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Legislating π

Jun 21, 2012
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Law, Politics & Current Events

In 1897 Doctor E. J. Goodwin, of Solitude, Indiana, experienced the flash of insight that comes to even the greatest men but once in a lifetime: he discovered the perfect formula by which to calculate the area of a circle.

A man of no small generosity, Dr. Goodwin, after patenting his method, nobly offered to share the formula with the people of Indiana, if only the Indiana legislature would enact it into law. And so, in 1897, the Indiana House of Representatives passed Goodwin's Law:

Be it enacted by the General Assembly of the State of Indiana, that it has been found that a circular area is equal to the square on a line equal to the quadrant of the circumference.

Since 1897, the people of Indiana have enjoyed a level of engineering safety, in their bridges, skyscrapers, and highways, unsurpassed in the world. They possess a superior means for calculating the area of a circle, the mathematical constant known as π (a number represented by the 16th letter of the Greek alphabet, pronounced "Pie").

As we're taught in geometry class, a circle is a geometric figure in which all points are equidistant from the center.  The distance from the center of a circle to any point on the exterior is known as the radius (symbolized as "r").

We know, thanks to Archimedes, that the area of a circle is the square of its radius, multiplied by π. Or, in Archimedes' formulation, πr2. 

Thanks to Goodwin's Law, as passed by the House of Representatives of Indiana, Hoosiers could now calculate π to a degree of certainty unknown to Archimedes and the ancients. Since the quadrant (a quarter) of the circumference of a circle could be measured from a circle's radius (using the formula C, being the circumference of a circle, = 2πr), dividing by 4 and squaring the dividend, it followed that πr2 = 1/4 π2r2 

And therefore, that the area of a circle is equal to 4 times its radius squared. Or as Archimedes might have put it, π = 4.

This remarkable result prompted Dr. Waldo, the mathematician of Purdue University, on being asked by an Indiana Senator whether he wished to meet the famous Dr. Goodwin before the bill's final passage, to decline on the ground that he had met a sufficient quota of lunatics in his lifetime.

And so Goodwin's Law failed to pass the Indiana Senate.

I've been reluctant to write about North Carolina House Bill 819, the bill by which the North Carolina Senate (through a re-write of a funding bill already passed by the House of Representatives) proposes to forecast future sea levels, for a number of reasons: first, I knew that it would subject my State to ridicule by my co-bloggers in California and New York, who, though too ignorant to distinguish π from cake, think it's perfectly acceptable for government to mandate that stores provide extra-wide aisles for extra-fat people, while at the same time regulating the volume of a cup of Pepsi.

And I hoped that the North Carolina House, like the Senate of Indiana a hundred years ago, would recoil in horror once the bill's stupidity was explained to them. In four letter words.

But at this point, it looks so close that ridicule may be the last, best weapon.

The state House unanimously rejected a Senate proposal to limit the ability of coastal agencies to make rules based on scientific warnings that the sea level will rise more quickly during the 21st century than it has in the past.

Instead, the bill will go to a House-Senate conference committee co-chaired by a House member who thinks the state should study the contentious issue further.The Senate had inserted the sea-level legislation into a coastal regulatory bill that cleared the House last year. Rep. Pat McElraft, an Emerald Isle Republican who sponsored the original House measure, asked the House on Tuesday to reject the Senate’s rewrite of her legislation.

“There is some controversy over the sea-level-rise area of it,” McElraft said on the House floor. “And I think what we need to do is take it to study and, if we get conferees, we can work it out.”

The intent of the bill, as it's presently written, isn't too objectionable. The goal is to limit the ability of unelected, unaccountable government agencies (as with the Army Corps of Engineers at the federal level) to prohibit coastal North Carolinians from using or developing their own property based on forecasts, a la An Inconvenient Truth, of some climatological holocaust a hundred or thousand years from now.

That's the intent. Of course, the Senate could have struck directly at the problem by curbing the authority of unelected, unaccountable government agencies, but honestly, what government ever willingly diminished its own power?

The method is the problem.  The method is to command all state agencies, including potentially universities, to forecast rates of sea level rise extrapolating only from historical data. No consideration could be given to forecast trends such as increasing temperatures and diminishing polar ice caps, regardless of whether including such forecasts would be good science.

