Toolbelt of Knowledge: Practices
Skepticism
Listening
Deconstruction
Rationality
Mindfulness
Steel Manning
Common Sense
On this blog, we have not treated common sense too kindly. “Common sense” is what we use to mean “you just know,” without having to go through all of the tedium of proving something. In general, it is a catch-all term for mental shortcuts that get us to answers quickly without getting bogged down in confusion. Because of this, common sense can be incredibly idiotic. However, there are also times when it is wise and practical. Today, we’re going to look at how to use common sense well, so that you come to conclusions that have high probabilities of being correct and useful.
The first type of common sense is a reality check. After you have gone through a process of deduction and calculation, does the answer you get make sense? For instance, suppose you are doing a homework problem to calculate the speed of sound, and the answer you get is 30 miles per hour. Do you turn it in? You may not know what the real answer is, but you do know you don’t hear a sonic boom every time a car speeds up nearby! Common sense says you better check your calculations.
Not considering the consequences of the choices we make or put off making can be considered a breach of common sense. If you’re making rice and you fill the pot with grains, it will overflow as it absorbs the water. If you have a pain in your wisdom tooth, waiting to see if it goes away on its own is not worth the risk that it’s infected. When you vote for politicians and leaders, you might want to avoid the ones who like to beat people down. Actions and consequences. Common sense.
Our next use of common sense is to accept true statements that are extremely difficult or impossible to prove. There is a form of argument called the syllogism, which is two premises and a conclusion. An example would be, “All men are human, Frederick Douglass was a man, therefore Frederick Douglass was human.” In the abstract, the syllogism looks like this:
A: If B, then C.
B: B.
C: Therefore, C.
It is obvious that if someone accepts both A and B, they must conclude C to be true as well.
But think about the statement in bold. It is a premise in itself, a hidden premise of the argument. So let’s bring it out of its hiding place, and add it to the syllogism as a premise Z.
Z: If A and B, then C.
A: If B, then C.
B: B.
C. Therefore, C.
There we go. Now we know the whole truth: if someone accepts A, B, and the hidden premise Z, they must conclude C to be true as well.
Oh no! In bringing out the hidden premise to prove the syllogism, we have discovered yet another premise! X: If Z, A, and B, then C. It becomes clear that there is a pattern: for every hidden premise we find, there is yet another premise hidden behind it. Rather than two premises and a conclusion, the syllogism in its true form has an infinite number of premises!
This is an interesting puzzle for the philosophy of logic. But for our everyday problem solving, the two-premise syllogism is good enough, and it is fine to act as if it is absolutely proven to be true. This is our next use of common sense: to take the improvable foundations of logic as if they are proven to be true.
Even when an argument is logically sound, common sense can sometimes veto one or more of its premises. For instance, we can go to the classic example of a faulty syllogism, “All men have beards. Socrates was a man. Therefore, Socrates had a beard.” Our common sense says wait a minute, only some men have beards, not all of them! Despite the argument being formally valid, the first premise is false, meaning the conclusion is invalid, and we can’t know if Socrates had a beard without more information.
However, we must remember, just because something is common sense doesn’t necessarily mean it’s true. At first glance, quantum physics seems to go against common sense, with photons and electrons behaving sometimes as particles and sometimes as waves, and seeming to teleport from place to place. But there is an enormous amount of theoretical and experimental evidence pointing to quantum physics being true, and we have a large amount of technology, such as the laser, that would not function otherwise. Therefore, despite quantum physics going against common sense, we have every reason to believe it is true.
This illustrates the problem with common sense: sometimes it is wrong. If we hear an idea that goes against our common sense, it is important to hear the arguments supporting it, and to give those arguments a good mull over, with the attitude that we might allow ourselves to be convinced to let go of our common sense belief.
Perhaps the worst danger of invoking common sense is to avoid looking at a question in its full complexity, and make out anyone who disagrees with us as fools. We all know of people who have defended their religious or political beliefs by saying, “it’s common sense,” brushing us off, and sending the message that because we don’t agree with their “common sense” view, our thoughts on the matter aren’t worth hearing. That’s not common sense, it’s stubbornness, and we must keep ourselves accountable not to fall into that kind of behavior.
Like rationality, common sense is not something we automatically have. In order not to cause more problems than it solves, common sense must be trained, and a great way to do that is to practice all of the other skills in the Toolbelt of Knowledge.
Showing posts with label logic. Show all posts
Showing posts with label logic. Show all posts
Friday, December 27, 2019
Friday, November 22, 2019
Why are Some Things Impossible?
Impossible. We’ve all heard this word. Sometimes it is used as an excuse to give up. Sometimes as a reason to pursue other things with our time. Sometimes in the context of science and technology. When we want to encourage imagination, we tell our kids (and sometimes adults) that nothing is impossible.
If something is impossible, it can’t be done. Seems straightforward enough. But what makes the difference between whether something is possible or impossible? In asking this question, we find there is not one single answer, but several tiers, each nested within the one before.
Logically impossible
At the most bedrock level, we have logical impossibilities. These are things that cannot exist or cannot be done because they contradict themselves. These include mathematical contradictions, as well as things that contradict their own definitions.
For example, suppose among the men in a certain town, there is a barber who shaves those, and only those, who do not shave themselves. Does the barber shave himself? If so, he is not the barber. Does he not shave himself? If so, then he shaves himself. Therefore, a barber who fits this description cannot exist.
Other things that are logically impossible: A square circle in cartesian coordinates. A solution to a 2x2 sudoku puzzle with a 1 in the top left and a 2 in the bottom right. A legal crime. A dry ocean.
Physically impossible
We don’t live in a universe where everything logically consistent is possible. Everything that exists has a nature, described by laws of physics, and these natures render a whole host of things impossible.
