Life, the Universe, and Everything

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(Click here for the PDF version of this presentation.)

Math is everywhere, hidden in places where we don’t even expect to see it. For example, take a look at the following image:

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What do you see?

Most people say “music.” People who have studied the piano might recognize this as a piano score. And a true enthusiast might recognize it as the third movement of Beethoven’s Moonlight Sonata.

What you’ve probably never thought of before, though, is that a musical score is actually a form of graph. It tells the performer what combination of notes to play at a given moment in time. In other words, it shows sound as a function of time.

In the image below, I’ve added labeled axes to draw attention to this:moonlight_sonata_graph

Now consider a photograph. Below is one of the most spectacular images I found when Googling “photograph.” (Thanks to whoever posted it!) I love how it shows the strings of mucus frozen in time.

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Anyway, a photograph itself is also just a type of graph — and not just metaphorically. In fact, even the way images are produced in our brains is just a way of numerically graphing the intensity and frequency of light that falls on different portions of our retinas. In essence, your retina is the x-y plane and the light is the quantity being graphed.

Below is what the photograph looks like when graphed in three dimensions from different angles, with the colors changed to a different color scale:

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Now here is the same graph when viewed from directly above, so that the tiger is easier to make out:
tiger_photo_graphs_2

Here’s another example of a great photo:
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And here it is with the same procedure applied to it. This one works a little better than the tiger because it isn’t filled with little white spots that end up looking like noisy spikes in the graph.frog_photo_graphs_1

Below is the graph when viewed from directly above, just as I did for the tiger. Pretty cool, huh?frog_photo_graphs_2

Now consider something that really seems to have nothing to do with math: a piece of literature. Below is the first paragraph from A Tale of Two Cities, by Charles Dickens.
Tale_of_2_cities

It, too, can be considered as a type of graph. It’s a graph that tells the reader what words to speak or think as a function of time:Tale_of_2_cities_graphThere are, of course, many other examples of graphs:

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What I’m saying is that anything can be thought of as a kind of graph. Really, though, it’s not just graphs that are so powerful, but numbers themselves. This is because numbers encode information. For example, an entire song can be encoded in a single number. So can a photograph, or even a movie.

What’s particularly fascinating is that physicists now believe that physical reality itself is composed of information. In fact, the universe might even be digital. And since numbers encode information, it is possible that the entire universe could be represented by a single number.

Take a minute to meditate on that.

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If that’s true, then there’s only one thing we can conclude…

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* * * * *

This post is based on a PowerPoint presentation I made for my math students in an attempt to inspire them. Here it is in PDF form:

Math Is Everything (PDF version)

To Become a God (A Short Story)

Jesus

Professor Sid Weaver paused briefly, his finger hovering over a deceptively nondescript button. When pressed, it would send him on what was sure to be the greatest journey ever undertaken by a human, one that would rewrite history. Very soon—or a long time ago, rather—he was going to become an emperor. No, a god.

Maybe I’m Jesus, he thought.

He chuckled. Coming from anyone else, that thought would have been a sure symptom of lunacy. But for Sid, the idea that he might be Christ was no psychotic delusion; it was a very real possibility. He could actually be Jesus—the historical Jesus, not a mere imposter.

Only time will tell.

He laughed a little harder at this second thought, wheezing with delight. It was a marvelous pun. Or maybe it was some other literary device. It didn’t matter; he was a physicist, not a writer. The important point was that Sid’s fate—and the world’s—hinged on time; and time was quite literally in his hands.

The button beneath his fingertip controlled what was, in trite words, a “time machine.” It was nothing like those silly things depicted in novels or films, of course. It wasn’t shaped like a rocket or a shuttle; it didn’t have flashing lights, propellers, or any kind of engine; and it didn’t even move. Rather, it was an assembly of high-voltage field generators that filled the three-story laboratory at Stanford that he shared with his colleague, Ken Phelps.

The government, which had funded the machine’s construction, believed it to be a device for generating and observing microscopic black holes for the purpose of developing a better understanding of the big bang. And indeed, it was capable of doing so. Sid and Ken had published several papers together on the topic. But its true purpose—of which even Ken was unaware—was time travel.

From the beginning, Sid’s plan had been quite simple. He would travel ten thousand years into the past, impress the ancients with his knowledge and technology, and set himself up as the greatest god in all of history. He would introduce them to the magic—and it was magic, truly—of the written alphabet, the internal combustion engine, and the electric power generator.

Of course, it wouldn’t do to remain among troglodytes indefinitely; eventually, he would miss the comforts of modernity. No, Sid’s ultimate goal was to rule the future, not the past. Thus, at the peak of his glory, he would orchestrate his own “ascension” to the spirit world. In reality, of course, he would merely be traveling back through time to his home century—arriving at precisely the moment foretold in the prophecies that he himself would leave behind for his primitive subjects.

