The Science Pundit

Happy Pi Day!

noreply@blogger.com (The Science Pundit) — Sat, 14 Mar 2015 08:12:00 +0000

Before I get to my post, let me say happy birthday Wacław Sierpiński!

Recently, I watched an Aperiodical video where a group of mathematicians used a variety of methods to estimate the decimal value of π under the constraints of a π-hour time limit and a ban on electronic calculating devices. Needless to say, none of these methods was particularly efficient. This got me thinking of how I might celebrate this mathematical "holiday" by estimating the value of π in my own inefficient manner. What could be more tedious than performing Newton's method on the sine curve?

Newton's Method: first step

The concept is fairly straightforward. Imagine that we're driving along a winding road at night. Since the headlights are affixed to the front of our car and facing forward, the beam of light always points in the direction that the car is moving. Now think of that road as the sine curve, our car as the point on the curve corresponding to our current guess of the value of π, and the headlight beam is what's called the tangent line, which always points in the direction of movement along the curve. Since the sine curve is continuous and crosses the x-axis at π, then as our x-coordinates approach π, our y-coordinates will likewise approach 0. Newton's method basically says that if we're close enough to π, then our car's/guess's tangent line will point towards an x value that's closer to π than our current guess is.

So if our initial guess is 3, then the tangent line through the point (3, sin(3)) will cross the x-axis at a value closer to π than 3 is. That value becomes our next guess, and then we repeat the process until satisfied. The closer that the sine of our guess is to 0, the closer that our guess is to π.

Determining the iteration formula makes for a good first semester calculus problem. I've gone ahead and done that as well as writing a short MATLAB routine* to perform it.
* see Appendix A

The guesses converged to 10 digits of accuracy in only two iterations.

initial guess	3
1st iteration	3.14254654307428
2nd iteration	3.14159265330048
pi	3.14159265358979

Of course, this is sort of like putting the cart before the horse since the procedure presumes that evaluating trigonometric functions is more basic than evaluating π. We can keep with the spirit of the original challenge by evaluating the sines and cosines with means which can be replicated with paper and pencil. This is where second semester calculus gives us the Maclaurin series. I've also taken the liberty of writing another MATLAB routine* that calculates the trigonometric functions using the first eight terms of their respective series. What else would I be doing on Pi Day? :-)
* see Apendix B

This time the accuracy was to 6 digits.

initial guess	3
1st iteration	3.14254589805078
2nd iteration	3.14159188052770
pi	3.14159265358979

I certainly hope that my Pi Day diversions have amused you. Thank you for reading!

Appendix A:

% Script File : Newtons_Pi
% by Javier Pazos
% March 12, 2015
% Estimates the value of pi using Newton's method on the sine curve.
% Initial guess is p = 3.

PiGes = 3;
eps = 1e-4;
SiPi = sin(PiGes);
CoPi = cos(PiGes);
format long

% Main loop.
% Each iteration finds the x-intercept of the tangent line of the
% sine function at the previous estimate.

while abs(SiPi) > eps

    % Iteration loop.
    % Sets PiGes = (PiGes*cos(PiGes) - sin(PiGes))/cos(PiGes)

    PiGes = (PiGes*CoPi - SiPi)/CoPi;
    SiPi = sin(PiGes);
    CoPi = cos(PiGes);
    PiGes % Prints latest guess.

end

Appendix B:

% Script File : Newtons_Pi_Taylor
% by Javier Pazos
% March 12, 2015
% Estimates the value of pi using Newton's method on the sine curve.
% Sine and Cosine are estimated using MacLaurin series.
% Initial guess is p = 3.

PiGes = 3;
eps = 1e-4;
SiPi = sinTay(PiGes);
CoPi = cosTay(PiGes);
format long

% Main loop.
% Each iteration finds the x-intercept of the tangent line of the
% sine function at the previous estimate.

while abs(SiPi) > eps

    % Iteration loop.
    % Sets PiGes = (PiGes*cos(PiGes) - sin(PiGes))/cos(PiGes)

    PiGes = (PiGes*CoPi - SiPi)/CoPi;
    SiPi = sinTay(PiGes);
    CoPi = cosTay(PiGes);
    PiGes % Prints latest guess.

end

function SiEst = sinTay(x)
% by Javier Pazos
% March 13, 2015
% Estimates sine using the MacLaurin series.

% Set number of iterations and initial sum.

n = 7;
sum = 0;
format long

% Main loop
% Sums first n+1 terms of the MacLaurin series for sine.

for j=0:n
    sum = sum + ((-1)^j)*(x^(2*j+1))/factorial(2*j+1);
end

% Returns value.

SiEst = sum;
end

function CoEst = cosTay(x)
% by Javier Pazos
% March 13, 2015
% Estimates cosine using the MacLaurin series.

