Predicting the Future

Visions of the Future:
Making Predictions

Ten thousand years ago, humanity transitioned from hunter-gatherer tribes to farming settlements, towns, and cities. This became known as the agricultural revolution, and is marked in history as the beginning of civilization. Two hundred years ago, the technological power of science was discovered, increasing the production of goods by thousands fold. This was the industrial revolution, and it again changed civilization. Now, we are in the midst of a third revolution, the digital revolution, which started when the use of computers began to spread, and is still in progress today. With every revolution comes a shift in the way people live their lives and view the world. This can be frightening, but by keeping a clear head and drawing on the knowledge we have of history and the enterprises underway today, we can weather the storm and rest in the knowledge that things will probably end up even better than before.

We humans have a tendency when thinking about the future to shrug and say, “who can know what will happen tomorrow?” The weather report is notorious for incorrect predictions, and every single poll was wrong about the most recent U.S. presidential election. But there is nothing magical about the future. It is true we cannot be sure of the details of what will happen tomorrow, but reality is not random. Random is a word that means “something a human brain cannot find a pattern in.” Nothing is truly random; that would be quasi-real. Instead, it is probabilistic. The more you know about how things work, the better you will understand the probabilities, and the better you will be able to predict the future.

Thousands of years ago, a solar eclipse was a mind-bending experience. The sun was not supposed to go dark, so when it did, it was seen as an omen of the most terrible things, such as the end of the world. When they would happen, only the gods knew. But once intelligent and learned people started to chart the paths of the moon and sun through the sky, they gained the ability to predict when the next eclipse would occur. Nowadays, using computers and Newton’s Law of Gravity, we can predict the time and length of a solar eclipse, as well as the track it will take over the Earth, a hundred years in the future, to the exact minute.

In his science fiction series of short stories, Foundation, the author and futurist Isaac Asimov proposed a fictional branch of psychology called psychohistory, which could predict the future of human history with mathematical equations. In the story, the psychologist Hari Seldon is able to predict the fall of the galactic empire and set events in motion so that over a thousand years, a new, grander empire will rise from its ashes. Each of the short stories in the series tells of a turning point in history, a “Seldon crisis,” predicted by Seldon’s model, such as an approaching war or a dictatorship trying to build its own empire, and how it is solved by those who trust in the mathematical power of psychohistory.

The better versed we are in the tools of science and mathematics, the better the educated guesses we can make about the future. The most knowledgeable collaborations of experts today have predictive ability about halfway between solar eclipses and psychohistory. We can make models of complex systems like the Earth’s climate for the next hundred years at a low resolution and an uncertainty of only a few percent. Though we cannot say with certainty what the future of humanity will be like, the more we know about history and philosophy, and the more practiced we are at critical thinking, the clearer it appears.

In this new series, Visions of the Future, I’ll talk about the ways I think things will change in the future as a result of the digital revolution. Some are positive, some are negative, and some depend on whether people can adapt their views. For the series, I make the common sense assumptions that people crave freedom and true knowledge. Because of this, though there might be periods of oppression and backward slippage, the long-term march of history is toward a better standard of living for all.

The Magic of Emergence

What is Knowledge?

Toolbelt of Knowledge: Concepts
Algorithms
Equivalence
Emergence
Math
The Anthropic Principle
Substrate-Independence
Significance

Suppose you have three blobs of paint, one blue, one red, and one yellow. They aren't very interesting, just puddles of color sitting in packets on a tray. Now suppose you have a large, blank sheet of paper. If you came across one of these while walking through a building, you would probably ignore it and forget that it was there. You also have a stick with fine hairlike bristles on the end. It is mildly entertaining to tickle your thumb on them. All these things are pretty boring on their own. Mostly they just sit there, doing nothing. But if you combine them, you can make something new: a painting. In fact, you can make an incredibly large number of different paintings. When you combine the right paintings, you can get an art gallery or museum.

In a logic-based universe like ours, there is a feature that is truly amazing. A few simple things can come together and make new things, which have properties and functions that are different than their parts. This is called emergence. The new things can then come together to create more things at a higher level of complexity, which can then come together in an even higher level of complexity.

Let's think about matter. Its basic building blocks are protons, neutrons, and electrons. It's actually more complicated than that, but this is correct enough for our discussion. These things, in various combinations, make up all of the atoms on the periodic table. These elements react together in chemistry making millions of different kinds of molecules. These molecules make up water, bricks, ink, plastic, DNA, and all of the kinds of matter in the universe. Types of matter come together to make systems, which can combine to make more complex systems, and so on and so on.

Emergence appears anywhere logic presides, including mathematics and computer programs, Many games use a few simple elements to create a huge variety of ways to play. Take chess, for example. It has a king, a queen, bishops, knights, rooks, and pawns, each with its own way to move. From the rules of these pieces emerge an unlimited number of games and strategies, like pins, forks, and Scholar’s Mate.

The fact that endless complexity can arise from simple parts is awe-inspiring. Knowing how emergence works can boost our creativity and help us understand all kinds of things we once thought inexplicable, opening doors of knowledge that lead to possibilities boundless and amazing.

Are We Entering a Post-Truth Era?

Turning on the news these days, it may seem like people have abandoned the idea of Truth in favor of their own beliefs. With news sources going at each other’s throats, politicians using stage manipulation tactics instead of rhetoric, and constant outrage plastered all over our social media, it can feel like nobody cares about reality anymore. The question arises, have we entered a time when the respect that we humans have for Truth will slowly decline until it fades away?

I think not. I think it likely that the idea of a post-truth era comes from the availability heuristic. As humans, we have a set of cognitive biases, shortcuts we take in our reasoning, which often lead us astray. The availability heuristic is a bias where we put more weight on what we see, without finding out whether this small amount of information is an accurate representation of the whole. Take a break from the screen and the newspaper, and pay attention to the people around you. You can probably tell that they are interested in true knowledge, even if you disagree with them on some things. The news runs on sensational stories, so the regular, polite, average person gets pushed to the side, and all we see are those who are loud and have their blind spots on display.

The truth of something is not always obvious to everyone. It would be easy to think of something that you know nothing about, such as the most abundant species of algae in the world. Yet there is someone out there who knows it like the name of a best friend. Even if something seems obvious to you, there are people who have never considered it before, and those people may have some knowledge that seems obvious to them, but that you have never thought of before.

I don’t think this state of many groups of people disagreeing about all kinds of things and having their own “truth” is new, I just think that with the age of the internet, these different views are being exposed to regular people on a global scale. For the first time in history, knowledge and opinions are easy to come by, so all of the weird things that people believe are suddenly on display. The tempting reaction to this is, “that’s not right, stupid. Have some common sense,” but we seldom realize that we ourselves may have views that they see as equally obviously wrong.