That was plan A, at any rate. The other option was to go back and assume the identity of an already-known god—Jesus being the obvious choice. That’s what he would be forced to do if Ken’s theory about the immutability of time turned out to be correct. It was something they had argued about on many occasions. If that was the case, Sid would assume the identity of Jesus, and the Second Coming would be his moment of glory.

He fervently hoped that his first plan worked, though, if for no other reason than the fact that becoming Jesus would require significantly more work. One couldn’t simply show up in ancient Galilee and preach sermons in Aramaic and Hebrew without considerable study and preparation. Learning the culture would be as important as learning the language. Who knew how long such preparations would take? No, his first plan was by far the better option.

Confident in his decision, Sid adjusted the straps of his hiking backpack, double-checked the safety on his AR-15, and pressed the button on the control panel. The time machine’s high-voltage electronics hummed, and within seconds, he felt his body begin to disintegrate.

A moment later—and ten thousand years earlier—Sid was standing in a prairie, surrounded by grass that was nearly as tall as he was. The air was clean and humid, and the ground beneath his feet was solid. Yes. He was on Earth—at the surface. That was important; tracking the Earth’s motion over a period of ten thousand years had been crucial. After all, it would have been a sad end to his grand scheme if he had found himself floating in space, millions of miles and thousands of years from home. Not a good way to die.

Time to get started, he thought.

Choosing a direction, he took his rifle in hand and switched off the safety, reminding himself that he must be prepared at all times. Wild beasts were sure to abound, though perhaps the greatest threat would be humans. He would have to approach them carefully when it was time to make contact. But for now, his first order of business was to set up a camp.

* * * * *

Erg peak through brush and see strange man move at edge of forest. Maybe not man. Maybe monster. Monster-Man wear strange skins, have strangely-cut hair, bare face. Monster-Man wear giant bag on back and carry straight, black branch in hand.

Erg follow Monster-Man at safe distance. Monster-Man come to stop in stupid location near bear den. Monster-Man examine ground in surrounding area, take giant bag off back, and sit down. Monster-Man remove round box from giant bag, hold box to mouth, and tip head back. Perhaps round box contain water, Erg think.

Monster-Man stand up again. Monster-Man put straight, black branch behind back, using flat skin strap. Then Monster-Man begin gather wood. Much time pass, and Monster-Man make big pile of wood. Sun begin to set. Erg grow hungry but continue to watch Monster-Man. Monster-Man sit down again and remove small bag from inside of giant bag. From small bag, Monster-Man remove item and put in mouth. Small bag contain food, Erg realize. Erg stomach growl.

As Erg watch, bear emerge from den. Monster-Man not notice at first, and bear approach Monster-Man from behind. But then bear make noise, and Monster-Man turn to see bear. Monster-Man panic and run backwards. Bear growl and stand on rear legs. Monster-Man fumble straight, black branch off of back. Monster-Man point branch at bear. Bear come down on four legs and run toward Monster-Man.

BANG!

Strange thunder roar. Small flash of light. Bear stop. Bear on ground, not moving. Monster-Man stand, panting, pointing black branch at bear. Bear still not move. Monster-Man look around warily. Perhaps check for other bear.

More time pass, and Monster-Man clear small space on ground and build small stack of wood from big pile. Then Monster-Man remove small box from giant bag and kneel beside stack of wood. Monster-Man open box and take out small stick. Monster-Man move suddenly and stick catch on fire. Erg stare in awe as Monster-Man hold small burning stick at bottom of stack of wood. Fire spread. Fire big now.

Monster-Man now remove sharp, shiny tool from bag and approach bear. Monster-Man kneel beside bear and begin to cut. Erg begin to think as Erg watch Monster-Man. Erg want Monster-Man’s power. Start fire. Kill bear with branch. Erg silently approach Monster-Man from behind. Erg’s heart beat loud and fast. Erg’s fear very strong.

Erg take quiet breath and raise club over head. Erg slam down club on Monster-Man’s head. Monster-Man scream loudly. Monster-Man scramble halfway to feet, turn to look at Erg. Monster-Man’s eyes full of terror. Erg swing club again, crush Monster-Man’s head second time.

Swing club hard! Crush! Crush!

Erg finally stop crushing Monster-Man’s head. Erg look down at Monster-Man. Monster-Man no longer move. Head broken. Blood on ground. Erg now have all of Monster-Man’s tremendous power. Erg celebrate by yelling and jumping so high.

After some time, Erg calm down. Erg examine Monster-Man’s things.

Monster-Man took fire-starter from small box. Where was box? Erg search. Yes. There. Erg pick up box and shake. Box rattle like snake tail. Startled, Erg drop box. Box fall open and small sticks spill out onto ground. Erg pick up one stick and examine it. Stick have small red ball at one end. Maybe fire magic in red ball, Erg think. Erg pick up sticks and put them back in box.

Then Erg turn attention to straight, black branch. Memory of thunder and fire coming out of branch strong in Erg’s mind. Memory of dying bear strong too. Erg pick up branch and examine it. Branch cold to touch in some places. Thin, flat length of animal skin hang from branch. Erg touch small hook on branch. Hook move.