% Set number of iterations and initial sum.

n = 7;
sum = 0;
format long

% Main loop
% Sums first n terms of the MacLaurin series for cosine.

for j=0:n
    sum = sum + ((-1)^j)*(x^(2*j))/factorial(2*j);
end

% Returns value.

CoEst = sum;
end

Fibonacci, the Golden Ratio and 2048

noreply@blogger.com (The Science Pundit) — Fri, 11 Apr 2014 22:47:00 +0000

Like many people, when I first discovered the Fibonacci sequence, I was immediately enamored. It has some wonderful properties, some of which I will discuss below. But first, we need to beware of the large amount of Golden Garbage and Fibonacci Flim-Flam that pervades the internet.

A few years back, I ran across this excellent article by Donald Simanek where he meticulously takes apart many of the more popular myths associated with the Fibonacci numbers and the Golden Ratio. If you have not read it, go read it now! The link is here. I highly recommend it! More recently, Keith Devlin made a video where he stomped out much of the pseudoscientific nonsense going around about the Golden Ratio. I have embedded the video below as it is well worth the watch.

Debunking 10 Golden Ratio Myths from Keith Devlin on Vimeo.

What really irritates me the most about all this--as well as Simanek and Devlin--is that the Golden Ratio really is a special number with some wonderful and beautiful properties. The nonsense is completely unnecessary. Anyway, now that we've visited the debunking, let's talk about some Fibonacci and Golden Ratio facts that I really like.

Some interesting facts about Fibonacci-like sequences

As Dr. Devlin pointed out in his video, it has been known for a long time that the ratio of consecutive Fibonacci numbers is the golden ratio Φ. There are many ways to show this. Here's one that I came up.

Let γ_n = F_n/F_n-1 be some ratio of consecutive Fibonacci numbers. Then γ_n+1 = F_n+1/F_n = (F_n+F_n-1)/F_n = 1+F_n-1/F_n = 1+1/γ_n. We can verify that γ₂ = F₂/F₁ = 1/1 and γ₃ = F₃/F₂ = 2/1 = 2 = 1+1/1 = 1+1/γ₂. Now assume as an inductive hypothesis that γ_n can be represented by the continued fraction 1+1/(1+...+1/(1+1/1) with n red 1's. Then γ_n+1 = 1+1/γ_n = 1+1/(1+1/(1+...+1/(1+1/1)) which is the continued fraction with n+1 red 1's. Hence as n --> ∞, γ_n --> 1+1/(1+1/(1+1/(1+...) = Φ. This identity can be verified since Φ is the positive root of the quadratic equation x=1+1/x. (The negative root of this quadratic, sometimes referred to as its algebraic conjugate is Ψ = -1/Φ. More on Ψ later).

Φ as a continued fraction

As an interesting side note, the fact that Φ can be represented by the infinite continued fraction of all 1's, is why it is considered to be the "most irrational number." So is Φ the most irrational number? (In my best Keith Devlin voice) That's TRUE!

Leonardo of Pisa originally described the Fibonacci sequence

Several years back, I was playing around with Fibonacci-like sequences--sequences with the same recursion relation as the Fibonacci sequence, but with a different starting point. I began to wonder how many of the Fibonacci-like sequences also had the property that the ratio of consecutive elements tended towards Φ. If one were to allow non-integer seeds, then it is apparent that if γ₁ = Φ, then γ_n = Φ for all n, and likewise for γ₁ = Ψ. This is true since both Φ and Ψ are roots to the quadratic x=1+1/x. But which other sequences go to Φ and which to Ψ? Does it go to whichever limit is closer to γ₁? Do most go Φ but those close enough to Ψ go to Ψ? Or is it something different? At the time, I conjectured that with the exception of the two above where γ_n doesn't vary with n, all Fibonacci-like sequences tended towards Φ. Unfortunately, I did not have the mathematical tools back then to prove it. I was determined to figure it out on my own though (what's the point of doing a puzzle if you just look up the answer without solving it yourself?).

Recently I was reminded of my old puzzle and finally worked out a proof. I'll just give you the gist of it without going into the details. Basically, I worked out a formula for the difference between γ_n and Φ (provided that γ₁ > 0). Then using some known inequalities involving the Fibonacci numbers, I was able to show that for any given ε > 0, there is an N s.t. for all n > N, |γ_n-Φ| < ε. Thus for any γ₁ > 0, the sequence of ratios tends towards Φ. Suppose now that γ₁ < -1. Then γ₂ = 1+1/γ₁ > 0 and the sequence tends towards Φ. And if γ₁ > -½, then γ₂ < -1 and the sequence tends towards Φ. If we continue in this vein, we find that if γ₁ < -1/F_2n or > -1/F_2n-1 for some n, then the sequence tends towards Φ. In other words, the set of initial ratios that spawn a sequence that tends towards Φ is R\{Ψ}.

