# Two Important Principles

There are many principles that guide our philosophies, our thought, our reason, and even our morality. Two of the most important ones for me are the Cosmological Principle and the Anthropic Principle. Despite their opposite-sounding names, they are not mutually exclusive!

The Cosmological Principle

It can be phrased many ways, with many different connotations. The essence of the principle is that, when viewed from a larger perspective, Earth is not special within the universe. More specifically, it states that the laws of physics govern equally and universally, with no preference for any particular region within it.

To believe such a thing in ancient times was considered heretical. After all, almost all old religion positioned the Earth as the center of the universe, at least metaphorically if not physically. But the more we learned about the universe, the more we learned the fact that we are not at the center of the universe, the perhaps painful fact that we are not special. A frightening fact indeed.

In 2006, the Cassini spacecraft took a picture where Saturn eclipsed the Sun. There was a little dot in one area. At first you might think it is just one of Saturn’s moons, or perhaps a stray asteroid. Surely that can’t be anything we call special, right?

That dot turns out to be the Earth entire.

Now, on to the second rule.

The Anthropic Principle

Only those universes with the conditions to have life would be observed by such life from within. Therefore, given that we are observing our own universe from within, our universe must have sufficient conditions for life. That is to say, just for having life, our universe is not special.

With a multiverse, there may be billions, trillions, and possibly even infinitely many universes. Even if only a tiny fraction of universes support life, the anthropic principle shows that given we can observe our own universe, we are automatically in that tiny fraction.

After all, if our universe could not support life, then we cannot exist within it. So, there would be nobody in that universe to realize it cannot support life. Someone who has studied conditional probability should be able to understand this. While the chance that a universe supports life might only be 0.01% (i.e., our universe is “fine-tuned”), the chance that our universe supports life is 100% regardless, because we are already here to make the observation in the first place.

The anthropic principle says that our universe is not special, while the cosmological principle says that Earth is not special within the universe. As humans, we cannot afford to satisfy ourselves with Earth, merely one of the billions of billions of rocks in the universe. Rather, it is imperative to explore the universe and understand its mysteries.

# Determinism from the Perspective of the Simulation Argument

It’s been almost two years since I last wrote about Free Will vs Determinism. The argument is the standard one, that since everything in the universe is governed by physical laws, it is completely deterministic. However, because it is not possible to to simulate the entire universe, it is at the same time unpredictable, so we should act as if there is free will.

However, one obstacle stood in the way of that argument: Quantum randomness.

With true randomness, we cannot say that the universe is deterministic. But with the basis that everything is governed by natural laws, it makes equally no sense to assert the existence of free will. Because, if all the same random events occurred the same way, another “run” of the universe would have the exact same result.

Even when you are thinking in your head at this very moment that you have free will, what is really most likely happening is that chemical processes in your brain have led your conscience to make that decision. If the entire universe “restarted” with the exact same sequence of random events, you would make the exact same decision again.

The Simulation Argument.

This is where the argument gets interesting. There is a very scary paper written by philosopher Nick Bostrom called, “Are You Living in a Computer Simulation?” It is scary because the implication, given a couple of premises, is that we are almost certainly living in a computer simulation. Not only that, but the argument posits that our simulators are themselves extremely likely to be in a simulation, and those simulators are likely too to be in a simulation, etc.

With the near certainty that we are in a simulation, determinism can only become stronger. You have probably heard of things called random number generators. A lot of these work by taking a seed number, and then running it through a specialized function over and over again, resulting in what is known as pseudorandom. These generating sequences that seem random but are completely deterministic, if you know where it started, i.e., the seed number and the algorithm.

This means that, providing our simulation ancestors, the beings who simulated our universe, are using similar ideas of random number generation, all the “random” quantum events we measure in our universe could actually be a completely determined sequence, perhaps by an algorithm so complex that it would be physically impossible to calculate from within this universe.

