Advanced elegance

I think it's a natural human tendency to be awed by what we don't understand.

I know when I see some abstruse concept that is far beyond my grasp, I'm impressed not only by how complex the universe can be, but that there are people who can comprehend it.  I first ran into this in a big way when I was in college, and took a class called Classical Mechanics.  The topic was the mathematics of why and how objects move, how that motion affects other objects, and so on.

It was the first time in my life I had ever collided with something that regardless of my effort, I couldn't get.  The professor, Dr. Spross, was a very patient man, but his patience was up against a classical-mechanics-proof brain.  On the first exam, I scored a 19.

Percent.

And I'm convinced that he had dredged up the 19 points from somewhere so I wouldn't end up with a single-digit score.  I ended that class with a C-, which I think Dr. Spross gave me simply because he didn't want me back again the following semester, spending another four months ramming my poor physics-deficient head up against a metaphorical brick wall.

There's one memory that stands out from that experience, over forty years ago, besides the overwhelming frustration.  It was when Dr. Spross introduced the concept of the "Hamiltonian function," a mathematical framework for analyzing motion.  He seemed so excited about it.  It was, he said, an incredibly elegant way to consider velocity, acceleration, force, momentum, and so on.  So I thought, "Cool!  That sounds pretty interesting."

Following that cheerful thought was an hour and a half of thinking, "I have no fucking idea what any of this means."  It was completely opaque.  The worst part was that a number of my classmates were nodding their heads, writing stuff down, and seemed to get it with no problem.

So either I was the only complete dunderhead in the class, or they were just better at hiding their dismay than I was.

Anyhow, I think that was the moment I realized a career in research physics was not in the cards for me.

To this day, the "Hamiltonian function" remains something that in my mind symbolizes the Unknowable.  I have deep and abiding admiration for people for whom that concept makes sense (first and foremost, William Rowan Hamilton, who developed it).  And I'm sure it is elegant, just as Dr. Spross said.  But experiencing that elegance was (and probably still is) entirely beyond me.

It's this tendency to find what we can't understand awe-inspiring that has led to the idea of the God of the gaps -- in which gaps in our scientific knowledge are attributed to the incomprehensible hand of the divine.  Theologian Dietrich Bonhoeffer realized what the problem with this was, at least for people who are religious:

How wrong it is to use God as a stop-gap for the incompleteness of our knowledge.  If in fact the frontiers of knowledge are being pushed further and further back (and that is bound to be the case), then God is being pushed back with them, and is therefore continually in retreat.  We are to find God in what we know, not in what we don't know.

Anyhow, that was a long-winded preamble as an explanation of why all of this comes up in today's post.  I immediately thought of the awe-inspiring nature of what we don't understand when I read an article yesterday about two researchers at the University of Rochester, Tamar Friedmann and Carl Hagen, who found that a method for calculating the energy levels of a hydrogen atom generates the well-known number pi.

[Image is in the Public Domain]

It turns out to have something to do with a mathematical function called the Wallis product, which says that you can generate π/2 by a simple series of multiplications:

π/2 = (2/1) x (2/3) x (4/3) x (4/5) x (6/5) x (6/7) x (8/7) x (8/9)....

The pattern is that the numerators of the fractions are 2, 2, 4, 4, 6, 6, 8, 8... and the denominators 1, 3, 3, 5, 5, 7, 7, 9, 9...  And the cool thing is, the more terms you add, the closer you get to π/2.

Now, as for why this is so... well, I tried reading the explanation, and my eyes started spinning.  And I've taken lots of math courses, including calculus and differential equations, and like I said earlier, I majored in physics (as much of a mistake as that turned out to be).  But when I took a look at the paper about the energy levels of hydrogen and the Wallis product and gamma functions, I almost could hear Dr. Spross's voice, explaining it in a tone implying it would be immediately clear to a small child, or even an unusually intelligent dog.

And all of those feelings from Classical Mechanics came bubbling up to the surface.

So I'm left with being a little in awe about it all.  Somehow, even though I have no real understanding of why, the same number that I learned about in geometry class as the ratio between a circle's circumference and its diameter shows up in the energy levels of hydrogen atoms.  Predictably, I'm not inclined to attribute such correspondences to the hand of the divine, but they do seem to be (in Dr. Spross's words) "elegant."  And even if I never get much beyond that, I can still appreciate the minds of the people who can.

****************************************

Advanced elegance

I think it's a natural human tendency to be awed by what we don't understand.