This is pretty amazing. It means that no matter how close to Ψ the ratio γ₁ is (just as long as it's not equal), there is some finite n for which γ_n is even closer to Φ. This naturally led me to wonder why and keep playing around. I guess there are many ways to explain this, but here's the one I came up with. Let's consider the Fibonacci sequence in reverse. We are used to thinking about the Fibonacci sequence as beginning with 1, 1 and moving forward following the recursion relation F_n+1 = F_n-1 + F_n. However, there is no reason why we can't follow the sequence backwards using the equivalent relation F_n-1 = F_n+1 - F_n. If we do this we get that F₀= 0, F_-1= 1, F_-2 = -1, F_-3= 2, F_-4= -3, ... , F_-n = (-1)ⁿ⁺¹F_n. Now consider what happens to F_n+1/F_n as n --> -∞. This is equivalent to looking at the limit as n --> ∞ of F_(-n)+1/F_-n = F_-(n-1)/F_-n = -(F_n-1/F_n) = -1/Φ = Ψ. Furthermore, using essentially the same proof as above, we can show that with the exception of the two sequences whose ratio doesn't vary, this happens for every Fibonacci-like sequence. So of course they all tend towards Φ no matter how close to Ψ we begin; looking at it this way, arbitrarily close to Ψ is where they all ultimately "originate." This at once made the original conjecture seem a little less amazing, while simultaneously being much more astounding (I can't think of a better way of explaining my emotions). When I realized this result, I pictured in my mind a graph of all the sequences as something akin to the magnetic field lines of a bar magnet with Φ and Ψ as the fixed poles. Quite lovely!

I showed my work to a Number Theorist here at the Math Department where I go, and after a few days he came back to me with three alternative ways to prove this. I will show you my favorite below which involves a linear equation. It is known that for Fibonacci-like sequences, the n^th term can be expressed as F_n = aΦⁿ + bΨⁿ where a and b are constants defined by the starting points of the Fibonacci-like sequence. For example, for the actual Fibonacci sequence a = 1/√5 and b = -1/√5 , for the Lucas sequence (which begins with 1, 3) a = b = 1 , for the Φ sequence b = 0, and a = 0 for the Ψ sequence. Consider, for a, b ≠ 0, what happens to F_n+1/F_n as n --> ∞. Note that |Ψ| < 0 and so the second term disappears in the limit while the a's in the numerator and denominator cancel leaving the limit as Φ. Now consider, for a, b ≠ 0, what happens as n --> -∞. We have F_n = a/Φⁿ+b/Ψⁿ, so the opposite happens and we're left with a limit of Ψ.

Beautiful!

Musings on a variation of 2048

In case you've been living under a rock and haven't heard of the game 2048, go check it out now. (WARNING: Game is highly addictive!) It's a fun little game. The basic idea is that you move tiles around on a 4X4 board. The starting position consists of two tiles randomly placed on the board, valued either 2 or 4 (randomly chosen). On each move you move all tiles on the board either left, right, up or down provided they have room to move. If two tiles of the same value are pushed together, they merge into a single tile with double the value of the original tiles. On each move a single tile, either a 2 or 4, is randomly placed on an open space. The game end when you run out of room to play. You WIN if you create the 2048 tile, although you may continue to play to see how high you can go.

Binary Exponential

One of the attributes of the game is that it's fairly easy at first. In fact, it's fairly easy for a while. You think that you're doing so well then, seemingly suddenly, the world caves in on you. This is due to the exponential nature of the game. Each level is "as big" as all the levels before it. For example, in order to make the 512 tile, you must first make two 256 tiles. In other words, once you reach the 256 tile, to get to the next level, you have to do everything that you've already done over again to make a second 256 tile, but with less room to work with (since you didn't have that first 256 tile taking up space the first time around). Of course it's actually a little messier than that. On the first go there were 14 empty spots to work with; It is quite unusual to clear the board that efficiently when creating the higher valued tiles. Naturally, many of the tiles cluttering the playing board at this time can be used to make the 256 tile, so it's not quite as dire as that. Bear in mind that at each level, the maximum number of free spaces is reduced by one. So (for simplicity, let's ignore the fact that the game sometimes gives 4's and pretend that it always deals a 2) to make the 2048 tile, you must first make two 1024 tiles. But to make that second 1024 tile, you must first make two 512 tiles. But to make the second 512 tile, you must first make two 256 tiles, etc. Therefore, while constructing the 2048 tile, you must pass through a position where the playing board only has 16 - 11 = 5 free spaces to work with (because 2048 = 2¹¹). There is no escaping this since making duplicate tiles in parallel rather than in series leaves you with less free spaces to work with. And getting the 4096 tile is even harder yet. Knowing what I know about the exponential nature of the game and how long it took me to get good enough to finally make that tile, I'm not too optimistic about being able to make the 8192 tile. Although if I stop and carefully plan out each move rather than use the heuristic algorithm that has been this successful so far, who knows? What I do know is that 2048 has been a real time hoover and I sure hope I'm getting over it soon.

