The World Wide Web is the only thing I know of whose shortened form takes three times longer to say than what it’s short for.

— Douglas Adams, The Independent on Sunday, 1999

In Spanish, it’s even worse, since each W requires four syllables with uve doble. Stephen Fry has suggested we say “wuh wuh wuh”, but that sounds like a dog barking to me.

Given the ubiquity of hypertext “web” documents, for me, it comes down to this:

The fact that you have to put the http:// before all of your web addresses anyway already tells your browser and the server and everybody that you’re looking for a hypertext document, so the “www.” is entirely superfluous!

But old habits die hard, even if they are a waste of resources. Just think of all the bandwidth we are dedicating on a daily basis to sending those four bytes to represent the “www.” across the wires!

Even Tim Berners-Lee, the creator of the whole darn thing, said back in 1999 that the WWW prefix was outdated:

Nowadays, however, the web server may be far and away the biggest service foo company has, and it might make sense to give it pride of place. Remember you can only do this with one service. You could use http://foo.com/ which is after all easier to type, even though people expect to have to type the “www”.

This issue seems even more important now that we’re in the age of Social Networking in which web links are passed around in dizzying quantities, giving rise to an entire industry of URL shortener services.

I hope that more and more companies will figure this out and buck the trend. It’s easy enough to forward a URL with “www.” to one without it, so your customers will still find you. In the mean time, you can find me at erikras.com, not www.erikras.com.

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How was this discovered? The Gregorian calendar – the one we use in modern 21st century western society – repeats itself every 400 years. Therefore, to calculate how many times the thirteenth falls on each day of the week, we only have to examine 400 years, or 4800 months. A bloke by the name of B.H. Brown did this by hand in 1933, but now we have computers. The program to do this is completely trivial once you have a calendar algorithm to follow the Gregorian calendar like all modern computer languages have built-in. Trivial or not, I couldn’t resist…let’s calculate how many times the 13th falls on each day of the week, shall we?

13th Histogram Calculator

When you click “GO!”, the calculator will start from today, January 13, 2012, and count which weekdays fall on the thirteenth of the month over the next 400 years until January 13, 2412. Here’s a hint: it goes up to 688.

GO!Reset

Exciting, huh? There was only one Friday the 13th in 2011, in May, so I've been waiting months to post this.

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This occurrence is so common that I felt it didn’t deserve much more than a tweet. What I heard a few minutes later was, ironically, exactly that, a bunch of tweeting. It is fairly common for birds to be perched on my building’s antenna at dusk, but today there were so many that they didn’t all have a place to sit. And then I saw…

Flocking birds really must be one of the most gorgeous phenomena in all of Nature. The natural ebb and flow and organic rhythm of their movement is what ballet dancers mimic on stage. Up and down and left and right, all in perfect synchronicity, and…without a choreographer!

What I love most about flocking birds is that we scientifically minded apes, using computers, have figured out just how incredibly simple an algorithm is needed to create such a seemingly complex emergent phenomenon. I know, because I wrote a program to do it. And yet, none of the beauty of said phenomenon is lost by our understanding of it.

My ability to identify birds is almost as strong as my ability to identify flowers or mushrooms or insects in that it’s pretty much non-existent, so I don’t know if these were starlings, and could thus merit the awesome term murmuration, a word which came to the attention of internauts recently with that video from Ireland. My video is not nearly as jaw-dropping as the one from Ireland, but I was certainly mesmerized as I was filming it and the several times I’ve watched it since. I just wish I’d had a less obstructed view and a better microphone to capture the whoosh! as they changed direction in an instant.

As quickly as they arrived, they departed, leaving me feeling lucky to have witnessed their momentary aerial ballet.

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After realizing that M was a showstopper, imagine my surprise when I figured out that I could write my last name, too! Radium-Samarium-Uranium-Sulfur-Selenium-Nitrogen!

At this point, I had come too far not to make little periodic table boxes with the atomic number and weight of each element to line up like Scrabble pieces. But what format to use? Periodic table boxes vary wildly, with different fonts, text alignment, and which values are included. ptable.com has a very impressive dynamic HTML periodic table, with various facts as you hover. periodictable.com went with pictures of each element. Pure substances are shiny!

