Truth vs Reality: How we evolved to survive, not to see what’s really there
Take the circumstances in your life seriously, but not literally. Here's why.
DONALD HOFFMAN: Galileo was quite controversial, of course, in his time, because he was claiming that something that we all could see with our own eyes wasn't true. We could all see that the earth doesn't move and that the sun, and moon, and stars go around the earth. And we believed that as a race for about 2,000 years. And Galileo was saying that your eyes are lying to you. The earth actually moves and it's not the center of the universe.
And he was put under house arrest for it. And we don't like to be told that our senses aren't telling us the truth. And then Galileo took it another step. He said, it's not just that our senses are lying about movement of the earth, he said that he thought that tastes, odors, colors, and so on reside in consciousness. Hence, if the living creature were removed, all these properties, these qualities, would be utterly annihilated. That's almost a direct quote in the translation.
So he was saying that our senses are also making up the tastes, odors, and colors that we experience. They're not properties of an objective reality. They're actually properties of our senses that they're fabricating. And by objective reality in this case, I'm going to use that term in a very specific way. By objective reality, I mean what most physicists would mean. And that is that something is objectively real if it would continue to exist even if there were no creatures to perceive it. So the standard story, for example, is that the moon existed before there was any life on Earth and, perhaps, before there was any life in the universe. But it still existed.
Its existence does not depend on the perceptions of any creatures. And so that's the sense in which I'll talk about objective reality. And what Galileo was saying was that colors, odors, tastes, and so on are not real in that sense of objective reality. They are real in a different sense. They're real experiences. And so I'll talk about real experiences. So your headache is a real experience, even though it could not exist without you perceiving it. So it exists in a different way than the objective reality that physicists talk about.
So Galileo was quite brave and quite out of the box in his thinking by saying not only the earth in his movement, but even colors, tastes, and odors are our perceptual constructions. But he wouldn't go the next step. He wouldn't say that shapes, and mass, and velocities of objects, and space, and time themselves are our constructions. He thought that those were objectively real. So the shape of the moon, the position of the moon, is an objectively real thing, including its mass and its velocities. So, this is a distinction that was later called the primary and secondary qualities of distinction by John Locke. Primary qualities are things like position, mass, shape, and so forth. These are presumed to exist even if no creature observes them. Whereas colors, and odors, and tastes are secondary qualities that are sort of mostly the contribution of our senses.
And in brief, what I'm saying is we need to take the next step beyond what Galileo said. It's not just tastes, odors, and colors that are the fabrications of our senses and are not objectively real. It's, rather, that space-time itself and everything within space-time-- objects, the sun, the moon, the electrons, quarks, their shapes, if objects have shapes, their masses, their velocities-- all of these physical properties are also our constructions. And I've come to that conclusion. It was a bit of a shock to me. We always assume that our senses are telling us the truth. So it was quite a stunning shock to me when I realized that maybe we needed to take a step beyond Galileo on this. And the reason I'm saying this is because of evolution by natural selection.
Most of my colleagues in the cognitive and neurosciences assume that our senses tell us the truths that we need to survive. That seeing reality accurately will make you more fit. And I would say that that makes perfect sense. The argument is that those of our ancestors who saw reality more accurately had a competitive advantage over those who saw it less accurately in the basic activities of life, like feeding, fighting, fleeing, and mating. And because they had a competitive advantage, they were more likely to pass on their genes which coded for the accurate perceptions. And so after thousands of generations of that, we can be quite confident that we see reality as it is. Of course, not all of reality. No one claims that our senses exhaustively tell us all the truths about objective reality
. But from an evolutionary point of view, the idea is we see those aspects of reality accurately that we need to survive. And so when we see space and time, we see physical objects with their shapes and motions, and so forth, we're seeing truths, objective truths. Truths about objects that would exist even if no creature were there to perceive them. That's the standard view. And it seems intuitively plausible-- the argument that I just gave is actually in the textbooks in my field. But it turns out that we don't have to just deal with plausibility here. Evolution by natural selection is a mathematically precise theory. There is the field of evolutionary game theory that was established in the 1970s by John Maynard Smith and has flourished. It's now a very advanced and very interesting mathematically precise field.
