The Epicycle

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1. Yesterday was squareday - for everybody, but it meant more to me. Yesterday was 4/25/09 – all square numbers. In a given century this’ll happen 135 days out of 36,525 about 1 in 250 days - so not that big of a deal. But for me it marked my 36^th birthday – also a square number. This was the only day in my life when this will happen. In fact, for around 1 in 400 people this will only happen once. For everyone else it will never happen. Of course, if you were born on one of the 15 square-days in ‘00 you should get at nine of these, maybe ten if you don’t smoke!
2. Oh, your birthday is all primes! Congrats. When will the special birthday come for you when your age and the year are both primes? Never. Sorry, if you were born in an odd-numbered year, you’ll turn an even age in odd years (primes must be odd), and an odd (potentially prime) age in even years.
3. What do you call the special class of numbers that individually are the difference between two consecutive square numbers? Let’s see. Let the first consecutive number be x and the second (x + 1). The difference in the squares is (x + 1)^2 – x^2 = y. Where y is one of the special class of numbers. Well, if you remember your FOIL method, y = 2x + 1. In order to ensure that both x and y are integers, the only stipulation is that y be an odd number. That’s it. All odd numbers can be created by the difference of two consecutive squares.
4. Trying to find a square-root without a calculator? Check this out this page. http://www.homeschoolmath.net/teaching/square-root-algorithm.php
5. So, some numbers have integer square roots (4, 25, 9, 36) but most have non-integer irrational number square roots. Is it possible to have a non-integer rational square root? I don’t think so. Coming back to the FOIL method, we could write an equation like: (a + x/y)* (a + x/y) = P. All of which are integers. Where a^2 < P (P is the number we’re taking the square root of); and x<y. A little manipulation gets us to:

   (P – a^2) = 2x/y + x^2/y^2
   with a little more manipulation we can get to 2xy + x^2 = Ky^2,

   Where K is some integer multiplier.
   Solving for x: x = y±√(4*y^2+4*K*y^2) = y ± 2*y*√(2*K)

   x = y(1 + 2√2K).

   Since √2 (square-root of 2) is irrational, no integer values of x,y or K will produce a rational number.

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Progressive Rock was dead by 1990. It was a nerd genre that defined my musical palette from ‘83 to ‘93 and it’s pomp and seriousness lead to its self-destructive in these last 2 decades. The 1989 release of Season’s End by Marillion tries really hard to save the genre. It’s a forgotten masterpiece of music that really sounds awful. I want to encourage you to hear it, but I’m afraid of what you’ll think of me. Let me explain.

The guitar and synth sounds are the finest 80’s cheese. The singer tries to sound like Michael Bolton but I fear his leather pants are too tight and his voice strains in unpleasant ways. But! But, the bass and drums are unbelievably tight. The music is so interesting. The lyrics are fatal – covering topics like global warming and abusive women’s prisons. And, the mix is even more fatal…in a glorious high-tech 80’s kinda way.

You will want to cringe but if you give yourself over to it, it’s quite a ride. This was the first album with a new singer. Can established bands really swap out the singer? Well, we see-hear the remaining members struggling with this question, but they work really hard at it, and in the end come up feeling pretty good about the result. The album cover reminds me of the music. It tries really hard but WTF?

Here are some highlights:

• the last half of “Easter”. The guitar solo and orchestration around it are stunning. When the group drops down into a 5/4 celebration groove – it’s goose-bump inducing.
• the title track it about global warming. You just might buy a hybrid afterwards - and this was in 1989.
• Feeling righteous and need a soundtrack? songs like Uninvited Guest and “King of Sunset Town” will have you punching the air with pleasurable indignation. The bass and drums stabs are off-beat, skillful, and memorable.
• The final track, “The Space…” with its haunting synth-strings is what synth-strings were made for.

Please listen to the whole album on headphones because a) the depth of the mix should be listened to loud to be appreciated, and b) you don’t want people to hear you listening to this pompous 80’s event. If they do hear it, tell them you were listtening to it for historical reasons: it’s 20 years old, and it’s the last great progressive rock album.

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Long ago, when I started this blog, I wanted to release some new clock designs. I was motivated by the TokyoFlash approaches, and wanted to come up with some based on epicyclic movement. Why would one bother? Longer ago, I had difficulty reading an ‘analog’ clock. I was a child of the digital age, and preferred to the red blocky LEDs that simply spelled it out. I still find the hour and minute hand confusing sometime – squinting across the room – it’s easy to confuse the two hands.

