseudoscience are human beings with real feelings, who, like the skeptics, are trying to figure out how the world works and what our role in it might be. Their motives are in many cases consonant with science. If their culture has not given them all the tools they need to pursue this great quest, let us temper our criticism with kindness. None of us comes fully equipped."  Carl Sagan
We begin where all pseudoscientific drivel begins, with an amateur mathematician. Now there’s no problem with being an ‘amateur’, however if one wants to tackle cutting edge problems in any particular field, having an established credibility does help, otherwise bring in a truckload of irrefutable evidence and proofs.
In our story, this particular math amateur was a physician that goes by the name of Edward Goodwin. His believes he had discovered a solution to a very ancient problem: how to construct a square with the same area of a given circle using only a compass and ruler.
This problem, called the squaring of a circle, have been pondered upon since the days of the Babylonians and Egyptians – recalling how much their civilisations depend on architectural geometry; but it was not until the Ancient Greeks got their hands on them did it came to be a seriously thought of. Since then and until the late 19th century it was deemed impossible, but mathematicians were unsure why – pretty much the equivalent of that nagging feeling you have after a multiple choice exam paper.
In order to prove that a square and circle may have the same area we have to do a bit of algebra, as below:
In our story, this particular math amateur was a physician that goes by the name of Edward Goodwin. His believes he had discovered a solution to a very ancient problem: how to construct a square with the same area of a given circle using only a compass and ruler.
This problem, called the squaring of a circle, have been pondered upon since the days of the Babylonians and Egyptians – recalling how much their civilisations depend on architectural geometry; but it was not until the Ancient Greeks got their hands on them did it came to be a seriously thought of. Since then and until the late 19th century it was deemed impossible, but mathematicians were unsure why – pretty much the equivalent of that nagging feeling you have after a multiple choice exam paper.
In order to prove that a square and circle may have the same area we have to do a bit of algebra, as below:
But wait a minute, in Part 1 we learned that π is transcendental, and thus is nonalgebraic, meaning that it cannot be expressed in a Cartesian coordinate system. We may indeed draw a square with the same area as a circle using a computer , but remember, the challenge is to only use a ruler and compass.
Back to our story, Mr Goodwin, mistakenly believes in his breakthrough, proposed the Indiana General Assembly a bill for “an act introducing a new mathematical truth and offered as a contribution to education to be used only by the State of Indiana free of cost by paying any royalties”. The language behind the bill is so technical (maybe even deliberately technical) as to cause confusion among the members of the assembly. But seriously, who wants to admit that they’re stupid, right?
There’s just one problem: Goodwin’s definition of π. In Section 2 of the bill, it plainly states that “the ratio of the diameter and circumference (of a circle) is as fivefourths to four”, meaning that for the first time the mathematical truth, π, will be defined by fiat as exactly 3.2; this flies in the face of the true definition of π as we had covered in Part 1.
Back to our story, Mr Goodwin, mistakenly believes in his breakthrough, proposed the Indiana General Assembly a bill for “an act introducing a new mathematical truth and offered as a contribution to education to be used only by the State of Indiana free of cost by paying any royalties”. The language behind the bill is so technical (maybe even deliberately technical) as to cause confusion among the members of the assembly. But seriously, who wants to admit that they’re stupid, right?
There’s just one problem: Goodwin’s definition of π. In Section 2 of the bill, it plainly states that “the ratio of the diameter and circumference (of a circle) is as fivefourths to four”, meaning that for the first time the mathematical truth, π, will be defined by fiat as exactly 3.2; this flies in the face of the true definition of π as we had covered in Part 1.
Notwithstanding all the confusion, it does speak in a language that politicians do understand: money. The bill entails that this discovery will effectively be a patent on Goodwin’s definition of π, and a royalty will be charged for its use with the exception of the State of Indiana.
On the fateful day when it was being deliberated, a professor of mathematics from Purdue University arrived in Indianapolis to secure some funds for the Indiana Academy of Sciences. By chance, our hero, Professor Clarence Waldo had met an assemblyman who was gushing over the ‘merits’ of the bill to him, and offered to introduce the good professor to this ‘genius’ who will put Indiana on the world map (for all the wrong reasons, though). Though entertaining as would have been, the good professor declined, saying that he’d met his fair share of the insane. A few days after the bill had been passed unanimously by the Indiana House of Representatives it was brought to the Senate for a second debate – just one step shy from being a law. Professor Waldo took it upon himself to coach the senators, and through consultations with the investigating committee authorized to scrutinize the bill, he managed to convinced them of their lack in power to determine natural truths. You can pass a law that says 1 + 1 = 3, but no power on Earth can change the fact that it’s false. 
