I am a little happy that Pi day is noticed, and perhaps gives an excuse to think deeply about something rather than just bake pies - but it's a pretty lame list. I propose my own:

1) Read about Tau vs. Pi. The arguments for what we can choose in mathematics vs. what is given, require one to think quite a bit about what is useful in math vs. what is convention and makes one, frankly, appreciate pi far more than any of the activities in the article.

2) Actually try to measure pi. Note I didn't say, 'calculate'. It is revealing how hard it is to actually measure things in the real world beyond three or four significant figures, and it makes one appreciate the beauty of abstract calculations.

3) Read about e. e is actually much cooler in many ways, but because there is no ridiculuously simple, visualizable definition of it, it doesn't get the limelight (such as it is.) A great historical book on e: "e": The Story of a Number

But if you insist on knowing what the slideshow list of ten things is:

1) Make a pi-themed pie
2) Rock a Pi Day T-shirt
3) Write Pi-kus or Pi-ems
4) Go on a pi scavenger hunt (this, at least, has some vague mathematical attraction, although you could accomplish the same with a random sequence)
5) See how many digits of pi you can recite
6) Watch "Pi" the movie (gibberish math, but a cool movie that gets a little bit of the obsessional nature that can capture those who dive into abstract mathematics)
7) Listen to Pi music
8) Tell Pi Day jokes
9) Celebrate Albert Einstein's birthday (same day)
10) Read a book about pi (they don't even suggest the classic historical work on pi, by Beckman: A History of Pi

Like I said - mostly silly, not very mathematical. I would prefer pi day be a day of observance rather than a secular holiday :-)

I used to spend hours randomly browsing through the articles. At some point, over many moves, they were given away. Now, I find I do the same thing, but on Wikipedia.

It used to be that when you visited someone's home for the first time, you could learn a bit about them by seeing what books they had on their shelves... which ones were worn, how chaotic or organized the books were, how many they had, what they were about, how many were lying around in mid-read... and if there was a set of encyclopedias somewhere. And, of course, if there was not a single book in the house, there was something suspect about them.

I suspect that in a decade or two, what I'll learn from seeing books in someone's house is that they are old. I'm sure I'll be included in that.

The weird thing is that the kids who hated math because it was useless outside of school seemed to love English class, which really is useless outside of school. Somehow they're able to get over the barrier of "school stuff is only useful in school" for English, but once they get into math class they have no imagination at all.

I suspect it really is incuriosity. They like English class because it's easy, you can make up whatever you want, and it doesn't have to be right because there is no right answer (although I seem to be very good at coming up with wrong answers somehow). If they applied some critical thinking to the situation, they'd realize it's a waste of time. Math on the other hand requires you to think.

I laughed at your 'incurious bastards' comment, too - there is, no doubt, a large component of laziness and dullness that results in students avoiding what they find hard. But the deeper issue of why they find Math hard and English easy is interesting, because as you acknowledge, you found English class difficult.

English class is about analyzing, above all, what someone else was feeling or why they did something. These kinds of questions admit no definite answers, but some kinds of reasoning about how other humans act and feel is far more plausable than others, and so some answers are better than others without there being a 'right' & 'wrong' answer. This focus on human motivation and emotion & with it a lack of precision is something that comes easily to many people. It is a natural ability we have, to empathize and gossip and wonder why someone else feels the way they do - no doubt, it is a skill that was evolutionarily highly selected for. The analysis of how other humans feel and why they act has been around as long as modern humans have, which is minimally tens of thousands of years.

Math, on the other hand, is a very recent development. It does NOT come naturally to most people beyond very basic size estimates and globbing and unglobbing small, easily visulaizable quantities. Unlike English studies, it is a highly structured, precise, deep and ordered discipline. The depth and ordering is the biggest problem from an educational perspective; if you, at some point, never quite 'get' fractions, it will be hopeless for you to try to understand anything that depends on them, which includes algebra, modular arithmetic, calculus, and all the mental models of the world that depend on them. When I used to tutor people in math (20 years ago - I'm getting old), that was usually the biggest problem - there was some previous bit of it that they never quite got, and all their subsequent math education was trying to pile bricks on sand. They usually gave up trying hard after a year or two of cluelessness. In essence, learning math takes a much longer peroid of time and it is much harder to teach correctly and effectively than English, and one big hole along the way will sink your future efforts.

