A Colored Version of the Flammarion Engraving

UPDATE: You can now get a poster of this at
https://shop.spreadshirt.com/the-transcendent-mind/

I couldn’t remember what it was called or where I’d seen it; but over the last couple of years, the image had been coming to mind again and again, and I realized that I’d begun to think of it as one of the most profound pieces in the history of art — one that perfectly captures what it means to be a scholar, an inquirer, or anyone who feels compelled to break through boundaries. It wasn’t until this fall (of 2017), as I was teaching a lesson on imaginary numbers, that I finally resolved to track it down and get a poster of it for my classroom.

Some trial and error on Google eventually led me to it. It’s called the Flammarion Engraving, after the French astronomer Camille Flammarion, in whose 1888 book it first appeared (L’atmosphère: météorologie populaire). Interestingly, no one is sure where the image originally came from — whether Flammarion commissioned it for his book, engraved it himself, or found it in some now-lost repository. This mystery only added to my delight.

When I searched for a poster of a colored version, I found one available for $430 — which was obviously out of the question. And so I decided to create my own. The original black-and-white image is in the public domain (available through Wikimedia), so I downloaded a high-resolution copy, had it printed on a 2-foot-by-3-foot piece of paper, and began to think about how I would color it in. Water color? Colored pencil? Bolivian yak’s blood mixed with cuttlefish pigment?

Here was what I would be working with:

I ended up going with colored pencil, since yak’s blood has an unpleasant odor — and since the art teacher at my school was willing to let me borrow a set of Prismacolors. I began by picking out the colors I’d use for the sky. I wanted a sunset that faded from yellow to orange to red to lavender to deep purple. After an afternoon of coloring, I ended up with this:

On the second day, I colored in the sun, the moon, the tree in the foreground, and the robed figure:

Then I spent a day coloring in the mysterious heavenly realm beyond the celestial sphere. I picked what I thought of as vibrant, other-worldly colors:

Then it was time for the distant part of the landscape:

And the foreground:

And then the water: (I also went over the sky and the robe a second time here.)

And finally, I filled in the border and then went back to make some of the other colors a little more vibrant (especially in the heavenly realm):

The last step was to take a high-resolution photo of it and touch it up digitally. (There’s one coloring error that I fixed. Can you find it?) I also decided to make the region outside of the border black instead of white, in order to detract less from the brightness in the interior of the piece. And I thought the text would look good in gold. Speaking of which, the text (which was Flammarion’s original caption for the piece) says, “A missionary of the Middle Ages tells that he had found the point where the sky and the Earth touch…”

Altogether, the project took me about three weeks. The image at the top of this post is the final version. (Click on it for a semi-high resolution version.) I’m really proud of how it turned out! Feel free to share it — but please give me credit for the coloring.

The Answer to the Ultimate Question

Perhaps I’m just being supremely arrogant (I wouldn’t deny this at all), but I believe that I actually know the answer to the Primordial Existential Question¹: “Why is there something rather than nothing?”

The canonical response is to reject the premise of the question—namely, the assumption that a state of pure nothingness is somehow more natural than any other state. Philosophers now tend to agree that there is no good reason to hold this assumption, and the question therefore does not require an answer at all beyond the cheeky one given by the Stanford Encyclopedia of Philosophy: “Well, why not?”²

While I don’t disagree with the above reasoning, I have a different response that I think is more meaningful. Specifically, I believe that the question contains yet another false premise: that “something” and “nothing” are mutually exclusive states. The question assumes that since we observe the existence of something (our selves, at the very least), it therefore cannot also be true that there is nothing. Although this assumption makes intuitive sense, I now believe it is wrong.

My initial epiphany was born out of my frustration with trying to make my voice heard over the din of the clamoring masses. While surveying the cacophony on the media, on Twitter, in the blogosphere, and now in the realm of podcasting, I realized that we are fast approaching a state in which everything is being said. And once the multitude of voices drown each other out in utter static, we reach a state that is equivalent to one in which nothing at all is being said. Thus, “nothing” and “everything” are, in a sense, equivalent. This idea is, I admit, little more than a faint analogy, a mere inkling—but it is one that I believe is worth pursuing further.

Imagine a blank projector screen. (It doesn’t matter whether your concept of blankness is pure white, pure black, or even pure gray.) Now let an image—any image—be projected onto the screen. Then let a second image be superimposed on top of it, and then a third, and a fourth, and so on. Consider the limit in which all possible images are projected onto the screen (with the intensities being averaged as each new one is added, if you like). Such an operation can actually be carried out with calculus, using discrete sums for digital images or continuous sums for analog ones. Either way, the result will be the same: convergence to an utterly blank screen.