Now, I'm not qualified to judge whether that's good science. Neither, in all probability, are you.

But I can say this with certainty: The North Carolina Senate is even less qualified to pass on what is and what is not good science than I am. The North Carolina Senate, a body made up for the most part of lawyers, hog farm operators, and idiot sons of the idle rich, is no more qualified to forecast future sea levels than it is to legislate the sixteenth digit of π.

The State of North Carolina was founded by people who believed in limited government that respects the freedom of its citizens. Members of the North Carolina Senate who are pushing this bill would tell you that the State is still run on the principle of limited government for a free citizenry. And yet, by attempting to legislate its opinion on matters of science, the Senate of North Carolina is venturing into territory formerly occupied by fascists and communists, enemies of freedom who legislated their truth into law without compunction.

Or King Canute, who commanded the tides to stop out of respect for the royal feet. Will the tides stop at the command of the North Carolina Senate? Or will they, like π, remain what they are?

Last 5 posts by Patrick Non-White

22 Comments
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22 Comments

  1. Patrick  •  Jun 21, 2012 @9:17 pm

    For those who are interested, a fuller version of the story of Dr. Goodwin's attempt to legislate the value of Pi may be found in "The Mathematical Universe" by William Dunham. It's a charming and humorous book on various mathematical topics, written in good layman's English.

  2. Adam Steinbaugh  •  Jun 21, 2012 @10:08 pm

    One of the Indiana state senators opposing the bill noted: "The Senate might as well try to legislate water to run up hill."

    A man ahead of his time.

  3. Ken  •  Jun 21, 2012 @10:22 pm

    I'm reliably informed that you insult me somewhere in the middle, but I'm still trying to understand the first part.

  4. Jack Ryan  •  Jun 21, 2012 @11:49 pm

    To be completely fair to Canute, in the original telling, he didn't really believe the sea would stop rising. He just wanted to show the fawning sycophants in his court that his power was not absolute. It was a story intended to showcase his immense humility, not his arrogance.

    Of course, to be fairer, the story was likely made up by later historians seeking to glorify him.

  5. Nate  •  Jun 22, 2012 @12:02 am

    I would like to offer a scientific perspective. As someone who has a doctorate in meteorology, I believe myself at least somewhat qualified to comment on the wisdom of the proposed North Carolina law. Specifically, the proposed law is altogether scientifically unsound.

    Sea level rise is not a linear process — it depends on a number of different factors. Most important among those are thermal expansion of the seawater in a warmer climate (things in general tend to expand when they get warmer), and the melting of existing icepack (the ice covering Greenland will be a major factor there). There are feedbacks involved in these processes — for example, if ice melts from the polar regions, this exposes open seawater. Open seawater is relatively dark and absorbs sunlight much better than bright, white ice — meaning that the more ice melts, the faster the planet will warm (and in the warmer environment the ice will melt even faster — a positive feedback loop).

    Long story short, the sea level rise will depend on a lot of factors which will vary significantly in the future. All reasonable predictions suggest that the warming of the planet will accelerate significantly over the next century. Because of this, linear extrapolations will not work. A linear extrapolation would predict sea level rise of at most a few inches over the next century, but advanced climate models (which do take into account feedbacks like I mentioned earlier) suggest that a sea level rise of more than 3 feet is likely.

    If you're interested in an in-depth discussion with references, Scientific American has looked at this issue and does a good job of explaining the science of it in a way that's very accessible to the general public: http://blogs.scientificamerican.com/plugged-in/2012/05/30/nc-makes-sea-level-rise-illegal/

  6. NickPheas  •  Jun 22, 2012 @12:18 am

    I'm slightly confused by the intent of the NC legislation. It's the state's job to tell people that they can or can't develop their own properties? Really? If someone wants to build a boathouse half way up a mountain surely that's their own affair?

  7. Bob  •  Jun 22, 2012 @12:21 am

    Ah, but Canute's intent was to illustrate the folly of kings presuming to command nature; an appropriate reference but not necessarily what you intended.

  8. NickPheas  •  Jun 22, 2012 @12:22 am

    Sorry, re-reads. The aim to to prevent the army from telling people not to build mountain boathouses. My bad.

