I attended a very interesting lecture by Fr. George Coyne, Director Emeritus of The Vatican Observatory, entitled The Fertile Universe. While I was listening and watching, I wrote, as is my wont, a joke.

“ He showed a beautiful slide on the screen of the Universe taken by the Hubble Space Telescope. As I stared at it, I saw a very interesting and heretofore unreported anisotropy in the distribution of galaxies. I whipped out my Blackberry and started texting my bulletin to the International Astronomical Union when I realized that it was just because I was sitting way off to the side.”

As my dear and wise friend Dr. V.V. Raman observed, there is truth beneath that quip.

I think that's why I love optical, sound, and word illusions so much. They’re so humbling. Whenever a learned lecturer waxes emphatic, there is this innate cynicism that boils up within me which threatens to spoil the illusion. I love reading about all the cosmological conjurings of dark matter and energy, star life-cycles, distribution of galaxies in the Universe and am astonished at how far we can get based on just a few assumptions. If these assumptions are not correct, everything unravels. Hubble's law is one example. The farther away an object is, the faster it is moving with respect to us, and hence further Doppler-shifted (changed in color) are the familiar spectral lines of familiar elements. If they’re moving away, it’s called a red shift, as the colors appear redder than if there was no relative motion. Conversely, we can determine the distance to an object by measuring this shift with the simplest of spectrometers. Did you know that early on we didn't know whether quasars were very near or very far? I mean that’s a pretty big uncertainty! Very far in Astronomy is really really far. Like 10 Billion lightyears or 5,8000,000,000,000,000,000,000 miles (I think that’s like a bazillion). They had huge Doppler shifts indicating a great distance, yet still appeared so bright as to outshine entire galaxies. How can they appear so bright and be so far away? Maybe Hubble’s Law must be suspended in their case. They’ve found a loophole. Maybe they’re really close but are moving at immense speeds, disproportionate to our previous notion of the relation between relative velocity and distance. Or maybe the red shift is due to a completely different phenomenon and has nothing to do with relative motion and therefore nothing to do with distance. Or maybe Hubble’s Law needs either major renovation or the ‘ole Heave Ho! So, are they really really close and that’s why they’re so bright, or are they really really bright and really really very far away as indicated by their spectral shift? There are so many assumptions that need to be made to choose which is true. All we can do is take a poll amongst the various theories and see which explains the most, not all, mind you, but just the most. These days, we choose the latter- They’re very very far away and very very bright. But who knows. Maybe that will change some day. Our ideas about the Universe are so tenuous. Terms like Quasar (quasi-stellar), dark matter, all keep us honest by reminding us of how uncomfortable we are with our ideas and how willing we are to change our views as new data is gathered. This characterizes the Scientific Method more than the equations themselves.

Scientists often seem to jump to conclusions. In reality, we 'jump' because it's far better than to stagnate with skepticism and never know where our line of reasoning will lead.

Isn’t thinking wonderful!?

## Sunday, February 22, 2009

## Sunday, February 15, 2009

### The Modest 3-4-5 Triangle

I was watching a deck being built. That’s how this all started. If you remember any geometry, you might remember the 3-4-5 triangle. It turns out that if the ratios of the sides of a triangle are 3:4:5, it will be a right triangle. In other words, the sides can be 3,4,5 inches, 3,4,5 feet, 3,4,5 furlongs, 6,8,10 furlongs, 6,8,10 feet, or any multiple. I mean, it could even be a 6 inch dachshund, an 8 inch dachshund and a 10 inch dachshund. If this is true, then one of its internal angles will be exactly 90 degrees. How can this be? If you take three anythings, whose lengths are related by 3:4:5, and put them together to form a triangle they will automatically make a perfect right triangle, perfect! In other words, one of the angles will be 90 degrees, exactly 90 degrees! What the heck do 3,4,5 and 90 degrees have to do with each other, I ask you?