I know when I see some abstruse concept that is far beyond my grasp, I'm impressed not only by how complex the universe can be, but that there are people who can comprehend it.  I first ran into this in a big way when I was in college, and took a class called Classical Mechanics.  The topic was why and how objects move, how that motion affects other objects, and so on.

It was the first time in my life I had ever collided with something that regardless of my effort, I couldn't get.  The professor, Dr. Spross, was a very patient man, but his patience was up against a classical-mechanics-proof brain.  On the first exam, I scored a 19.

Percent.

And I'm convinced that he had dredged up the 19 points from somewhere so I wouldn't end up with a single-digit score. I ended that class with a C-, which I think Dr. Spross gave me simply because he didn't want me back again the following semester, spending another four months ramming my poor physics-deficient head up against a metaphorical brick wall.

There's one memory that stands out from that experience, nearly forty years ago, besides the overwhelming frustration.  It was when Dr. Spross introduced the concept of the "Hamiltonian function," a mathematical framework for analyzing motion.  He seemed so excited about it.  It was, he said, an incredibly elegant way to consider velocity, acceleration, force, momentum, and so on.  So I thought, "Cool!  That sounds pretty interesting."

Following that cheerful thought was an hour and a half of thinking, "I have no fucking idea what any of this means."  It was completely opaque.  The worst part was that a number of my classmates were nodding their heads, writing stuff down, and seemed to get it with no problem.

So I was either the only dumb one in the class, or they were just better at hiding their dismay than I was.

Anyhow, I think that was the moment I realized a career in research physics was not in the cards for me.

To this day, the "Hamiltonian function" remains something that in my mind symbolizes the Unknowable.  I have deep and abiding admiration for people for whom that concept makes sense (first and foremost, William Rowan Hamilton, who developed it).  And I'm sure it is elegant, just as Dr. Spross said.  But experiencing that elegance was (and probably still is) entirely beyond me.

It's this tendency to find what we can't understand awe-inspiring that has led to the idea of the god of the gaps -- in which gaps in our scientific knowledge are attributed to the incomprehensible hand of the divine.  Theologian Dietrich Bonhoeffer realized what the problem with this was, at least for people who are religious:

How wrong it is to use God as a stop-gap for the incompleteness of our knowledge.  If in fact the frontiers of knowledge are being pushed further and further back (and that is bound to be the case), then God is being pushed back with them, and is therefore continually in retreat.  We are to find God in what we know, not in what we don't know.

Anyhow, that was a long-winded preamble as an explanation of why all of this comes up in today's post.  I immediately thought of the awe-inspiring nature of what we don't understand when I read an article yesterday about two researchers at the University of Rochester, Tamar Friedmann and Carl Hagen, who found that a method for calculating the energy levels of a hydrogen atom generates the well-known number pi.

[image courtesy of the Wikimedia Commons]

It turns out to have something to do with a mathematical function called the Wallis product, which says that you can generate π/2 by a simple series of multiplications:

π/2 = (2/1) x (2/3) x (4/3) x (4/5) x (6/5) x (6/7) x (8/7) x (8/9)....

The pattern is that the numerators of the fractions are 2, 2, 4, 4, 6, 6, 8, 8... and the denominators 1, 3, 3, 5, 5, 7, 7, 9, 9...  And the cool thing is, the more terms you add, the closer you get to π/2.

Now, as for why this is so... well, I tried reading the explanation, and my eyes started spinning.  And I've taken lots of math courses, including calculus and differential equations, and like I said earlier, I majored in physics (as much of a mistake as that turned out to be).  But when I took a look at the paper about the energy levels of hydrogen and the Wallis product and gamma functions, I almost could hear Dr. Spross's voice, explaining it in a tone that implies that it would be immediately clear to a small child, or even an unusually intelligent dog.

And all of those feelings from Classical Mechanics came bubbling up to the surface.

So I'm left with being a little in awe about it all.  Somehow, even though I have no real understanding of why, the same number that I learned about in geometry class as the ratio between a circle's circumference and its diameter shows up in the energy levels of hydrogen atoms.  Predictably, I'm not inclined to attribute such correspondences to the hand of the divine, but I do think they're (in Dr. Spross's words) "elegant."  And even if I never get much beyond that, I can still appreciate the minds of the people who can.

In the dark

In this line of business, it's all too common to run into something so stupid that at first, you think it's a joke.  No one, you think, no one could possibly be that gullible and/or ignorant of science.

And then you look into it, and you find that, lo and behold, (1) it's not a joke, (2) there are in fact people that gullible and ignorant, and (3) it really freakin' hurts when you do a faceplant into your computer keyboard.