Of course, this is provided two premises:

1. We are in a simulation.
2. Our simulation could use pseudorandom number generation.

Premise 1 is actually very likely, from sheer numbers in the argument. It is Step 2 that is undecidable and for us to choose. If we accept it, this would imply our entire universe, including quantum events, is completely determined. And if we reject it, it would not rule out the possibility of total determinism either.

Possibilities

Given some invented definitions, here are the levels for free will vs determinism in the simulation framework:

1. Total Free Will: Consciousness is special, i.e. not bound by physical laws. Free will comes from a higher source. (Question: What if this higher source is bound by physical laws in its universe?)
2. Weak (Random) Free Will: Consciousness is not special, i.e. it is bound by physical laws. However, there are events in the universe that exhibit true randomness, so it is not fully deterministic.
3. Weak (Random) Determinism: True randomness exists. However, given a specific set of outcomes of random events, the universe runs the same way.
4. Total Determinism: True randomness does not exist, only pseudorandom exists. Thus, our universe will always run the same way under the same starting conditions.

# 2012 Embassy Attacks and the Tolerance Paradox

Due to recent events in the world, I’d like to dedicate a post on the concept of tolerance and its paradoxical nature.

This paradox is usually explained as the Barber paradox. If there is a barber in town who cuts the hair of only those who do not cut their own hair, then does he cut his own hair? If he does, then he is the category of those who do cut their own hair, so he can’t cut his own hair. But if he doesn’t cut his own hair, then by definition he does cut his own hair. Either way is a contradiction.

More formally, this is given as Russell’s paradox: Imagine a set that contains all sets that do not contain themselves. Does such a set contain itself? If it does, then it is not a member of itself, which is a contradiction, and if it does not contain itself, then by definition it is a member of itself, which is another contradiction. So, such a set is an impossible construction.

The notion of all-tolerance leads to a paradox as well. If there is a person who tolerates everything, then by definition he also tolerates intolerance. But if he tolerates intolerance, then he is then not all-tolerant. Thus it is logically impossible to tolerate everything, because intolerance is included in the set of everything.

Whenever there is a clash of tolerance versus intolerance, the more tolerant side cannot be fully tolerant. It would be naive to believe it would be possible. The best the tolerant side can do is to not tolerate the intolerance of the other side.

How Tolerant Can We Be?

Now, if we do not tolerate the intolerance of the other side, then aren’t we too becoming intolerant? Yes and no. Yes only in the technical sense. No, because the only thing we are being intolerant of is at a meta level, not a real level.

For example, if person A tolerates all forms of clothing and person B does not tolerate jeans, then person B has an intolerance at the real level. If person A were to not tolerate person B’s intolerance of jeans, he is only not tolerating at the meta level. His intolerance of B’s intolerance is really just a defense of the real-level tolerance. So, person A is more tolerant than person B.

In the United States, we have the freedom of speech and expression, which is a supreme tolerance. If some Congressman were to argue that free speech should be taken away, then when you protest that choice, you are not really being intolerant of the Congressman’s intolerance of free speech. You are defending tolerance in the form of freedom of speech.

In a way, the intolerance of intolerance can be considered a form of tolerance after all, which is one resolution of the paradox. But even so, at some point to defend tolerance, you must disagree with the Congressman who is intolerant. And their side, in a non-logical defense, will claim your side is being intolerant and that their side is the tolerant one.

Religion and Tolerance

Some religions work the same way, claiming they are the tolerant ones while the other side is being intolerant, when it is really the other way around. Islam and Christianity seem to be serial offenders, each claiming itself as tolerant but neither one of them really being that tolerant at all.

Not only have these religions used verbal mockery, but time and time again throughout history, they have used physical force and oppression to attack those who disagreed with them, under the guise of being tolerant. When Galileo made his astronomical observations supporting Copernicus’s heliocentrism (that Earth orbits the Sun, not the other way around), he was charged with heresy.

The whole idea of calling someone a heretic goes completely against the idea of tolerance. And then taking oppressive and violent actions on such a person goes even further.

In the 2012 embassy attacks so far, the condemnation should fall strictly on the attackers, not on any filmmakers. At this point, as defenders of tolerance, we should no longer stand still and watch the violent intolerance against free thought.