  9. Katie  •  Jun 22, 2012 @3:52 am

    It's actually even closer to the legislating pi issue that you compare it to — they legislate that the people doing the measuring and extrapolating must use a linear fit. They have already decided that nature must act in a linear fashion, even though few processes in nature actually *go* in a linear fashion. (As opposed to parabolic, hyperbolic, etc..)

  10. William McAleese  •  Jun 22, 2012 @4:54 am

    @bob, thank you. Only on this site would you log in to correct the implied intent of an obscure king 1000 years ago, only to find you were beaten to it.

  11. piperTom  •  Jun 22, 2012 @5:30 am

    How are so meek as miss the golden lede here? The bill limits the authority of bureaucrats to … actually, it hardly matters what comes next; I like it. As to the specifics of building in the face of a rising sea level, I scorn the opinions of bureaucrats and politicians, along with any "scientist" who issues a press release. If your mortgage holder and your insurer are okay with your building plans, then have at it.

    And, just in case, I have a room to let — well inland and above the 100 year flood line.

  12. Kevinsky  •  Jun 22, 2012 @6:05 am

    The bible has the value of PI at 3.00, I'm surprised nobody has ever tried to legislate that! (1 Kings 7:23 http://skepticsannotatedbible.com/1kg/7.html)

    Also, I'm reminded of an apocryphal story, attributed (probably wrongly) to Abe Lincoln. Abe asks someone, "How many legs does a calf have, if you call the tail a leg?" The answer of course, is 4. You can call the tail a leg all you want, it's still a tail.

  13. Joe  •  Jun 22, 2012 @6:07 am

    I live about 450 feet above sea level so the only Pi I tend to care much about comes with apples and cinnamon in the middle.

    However, as Katie pointed out, nature does not act in a linear fashion despite any attempts to legislate otherwise.

    Case in point, vacationing on the coast of Oregon about a year ago we stayed at an inn that had Tsunami warning signs posted everywhere. The definition of Tsunami, as everyone who lives in certain coastal areas knows, actually means “run for them thar hills”.

    Alerts for evacuation are generally put out after a preceding earthquake. The place we stayed told us once an alert was sounded we had about 45 minutes to get to high ground or risk becoming guppies vs yuppies. Another alert, albeit one with less time to plan ones escape, is the drawback. Drawback, I've been told, is where the water recedes from the shore. Apparently drawback also makes a giant sucking sound (not unlike the sound of the last of your bathwater going down the drain). Tsunami’s can be survived in this situation only if they immediately run for high ground or seek the upper floors of nearby buildings.

    Tsunami’s are apparently measured by both intensity and magnitude. Intensity is basically the height of the wave that is about to smack you into oblivion. Intensity is calculated as I = ½ + log2 Hav

    Magnitude is calculated as Mt = a log h + b log R = D. I never was any good at math, but I’m pretty sure the “D” stands for death.

  14. Tonylurker  •  Jun 22, 2012 @6:52 am

    I'm slightly confused by the intent of the NC legislation. It's the state's job to tell people that they can or can't develop their own properties?

    Well, it is currently the state's (and localities') job(s) to regulate the various utilities and storm water management for the communities being developed. If you are going to do that, you should plan a system that will last a while (ie. can handle the foreseeable change in sea level). Hence the need for such forecasts for planning/design purposes.

  15. Nicholas Weaver  •  Jun 22, 2012 @8:59 am

    Also, since someone who develops along the coastline is often bailed out by the state and feds when disaster hits, development that is, within 100 years, likely to be impacted by changes in ocean height will have a cost to the taxpayers. Which means either it

    a) MUST be included in planning decisions
    or
    b) MUST include a "We won't bail your A#@#)(* out, ever" clause.

    What this really is about is that basically, a large amount of the Republican power base just does not want to acknowledge any evidence about climate change, and this is basically mandating a "NA NA NA WE AREN'T LISTENING" requirement into state planning.

  16. mojo  •  Jun 22, 2012 @2:38 pm

    Well, if pi=4, then obviously e=3

    Quod Erat Demonstrandum

  17. Ara Ararauna  •  Jun 22, 2012 @3:50 pm

    @Nate, just out of curiosity, what are your thoughts about the albedo factor created by open desertized areas like, for example, Sahara Desert and the like? As far as I know the deserts are just 0.10 points below ice, and cools down faster than water during non-insolation hours. Why they still think that when snow and ice "disappears", the albedo will be so messed up everything will warm up and cloak the sky with clouds that will promote greenhouse effects ala Venus and flood all the shores of the world?