It unites Darwinian evolution by natural selection with the tools of game theory. And it's very, very powerful. So we don't have to guess or wave our hands anymore. We can actually run simulations and prove theorems about the effects of natural selection on our senses. We can ask a technical question. Does natural selection favor organisms with sensory systems that tell them truths about reality, objective reality? It's a clean technical question. And it turns out there is a clean technical answer that comes from evolution. And it is quite surprising. I first started this about 12 years ago with a couple of graduate students of mine-- Justin Mark and Brian Marion.
We ran hundreds of thousands of evolutionary game simulations in random worlds with resources and creatures that had to forage for these resources. And we played god. Some of the creatures got to see the truth. Others didn't. And the ones that didn't, we had them just perceived the fitness payoffs. And we can talk a little bit about fitness payoffs a little bit later. That's a key, key notion in evolution. And what we found was in the simulations organisms that saw the truth never out-competed never outperformed creatures in our simulations that saw none of the truth and were just perceiving the fitness payoffs. So that gave me some confidence that maybe there was a theorem here. And so I proposed a theorem to a very talented mathematician named Chetan Prakash with whom I've worked for many years.
Chetan and I discussed it, worked on it. And Chetan brought it home. He proved the theorem. An organism that sees reality as it is is never more fit than an organism of equal complexity that sees none of reality and is just tuned to the fitness payoffs. Translated, that means if you see the truth, you'll go extinct. And so the question is, of course, what our fitness payoffs? And what's going on there? And it's a technical term in game theory. The payoffs are what sort of drive the game. But I think an analogy can help. Think of life as like a video game. In a video game, you have to, in many video games, you have to try to grab as many points as quickly as you can at the level that you're at. And if you get enough points in the minimal time, you might get to the next level. If you don't, you die. And you have put in some more money or start over.
And the idea is that life is like that. It's like a video game, but instead of the points in a game, we have fitness payoffs. Getting the right kind of food, high-quality food, not eating poisonous things, breathing the right kind of air, finding the right mate and so forth. These are all fitness payoffs that we can get. And if we get more fitness payoffs than the competition-- it's not like getting millions of fitness payoffs, you just have to do a little bit better than the competition-- then you have a better chance of passing on your genes that code for your strategies for getting fitness payoffs. So you don't go to the next level like in a video game, but your genes and your offspring go to the next level. And so that's, informally, the idea of fitness payoffs.
They're what drive success or failure in evolution and life. And what we discovered was two things-- First, that fitness payoffs themselves destroy information about the structure of the world. It's truly stunning. Fitness payoffs depend on the state of the world. And I can give you an example. So what is the fitness payoff of, say-- I like this example of a T-bone steak. Well, for a hungry lion looking to eat, that T-bone steak offers a lot of fitness payoff. It will help it to stay alive and be strong. For that same lion that's well fed and looking to mate, the T-bone steak offers no fitness payoffs. And for a cow, in any state, a T-bone steak is not a good thing.
So the payoffs depend on objective reality, whatever that might be, whatever the state of the world might be. And also on the organism, like lion versus cow, its state, hungry versus fed, and its action, eating versus mating, for example. So fitness payoffs, as you can see, are complicated functions. They depend on the state of the world, whatever the world might be, but also on the organism, its state, and its action. And if we fix an organism, state, and action, then fitness payoffs are functions from the world, whatever the world might be, into a set of payoff values, say from 1 to M, fitness payoff values where 1 means you're dead, M means you're getting the most you could possibly get.
And what we've discovered is that function, those fitness functions, almost surely destroy information about the structure of the world. I can give you a concrete example of what I mean by that. So suppose-- and by the way, when I said that, I don't need to know anything about the world. I don't need to propose I know anything what reality is. These terms hold anyway. That's the nice thing about the mathematics. You might say, well, you know, how could you prove such a theorem unless you know what the world is? It turns out you can. These theorems hold regardless of what the world is. Suppose we take, for sake of argument, a world in which there really is oxygen concentration.