It used to be that individuals such as Galileo were hated for using reason. But now, nations of the West are hated and their embassies attacked because of the non-violent free-expression of a few.

Obviously, not every Muslim is of the mindset of the attackers, and in fact only a small minority was violent. However, that does not absolve the religion itself from guilt. The attacks should not be blamed on any group in the Muslim population, nor against even those who perpetrated such actions, as these people were no doubt just doing what they thought were right, what they thought God wanted them to do. The root problem is the worldview itself and how it facilitates and justifies such violence. That is where the real blame lies. Unfortunately, judicial systems around the world judge people or groups of people, not ideas and worldviews. So until the judicial system adapts (along with a whole bundle of other factors, primarily education), religious intolerance is not going to stop. And this is not just referring to Islam, but especially Christianity as well.

Response to the Attacks

There is nothing wrong with condemning the attacks. By condemning the attacks, you are not being intolerant of Islam, but rather, tolerant of freedom of the press. Similarly, if you condemn the Salem witch trials, you are not being intolerant of Christianity, but rather, tolerant of the right to fair trial. It’s not that the “witches” were causing any threat to the religion, but rather, it was religion that was demonizing the victims. Similarly, the violent protesters make it seem as if their religion was strongly threatened, when in fact, it was them who were terrorizing others. So don’t be fooled when religions play the victim card. They claim to be the victim but act the bully. They claim to be tolerant, when they are highly the opposite.

The legal systems of countries adapt all the time. Societies adapt, humans adapt, and all life adapts to new situations. Language adapts, technology adapts, and science adapts to new facts. But some religions absolutely refuse to adapt (though not all religions). Sometimes it might take a hundred years for a religion to accept something, such as the fact that Earth orbits the Sun and not the other way around. Or the fact that the Earth is round, not flat. Or the fact that biology is driven by evolution, not magic. As long as major religions stay in the same position and refuse to adapt, there will always be intolerance.

# The Disintegration of the Persistence of Memory

Many people are familiar with Salvador Dalí’s The Persistence of Memory. It is one of the iconic images of the twentieth century.

However, his follow-up work, The Disintegration of the Persistence of Memory, is less widely known.

It is a vision of the same place—but this time, the land has been filled by water, and the objects, which are now able to freely float, are breaking up into their atomic parts. Even the tree has begun to disintegrate.

The more you look at this painting, the more mind-blowing it becomes.

# An Atheist’s View on Morality

This is in response to my previous article, “Ethical Dilemmas and Human Morality.” In that article I listed several questions in several situations and asked you, the reader, what you would do in each case. At the end, I promised to explain my own moral principles as well. So, this post is my own view of ethics and morality, from an atheist.

What Is the End Goal?

First of all, what is the goal of morals? To create a better society is a satisfactory explanation to many, but what then? If a nearly perfect society were to exist some time in the future, would morals still matter? My answer is Yes.

I am optimistic in the future of humanity, and I hope there will be a time when humans can peacefully explore the stars, the galaxies, and the universe. When we are at this stage of civilization, we will be long past the petty conflicts that determine morals today.

Thus, a more long term goal is needed. I propose the following primary objective:

• To preserve life in the universe.

There is no pure logical reason to put this directive above all others. However, if we start with this assertion, that a universe with life is better than a universe with no life, then many moral questions can be answered in a systematic way.

A Moral Hierarchy

It is systematic enough to put morals into a hierarchy:

Levels
6. Preservation of Life
5. Preservation of Intelligent Species
4. Preservation of Diversity of Species
3. Preservation of Well-Being of the Species
2. Preservation of Self
1. The Following of Social Norms/Cultures/Religion/Laws
0. Natural Instinct and Personal Wants

The way to read this is for any action, start at the bottom and see if it fits with the statement at that level. Then an action is morally justified if it fits a given level and to the best of your knowledge, it does not contradict a higher level. On the other hand, an action is morally wrong if it fails to fit the highest level that you are knowledgeable of.

