## Metaphors for Our Times. #8

“Just the place for a Snark!” the Bellman cried,
As he landed his crew with care;
Supporting each man on the top of the tide
By a finger entwined in his hair.

“Just the place for a Snark! I have said it twice:
That alone should encourage the crew.
Just the place for a Snark! I have said it thrice:
What I tell you three times is true.”

—Lewis Carroll, The Hunting of the Snark (1876), Fit the First: The Landing

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## Metaphors for Our Times. #7

Mildred sat a moment and then, seeing that Montag was still in the doorway, clapped her hands. “Let’s talk politics, to please Guy!”

“Sounds fine,” said Mrs. Bowles. “I voted last election, same as everyone, and I laid it on the line for President Noble. I think he’s one of the nicest looking men ever became president.”

“Oh, but the man they ran against him!”

“He wasn’t much, was he? Kind of small and homely and he didn’t shave too close or comb his hair very well.”

“What possessed the ‘Outs’ to run him? You just don’t go running a little short man like that against a tall man. Besides—he mumbled. Half the time I couldn’t hear a word he said. And the words I did hear I didn’t understand!”

“Fat, too, and didn’t dress to hide it. No wonder the landslide was for Winston Noble. Even their names helped. Compare Winston Noble to Hubert Hoag for ten seconds and you can almost figure the results.”

“Damn it!” cried Montag. “What do you know about Hoag and Noble!”

“Why, they were right in that parlor wall, not six months ago. One was always picking his nose; it drove me wild.”

“Well, Mr. Montag,” said Mrs. Phelps, “do you want us to vote for a man like that?”

—Ray Bradbury, Fahrenheit 451, p. 93 (1951)

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## Metaphors for Our Times. #6

You could feel the war getting ready in the sky that night. The way the clouds moved aside and came back, and the way the stars looked, a million of them swimming between the clouds, like the enemy disks, and the feeling that the sky might fall upon the city and turn it to chalk dust, and the moon go up in red fire, that was how the night felt.

—Ray Bradbury, Fahrenheit 451, p. 88 (1951)

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## Metaphors for Our Times. #5

The old man nodded. “Those who don’t build must burn. It’s as old as history and juvenile delinquents.”

—Ray Bradbury, Fahrenheit 451, p. 85 (1951)

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## Metaphors for Our Times. #4

“Remember, the firemen are rarely necessary. The public itself stopped reading of its own accord. You firemen provide a circus now and then at which buildings are set off and crowds gather for the pretty blaze, but it’s a small sideshow indeed, and hardly necessary to keep things in line. So few want to be rebels anymore. And out of those few, most, like myself, scare easily.”

—Ray Bradbury, Fahrenheit 451, p. 83 (1951)

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## Metaphors for Our Times. #3

“Mr. Montag, you are looking at a coward. I saw the way things were going, a long time back. I said nothing. I’m one of the innocents who could have spoken up and out when no one would listen to the ‘guilty,’ but I did not speak and thus became guilty myself. And when finally they set the structure to burn the books, using the firemen, I grunted a few times and subsided, for there were no others grunting or yelling with me, by then. Now, it’s too late.”

—Ray Bradbury, Fahrenheit 451, p. 78 (1951)

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## Metaphors for Our Times. #2

He could hear Beatty’s voice. “Sit down, Montag. Watch. Delicately, like the petals of a flower. Light the first page, light the second page. Each becomes a black butterfly. Beautiful, eh? Light the third page, from the second and so on, chain-smoking, chapter by chapter, all the silly things the words mean, all the false promises, all the secondhand notions and time-worn philosophies.” There sat Beatty, perspiring gently, the floor littered with swarms of black moths that had died in a single storm.

—Ray Bradbury, Fahrenheit 451, p. 72 (1951)

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## Metaphors for Our Times. #1

“Let me alone,” said Mildred. “I didn’t do anything.”

“Let you alone! That’s all very well, but how can I leave myself alone? We need not to be let alone. We need to be really bothered once in a while. How long is it since you were really bothered? About something important, about something real?”

—Ray Bradbury, Fahrenheit 451, p. 49 (1951)

·

## This is America

This is America.