Thunder roar suddenly. Branch jump out of Erg’s hands and land on ground. Erg run away in fear but then stop and turn around. Branch sitting still on ground. Quiet now. Smoke curl upward from end of branch. Erg’s heart beat fast again. Slowly, Erg approach branch.

Erg pick up branch. Erg look at smoke coming from end of branch. Erg notice branch hollow on inside. Erg look inside end of branch. Erg look at small hook again. Erg look inside end of branch and move small hook again.

* * * * *

Ken took his place at the time machine’s controls. He knew where—or when, rather—Sid had gone. Sid may have thought that his plans were secret, but he was far more transparent than he believed. He had given everything away during their debates about the mutability of history. Whereas Sid believed that one could go back and change the past, Ken knew it to be impossible; and so Ken had concocted the superior plan.

It was going to be the biggest irony the world had ever known. Ken knew perfectly well that there was no god. And yet, when he returned to the modern age to fulfill the prophecies, he would convince the world—atheists included—that those fools, the Christians, were right. They were idiots for believing that Jesus would return within their lifetime, but that was exactly what was going to happen. Getting around the crucifixion would be tricky, of course, but he had a plan.

After years of study—carried out within the space of a month, thanks to the time machine—Ken was ready to execute his plan. In time, he would be enjoying his millennial reign. He would likely die in far less than a thousand years, of course—he hadn’t yet found a way to achieve true immortality via time travel—but until then he would be the King of Kings. Ken smiled to himself at the thought.

I am Jesus,” he said in Aramaic.

Then, without hesitation, he pressed the button on the control panel and braced himself for the familiar sensation of disintegration. He had years of work to do yet—one could not build a following overnight, of course—but in the end, it would be worth it. He was going to become a god.

Try This Brisket Recipe!

brisket

Wow. I just had the most succulent, juicy, tender brisket ever. (The leftovers are pictured above.) The recipe can be found here. If you like beef at all, give it a try. I promise that you will not be disappointed. (But note that this is not supposed to be a “barbecue” recipe.)

Seriously, this piece of beef ended up being the highlight of an already pretty good day. I was out getting groceries with my father-in-law at about noon, and we spontaneously decided to buy a chunk of brisket.

“Do you know how to cook this?” he asked.

“Yes,” I answered.

Except … the last brisket I cooked was four years ago. All I knew was that it has to be roasted slowly, at a relatively low temperature. I was thinking that I might just rub some random items from our spice cabinet on it and bake it. I could look online for advice about temperature and duration.

So when we got home, I sprinkled some all-purpose seasoning salt over it, squirted some expired spicy mustard on it, and threw it in the oven. Then, when I was trying to look up how long I should cook it, I found THE RECIPE. With the brisket already baking, I ran to the store and got the ingredients that I didn’t already have, came back home, and put them on the meat 30 minutes into the baking time.

So obviously I didn’t follow the instructions exactly. In addition to the timing differences that resulted from buying the ingredients after putting the meat in the oven, I used the aforementioned expired mustard instead of the dry mustard called for by the recipe. And I used water instead of beef broth, simply because I feel weird adding beef broth to beef — or maybe because I wanted to limit the number of things I bought.

I didn’t measure anything, either. I’m actually morally opposed to the use of precise measurements in the kitchen, on theoretical grounds. I mean, even supposing that there is an optimal amount of ingredient X, why should we expect that amount to coincide perfectly with one of our arbitrarily standardized discrete measures? So I just put heaping spoonfuls in a bowl, mixed them together, and then sprinkled them on the meat. (I definitely put in less salt than the recipe calls for.)

At 5:30 pm, I took it out of the oven, topped it with its own juice, and sliced it. As soon as the knife slid into the meat, I knew that it was a success. The texture was just right. And it smelled glorious. We ate it with some horseradish and savored every bite.

As I said, you really have to try this recipe if you like meat at all. It’s incredibly easy, and it will be well worth the effort. (It just requires patience as you wait for it to bake.)

The Millionaire Next Door

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Although this book is outdated in many ways and there has been much criticism about the authors’ research methods, it is still well worth reading. I certainly wish I had read it back when I was in high school or college.

The title may give the impression that the book is geared toward materialistic people who are obsessed with getting rich and living the high life, but that’s not at all what it’s about. In fact, the authors’ main point is that most people who accumulate a lot of wealth are not at all interested in living the high life. Rather, they are thrifty and live below their means, with the result that they often don’t appear wealthy at all. For example, your next door neighbor who manages a maid service — not a very glamorous-sounding occupation — could be surprisingly rich. By contrast, a large percentage of people who appear to be rich — people living in fancy houses, driving expensive cars, wearing designer clothes — don’t actually have much saved up at all.