There is air and there's oxygen. And oxygen concentration can go from 0 percent to 100 percent. That's what mathematicians would call a total order 0 is less than 1 less than 2, all the way up to 100. That's a total order. And it turns out that-- so that would be a structure in the objective world in this example. Now the percentages of oxygen that will maintain human life is about 19.5 percent to 22.5 percent. If you get outside that range, you'll be in distress and eventually die. And so there's this very narrow range of oxygen concentrations that are useful for life. So suppose you had a creature that had only two colors that they perceived.
So a very simple creature. It just sees green and red. And let's assume that we're going to say green is greater than red, just we'll just put an order on green and red. We can put an arbitrary order on them. So green is greater than red. And suppose-- look at two different creatures. One sees as much of truth as possible with just two colors. In that case, you might use red for 0 percent of oxygen to 50 percent. So red is for very little oxygen to medium. And green would be from medium to 100 percent. That way if you saw red, you'd know there was less oxygen. And if you saw green, you'd know there was more.
And so you're knowing as much about the truth of the objective reality-- namely the amount of oxygen-- as you could possibly know given the limits of your sensations. So that will be a truth organism. Now consider a fitness organism that only, again, has two colors, green and red. To encode fitness, you could do the following: Let's use red for 0 through 19.5, which will kill you. And for 22.5 to 100, which will also kill you. In other words, we use red for those amounts of oxygen that will not sustain life. And we'll use green for that narrow band from 19.5 to 22.5 that will sustain life. So if I see green, I know I'm good. I don't need to change anything. I'm going to live. If I see red, I know I'm in trouble. I need to do something differently. But notice if I see red, I have no idea about the truth, about how much oxygen there is.
There could be 100%. There could be 0%. I have no idea. So that concrete example gives you an intuition about why seeing the truth is a very different thing than seeing fitness and why that they're really at odds. They're not the same thing. Our intuitions are, of course, if I see the truth, that will make me more fit. And this example makes it very, very clear that seeing the truth is the opposite in most cases of seeing what's fit. And we were actually able to prove that-- this is now inside baseball language, but I'll throw it out there-- the set of fitness payoffs, if the world has N states, N as in Nancy, and the fitness payoffs have M values, M as in Mark.
There are going to be M raised to the N power, total fitness payoffs, very simple math, combinatorics. And you can for any structure in the world that you want to consider, a total order, a symmetric group, a cyclic group, a measurable structure, a topology, you can ask in each case how many of those M to the N fitness payoffs will preserve that structure. Mathematicians call them homomorphisms. So the homomorphisms of a topology are what we call continuous functions. The homomorphisms of measurable structures are what we call measurable maps and so forth.
It's straightforward to show in each case that the probability-- well, nah, I wouldn't say straightforward. If you a mathematician working with you, then looking over their shoulder, it looks straightforward, but, of course, it's hard work for the mathematicians. But it's combinatorics. And some of the combinatorics is pretty straightforward for mathematicians. In each case, we show that the ratio, the number of homomorphisms, the fitness payoffs, that preserve the structure of the world, that tell you something about the truth, to the total number of fitness payoffs, that ratio-- so the truth preserving payoffs versus all payoffs, we look at that ratio. And that ratio goes to 0 as the number of states in the world increases and the number of fitness payoffs increases, and that means the fitness payoffs generically destroy information about the structure of the world. Our senses will be tuned to the fitness payoffs.
And being tuned to the fitness payoffs means that you will not be tuned to the structure of the world, because the fitness payoffs have lost that structure. And so that's how devastating this is. So we're in a dilemma here. We have two things that we deeply believe. We deeply believe in evolution by natural selection. And we deeply believe in physicalism. That space-time and physical objects as we perceive them are a true representation of reality as it is. Those two claims are in conflict. Both cannot be true. And that's what we've done. I'm saying that space and time and physical objects don't exist unless they're perceived.