Eventually I found this list of periodic table PDFs available for downloading and printing. The first one on that page is the standard one for the California Standardized Test. As soon as I saw it, I was immediately thrust back to my lab bench in Chemistry class calculating moles and reaction yields. I had my format!

So here we go…

And finally, in her highly radioactive two element glory…

I might have to make some t-shirts of my own…

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To the geometrymobile!

This is the composite photo, taken by Letian Wang in Beijing, China, on December 10, 2011, that originally sparked my interest. You can see that the radius of the Earth’s shadow is slightly greater than the Moon’s diameter.

First of all we need to define what we mean by “shadow”.

For the purposes of this post and subsequent calculations, we will only be dealing with the umbra, the dark bit where no direct sunlight hits the moon. We will be ignoring the indirect sunlight that is refracted through the Earth’s atmosphere during an eclipse, bathing the lunar surface in reddish hue.

Okay, let’s do some math!

Here we can see the relationship between the radius of the umbra to all the distances involved. Do I even have to mention that the diagram is not to scale?

If we draw two more lines, we get two congruent right triangles.

Since we know they are congruent, we know their sides are proportional and can write the following equation:

…which we can solve for the radius of the umbra:

When we plug in the values for the radii of the sun and Earth, we get:

Over time, with the two elliptical orbits involved, both the numerator and the denominator of our distance ratio vary. The ratio of the distance from the Earth to the Moon (d_moon) to the distance from the sun to the Earth (d_earth) is at its maximum when the Moon is at its apogee and the Earth is at its perigee (we are ignoring the likelihood of these two extremes coinciding, of course).

The ratio is at its minimum when the Moon is at its perigee and the Earth is at its apogee.

When we plug these back into our bigger equation, we discover that the radius of the Earth’s shadow at the distance of the moon varies from 4479 km to 4735 km, or from 2.578 to 2.725 moon radii.

To visualize this, let’s look at the minimum and maximum shadow sizes compared to the Moon.

Not a very big difference, I think you’ll agree. We did, however, answer our question.

At least now astrophotographer and artist Laurent Laveder will know the range of sizes for his hoops for his incredible lunar eclipse photography.

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The laptop was very interesting, loaded with about twenty different apps, from drawing programs to reading programs to a programming app much like the original Logo Turtle that captivated many hours of my prepubescent youth. There’s a front-facing video camera for video conferencing and a fully featured web browser. Another key feature is its durability. You can drop it off a table with no damage, and you can even use it in the rain. It won’t work actually underwater, but how many laptops do you know of that work in the rain?

It’s cool to play around with, and I’m glad I quenched my curiosity about it, but with a powerful Mac with a 30″ screen in my office, the OLPC laptop doesn’t get much attention. My secondary motivation for purchasing the laptop was to give it to my first born child as a first computer. But then her grandfather gave her a freakin’ iPad, and she loved it, so I thought the OLPC laptop would be a lost cause.

When my parents were visiting last week, I set up an old MacBook Pro of mine for my parents to check their email when I was working in my office, and Nora became fascinated with the MacBook. When her pawing at it got a little too vigorous for my liking, I told her to leave it alone. She cried that she wanted a computer, and then I remembered the OLPC laptop. I pulled it out and plugged it in to charge it up. She absolutely loved having her own computer that didn’t require a constant stream of Be Careful’s from adults. She learned how to open it (it’s not easy the first time you hold one) and turn it on. The trackpad and keyboard elude her capacity so far, but she loves pretending to be a computer user like her old man. Her playhouse was designated as her “office” and she set up a chair and desk to work in there.

My little entrepreneur in her office. She works in her pajamas, just like her old man!

The Give One Get One program ended on December 31, 2008. Now you can only make selfless – though tax deductible – donations, but I’m sure you could probably find one on eBay. Click here to donate.

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I picked up a bottle and continued shopping. At the checkout, I asked the cashier if she knew anything about this wine, and she responded that it was a great wine for the price, a good “weekday” wine, and it was the wine that her father drank with his lunch everyday.