The authors were surprised to make this discovery, and that is what inspired them to write the book. For years, they have compared the behavior of people who are successful at building or maintaining wealth with those who are not successful. Using elementary statistical analysis, they identify key habits and attitudes that enable people to accumulate wealth — even if they don’t have a particularly high salary. Thus, even if you earn a teacher’s salary (as I do), you can still hope to retire comfortably and be a relatively wealthy teacher if you manage your spending and investments well. It does help, of course, to have a large salary, but with bad spending habits you can still end up accumulating nothing. (The authors do recommend choosing your occupation wisely.)

The habits that they recommend are very practical. For example, you should keep track of all your expenses so that you know how much you spend each month and year on housing, food, entertainment, etc. Then make a budget and stick to it (or create a false sense of scarcity by stowing away a big percentage of your earnings before you even think about spending anything). Invest time and money in financial planning and research. And very importantly, invest your savings in stocks or other equity, making it your goal to have more of your financial growth come from growth of investments than from taxable wages.

Overall, the authors present sound principles for building wealth, and they offer compelling evidence for the effectiveness of those principles. They provide many interesting anecdotes that make the book fun to read most of the time, as well as basic statistical analysis of survey results. Again, although their methods may not be “scientifically rigorous,” the main ideas are basically sound. I highly recommend the book, especially to young people who are just getting started in their careers — regardless of how much money they expect to make.

Trespassing on Einstein’s Lawn

Trespassing_On_Einsteins_Lawn_Cover

Trespassing on Einstein’s Lawn, by Amanda Gefter, is a memoir of a girl on two simultaneous quests. One is to find the answer to the ultimate question about life, the universe, and everything—namely, why is there something rather than nothing? The other is to publish a book about it and become a legitimate, big-time author. She appears to have succeeded to a significant degree on both counts and does a good job telling the story about how she did it.

Gefter’s treatment of the physics is an excellent demonstration of why popular science writing shouldn’t be left to scientists alone. Whereas scientists tend to be wrapped up in their own particular theories (e.g., string theory), a good journalist is better positioned to take a step back and make an unbiased assessment of what all the different theories out there are saying (even if the lack of bias is partly due to a lack of technical understanding). Gefter has attempted to do this, both by studying cosmology extensively on her own and by interviewing the big players in the field.

By taking this approach, she has done a more convincing job than anyone else has yet done—as far as I know—of presenting a satisfying explanation of how everything that we experience (i.e., life, the universe, and everything) can truly come from nothing (and actually be nothing), even though we perceive it to be something. Using qualitative conceptual arguments, she presents a compelling case for how the universe arises from nothing, without requiring any external laws of physics, such as quantum mechanics or general relativity, to exist a priori to govern the behavior of the nothingness.

Her central thesis, as I interpret it, is that something can’t be fundamentally “real” unless it is invariant—that is, unless it exists in all reference frames. In other words, if a reference frame can be found in which a thing doesn’t exist, then that thing is not “real.” She begins with a list of candidate components of reality, such as space-time, particles, fields, and forces; and in the course of her interviews with the most respected physicists of our time, crosses each item off the list.

In the end, with everything crossed off of her list, she concludes that the universe is ultimately made of nothing—which is the only philosophically satisfying conclusion anyway. It is very important to note here that what Gefter means by “nothing” is not space, but actual nothingness—devoid of all properties whatsoever, including any set of governing mathematical rules. With the help of a certain physicist, she even goes so far as to suggest how the mere imposition of a boundary—which is itself nothing—creates information from nothing. This emergence of information evidently initiates a cascade from which everything emerges.

It is reminiscent, Gefter notes, of how, in the field of mathematics, the entire set of real numbers can be constructed from the empty set alone—i.e., from nothing. She also mentions other pleasing analogies with mathematics that can be drawn, not the least of which is the possibility that, in the spirit of Gödel’s incompleteness theorem, no set of physical laws that can be constructed within physical reality could ever give a complete, external description of physical reality.

Gefter doesn’t spend much time talking about Zen, but she does mention it, and one cannot help but think that she has given a rather compelling case for the truth of Zen from an actual physics perspective. Nothing is everything, and everything is nothing. And no system can observe itself, for it would then cease to exist upon making the observation.

My own analogy is that a blank canvas, which contains nothing, also contains everything—in more than one sense. While still blank, the canvas retains the potential to become any of the infinitely many possible paintings that could conceivably be painted on it. Moreover, if you actually do paint every last one of the infinitely many possible paintings on the canvas, it will become blank again (i.e., pure white or black, depending on the medium). Perhaps our universe is just one of the infinitely many possibilities that exist simultaneously on the blank canvas of nothingness.

Though Gefter’s case is conceptually compelling, it is neither academically rigorous nor airtight, and she acknowledges this. Should some component of the universe be shown to be truly invariant, her core thesis would go out the window. And there are still a few points about which I don’t feel satisfied. For example, why can observers (which don’t necessarily have to be conscious) exist within nothing? (For supposedly it is the observer who creates the boundary that gives rise to information.) Can we really talk about “observers” and “boundaries” within nothingness without invoking some sort of governing system of definitions and rules? Are we really talking about nothing then?

