The Map

Let’s start with a simple question. How long is the coastline of Lake Superior? Here, let me google that for you. “Shore length 1,729 mi (2,783 km) plus 997 mi (1,605 km) for islands”. Thanks, Wikipedia! Right away we can see a problem. Are you counting those islands or not? I’m saying count every last thing. All of it. Okay, include the islands. What other complications are we going to run into?

Is that the whole length or are we omitting some coves? Did the surveyors who measured this include every little inlet along the coast? What if it’s only a foot across? What do you do at the mouth of a river? Where does the river stop and the lake start? If a lake is just a bunch of water in the middle of land (hey, it’s a reasonable definition) then you could argue that you’d require twice the length of the river to get everything. “How long is the Brule River” is a recursive question; you get into much the same problems. Okay, set that aside. Do you count man-made breakwaters? If you don’t, what about man-made shoreline? Our tendency to draw in straight lines will shorten the final length. How about these boulders by the shore; are they part of the coastline? I want the most accurate answer possible, so measure the water line on each individual rock. See those waves crashing on the shore? Do you measure the shoreline at their furthest reach? Where they would be on a completely still day? High tide or low tide? Hey, while you’re measuring around individual boulders how big are your boulders? I’ve got some grains of sand for you to measure around here. What do you mean you aren’t going to count the individual molecules?

Fractal Rock

I first encountered the problem of the length of a coastline in a description of fractals. “Fractals” is a mathematical concept describing a bunch of shapes you generate by repetitious behavior. Let me show you an example. Start with the Triforce.

The smaller triangles represent Power, Wisdom and Courage respectively.

In the Zelda games, the Triforce is an artifact of great power. It’s comprised of three equilateral triangles. Together they make one larger equilateral triangle with a space missing from the middle. Suppose one day Ganon realizes he can make his artifact even more powerful by carving smaller triangles out, like so:

Let’s see, you’ve got Command, Control, Cash on the top, (Prudence, Understanding, and Smarts on the left, and Bravery, Nobility, and Foolhardiness on the right.

What’s to stop him from continuing the chain, and making them smaller and smaller?

You’re on your own for this one.

In the end, you’ve got something called the Sierpinski Gasket, named after a mathematician who probably would have made a good Zelda villain. He’s practically got the word “Serpent” in his name already. Mathematicians entertain each other by posing questions about this kind of thing. (Assuming Ganon made an infinite series of smaller and smaller carvings what’s the total area of those triangles?) I’m not going to go through the math. Let’s see what it looks like in terms of our question of coastline. This could be a similar set of approximations of a coastline:

This is a modification of the Koch Curve, or Koch Snowflake. In The traditional variant, the top point also goes fractal, which ultimately leads to the line summing up to an infinite length. I’m not going to stand for that.

You’ve got a lot of peninsulas and coves, the deviations get smaller and smaller until you’re dealing with boulders and grains of sand, all of which happen to be pointy. If you add up all those line segments you get a definite length. It’s not infinite even though we’re adding an infinite number of things together because the line segments get shorter and shorter with each iteration. (This is the kind of thing that fascinates your garden variety mathematician.) The point is, even if you can do the math you can’t actually go through and measure each bit. Let’s go back to the actual coast of superior:

You can sorta see the triangles on the southern edge. You can if you believe in yourself!

The shoreline doesn’t conform to the neat geometrical realities the mathematicians deal with. In principle, you can’t even solve the math to get an exact length. The mathematicians have tools to estimate the fractal nature of a real coastline (or a piece of broccoli) but it’s got to be an estimate. At best you’ve still got an imperfect approximation.

The Thing about Fractals, it’s Fractals All the Way Down.

The point of this whole discussion is to show that things as certain as data from an almanac really aren’t as certain as advertised. I can go on. The institute of standards in Paris, France maintains a one kilogram mass. If you moved that kilogram to La Paz, Bolivia it would weigh slightly less than one kilogram. (Why? Difference in elevation, difference in latitude, but mostly because the guy in the terminal figured it was valuable and swiped it.)

Do you believe your own eyes? Why? What you’re seeing isn’t simply a map of all the photons in your local area. It’s highly edited by your brain to give you a coherent picture. Optical illusions are designed to take advantage of the brain’s tricks to make sense out of the noise it gets. Change Blindness is when you’re operating off the assumption that the thing you saw a moment ago is the same thing that you’re still looking at. In the end your eyes aren’t giving you a true picture of what’s out there, only a model. Just one that you can rely on 99% of the time.