So, in this first installment, I show the simplest design. It’s so simple that it may be deceiving how to read it. There is no hour hand. Instead the face of the clock moves to follow the minute hand. The minute hand is the most important anyway, right. Chances are when you look at a clock, you already know the hour, and you simply want to know the minute. In this clock (yes, I realize I need a better design – any offers?), the hour is indicated by the last number the minute hand passed. Get it? You can also download a Vista Gadget of this clock (remove the .zip from the end when you save), but it requires you to also install the following XAML extension: Windows Sidebar Styler.

Finally, I really would like a second hand to show some movement so that you know that the clock is working. So, in this modification, I’ve added an outer dial to show the seconds. The dial moves backwards and the exact second is indicated by the minute hand as well. In this way, your eyes need only go to where the minute hand is pointing to determine hour, minute, and second. Here’s the Vista Gadget for this one (again remove the .zip from the end when you save) (don’t forget the sidebar styler extension as well).

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There are only a few magazines I read so thoroughly that I run out of articles before the replacement shows up on the newsstand, but Newsweek is one of them. The last page alternately written by Anna Quindlen and George Will is a favorite. While Ms. Quindlen is a superior writer (I’d kill for that clarity and flow in writing), I usually find George Will’s perspective refreshing and enlightnening.

However, this weeks foray into the interdependence of our economy as constrained by all other world economies misses the mark for me on one key issue. The anecdote of a wooden pencil being the product of four distinct parts that are based on raw material from four regions of the world is cute and awe-inspring, but it doesn’t happen the way Will and the economists he endorses say it does. He states, “goods … result from innumerable human actions but not from any human design”

Really?! All the artifacts around us just happen out of “emergent behavior”? You are missing a very important player in this – the designers – both the engineers and the industrial. Without them, the pencil would not exist. Perhaps this isn’t of interest to these pundits and economists, but we shouldn’t forget that inventor spirit. It’s what made this country great. Seriously, that sounds corny, but I’ll go further and say it wasn’t freedom of religion, or a “perfect” democracy, but the inventions that Americans bore. These inventions went on to change infrastructure, create jobs, and a quality of life beyond what is percievable by only examinig such economics. In the current crisis, we have shouldn’t forget this. Plus a career inventing things would be pretty damn fulfilling.

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A few weeks ago, I finally got around to watching “The Inconvenient Truth.” The next day the Wired magazine showed up with a special on cutting carbon. How could we have been stupid for so long? Well, the following equation is just so damn easy on this planet:

_C_nH_m + _O₂ = _CO₂ + _H₂O + energy…………………….(1)

It’s the combustion equation. We use it solely to produce the energy (Gibbs free energy) that comes out of the right hand side. You do this when you throw logs on your campfire, when you throw coal in your potbelly stove, and when you put globs of Texas Tea in your Horseless Carriage. It’s even what happens in your lungs. All we wanted was the energy but when you examine the other terms you see the problem. The left side wants some hydrocarbon (with various m’s and n’s that produces dollars and wars in the Middle East) and the right side produces carbon dioxide – that’s the gaseous carbon causing all the problems. If you want to get technical, there’s a host of other chemical reactions that are also in there. Nothing we can do about the equation. It’s not inherently evil. It’s just that we’ve done it 10⁴⁰ times in the last 5000 years.

Therefore, what we need to do is create other machines that perform other chemical conversions to offset the problems this one has caused - and run those machines 24-7 to set things right. One of the more popular ideas is to fuel cells to create energy instead. This is done by:

_H₂ + _O₂ = _H₂O + energy …………………….(2)
This is what futurists call the hydrogen economy. But where the heck are we going to get hydrogen in bulk quantities?

In order to do either of these energy producing equations when we want where we want, we should seek to build plants or devices that do the reverse. Unfortunately, doing the reverse will require energy. So these things will have to be solar powered. Somehow, we need to do this: energy + _CO₂ + substrate = _O₂ + carbon filled substrate…………………….(3)

It seems a couple people have had similar ideas in recent years. Perhaps the best one is Nobel Prize winner Dr. G.A. Olah and the Methanol Institute approach to make methanol from carbon dioxide and hydrogen. But still, where do we get the hydrogen? The most tried and true way is simple electrolysis.
energy + 2*H₂O = O₂ + 2*H₂ …………………….(4)

That’s just zapping water with electricity.