How did this triangle get so smart? I will not attempt to answer for I will be lured into a world with which I do not want to associate. - The Occult. As a matter of fact, I don’t WANT to know how this can be. I just know it is, and it’s as close to a religion as a guy can get. As a matter of fact, the secret society The Pythagoreans, who believed in the sanctity of whole numbers must have revered the 3:4:5 triangle. But don’t get them started on the 1:1:? triangle. That bad boy has a third side that’s not a whole number. Now, a 1:1:? triangle is half of a square with the ? side the diagonal of the square. A square is a beautiful thing, being all square and all. Matter of fact, the Pathagorean motto was, “Be There AND be Square.” A guy, a Pathagorean, was killed accidentally on purpose after discovering this ugly not a whole number number inside the Holy Square and then blabbing all over Greece that the number wasn’t even rational. It was The Ugly of Uglies. It was the square root of two. It was supposed to be a secret. I think that sealed his fate.

Want to hear a cool way of using the 3-4-5 triangle? No? Too bad. Suppose you’re building a deck (yes, THAT deck) on the back of your house. You make a rectangular area by taking three 2 x 10’s toenailing them to a ledger board on the side of the house and then to each other. Now, how can you make them square? They wobble all over making every sort of parallelogram except the one you want, a nice rectangle. You can’t use a little dinky carpenter’s square- the sides aren’t long enough to give you an accurate set. Here’s what you do. Mark one joist 3 feet from the corner, mark the adjacent one 4 feet from the corner. Then take a 2 x 4, drive a nail in one end, measure 5 feet and drive another nail in. Now drive one of the nails clear through and into one of the joists at the 3 foot mark. Now, wiggle the whole thing until the second nail strikes the second joist exactly at the 4 foot mark. What do you have? A 3-4-5 triangle. That means the angle between the two joists is exactly 90 degrees and the three joists defining the perimeter of the deck is now a nice rectangle! I LOVE that.

I know smarty-pants topologists call this child’s play, but it doesn’t prevent me from being mesmerized by it all. Just the thought that this is true throughout the Euclidean Cosmos is awesome. Now, you might think it depends on us using the base 10 number system, supposedly originating from the fact that we have 10 fingers. Well, that’s not exactly true. As long as you use a base 6 or above, the ratio will still look like 3:4:5. Any lower than that and you’re in trouble because of carrying and the numbers look odd. From this, it follows that we are NOT the only intelligent life in the Universe and they all have more than 5 fingers! Sagan and Drake! Jealous? Q E freekin’ D.

How did this triangle get so smart? I will not attempt to answer for I will be lured into a world with which I do not want to associate. - The Occult. As a matter of fact, I don’t WANT to know how this can be. I just know it is, and it’s as close to a religion as a guy can get. As a matter of fact, the secret society The Pythagoreans, who believed in the sanctity of whole numbers must have revered the 3:4:5 triangle. But don’t get them started on the 1:1:? triangle. That bad boy has a third side that’s not a whole number. Now, a 1:1:? triangle is half of a square with the ? side the diagonal of the square. A square is a beautiful thing, being all square and all. Matter of fact, the Pathagorean motto was, “Be There AND be Square.” A guy, a Pathagorean, was killed accidentally on purpose after discovering this ugly not a whole number number inside the Holy Square and then blabbing all over Greece that the number wasn’t even rational. It was The Ugly of Uglies. It was the square root of two. It was supposed to be a secret. I think that sealed his fate.

Want to hear a cool way of using the 3-4-5 triangle? No? Too bad. Suppose you’re building a deck (yes, THAT deck) on the back of your house. You make a rectangular area by taking three 2 x 10’s toenailing them to a ledger board on the side of the house and then to each other. Now, how can you make them square? They wobble all over making every sort of parallelogram except the one you want, a nice rectangle. You can’t use a little dinky carpenter’s square- the sides aren’t long enough to give you an accurate set. Here’s what you do. Mark one joist 3 feet from the corner, mark the adjacent one 4 feet from the corner. Then take a 2 x 4, drive a nail in one end, measure 5 feet and drive another nail in. Now drive one of the nails clear through and into one of the joists at the 3 foot mark. Now, wiggle the whole thing until the second nail strikes the second joist exactly at the 4 foot mark. What do you have? A 3-4-5 triangle. That means the angle between the two joists is exactly 90 degrees and the three joists defining the perimeter of the deck is now a nice rectangle! I LOVE that.