In addition, knowing what math is useful for requires, well, knowing what math is useful for. You know it. I know it. But if a kid's teacher doesn't, and their parents don't, and society teaches that Math is for nerdy boys who will never kiss a girl (and don't even bother if you ARE a girl) well, that will squelch a lot of curiosity. I learned it from my dad. He taught me from a very young age how to navigate a boat. It was amazing - you draw lines of some plastic, run some numbers through a whizz wheel, steer your boat as it says, and you wind up where you want to go when you expected to get there! So for me personally, lines and courses and degrees and speeds and drift and times all had a reality and a practicality and a power - a power to predict the world - from as young as I can remember.

On the other hand, I found Shakespeare, as taught in schools, tedious at best - incomprehensible was more like it. The words were all weird, these people were running around knifing other people for no reasons that I could understand, random suicides offstage - I just didn't get it. Years later, a friend took me to see Shakespeare - live, not read out of a small book in a classroom. Wow - it suddenly made so much more sense. The fact that you didn't understand the words was made up for by the fact that you could see the pain, the love, the fear in the faces of the actors, in the dimness of the stage, or the clash of the swords; the wry observations of the servants, the nightmares of the queens, the guilt of the kings, and the wistfulness of the old. It was a story now, a recalling of those feelings that bond us all. Now, I love Shakespeare - but I had to see it as it was meant to be presented, as a play, not the 'scaffolding' - the script, stage directions, etc., and I needed a friend to introduce me as I had concluded it was all nonsense up to that point. And, I probably needed to be old enough to understand the panoply of emotions in a typical Shakespeare play; perhaps my emotional intelligence was below average.

So, it's worth condsidering that that is how the English major views Math. He/she doesn't see its power, predictive abilities, or raw beauty - there is no view of the creativity, the artistry, the variety, the cleverness, the struggle to understand, the complexity and the simplicity. They don't hear the music, they just see the notes - some spare black and white graphs, a bunch of circles and trianlges and lines all mismashed, a bunch of numbers festooned with ugly symbols that get pushed around on a page, which people claim is by some rules, but whenever they try, they do it wrong, they don't understand why, and they conclude it's just some arbitrary intellectual game with no relation to anything useful or that they care about. They never had someone make it real, or useful, or interesting for them, nor do they have the real world experience that comes with age to see that on their own, before they put it in the 'not for me' section of their mind.

For what it's worth - just another perspective. The "I don't think that students are not taught how math applies to real life. I think they are merely incurious bastards." is much funnier, though :-)

It is a consequence of three things, the assumption that revenue as a function of tax rate is continuous (loosely, that small changes in tax rate mean small changes in revenue), the above assumption that there is zero revenue at 0 and 100% tax rate, and Rolle's Theorem [wikipedia.org]. The combination of those three things yields the Laffer curve. The theorem is unassailable. That means one of the two assumptions have to be wrong before the Laffer curve model is wrong.

Really? You do realize a seismograph plot of an earthquake is legitmate Laffer curve then, right? As is a flat line? Or a sine curve? Or my personal favorite, y=x-x cos(2pi/x)? (Go ahead, plot it. You know you want to :-) So, if by the 'Laffer curve model' you mean that tax revenues can jump around any which way with tax rates, I guess it's correct. It's also useless.

When I look at the diagrams that Laffer himself suggested, and that most others use to argue with, they have many, many more assumptions, frequently including a single, narrow peaked curve. Rolle's theorem says nothing about that - Laffer himself is more careful, and does not invoke fancy mathematics (n.b. I was a math major, so I recognize when math is being used to illustrate an idea, obscure it, or decorate it with some authoritative words) to justify his napkin drawing, and he acknowledges there may be multiple peaks and a complex curve shape. His deception is more subtle. His argument was (back in 1974) that raising tax rates would probably not lead to greater federal revenues (using the Laffer curve diagram to illustrate this), so therefore lower tax rates would not lead to reduced federal revenue (which sounds good but doesn't logically follow from the previous statment), and that previous periods of tax cutting in the U.S. lead to desirable outcomes. To quote Laffer directly:

"Over the past 100 years, there have been three major periods of tax-rate cuts in the U.S.: the Harding-Coolidge cuts of the mid-1920s; the Kennedy cuts of the mid-1960s; and the Reagan cuts of the early 1980s. Each of these periods of tax cuts was remarkably successful as measured by virtually any public policy metric."