The thought that in some golden age of the past everybody had common sense and believed the truth, is an illusion. Everybody believed whatever they wanted in the past too, we just couldn’t see it. But that’s not all. You see, there is something special about Truth: it fits together like a giant jigsaw puzzle. With information freely available, even with so much nonsense out there, anyone with an honest interest in the pursuit of Truth has a much easier time nowadays than they did in the past. I think it is safe to assume that the average person desires to become smarter and wiser, and because of this new opportunity, they will, and so will humanity as a whole. Instead of entering a post-truth era, I believe we are emerging from a pre-truth era. The unrest and outrage we see all around are merely the birth pangs of a new age of Enlightenment, where knowledge and wisdom abound, and the good people of humanity can join together in creativity and cooperation.

Moral Theory VI: So How Should We Live?

Moral Theory:
I. Intuitionism
II. Authoritarianism
III. Divine Command and Attributes
IV. Ethical Egoism
V. Utilitarianism
VI. Virtue and the Golden Rule

Negative Morality:
Divine Hierarchy

Last time in the Moral Theory series we started from basic observational facts about human beings, and building on them with logic, came to the conclusion that the objective truth of morality is Utilitarianism, where utility (the good to be maximized) is defined as the sense that things are as they should be, both outwardly and internally, which I summarized with the word “satisfaction.” Yet even though this is built on a bedrock of logic and facts, it still has a lot of problems. The most glaring is the information problem. To do what is best, one must know two impossible things: the subjective experience of other people, and all dimensions of all possible consequences of all possible actions. Almost all of the people in the world know what is good for them better than anyone else does, with the exceptions of young children and sometimes people who are very close to one another, and most of us are bad judges even of what is best for ourselves. The effects of moral actions are part of a vast, chaotic system, where one thing causes eight more, which each cause many more, and so on. We know so little about the broader consequences of our actions that we might as well be clueless.

But we don’t have to rely on Utilitarianism alone for moral guidance. That would be like using only quantum physics to try to figure out how to use a new coffee machine. Sure, quantum physics is the bedrock truth of how matter works, but there are easier ways of thinking about coffee makers to get them to do what you want. The same is true with morality. Utilitarianism may be the bedrock truth, but there are other, simpler systems that can guide us to do what is good. Throughout the series, we have talked about some of these systems, but now with Utilitarianism we have the tool we need to evaluate each system and compare them to each other, to determine which is best for which situation.

The simplest, most elegant system for good moral behavior is the Golden Rule. It has several different phrasings. The Book of Matthew in the Bible says, “do to others as you would have them do to you.” Confucius said, “Do not impose on others what you do not wish for yourself.” But my favorite, and what I think strikes best at the heart of the rule’s meaning, is the way Immanuel Kant stated it, which he called the Categorical Imperative, “act so as to treat people always as ends in themselves, never as mere means.” This means that nothing is more important than people, and everything we do should be for the benefit of people. This might seem familiar. After all, it is basically the same good as identified with Utilitarianism, except explained in way that is easier to apply to our everyday encounters with others.

The Categorical Imperative has an added bonus, in that it resonates strongly with our moral intuitions. It just feels right. When searching for a way to live morally, the Categorical Imperative is a great place to start, and even if one lives their entire lives without moving to something more complex and nuanced, it has a very high chance of leading to a life full of goodness.

However, no one is perfect, and people fail to live up to the moral expectations of others and of themselves. People break rules, they lie, they steal, they shout at each other and refuse to understand. Despite this dismal truth, though, there is no need to despair. Instead, we can look to Virtue Ethics, the principle of accepting ourselves and others as we are, and always looking for the next step to become better.

It is not reasonable to expect anyone, least of all yourself, to become perfect overnight. People can change, but only through small, gradual changes over time. Virtue Ethics is a way to focus on that change in ourselves, not to compare ourselves to others, but to measure ourselves against what we were yesterday, or last week, or last year. When we succeed at this, we feel an amazing sense that the ancient Greeks called eudaimonia, which is revered by philosophers as a state of mind more desirable than happiness. It is the sense that, though things may not be perfect, we are moving in the right direction internally, and because of that we can accept life as it is given to us.

Virtue is a clean, nourishing word. It brings to mind traits like patience, courage, and self-control. However, virtues are not a set of rules for how to live, rather they emerge as side-effects of a person's never-ending journey toward being a better person. Virtue Ethics is all about the journey, not the destination.

Utilitarianism may be the bedrock factual truth about morality, explaining what is good, but it does a lousy job at telling us how good we should be and what to do to get there. So instead of being a guide to morality itself, it works better as an objective standard by which to compare other moral systems that are subjective, but easy to digest. Most of what we have talked about in this series does not score very well. However, the Categorical Imperative, considering its simplicity and all the good it leads to, gets an A, and the contagious positivity of Virtue Ethics gives it an A+. Combining Utilitarianism's objective scale, the reference point of the Categorical Imperative, and Virtue Ethics’s push to always move forward, we have found a robust system of morality, which can be as complex or simple, as nuanced or general, as global or personal as we need it to be.

Announcing: Short Story Series, The Well of Images

Read Part 1: "Pandora’s Gate," at WritersCafe.org

After years of blogging, practice writing, and listening to experts, I am proud to announce the debut installment of an original series of short stories, called The Well of Images, formerly under the working title of Project Soul. It tells of the adventures of two college students who discover that the Jungian collective unconscious is literal, and they have the ability to go there and explore. In this series of worlds made out of mind stuff, the characters meet mythical archetypes, face sides of themselves that they didn’t know they had, and confront deep questions about the natures of humanity and reality.

The series will be laid out with several “books,” which have overarching plots and themes, which are broken into “parts,” or “chapters,” which each contain their own plot. It is like a TV show, with the books being seasons, and the chapters being episodes. The first book, The Mentor, The Hero, and the Trickster, will have five parts, and the others may have more. I do not have a release schedule, since I do not know my own writing speed well enough to know the correct pacing, but I would not expect more than one part every two months. The first part, "Pandora’s Gate," is finished and available for reading.

November is over, which means National Novel Writing Month (NaNoWriMo) has come to a close. This year, I wrote drafts and scenes of The Well’s upcoming chapters. The default goal of the event is to write 50,000 words by the end of the month, but I kept instead to my personal goal to write at least 1000 words every day. I found this to be easier than last year, and it gave me better results too, leaving me with workable material instead of pure trash.