The wine was quite good, definitely one of the highest quality/price ratios I’ve ever consumed. I won’t bore you with those bizarre adjectives wine connoisseurs use, as I’m not one. But I am a bit of a psychology connoisseur, so I would like to discuss things this winemaker did very, very right in packaging their wine.

First of all, the name is genius. It literally means “red [horse] mane”, hence the horse logo, but out of the corner of your eye, or with the movement of someone pouring you a glass, any Spaniard or wine drinker knowledgeable about Spanish wines is going to see the words Crianza and Rioja, both of which are marks of quality and their usage is highly regulated. You have to get official certification to put either word on your wine bottle. Crin Roja is neither crianza nor Rioja; it’s from a vineyard called Vinícola in Castilla La Mancha.

Secondly, you almost never see gold netting on bottles of wine in my price range. Only the very finest wines, usually reserva or gran reserva are netted. The internet tells me that this tradition originates from an intent, by rich Europeans of yore, to prevent the house staff from opening the expensive bottles in the cellar for themselves before refilling and recorking them with an inferior wine.

Why is all this important? Not only do these clever tricks make the wine sell better, but they actually make it taste better!

The industry of expensives wines is mostly all bullshit. Blind taste test after blind taste test have shown that those of us that are not wine experts (and the experts, too, to some extent) base our estimations of wine quality on subliminal and priming stimuli, with price being the primary factor. As neuroscientist Jonah Lehrer explains in his book, Proust Was a Neuroscientist,

What these wine experiments illuminate is the omnipresence of subjectivity…Our human brain has been designed to believe itself, wired so that prejudices feel like facts, opinions are indistinguishable from the actual sensation. If we think the wine is cheap, it will taste cheap. And if we think we are tasting a Grand Cru, then we will taste a Grand Cru.

Our sensations from drinking wine are interpreted by a subjective brain that is also factoring in biases and beliefs and expectations. Just like the placebo effect still works even when the patient knows they are getting a placebo, cheap wine in a fancy gold netted bottle with words that look like crianza and rioja will taste better, even if you know it’s all just clever packaging.

¡Salud!

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Today on my walk around town, when I hit “shuffle” on my iPhone, it chose a random song to play from my entire music collection, which, currently at 53 gigabytes, doesn’t even come close to fitting on my iPhone.

Of course this is a natural consequence of both higher wireless bandwidths and higher storage and retrieval capacities of enormous server farms (a.k.a. The Cloud). If your iDevice is always online with cloud computing, then the need for syncing data from your computer to your iDevice has pretty much vanished, if all the data is available on high bandwidth servers.

It’s pretty clear to me that the future revenue model of the music industry will be one of subscriptions to stream any music the subscriber desires (or to download with a small fee per track). The artists would receive a certain amount every time their song was streamed or downloaded. This is called the Open Music Model and is just what Spotify does.

For now, at least, to my mind conditioned to the current model of music ownership, iTunes Match is one of the coolest services I’ve used in a while. It’s definitely worth $24.95 of my money every November 15th.

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That’s a big girl!

I did, however, get a cute shot and anecdote from my experiment.

This is one of my attempts to capture her in dance pose, but my hand is covering her arm too much.

When I was folding up the tripod to put it away, Nora declared that she was “going to get her camera”, which turned out to be the toy phone from her playhouse. She set it up, leaning against the wall, “pressed a button” to set its imaginary camera timer, and then ran over to me to pose. “You have to be here, like this,” she’d instruct. When we were posed, I would click my tongue to simulate the shutter noise, and then she’d run over and “set up the camera” again. We did this about fifteen times. Do they make toy photography tripods? She already took her first photo with my iPhone last week.

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I did not draw this car, René van Belzen did.