The game's popularity has spawned several variants. There is the pi variant. If you, like me, enjoy British sci-fi, then the Doctor Who variant is for you. The last two aren't "true" variants as the only difference is what's on the tiles; the next two are quite clever. If you're in the mood for a good laugh, I recommend the Numberwang! variant. (Note: If you are unfamiliar with the show That Mitchell and Webb Look, then watch the video below or else that variant won't make any sense.)

My favorite though, has to be the Fibonacci variant (via). The one thing that I don't like about that particular version of the variant is that it stops play after achieving the 2584 tile. Perhaps one of the other versions available are more like the app I have on my Android and let you keep playing (although that one might stop after the 6765 tile--not that I could do much better--although I have made the 4181 tile a handful of times). Anyhow, allow me to rewind a bit and relate a story.

I first became aware of 2048 when I saw this xkcd cartoon which I didn't understand at the time (late to the game, as usual). I soon became hooked and when I saw that the Garden State Mathematics Conference was looking for speakers, I thought that perhaps all this play wasn't a complete waste of time after all. I prepared an outline and abstract for the talk and submitted it and was approved. Then, a couple of days before my talk, I discovered the Fibonacci variant. That changed everything. How could I not make half my talk about that? So I did.

There are some key differences between the games. For one, instead of merging like numbers to get double, you merge consecutive Fibonacci numbers to get the next Fibonacci number. Except for 1, like tiles don't mesh, but each tile does have two different values that it can merge with. One needs to be a little more careful here. For example, if you're trying to merge a 13 with a 21 to get 34, you could accidentally bump into an 8 and get stuck with a pair of 21's. But don't fret it; not all is lost. If you make another 13 then hit the two 21's in sequence, you'll make a 55. Another thing to be note is that making the F₁₈ tile takes about the same amount of room as making the 2¹¹ tile does in regular 2048. (see figures below)

Set-up for the win in 2048

Similar situation for 2584

As you can see, in the Fibonacci variant, each F_n is not adjacent to the F_n-1 and F_n+1 tiles but rather to the F_n-2 and F_n+2 tiles. Also, Unlike regular 2048, for each level you don't need to repeat everything you've done, but merely to the level below. Hence the game's increase in difficulty is not as fast as the binary exponential growth of regular 2048. However, it is exponential. Can you guess what the base is? (hint: Φ)

I should note here that since I figured all this out the day before my presentation, I made a mistake. I incorrectly reasoned that since the ratio of the number of levels needed to reach each level was n(n-1)/n, that the game's difficulty would approach 2ⁿ in the limit. This didn't quite sit right with me and when I realized that that last level is the "biggest" of the levels, I recalculated to get the result below. I will be giving the same talk again in a week or two and the mistake has been corrected.

There are many to show that it approaches Φ in the limit including continued fractions (which I did). There is also a simpler way to look at it. Since the game gives you nothing but 1's (F₁ = F₂ = 1, unlike in regular 2048 where 2¹ = 2 ≠ 2² = 4), every tile is built up from 1 tiles in the quantity of the face value of the tile in question. In other words, each level's "size" is equal to its value. So the increase in the difficulty of achieving each level relative to the previous level is just the ratio of consecutive Fibonacci numbers, which we've already shown is Φ. There you have it: the difficulty of each level of the Fibonacci variant of 2048 basically increases exponentially in Φ.

WONDERFUL!

First of May!

noreply@blogger.com (The Science Pundit) — Tue, 01 May 2012 17:56:00 +0000

Warning: NSFW!

Famous Blue Raincoat

noreply@blogger.com (The Science Pundit) — Mon, 23 Apr 2012 22:47:00 +0000

Inspired by this Paul Krugman post, I give you First: the original
The cover (which, like Krugman, is how I first heard the song)

I absolutely love this song! I'm not sure if it's the haunting melody or the cryptic story, but it's awesome.

Jeffrey Sachs speaks the truth!

noreply@blogger.com (The Science Pundit) — Wed, 16 Feb 2011 20:33:00 +0000

Here's a video (you'll have to click on the word 'Here' to watch the video on YouTube, as BloombergTV has disabled embedding) from a couple of days ago of (one of my all time favorite economists) Jeffrey Sachs being interviewed on Bloomberg Television. He really hammers home the point that (many others have also made) that before we can start seeing any real progress in this country, we're going to need to go to the public financing of campaigns. Well, he didn't exactly use those words, but the case he laid out and the evidence he presented clearly support that position. I was also amused by the way he handled the question about the Laffer Curve: he answered it the way any good biologist would answer a similar question about Intelligent Design.