We act off models. A model is an approximation of how the world works. It’s true over a certain domain and it breaks down once you get outside of that. I have this idea that when I give the gas station man my dollars he’ll give me gas. This model is broadly true, but it fails in the event of Lord Humongous taking control of Australia. I figure one kilogram of mass weighs one kilogram anywhere on the earth’s surface and somehow that model is close enough to reality to get me through the day. If I were in La Paz getting something measured by the kilo and they suggested that I was getting less because of the way physics works my model of reality would list “this guy’s a scumbag” as a more probable explanation than any of those complications I mentioned I mentioned up above.

The thing about models is that they can be true without being entirely correct. “Eat your broccoli, it’s good for you.” That’s a model of how nutrition works, and for most of us it’s true. My mother though, she’s allergic to broccoli. It is not in fact good for her. You can make your model more complex, in which case it gets closer to what’s actually true, but it’s still an approximation. That’s why I started this with a discussion of fractals. Fractals make a pretty good framework for how models work. First layer on a fractal, “Broccoli is good for you.” It gets you most of the way there. Second iteration: “…unless you’re allergic to broccoli”. Third iteration: “Or you’re badly nauseated. Won’t do you no good if’n you can’t keep it down.”. Fourth iteration “Oh, and try not to eat so much of it that you burst your stomach.” Each iteration of the fractal makes your statement closer to true in all circumstances. And much like how you can’t follow fractals all the way down you’re inevitably going to miss some cases.

The bailiff, then, who asks you to tell the Truth, the Whole Truth and Nothing but the Truth is making a pretty big ask. “How long did it take you to proceed from the grocery store to the bank?” It took me precisely thirteen minutes, twelve seconds, one hundred fifty three milliseconds, seven hundred and nineteen microseconds, three hundred sixty even nanoseconds…. In this life all we ever deal in are approximations. “About fifteen minutes”. The prosecutor wheels on you. “About fifteen minutes? May I remind you that a man’s life hangs in the balance!” “My grocery store receipt says 3:14, and when I walked into the bank I noticed that the wall clock said 3:27. I took particular note because I had to pick up my daughter at four.” That statement is true, as true as the guy on the witness stand can make it, but it’s not perfectly true. He rounded off a whole lotta nanoseconds. Assuming both clocks were perfectly accurate, which they weren’t.

We can never really know truth in an absolute sense, in the same way that we can only follow a fractal some of the way down. But in the same sense that we get a better and better knowledge of the length of the coastline of superior the closer and closer we measure it then we get closer and closer to the truth the more levels of the fractal we explore. The map is not the territory, but we can never actually know the territory. All we have are models of what it’s like. Some of these models are more accurate than others. The point isn’t to throw your hands in the air in frustration, it’s to acknowledge the inherent limitations on what we observe to be true.

What is Truth?

I had a discussion with @iWe at the Mackinac meetup lo these many years ago. The question was of people who hear God talking to them when they’re praying. I used the phrase “in objective reality”, and we got into a talk about whether objective reality exists. Does it exist? There’s a definite time between when that person left the grocery store and when he arrived at the bank. Some discrete quantity in objective reality which we can never know but can only approximate. If objective reality exists; iWe’s contention was that there’s no such thing, that reality exists as a negotiated agreement between all concerned parties. If you and I agree that the price of gas is eight cents a gallon then I’m filling up my tank. If you and I agree that there’s no table here then I guess I’m not going to bust my shins on anything, am I?

I’m not doing iWe’s argument justice, and for that I apologize. It’s been quite a while since the discussion. It does explain some things like psychosomatic healing better than a materialistic objective reality would. But the argument I came up with that settled the discussion in my own mind revolves back to that original question. The people who hear God talking to them; is God actually talking? If reality is a negotiated agreement between all concerned parties then you’ve got to count God as one of those parties. And if you’re counting God’s vote, why are you counting anyone else’s? Objective reality then is how God views reality, and all our approximations are approximations of the Truth as the Good Lord sees it. God can follow the fractals all the way down; He can tell you the exact length of the Lake Superior coastline, whether broccoli is good for any given person, and any other such puzzles as you could set before Him.