This was my experience when a friend and loyal reader of Skeptophilia sent me a link a couple of days ago entitled, "NASA Confirms Earth Will Experience 15 Days of Darkness in November 2017."  This article, by one David Vanallen, appeared on the site Reflection of Mind earlier this year, and warns us that in a couple of months, we're gonna be in for some serious shit.

He doesn't put it quite that way, however.  Here's a capsule summary of what Vanallen says NASA has "confirmed:"

1. This November, Jupiter and Venus will come into "close proximity" of each other, being separated in the sky by a distance of only one degree.
2. Venus will, at that point, be shining at ten times the luminance that Jupiter is.
3. The bright light from Venus will heat Jupiter's gaseous surface, causing it to launch an "absurdly high amount of hydrogen" into space.
4. Said hydrogen will fall directly into the Sun, arriving there at precisely 2:50 AM on November 15.
5. The additional hydrogen will cause a thermonuclear detonation to occur on the Sun's surface, raising its temperature to 9,000 C, and turning the Sun's color to a "bluish shade."
6. This will cause the Sun to appear dimmer from the Earth.  
7. The effect will last until precisely 4:45 on November 30, at which point the Sun will return to normal.

That scary stuff notwithstanding, former NASA director Charles Bolden said we shouldn't be worried.  All that's going to happen, Bolden said, is a huge increase in the Earth's average temperature:

We do not expect any major effects from the Blackout event.  The only effect this event will have on Earth is an increase of 6 – 8 degrees in temperature. the polar cap will be mostly affected by this.   No one should worry much.  This event would be similar to what Alaskans experience in the winter.

Okay, now, hang on a moment.

Jupiter and Venus won't be in "close proximity."  They will just appear that way because from Earth, they'll be kind of lined up in the sky.  This is like saying that as you're standing on a beach in California watching the Sun set over the Pacific Ocean, the ocean is in danger of boiling away because it's so much closer to the Sun than it was at noon.

Furthermore, if the luminance of Venus was high enough to cause major gaseous eruptions on Jupiter, it would fry us here on Earth.  Jupiter and Venus are an average of 750 million kilometers from each other; at its farthest, Venus is 260 million kilometers from Earth.  There's this thing called the inverse-square law that shows how all of this works, but my guess is that David Vanallen never got past 8th grade physical science, so maybe he's never heard of it.

In any case, the reason Venus is brighter than Jupiter has nothing to do with its being hotter (although it is, in fact, by a large margin).  Venus is just closer to the Sun.  End of story.

[image courtesy of NASA]

As far as "absurd amounts of hydrogen" causing a thermonuclear explosion, well... the Sun is kind of one big thermonuclear explosion already.  Adding hydrogen, in however absurd amounts you like, wouldn't make much of a difference, especially given that Jupiter's radius is ten times smaller than the Sun's.  And that's the whole planet, not just some absurd hydrogen cloud it's jettisoned.

Then, the hydrogen is supposed to make the Sun heat up, which will make it dimmer, which will cause it to be dark here on Earth, which in 15 days will make the Earth's temperature rise by an amount that's four times the increase we've experienced from all of global warming put together, which will make the Arctic ice caps melt, but we shouldn't worry about it.

Because all of that is "just like Alaska in winter."

To which I just have one thing to say: What the actual fuck?

Oh, and I doubt highly that Charles Bolden, who is not only a pretty smart guy but has a B.S. in electrical engineering and a M.S. in systems management, had anything to do with any of this.

What makes me facepalm the worst about all of this is that there are dozens of sites now reprinting this story pretty much verbatim, and none of the ones I looked at added, "... and anyone who believes this must have their skull filled with dust bunnies, cobwebs, and dead insects."  All of the ones I saw were posting it because, apparently, they believe that it's true.  And one of them had been shared, tweeted, and reposted over 10,000 times.

Which just goes to show that if you append "NASA officials confirm" in front of damn near anything, you can get people to believe it.  Oh, and that reminds me: I should warn you that NASA officials have confirmed that today's solar eclipse is going to cause the Earth's magnetic poles to flip, which will mean all clocks will start running backwards, which will reverse the polarity in your DNA's quantum frequency vibrations, meaning you'll start to age backwards.  Tomorrow morning, we're all going to wake up feeling younger, stronger, and healthier, which would be cool except for the fact that it will also make our neurons run in reverse, so we'll remember the future and have no idea about the past.

I'd say "remember, you heard it here first," but the last part kind of makes that impossible.  Oh, well.   Sic transit gloria mundi.