Anyway, my idea is to set up household machines. Machines for every rooftop in the nation (in the world), which just toil away at the latter two equations whenever the sun is shining. The hardest one is the third equation. But perhaps, we could use carbon nanotubes or the like with billions of activation centers to reach out and grab the carbon dioxide and add the carbon to itself. I don’t know if it’ll work. In the meantime, plant a tree. Plant life does the 3^rd equation one pretty well.

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Last night I saw Return to Forever in concert. The opening date of their first tour in 25 years. Their nervousness and the crowd’s anticipation nearly stifled their astounding performance. But I must say, it was quite a thrill. Afterwards, I overheard fans fantasizing about seeing reunions of other jazz-fusion supergroups of that same era - Weather Report and Mahavishnu Orchestra. Thinking of that triumvirate lead me to this most dorky of all analogies. Return to Forever is to Microsoft as Mahavishnu is to Mac as Weather Report is to Linux. Let me explain.

Return to Forever is the least rebellious (some would say least cool). Their products are often overly complex and that sometimes complicates the central goal. Some product features are added to great effect others not so much (Hello Again?).

Mahavishnu Orchestra on the other hand consistently put out lethally brilliant pieces that appealed to hip rockers. It was, however, ruled by an overcontrolling tyrant.

Finally, Weather Report started out with creations that were free. It had a huge roster of brilliant but forgettable players that didn’t stick around for long. They had a slow evolution from eclectic pieces to more commercial stuff that, in the end, consistently missed opportunities to be truly innovative. And maybe Jaco is Google! Taking the group towards its cohesive peak and later breaking off to develop his own successful (and better) material.

Well that was fun, but I don’t suppose we’ll be hearing Celestial Terrestrial Commuters in an Itunes commercial anytime soon.

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This is a repost from two years ago. That post had become inundated with splogger comments, so I’m reposting it. I’ve taken the liberties (or perhaps you view it as an injustice if you are the original author) to rewrite a puzzle I once heard. I can find no reference to it online, so here goes.
Tale of the Diseased Monks
One Sunday evening after working in the fields, the secluded monks of the Kaetorsian order gathered for evening prayers. After the usual somber songs and pious prayers, the high priest said, “I have a grave announcement. It appears a horrible disease has fallen on our community this fine spring day. I know this because the disease results in a purple spot on your forehead, and I can see that some of you have this. From what I know of this most evil disease - you will remain unharmed for 14 days. After which, the disease will spread to others, and you will experience a most painful passing that may last months. If we are not careful, this disease will completely destroy our peaceful monastery. Therefore, I ask that those of you who have this spot to please remove yourself from our community immediately. I pray (for my sake!) that this matter will be resolved before these two weeks are over. Despite the fact that all of you have taken a vow of silence, and a vow of humility, and thus will not be able to inform one another of the forehead spot, and even though we lack mirrors and the lake is choppy and you are unable to see for yourself whether you have this spot, you are all trained highly in the ways of logic and will be able to deduce on your own whether or not you have become infected. In this way, we will carry on as we always have: working solitarily all morning and congregating here every evening to share in this holy life. Some of you would prefer that I simply point out those of you who are diseased and while I have not taken the vow of silence that you have taken, my vow of humility prevents me from calling attention to your dysfunctions. Good night”
The next few days passed as they always have. The monks that had been infected seemed as good natured as the others, and no one treated one another any differently. However, after more than a week, as the two week deadline approached, an air of nervousness crept in. The second Saturday after the high priest’s announcement was particularly tense. The next day marked the two week deadline before the disease was to spread again, and the diseased monks were still working and praying along side the healthy ones. After the congregation disbanded from the Saturday evening prayers, the monks returned to their private quarters. On Sunday, two weeks after the high priest announcement, all of the diseased monks were gone. Through their highly tuned logic skills, they were able to determine that they had been affected and sacrificed themselves for the good of the monastery.

How many monks were infected (the actual number, please)? And how did they determine it?

My only hint is the following. What would you notice if you were the only one infected?

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