In that sense, we can consider truth as a fractal. The whole fractal, the sum of all the parts, is what is true in a Biblical sense. Reality as God sees it. When we go to find out the truth we start at the top of the fractal. You can learn the big part pretty easy, and first complications after that aren’t that hard. But there are always more complications. These complications don’t obviate the truth of the higher levels of the fractal; those are still true, just not the whole truth. And we can never follow the whole truth all the way down.

Pontius Pilate asked the question “What is Truth?” He meant it as rhetorical and unanswerable. In one of history’s greatest ironies, he asked it of the Way, the Truth and the Life. If Pilate had actually wanted the truth there was no one in a better position to get it. He didn’t, he didn’t want to know what was true, but what was expedient. For all his protestations Pilate already knew what was true. The first iteration on the fractal was that the man before him was innocent. He knew this. Hiding behind some philosophical pretension doesn’t change that.

The Impossibility of Communication

We’ve seen that it’s impossible to know the truth fully, completely, and without error. It’s worse if you’re trying to talk to someone. If you attempt to communicate with another person you’re first working off the truth as you know it. That model isn’t perfectly expressed in your message; you can spend all day prevaricating and not convey the entirety of what you know and believe. Finally, the words your listener hears aren’t going to be the words you spoke, only the words they think you spoke. Pretty much every prophecy story in the world has that distinction as its core conflict. “A great nation will fall” and the genius doesn’t stop to ask “wait, his or mine?”

Even if your interlocutor isn’t being particularly oracular (or insists on using $7 words like interlocutor) you suffer a pretty good chance of misunderstanding his meaning. Maybe your mind wanders for a bit and you miss a word. Maybe he uses a phrase in a way you’re unfamiliar with, or he misses spelling out an acronym. Maybe his logic contains an assumption that you miss. If you read Thomas Aquinas’ famous five proofs of the existence of God, one of them starts out “As gold is a more noble metal than silver”. Huh? I can tell you a decent amount about gold; how it’s corrosion resistant, about what you’d expect to get for it on the open market, and even why it glows gold. I can’t judge for myself whether or not it’s more noble than silver. I can take your word for it but my thoroughly modern mind isn’t prepared to think of something utilitarian like atoms in that fashion. Never mind the rest of his proof I’m having trouble just reading his postulates.

Interestingly enough the Apostle Paul acknowledges this problem in the letter to the Romans. “For we do not know what we should pray for as we ought, but the Spirit Himself makes intercession for us with groanings which cannot be uttered.” Romans 8:26 God, in addition to little things like speaking the universe into existence, is apparently able to understand not just what we mean when we pray but what we ought to mean. I don’t know about you, but considering everything I’ve said up until this point about the impossibility of knowledge and communication I find that comforting.

On Truth, Lies and False Witness

Up until this point we’ve been talking about the unavoidable errors we make when we’re trying to know and state the truth honestly. Now we move on to lies, white lies, and skip lightly over statistics. “You shall not bear false witness against your neighbor.” The Ten Commandments sets the rule down. But what does it mean to bear false witness?

First level of the fractal, the sort of way you’d explain it to a three-year-old. “Don’t lie. Lying is wrong.” And now I’m thinking back to my ten-year-old self, the kid who’s figured out that there exists such a thing as a lie by omission, and who’s unwilling to say anything without a lot of “well actually” prevaricating. Or my thirteen-year-old self who’s so concerned with the truth that he’s unwilling to tell a joke without making sure his audience understands that it’s a made-up thing. To this day I’ll feed you a line but immediately discard the pretense when asked about it. Any sort of fiction is necessarily a lie, but not in the same sense as a malicious untruth.

Consider that courtroom scene I painted up above. The honest and forthright witness is nevertheless giving incorrect information because he didn’t include nanoseconds. In the model, his first iteration is true (about fifteen minutes), and his second iteration is also true (precisely thirteen minutes based on the clocks I observed.) Somewhere further down the fractal, he misses his nanoseconds. False witness? Obviously not. False witness means that you are deliberately altering, shading, misconstruing or outright fabricating the truth such that it leads to the harm of another.