I should pause to mention the distinction between the true nature of reality and our current theoretical understanding of it. Science is very much a work in progress, so there are many things we don’t know yet, and many we think we know but are wrong about. Nevertheless, there are things that are logically possible, but impossible within the true laws of physics, whatever they turn out to be at perfect resolution.
With that in mind, we can talk about what would be impossible if our current understanding were correct, and let it be a proof of concept. Some things that are impossible in our universe, but logically acceptable, are perpetual motion, going faster than light or backward in time, getting out of a black hole, and reducing the total entropy of a closed system.
Technologically impossible
Even within the laws of physics, many things are not possible to us yet, because we do not have the technology to do them. This tier is vast and rich, and in considering what is inside it, we can imagine mind-bogglingly bizarre futures.
In the near term, we have things like mind-computer interfaces, autonomous cars, and quantum computers. A little further out, we might expect to invent nuclear fusion power plants, space elevators, superconducting power lines, weather control, conscious artificial intelligence, biological immortality, revival of extinct species, human colonies all over the solar system, and so much more.
These may seem like science fiction magic to untrained ears, but the difference between them and magic is that people can envision a path toward inventing them that makes sense in the context of modern science.
Economically impossible
Even when we know how to do things, we still need the will and the resources for them. As humanity finds new ways to harness energy and resources, especially in space, more and more things become possible. These include things like space ships with spin gravity, particle accelerators that dwarf CERN, interferometer telescopes the size of the solar system, and buildings tens of thousands of meters high.
But when we’re talking about the merely economically impossible, we don’t have to limit ourselves to such small scales. We could build an orbital ring around the Earth’s equator, orbiting just outside the atmosphere, with launch platforms for shuttles and rockets. We could mine asteroids and use their materials to build giant ships in space. We could envelop the sun entirely in solar energy collectors, a Dyson sphere. We could build giant reflectors to direct all of the sun’s light in one direction, effectively a rocket thruster that could move the solar system. All under known science, and with technology that has already been invented.
Cognitively impossible
Here we come to the last, most easily surpassed level of impossibility. These are things which are impossible only because people believe they are. As soon as people put their minds and efforts toward it, it becomes possible. Many of the great inventions of history came about because someone or some group of people decided they were going to do what everyone else assumed to be impossible, from the Wright brothers inventing the airplane, to the USSR sending a man to space, to the US putting boot prints on the moon.
Today, the biggest example of someone challenging the cognitively impossible is Elon Musk. From SpaceX building bigger and better rockets, to the Boring Company digging tunnels under Los Angeles to solve traffic congestion, to Neuralink connecting people’s brains with computers. He, those who work for him, and many other entrepreneurs, bring the cognitively impossible into existence.
Other things that seem cognitively impossible: World peace. Meeting the basic needs of everyone on Earth. Tolerance and good will across political and religious divides. Governments that work for everyone. A business culture that cares about the poor, the workers, and the environment. Cultures where there are no social minorities or majorities. Cities floating on the ocean. Powering civilization and the global economy with sustainable resources.
All of these things are possible and doable given the technology and economic infrastructure we have now. Why don’t we? Well, there are a million reasons, all of which are unique to their particular challenge. But many of them can be overcome if enough people or the right few see through the curtain of the way things are, and aim their sights on achieving what many brush off as impossible. Not everything is possible. But the number of things that are is vast.
If something is impossible, it can’t be done. Seems straightforward enough. But what makes the difference between whether something is possible or impossible? In asking this question, we find there is not one single answer, but several tiers, each nested within the one before.
Logically impossible
At the most bedrock level, we have logical impossibilities. These are things that cannot exist or cannot be done because they contradict themselves. These include mathematical contradictions, as well as things that contradict their own definitions.
For example, suppose among the men in a certain town, there is a barber who shaves those, and only those, who do not shave themselves. Does the barber shave himself? If so, he is not the barber. Does he not shave himself? If so, then he shaves himself. Therefore, a barber who fits this description cannot exist.
Other things that are logically impossible: A square circle in cartesian coordinates. A solution to a 2x2 sudoku puzzle with a 1 in the top left and a 2 in the bottom right. A legal crime. A dry ocean.
Physically impossible
We don’t live in a universe where everything logically consistent is possible. Everything that exists has a nature, described by laws of physics, and these natures render a whole host of things impossible.
I should pause to mention the distinction between the true nature of reality and our current theoretical understanding of it. Science is very much a work in progress, so there are many things we don’t know yet, and many we think we know but are wrong about. Nevertheless, there are things that are logically possible, but impossible within the true laws of physics, whatever they turn out to be at perfect resolution.
With that in mind, we can talk about what would be impossible if our current understanding were correct, and let it be a proof of concept. Some things that are impossible in our universe, but logically acceptable, are perpetual motion, going faster than light or backward in time, getting out of a black hole, and reducing the total entropy of a closed system.
Technologically impossible
Even within the laws of physics, many things are not possible to us yet, because we do not have the technology to do them. This tier is vast and rich, and in considering what is inside it, we can imagine mind-bogglingly bizarre futures.
In the near term, we have things like mind-computer interfaces, autonomous cars, and quantum computers. A little further out, we might expect to invent nuclear fusion power plants, space elevators, superconducting power lines, weather control, conscious artificial intelligence, biological immortality, revival of extinct species, human colonies all over the solar system, and so much more.
These may seem like science fiction magic to untrained ears, but the difference between them and magic is that people can envision a path toward inventing them that makes sense in the context of modern science.