In a continuing story like this, there is no way to predict everything that will need proper setting up. I might look back on the early chapters with the wisdom of hindsight, and want to touch them up and make slight alterations to the events. Because of this, I’m reserving the right to come back and edit these early parts if I feel it is appropriate.

They say you need to write a million words in practice before your first book gets published. Right now, I’m at a few hundred thousand, and The Well will be the key to the rest. It is my first serious attempt at an original story with the knowledge I have gained from blogging and from listening to experts, and I feel like I am making good progress. Someday, I just know, I will be able to walk into a bookstore and find something with an eye-catching cover and my name on it, but for now it’s a step forward to post stories on the internet for free.

The Mentor, the Hero, and the Trickster:
1. Pandora’s Gate
2. Where Secrets Lie
3. Limits of the World
4. The Fool’s Gift
5. Loki’s Game

If you like "Pandora's Gate," why not support me on Patreon? It means a lot to me to know that others find what I am passionate about to be meaningful.

NaNoWriMo 2017

As November approaches, writers prepare for National Novel Writing Month, an event meant to get the creative juices flowing and motivate writers to prove to themselves that they have what it takes to finish a draft of a book.

Last year I cranked out a 30,000-word science fiction novel about a space station at the end of time, called The Void Stared Back. It was rough, and there were times when I felt like I was torturing myself, but I pulled through and gained valuable experience. As December finally arrived, I breathed a sigh of relief and told myself I never wanted to do it again. For the next eleven months, I planned on not participating this year. However, once the coolness of fall arrived, I started to feel a strange sensation: that it is writing season. I became excited to write, and ideas started coming in a deluge. As October progressed, I came to realize that I actually do want to participate in NaNoWriMo again.

For my topic, I have several options. I could try for a better version of Void, I could go for the sequel to Raiders, or I could focus on Moebius and finally finish a draft. However, after realizing my skills are not at publishing level yet, I've decided to take a break from novels and practice on a series of fantasy short stories, which I will publish for free online somewhere. So this November, I am committing to write at least 1,000 words every day for this series.

Although I have a skeleton outline for the major themes of the series, I doubt I'll be able to write the 30,000 words in chronological order. Instead, I will work on the many different scenes floating around in my head, and sort through what to toss and what order to put the rest in later.

Committing to NaNo for a second time is more daunting than it was the first time, because I know the pain I will be calling down upon myself. But I also know I can succeed, and that the experience I get will give my skill and diligence a leap forward. With a sweatshirt around my shoulders and a cup of hot coffee on my desk, I will resolutely face up to the challenge.

This blog may not see much action for the next few weeks, since I will be busy writing something else most of the time, and I still have teaching and grading duties to keep on top of. However, I did manage one discussion last year, and I don't have homework problem sets to do this year, so we'll see.

Moral Theory V: The Greatest Good

Moral Theory:
I. Intuitionism
II. Authoritarianism
III. Divine Command and Attributes
IV. Ethical Egoism
V. Utilitarianism
VI. Virtue and the Golden Rule

Negative Morality:
Divine Hierarchy

Note: I did not explain good very well in this discussion, so a year later I wrote a better explanation. You can read it here.

So far, as we have examined moral systems in our search for objective morality, we have gotten lucky and found contradictions. However, there may be many moral systems that have no internal contradictions. If we want to be able to compare them objectively, we will have to approach the question from a different angle. Today, we will see what we can find out by starting with observations and building upon them with logic.

So far, we have asked “what is morality?” But when we look closer, we can see that question can be broken up into two: “what is good?” and “what should we do?” The second question looks like it depends on what “good” is, so let’s put it aside for later and consider the first one.

To begin, let’s take a step back even further and ask why we have moral systems in the first place. Why do we care about how we and others choose to live our lives? The answer is because we want to strive to create a state of affairs that satisfies us, about which we can say, “this is good.” Although each of us has different ideas of what “good” is, we all have something in common, in that we want to be satisfied by the way things turn out and the actions we and others took to get there.

Perhaps, then, we are blinded by the actions we think of as good, like helping people, being rewarded for hard work, etc., and are missing the real purpose of morality: to be satisfied with what we and others have chosen to do, and with the results that have come from it. Satisfaction is the goal of every system of morality, which means satisfaction is equal to goodness. The answer to “what is good?” is satisfaction.

Knowing this is not enough, though. We are still left with a bunch of competing moral systems, all of which differ in whose satisfaction matters and what types of satisfaction are emphasized. We need a way to take morality from the subjective view to the objective. 50 years ago, philosopher John Rawls suggested we view the world from the Veil of Ignorance, where we look at the world as if we do not know who we are. From this objective perspective, all people are equal, and no one’s need for satisfaction deserves more weight than anyone else’s. The objective good, then, is to increase the total amount of satisfaction experienced by humanity, and all creatures capable of experiencing it.

This leads us to the moral theory of Utilitarianism, the idea that the best, most moral actions are those that create the greatest good for the greatest number of people. As John Stuart Mill said 150 years ago, “actions are right in proportion as they tend to promote happiness, wrong in proportion as they tend to produce the reverse of happiness.” Mill called it “happiness,” and I call it “satisfaction,” but context shows that what we mean by these words is in principle the same thing.

Utilitarianism brings up a lot of questions whose answers are not immediately clear. For one, how do we deal with the fact that sometimes people get satisfaction out of hurting others? Do we say that some kinds of satisfaction are good and some are bad? That would seem to undermine the whole argument. However, we don’t have to say that; Utilitarianism takes care of it naturally. All satisfaction is good, but it must be totaled up over all people. If someone takes satisfaction at another’s expense, it is usually worse overall than if they had left each other alone, and always worse than if they had worked together to increase both of their satisfaction.

But what if there is no possible way for everyone to be satisfied? What if no matter what anyone does, someone will have to suffer? There is a classic counterargument to Utilitarianism that goes like this: suppose there are five patients in a hospital who each need an organ transplant, or they are going to die. In the waiting room, there is a perfectly healthy person here for a visit. Wouldn’t Utilitarianism say that it would be better to kill the one person in the waiting room and take their organs than to let the five patients die?

The answer is no, as killing someone in the waiting room has broader consequences beyond the six people in the example. If people can be killed for their organs, it creates what I call a Shadow of Fear, a stifling blanket over everyone in society, as they are afraid of being killed for their organs. The amount of satisfaction lost from everyone in society under a Shadow of Fear outweighs the satisfaction of continued life from the five people who were going to die.