Happy Valentine's Day!

noreply@blogger.com (The Science Pundit) — Mon, 14 Feb 2011 06:00:00 +0000

Why celebrate Darwin Day?

noreply@blogger.com (The Science Pundit) — Sat, 12 Feb 2011 15:43:00 +0000

Why Celebrate Darwin Day? from American Humanist Association on Vimeo.

More poop Mommy; I'm hungry!

noreply@blogger.com (The Science Pundit) — Thu, 19 Aug 2010 01:23:00 +0000

A few years ago, a cousin of mine told me the story of the time she was at a public swimming pool (in Utah, I believe) when her infant son demanded to be fed. She did what came naturally: she began to breastfeed her son. This act didn't go over very well with at least one of the pool's patrons, who came over to my cousin and sneered "That's disgusting! I have young children and they don't need to see that!" My cousin mused on how curious it was that this lady wasn't bothered by her children seeing dozens of women and girls of various ages walking around the pool in scant string coverings, but a mother breastfeeding her infant was disgusting. (For the record, The Science Pundit is okay with both breastfeeding mothers and scantily string-clad bathers.)

What is or isn't disgusting is a matter of subjective opinion, but breastfeeding--or more generally, lactation--is a natural process for all mammals. Many animals don't care for their young, but those that do have evolved a variety of strategies for feeding and protecting their progeny. Lactation is the strategy that mammals have evolved for that purpose. The "most primitive" mammals, the monotremes such as the duck billed platypus, give us a clue as to how lactation might have evolved. Suckling probably started as young proto-mammals liking their mother's skin to gain moisture and nutrients from the oils and perspiration exuded from the pores. Something similar to this (but more evolved) is seen today in the platypus. The most highly developed lactators (by which I mean the most developed mammary glands) are the placental mammals (which includes we humans). The milk we feed our youngest contains not only nutrients, but antibodies to help with immunity development. I wouldn't dream of calling this disgusting.

When I think disgusting, I think of something that promotes the gag reflex, in other words: puking. This brings me to the next strategy for feeding one's young. The simplest and most obvious strategy is for the parents to go get food and put it into their offspring's mouth. This strategy is also practiced by many species of mammal during a period known as weaning. This strategy does have some shortcomings, though.

For one, it can be quite cumbersome carrying around food. Also, infants or hatchlings often need time for their digestive systems to fully develop, particularly if the animal relies on gut microbes to help digest its food. So what could be a good way for a mother or father to help its young digest food, while introducing beneficial microbes to its system, and making the journey easier? If you're thinking of vomitting, then you get a cigar (which curiously enough creates a smoke which triggers the gag reflex in some people). Personally, I think that when it comes to disgusting, regurgitation beats breastfeeding hands down.

So do we have a champion? Not by a long shot. Let's not forget that there is another way for the body to release nutrients which is intimately tied to the digestive system. I am of course speaking of excrement.

Eating excreta is a time honored tradition in the animal kingdom. The most famous coprophages are green fly larvae and the esteemed dung beetle. And some animals even eat their own droppings. Rabbits, for example, unlike their grass eating cousins the ungulates, have only one stomach and so can't adequately digest their meals in a single pass. Bugs is left with little choice but to consume his own cecotropes.

But is there an animal out there that actually craps out a partially digested meal to feed its young? Behold Ctenocephalides felis, the common cat flea!

The cat flea is the most common flea found biting pets and people. Even though there is a dog flea (Ctenocephalides canis) and human flea (Pulex irritans), the fleas you are most likely to find sucking away human or canine blood are cat fleas. So let's talk a little about our friend's life cycle.

Let's get a couple things clear. The male cat flea is a blood sucking and pooping machine (as evidenced in the picture to the left EDIT: The flea in the picture is female; thanks Christine.), and the female cat flea is a blood sucking, egg laying, and pooping machine. Adult fleas are constantly shedding eggs and doodies. The flea dingleberries naturaly outnumber the eggs since (a) only females lay eggs, and (b) the nutrition required to produce a single egg results in several berries. It is also worth noting that female fleas will lay eggs even if they haven't mated, and mated females will lay non-viable as well as viable eggs.

While adult fleas have hooked barbs on their feet and legs to keep them attached to their host (not to mention mouth parts), eggs and scat don't avail of such adhesives. So what happens is that eggs and turds drop off the animal with the largest concentration (as statistically expected) falling off where the pet spends most of its time. The viable eggs then hatch into worm like larvae, a good proportion of which will find themselves surrounded by huevos and caca. This is a veritable smorgasbord for the larvae since that is what they eat.