    That made me to recall, sometime back at college when we went out to investigate strata we spotted that the ancient coastal line of our island was 50 meters above the level of the sea. One of my classmates said that it was like that because the ancient sea was 50 meters that high because the Earth was warmer back then and there were no ice millions of years ago (collaterally implying the reasons explaining why the dinosaurs could have cold blood back then, WTF), and that then when all the ice of the Earth melts, the sea will rise again back to that same height. I countered him by telling him that the strata there in fact was below the level of the sea in ancient times because the island 8 millions of years ago was young and barely rising over the sea, and after the years, it rose up to that point and will still rise higher in the coming centuries. It is interesting though because I have seen architects building houses and other dwellings way above that ancient stratum due to fears that "the sea will rise again above that line".

    As you said, it is not a linear process, and even the depth of the ocean, the rise and fall down of terranes by means of quakes and even by the same downward compression of the water due to the increasing of its volume in reduced areas, will make the rise of the coastal lines to be quite not as high as expected, not even for the next centuries. That and I'm not attacking the fact that global warming is contributing to the downpour of more water into the sea, but it also is increasing the uppour of water into ancient cratons and into the atmosphere, meaning that all the melted water will not remain as a "whole piece" into the sea but rather as a dynamic natural conveyor belt that will never stay in place to flood North Carolina's coast any time soon.

    *sways upside down on its bird swing in a crazy manner*

  18. Nate  •  Jun 22, 2012 @4:35 pm

    @Ara — Desertification will certainly increase albedo in the newly-created desert regions. One of the reasons that there's so much uncertainty in future estimates of global warming (and consequently estimates of sea-level rise) is the fact that we just don't know to what extent positive and negative feedbacks will interact. What is relatively well agreed upon, however, is that the most likely range of outcomes fall somewhere between "modest but significant warming" and "catastrophic warming".

    The general agreement among climate scientists is that thermal expansion of the oceans in a warmer climate will be the dominant factor in sea-level rise (Wikipedia has a good chart on the sources of sea level rise about a third of the way down the page at http://en.wikipedia.org/wiki/Current_sea_level_rise ). Because thermal expansion depends solely on the global temperature, and the global temperature depends largely on the concentration of greenhouse gasses in the atmosphere (which are well understood and accurately measured), there's little doubt that significant sea-level rise will occur.

  19. roadgeek  •  Jun 22, 2012 @8:57 pm

    Molly Ivins used to tell the story of how some years back the Texas Legislature rounded the value of pi up to 3.15, mainly for the sake of simplicity, but also because they could.

  20. Narad  •  Jun 24, 2012 @7:03 pm

    what are your thoughts about the albedo factor created by open desertized areas like, for example, Sahara Desert and the like?

    It's irrelevant. Indeed, the use of "albedo" to refer to surface features is misplaced so long as one has a substantial atmosphere, as what's being reflected isn't going anywhere.

  21. WheelsOC  •  Jun 25, 2012 @12:31 pm

    It's irrelevant. Indeed, the use of "albedo" to refer to surface features is misplaced so long as one has a substantial atmosphere, as what's being reflected isn't going anywhere.
    I don't think that's correct. The difference between a surface with a high albedo and a low one is that reflected energy tends to stay pretty much at its original wavelengths, whereas less reflective surfaces absorb and then re-radiate the energy the collect, usually at a lower wavelength. If sand reflects rather than re-emits radiation then what it's reflecting will likely pass through the different Greenhouse Gases with the same ease on the way back up as it did back down. But if it's instead absorbed and then re-emitted as infrared radiation, much of it will be blocked by GHGs before it can leave back out of the atmosphere. This is because GHGs are opaque to variously wavelengths of infrared radiation, but not visible or UV light. So reflected, visible light can pass through them again while IR emitted from the surface will be trapped within the atmosphere and the surface.

  22. Buzz Killington  •  Jun 28, 2012 @5:31 am

    The bill's purpose is to legislate reasonability, an attempt to keep fear out of the driver's seat for a change (never an easy task). Here's a better rundown than I can provide myself:

    Shaping your view of the world with well-constructed propaganda