What if the doctors cover it up? What if they claim the person in the waiting room died from a heart attack, and so using their organs was justified? This would seem to eliminate the Shadow of Fear, bringing Utilitarianism back under fire. However, such a lie is unstable. If the truth were to come to light, it would create a stronger Shadow of Fear than if they had been honest from the start. Not only would there be a Shadow of Fear about the possibility of being killed for one’s organs, but there would be a further Shadow of Fear about the deception; people would be worried that there are other cover-ups that they don’t know about, and they might be harmed or killed for all kinds of unknown reasons. The mere risk of such a shadow outweighs the satisfaction gained by the five saved patients, and Utilitarianism prevails again.

Another common counterargument regards sacrificing oneself for the greater good. Hypothetically, if there was some kind of monster who would gain tremendous satisfaction from eating you, so much that it would outweigh all the satisfaction you would have in the entire rest of your life, wouldn’t Utilitarianism say that it is best for you to feed yourself to that monster?

Maybe, but maybe not. Humans are extremely bad at predicting all possible futures, so in almost every case, we would have no way to know whether we would have more satisfaction in the rest of our life than the monster would gain by eating us. But there might be some kind of extreme circumstances where we would know, and that seems troubling.

However, we actually make this decision all the time; it’s called eating meat. We sacrifice the futures of animals for our own pleasure, even raising them from birth for the purpose of eating. The amount of satisfaction from the pleasure we get from eating a meal is certainly less than the amount of satisfaction the animals would have experienced in the rest of their life, yet we feel it is justified. So then, so what if Utilitarianism tells us that there are possible circumstances where it would be better to feed ourselves to a monster? What license do we have to complain about the perceived speck in Utilitarianism’s eye, when we have this plank in our own?

What about intentions? Utilitarianism is a consequentialist theory, which means the goodness of an action is determined by its consequences, not the intentions of the person who performed it. This will lead to situations where people with malicious intent end up doing good things, and people with good intent end up doing bad things. At a glance, Utilitarianism seems to say the person with good intent is worthy of condemnation and the person with bad intent is worthy of praise. But this once again ignores the broader context. People with good intentions are more likely to do good in the future, and people with bad intentions are more likely to do bad. So the desire and effort to do good can be as praiseworthy as good consequences, or even more so. It is also noteworthy that it is more satisfying to oneself to have good intentions than bad.

There are still many questions left about Utilitarianism that I don’t have the answer to. What level of satisfaction, if any, is low enough that it is equal to nonexistence, and are there states of living that are worse than death? Would it be better to have billions of people in near-death misery, or millions in luxury? What about animals, whose brains are not powerful enough to have moral intuitions, but can feel pleasure and pain? These questions are interesting puzzles for philosophers to debate over and solve. Despite the uncertainty, I am convinced that Utilitarianism is the objective foundation of morality.

There is one major problem left, though. Utilitarianism is only half the answer; it tells us what “good” is, but it does not tell us how to act. We cannot be obligated to always and only do that which is best, because it is impossible for us to know anything close to the amount of information required to make that kind of decision. Other than that, Utilitarianism does not provide a clear line between good and bad, nor give us instructions on how to increase goodness. So how can we hope to live good, moral lives? The answer is that Utilitarianism is not exclusive. It allows and even encourages other moral systems, including those we have already talked about. Utilitarianism gives a way to know when to follow rules, when to trust your intuitions, when to serve yourself, and provides a foundation for God’s nature and commands. Utilitarianism does not tell us what to do, but gives us a measure by which to compare prescriptive moral systems against each other. Next time, we will look at a final two moral systems in our quest to answer the final question, “how should we live?”

What is at the Edge of the Universe?

When we think about objects, we usually picture them as having some size, some volume of space they take up. There is an inside, and an outside. Inside, we say the object is “there,” and outside of it, the object is “not there.”

But what about the Universe? Does it have an edge? Is there some place we could go that we could say we are not in the Universe anymore? Perhaps if we got into a space ship and went far enough, we might come to some kind of boundary that stops us from going any farther. Yet once there, the next natural question to ask would be, “what is beyond this wall?” If we dug at it with picks and shovels, could we chip away at it, and maybe break through? Wouldn’t that mean there is actually more of the Universe past it?

Before we go any further, what exactly is the Universe? Our intuitive understanding is that the Universe is all of space and time and everything in it, but there are places and times where this definition gets fuzzy. So let’s try specifying it further. The Universe, for the purpose of this discussion, is all of space and time that can be gotten to by some smooth path through space and time, and everything in it. This would mean that if we came to a boundary that was the edge of the Universe, there would be nothing beyond it. In fact, there would be no “beyond it” at all. It might be possible to push against the barrier and make a dent in it, but we would be creating new space rather than discovering what was already there. This is very hard to imagine, even for me. Interestingly, such a barrier is physically possible: it could be an event horizon, a surface that requires going faster than the speed of light to pass. If nothing, not even space itself, could get to the other side, then we would have ourselves an edge of the Universe.

Such an event horizon would cause the shape of the Universe to be curved in ways that would be observable in the distribution of galaxies and how their light travels as it comes toward us. We see no sign of such things. As far as we know, the Universe is infinite in size. Nevertheless, it has a finite age, 13.8 billion years. Light takes time to travel, so the farther away something is, the closer to the beginning of the Universe we see it. In fact, there is a surface so far away that it is basically the beginning of time compared with the age of the Universe.

The entire sky unfolded.

In its cradle days, the Universe was thousands of degrees, so hot that electrons and protons could not stick together to make atoms. As the Universe expanded, it cooled, until the protons and electrons merged to form hydrogen, and the light that had been bouncing around the plasma soup became free to fly across the universe unbounded. This light started out visible, but got redshifted as the space it traveled through expanded, until today, when it is in the microwave spectrum. We now call this light the cosmic microwave background. It comes from the same distance in all directions, making its source the surface of a sphere centered on us, which we call the surface of last scattering, which for some reason sounds incredibly poetic to me.

As far as we know, there was no time before the big bang. Time literally started then, so the phrase “before the big bang” is meaningless. It is theoretically possible that future space-based gravitational wave observatories will be able to detect gravitational waves from before the big bang, but so far we have no reason to believe such a time existed. Thus, there is a certain distance that cannot cannot be seen past, because light from beyond it has not had time to reach us in all of time. This distance marks the edge of what is called the observable universe. Indeed this is not far beyond the surface of last scattering, 13.8 billion light years away.

The first moment of the big bang is not really a boundary in space, but in time. However, space and time are united by the speed of light, so if we think from the perspective that the farther something is away from us the further back in time it is, we could say the edge of the observable universe is the edge of the Universe.