It seems that the larval diet shifts from primarily feeding on stools in the first stage to actively seeking out eggs and sucking out their yolks in the third. I suppose that this is an improvement since being told to go suck an egg isn't quite as insulting as being told to eat shit. But this raises the interesting question: are fleas not only blood suckers and shit eater, but also cannibals? As long as you don't consider eating non-viable eggs as cannibalism, it seems the answer is yes, but they keep it to a minimum. There is some evidence that non-viable eggs are stickier than viable eggs and so easier for a larva to latch on to, but I think that the primary explanation is one of statistics. Viable eggs hang out for a limited period of just a few days, while non-viable eggs hang around until either they're eaten or sucked up by the pet owner's vacuum cleaner (I was taught that if you have fleas, you should put moth balls in your vacuum cleaner bag. That makes sense now.)

So which is the more important part of the flea larva diet: eggs or droppings? That's the question Drs. Hsu, Hsu, and Wu looked into back in 2002. The flea larvae were divided into five groups based on diet. The MF group was fed exclusively adult male feces. The FF group was fed exclusively adult female feces. The NE group was fed exclusively non-viable eggs. The FF+NE group was fed a mix of adult female feces and non-viable eggs. And the control group PBCP group was fed exclusively porcine blood curd product (The Science Pundit hereby renames the control group "bacon eaters"). There were thirty larvae in each group, which is large enough to see patterns, but The Science Pundit (that's me) would like to see a larger more comprehensive study. The FF+NE and bacon eaters both did fairly well with 90% & 83% survival to adulthood, respectively. The MF group did a bit more poorly with a 13% survival rate, but both the FF and NE groups were completely wiped out.

I guess the lesson here is that if you're a cat flea larva you should eat shit and suck eggs, but if you can only do one, then eat your daddy's poop.

Hsu, M., Hsu, Y., & Wu, W. (2002). Consumption of flea faeces and eggs by larvae of the cat flea, Ctenocephalides felis Medical and Veterinary Entomology, 16 (4), 445-447 DOI: 10.1046/j.1365-2915.2002.00388.x

Guerrilla Cinema

noreply@blogger.com (The Science Pundit) — Wed, 18 Aug 2010 01:37:00 +0000

I've been a fan of guerrilla theatre for quite a while now. The very idea of an acting troupe showing up unexpected (and often uninvited) to a public location to do a surprise performance for their unsuspecting audience is both clever and intriguing. Seeing a performance live is even better. After the initial surprise, it's lots of fun and turns into something you'll remember.

However, up until I saw the clip below, I had never heard of it being done for cinema. The trailer below is absolutely brilliant! The plot seems mundane and ordinary enough, but it's not really the plot that makes it so great. I have to wonder how long they were able to record each scene before getting kicked out (or did they?). I would imagine that they probably rehearsed the scenes to death, then went on location and tried to shoot each scene in a single take (unless something went wrong--like getting kicked out). Obviously the bed scene was done in multiple takes since they're in different beds with practically every change in camera angle. I don't know whether that was intentional or the result of being constantly chased out by management, but either way: Bravo!

End of the sausage link line

noreply@blogger.com (The Science Pundit) — Mon, 14 Jun 2010 17:21:00 +0000

Jimmy Dean (1928-2010)

Dennis Hopper R.I.P.

noreply@blogger.com (The Science Pundit) — Sat, 29 May 2010 18:05:00 +0000

This makes me sad.

Here's a classic scene:

Roy Zimmerman house concert

noreply@blogger.com (The Science Pundit) — Thu, 27 May 2010 00:11:00 +0000

Last night my sister Lali and I went to the Roy Zimmerman house concert at the lovely home of Freethought Society president Margaret Downey. I have to give Margaret a thousand thanks for putting on such a wonderful event. The accomodations were great and Roy was fantastic. He played mostly songs from his new album Real American, many of which I was hearing for the first time. He certainly hasn't lost his touch. I think that songs like The Orange County Rolling Acres Senior Center Cannabis Club and Buddy, Can You Spare a Trillion Dollars? will be fan favorites for years to come. And of course he played several of his classics; his final encore was Defenders of Marriage, which he nailed. If you're unfamiliar with the song, here it is

After the show, we got a chance to sit around and have a conversation with Roy about politics, his music, freethinkers, and other topics. I again must thank Margaret for being such a gracious host. It was really nice. And we even got to pose with Roy for a couple of pictures.