Economically impossible
Even when we know how to do things, we still need the will and the resources for them. As humanity finds new ways to harness energy and resources, especially in space, more and more things become possible. These include things like space ships with spin gravity, particle accelerators that dwarf CERN, interferometer telescopes the size of the solar system, and buildings tens of thousands of meters high.
But when we’re talking about the merely economically impossible, we don’t have to limit ourselves to such small scales. We could build an orbital ring around the Earth’s equator, orbiting just outside the atmosphere, with launch platforms for shuttles and rockets. We could mine asteroids and use their materials to build giant ships in space. We could envelop the sun entirely in solar energy collectors, a Dyson sphere. We could build giant reflectors to direct all of the sun’s light in one direction, effectively a rocket thruster that could move the solar system. All under known science, and with technology that has already been invented.
Cognitively impossible
Here we come to the last, most easily surpassed level of impossibility. These are things which are impossible only because people believe they are. As soon as people put their minds and efforts toward it, it becomes possible. Many of the great inventions of history came about because someone or some group of people decided they were going to do what everyone else assumed to be impossible, from the Wright brothers inventing the airplane, to the USSR sending a man to space, to the US putting boot prints on the moon.
Today, the biggest example of someone challenging the cognitively impossible is Elon Musk. From SpaceX building bigger and better rockets, to the Boring Company digging tunnels under Los Angeles to solve traffic congestion, to Neuralink connecting people’s brains with computers. He, those who work for him, and many other entrepreneurs, bring the cognitively impossible into existence.
Other things that seem cognitively impossible: World peace. Meeting the basic needs of everyone on Earth. Tolerance and good will across political and religious divides. Governments that work for everyone. A business culture that cares about the poor, the workers, and the environment. Cultures where there are no social minorities or majorities. Cities floating on the ocean. Powering civilization and the global economy with sustainable resources.
All of these things are possible and doable given the technology and economic infrastructure we have now. Why don’t we? Well, there are a million reasons, all of which are unique to their particular challenge. But many of them can be overcome if enough people or the right few see through the curtain of the way things are, and aim their sights on achieving what many brush off as impossible. Not everything is possible. But the number of things that are is vast.
Friday, May 10, 2019
Mathematics: The Language of the Universe
Nature of Reality:
Quasi-Realism
Representational Realism
Existence and Natures
Knowledge of Reality
The Language of Reality
Toolbelt of Knowledge: Concepts
Algorithms
Equivalence
Emergence
Math
The Anthropic Principle
Substrate-Independence
Significance
In our discussions about the nature of reality, we have come to the view that reality is a thing unto itself, independent of perception, belief, or knowledge. Anything we perceive or think we know about reality is not reality itself, but only a representation we have constructed in our minds. A representation is true to the degree that its logic matches with the logic of the real thing it is describing. Today, we are going to talk about that logic, mathematics.
A lot of people see math as something mysterious that they will never understand. But math is not supernatural. It is not hidden knowledge available only to an elite few. People who know math are not wizards or prophets, they are normal people just like you. I hope that after reading this discussion, you will be convinced that you can learn math too, if you so desire.
To start, let’s forget about numbers and just think about something physical, like air pressure. We know from centuries of experiments that, the pressure in a given volume is proportional to the number of molecules in the volume and the temperature. This may sound complicated, but all it means is if more air is added or the temperature is increased, the pressure increases.
Let’s look at the italicized statement. We have four physical quantities: pressure, volume, number of molecules, and temperature. Let’s shorten each of these to just their first letters: P, V, N, and T. “Is proportional to” means if you change what comes after it, then what comes before it changes by the same percentage. We can represent this by an equals sign and a constant, the letter k. Put this together, and we have,
It’s an equation! We have just done something marvelous; we have taken a fact about reality and written it as a mathematical statement. By doing this, we realize a profound truth: math is not just a tool to work with numbers and get answers to homework problems; it’s a language and a writing system. By becoming math-literate, we break into a higher level of understanding the universe.
Let’s try it again. This time we’ll start with an equation, and figure out what it means.
The first thing we need when trying to read this equation is what the letters mean. In normal languages, letters have mostly the same sounds wherever they appear. In math, it is not so; we must be told what each letter means every time. It is the organization, operations, and numbers that have consistent meaning. So here is what the letters in our new equation mean: capital T stands for temperature, small t stands for time, and k is a constant.
What operations does this equation have? The first thing we notice is d/d. This means, the rate at which the thing on top changes as the thing on the bottom changes. So for us, it would be the rate the temperature changes over time. Next, we notice a triangle before the T on the right. This triangle means the difference between two of what comes after it. So in our case, ΔT means the difference between the temperatures of two objects.
Putting all this together, we can read the equation. It says, “The rate at which temperature flows between two touching objects is proportional to the difference in temperature between the two objects.” This means if two touching objects have very different temperatures, heat will flow quickly between them, but if their temperatures are near each other, the heat will flow slowly.
There is one final piece to the equation, and that is the minus sign. This tells us that the temperatures are changing closer to one another, not running away to extremes. This makes sense. Cold things heat up when they touch hot things, and hot things cool down when they touch cold things. Heat always flows toward equilibrium.
The ability to read equations is only one small part of math. There is also geometry, group theory, set theory, vectors, tensors, and much more. All of these fields of study are called the same thing, math, so what do they all have in common? The answer is that mathematics is the set of all well-defined abstract ideas that follow the principle of non-contradiction. To create math, we must declare one or more axioms, statements that define an imaginary object.
Let’s take an example. "A circle is a shape where every point on its boundary is the same distance from its center." Based on this axiom, we can figure out all kinds of things about lines drawn through circles, intersecting circles, circles in curved space, and more. Everything in math is like this; we start with axioms, and then use logic on them to figure out all that we can about them.