Examples

Perhaps this hierarchy is a bit confusing, so I will give a few examples.

Example 1: You see a dollar bill is on the ground and nobody else is around. Is it right or wrong to take the dollar bill?

• According to Level 0, you are allowed the action of taking the dollar bill. You go up one level, to Level 1, and the action is still allowed by society. You don’t believe it will affect any of the higher levels. So, the decision to take the bill is morally justified.

Example 2: Someone has $1,000. Is it morally right or wrong to steal the money from this person? • The action fits Level 0, but it fails at Level 1, as it is against the law. You do not believe it will affect any higher level. Since Level 1 is the highest relevant level to your knowledge, the action is morally wrong. Example 3: Thousands of nuclear weapons around the world are about to explode, and the only way to stop them is to extract a certain code from a captured terrorist. However, the terrorist will not speak. Is it morally justified to torture the terrorist? • Torture is against social norms and the law, so the action fails at Level 1. But, Level 3 and Level 4 are very relevant, as the large number of nuclear detonations would kill billions, collapse ecosystems, and cause catastrophic changes to the environment. It would not only threaten human civilization (Level 3), but also wipe out many, many species (Level 4). It could even wipe out humans (Level 5). Thus, to preserve Level 3, Level 4, and Level 5, the action is morally justified. Example 4: An alien species is about to create a super-massive black hole that will devour millions of galaxies and eventually the whole universe. The only way to prevent this is to preemptively wipe out this alien species. • Killing the alien species is against the law, so the action fails at Level 1. Even worse, it would kill an entire species, an act of xenocide, so it fails at Level 4. However, it satisfies the highest objective, Level 6, as it prevents a case where all life in the universe could be destroyed. So, wiping out this alien species is morally justified. Reasoning The reasoning for each level is as follows: • Level 1 overrides Level 0: The society most likely has a better chance to function with rules than without rules. This gives it a higher chance to advance. • Level 2 overrides Level 1: An individual should be allowed to preserve one’s own life regardless of what other people assert, as long as the individual believes the actions necessary do not contradict any of the higher levels. This is because an individual may discover truth that is contradictory to the rest of the society. • Level 3 overrides Level 2: It is justified for an individual to sacrifice one’s own life to improve the quality of living for the species. This increases the chance that the society will be able to preserve itself. • Level 4 overrides Level 3: It is justified to lower the quality of living of a species to preserve the diversity of life, i.e., the number of species. This way, if some catastrophe wipes out one species, there are a large number of species remaining to preserve life. • Level 5 overrides Level 4: An ecosystem has a better chance to survive if the most intelligent and advanced species is alive. For instance, if a massive asteroid is on a collision path with Earth, it will require Space Age technology (achieved only by humans) to preserve life on Earth, so humans are more important to Earth’s ecosystem than any other species. • Level 6 overrides Level 5: It is better for a technologically advanced species to sacrifice itself if it allows life to continue in the universe if life would otherwise be destroyed. The Role of Knowledge This hierarchy of morality is strange in that the determination of whether an action is morally justified depends partially on the knowledge of the individual. For example, suppose that someone were brainwashed when they were young by a society or religion, and that he is led by it to an action that contradicts one of the higher levels. On Earth, for instance, it is common for many of the popular religions to contradict Level 2: Preservation of Self, and Level 3: Preservation of Well-Being of the Species. Level 3 is particularly relevant in today’s age, when the understanding gained from stem cell research, particle accelerators, and evolution have the result of giving life on Earth a much higher chance to survive potential global or cosmic catastrophes. When someone who is brainwashed by a religion commits an act that contradicts Level 2 or 3, then according to this moral system, the person is not to blame—the fault is with the religion, and with the society for allowing that particular religion to be so pervasive. Who Exactly to Blame? Imagine a massive asteroid that will crash into Earth in the year 2050. At the rate of advancement of our current technology, with a few years of advance warning, we as a species will be able to send multiple rockets armed with nuclear weapons to knock the asteroid off course and save not only our lives, but the lives of all species on Earth, and all of Earth’s children. But say religion had been more prominent and had delayed the onset of the Renaissance and the Scientific Revolution by just 100 years. Then when the asteroid hits, we would only have what we know as 1950 technology, and likely all of humanity, and all life on Earth, could be destroyed. Surely this is not the fault of any person, but the fault of religion. The corollary to this question is, What