On the other hand, perhaps the Universe has a finite size, but no boundary. It was once thought that the Earth had an edge, and that you could fall off. However, we now know that the Earth is a sphere; if you travel far enough, no matter which way you go, you will eventually end up where you started. It is theoretically possible for the same thing to be true of the Universe; if you go far enough in any direction, you will end up back where you started. It would be like the old arcade games, where going off one side of the screen puts you on the other side. This can be difficult to imagine for the Universe, since the Universe has three dimensions whereas the surface of the Earth has only two, but there is nothing wrong with it in theory. However, such a geometry to the Universe would leave signs in the structure of the filaments and voids, which we do not see. As far as our current knowledge can tell, the Universe is infinitely big.

The tunnel leading to the left connects with the one leading to the right.
If there were no walls, the game would be finite in size, but unbounded.

An infinite Universe brings up a new question; what is it expanding into? If the galaxies are moving away from us, wouldn’t they run into the galaxies that are farther away? The key to understanding is to realize it is not the galaxies that are moving, but the space between galaxies which is stretching out. The farther galaxies are being carried away faster than the close galaxies, and the galaxies that are even farther are being carried away even faster, and so on and so on to infinity. Bizarre, but it is theoretically solid. The reason this concept seems so strange to us is because we do not have everyday experiences with infinitely large things.

What if there is not an edge of space, but an edge of stuff? Might there be some distance we could travel, that when we got there we would see nothing beyond but an empty void for all eternity, behind us the brilliance of stars and galaxies uncountable, before us nothing but darkness? When astronomy was young, we though the bunch of stars around us making up the Milky Way galaxy was all there was, and assumed that outside of our galaxy there was a vast expanse of emptiness. Then along came Edwin Hubble, who measured the Andromeda Nebula to be far outside the Milky Way. This meant it was not a nebula at all, but another galaxy. For a time, galaxies were called “island universes,” until we decided that it was more convenient to speak of them as objects in the one Universe. But is there an edge to the galaxies? Galaxies clump into clusters, and galaxy clusters clump into filaments (sometimes called superclusters). Between filaments, there are vast empty regions called voids, which have no galaxies in them. It turns out that as far as we can see, no void is endless, and the galaxies continue on forever.

There actually is a kind of barrier in space right now. Einstein taught us that nothing can go faster than the speed of light, and Hubble taught us that the Universe is expanding. By “expanding,” we do not just mean that things are getting farther apart, although that is true, but that space itself is stretching out. Nothing can go faster than light through space, but there is no limit on how fast space can stretch. Therefore, there is a distance called the cosmic event horizon (not to be confused with the hypothetical event horizon at the edge of space we talked about above), where space is expanding away from us at the speed of light, and everything past it is expanding away faster than light. No matter how fast we go to chase this horizon, we will never be able to reach what has passed beyond it.

However, if we think about it, the cosmic event horizon does not feel like a boundary, because it never stops us from going farther. Indeed, it is always about 16 billion light years away from you in all directions, no matter where you are and how far or fast you have traveled. Everything is in the center of its own cosmic event horizon. Thus, if you were to get on a space ship and fly at the speed of light for 16 billion years, you would never be stopped by any kind of edge of space. However, Earth would pass out of your cosmic event horizon, and you would never be able to go home.

Following the cosmic event horizon to its logical conclusion, we find that sometime in the far distant future all of the galaxies that are not in our own gravitationally-bound cluster, the Local Group, will continue to expand away from us, until they have all passed the cosmic event horizon. Once this happens, the edge of the Local Group will be the edge of stuff, because no matter how far or fast we fly away from it, we will never reach anything else. Then, the age-old hypothesis of the island universe will become true.

Credit: NASA/CXC/M.Weiss

So if the Universe is infinite in all directions, with nothing stopping us from going in a straight line forever—excluding the odd bit of matter we may have to go around—there is really no edge to the Universe, right? The question does not make sense, because there is no place that would be outside the Universe. . . . Except there is still one little detail we have overlooked: the Universe has three dimensions. We have up-down, left-right, and forward-backward. Where exactly each direction points does not matter; what is important is that we can have three lines intersect at a single point and all be at 90 degree angles from each other. But what if there is a fourth dimension? Other than time, I mean; time makes everything more complicated.

A fourth dimension in space is extremely hard to visualize. We may wonder if there is any reason to think about it, since it seems impossible. However, we know of no reason why our Universe had to have three dimensions. As far as we can tell, it was more or less coincidental. There is a theory, beyond the edge of currently measurable physics, that suggests there are many universes with different numbers of dimensions. It is called String Theory.

String Theory deals with things called D-branes, which are objects with a certain number of dimensions, and to which the hypothetical 1-dimensional strings that make up all matter are attached. The only thing we know of that could be classified as a D-brane is the Universe itself. If String Theory is true, our universe is a mere 3D subspace of a 9- or 10D hyperspace, and all the matter we have ever observed is stuck to it.

Think of an infinitely large piece of paper. Imagine drawings that can move. These drawing can go up, down, left, and right, but no matter what they do they cannot get off the paper. Now think of us and the Universe. We can go up, down, left, right, forward, and backward. But if we could step even a single inch into a fourth dimension, we would find ourselves outside the Universe.

Whether or not String Theory is true, whether or not there is any higher-dimensional space or not, we have found the edge of the Universe. We won’t find it by looking out into space. No, the edge of the Universe is here. We are touching it right now. Bounded within these three dimensions, unable to reach even a millimeter into a fourth. This is the edge of the Universe.

Gravitational Waves, LIGO, and the Nobel Prize

Every year, the Nobel Foundation awards a prize of over a million dollars to people who have made groundbreaking impact in each of six categories: peace, literature, medicine, economics, chemistry, and physics. Each prize can be split between up to three people. On Tuesday of this week, the winners of the physics prize were announced: Rainer Weiss, Kip Thorne and Barry Barish, leaders of the LIGO Collaboration. LIGO, the Laser Interferometer Gravitational-Wave Observatory, heard humanity’s first gravitational wave two years ago. My own research involves looking through LIGO data for signals. Although I came on board after the famous first hit, I still feel awash in team spirit at the Nobel Prize announcement.

Left to right: Rainer Weiss, Kip Thorne, Barry Barish

A gravitational wave is a ripple in spacetime that travels across the universe at the speed of light. Put simply, gravitational waves are to gravity what light is to electromagnetism. But to understand it more in depth, we need to shake loose a common paradigm about space. We all start out thinking of space as flat. By flat, I of course don’t mean squished, but that parallel lines stay parallel no matter how far you go, the inner angles of all triangles add up to 180 degrees, and if you go in a straight line in any direction in space, you will have to turn around if you want to get back to where you started. Flat space may seem obvious to our minds, and maybe even the only possibility, but it is actually not true.