Philosophers and scientists have often wondered at how well math is able to describe the universe. To some, it seems miraculous. However, based on everything we have talked about in the Nature of Reality series, I think it makes perfect sense. Here’s why:
1) A representation is true to the degree that its logic lines up with the logic of the part of reality it is meant to represent.
2) An idea is a representation.
3) Reality is well-defined and always follows the principle of non-contradiction.
4) Every idea that is well-defined and follows non-contradiction is mathematical.
Therefore, everything in reality can be truthfully represented by mathematical ideas.
If we accept the views of reality we have argued for on this blog, this is why Mathematics is the language of the universe.
Quasi-Realism
Representational Realism
Existence and Natures
Knowledge of Reality
The Language of Reality
Toolbelt of Knowledge: Concepts
Algorithms
Equivalence
Emergence
Math
The Anthropic Principle
Substrate-Independence
Significance
In our discussions about the nature of reality, we have come to the view that reality is a thing unto itself, independent of perception, belief, or knowledge. Anything we perceive or think we know about reality is not reality itself, but only a representation we have constructed in our minds. A representation is true to the degree that its logic matches with the logic of the real thing it is describing. Today, we are going to talk about that logic, mathematics.
 |
| By WyrdWolf on Deviantart |
To start, let’s forget about numbers and just think about something physical, like air pressure. We know from centuries of experiments that, the pressure in a given volume is proportional to the number of molecules in the volume and the temperature. This may sound complicated, but all it means is if more air is added or the temperature is increased, the pressure increases.
Let’s look at the italicized statement. We have four physical quantities: pressure, volume, number of molecules, and temperature. Let’s shorten each of these to just their first letters: P, V, N, and T. “Is proportional to” means if you change what comes after it, then what comes before it changes by the same percentage. We can represent this by an equals sign and a constant, the letter k. Put this together, and we have,
It’s an equation! We have just done something marvelous; we have taken a fact about reality and written it as a mathematical statement. By doing this, we realize a profound truth: math is not just a tool to work with numbers and get answers to homework problems; it’s a language and a writing system. By becoming math-literate, we break into a higher level of understanding the universe.
Let’s try it again. This time we’ll start with an equation, and figure out what it means.
What operations does this equation have? The first thing we notice is d/d. This means, the rate at which the thing on top changes as the thing on the bottom changes. So for us, it would be the rate the temperature changes over time. Next, we notice a triangle before the T on the right. This triangle means the difference between two of what comes after it. So in our case, ΔT means the difference between the temperatures of two objects.
Putting all this together, we can read the equation. It says, “The rate at which temperature flows between two touching objects is proportional to the difference in temperature between the two objects.” This means if two touching objects have very different temperatures, heat will flow quickly between them, but if their temperatures are near each other, the heat will flow slowly.
There is one final piece to the equation, and that is the minus sign. This tells us that the temperatures are changing closer to one another, not running away to extremes. This makes sense. Cold things heat up when they touch hot things, and hot things cool down when they touch cold things. Heat always flows toward equilibrium.
The ability to read equations is only one small part of math. There is also geometry, group theory, set theory, vectors, tensors, and much more. All of these fields of study are called the same thing, math, so what do they all have in common? The answer is that mathematics is the set of all well-defined abstract ideas that follow the principle of non-contradiction. To create math, we must declare one or more axioms, statements that define an imaginary object.
Let’s take an example. "A circle is a shape where every point on its boundary is the same distance from its center." Based on this axiom, we can figure out all kinds of things about lines drawn through circles, intersecting circles, circles in curved space, and more. Everything in math is like this; we start with axioms, and then use logic on them to figure out all that we can about them.
Philosophers and scientists have often wondered at how well math is able to describe the universe. To some, it seems miraculous. However, based on everything we have talked about in the Nature of Reality series, I think it makes perfect sense. Here’s why:
1) A representation is true to the degree that its logic lines up with the logic of the part of reality it is meant to represent.
2) An idea is a representation.
3) Reality is well-defined and always follows the principle of non-contradiction.
4) Every idea that is well-defined and follows non-contradiction is mathematical.
Therefore, everything in reality can be truthfully represented by mathematical ideas.
If we accept the views of reality we have argued for on this blog, this is why Mathematics is the language of the universe.
Friday, August 24, 2018
Why I Changed My Mind about the Quantum Multiverse
Recommended Pre-Reading:
Quantum Entanglement
Multiverses (Quantum Many Worlds section)
A truth seeker must always be open to new evidence. The new evidence must be added to the old, and all of it re-evaluated together. Sometimes the evidence in its greater context points in a direction other than what you thought was true, and when this happens, the wise person adjusts their beliefs accordingly. As a case in point, we’ll look at something I have had a strong opinion about on this blog, the quantum multiverse.
If you’ve read a lot of my science posts, you know I’ve been pretty hard on the quantum multiverse, also called the Many Worlds Hypothesis. In the multiverses discussion, I said I thought it was the least likely to be true out of the hypothetical multiverse types that come from physical theories. Since then, however, I have learned more about the arguments for its existence, most importantly the story of how the hypothesis came to be, and now I think it is reasonable to believe it exists.
Before we go any further, though, let’s remind ourselves what we are talking about. When quantum physics is mentioned, the layperson might think of the science of consciousness, or of parallel realities where events that were important to individual people or to human history played out differently. These are not quantum physics, they are purely science fiction, playing to our human bias that the universe revolves around us, and where “quantum” is used as a sneaky replacement for “magic.” Quantum physics, the real science, is the study of matter and energy at the scale of molecules and atoms and smaller.