if an asteroid had crashed into Earth in the year 1850? There would have been absolutely nothing we humans could have done at that time to stop it. If that were the case, then we could not blame anyone in that time period. Instead, we would blame the Dark Ages, for practically halting the advancement of technology for a thousand years. Ethics in Religion If we value life, and if we want life to prosper in the universe, then humanity as a whole needs to adopt a new form of ethics. Maybe not the one above, but it must embrace one that is based on the existence and diversity of life, not based on myths that were invented in an ancient past. This is why, among religions, a tolerant religion such as Buddhism is better for the future of humanity than an heavily indoctrinated one such as Christianity or Islam. Religions of the latter category only claim to be “tolerant,” but in practice are often not. See Galileo, the Salem witch trials, or the recent anti-free speech protests in the Middle East. These kinds of religions are fundamentally resistant to change. Whereas, truly tolerant religions are always open to change. If science proves some belief of Buddhism wrong, then Buddhism will have to change. -Dalai Lama All the world’s major religions, with their emphasis on love, compassion, patience, tolerance, and forgiveness can and do promote inner values. But the reality of the world today is that grounding ethics in religion is no longer adequate. This is why I am increasingly convinced that the time has come to find a way of thinking about spirituality and ethics beyond religion altogether. -Dalai Lama Sure, the less tolerant religions may teach values they consider to be good, but for life to survive, sometimes the rules must adapt. Say a powerful alien species abducts you and gives you two options: (1) to kill a fellow human and the aliens will befriend the human race and help us advance, or (2) to refuse to kill a human but then the aliens will destroy the entire Earth. You could blindly follow “Thou shalt not kill” as in option (2) and let all the millions of species on Earth die, or you could rationalize that the survival of millions of species, including your own, is more valuable than any single individual member of the species, and instead advance life as in option (1). Some Concluding Remarks To preserve life and to let it flourish through the stars, and eventually throughout the universe, we must use an ethics system that adapts to the given situation, not one that proclaims to be absolute and forever-lasting. Some nations, particularly many of those in Europe, have already realized this. When the United States finally realizes this as well—and hopefully before it’s too late—the rest of humanity will follow, and then finally, the human species will be one of progress, discovery, and peace. # Ethical Dilemmas and Human Morality Introduction This article is the result of numerous debates I’ve had concerning ethics and morality. The debates were very friendly in nature, as we tried to pick each other’s brains. Sometimes we agreed on certain situations, other times we completely disagreed. It was very interesting to see the way different people view the world. Some key information for the rest of the article: • The debates were largely conducted by creating hypothetical situations (thought experiments) and asking each other what we would do in such examples. • Often when one said X for a situation, we would try to adjust one variable to change the situation slightly, in order to see what exactly in the situation was important. This is sort of like the scientific method applied to ethics. • Most of the group was not highly religious. This post is written by an atheist. • The group consisted of Cornell students. • There was no name-calling or mocking in the debates. Disagreements were handled with civility. Situation 1: The iPhone Return Dilemma This is based on a real-life example. I could simply the situation considerably, but because of the reality of it, I am including all the important details. Suppose your income was largely based on buying and reselling iPhones for higher prices. That is, you could buy an iPhone for$400 and resell it on eBay for $800 to someone in a country where the iPhone is not sold. Now, someone in South Africa buys your iPhone. There is a 14-day return policy; however, this 14-day count starts the moment the transaction is made. The iPhone takes 22 days to ship from the USA to South Africa. The buyer is aware of this. But when the iPhone arrives, the buyer finds that the iPhone does not work, and takes it to a local repair shop. The repair shop opens up the iPhone but cannot make it work, because the iPhone simply doesn’t work in South Africa. Five days after he receives the phone, the buyer emails you, demanding a refund. Since it is now 27 days since the transaction, or 13 days past the return deadline, you do not respond to the email. The buyer opens up an official return investigation on eBay. A week later, eBay rules in your favor, stating that you are not obligated to provide a refund. Now, without informing you, the buyer had shipped the iPhone back to you in the middle of the eBay investigation. Three weeks later, the iPhone arrives on your doorstep, a complete surprise for you. Five days later, the buyer emails you. He knows that eBay ruled in your favor, so instead of asking for the$800 back, he asks for the iPhone back. Since he voluntarily shipped you back the iPhone, it is legally yours.