And someone might say, "Well, look, Don, if you think that that train coming down the tracks is just some little thing that you're creating on the fly, you're making that up, it's just an icon in your desktop, or a symbol in your virtual reality, why don't you step in front of that train? And after you're dead, and your ideas with you, we'll know that that train was real and it really can kill." And I wouldn't step in front of the train for the same reason that I wouldn't, for example if I'm, say, writing an email. And the email icon is blue and rectangular and in the middle of the screen.
That doesn't mean the email itself on the computer is blue and rectangular in the middle of the computer. So I don't take the icon literally. It's not literally true about what's in the reality. But I do take it seriously. I would not drag that icon to the trashcan carelessly. If I drag the icon to the trashcan, I could lose all of my work. So I take my icons seriously, but not literally. And that's the case with the train as well. Evolution by natural selection has shaped us with perceptions that are designed to keep us alive. So if I see a snake, don't pick it up. If I see a cliff, don't jump off. If I see a train, don't step in front of it. We have to take our perceptions seriously, but that does entitle us to take them literally.
So another objection is, I look over there and see a train, and I ask all of my friends, they'll also say that they see a train. So given that we all see the train, surely that means that, therefore, there is a train in objective reality. There really is a train. And that seems very compelling. Of course, we all look, we see the moon. We all agree that there is a moon. So therefore, the moon must really exist. But again that's a logical error. In the visual example that we looked at earlier with the cubes that were floating in front of the disks, we all would agree that we saw a cube. But we would all agree that the reason you saw a cube was because you created the cube. The cube doesn't exist unless you create it.
So the reason we agree about trains, and the moon, and cars, and apples, and so forth is because we have a similar interface. We're constructing similar objects. And because we construct our worlds in similar ways, we tend to agree. Although 4 percent of us have synesthesia and can view the world in very, very different ways from the rest of us. So the bottom line is agreement only means agreement, it doesn't mean that we're seeing objective reality. Descartes famously said, "I think, therefore I am." And that does raise a really interesting question about consciousness and what we call the physical world.
A physicalist would say, "Look, I know about things like umbrellas, and the moon, and rocks. I mean all of this concrete, stable stuff, I know about that reality. But when you talk about consciousness and conscious experiences, I'm not sure that you're really talking about anything real. It might just be an illusion. It might be a figure of speech. We could be very, very deeply wrong." So that's the view of most of my hard-nosed physicalist colleagues. "I know about this physical world out there. That's really solid. It's something we can really look out and test. This stuff about consciousness is airy fairy, wiggly. I don't know what you're talking about. It's too squishy for me." But there is a completely different point of view. It's to say, "Look, when I look over here, I'm having an experience, say, that I would call an apple. And so I know that I'm having an experience. And when I close my eyes, my experience of the apple stops. Now I'm just experiencing a gray field. And you want to tell me that, in fact, there's a red apple that still exists even when I'm perceiving a gray field. Well, that's actually more than I know. All I know is that when I open my eyes, I'm experiencing a red apple. And when I close my eyes, I'm not. It's an extra step. And it's a big jump to say that experience of the red apple is actually true of a real red apple. And that red apple still exists even when I'm stopping, when I don't have that experience. That's more than I know. I think it's far less problematic and less going out there on a limb to just say I have my experiences. And I don't know what the objective reality is that's out there."
So physicalism is actually a stronger and more problematic claim. It's saying that there is a reality that in some way matches our experiences and continues. I'm just saying we have these experiences. So the "cogito, ergo sum" that "I think, therefore I am," I think Descartes wasn't just talking about thinking in the normal sense of like abstract cogitation, doing reason. I think he was talking about perceiving. And in that sense, I would say yes. I'm having experiences. I'm perceiving. My, thoughts my rationality, I'm experiencing that as well. That's the starting point. And I would say I wouldn't go all the way with Descartes. He says therefore I am. I don't know what the word "I" refers to there. Certainly conscious experiences seem to exist from that. The "I" may be another construct, another symbol that I make. So the symbol that I call Don, the I, may not be absolutely necessary for the experience.