Republican politicians cynically abandon every American value, values we the people—some of us—hold dear. You who voted for Donald Trump and for other high-office Republicans: you are lost, only half a step behind your callous leaders, none of whom give a damn about you.

You voted into the highest office in the land a misogynist bigot and con man, an ignorant billionaire and narcissistic pig who spent his entire life crushing people just like you, without a second’s thought.

You excuse yourself for voting for this monster, for inflicting this hideous thing on our country. You tell yourself that it’s okay because you are mad at … at … you can’t legitimately articulate what you are mad at or why, can you? You excuse yourself, but you have fooled nobody—not even yourself. Somewhere inside, you know that you have done something terrible.

You make me sick.

Look at who you have become, what you have abandoned. Look at it, and remember, over the coming weeks and months and years. Your thoughtless action identifies you with Trump, the vile putridity that he stands for, that the Republicans stand for, and has put you as far from this, our America, as is humanly possible. You own this. Read, and be ashamed for what you have done, for what you chose, for what you have become. Because this is America, and you are no longer a part of it:

Not like the brazen giant of Greek fame,
With conquering limbs astride from land to land;
Here at our sea-washed, sunset gates shall stand
A mighty woman with a torch, whose flame
Is the imprisoned lightning, and her name
Mother of Exiles. From her beacon-hand
Glows world-wide welcome; her mild eyes command
The air-bridged harbor that twin cities frame.

“Keep, ancient lands, your storied pomp!” cries she
Your huddled masses yearning to breathe free,
The wretched refuse of your teeming shore.
Send these, the homeless, tempest-tost to me,
I lift my lamp beside the golden door!”

–Emma Lazarus, 1883

## Thor’s Day Morning Mathematical Musings

1. Can you completely mix a mug of coffee, such that, at every point inside the mug, the coffee at that point is different after stirring from before stirring? Go get a cup of joe (or tea), stir it, and see what you think.
Answer: no. There will always be at least one point that is the same after the liquid has settled, no matter how vigorously you stir it. It is mathematically impossible for there to be no such points inside the mug.
2. Do there exist on the surface of the Earth, at any given time, two antipodal points that have exactly the same surface temperature?

Answer: yes. What about two antipodal points that have exactly the same barometric pressure? Also yes. Two antipodal points that have exactly the same surface temperature and exactly the same barometric pressure? Yet again, yes. This is mathematically inescapable.‌

At any time there exists a continuous curve on the Earth’s surface on which every point has an antipodal point that also lies on the curve and that has the same temperature. There is a different continuous curve on which antipodal points have the same pressure. And the two curves must intersect, since both encircle the globe, each separating it into two pieces. So that means there must be, at any time, at least one pair of antipodal points somewhere on the surface of the Earth that have the same temperature and the same pressure.

You’ve probably surmised by now—you drank that cup of joe, right?—that this is true not just for temperature and pressure but for any two continuously variable parameters (such as temperature, pressure, humidity, wind speed, solar and terrestrial radiation, cloud ceiling, particulate density, atmospheric composition, and so on). You would be correct.
3. Think of a multi-digit positive integer. Any such number will do—for example, $76.$ Now add up its digits and subtract that sum from the original number. $76\,- (7+6) = 63.$ Now apply this algorithm to the new number: $63\,- (6+3) = 54.$ Keep doing this until the resulting number has shrunk to just one digit. $54\,- (5+4) = 45$, $\dots, 18\,- (1+8) = 9.$

Ta da! (Yes, really.) No matter your starting number (as long as it has more than one digit), you will always end up at $9$.

Here is a quick and dirty python program that performs this task for any positive integer, returning the end result (which had better be nine!) and the number of iterations it took to get there:

def digi9(n):
count = 0
while True:
k = sum(list(map(int,','.join(str(n)).split(','))))
m = n - k
if len(str(m)) == 1:
return m, count+1
n = m
count += 1

Let’s consider an example:

>>> digi9(72459075)
(9,2191634)

Starting with the randomly chosen number $72,459,075$, over two million iterations later we indeed end at $\dots, 27\,-(2+7) = 18,$ $18\,- (1+8) = 9.$

How are the answers to these little puzzles so? Welcome to the world of fixed point theorems! In mathematics, a fixed point is a member of a set such that an operation on the set at that point maps back to the point. The set can be anything—the set of integers, a Euclidean line, surface, or volume, etc. This concept has wide application and profound consequences in many branches of mathematics. The above puzzles are examples of fixed points in their respective sets. Put that in your mug and stir it!