Questions

1. You are not legally obligated to return $800 or the iPhone. However, are you morally obligated to do so? 2. Would you return the iPhone? 3. The shipping fee from USA to South Africa is$100. If you do feel obligated to return the iPhone, should you pay the $100 shipping fee or should you ask$100 from the buyer in South Africa to provide it?

4. If you choose not to return the $800 or the iPhone, then who is to blame for the buyer’s loss? Is it your fault or his own fault? 5. Instead of an$800 iPhone, what if the item cost $5 or$100,000? How would this affect your responses?

Situation 2: The Million Dollar Button

From this point on, all situations are strictly hypothetical.

You are in a room with a button. If you press the button, a random person in the world dies, but you gain one million dollars. Nobody else in the world knows about this room or the button, and nobody would know that you pressed the button.

This situation completely shocked many of us when it was first asked in the debate. Most people’s gut instinct was to say, “Of course not!” But is that actually what people would do? People might say “No” to maintain their reputation in a public setting, but deep down, would their answer be “Yes”?

Questions

1. Would you press the button?

2. Suppose you know 5 people who are homeless and jobless. If you press the button, you could give them $200,000 each. Would you press the button? 3. Instead of one random person in the world dying, one random convicted criminal in the world dies. Would you press the button? 4. Instead of one million dollars, you gain one billion dollars. You could donate massive amounts to charities and fund scientific research to cure diseases. Would you press the button? 5. Instead of a random person dying, a random person goes into a coma for a month. Would you press the button? 6. If the answer to any of the questions was yes, then how many times would you press it? Situation 3: The Doomsday Asteroid In the future, there is a nuclear-powered manned spaceship in the outer solar system. Scientists detect an asteroid heading to Earth that has a 100% probability of impact. The asteroid is large enough to annihilate all of human civilization, kill billions, and set back humanity to the Stone Age. The only way to deflect the asteroid before it gets too close is to have the crew of the manned spaceship suicide the craft into the asteroid and blow it up with nuclear power. There is one person on the ship. Questions 1. If you were the captain of the ship, would you be morally obligated to send the ship into the asteroid? 2. Suppose instead you are the director of NASA, back on Earth. The captain on board the ship refuses to impact the asteroid, even though it is the only hope to maintain current human civilization. You can issue an order to the ship itself that places the ship on computer autopilot, so that the captain cannot control the ship. Should you autopilot the ship into the asteroid? 3. Suppose that, at the time of the decision, there is only a 10% probability of the asteroid hitting Earth. However, we will not know for certain whether it will happen until it gets close enough to be unstoppable. Should the captain preemptively suicide him/her-self into the asteroid, before it gets close enough? 4. Suppose that the asteroid is large enough to annihilate not only human civilization, but also all life on Earth. Does this change the answer to any of the other questions? 5. Suppose that instead of there being 1 person on board, there are 1,000 people aboard that spaceship. Does this change any of your answers? Situation 4: Alien Attackers You are the president of the United States. An advanced alien race is about to attack the Earth, but before they do, they snatch you on board and give you two options. Option 1 is for you to kill half of humanity, and the aliens will leave Earth alone. Option 2 is to let the aliens destroy all of humanity. There is no hope of beating the alien technology. Questions 1. Which option would you take? 2. Suppose Option 1 were, instead of you killing half of humanity, you let the aliens kill half of humanity. Does this change the answer? 3. Suppose Option 1 were, instead of half of humanity, 99% of humanity. Does this change the answer? 4. Suppose Option 1 were, instead of half of humanity, 1% of humanity. Does this change the answer? 5. Suppose human technology is actually far more advanced than it is now, and the best human military analysts claim there is a 5% chance to repel the alien attack if they attempt Option 2. Which option do you take? Situation 5: The Million Dollar Button, Version 2 The following is the same as Situation 2: The Million Dollar Button. However, the variations are different. “You are in a room with a button. If you press the button, a random person in the world dies, but you gain one million dollars. Nobody else in the world knows about this room or the button, and nobody would know that you pressed the button.” Questions: 1. Instead of a random human in the world dying, a random dog in the world dies. Would you press the button? 2. Instead of a random human, it is a random cat. Would you press the button? 3. Instead of a random human, it is a random fly. Would you press the button? 4. You are not the one pressing the button. Someone else is pressing the button, but you have a special button that electric shocks the other person, stopping them from hitting their button. Supposing you know the other person is just about to press the button, should you push your special shock button? 5. When you press the button, a random person in the world dies, but you gain one million dollars AND a random person in the world who has cancer is suddenly cured of cancer. Would you press the button? 6. If you said no in the previous case, what if 100 people were suddenly cured of cancer? Results Some people had a view that it is always wrong to take away someone’s freedom. Such people of course said “No” in the button example, but surprisingly, they also said “No” in the spaceship example with the NASA director. They said that if the crew refused to crash into the asteroid, it is wrong for someone on Earth to force them into doing so, even if it is the only way to save humanity. Some, especially religious people, were okay with pressing the button because they viewed humans as “inherently evil,” so they had no problem terminating a random human’s life. I personally found this view to be quite scary! 1. The iPhone Return Everyone agreed that you are not morally obligated to return the$800. However, there was disagreement over whether to return the iPhone back to the buyer. Those claiming there is no moral obligation used the argument that the buyer should have been more careful with money, while those claiming there is a moral obligation used the argument of intention, that the buyer did not intend to just give back the iPhone for no refund.