So I don't know if I'd go all the way with Descartes on that. But I would go part of the way and say, yes, saying that there is a world of experience is going less out on a limb than saying that there is a world of objective objects that resembles my world of experience, in addition to my experiences. So in my own scientific investigations, I've proposed a very controversial theory. And I've gotten lots of very pointed and sharp criticism, some in print, some published, some in person. And what I found is I've learned a lot from each of the criticisms. In many cases, they forced me to think about an aspect of the theory that I had not thought about that way before.
And in some cases, they put me into days of doubt, where I was looking at that part of the theory, wondering about it, and then either revising the theory or realizing, "oh, wow, the theory has resources that I didn't realize to deal with that problem." And that's the power of a nice theory, by the way, a mathematically precise theory. When you write down the theory, the theory then becomes your teacher. It becomes smarter than you in a way. When Einstein wrote down the equations of general relativity, he did not know that they entailed the existence of black holes. In that sense, the equations were smarter than Einstein. Einstein didn't believe in black holes for decades.
The equations were very clear that they could exist. Einstein said, no. And it turned out Einstein was wrong and the equations were right. So it is very interesting. We do these theories because we can learn from them. But when you have criticisms, it forces you to-- it forced me to examine parts of my theory very, very carefully and ask, "Is this correct? Do I need to revise? Or are there the resources within the theory to handle this objection?" And in many cases, I discovered new strengths in the theory that I hadn't known before.
And then I would use them later on as advertisements for the theory: "You might say such and such is a problem, here's the answer." And that often, then-- a lot of my colleagues now when I talk with them, I know the first 10 objections they're going to have because I've been given those objections. I've thought about them. So I give them the objections. I give them the answers. And so it forces the discussion to a new level which is good. All the easy objections, quote unquote "easy objections" are taken out of the picture. Let's go deeper. Give me an objection I've not heard before so I can learn something new. And that's sort of the attitude. Take the objections. Learn from them. It's always a growing experience. If you have the attitude "If someone is disagreeing with me, no, I'm not going to listen to that," that's when you stop learning.
- Galileo was quite controversial, in part, because he argued that Earth moved around the sun, despite people's senses deluding them that the world was static.
- Evolution may have primed us to see the world in terms of payoffs rather than absolute reality — this has actually helped us survive. Those who win payoffs are more likely to pass on their genes, which encode these strategies to get to the "next level" of life.
- It's important to listen to people's objections because they may bring something to your attention outside your ken. Learn from them to make your ideas sharper.
- Does the Language We Speak Affect Our Perception of Reality ... ›
- If reality is a data structure, can the simulation theory hold up? ›
- We Survive Because Reality May Be Nothing Like We Think It Is ... ›
- Did we evolve to see reality as it exists? - Big Think ›
Nazi supporters held huge rallies and summer camps for kids throughout the United States in the 1930s.
- During the 1930s, thousands of Americans sympathized with the Nazis, holding huge rallies.
- The rallies were organized by the American German Bund, which wanted to spread Nazi ideology.
- Nazi supporters also organized summer camps for kids to teach them their values.
A Bund parade in New York, October 30, 1939.
Credit: Library of Congress
1930s AMERICAN FASCIST BUND CAMP HOME MOVIE BERGWALD NEW JERSEY<span style="display:block;position:relative;padding-top:56.25%;" class="rm-shortcode" data-rm-shortcode-id="69d54b175b0d317cf9bfd688e4fa04f3"><iframe type="lazy-iframe" data-runner-src="https://www.youtube.com/embed/gOPeDaDcw3w?rel=0" width="100%" height="auto" frameborder="0" scrolling="no" style="position:absolute;top:0;left:0;width:100%;height:100%;"></iframe></span>
Tea and coffee have known health benefits, but now we know they can work together.
Credit: NIKOLAY OSMACHKO from Pexels
- A new study finds drinking large amounts of coffee and tea lowers the risk of death in some adults by nearly two thirds.
- This is the first study to suggest the known benefits of these drinks are additive.
- The findings are great, but only directly apply to certain people.