Curved space is not easy to comprehend, nor to explain, and adding time to the mix just makes everything crazy. Nonetheless, the universe we live in can and does bend, compress, expand, and warp. Have you ever had a dream where you were running down a hallway, only to find that the end kept getting farther away from you instead of closer? That’s what expanding space is like, except it’s cool instead of scary. If you imagine a hallway where you stay still but the end moves back and forth, closer and farther—on a solid foundation, without motors or anything—that is spatial expansion and compression. There is more to the curvature of spacetime, but for today, all that really matters is compression and expansion.

Image credit: NASA

Gravity is commonly thought of as the force that binds the universe together. It keeps planets moving around stars, and stars inside their galaxy. But technically, gravity is space that is ever so slightly bent. If you could measure triangles with extreme accuracy, you would find that a triangle that wraps around the sun will have interior angles that add up to ever so slightly more than 180 degrees. If that is difficult to understand, don’t worry, the important thing is that gravity is a distortion in spacetime.

What would happen if the sun were to suddenly disappear? We might think that all of the planets would immediately stop orbiting and fly off into interstellar space. But that is not correct. The effect of gravity is not instantaneous, but is limited to the speed of light. The sun is 8 light minutes from Earth, so it would be 8 minutes before the Earth stopped feeling the sun’s gravity. It would be longer for the outer planets.

The sun disappearing is completely unrealistic, but there are more realistic phenomena that cause gravity to change extremely quickly. There are things in the universe that are so massive and so tightly packed as to defy comprehension. Neutron stars, for instance, have masses slightly greater than the sun’s, but they are packed into a space the size of a mountain. Their gravity is so strong and it crams the matter they are made of so closely together that their atoms collapse and only neutrons are left. When two of these monsters orbit each other closely enough, they whip around in circles thousands of times every second. That’s some serious changing of the gravitational field! Because they orbit in a circle, the change in gravity is periodic, meaning it repeats itself. A periodic change in gravity traveling outward at the speed of light is a gravitational wave.

The waves actually go more up and down than sideways, and they are invisible. Probably.

Neutron stars whipping around each other at insane speeds is one source of gravitational waves. Black holes, objects more massive and even more dense than neutron stars, are another. But the real money comes when they collide, throwing off so much energy that they are the most powerful type of event in the universe next to the big bang itself. Indeed, all of LIGO’s signals so far have come from colliding black holes. At first they orbit, multiple times the sun’s mass whipping around hundreds of times every second, until, bam, the two black holes become one. At this point, several suns’ worth of mass is converted into gravitational energy at once and sent across the universe in something like a shockwave in all directions. When this front washes over the Earth, our detectors send out the alert.

When a gravitational wave passes over us, what does it look like? Imagine holding a large, rubber loop, between your hands in front of you so that you can see through it. You start squishing the loop and relaxing, getting a nice bouncy rhythm. As your hands move closer together, the sides of the loop get squished and the top and the bottom get longer, and when you move your hands apart, the sides of the loop get longer and the top and bottom get squished. The space a gravitational wave travels through is like the loop. As the gravitational wave passes through it, it expands space in one direction and compresses space in the other direction, and then the expanded direction compresses and the compressed direction expands.

After traveling billions of light years across the universe, gravitational waves become super weak and ridiculously hard to detect. We’re talking one part in a hundred quintillion (1 in 1 followed by 20 zeros). This number is so small that our brains are not equipped to deal with it. We are looking for a change as small as a thousandth the width of a proton compared to 4 kilometers, or the width of a human hair compared to the distance between the sun and the nearest star. That’s a big difference. To detect such infinitesimal changes, we are going to need some seriously high-tech machinery.

That’s where detectors like LIGO come in. LIGO is an interferometer with 4-kilometer arms, which act as moving hallways for the light that travels down them. A laser is shone through a beam splitter, which makes half the beam go down one arm and half the beam down the other. Mirrors at the ends bounce the light back, and the beam splitter reunites them and shines the recombined beam toward the light detector. Normally, the returning beams are out of phase, which means the detector sees nothing. But if a gravitational wave comes by and changes the length of the arms while the light is in them, even by a distance smaller than a proton, the light will change phase ever so slightly and suddenly the faintest shimmer will make it to the light detector. That shimmer is all we need to find out everything we want to know about the source of the gravitational wave.

And we have not even mentioned all the noise-countering technology involved. Wind, tiny earthquakes, a car driving by, a change in temperature or humidity—all these things will contaminate the data. So we need a plethora of other sensors around so that we can log every tiny thing that happens and cancel it out from LIGO's data. Despite how monumental the challenge, LIGO is successful. In its two six-month-or-so runs, it has confidently found four pairs of merging black holes.

Before LIGO, we had two windows into the universe. The first was light, not just what is visible, but the entire electromagnetic spectrum. This showed us that there are billions of stars in our galaxy, and billions of galaxies in the observable universe. The second was particles, cosmic rays, neutrinos, and more. These taught us about the magnetic fields between the stars and the chemical and nuclear processes that happen in stars and nebulae. Now, there is a third window open, of gravitational waves, which will let us hear the hidden mysteries that cannot be seen. It is right and just that those who contributed the most effort toward opening this window receive their due recognition and be remembered by history, as Galileo has been for inventing the astronomical telescope.

Moral Theory IV: Serving Oneself

Moral Theory:
I. Intuitionism
II. Authoritarianism
III. Divine Command and Attributes
IV. Ethical Egoism
V.  Utilitarianism
VI. Virtue and the Golden Rule

Negative Morality:
Divine Hierarchy

Last time, we argued that objective moral Truth is independent of the existence of God. After learning this, one might come to believe that without a divine source, the only measure of morality left is for people to do what is best for themselves, to spend life pursuing their own goals, interests, and desires. In this view, if helping others does not benefit someone, they have no moral obligation to do so. Basing one’s moral principles on self-interest is called Ethical Egoism.

Ethical Egoism is a two-sided coin. On the one hand, it can inspire people to work hard and put lots of effort into mastering skills, learning, and becoming a better person. The book Atlas Shrugged by the infamous Ethical Egoist Ayn Rand, despite its mind-numbingly shallow characters, has inspired and motivated people to compose beautiful songs, write best-selling novels, or start successful businesses. A few hours after I started reading it, I put it down and cleaned my apartment. There is just something about the call to get up and do something worthwhile that puts fire in people’s veins.

The cover for Faith of the Fallen by Terry Goodkind,

who portrays Ethical Egoism as heroic.