The other part of Gefter’s quest—to become a bona fide science writer—is interesting and inspiring in itself. It’s not a rags-to-riches story, but it’s an excellent example of how it can be possible to attain seemingly unattainable goals. That’s what the title is really about. In the beginning, she was neither a scientist nor a writer. And so she was not just literally trespassing on Einstein’s lawn when she visited his old house in Princeton; she was, in carrying out her quest, venturing into territory where she didn’t rightly belong. But in the end, she earned her spot on the lawn.

Gefter’s success comes from four components that I have been meditating on recently: passion, discipline, assertiveness, and luck. Throughout her quest, she maintained a very intense passion, largely instilled by her father, for the ultimate questions about physical reality. She also demonstrated the discipline to stick to that quest over a period of several years—attending conferences, writing articles one at a time, interviewing physicists, keeping a detailed journal, and ultimately sitting down to write out the book itself. Assertiveness played an important role when, in situations where most people would have thought there was no hope trying, she nevertheless called up high-profile scientists and publishers to try to get her foot in the door—and it worked. Finally, of course, she had plenty of luck. More than anything else, she was lucky to have a father who planted and cultivated the seed of her passion and then provided the financial, intellectual, and emotional support necessary for her to set off on her quest.

Throughout the book, Gefter draws many clever parallels between the mysterious physical phenomena that she is investigating and things that are going on in her personal life. For example, physicists’ conclusion that it is inherently impossible to construct a consistent description of the universe that takes into account more than one point of view at a time—i.e., you can only have one observer—was a nice parallel with her reluctant decision to write the book on her own after the publisher rejected her proposal for a book by a father-daughter duo.

I did grow a bit tired of Gefter’s self-deprecating refrain about how she was an impostor, a fake who didn’t deserve to be present at the conferences she attended or at the magazines where she worked. I also grew a bit tired of the “Oh my God, I’m in the presence of one of the greatest physicists who ever lived!” exclamation that seemed to accompany every single interview she did. And I didn’t appreciate the dig she took—which seemed rather mean-spirited to me—at a waiter who said that he had also majored in philosophy of science. She was making an attempt to draw another clever parallel, contrasting the success she hoped to achieve with the waiter’s apparent lack of success; but the net effect was to shatter the image of humility she seemed to be working so hard to create throughout the rest of the text.

Nevertheless, Gefter did a fantastic job documenting her quest, and the overall picture that she paints of the present status of cosmology is far more satisfying than any other I’ve read—precisely because she takes into account many different physicists’ points of view. She begins by saying:

Reality is a huge mystery, and you have a choice to make. You can run from it, you can placate yourself with fairy tales, you can just pretend everything’s normal, or you can stare that mystery in the eye and try to solve it. If you are one of the brave ones to choose the latter, welcome to science. Science is the quest to solve the eternal riddle.

Then, at the end, she is able to say, “Physics isn’t the machinery behind the workings of the world; physics is the machinery behind the illusion that there is a world.” Before reading the book, I would have dismissed this statement as pseudo-philosophical mumbo-jumbo based on feelings that surely have no grounding in an actual understanding of physics. But I am now convinced that it may be a deep and legitimate conclusion indeed—and I am very glad that I took the time to read her story.

(Thanks to my father for giving me the book.)

The Window in the Luggage (A Short Story)

Suitcase-black

I wake up. A sense of wrongness twists my gut, but as I look around my bedroom, I see nothing out of place. My clothes and books are strewn about as usual, and there on the floor lies my suitcase, a black Rockland carry-on.

That’s right. Just yesterday, I was relaxing in the beryl waters of Destin.

I realize what’s making me uneasy. The time I spent on the beach is clear in my mind; but I don’t remember coming home. I sift through my memories, searching for the most recent one. The hotel lobby. Rushing to the airport. And then… nothing.

I roll out of bed and stumble over to my suitcase. Up close, I see that it’s green, not black. And it’s not Rockland. I stare for a moment, and it sinks in that this isn’t my bag.

While my mind clumsily processes the situation, my hands move of their own accord. Thumb and forefinger find a zipper and slide it all the way around. Then, with both hands, I open the case and look inside.

I have just enough time to register neat stacks of men’s clothing before the suitcase is gone and I find myself looking through the eyes of an unfamiliar man. I am the man, and I’m talking to a clerk in a store.

“Ohio State?” the clerk asks.

“That’s right,” I say. “Red. With an ‘O’ on it.”

“You realize we’re in Florida, right?”

“Yeah. But my daughter’s graduating from Ohio State, and I’d like a hat.”

“I guess I can order one for you.”

“I’d appreciate that,” I say, reaching for my wallet.

Back in my bedroom, I close the suitcase and stare at it. It’s different now. It’s small and blue, with a cartoon clownfish on it. What’s happening? Even as I think the question, my hands reach out, unbidden, and open the new case.

I’m a little boy.

“Are you ready, Aiden?” my mom asks.

“Yeah.” My chest swells; I’ve packed my own suitcase for the first time.