I know smarty-pants topologists call this child’s play, but it doesn’t prevent me from being mesmerized by it all. Just the thought that this is true throughout the Euclidean Cosmos is awesome. Now, you might think it depends on us using the base 10 number system, supposedly originating from the fact that we have 10 fingers. Well, that’s not exactly true. As long as you use a base 6 or above, the ratio will still look like 3:4:5. Any lower than that and you’re in trouble because of carrying and the numbers look odd. From this, it follows that we are NOT the only intelligent life in the Universe and they all have more than 5 fingers! Sagan and Drake! Jealous? Q E freekin’ D.

### The Underwhelming Celestial Event

Feb 9,2009

Last night, the Sun, Moon and Earth were aligned in such a way that the sunlight illuminating the Moon was blocked by the Earth. But this shadow, tonight, is very ill-defined. It’s so ethereal that I had to use my imagination to conjure up any evidence of the event. It is so subtle that I thought I saw some difference in the appearance of the Moon when, in fact, due to a very small error in my computations, I was looking on the wrong night.

The next night, which was the correct time to look for the event, I thought I detected that the top of the Moon was not as brightly illuminated as the bottom. But the topography of the top is different than the bottom, so even now, I have second thoughts as to whether or not I was observing the event. The Moon was low, as well, obscured by tree limbs and the atmosphere. My wonderful computer program, Starry Night, recreated the event for me, showed me the subtlety of the effects and convinced me, finally, that I was indeed seeing this underwhelming phenomenon, a Lunar Penumbral Eclipse, a much fancier sounding name than befits the event itself. I’ve actually renamed this phenomenon. I think Subliminal Lunar Penumbral Eclipse is more apt.

But the experience was as vivid as the phenomenon was subtle. I enjoyed the idea that I was looking up at the sky, just as the Sun, Moon and Earth were in alignment. Nevermind that ninety-nine percent of the experience was mental. It doesn’t matter. Our experiences only exist through the wonder of self-awareness. Our realities and fantasies are simply neurons and chemical reactions. It’s depressing, really, and I don’t want to talk about it any more.

Last night, the Sun, Moon and Earth were aligned in such a way that the sunlight illuminating the Moon was blocked by the Earth. But this shadow, tonight, is very ill-defined. It’s so ethereal that I had to use my imagination to conjure up any evidence of the event. It is so subtle that I thought I saw some difference in the appearance of the Moon when, in fact, due to a very small error in my computations, I was looking on the wrong night.

The next night, which was the correct time to look for the event, I thought I detected that the top of the Moon was not as brightly illuminated as the bottom. But the topography of the top is different than the bottom, so even now, I have second thoughts as to whether or not I was observing the event. The Moon was low, as well, obscured by tree limbs and the atmosphere. My wonderful computer program, Starry Night, recreated the event for me, showed me the subtlety of the effects and convinced me, finally, that I was indeed seeing this underwhelming phenomenon, a Lunar Penumbral Eclipse, a much fancier sounding name than befits the event itself. I’ve actually renamed this phenomenon. I think Subliminal Lunar Penumbral Eclipse is more apt.

But the experience was as vivid as the phenomenon was subtle. I enjoyed the idea that I was looking up at the sky, just as the Sun, Moon and Earth were in alignment. Nevermind that ninety-nine percent of the experience was mental. It doesn’t matter. Our experiences only exist through the wonder of self-awareness. Our realities and fantasies are simply neurons and chemical reactions. It’s depressing, really, and I don’t want to talk about it any more.

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