However, once you admit that you may have a more complex curve than a single peak, you should then honestly say that the only thing you can conclude is you don't know if tax revenues will go up or down with decreases (or increases) in tax rates. That is about the intellectual content of the Laffer curve, and anything beyond that is selling something. Laffer was selling tax cuts to an enthusiastic audience: Donald Rumsfeld and Dick Cheney in 1974. Considering that the Harding-Coolidge tax cuts of the mid-20's were followed by the Great Depression within 5 years, and the tax cuts of Reagan were followed by rise of the public debt from 22% to 40% of GDP, stating that "Each of these periods of tax cuts was remarkably successful as measured by virtually any public policy metric" indicates his ideas of public policy metrics were very narrow, or he was selling something. I think it was the latter.

I read this a long time ago, and the current situation reminded me of it:

Einstein's God

In 1919 Einstein's theory of relativity was confirmed by two expeditions to Brazil and the West African coast to observe the total eclipse of the sun. The eminent British astrophysicist Arthur Eddington led the project. To the amazement of Eddington and the rest of the world, Einstein had correctly calculated that space could be distorted and light curved by gravity. Einstein was on the front page of newspapers worldwide, but when asked what he would have said had his theory not been proven correct by observation, Einstein replied, "I would have had to pity our dear Lord. The theory is correct all the same."

I always smile a little at Einstein's utter confidence in his connection to what makes the universe tick. I guess you would have to be that confident to overturn two centuries of Newtonian Physics.

Considering that (depending on which survey you choose to believe) your average American spends somewhere between 2.4 and 5.0 hours a day watching television, I generally don't believe someone when they say they don't have time to exercise.

When someone in a modern nation says they don't have time to exercise, what they are really saying is that their physical health is not very important to them. This is true whether you work 10 hours a week or 80. The extra money is not likely to buy you a new cardiovascular system.

Being physically healthy is not something you can push a button to get to. Whether it is through interval training, endurance training whatever, just having fun being active, you have to devote significant & consistent amounts of time to it - it has to become part of your life, not just a 'thing' you do to keep the fat off and the potato chips flowing. If you don't find a way to enjoy it and bring it into your life in a meaningful way, you'll get tired of it and quit.

Personally, I think the way to get people active is to make it fun - integrate it into social activities, play with a team, track your stats, do endurace travelling, bike to and from work with friends, hike through different parks on different days, rock-climb, kayak, surf, swim, whatever gets you going, where you want to spend MORE time doing it, not less. There is a native joy to being active that has been neglected. Remembering and capturing this joy at physical exertion, rather than concentrating on minimizing the time you need to 'suffer' exercise, I think would bring more people into it

If the radiation from the machine itself was negligible then it means that a test with just the machine would not really matter.

That is only true IF you assume that radiation from the machine is the only possible cause of the sperm damage. However, that's what they are trying to prove, so assuming their desired conclusion when they designed their control is pretty bad experimental design, one that makes the whole thing almost worthless.

That may work well for airliners in areas where all aircraft are required to have a working transponder (roughy speaking, within 30 miles of 'large' airports - or above 18,000 feet)... but large majority of the U.S. airspace doesn't require this, and most smaller aircraft don't have TCAS, or sometimes even a transponder. 'See & Avoid' (or if you are feeling cynical, "The Big Sky Theory") is supposed to be the primary method of collision avoidance in VFR conditions, and even in IFR, you are expected, if you see something, that 'shouldnt be there', to avoid it!

When limitations of See & Avoid [SAA] were encountered in the past, specific mechanisms were implemented to preserve the concept while carving out sensible guidelines for exceptions. For instance, the military has some mighty fast airplanes that are designed to be extremely low visibility - not so good from the SAA perspective. So, large chunks of airspace called Military Operations Areas were carved out where they could go play. When an MOA is hot, you are not prohibited from going in there... but most sensible pilots do. Airliners fly in all sorts of weather & lighting, and as flights became longer in duration and more 'heads down' (navigating by instruments, more radio work, attitude instrument flying, systems monitoring, etc.), and in much faster aircraft, SAA became harder & harder to maintain. So, above 18,000 in the US, you are in class A airspace, which used to be called, much more descriptively, Positive Control Airspace. Every airplane there is under ATC control, and they take responsibility for aircraft separation. No VFR traffic allowed. Since this is generally above the altitudes most private airplanes fly, it was a nice idea that gained safety for the airlines while allowing general aviation to keep its freedoms & flexibility.

I hope something sensible like that will be done, perhaps to restrict drones to certain types of airspace... require some form of piloting qualifications for drone operators... require transponders on all drones, or... well something. Or one day, a drone is going to be enginebait & cause an accident. One of the biggest incentives for safety as a pilot is the fact that you are first to arrive at the scene of an accident. Drone operators don't have that, and I wonder if it will be possible to maintain such a robust safety culture without it....