2. The Million Dollar Button

Depending on the situation, most people found some case where it was justifiable to press the button. As said above, some religious people justified it by saying humans are “inherently evil.” Those of a utilitarian view justified it by saying the million dollars could go towards good purposes and advance the human race better than an average person could.

3. The Doomsday Asteroid

Most people agreed that in almost all cases, the ship should crash into the asteroid. To my surprise, there were people who said that even if the asteroid were guaranteed to wipe out all life on Earth if it hit, that if the captain refuses, NASA should not force the ship via autopilot to crash into the asteroid. I view this as a human imperative. Not only would we be ending our own species, but also millions of others on Earth. The survival of millions of species is far more important than the decision of one individual of one species.

4. Alien Attackers

There were people who  preferred letting all of humanity be killed by the aliens than to kill half of humanity. The decision for them rested in who was doing the killing. So when the question was rephrased to letting the aliens kill 50% of humanity vs letting the aliens kill 100% of humanity, the answer was unanimously let the aliens kill 50%. But when we ourselves were killing 50%, some people would rather let the aliens kill 100%.

5. The Million Dollar Button, Version 2

Most were more likely to press the button in the animal case than in the human case. However, there were some who would rather a human than a dog die. These were the same people who, in situation #2, claimed that it was justifiable to let a human die because humans are inherently evil. They claimed that dogs are not inherently evil, and so would not press the button in the case of a dog.

My Own Perspective

Overall I think the survival of the species is more important than the life of any one particular individual of the species. I may have hinted at this a few times in the article. But I will write a post specifically on my own views of morality later on.

What would you do in these situations?

# The Math You Weren’t Allowed to Do

You probably learned a bunch of things in school math about what you can and can’t do. When you were a first grader, perhaps you learned that that you can’t subtract 5 from 2, but later on, you learned about negatives: 2 – 5 = -3.