When enough quantum particles interact together (millions, billions, trillions, and more), we get the classical physics that we know in our everyday life. We says that classical physics emerges from quantum physics. But classical physics is not the only thing that can emerge from quantum physics. Any property of quantum physics, when scaled up, can affect the macroscopic realm. Because of this, scientists and inventors have come up with technologies that use the unusual properties of quantum physics in technology, the most well-known example being the laser. Our experience of reality comes from the deeper reality of quantum physics, not the other way around. If quantum physics has implications that are counter-intuitive, we have every reason to take those implications seriously.
We’re going to talk about interpretations of quantum physics, so first things first, what exactly needs to be interpreted? It comes down to why we say quantum physics is weird: a quantum-sized particle can be in two states at once. What does that mean? Well, for example, an electron can be 50% spin up and 50% spin down at the same time. This is called superposition of states. It is like saying a basketball is spinning both clockwise and counterclockwise at the same time. It seems like a contradiction, and for macroscopic objects like basketballs it is, but for subatomic particles, it is normal. If you measure the electron’s spin, you will find it to be 100% either spin up or spin down, and then it will behave differently. But it was not 100% up or down before the measurement; the very act of measurement has changed the particle’s properties. This is called “collapsing the wave function,” and it is what needs interpreting.
For the Copenhagen Interpretation, that is the end of the story. The universe has probability baked into it, and measurements roll the dice. But the Copenhagen Interpretation has a problem: what counts as a measurement? If you try to measure the property of a particle by using another particle, the wave function does not collapse. Instead, the particles become entangled, that is, they are both in a combined superposition of states. For example, if you try to measure an electron’s spin using another electron, then both electrons will end up 50% spin up and 50% spin down. But here is where things get interesting. By using more traditional measuring devices, when we measure the electrons’ spins, we will find that one of them is spin up and the other one is spin down. We can’t know which is which beforehand, because there isn’t an answer beforehand. The only thing that is set in reality before the measurement is the fact that their spins will turn out to be opposite.
But what makes a traditional measuring device different from a particle? All measuring devices are made out of particles themselves, after all. So shouldn’t the machine we use become entangled with the electron as well? The machine only shows us one answer, not a superposition of answers, so that seems not to be the case. Why not? This is the famous measurement problem.
One proposed resolution for the measurement problem is that the collapse of the wave function happens when the experiment is observed by a conscious being. That is, the instrument used to take the measurement registers both spin up and spin down until someone looks at it, whereafter the entangled wave function of the particle and the device measuring it collapses, showing just one result. In other words, perception defines reality. However, this requires substance dualism, the idea that consciousness is fundamentally different from the rest of reality, that mind and matter are completely different things. People have had a dualistic view of mind and matter for all of recorded history. It is intuitive; our DNA comes pre-loaded with a disposition toward believing it. It just feels true. But feeling true has no bearing on whether something actually is true, and the lack of scientific evidence in support of dualism suggests that there is some kind of equivalence between consciousness and matter, which would mean the conscious observation interpretation of quantum physics is impossible.
One day in the late ‘50s, physicist Hugh Everett came onto the scene with a radical suggestion: what if the wave function does not collapse at all? What if any interaction between particles makes them entangled? This would mean that two interacting electrons become entangled; when they are measured, the instrument that measures them becomes entangled; when the scientist interacts with the instrument, the scientist becomes entangled; and when the scientist interacts with the rest of the world, the rest of the world becomes entangled. This would mean that after the measurement, the entire world exists in a superposition state, which is 50% reality where the electron is spin up, and 50% reality where the electron is spin down. Put simply, it can be thought of as if there is one universe where the scientists observe the electron to be spin up, and another universe where they observe the electron to be spin down. This is the essence of the Many Worlds Interpretation.
This sounds weird, and it’s only going to get weirder. As they say, extraordinary claims require extraordinary evidence. So what made me change my mind? What makes the Many Worlds Interpretation more reasonable than any other? It all comes down to consistency. When particles only interact with one another, they get entangled. This is a well-documented scientific phenomenon. The larger the number of entangled particles, the harder it is to control all of them, so the easier it is for something external to the experiment to “mess up” the entanglement. But what would it mean to “mess up” an experiment? It’s just more particles interacting with the entangled system. And we know that when particles interact with other particles, they get entangled. So we could think of it as the external world coming in and messing up the experiment, but if we want to be consistent, we should say the entanglement is escaping to the rest of the world, including the brain of the person doing the experiment.
This is extremely counter-intuitive. I certainly feel like I am in one specific state, not a superposition. But what would being in a superposition feel like in the first place? We might imagine two images playing over our eyes, like a transparent movie playing over another movie. But that would only happen if the information from both states came together in the same brain. Remember, our brain is also in a superposition, not working as a single machine in both states. So a person in quantum superposition would feel completely normal, as if they and the objects they see and interact with are in state A, and not state B. And they would also feel as if they and the objects they interact with are in state B, and not in state A. Both are true, and they would notice nothing weird at all, because the states of their brain are completely cut off from each other. In effect, the universe has split in two, and that is where the “multiverse” idea comes in. More generally, as I argued in the multiverses discussion, it is not the splitting of distinct universes, but an infinite-dimensional smear of universe-ness.
And now, when I look back at my former self, I see a hypocrite. In the multiverses discussion, I said people are drawn to the Many Worlds Hypothesis because the idea that reality is simply probabilistic at the quantum scale is too weird. But I got it backward. The reason that people like my former self cling to the Copenhagen Interpretation is because the Many Worlds Hypothesis is too weird. But weird as it is, it is the only interpretation that solves all the puzzles of quantum physics and leaves no loose ends behind. It is the natural logical conclusion of entanglement, and it makes the measurement problem go away. Out of all the interpretations of quantum physics, those we discussed and those we did not, I now think Many Worlds is the most likely to be true.