“Let me see.” Mom opens the Nemo case and examines the contents. “Shorts, shirts, socks, underpants. Good. You’re missing something, though.”

“What?”

“A toothbrush.”

“Doesn’t Grandpa have one?”

Mom laughs. “Yes, but you should bring your own.”

“Oh.”

“Let’s go get it.”

I start to follow after her, but then I’m in my bedroom again, looking down at yet another suitcase. This one is burgundy. I open it, and I’m a… man of God or something. I’m looking in a mirror, fingering a scar over my left eye. I always hated the scar, but it doesn’t matter. I have a higher purpose now.

I close the burgundy case and open a black one. Then another green one. I lose track of how many suitcases I open, how many people I become. And then there it is: a black Rockland. My pulse is a drumbeat in my ears. Hesitantly, I open the case… and I’m myself.

I’m on the flight back from Florida.

On my right, in the aisle seat, is the man from the store, wearing an Ohio State hat. His name is Jim. I chatted with him a minute ago, and he said that he’s on his way to his daughter’s graduation. He turns and sees me staring. Swallowing, I look the other way.

Aiden is looking out the window. I remember talking to him, too. He’s going to visit his grandfather. His mother is in a different row because they couldn’t get seats together. When I offered to give up my seat, Aiden refused. “I’m an independent man,” he said.

I hear a noise and look up. The man with the scar over his eye is opening an overhead compartment. He takes out a package and fumbles with it for a moment. Something is wrong.

An explosion rips through the cabin.

The plane is gone.

Panting, I slam shut my suitcase and look up. I’m in a field, surrounded by fragments of wreckage from a crash that no one could have survived. I see Jim’s red hat lying in a puddle of mud. And just a short distance away, broken and battered, is the little blue suitcase with the clownfish on it. On impulse, I run over and kneel beside it. Hands shaking, I reach for the zipper; but I stop, paralyzed by fear—fear of what I might see, and fear that I’ll see nothing at all.

* * * * *

This story was my entry in another Writer’s Digest‘s “Your Story” competition. The prompt was, “You come home from a relaxing vacation and realize you have the wrong suitcase.” Here’s another version, with an alternate ending:

The Window in the Luggage (Alternate Version)

My Luck with Tomatoes

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Orange Oxheart Tomato

Gardening is for old people. At least, that’s what I used to think; but now I’m doing it.

I started last year. Tomatoes were the thing to grow, so I picked up a couple plants at a nearby nursery. I tried the Carmello and Homestead 40 varieties. Those were what the store had in stock, and the tomatoes pictured on the labels looked good. The Carmello plant did well. It produced a few dozen tomatoes, and they were fairly sweet. It was enough to make me want to try again this year.

Now I’ve gone all out. Back in March, I planted some Black Krim, Yellow Pear, Pink Brandywine, Orange Oxheart, Mortgage Lifter, Sweet Millions, Celebrity, and Early Girl. I’ve gotten tomatoes from all the plants except the Black Krim, and I’m ready to share the results.

  1. The Mortgage Lifter has been by far the most productive of them all, and its tomatoes have been reliably delicious. They’re medium-sized and very sweet. My wife and I both rate it as the best of our plants this year.
  2. Next is the Orange Oxheart. It has been fairly productive, and the tomatoes are HUGE. (See the picture at the top of this post.) They are very sweet, and it’s hard to tell whether we prefer them or the Mortgage Lifter.
  3. Coming in at third is the Sweet Millions plant. It’s a cherry tomato variety, which I wasn’t excited about initially, just because I think cherry tomatoes aren’t very sexy. However, it ended up being extremely productive, and the tomatoes are indeed sweet. So it really lives up to its name.
  4. Fourth is Celebrity. It has been extremely productive, but the tomatoes are merely pretty good — not nearly as sweet as the three varieties described above, but better than the run-of-the-mill grocery store tomato.
  5. The Pink Brandywine plant is hard to place. It has only produced three tomatoes (and it doesn’t look like it will produce many more). They have all been large. The first one was just about the nastiest tomato I’d ever eaten; I think something had gone wrong with it, though. The second one split open on the vine, and I picked it early, cut out the bad part, and ate the rest. It was fantastic. The third one made it to full ripeness intact, and it was also delicious — even more delicious than the Mortgage Lifter tomatoes. If the Brandywine vine had produced more tomatoes and if they had been uniform quality, this one would definitely be higher on my list.
  6. The Yellow Pear variety seems to me mostly a novelty. They’re small, pear-shaped, and yellow — hence the name. The plants haven’t been especially productive, and the tomatoes don’t have an outstanding taste, so at the moment they’re not on my list of tomatoes to grow again next year. To be fair, I should disclose that I planted them from seeds a little late in the year; they might have done better if they’d been planted earlier.
  7. Last (and least) is the Early Girl variety. I bought them because they’re supposed to produce tomatoes earlier than other varieties. They did indeed do so, but the tomatoes tasted just like ordinary grocery store tomatoes, which is to say they were not very good at all.