As you can see, we're all wearing our towels (if you remember from yesterday's post, it was Towel Day). Roy was quite tickled to finally meet a couple of the people involved the collaboration video covering his song Creation Science 101 (see Roy sing it here)

Our part begins at around 1:12 and we sing the line "which means they must have been incestuous". Roy appreciated the joke, but I must confess that I am not in fact incestuous--although that will come as a shock to all of my family members that I've hit on. (For those of you who've never seen Roy play live before, he will often introduce one of his songs with the joke "I'm not gay, although that will come as a shock to several members of the audience who I've been hitting on.")

Anyway, the concert was great and if you ever get a chance to see Roy Zimmerman perform, do it!

Happy Towel Day!

noreply@blogger.com (The Science Pundit) — Tue, 25 May 2010 16:00:00 +0000

Happy Towel Day everyone!

Last night I went to see Roy Zimmerman perform and tonight I will be going again with my sister Lali. The shows are sponsored by the Freethought Society. Full report to follow tomorrow.

Air friction myths

noreply@blogger.com (The Science Pundit) — Fri, 16 Apr 2010 18:10:00 +0000

1. Drag

Ever since I was a young kid, I remember people telling me how air friction slows objects moving through the atmosphere. The problem with this claim is that it's wrong. Well, technically it's partially right: there is a friction force at play and it does have a slowing effect. The thing is that the effect of air friction is so negligible compared to what is really slowing moving objects down that it can safely be ignored in just about all cases. The claim that air friction is what slows moving objects down is akin to saying that the recoil of a rifle is due to the backward force of your finger upon the trigger.

So what is this force that really slows flying objects? It is called aerodynamic drag. When I correct people about this, I often hear the excuse that when they say air friction, that's just shorthand for aerodynamic drag. I don't buy it! Air friction exists and is quite distinct from drag. So what exactly is aerodynamic drag? I shall attempt to explain it here.

A moving object displaces air as it moves through its gaseous medium. In other words, it pushes air out of the spot where it's going and leaves emptiness in the spot where it has been. Air immediately rushes in to fill the void left behind the moving object in much the same way that air or liquid rushes to fill the vacuum within a syringe when you pull back on the plunger. Of course it takes time for this void to fill in and reach equilibrium with the surrounding air. This leaves a region—called the slipstream—of relatively low pressure behind the moving object. The farther from the moving object within the slipstream, the more air which has been replenished and the closer to equilibrium with the atmosphere that it is. Naturally, the faster an object is moving, the larger the size and lower the pressure of its slipstream.

(via)

The pressure difference between the air in front of a moving object and the air behind it creates a force upon the object that is against the direction of motion. The faster the object is moving, the stronger this force is (in fact, the force is proportional to the square of the velocity of the object). This repulsive force is what is known as aerodynamic drag.

Racers know about aerodynamic drag and are able to use it to their advantage. Drafting is the technique where a racer will move into the slipstream of another racer in order to lessen the pressure difference between fore and aft, therefore lowering the drag force resulting in energy savings for the racer.

So the next time somebody tries to tell you that flying objects are slowed down due to air friction, be sure to correct them and tell them all about aerodynamic drag.

2. Shock

A very bright meteor was recently captured on video out in the mid-west. Greg Laden pointed out how the CNN report of the event said that air friction caused the meteor to heat up. This reminded me of the old Tom Glazer/Dottie Evans song What is a Shooting Star?

A shooting star is not a star, is not a star at all.
A shooting star's a meteor that's heading for a fall.

A shooting star is not a star; why does it shine so bright?
The friction as it falls through air produces heat and light.

You might recognize this song from the cover version by They Might Be Giants on their recent album Here Comes Science. Unfortunately, the last time that TMBG covered a Tom Glazer/Dottie Evans song, they picked one with a major scientific inaccuracy.

The sun is a mass of incandescent gas,
A gigantic nuclear furnace.

They were forced to write a new song (titled Why Does The Sun Really Shine?) to correct the falsehood.

The sun is a miasma of incandescent plasma,
The sun's not simply made out of gas. No, no, no!

So will TMBG need to write a new retraction song about why a meteorite really gets hot and bright? Alas, I'm afraid that they will. Once again, air friction exists and does indeed produce heat, but is so negligible that it can be ignored. In fact, at subsonic speeds, the dominant heat exchange effect on (warmer than air) objects is wind chill. Warmer than air objects radiate heat into the surrounding air creating an insulating "blanket" around them slowing heat loss. But if the object and the surrounding air are moving relative to each other, then this layer of warm air is stripped away causing the object to radiate heat faster, ergo the familiar chilling effect. However, at supersonic speeds, a new effect comes into play.

(via)

As an object moves through the air, it displaces the air in its path by pushing it forward and aside. The air moves away from the object as a series of compression waves (similar to the waves that a boat creates as it moves through the water). Now if you remember back to science class, you'll know that compression waves have another name: sound. So what happens when the object is moving faster than the speed of sound? Aha!