The key point in the above exercise is that the very act of projecting everything onto the screen gives rise to nothing. Crucially, this phenomenon is not limited just to the superposition of images on a screen; it can be generalized to any information-bearing medium to show that the sum of everything, in terms of information content, is nothing. Perhaps also relevant here is the result from information theory stating that the signals that contain the most information are those which, paradoxically, are composed of completely random static—i.e., nothing.

Consider also the famous quote attributed to Michelangelo: “Every block of stone has a statue inside, and it is the task of the sculptor to discover it.” I like to modify this idea as follows: A block of stone contains within it every possible form—a dolphin, say, or an airplane, or a tree—until the sculptor chooses one and carves away the excess stone from around it. In other words, when you have a big block of marble, which is, in a sense, nothing (since it has not yet been sculpted into any form at all), you have at the very same time everything. And if you were to attempt to carve all possible forms out of the block, every last bit of marble would be scraped away and you would end up with nothing. In other words, creating everything will leave you with nothing.

Perhaps all of these analogies add up to nothing more than a rhetorical trick, and perhaps I am deceiving myself; but right now I think there really is something to it. I suspect that nothing and everything really are opposite sides of the same coin. In a very real sense, everything resides within nothing—while at the same time, nothing resides within everything. Moreover, I suggest that it is not even possible to have one without the other.

And so I think the best answer to the question, “Why is there something rather than nothing?” is this: There is something precisely because there is nothing—for each one is contained within the other. Everything is necessarily born out of nothing, and nothing is necessarily born out of everything. Thus, the reality we inhabit is a bubble of something within the great cosmic soup of nothing and everything. With this in mind, I once again present the following little “poem” I posted previously, which captures my understanding of existence and the meaning we find within it:

Everything from nothing,
And nothing again from everything.
Meaning is in the middle.

And here are some other related tidbits I’ve run across:

“I have nothing to say, and I am saying it.” —John Cage

1. So named, I believe, by Adolf Grünbaum.
2. https://plato.stanford.edu/entries/nothingness/

Join me on Twitter: @OlenRambow

Life, the Universe, and Everything

(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:

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:

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.

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:

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

Here’s another example of a great photo:

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.

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

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.

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:There are, of course, many other examples of graphs:

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.

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

* * * * *

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)

Will We Reach the Stars? A Physicist’s Analysis (Part II)

In my previous post, I presented some simple calculations showing how much energy it would take to send a space shuttle to the nearest star, Proxima Centauri, in ten years. It turned out that we would need the amount of energy that the world’s largest power plant produces in 820 years (if we could run it for that long). This led me to conclude tentatively that we’re not likely ever to reach other star systems; but I promised that in my next post I would examine potential breakthroughs in science and technology that may one day make interstellar travel possible. So here we go.

Assuming we manage to keep from destroying ourselves in a nuclear war, humanity will certainly accomplish some impressive breakthroughs in science and technology in the future. For example, we can expect significant advances in the miniaturization of electronic and optical devices. And, as has long been predicted, we will almost certainly see the successful integration of biological systems (e.g., the human brain) with artificial systems (e.g., computers). At first glance, these advancements seem unrelated to interstellar travel, but I think it will turn out that, if interstellar travel is at all possible, these things will play an integral role.

In light of my previous post, however, the developments that seem most relevant to space travel will be those related to energy production, including the development of novel energy sources and improved efficiency of existing technology. The question at the heart of our discussion here, then, is this: Will these advancements be enough?

The way I see it, one of three possible developments will be necessary in order to make interstellar travel possible. Let’s consider each one in turn.

The first possibility is simply to find a better source of energy. Thus far, the vast majority of our energy has come from burning hydrocarbons. The burning of fuel, whether it be gasoline or the solid rocket propellant used by the space shuttle, is simply a chemical reaction. Energy is released because the atoms and molecules start out bonded together in one configuration and end up in a different, lower-energy, configuration. The energy difference between the two configurations is the amount of energy that we get out of the reaction and can use to power our devices.

Other means of production include harvesting the energy of mechanical motion, such as the motion of air (wind energy) or water (hydroelectric power), or collecting sunlight. These are all great sources of energy, but the fact is that you have to have a huge number of collection devices spread all over the place in order to get an appreciable amount of energy. That won’t help us with space travel unless we can store all of that energy in a compact battery that can fit on our space shuttle. And once again, the energy stored in a battery is chemical in nature and has a limited density.

What we need is something with a high energy density — a lot of energy packed into a small amount of volume and mass.

Modern physics places a limit on this. The total amount of energy contained in a given amount of mass — and hence the absolute maximum amount of energy that can be extracted from said mass — is given by Einstein’s famous equation, E=mc^2. This equation governs how much energy is produced in nuclear power plants.