Maybe you should enjoy this article with a cup of coffee or tea.<p> The <a href="https://drc.bmj.com/content/8/1/e001252?T=AU" target="_blank" rel="noopener noreferrer">study</a> involved 4,923 type 2 diabetics living in Japan. The average participant was 66 years old. All of the participants were taken from the rolls of the Fukuoka Diabetes Registry, a study geared at learning about the effects of new treatments and lifestyle changes on the health of diabetics. <br> <br> The participants filled out questionnaires concerning their health, diet, habits, and other factors. Among the questions were two focused on determining how much green tea or coffee, if any, the participants consumed over the course of a week. The health of the participants was recorded for five years. During this time, 309 of the test subjects died from a variety of causes. <br> <br> Subjects who drank more than one cup of tea or coffee per day demonstrated lower odds of dying than those who had none. Those who consumed the most tea and coffee, more than four and two cups a day, respectively, enjoyed the most significant reductions in their risk of death. This level of consumption was associated with a 40 percent lower risk of <a href="https://www.sciencedaily.com/releases/2020/10/201020190129.htm" target="_blank" rel="noopener noreferrer">death</a>. </p><p>Most interestingly, the effects of drinking tea and coffee appear to combine to reduce risk even further. Those who reported drinking two or three cups of tea a day and two or more cups of coffee were 51 percent less likely to die during the study, while those who drank a whopping four or more cups of tea and two or more cups of coffee had a 63 percent lower risk of <a href="https://www.medicalnewstoday.com/articles/diabetes-coffee-and-green-tea-might-reduce-death-risk" target="_blank" rel="noopener noreferrer">death</a>. </p>
So, should I start swimming in a vat of coffee and green tea?<iframe width="730" height="430" src="https://www.youtube.com/embed/LY0E-JQxeoY" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe><p> Not quite. </p><p> The primary takeaway from this study is that Japanese adults with type 2 diabetes who drink a lot of green tea and/or coffee die less often than similar people who do not. If this effect is caused by something in the drink, lifestyle choices people who drink that much tea all make, or something else remains unknown. The finding must be considered an association at this point. <br> <br> The eye-popping reductions in mortality rates are compared to the risk of death of others in the study. The people who died reported drinking less tea and coffee than those who lived. Unless you have several demographic and conditional similarities to the subjects of this study, you probably won't suddenly be at a two-thirds lower risk of death than your peers because you drink green tea. </p><p> Like all studies that depend on self-reporting, it is also possible that people misstated how much they consumed any one item. The study also did not look into other factors like socioeconomic status or education level, also known to impact death rates and potentially linked to coffee and tea consumption. </p><p> However, it is yet another study in the pile that suggests that <a href="https://www.healthline.com/nutrition/top-13-evidence-based-health-benefits-of-coffee" target="_blank" rel="noopener noreferrer">coffee</a> and <a href="https://www.healthline.com/nutrition/top-10-evidence-based-health-benefits-of-green-tea" target="_blank" rel="noopener noreferrer">green tea</a> are good for you. That much is increasingly <a href="https://www.health.harvard.edu/press_releases/health-benefits-linked-to-drinking-tea" target="_blank" rel="noopener noreferrer">agreed</a><a href="https://www.rush.edu/health-wellness/discover-health/health-benefits-coffee" target="_blank" rel="noopener noreferrer"> upon</a>. This study also suggests the benefits are additive, which is a new development.</p><p><br> So, while it isn't time to start the IV drip of green tea, a cup or two probably won't <a href="https://www.webmd.com/diabetes/news/20201022/coffee-green-tea-might-extend-life-for-folks-with-type-2-diabetes" target="_blank" rel="noopener noreferrer">hurt</a>. </p>
Logic puzzles can teach reasoning in a fun way that doesn't feel like work.
- Logician Raymond Smullyan devised tons of logic puzzles, but one was declared by another philosopher to be the hardest of all time.
- The problem, also known as the Three Gods Problem, is solvable, even if it doesn't seem to be.
- It depends on using complex questions to assure that any answer given is useful.