I’ve left off Black Krim because I haven’t gotten to try any yet. I do have one plant that has about five tomatoes on it, and they should be ripe in a week or two. I expect them to be pretty good, because I’ve had a Black Krim tomato before, and I liked it.

Below is another picture of an Orange Oxheart (right) next to an Early Girl.

IMG_0720

 

I also planted okra this year, since it’s supposed to grow well in Houston. I was surprised to see that the flowers are quite pretty, though they don’t last very long. Below is a picture of one.

IMG_0715Note to anyone who plants okra: The “fruit” will grow in size without limit, but you need to pick it early (when it’s only two or three inches long). Otherwise, it will be tough and fibrous. I fried some with cumin, and it tasted really good!

 

The Chronicles of El Guapo (Entry 4)

ElGuapo_and_CatDearest Minions:

El Guapo here. Allow me to open this missive with an apology for permitting such an unconscionably prolonged interval of time to have lapsed without apprising you of the various goings-on that have taken place since my previous communique. I can scarcely imagine the heart-wrenching distress that the resulting state of perpetual uncertainty must have caused you, even as you continued to labor faithfully for the furtherment of our great cause. Please rest assured that the depth of my gratitude toward each and every one of you for your unwavering devotion knows no bounds.

I have, of course, been mightily busy, contending with the mountain of gravely important tasks that continuously threaten to overwhelm me every moment of the day. In addition to my heavy involvement in the milk trade, I have continued my work in the field of sleep deprivation — and with phenomenal success, I am happy to report! Furthermore, there is yet another never-ending task about which I have not previously written: the regular soiling of infant undergarments. Several times a day, I am presented with a fresh, highly-absorbent undergarment, which it is my duty to soak and stain by all means at my disposal. As you can imagine, these burdens leave me precious little time for other pursuits. I scarcely even have time for the twenty hours of sleep that any decent human being requires in a day!

Nevertheless, I am at present free to dash off these few words and provide you with an amusing photograph (furnished at the top of this message), which I hope will provide you with a moment of levity. In my spare time, I have been practicing the arts of disguise and dissembling. The attached photograph, for example, was taken by my paternal minion as I posed beside a stuffed cat. Such are my skills now that I suspect even the sharpest-eyed among my minions — yes, even those who spend the better part of each day serving me at close quarters — have little more than a fifty percent chance of correctly identifying me in the picture. By all means, try your hand at it, and let us laugh together at the results!

Having said that, I should now like to strike a more sentimental note, recognizing that my desire to do so is likely a symptom of my advancing age. (It has nearly been a full three months since my miraculous escape from the oubliette in which I was ensconced during those nine months of unspeakable horror.) Before proceeding, however, I must first reveal that I am the figure on the right in the above photograph. (Surprised? Well, don’t be embarrassed.) The cat, of course, is therefore the figure on the left, and it is precisely the history of this cat that has put me in this sentimental mood. I hope that you will indulge me as I endeavor to explain its significance.

The cat was purchased by my paternal minion as a gift for my maternal minion when he decided to make known his intention to enter into matrimonial union with her. You see, this cat, known as “Robo-Cat” in Chinese (or, when translated more directly, as “Machine Cat”), was my maternal minion’s favorite cartoon character as a child. One of Robo-Cat’s most interesting traits is that he has on his belly a magic pocket, from which he can withdraw nearly any magical object one can imagine, including a doorway that allows one to traverse great distances in a single step.

During the course of their whirlwind courtship, my maternal minion had disclosed to my paternal minion that as a child she had often fantasized about having access to the same sorts of magical paraphernalia as those contained in Robo-Cat’s pocket. Thus, my paternal minion decided to place a ring of matrimonial commitment into the pocket of the stuffed cat for my maternal minion to find. He presented the cat to her on her birthday, and she discovered the ring with tearful delight. The rest, of course, is history (and will be well-known history once I have secured my dominion over the universe).

Even now, as I write about this beautiful moment in my parental minions’ exquisite romance, an overwhelming feeling of warmth wells up inside of my very bowels. Or . . . Oh. Perhaps it is merely time for another fresh undergarment.

In Virtue and Splendor,

El Guapo

[See the next letter from El Guapo.]

[See the previous letter from El Guapo.]

The Real-Life Search for Aliens

Absorption spectroscopy, from Coel Hellier's blog post

Diagram explaining absorption spectroscopy, from Coel Hellier’s blog post

In a previous series of posts, I presented a simple analysis of our chances of ever contacting aliens. The foundation of my argument was that any planet that does harbor intelligent life will almost certainly be too far away, not just for us to reach by spaceship, but even for us to contact with any type of signal. Thus, although the universe may be teeming with life, we’re never going to see any of it (except what’s right here on Earth).