The essential question of a lie isn’t how well you can represent the truth fractal, it’s the harm you intend for (or are unconcerned with happening to) the person you’re lying to. The relationship model of reality has this going for it: the most important thing in this world is the people populating it, and the relationships we have with those people. A lie is harmful because it damages that relationship.

A pregnant lady, her hair all frumpled and her breath still bitter from morning sickness asks her husband “Do I still look beautiful to you?” And he answers, if he’s any kind of man at all, “Yes.” Maybe she doesn’t look as beautiful as she did in the cathedral in that long white dress with her makeup perfect and her hair held in place by a million pins. But she’s still beautiful. When he says “yes” he’s saying “I promised to love and cherish you until my dying day. You are the most important thing in the world to me. I know that you’re feeling ill, that you don’t believe you’re beautiful right now, but there’s nowhere in the world I’d rather be than holding you, giving you comfort. And yes, you are beautiful. You may not think it, but I’m the judge. Bloated and discolored, shaved bald and slathered in mud I’d still judge you the most beautiful woman in the world.” Now, he might not think she’s at her top form, and being a mortal man he’s going to fall short of the standard of perfection as we all do. But he’s going to tell her that she’s beautiful even if he isn’t precisely feeling it at the moment. The statement which is false on the surface nevertheless conveys the more important truth that he loves her.

That’s the marriage relationship; it guarantees love and sacrifice for the sake of the other. On the other end of the scale you’ve got a purely commercial transaction. I go to a distillery website and it says “please enter your birth date to continue.” I tell it I was born on 1/1/1979. This is a lie, but I don’t count it as bearing false witness. Why? The question they’re actually asking is if I’m legally old enough to access their site. To the extent that they need my exact age it’s to sell that demographic information to their ‘partners’. It’s not something I would offer them if I was speaking to someone face-to-face. When I give them the wrong birth date I’m telling them “I am old enough to view your content, but not willing to trust you with my birth date because I don’t trust what you’d do with the information, the people you’d provide that information to, and I certainly don’t trust the hackers who will inevitably compromise your database.” My relationship with the distiller is solely commercial; they may ask for more information but I don’t feel the obligation to provide it to them.

Let’s try the opposite side. Lemme think of an example of a harmful lie. “If you like your doctor you can keep your doctor. Period.” Too easy. Howabout a harmful truth? “It ain’t the dress making your butt look big.” Remember that we’re down the fractal from the three-year-old’s perspective. Most of the time the situation is governed by the first iteration. That is, most of the time lying is just bearing false witness. Don’t go arguing yourself into believing you’re doing the right thing when you’re not.

The question of relationships explains small talk too. “How are you doing on this fine morning?” they say. This morning is all right, I’ll let the adjective pass. “I’m still pretty groggy from waking up this morning; worried about the health of my relatives, rather be doing anything else than walking in to work, and not at all happy to be passing the time with you. I’m sure you’re a wonderful person and all but I really don’t want to be dealing with you.” That would be a more truthful answer, but I just say “Fine.” And that’s okay. The truth fractal they’re attempting to convey is “Socially I’d like to acknowledge that we’ve converged in this hallway and that you’re another person. I don’t actually want your life story, I just want to be pleasant.” And the truth fractal I’m signalling back is “Message received; you are a decent human being but I for one am not interested in conversation. I will offer you a cheerful-ish response to show that I too subscribe to the norms of society and then we can continue on this walk in mutual silence, our obligations satisfied.” Actually, I might try saying literally that sometime. I have a strong tendency to do something odd just to see how people react.

The Lies We Tell Ourselves

Okay, but what about self-deception? You’re not harming another person when you’re only lying to yourself. Let’s stipulate that you aren’t hurting anyone else. Odds are that you are, but never mind that for now. What lies exactly are you telling yourself? Are they grand and ennobling things? The self-affirmations in the mirror in the morning? “Just one more rep” as you’re burning to give up on your dead lifts? The willful smile-until-you-feel-like-smiling plan?

Listen to yourself. Listen to the lies you’re actually telling yourself. That isn’t it. It’s “I can have a candy bar today; I’ve earned it because this morning was so awful” (by which we mean mildly unpleasant). “It doesn’t matter that I cut that guy off in traffic; he deserved it anyway.” “Only three likes on that comment; people must hate me.” “Everyone cheats a little.” “Nobody will care if I slack off.”