The Three Gods Problem<iframe width="730" height="430" src="https://www.youtube.com/embed/UyOGZk7WbIk" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe><p> One of the more popular wordings of the problem, which MIT logic professor George Boolos <a href="https://www.readersdigest.ca/culture/hardest-logic-puzzle-ever/" target="_blank">said</a> was the hardest ever, is:<br> <br> "Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for <em>yes</em> and <em>no</em> are <em>da</em> and <em>ja</em>, in some order. You do not know which word means which."<br> <br> Boolos adds that you are allowed to ask a particular god more than one question and that Random switches between answering as if they are a truth-teller or a liar, not merely between answering "da" and "ja." <br> <br> Give yourself a minute to ponder this; we'll look at a few answers below. Ready? Okay. <strong><br> <br></strong>George Boolos' <a href="https://www.pdcnet.org/8525737F00588A37/file/31B21D0580E8B125852577CA0060ABC9/$FILE/harvardreview_1996_0006_0001_0060_0063.pdf" target="_blank" rel="noopener noreferrer">solution</a> focuses on finding either True or False through complex questions. </p><p> In logic, there is a commonly used function often written as "iff," which means "if, and only if." It would be used to say something like "The sky is blue if and only if Des Moines is in Iowa." It is a powerful tool, as it gives a true statement only when both of its components are true or both are false. If one is true and the other is false, you have a false statement. </p><p> So, if you make a statement such as "the moon is made of Gorgonzola if, and only if, Rome is in Russia," then you have made a true statement, as both parts of it are false. The statement "The moon has no air if, and only if, Rome is in Italy," is also true, as both parts of it are true. However, "The moon is made of Gorgonzola if, and only if, Albany is the capitol of New York," is false, because one of the parts of that statement is true, and the other part is not (The fact that these items don't rely on each other is immaterial for now).</p><p> In this puzzle, iff can be used here to control for the unknown value of "da" and "ja." As the answers we get can be compared with what we know they would be if the parts of our question are all true, all false, or if they differ. </p><p> Boolos would have us begin by asking god A, "Does "da" mean yes if and only if you are True if and only if B is Random?" No matter what A says, the answer you get is extremely useful. As he explains: <br> </p><p> "If A is True or False and you get the answer da, then as we have seen, B is Random, and therefore C is either True or False; but if A is True or False and you get the answer ja, then B is not Random, therefore B is either True or False… if A is Random and you get the answer da, C is not Random (neither is B, but that's irrelevant), and therefore C is either True or False; and if A is Random...and you get the answer ja, B is not random (neither is C, irrelevantly), and therefore B is either True or False."<br> <br> No matter which god A is, an answer of "da" assures that C isn't Random, and a response of "ja" means the same for B. </p><p> From here, it is a simple matter of asking whichever one you know isn't Random questions to determine if they are telling the truth, and then one on who the last god is. Boolos suggests starting with "Does da mean yes if, and only if, Rome is in Italy?" Since one part of this is accurate, we know that True will say "da," and False will say "ja," if faced with this question. </p><p> After that, you can ask the same god something like, "Does da mean yes if, and only if, A is Random?" and know exactly who is who by how they answer and the process of elimination. </p><p> If you're confused about how this works, try going over it again slowly. Remember that the essential parts are knowing what the answer will be if two positives or two negatives always come out as a positive and that two of the gods can be relied on to act consistently. </p><p> Smullyan wrote several books with other logic puzzles in them. If you liked this one and would like to learn more about the philosophical issues they investigate, or perhaps if you'd like to try a few that are a little easier to solve, you should consider reading them. A few of his puzzles can be found with explanations in this <a href="https://www.nytimes.com/interactive/2017/02/11/obituaries/smullyan-logic-puzzles.html" target="_blank" rel="noopener noreferrer">interactive</a>. </p>
But most city dwellers weren't seeing the science — they were seeing something out of Blade Runner.
On Sept. 9, many West Coast residents looked out their windows and witnessed a post-apocalyptic landscape: silhouetted cars, buildings and people bathed in an overpowering orange light that looked like a jacked-up sunset.