On the other hand, Ethical Egoism has no judgment for those who can screw other people over and get away with it. It would say there is nothing wrong with being a con artist or a thief or a money-grubber if doing so won’t have any negative effect on you or your future. And since competition inevitably favors those who play underhandedly, societies built on Ethical Egoism make it easy for the selfish and devious to rise to the top. Once in power, they rewrite the laws to further benefit themselves at the expense of everyone else. It is Social Darwinism, survival of the fittest applied to human wellbeing, and Ethical Egoism only shrugs.

It is a mixed package. The grandness of the life it offers is tempting, but there is a terrifying ugliness to the world it leads to. Our instincts pull us both ways. But we are looking for an objective foundation for morality, so for the moment, we will try to put aside our emotions and see whether Ethical Egoism has a rational foundation.

Ethical Egoism says that we should always aim toward that which would be the most fulfilling to ourselves, or in other words, we should always seek to maximize our own satisfaction. But if we follow that to its logical conclusion, we get a world of Social Darwinism, where the vast majority of people are trodden underfoot and forgotten. This does not feel like what morality should be, However, that is not actually a refutation of the theory, but an appeal to intuition, and we have already shown that intuition is not the basis for morality.

One could, in fact, still make a case that Ethical Egoism is the ultimate answer to objective morality. It may be that by everyone doing what is best for themselves, the standard of living is raised for everyone, even though the inequality between the top and the bottom makes it look unfair. However, it can be proved that is not the case. There is a thought experiment in game theory called the Prisoner’s Dilemma, which exposes Ethical Egoism’s fatal flaw. As I explain it, you can follow along in the image below.

Suppose you and someone else are partners in crime. You are caught, and questioned separately. The system is not very just, and you are given an offer: If neither you nor your partner confess, you will both get one year in prison. If you both confess, you will both get three years in prison. If one of you confesses and the other does not, the one who confesses will get off free and the other will get four years in prison. You are told that your partner has also received the same offer.

Now you weigh the possibilities. If your partner confesses, you get three years if you confess and four if you don’t. If your partner does not confess, you get one year if you do and none if you don’t. Either way, it is better for you if you confess. If you and your partner are Ethical Egoists, you will both confess and get three years. However, if you and your partner are playing as a team, neither of you will confess, so that you both get one year, which is best overall.

In cases like the Prisoner’s Dilemma, Ethical Egoism actually leads to outcomes that are worse for the people making decisions than some more altruistic moral system would. One could argue that the true option that lines up best with one’s self-interest would be to not commit crimes and to try to improve the legal system, but the Prisoner’s Dilemma is a proof of concept; only the logic matters, not the details. Ethical Egoism defeats itself, failing as a candidate for objective morality.

So far in the Moral Theory series, we have looked at the naive ideas of morality that people fall into with no or little thought, and which professional moral philosophers no longer consider worth pursuing. For the final two episodes, we will take on the big guns. We hope that the glimpses they provide us of moral Truth are as inspiring as Ethical Egoism, without the looming specter of Social Darwinism.

More Musings on Consciousness

Recommended Pre-Reading:
Consciousness 1
The Scientific Jigsaw Puzzle
Equivalence

Eighty years ago, there was a puzzle in science. Sometimes atoms broke apart into smaller atoms, releasing even smaller particles and energy. But when all of the remaining energy and momentum was totaled up, some of it was missing. Conservation of energy and momentum are two of the foundational laws of physics, so this was a real problem. To try to solve it, the physicist Wolfgang Pauli proposed that there was another particle, a neutrino, that escaped detection. Decades passed, and then finally someone was able to build a detector to search for these neutrinos, and found them.

The story of the neutrino is one way that things are discovered in science. There is a puzzle with a missing piece, people make suggestions for what that piece might be, and eventually someone finds the answer. Consciousness, however, is a different story. When we look at the human brain, it seems to function completely fine on its own, with just matter and electricity. Human behavior, decision-making, aesthetic taste, and basically everything about us can be understood by our DNA and the electrical signals running through our neurons. Unlike atomic decay with a neutrino-shaped hole, the brain puzzle is complete, and we perplexedly have a consciousness-shaped piece left over.

An extra puzzle piece that we cannot find a place for means something is wrong with the picture as a whole. In order to solve this problem, we have to identify and question our basic assumptions about our paradigm. Examining my own beliefs, I find I have always assumed an idea similar to substance dualism, that consciousness is its own substance, independent from other things. But what if it is simpler than that? What if consciousness is just what matter, or some forms of matter, looks like from the inside? This equivalence would mean that what seems to be its own piece of the puzzle is really just another way of looking at the pieces that are already in place.

At first, this seems preposterous. Rocks don’t have consciousness. Wind doesn’t have consciousness. Statues cannot see or hear. But this is where something like Integrated Information Theory comes in. A conscious experience would be meaningless unless it happens in a system of interconnected elements, each of which affects all of the others. Another way of saying this is that consciousness can only be meaningful if the information in the system is irreducibly complex and under constant change. Think of a brain. It is a vast network of neurons, connected in loops, branches, and highways. When a neuron fires, it pulses against other neurons, some of which are set off in turn. This is part of an unbroken, lifelong chain of cycles and patters. This is integrated information.

Let's do a thought experiment, where we imagine a mind whose only experience is seeing the color black. This mind has no concept of the outside world, no concept of sound, or touch, or space or time. Its entire existence is the perception of the color black. But by having nothing to compare the color black against, it does not even truly experience sight. So even though it experiences a quale, the color black, it is not conscious in the sense that we think of the word. Instead, we might call it proto-conscious.

Now imagine a mind whose subjective experience consists of only a single, unchanging scene, perhaps the equivalent of a photograph of a sunny day at the park. This mind does not think, it does not feel, and it does not get bored. Because it does not analyze the image nor remember having seen it moments before, the mind does not perceive time passing. To it, the entire lifespan of the universe is a single instant. This mind too is only proto-conscious.

The idea of proto-consciousness being everywhere in the universe, even in non-meaningful states devoid of change or organization, seems like something a mystic or spiritualist would claim. Nevertheless, given the information we have, I believe it is a sensible possibility. I am sure you have had the experience of waking up from sleep feeling a strong emotion, as if you were just in the middle of doing something stimulating, but could not remember what you were dreaming. When we are awake, our stream of consciousness is full of thoughts that flit in and out of our awareness. Most of the time we forget them instantly, and it is as if we never thought them in the first place. In other words, we have conscious and semi-conscious experiences that fade from existence and are forever lost to memory. Of course, even these examples require brains full of neurons in order to exist, but even so, is it unreasonable to hypothesize that qualia momentarily pop in and out of existence in matter all over the universe like virtual particles in a vacuum?