But it’s just an interpretation, isn’t it? If it can’t be tested, then what is the point of debating it? Well first of all, here on A Scientist’s Fiction, we search for truth in whatever way we can, and if that means using pure logic, that is what we use. However, in this case, we don’t have to. We can test the quantum multiverse. After all, it’s not just parallel realities. That’s TV sci-fi. The quantum multiverse is an extension of regular old quantum entanglement, which we see in the lab all the time. It makes a prediction: if we have the right kind of experiment, we should be able to put a human being in quantum superposition. Researchers keep finding quantum properties in larger and larger systems, so it should be theoretically possible.
I don’t know how the exact details of such an experiment would play out, but it might go something like this. Imagine we send a human test subject into a room that is 100% soundproof, vibration-proof, and heat-proof. After we close the door, the subject sees either a red light or a blue light, triggered by the measurement of an electron’s spin within the room. To all outside observers, the subject would be in a superposition state of red + blue. Suppose this person was instructed to lightly touch one of two sensors, which connected to a second electron, telling it to either be spin up or spin down. The experimenters outside the room would then do tests on the two electrons, to see if they are in a superposition of states. If they are, then the human test subject is also in a superposition of states. Then they open the doors, the test subject walks out, and tells the researchers what color of light he or she saw. They then measure the particles, and indeed their spin is oriented in accordance with the prediction. This would mean that the test subject was entangled with the electrons, in a superposition of states, and now there are two universes, one where the subject saw red, and one where the subject saw blue. The quantum multiverse hypothesis would be supported by evidence from a prediction of its own.
Changing my mind due to more complete evidence is something I am well-practiced at, so when it came time for the quantum multiverse, it was no big deal for me. However, for those less practiced, it can be frightening. Maybe after reading this you are not convinced that the quantum multiverse exists, and that’s fine. Skepticism is healthy, especially for topics as complicated as quantum physics. But it is also healthy to direct your skepticism toward the beliefs you already hold, and I encourage you as a fellow truth seeker to reexamine your beliefs every now and then. Whether you find them to be valid or in need of replacement, I can guarantee the practice will make you wiser and bring you closer to the truth.
Quantum Entanglement
Multiverses (Quantum Many Worlds section)
A truth seeker must always be open to new evidence. The new evidence must be added to the old, and all of it re-evaluated together. Sometimes the evidence in its greater context points in a direction other than what you thought was true, and when this happens, the wise person adjusts their beliefs accordingly. As a case in point, we’ll look at something I have had a strong opinion about on this blog, the quantum multiverse.
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| By Paul Anglada on Flickr |
Before we go any further, though, let’s remind ourselves what we are talking about. When quantum physics is mentioned, the layperson might think of the science of consciousness, or of parallel realities where events that were important to individual people or to human history played out differently. These are not quantum physics, they are purely science fiction, playing to our human bias that the universe revolves around us, and where “quantum” is used as a sneaky replacement for “magic.” Quantum physics, the real science, is the study of matter and energy at the scale of molecules and atoms and smaller.
When enough quantum particles interact together (millions, billions, trillions, and more), we get the classical physics that we know in our everyday life. We says that classical physics emerges from quantum physics. But classical physics is not the only thing that can emerge from quantum physics. Any property of quantum physics, when scaled up, can affect the macroscopic realm. Because of this, scientists and inventors have come up with technologies that use the unusual properties of quantum physics in technology, the most well-known example being the laser. Our experience of reality comes from the deeper reality of quantum physics, not the other way around. If quantum physics has implications that are counter-intuitive, we have every reason to take those implications seriously.
We’re going to talk about interpretations of quantum physics, so first things first, what exactly needs to be interpreted? It comes down to why we say quantum physics is weird: a quantum-sized particle can be in two states at once. What does that mean? Well, for example, an electron can be 50% spin up and 50% spin down at the same time. This is called superposition of states. It is like saying a basketball is spinning both clockwise and counterclockwise at the same time. It seems like a contradiction, and for macroscopic objects like basketballs it is, but for subatomic particles, it is normal. If you measure the electron’s spin, you will find it to be 100% either spin up or spin down, and then it will behave differently. But it was not 100% up or down before the measurement; the very act of measurement has changed the particle’s properties. This is called “collapsing the wave function,” and it is what needs interpreting.
For the Copenhagen Interpretation, that is the end of the story. The universe has probability baked into it, and measurements roll the dice. But the Copenhagen Interpretation has a problem: what counts as a measurement? If you try to measure the property of a particle by using another particle, the wave function does not collapse. Instead, the particles become entangled, that is, they are both in a combined superposition of states. For example, if you try to measure an electron’s spin using another electron, then both electrons will end up 50% spin up and 50% spin down. But here is where things get interesting. By using more traditional measuring devices, when we measure the electrons’ spins, we will find that one of them is spin up and the other one is spin down. We can’t know which is which beforehand, because there isn’t an answer beforehand. The only thing that is set in reality before the measurement is the fact that their spins will turn out to be opposite.
But what makes a traditional measuring device different from a particle? All measuring devices are made out of particles themselves, after all. So shouldn’t the machine we use become entangled with the electron as well? The machine only shows us one answer, not a superposition of answers, so that seems not to be the case. Why not? This is the famous measurement problem.
One proposed resolution for the measurement problem is that the collapse of the wave function happens when the experiment is observed by a conscious being. That is, the instrument used to take the measurement registers both spin up and spin down until someone looks at it, whereafter the entangled wave function of the particle and the device measuring it collapses, showing just one result. In other words, perception defines reality. However, this requires substance dualism, the idea that consciousness is fundamentally different from the rest of reality, that mind and matter are completely different things. People have had a dualistic view of mind and matter for all of recorded history. It is intuitive; our DNA comes pre-loaded with a disposition toward believing it. It just feels true. But feeling true has no bearing on whether something actually is true, and the lack of scientific evidence in support of dualism suggests that there is some kind of equivalence between consciousness and matter, which would mean the conscious observation interpretation of quantum physics is impossible.