Sin, in the Biblical sense, sin is fundamentally an act of rebellion against God. When Cain struck down Abel he did so because he was angry with God’s preferring Abel. When David slept with Bathsheba he did so because he believed that the pleasure of the act was more valuable than the marriage covenant established by the Almighty. When Pontius Pilate washed his hands of Christ he did it because he valued his own political position more than the life of an innocent man. Sin is fundamentally an act of rebellion, but every sin is also accompanied by a lie we tell ourselves. “I know what is right and what I ought to do, but in this case, it’s justified because…”. Spoiler alert, it isn’t justified.

When Benedict Arnold betrayed his country he did so because he first felt betrayed by it. He had to use that betrayal as justification for his sin. When Andrew Jackson engineered the Trail of Tears he did so because he had convinced himself that Indians were less than human. You’ll note that the rhetoric in defense of slavery moved from a painfully necessary phenomena to “It’s for the good of the slaves” as the Civil War approached. The perpetuation of that monstrous evil forced it’s adherents to lie to themselves and convince them that it wasn’t actually monstrous. Much like how today you’ll hear the radical feminists arguing that murdering babies is a positive good. Bill Clinton callously used Monica Lewinsky because he had lied to himself about the relative value of getting his rocks off versus the effect he’d have on another person’s life.

I stipulated that you’re not hurting anyone else, but apparently I couldn’t. Every single example of sin and the lie that accompanied it involved grievous harm to one or more other people. That’s another thing that’s inherent in sin; it’s terribly corrosive to all that it touches.

Art, Lies, and Disused Clay

This model (and remember this is a model of reality we’re talking about. The map is not the territory but we never actually know the territory, just maps with greater or lesser accuracy). This model is also useful to explain the nature of fiction, and art in general. A proper portrait will show you a more true image than a photo that’s, well, photorealistic. My sainted grandmother Grace passed away and I saw her in the coffin for the visitation. I got a very strong sense that that body wasn’t her. Partly because her face was in a solemn, dignified repose, and largely because she was the most vivacious person who had walked this earth. Now, that was the best possible representation of her; the corpse literally had her features. But her spirit has passed, and all I was seeing was disused clay.

Some years later Grandpa came and lived with us for a spell; this man who was made of iron in his youth had become old and feeble enough that he could no longer live alone. Across from his chair, he prominently placed a portrait of my grandmother. Now I had never seen her as she looked in that portrait; a young beauty with long, dark hair in the style of an earlier age. No one had for the past half-century. In all my memories of Grandma, she’s got gray and white hair (and a great big wide smile). I could recognize my Grandma’s character in that picture.

That portrait of her was a truer representation of the person than the corpse could have possibly been. The truth fractal of artwork is funny that way; the first iteration is quite plainly false. If audience doesn’t know that then it isn’t a story but a prank. The iterations further down are where the interesting things happen. Art, if it’s any good, gives you glimpses deeper into the truth fractal. Your model of reality gets a little deeper and more complex.

I’ve become more careful over the years about what kind of things I read. I’m always skeptical of the authors. They’re subject to all the unintentional errors I’ve described, but also they may simply hold to an incorrect worldview. The best example of this is Game of Thrones. George R. R. Martin is a talented writer. He creates a world that is fascinating, interesting characters, and beautiful sentences. Even so, I find I can’t stand his books. His writing exhibits a strong nihilistic spirit. He doesn’t believe in a universe with a moral order and that shines through in the stories he tells. It isn’t the sex or the violence that puts me off; it’s the feeling that he’s consistently lying to me.

Wending Back Up the Fractal

This is more of a postscript than a proper section. Remember that you can go back up the fractal too. The first iteration of your model ought to give you a pretty good picture of how the world works. If it doesn’t it’s a bad model and should be discarded. No matter how much someone prevaricates around the statement “Communism has never worked anywhere it’s been tried” is still fundamentally true.

That’s about as far down the truth fractal as I can take you. Even those of you who bothered to read this far. Remember that all the statements about truth and how to communicate it apply to this post and everything therein. Whatever is true about the nature of truth I at best have an imperfect grasp on it. You’re going to not understand me perfectly, no matter how long-winded my explanation (though I can still put up a yeoman’s effort, apparently.) You might disagree with my interpretation and you might actually be right.

No human model is perfect.