No they don't. If it's not a puddle jumper, the damn thing lands itself.

Well, unless you count 737s, 757s, 767s, 777s, and a few dozen other 100+ seat commercial aircraft as 'puddle jumpers', you are wrong. These airplanes have the capability to autoland, under a highly restricted set of conditions, involving maximum wind speeds (on the 737, max headwind 25 kts, xwind 15 and tailwind 10), clearing a large ILS safe zone on the surface of the airport to assure no interference with the localizer & glide slope antennas, minimum visibilites (because many autopilot systems work only the ailerons & elevator, not the rudder, and once you are on the deck you need the rudder to track the centerline, which the autopilot can no longer do, and neither can you if you can't see), etc., etc., etc.

I flew 600 hours for a major airline on the 737 last year. I did exactly one autoland in the entire year, and it was because the Captain & I wanted the procedural practice, the airport had a CAT III ILS, and it was a quiet day & ATC was accommodating.

I really wish I knew what urges people to forcefully declare they know about something when they plainly don't. It only subtracts from the discussion and your credibility.

I'm sorry, but I had to correct this:

according to special relativity, there are no privileged frames of reference.

This is quite untrue. By a 'privileged frame of reference', physicists have always meant ones in which the laws are particularly simple. There are, in special relativity, a privileged set of frames called internal reference frames. These are the same priviliged reference frames as existed under Newton's Laws. What Einstein did is hypothesize (to explain the negative result of the Michelson-Morely experiment as well as the seeming demand for some sort of absolutely special, 'non-moving' internal reference frame from Maxwell's equations) that the transformation equations between two used by Newton were incorrect. The Galilean transforms, which (roughly speaking) say if a pitcher throws a 90 mph fastball directly to the rear of a train moving forward at 50 mph, it will emerge from the train's rear (i.e. from the perpective of an observer on the side of the tracks) at 90-50=40 mph, are not quite right. Einstein derived the Lorentz transforms (after Lorentz, somewhat in desperation, came upon them as a way to explain how the speed of light might be the same for all observers) from some basic postulates, which change the addition of velocities in such a way that they never add up to c. The reason it's called special relativity is because it apples to only a special subset of all possible frames of reference - the inertial ones.

The idea that one can, with additional difficulty, calculate and make correct predictions in non-convenient frames of reference predates Einstein by quite a bit. The General theory of relativity, I believe, applies in the same form to all reference frames but it's not simple at all.

If you want a quick mental experiment to demonstrate that Special Relativity isn't meant to apply to all reference frames, consider the following. Special Relativity says that if you wish to preserve causality, no object can travel faster than the speed of light. Go outside on a clear night. Look at the Andromeda Galaxy. Rotate your body 90 degrees. Consider what speed the Andromeda Galaxy would have to be moving from the point of view of your (briefly) rotating reference frame.

Well, I don't think these guys and gals are a bunch of 'dirty twenty-somethings'.

http://photoblog.msnbc.msn.com/_news/2011/09/27/7995471-pilots-from-continental-and-united-airlines-demonstrate-on-wall-street

Only about 800 pilots, to be sure. But I don't think the focus was that 'rich people are rich' - more like, 'our highly paid executives are mismanaging our company, and we are stuck with the results.'

Regardless of whether you agree with the message, perhaps you will agree that the major media tends to ignore peaceful, organized and coherent messages in favor of 'bad boy' protestors & violence.

Very little mention was made in the media of the pilot protests on Wall Street today, despite significant organization, and a coherent message.

A Video of such, you can skip the first minute.

IMHO, traditional media outlets do tend to ignore marches and protests, unless something violent occurs. To wit, how many of you reading this were even aware of pilots picketing Wall Street today, with 5x the numbers of the other Wall Street protestors? Because we were organized, polite and non-violent, we didn't garner much media attention. Because the other protestors were scruffy, angrier, and less compliant, they were 'noticed'.

On the other hand, the NYPD was extremely helpful with the mechanics of the protest. It helps to be well behaved in some ways.

As we all know (speaking at least for the fifth row), Dedekind is famous for the line: God made the natural numbers. Everything else is the work of man.

Not to be rude, but Dedekind said nothing of the sort - considering that Dedekind cuts defining the Reals in terms of the Rationals was, well, Dedekind's invention, he obviously felt that there was more to mathematics than Z. Leopold Kronecker was the source of your quote.