One day in the late ‘50s, physicist Hugh Everett came onto the scene with a radical suggestion: what if the wave function does not collapse at all? What if any interaction between particles makes them entangled? This would mean that two interacting electrons become entangled; when they are measured, the instrument that measures them becomes entangled; when the scientist interacts with the instrument, the scientist becomes entangled; and when the scientist interacts with the rest of the world, the rest of the world becomes entangled. This would mean that after the measurement, the entire world exists in a superposition state, which is 50% reality where the electron is spin up, and 50% reality where the electron is spin down. Put simply, it can be thought of as if there is one universe where the scientists observe the electron to be spin up, and another universe where they observe the electron to be spin down. This is the essence of the Many Worlds Interpretation.
This sounds weird, and it’s only going to get weirder. As they say, extraordinary claims require extraordinary evidence. So what made me change my mind? What makes the Many Worlds Interpretation more reasonable than any other? It all comes down to consistency. When particles only interact with one another, they get entangled. This is a well-documented scientific phenomenon. The larger the number of entangled particles, the harder it is to control all of them, so the easier it is for something external to the experiment to “mess up” the entanglement. But what would it mean to “mess up” an experiment? It’s just more particles interacting with the entangled system. And we know that when particles interact with other particles, they get entangled. So we could think of it as the external world coming in and messing up the experiment, but if we want to be consistent, we should say the entanglement is escaping to the rest of the world, including the brain of the person doing the experiment.
This is extremely counter-intuitive. I certainly feel like I am in one specific state, not a superposition. But what would being in a superposition feel like in the first place? We might imagine two images playing over our eyes, like a transparent movie playing over another movie. But that would only happen if the information from both states came together in the same brain. Remember, our brain is also in a superposition, not working as a single machine in both states. So a person in quantum superposition would feel completely normal, as if they and the objects they see and interact with are in state A, and not state B. And they would also feel as if they and the objects they interact with are in state B, and not in state A. Both are true, and they would notice nothing weird at all, because the states of their brain are completely cut off from each other. In effect, the universe has split in two, and that is where the “multiverse” idea comes in. More generally, as I argued in the multiverses discussion, it is not the splitting of distinct universes, but an infinite-dimensional smear of universe-ness.
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| By Maria Morri on Flickr |
But it’s just an interpretation, isn’t it? If it can’t be tested, then what is the point of debating it? Well first of all, here on A Scientist’s Fiction, we search for truth in whatever way we can, and if that means using pure logic, that is what we use. However, in this case, we don’t have to. We can test the quantum multiverse. After all, it’s not just parallel realities. That’s TV sci-fi. The quantum multiverse is an extension of regular old quantum entanglement, which we see in the lab all the time. It makes a prediction: if we have the right kind of experiment, we should be able to put a human being in quantum superposition. Researchers keep finding quantum properties in larger and larger systems, so it should be theoretically possible.
I don’t know how the exact details of such an experiment would play out, but it might go something like this. Imagine we send a human test subject into a room that is 100% soundproof, vibration-proof, and heat-proof. After we close the door, the subject sees either a red light or a blue light, triggered by the measurement of an electron’s spin within the room. To all outside observers, the subject would be in a superposition state of red + blue. Suppose this person was instructed to lightly touch one of two sensors, which connected to a second electron, telling it to either be spin up or spin down. The experimenters outside the room would then do tests on the two electrons, to see if they are in a superposition of states. If they are, then the human test subject is also in a superposition of states. Then they open the doors, the test subject walks out, and tells the researchers what color of light he or she saw. They then measure the particles, and indeed their spin is oriented in accordance with the prediction. This would mean that the test subject was entangled with the electrons, in a superposition of states, and now there are two universes, one where the subject saw red, and one where the subject saw blue. The quantum multiverse hypothesis would be supported by evidence from a prediction of its own.
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| Schrödinger's Cat |
Friday, July 27, 2018
What is Knowledge?
When we are children, knowledge is simple. Our parents and other people we trust tell us things, and we believe them. For the purpose of this discussion, I will call this method radical credulity. Of course, now that we are older, we understand that this way of thinking lets incorrect ideas in just as easily as correct ones. This is one reason we keep our kids in safe environments with trustworthy people.
A simple method to filter out ideas that are probably incorrect from ideas that are probably correct is to believe things that are reliably useful. This is called pragmatism. How do we know the Earth is more sphere-like than flat? Because treating the Earth as a sphere gets our airplanes to their destinations, while treating it as flat does not. The pragmatist view is that we believe things that let us reliably predict the consequences of our actions, so that we can effectively do what we are trying to do. It’s as the old defense of the scientific method says: we believe it because it works.
But pragmatism has its shortcomings. For example, most of the time, we live as if the Earth is flat, so there is not usually any problem with believing it to be so. However, there are circumstances where this belief could be catastrophic. Of course the pragmatist will say that we should treat the Earth as flat or round depending on the situation, and the real truth of its shape doesn’t matter. However, for many of us, it isn’t good enough to believe things because they are useful; we want to believe things because they are justifiably true, and pragmatism does not do this for us.
In the middle of the last century, psychologist Jean Piaget came up with a theory of knowledge called constructivism, which says we don’t simply acquire knowledge, we create it as a logical network. When we hear a new claim, we evaluate it by how well it fits with what we already know, and if we find no contradictions, we add it to the network. If we do find a contradiction, we either toss it out or reevaluate the belief that it conflicts with. Right away, we see something in constructivism that was missing from radical credulity and pragmatism: logic. The beliefs we hold are connected to each other by threads of non-contradiction.