What happens is that the air gets pushed forward and aside faster than it can naturally escape. As long as the object is moving slower than sound, the compression waves outrace it and take most of their energy with them. But at supersonic speeds, the air keeps getting compressed and compressed and compressed as the object pushes it forward faster than the air can get away. So similarly to the freon in a refrigerator's compressor or the fuel mixture in the cylinder of a diesel engine, the leading air gets superheated by the crushing force of the supersonic object.

Basically, the supersonic object creates its own oven by compressing the air in front of it. Furthermore, if the object is made of an oxidizable material (such as iron, aluminum, or carbon) and the air is oxygen rich (such as the earth's atmosphere), then the object may quite literally burn up.

So the next time somebody tries to tell you that air friction causes a meteorite to burn up in the atmosphere, be sure to correct them and tell them all about supersonic shock.

Puppets sing about the financial crisis

noreply@blogger.com (The Science Pundit) — Thu, 15 Apr 2010 12:07:00 +0000

From The Dylan Ratigan show. Brilliant!

Visit msnbc.com for breaking news, world news, and news about the economy

Happy Zombie Day!

noreply@blogger.com (The Science Pundit) — Sun, 04 Apr 2010 19:38:00 +0000

Simon Pegg (star and cowriter of Shaun Of The Dead) has written an interesting article delving into the debate between slow zombies and fast zombies. As expected, he takes the side of slow zombies--"Zombies don't run!" he opines--and I must agree with him. The fast zombies just aren't as scary as the traditional ones. If zombies can run and jump, what makes them unique? How are they different from other movie monsters? It's that slow, plodding, neverending approach of rotting corpses that makes zombies so creepy and scary.

Pegg brings up all these points in his essay, but he also raises one that I hadn't really thought of before: the zombie as metaphor for death.

Where their pointy-toothed cousins are all about sex and bestial savagery, the zombie trumps all by personifying our deepest fear: death. Zombies are our destiny writ large. Slow and steady in their approach, weak, clumsy, often absurd, the zombie relentlessly closes in, unstoppable, intractable.

However (and herein lies the sublime artfulness of the slow zombie), their ineptitude actually makes them avoidable, at least for a while. If you're careful, if you keep your wits about you, you can stave them off, even outstrip them - much as we strive to outstrip death. Drink less, cut out red meat, exercise, practice safe sex; these are our shotguns, our cricket bats, our farmhouses, our shopping malls. However, none of these things fully insulates us from the creeping dread that something so witless, so elemental may yet catch us unawares - the drunk driver, the cancer sleeping in the double helix, the legless ghoul dragging itself through the darkness towards our ankles.

Exactly right! And that only begins to scratch the surface of why the metaphor is perfect. This is also why the zombies must always win in the end. You can cheat death--for a while--but the horde of walking dead have time on their side. And those trying to cheat death damn well know it!

Enjoy Zombie Day by watching some good zombie movies. You owe it to yourself.

Rachel Maddow on fake outrage and lies

noreply@blogger.com (The Science Pundit) — Sat, 03 Apr 2010 15:44:00 +0000

Visit msnbc.com for breaking news, world news, and news about the economy

When Abortion was Illegal

noreply@blogger.com (The Science Pundit) — Sat, 20 Mar 2010 22:23:00 +0000

Part I:

Part II:

Part III:

(via Laci Green)

Happy Darwin Day!

noreply@blogger.com (The Science Pundit) — Sat, 13 Feb 2010 02:09:00 +0000

And if you happen to live in Broward County FLA, here's something you can do tomorrow to celebrate.

GO GREEN for Iran!

noreply@blogger.com (The Science Pundit) — Wed, 30 Dec 2009 18:24:00 +0000

This blog has officially gone green for Iran.

Happy Saturnalia!

noreply@blogger.com (The Science Pundit) — Thu, 17 Dec 2009 22:31:00 +0000

To celebrate Saturnalia, enjoy Saturn's hexagon.

Happy Birthday Rafael Darwin!

noreply@blogger.com (The Science Pundit) — Wed, 16 Dec 2009 21:20:00 +0000

Today is my nephew's 1st birthday. Go send him some love!

QualiaSoup on Dualism

noreply@blogger.com (The Science Pundit) — Sun, 13 Dec 2009 00:22:00 +0000

I'll have more to say about this later, but in the meantime, enjoy this video:

Today's APOD is just too Saturn cool!

noreply@blogger.com (The Science Pundit) — Tue, 10 Nov 2009 08:07:00 +0000

(via)

The ultimate movie monster

noreply@blogger.com (The Science Pundit) — Fri, 06 Nov 2009 20:55:00 +0000

(via Somethink Fun)