Now go get some more coffee.

#### Show Me!

Suppose we have a function $f(x)$ such that $f(x) \in [a,b]~~\forall~x \in [a,b]$. That is, the function maps back to its domain. Then $f(x)$ has a fixed point $f(c) = c$ somewhere in the closed interval $a \le c \le b$.

Why? Well, it must be true that

$$f(a) \ge a~~~ \mathrm{and} ~~~f(b) \le b \label{condition}$$

The intermediate value theorem says that if a function $f(x)$ is continuous on a closed interval $[a,b]$, then, for a given $c$ such that $f(a) \le c \le f(b)$, there must exist at least one value $x_0 \in [a,b]$ such that $f(x_0) = c.$

Since the range of our function is restricted to its domain, $f([a,b]) \in [a,b]$, we have from eq. \eqref{condition} that $f(a)-a \ge 0$ and $f(b)-b \le 0.$ If we define $g(x) \equiv f(x)-x$, this is $g(a) \ge 0 \ge g(b).$ By the intermediate value theorem there must then exist a value $c \in [a,b]$ such that $g(c) = 0$. Hence, there must exist at least one fixed point, $f(c) = c.$

This—or, rather, its generalization to any Euclidean space—is essentially a statement of the Brouwer fixed point theorem:

Every continuous function from a closed ball of a Euclidean space into itself has a fixed point.

Legend has it that Brouwer was lead to his theorem by pondering the surface of a cup of coffee upon stirring in a lump of sugar. (That someone would debase a good cup of coffee with sugar is a wholly different issue.)

Vsauce has an interesting video about fixed points, from which I stole the three examples above:

## Quintessence

Because, now and then, for the well being of your soul, you have to evict the empty diversions, addictive distractions, the noisome bile, and ponder, in the brief space exhumed by an image, a note of music, a spiraling leaf, a stranger’s touch, a kindness, a child’s wonder, or Earthshine married to sliverous Moon, in this volume of relief, this anomalous bliss, this sudden expanse of silence—how is it that we, somehow, have willingly mongered purposeful calm for mindless glitter, mere noise?—and reflect on the inverse of nothing.

## How to Move the BOINC Data Directory (Linux)

Move your Linux machine’s BOINC data directory like this:

1. sudo service boinc-client stop
2. sudo mv /var/lib/boinc-client/* /path_to_new_dir/boinc-client/
3. sudo rm -rf /var/lib/boinc-client
4. sudo ln -s /path_to_new_dir/boinc-client /var/lib/boinc-client
5. sudo service boinc-client start

Works like a charm.

## Thursday Morning

Windows wide,

birds chirping front and back,

Tchaikovsky’s Fourth Symphony

fills the house.

Life could be worse.

## Passage

Rest in peace, Suki.

Littlest Kitty, Squirt, faithful companion.

Shoulder rider, lap sitter, mouse catcher, jumper.

Lover of chin scritches and forehead scritches and string cheese and pizza sauce.

Head butter, snuggler, blinds cord chewer, prancer.

Fearless imperious disdainer of the Dread Great Vacuum Monster.

Heater hog.

Conqueror of Puffs.

The sweetest kitty.

April 2002 – 28 April 2016.

## When I am at my desk, preparing for tonight’s observing. And it is evening.

Notes to self, part 437.