The press had a field day on the matter, turning the Indiana House of Representatives and Dr Goodwin into a national laughing stock. Professor Waldo became a scientific superstar overnight, though he humbly credited that “it was probably the Indiana Academy of Science alone which prevented [this monstrosity]. If this deduction is correct, then that one act of prevention was worth more to Indiana, jealous of her fair fame as she is, than all she ever contributed or can contribute to the publication of the proceedings of her Academy of Science.” Needless to say, after the Indiana senators, the press and the Academy of Science got into the discussion, the bill was shot down, unanimously.
Implications
But what would have happened if the bill had passed into law? Or rather what of politicians, in all their ignorance, were to simply declare falsehood as truths by power of fiat? Let’s look at the applicable consequences.
If π were to be even slightly off, a perfect circle cannot be constructed. In Dr Goodwin’s case, if π = 3.2, the circumference of a circle will actually be off, and fitting it to the prescribed radius would be impossible without errors – it’s like pushing an oversized basketball through a regular hoop, either one or the other have to give in. All manner of constructions involving circular, spherical assemblies or arcs will be structurally compromised – wheels, satellite dishes, bridges, engines, turbines in dams, and even the dams themselves. Civil and mechanical engineering would be impossible.
It also covers purely conceptual elements. Nautical calculations, which follows the curvature of the Earth will be off by kilometers making navigational shipping and flight unreliable and dangerous, leading to the breakdown of international trade and therefore the global economy. Putting a satellite into orbit would be impossible as a geosynchronous orbit must be perfectly circular or elliptical (yes, the latter requires π).
Even if we were to leave the Earth, we’re still sucked in – π is a universal constant. Want to direct a space probe to flyby Jupiter for some nice photos? First you need to know where Jupiter is (elliptical orbits, again). Then when you want to send your probe there, you'd want to use another planet as a gravitational slingshot, and for that you need to know how to approach the planet, which requires the application of trigonometric functions, which involves….that right, π!
So what have we learned today? Math is serious business, and is certainly not an area for politicians to mess around with. We were lucky that Clarence Waldo was there to guard the realm of science from these people, now if only we can do the same with evolution….
Implications
But what would have happened if the bill had passed into law? Or rather what of politicians, in all their ignorance, were to simply declare falsehood as truths by power of fiat? Let’s look at the applicable consequences.
If π were to be even slightly off, a perfect circle cannot be constructed. In Dr Goodwin’s case, if π = 3.2, the circumference of a circle will actually be off, and fitting it to the prescribed radius would be impossible without errors – it’s like pushing an oversized basketball through a regular hoop, either one or the other have to give in. All manner of constructions involving circular, spherical assemblies or arcs will be structurally compromised – wheels, satellite dishes, bridges, engines, turbines in dams, and even the dams themselves. Civil and mechanical engineering would be impossible.
It also covers purely conceptual elements. Nautical calculations, which follows the curvature of the Earth will be off by kilometers making navigational shipping and flight unreliable and dangerous, leading to the breakdown of international trade and therefore the global economy. Putting a satellite into orbit would be impossible as a geosynchronous orbit must be perfectly circular or elliptical (yes, the latter requires π).
Even if we were to leave the Earth, we’re still sucked in – π is a universal constant. Want to direct a space probe to flyby Jupiter for some nice photos? First you need to know where Jupiter is (elliptical orbits, again). Then when you want to send your probe there, you'd want to use another planet as a gravitational slingshot, and for that you need to know how to approach the planet, which requires the application of trigonometric functions, which involves….that right, π!
So what have we learned today? Math is serious business, and is certainly not an area for politicians to mess around with. We were lucky that Clarence Waldo was there to guard the realm of science from these people, now if only we can do the same with evolution….

Ponder this
Get out your ruler and compass and try to square the circle, seriously, just try it.
Many laws seems arbitrarily enacted and imposed, and those who made them are not career academics or professionals (who tend to only act as advisors). Should academic and professionals be given more leverage on lawmaking? Why, why not?
Discuss
We understand now that π is not created, but discovered. The ratio between the circumference and diameter of a perfect circle have always been and will always be there, unchanging. How should this be applied in our life? What other unchanging truths are there? And are there other cases where people are tampering with them?
Further readings
Clarence Abiathar Waldo, know more about the man who saved π.
The law of identity, one of the three classical laws of thought. Used in philosophy and logic, and applied in legal, STEM and other professions.
Text of Indiana House of Representatives Bill No. 246, read it for yourself and understand why the politicians were confused.
The Emperor's New Clothes, a fable that may explain why the bill was passed by the members of the Indiana House of Representatives.