I often wonder if computers might have some kind of consciousness. They work completely differently from brains, storing and processing information as static bits instead of unbroken flows like neurons, but considering what we have been talking about so far, I think it is a reasonable question. If they are conscious, is it anything like human consciousness, or is it completely alien, impossible for us to imagine or comprehend? I see no reason why human consciousness should be typical of consciousness in the universe, and that there would not be senses and emotions impossible for human brains to have, or even other types of experiences we cannot imagine.

I don’t know whether mind-matter equivalence is the answer, but if it is, it would answer a lot of questions and eliminate a lot of assumptions. The puzzle would fit together, all its pieces intact, revealing a new edge to build from and explore. Perhaps we could figure out how to build artificial consciousness, or enhance our own to experience things never dreamed of. Perhaps we could learn exactly how conscious animals are, and how best to treat them ethically. A new ocean would be revealed, ready to be explored by science and science fiction.

The Profoundness of Equivalence

What is Knowledge?

Toolbelt of Knowledge: Concepts
Algorithms
Equivalence
Emergence
Math
The Anthropic Principle
Substrate-Independence
Significance

Have you ever had an argument with someone, only to find that you actually agree, but were just using different words? Have you ever memorized a long number in chunks, and then found out that someone else had memorized the number by breaking up the chunks differently? What you have stumbled upon is the principle of equivalence, the fact that something that is true can be thought about in different, yet equally valid ways.

For example, we all have our own ways of representing reality. Some of us think of reality in pictures. Some see everything in terms of words. Others see everything as equations. These are all different, but they are equally valid ways of representing reality. They are equivalent.

Equivalence appears all the time in physics. The most famous example is Einstein's Elevator, a thought experiment that led Einstein to formulate his theory of gravity, General Relativity. Einstein imagined waking up in an elevator, his body floating above the floor as if in space. There would be no way to tell if he was actually in space, or if he was freely falling down the elevator shaft. This showed him that zero-gravity and free-fall are equivalent, which, with some help from math and a few experiments, led to the realization that gravity is not truly a force but a distortion in spacetime.

For a more down-to-earth example, suppose you are holding a brick. We call it a solid object, and think of it as the stuff taking up the space within its boundaries. But we also know it is made of atoms, which are mostly empty space. So is the brick a solid substance, or is it mostly empty space? It is both. “Solid substance” and “mostly empty space of rigidly arranged atoms,” though they seem completely different, are two ways of saying the same thing. Equivalent.

Of course we also have to watch out for false equivalence, when we treat two things as the same when they are really not. Nothing is as simple as it first seems, and figuring out how to tell the difference is part of learning. The glass is half empty, and it is half full.

Being aware of equivalence and learning to identify it can help us make sense of the world and what is happening around us. Sometimes things that seem unrelated or even contradictory are actually the same thing. If we practice finding these connections, we start to see that the world is a lot more understandable than we may have realized.

Legendary Heroes

See also:
Legendary Villains

In each of our minds, we hold an ideal person that we want to be, a standard that we strive for. But none of us is perfect, and none of us measures up to the archetype we set up. Our failures discourage us. But in fiction we can find characters who pass the test, who succeed in embodying these ideals we want to see in ourselves. When we see the struggle and pain they overcome to keep from failing, our hope is renewed and we are inspired to pick ourselves up and try again, ever improving ourselves toward that unattainable standard we strive for. The characters who do this for us we call heroes. Some heroes resonate with us so well that they transcend the stories they come from and become icons of the culture. They become legends, and are known even to those who have never heard their stories.

Superman

There is no other way to start a discussion of heroes than the cape-bearing face of heroism himself. With a heart of gold and always putting others before himself, Superman is hand-crafted to be the perfect image of what is good. Not only this, but he has the power to act on his compassion, with his ability to fly, his unlimited strength, his invulnerability, and many lesser-known superpowers. Yet with knowledge as limited as any other man, Superman has to deal with a heavy burden of responsibility. He knows he can save the world, but also that by not knowing enough or losing control for a moment he could become the cause of its destruction. All this combined gives us the closest thing to the hero archetype that humanity has ever put to the page.

Batman

Almost Superman's opposite, Batman has no superpowers, just loads of money and technology and a desire for justice. Batman deals with everything dark, from a dark city to a dark costume to enemies who embody the dark parts of humanity. Batman is the yin to Superman’s yang. His lack of powers and the fact that he continually has to face and conquer his own dark side makes Batman more relatable than Superman. His nemesis, the Joker, embodies the monster that Batman is always in danger of slipping into if he gives up for even a moment. His strength in the face of humanity’s ugliest depths and his incredible drive to press on in the face of it all has inspired many a child and adult alike.

Goku

Goku is the face—and the hair—that brought Japanese animation to the rest of the world. As far as powers go, he is basically Japanese Superman. However, in place of Superman’s compassion toward humanity and drive to service, Goku values honor above all else. To prove himself the best, Goku will not fight anyone except at their strongest, often risking the lives of his friends, innocent bystanders, and sometimes entire planets to do so. He will also let his friends fight for their lives and get beaten down to the brink of death—and sometimes past it, given that his universe has a few death-reversing loopholes—before interfering, because he wants them to push themselves to their limits and have an honorable defeat. Yet when there truly is no other option, Goku proves himself worthy of the title of hero by showing that he is willing to sacrifice himself to save those he cares about.

The Doctor

A nameless, immortal time-traveler who has a tool that can do almost anything, and who cheats death by generating a new face. He has saved Earth about fifty times in as many years, though he himself has aged thousands. He has even been known to save the entire universe now and then. After twelve personas and a life so long as to boggle the minds of mortals, the Doctor faces existential questions that humans almost never run into, questions that drive his enemies to hatred and nihilism. His greatest weapon: his wit. The Doctor almost never carries a weapon, opting instead to win all of his battles by thinking ahead of his opponent—or guessing, no one can ever be really sure he knows what he is doing. The Doctor is a legend and a myth, a savior and a destroyer, as wise as God and as foolish as a child. He is a hero, an angel, a mentor, a messenger, a destroyer, and the universe’s instrument of fate. A hero, but more than that. He is the Doctor.

This is the end of my list. I am sure there are others. I feel that some heroes from mythology like Beowulf or Hercules or Thor deserve a place among the legends, but I do not know enough about them to do them justice. I also did not mention any run-of-the-mill protagonists, defined by the story following their viewpoint and making us want them to succeed, as the term “hero” is popularly used today. These “heroes” include the likes of Luke Skywalker and Harry Potter, who are not exactly beacons of wisdom and self-discipline. The ones who made it are those who will be remembered long after their stories have been forgotten, who shine like the mythical figures of the ancient Greeks, half human, half god.