If we stop to think about it – and we should, as it’s good practice – two features of the plot of our “minimum speed to keep the rear window dry given the angle, Ɵ” equation can be deduced. Firstly, when Ɵ is 90º, the minimum speed will be zero, since the rain – which we are assuming, for simplicity, is falling straight down – won’t hit it even if we are stopped. Secondly, as Ɵ approaches 0º, the minimum speed to keep the rear window dry will shoot off to infinity. Note that we shall also be ignoring near-speed-of-light Einsteinian physics, as the Newtonian model is more than sufficient for the speeds I drive. So we can picture our graph dropping down from infinity and then making its way down to the x-axis, maintaining a negative slope the entire time, until it hits 90º on the x-axis.

The time it takes the rain to fall the vertical height of our window is going to be the height divided by the terminal velocity of the rain. And the time it takes the car to move the horizontal length of our window is going to be the length divided by the velocity of the car. When those two times are equal, the car is traveling at the minimum velocity to keep the window dry.

Okay, so we have our equation, but we have too many variables. We need to find a way to write h in terms of l, and we need a rain velocity.

Simple trigonometry tells us that the tangent of the angle in a right triangle is equal to the opposite side divided by the adjacent side, so…

Thus we can replace h in our previous equation, giving us:

The length cancels out, and we get our final equation:

There are two things that I like about this. Neither the height nor length of the window really matter, just as my wife’s brain intuited instantly. The second is that of course the tangent operation is involved, since it zips off to infinity, yet calms down near the x-axis. Since we need it to zip off to positive infinity near the y-axis, it must be inverted. What I love about math and physics is just how intuitive it can become. My mathematician readers were probably already thinking about the inverse tangent function when I discussed the general shape of the data, particularly given that an angle – and thus trigonometry – was involved. Let’s continue!

Wait, before we continue, let me go off on a bit of a tangent (oh dear, trigonometry jokes are a bad sine)… After I finished writing this post and was lying in bed trying not to think about angles and hypotenuses, it occurred to me that the tangent only has to be inverted because of my arbitrary definition of where we start measuring the angle. If we define 0º as being the vector pointing straight down, the direction the rain is falling, and measure the angle away from the movement of the car, then we get a plot that starts at 0 mph at 0º and goes up to ∞ mph at 90º, just like the normal, unmodified tangent function does! But wait, this mathematical model gets even better! What happens if you increase the angle past 90º (sort of like a spoiler)? The tangent function flips back to negative infinity and comes up to 0 mph at 180º, which still accurately models the speed the car would have to travel to keep the rear window dry, since it would have to be going very fast in reverse, and then less fast as the angle approaches the vertical 180º! This is exactly the kind of real world application of a mathematical principle that is so often lacking in our education system. Anyway, I thought that was cool. Back to our regularly scheduled post…

We need a velocity for the rain. What is the terminal velocity for a rain drop? I asked the internet, and the internet said that a small drop of light stratisform rain falls at about 4.6 mph, and the largest possible drop – they can’t be bigger than 5 mm or they break up (awesome high speed video!) – from a huge thunderhead falls at up to 20 mph. We’re going for a minimum speed to guarantee a dry rear window, so we’ll use the 20 mph figure.

When we substitute 20 mph for our rain velocity and convert from radians to degrees, our final equation looks like this:

And now we’re ready to plot it! Drumroll please…

Exactly what we expected, isn’t it?

Examples

This Wolsely Hornet has a rear window angle of 57º. That means that, if it goes more than 13 mph in even the harshest thunderstorm (of absolutely vertical rain), no rain will hit its rear window. Isn’t that incredible? It seems slow to my internal physics engine.

This Peugeot 203 Limousine has a 35º rear window, so it will need to accelerate up to 28.5 mph in order to keep it dry. As you would expect, if you have a 45º window, the velocity you need to travel is 20 mph, exactly equal to the rain’s velocity.

And lastly, this Porsche has a 16º rear window, and thus it will need to zip up to 70 mph to keep dry. Obviously this will be no problem for the Porsche, but you can see how the velocities are increasing very rapidly as we approach the horizontal, due to the very nature of the tangent function.

My curiosity is satisfactorily quenched on this topic, and I hope you learned something. Math is all around us and lets us know things about the world through mere thought and some pen and paper. Isn’t that fascinating?

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