You also might have been told that you can’t divide 2 by 6, but then you learn about fractions. And by now, you are no doubt an expert at splitting 2 pizzas among 6 people.

Even so, there is much more that you may not have known…

1. You Can’t Count to Infinity

Actually, you can. It can be done via ordinal numbers.

You start out counting by

1, 2, 3, 4, 5, 6, 7,… 700,… 30,000,000, etc.

When you played a “what’s the highest number?” game with someone, every time you said a number, they countered by saying your number plus one, that is, unless you said infinity. Because infinity plus one is still infinity, right?

Here is where ordinals come into play. The ordinal number $\omega$ (ω, omega) is defined as the first number after ALL of the positive integers. No matter what normal number they might say, whether it’s ten billion or a googol, the ordinal number $\omega$ is far, far larger. It is practically infinity.

But then you can add one to it, and it becomes an even bigger number. Add two, and it becomes even bigger.

$\omega, \omega+1, \omega+2,..., 2\omega,...,3\omega,...,n\omega,....,\omega^2,...$

What the heck is going on? If you count an infinite number of numbers after omega, you get two omega? Is this two times infinity? And then three omega? And then omega squared?

It turns out to keep on going. Eventually you will get $\omega^\omega$, and then $\omega^{\omega^\omega}$, etc. And then you reach $\Omega$ (big omega), which is larger than all things that can be written in terms of little omegas. And then you can make bigger things than that, with no end.

So the next time someone claims infinity is the largest number, you can confidently reply, “infinity plus one.”

2. You Can’t Divide by Zero

Actually, under certain conditions, you can.

The field of complex analysis is largely based around taking contour integrals around poles. Another word for pole is singularity. And another word for singularity is something you get when you divide by zero.

Consider the function $y = 1/x$. When x is 1, y is 1, and when x is 5, y is 1/5. But what if x is 0? What happens? Well, 1/0 is undefined. However, if you look at a graph, you see that the function spikes up to infinity at x = 0.

What you do in complex analysis is integrate in a circle around that place where it spikes to infinity. The result in this case, if done properly, is $2\pi i$. It’s quite bizarre.

3. You Can Only Understand Smooth Things

Actually, there is much theory on crazy, “pathological” functions, some of which are discontinuous at every point!

The image above is kind of misleading, as it is a graph of the Cantor function, which is actually continuous everywhere (!), but nonetheless manages to rise despite having zero derivative almost everywhere.

There is another function with the following properties: it is 1 whenever is x is rational and 0 whenever x is irrational. Yet this function is well understood and is even integrable. (The integral is 0.)

Then you have things that are truly crazy:

The boundary of that thing is nowhere smooth, and is one of the most amazing things that have ever been discovered. Yet it is generated by the extraordinarily simple function $z^2 + c$, which most people have seen and even studied in school.

4. You Must “Do the Math” and Not Draw Pictures

Actually, math people use pictures all the time. The Mandelbrot set (the previous picture) was not well understood until computer images were generated. There is no such thing as doing the math in a “correct” way. Some fields are quite based on pictures and visualizations.

How else would anyone have thought, for example, that the Mandelbrot set would be so complex? Without seeing that in pictures, how would we have realized the fundamental structure behind the self-similarity of nature?

Yeah, that’s a picture of broccoli. Not a mathematical function. Broccoli.

5. If It Doesn’t Make Sense, It’s Not True

Actually, many absurd things in math can be perfectly reasonable.

What’s the next number after 7?

8, you say. But why 8? What’s wrong with saying the next number after 7 is 0? In fact, I can define a “number” to only include 0, 1, 2, 3, 4, 5, 6, and 7. Basic operations such as addition and multiplication can be well defined. For example, addition is just counting forward that many numbers. So 6 + 3 = 1, because if you start at 6 and go forward 3, you loop back around and end up at 1.

Even weirder is the Banach-Tarski Paradox, which states a solid sphere can be broken up into a finite number of pieces, and the pieces can be reassembled to form TWO spheres of the exact same size as the original!

I hope this was understandable for everyone. May the reader live for ω+1 years!