Nuclear reactors work by converting a tiny fraction of the fuel’s mass into energy. (In fact, the same is true of chemical fuels as well, but the change in mass is so tiny that nobody ever talks about it.) However, since only a tiny fraction of the mass is converted to energy, nuclear reactors are not very efficient. We need something even better than conventional nuclear power.

According to modern physics, the absolute best that we could ever hope to achieve would be to convert all of a fuel’s mass into energy. The best way to do this is to combine matter and anti-matter so that all of the mass is annihilated, leaving nothing but energy. Producing the amount of energy that we need for our journey to Proxima Centauri would require the annihilation of about 6,500 kilograms of mass, half of which would have to be anti-matter.

So why don’t we do that?

Well, the problem is where to get the antimatter. Producing or even harvesting the antimatter in the first place would take a tremendous amount of energy. So that really puts us in a catch-22: We need energy to get energy.

Thus, barring some absolutely revolutionary breakthrough in our understanding of the nature of matter and energy, it appears as though nature has put an upper limit on how much energy we can extract from a given amount of material. And even if we’re able to reach that absolute limit, we’ll find ourselves hard-pressed to use that energy to send a ship to another star. I therefore conclude that our first option — finding a better source of energy — is not very promising.

Let’s look at the second possibility, then.

The second advancement that might enable interstellar travel would the development of the ability to bend space-time somehow — i.e., create a wormhole or something similar. We’ve all seen this in science fiction movies, and if you’ve read any popular literature about general relativity, then you have some conceptual idea about how wormholes work in principle. The problem here is that even if it is possible to create a wormhole, doing so would probably require more energy than simply sending a ship the required distance.

That doesn’t mean we won’t ever be able to do it. I can imagine, for instance, setting up a huge power plant — perhaps a space station that orbits a star and directly harvests nuclear power from it — dedicated to opening and closing wormholes. It would serve as a sort of interstellar space port that builds up and stores energy and then releases it in huge amounts on occasions for which the creation of a wormhole is desired.

But that is probably something we’ll only be able to do after we already manage to travel to other stars. So let’s keep thinking.

The heart of our problem thus far is finding the means and the energy to transport a certain amount of mass (i.e., our bodies) over a great distance. My third proposal represents not a solution to this problem but a reformulation of the problem: What if, instead of transporting our bodies across space, we first converted ourselves into something much lighter? Then a much smaller amount of energy would be required for the transport.

By our current understanding of reality, we are composed, at the most fundamental level, of information. In principle, you or I could be converted into pure information, which could then be encoded in a beam of light. This would be helpful because light has no mass at all and travels at the maximum possible speed (the speed of light). And according to relativity, if you were converted into light and traveled the 4.24 light-year distance to Proxima Centauri, no time at all would pass for you, while exactly 4.24 years would pass on earth.

There is one problem with this, though. There’s no device on Proxima Centauri that can receive the signal in which you are encoded and convert you from light back into a more preferable form. When you hit Proxima Centauri, your photons will be absorbed by the matter in the star and disappear forever, which is the same outcome that you would get if you just plunged into the star at 39% of the speed of light while riding in a shuttle!

Darn.

Although I think this is the most exciting possibility, it once again requires that we first find some way to transport mass across distances from one star to another. And so here I come back to my earlier mention of miniaturization and bionics: specifically, the miniaturization of optoelectronics and the development of brain-computer interfaces.

Rather than trying to send people at first, we could begin by sending robots (i.e., computers) to another star as pioneers. This way, we could take advantage of miniaturization of technology to make these robots so tiny and lightweight that a relatively small amount of energy would be needed. (And they wouldn’t need food and water for the journey, either.) Once there, these robots could build the hardware necessary to receive future signals sent from the earth. Then we could begin sending people (and, in principle, anything else) encoded in beams of light. Hence, we could truly realize interstellar travel by means of teleportation.

There is one obvious and very basic philosophical problem here: If you are physically disintegrated at one location and reintegrated at another, is the new you still you? Or did you die, and is the new you just a copy that other people won’t be able to distinguish from you? Or, if you are merely copied without disintegrating the original you, what’s the difference between the new you and the old you?

It’s a disturbing question. My own graduate quantum mechanics professor commented on quantum teleportation by saying that if the technology ever reaches the level at which humans can be teleported, he would never volunteer for it because he couldn’t be sure that what came out of the other end would really be him.

Hm.

Well, at least it’s a cool idea. And we might be able to watch other people be teleported. (There are, after all, people signing up for the Mars One suicide mission.)

In the end, maybe it’s just that I’m a pessimist, but if I had to make a bet, I’d say we’re much more likely either to blow ourselves up with nuclear weapons or to permanently strand ourselves on this rock by exhausting all of our energy supplies than to make it to another star system. So I have to conclude that in all likelihood, we’re never going to make it to another star system.

I do hope someone will prove me wrong, though.