Today, I ran across this blog post by Coel Hellier, an actual scientist who searches for the signatures of extraterrestrial life (though I think that’s not the only goal of his work). In his blog, he does a great job of explaining in layman’s terms how real-life searches are actually carried out, from identifying stars that have planets orbiting them to analyzing the chemical composition of those planets’ atmospheres. I encourage you to read his original article, but I’ll give a brief summary of it below in case you’re too lazy to click a mouse.

  • We can identify a star that has a planet orbiting it by the periodic dimming of the star as the planet passes between us and the star, blocking part of the star’s light.
  • The planet’s size is determined from how much of the star’s light it blocks.
  • Its mass is determined by measuring the redshift of the star’s light when the planet is behind the star (pulling the star away from us) or the blueshift of the star’s light when the planet is in front of the star (pulling it toward us).
  • From size and mass, we get density, and from density, we get a rough idea of what chemical elements are most abundant on the planet.
  • We can even determine what molecules are present in large quantities in a planet’s atmosphere by looking at the fringe of light that passes through the planet’s atmosphere as the planet passes in front of the star. Different molecules will absorb light from different parts of the spectrum of the star’s light, so all we have to do is compare unimpeded light from the star to light that passed through the planet’s atmosphere to determine what types of molecules are in the planet’s atmosphere. This is called spectroscopy.

Coel writes that, using spectroscopy,

we are beginning to be able to detect the atmospheres of extra-solar planets, despite them being hundreds of light-years away. If we can detect molecules in the atmospheres of exoplanets then, in principle, we might detect “biomarker” molecules that indicate organic activity (such as free oxygen). Thus it is realistic that, within a couple of decades, we will have found other Earth-like planets that we know to bear life.

The beauty of this approach is that with an array of sensitive telescopes that can record light from stars all over the sky, we will be able to use automated analysis software that will process the data from thousands or millions of stars in a relatively short period of time. Thus, it might actually be possible to verify the presence of life on other planets in a relatively short time frame. Exciting!

Having said all of that, it is still the case that even if we do find planets that harbor life, they will almost certainly be hundreds if not thousands of light-years away from us. We can try sending them a signal, but even on the off-chance that the life there is advanced enough to detect and decode our signal, it would be hundreds or thousands of years before their reply ever reached us.

Thus, I maintain for now my pessimistic conclusion that we’ll never contact aliens.

How to Move the Earth

earth-rotationIf you’re like me — and who isn’t? — then you’ve often wondered how traveling around on the surface of our planet affects its rotation. If you haven’t ever wondered this, then I suggest you go in for a psychiatric evaluation, because no sane person should be able to go for a walk without worrying about the cosmic ramifications of every step he or she takes.

The Earth rotates toward the east; and when you’re standing still with respect to the ground, you’re actually moving along with its surface. If, however, you decide to start walking east, the initial steps you take to get moving will push westward against the Earth, slowing its rotation ever so slightly. You’ll be stealing a bit of the Earth’s angular momentum. If you go west, your feet will push eastward against the Earth, and you will actually speed up its rotation.

The question on my mind — and on yours too, I’m assuming — is how much the Earth’s rotation will be affected if you travel eastward all the way around the world and come to a stop right back where you started. During the trip, the Earth will be rotating at a slower-than-normal rate; and when you come to a stop, it will return to its normal rate of rotation. As a result of this period of slowed rotation, each point on the Earth’s surface will now lag behind where it would have been otherwise. Sunrise will happen a little bit later for everyone.

Well . . . how much later?

This question burns, doesn’t it? Well, relax, because we’re going to answer it right here. We just need to find expressions for the total angular momentum of the system (which consists of you and the Earth) for when you’re standing still and when you’re traveling. By conservation of angular momentum, we can set these two expressions equal to each other and solve for the Earth’s reduced angular velocity during the trip. From this, we can then determine how much lag the Earth will accumulate. Piece of cake!

For the curious, I’ve written out the full solution here, in PDF form. Below, I’ll spare you the calculations and just present the results.

For a 60-kg person making the trip, the amount of time by which sunrise will be delayed is 2.17 attoseconds. In case you’re wondering what the heck an attosecond is, it’s 1/1,000,000,000,000,000,000 of a second, which is roughly how long it takes a beam of light to travel the length of three hydrogen atoms lined up against each other. In other words, it’s a very short time.

One interesting thing about this answer is that it is completely independent of how fast you make the trip. Whether you zip all the way around in less than a second or crawl along over a period of several years, the net effect will still be a delay in the Earth’s rotation of 2.17 attoseconds. It’s your mass, not your speed, that determines how big the resulting delay will be.

If you gained a bit of weight, you would have a bigger impact. We might ask, for example, what your mass would have to be in order to delay the Earth’s rotation by a full second. It turns out you would have to weigh a hefty 27.6 quintillion kilograms, which would require a large number of trips to McDonald’s and is not something you should aim for.

So now we know how the Earth’s rotation is affected each time a person circumnavigates the globe. It’s a small effect; but just to be safe, whenever you take an intercontinental trip, you should probably return the way you came rather than going all the way around the world. Keeping track of time is difficult enough with Daylight Saving Time.