However, as we all know, it is possible to have beliefs that are false. Adding a new belief that doesn’t conflict with a false belief doesn’t help us come to the truth. One way to attempt to rectify this is to take the beliefs that we are most confident and passionate about as an immutable foundation, and build our knowledge of the world around them. In philosophy lingo, these beliefs are called basic beliefs.
Of course, if people just take whatever they please as basic beliefs, we will find people with all kinds of beliefs that contradict each other’s, and they’ll stubbornly yell at each other until they’re blue in the face. Faced with this problem philosophers sought what could be called properly basic beliefs, truths which are so obvious and undeniable that it is impossible for them to be false. DesCartes famously took his own existence to be properly basic, and the philosophy of empiricism holds the validity of logic, mathematics, and observation as such.
Unfortunately, we run into another problem: we cannot agree on what beliefs should count as properly basic! Take any belief that is proposed as properly basic, and you will be able to find people who doubt it. Mathematics? Can be doubted. Objective reality? Can be doubted. “I think, therefore I am”? Can be doubted! What’s more, since properly basic beliefs are supposed to be the foundation upon which all other knowledge is constructed, the only argument that can be made for a belief to be properly basic is, “can’t you see it’s obvious?” Not exactly up to academic standards!
In the absence of anything that could justifiably be called properly basic, we might, with heavy heart, be tempted to conclude that knowledge is, in fact, impossible, and that everything is just mights and maybes. This is a pessimistic outlook, and not one most of us are comfortable with. In order to avoid it, we might choose a basic belief on radical credulity, usually called “faith” in this context. Or we might revert to pragmatism, and choose a belief that has proved reliable time and again as our basic belief.
I, however, subscribe to a third option, and that is to view knowledge in terms of probabilities instead of just yes or no. Although it may be impossible to know anything with a justified certainty of 100% with an infinite number of decimal places, we can be justifiably 90% certain, or 99.999% certain. We may not be able to calculate the numbers, but with practice we can guess the ballpark.
How is the level of certainty of a belief determined? By how well it connects into the knowledge network. Reality itself is one giant network where everything connects to everything else, so the larger a person’s knowledge network and the more interconnected it is, the more likely the beliefs in the network are to be true. To understand why, the jigsaw puzzle analogy is apt. When building a puzzle, there is a small chance that two pieces will fit, even though they don’t actually go together. But the chance that the same piece will fit incorrectly on two sides is much smaller. So to be sure you have the right piece, you want to try to connect it to the picture by more than one side. The chance of it being the right piece is even higher if there is a fourth piece connecting the two connecting pieces together, so that you have a square of four pieces. And the more pieces that can be added on to the connecting pieces, the higher the chance of each of them being the right piece.
Knowledge is like that, except there are plenty of extra pieces that don’t go to the puzzle, the chance of an incorrect connection is much higher, and the pieces can hook on to an arbitrarily large number of other pieces, which don’t have to be right next to each other. The knowledge puzzle also gets scaled up to more complex levels. With knowledge, you can have two packages of tightly-knit beliefs, but these packages only have a few connections between them. Imagine two balls of string connected to each other by three threads. Each ball is tightly connected, so they each individually have a high chance of being true, but their connection to each other is tenuous. If you discover that the two packages of beliefs contradict each other, either by learning something new or by thinking about them both in new ways, then you might have to make the tough decision to let one of them go.
When a contradiction is found between two sets of beliefs that one has, it is called cognitive dissonance, and depending on the complexity of the beliefs in question, as well as how attached we are to them, it can manifest as a physical headache. We instinctively want to get rid of the cognitive dissonance as quickly as possible. There are two ways to do this. The first, is to commit to whichever beliefs are most important to you, taking them, at least temporarily, as basic beliefs. The second takes longer, but it leaves you in a more stable place, and that is to take apart each package of beliefs and reevaluate them in the broader context of your total knowledge network, and by learning about the relevant topics from a variety of external sources.
A mind well-practiced in the art of knowledge construction will take time every so often to reevaluate the pieces of their knowledge network, to make sure it all fits together properly. There are many techniques to this, which we explore on this blog in the “Toolbelt of Knowledge” series.
There is still one teeny tiny issue with constructivism without basic beliefs, which you may have picked up on. Constructivism itself is a model, a sub-network of nodes within the larger network of a person’s knowledge. In particular, the belief that “the more solidly integrated a belief is within the network, the more likely it is to be true,” is itself a node in the network. This means that it must be subject to the same reevaluation process as everything else, or be taken as properly basic on faith.
But we don’t do that kind of faith here at SciFic. As you know if you’ve read “The Limit of Philosophy,” we prefer to race headlong into the trippy world of metalogic. So what happens when we allow ourselves to doubt the very method we use to determine what is true? Well, we just do the same thing we do with everything else: evaluate it. If it does not measure up to its own standards, then we get rid of it. If it is self-consistent, and we don’t have any alternative methods that are more self-consistent than this one, then we might as well use it. But one last question: why should we use self-consistency as a measure for whether a method of determining truth is valid? Because, as human beings, we are psychologically driven toward consistency. Of course, that’s not a logical reason, but remember, the most fundamental question is not “what is true?” but “what should we do?” and our action is driven by our unconscious psychology rather than logic.
As children, we are told all kinds of claims, which we accept on radical credulity. Then, we evaluate new things by a combination of how useful they are and how well they integrate into our networks of knowledge. A mature, practiced thinker will not take any claim as foundational, but evaluate and reevaluate every part of their network by how well it connects with the rest. That is knowledge.
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