1. When I am at my desk, preparing for tonight’s observing.
1. And it is evening.
2. If an email arrives from the satellite tracking app, you could open it.
1. Be aware that this alert is for tonight.
2. You did bring clothing for the weather, right?
1. Not that it matters. You don’t pay attention to these things.
2. Maybe you should.
3. Come to think of it, you do recall thinking, this morning, that you could get away with not paying attention today, since you figured you’d be inside anyway.
1. Running late, you were in a hurry.
2. And you are lazy, when possible: it makes life more efficient.
3. You bring your digital camera with you to the Observatory, because you never know what will demand photos on any given day.
1. Or night.
2. Mountain weather dances, flits, pirouettes.
1. Cloud formations tend to be awesome.
2. Atmospheric effects abound.
3. Evanescent.
4. Most, even in such a wondrous, sky-dance land, never look up.
1. Is the mundaneness of our daily routines so important? That we must concentrate our gaze, glazed, on the mud of our feet?
2. This is a great sadness.
4. According to the alert, the International Space Station is due to pass overhead.
1. Tonight.
2. It is an especially good pass:
1. For once, its path will track straight overhead.
2. For once, it will largely miss the Earth’s shadow.
1. This means the ISS will be a bright beacon from nearly horizon to horizon.
2. This means it must be nearly either a north-to-south or a south-to-north pass. Ah, spatial geometry.
3. For once, this good fortune is not tied to a predawn pass.
1. You do not function well in the predawn hours.
3. To compensate, Murphy’s Law will demand its due.
1. It always does.
1. This is consistent with observation.
2. You hypothesize that this is a conservation law.
3. Murison’s Corollary: When fortuitous good things happen, the balance of the Universe must be restored.
1. Count on it.
5. Fire up the satellite ephemeris program you wrote.
1. Fetch the latest orbital elements from space-track.org.
2. Create plots of azimuth and height above the horizon.
6. Glance at the outside temperature: +12°F.
1. You are surprised.
2. But then you remember this morning, and your decision to leave the coat, the scarf, the gloves, behind.
3. Tell yourself: that’s okay, this should be quick, it’s not that cold.
7. Grab the camera and head outside ten minutes early.
1. Always start early. Things go wrong.
2. Rats: you didn’t bring a tripod.
1. Hand-held video recording it is, then.
2. You are secretly a little relieved at not being able to try anything fancy.
1. Even though nobody else is here, it feels like a secret.
2. Can we really keep secrets from ourselves?
8. The door locks behind you: click.
1. Memory trigger.
2. Check your pocket for keys. After it locks behind you.
3. This strikes you as humorous.
9. Find a good spot: the middle of the small parking lot.
1. Unobstructed view north, west, and south.
2. The main telescope dome, three stories high, with a halo of Flagstaff light pollution, swallows the eastern sky.
3. The satellite is on a south-to-north path tonight.
4. Yes, this is perfect.
10. The southwest wind is brisk.
11. Unpack and check your camera.
1. Breathe. Go slow. Be methodical. Think.
2. Everything functions as expected.
3. You don’t expect this. What will be the yin to this yang?
12. +12°F is cold.
13. Bare hands in +12°F will quickly go numb.
1. Forty-five seconds to a minute, tops.
2. You will marvel at the pain, though you cannot feel anything.
3. Configure and start your camera before this happens.
14. Check your watch: seven minutes to go.
1. This, too, is unexpected.
2. Try not to think about your body heat rapidly fleeing with the wind, that thief.
1. Your warm, warm, cozy, comfortable body heat.
3. When did these jeans become so thin?
3. Seven minutes is an eternity.
1. When there is nothing to do but not think about how uncomfortable it is.
2. When standing exposed in the wind.
3. When it is +12°F.
15. Keep your eyes on the view through the camera.
1. Is that it, there, low in the southwest?
2. Look up, blink-flick distorting tears, and verify with your eyes: yes, there it is.
1. Right on time.
2. In the right place.
3. Glorious.
16. Follow it slowly up, and over, and down to the northeast, where it softly slips into shadow before reaching the treeline. The five-minute pass passes quickly.
1. Now you cannot feel your feet.
17. It is done.
1. Note the satisfaction in your gut: good data acquired, it says.
2. Bask in that warmth as you lean down to pack up.
3. And then your circumstances impinge.
18. Fifteen minutes is a surprisingly long time when it’s +12°F out.
1. And you’re wearing only a t-shirt and light jacket.
2. And Birkies.
19. If you can’t feel anything with the stumps at the ends of your arms, there will be consequences.
1. You won’t be able to turn off or stow your camera.
2. It will be surprisingly hard, and hence take a surprisingly large number of tries, and hence take a surprisingly long time, to get your key into the door lock and scurry back inside, to your office.
3. Where it is not +12°F.

Camera: Canon G3 X. Video processed using kdenlive.