## Tittiebone

No, you didn’t read that title wrong. In fact, it’s probably causing you as much confusion as it caused me when I was eight.

I grew up in the 1960′s, in Cheyenne, Wyoming. I started Kindergarten in 1962, a year before JFK was assassinated. Wyoming has always been at least ten years behind the rest of the country — “the 60′s” wouldn’t begin for another fifteen years. We were still buried deep in the 1950′s, maybe even the late ’40′s. The closest thing we had to “pornography” was Playboy Magazine, which in those days was just a tiny bit racier than a pin-up calendar you might find in the mechanic’s office: bare breasts, maybe a glimpse of a patch of pubic hair peeking out from behind a draped towel or a silk robe. The hardcore magazines weren’t easy to come by: you had to know someone whose father kept a stash in the footlocker in the basement where he kept his gun.

As a result, everything we actually knew about sex (and girls) came from older brothers, who were not very much more knowledgeable than we were. On top of that, they enjoyed tormenting their little brothers with misinformation. “Santa Claus” doesn’t even amount to a sno-cone shaved off the iceberg of misinformation we carried around daily.

I didn’t have any older brothers. But I had plenty of friends with older brothers, and those friends were the “worldly” kids in our school classes. They were the ones who taught the rest of us how girls got pregnant, and how babies were born, and what kissing was all about.

It reminds me now of the old joke:

Q: Why do blonde women have bruises around their belly buttons?
A: Because blonde men are dumb, too.

Yes, when I was in third grade, belly-buttons had something to do with sex. We weren’t entirely sure what, but we were sure of that much. After all, Craig Johnson’s brother had told him so. And he had a girlfriend.

So I think it was around third grade — I’d have been eight, going on nine — that the term “tittiebone” entered into our vernacular. Not a single one of us knew what it meant, so it quickly became an all-purpose pejorative. It’s something you’d shout at the opposing pitcher in a Little League game: “You TITTIEBONE!” School cafeterias served up tittiebone sandwiches. We’d call someone we didn’t like a tittiebone.  Anyone who touched a tittiebone got girl germs.

Within a year, the word was gone, swallowed up into the etymological void from which it sprang. It’s a word that will bring a faint smile to the lips of anyone who was in third grade in Cheyenne in 1965. Anyone else will scratch his head in befuddlement.

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I don’t know if it’s appropriate or inappropriate to be talking about this subject after the tragedies recently in the news. But I’m troubled, and angry, and sad — and disgusted, and appalled, and then sad some more. I doubt that I’m the only person in the country who feels this way.

A friend and I, both distressed by the news, fell to talking the other night until the wee hours of the morning about a wide range of subjects that included terrorism, bombs, and guns, and that led to the discussion of a gun for “protection” in the house.

I don’t own any guns for any purpose, and I’ve occasionally wondered if I should have one for protection. I had a girlfriend once break up with me because I didn’t have a gun I could use to protect her and her daughter when the End of the World came, which she was convinced would be initiated by the Y2K computer bug.

I’ve tried to picture any realistic scenario in which a gun would protect me in my home.

I fail.

For instance, there’s the nightmare scenario where I live in a bad part of town, and someone bursts through my door without knocking. It turns out to be a SWAT team that really meant to be knocking down the door of a neighbor down the hall who runs a meth lab in his kitchen, and when I reach for my trusty nine, they make hamburger out of me before it clears my belt-line…. Skrrrrk. (That’s the sound of the rewind-erase button being pressed.)

For instance, there’s the nightmare scenario where I live in a bad part of town, and someone bursts through my door without knocking. It’s a drug-crazed customer of the neighbor who runs the meth lab in his kitchen. When I reach for my trusty nine, he puts sixteen bullets through me before it clears my belt-line…. Skrrrrk.

For instance, there’s the nightmare scenario where I live in a bad part of town, and someone bursts through my door without knocking. It’s a drug-crazed customer of the neighbor who runs the meth lab in his kitchen. He catches me with a beer in one hand and a bowl of popcorn in my lap. My trusty nine is on the end-table next to my bed in the other room; I don’t wear it inside my own apartment, particularly on a hot summer evening when I’m in my underwear, because it chafes. I smile and politely ask the meth-head to excuse me while I go get my gun…. Skrrrrk.

Right, so there’s this nightmare scenario where I’ve gotten a little older with a better-paying job and I’ve moved to a better neighborhood so I can raise my kids in relative safety, and some guy breaks into my house to steal my 12-year McCallan (even the thieves are higher-end here). It’s two in the morning, and I have to turn on the light to find my glasses, so I can hunt around in my dresser drawer for my trusty nine, which is currently unloaded because I keep the ammo separate from the gun, as is recommended by even the NRA when you have children in the house. The light and sound scares off the intruder, and I spend the rest of the night cursing up a blue streak because I can’t find the key to the ammo drawer…. Skrrrrk.

So the intruder at two in the morning is hopped up on bad drugs. When I turn on the light, he gets angry instead of scared and comes looking for me. He catches me in my underwear, blinking in the light, my trusty (unloaded) nine in my hand, trying to remember where I put the key to the ammo drawer, and …. Skrrrrk.

Okay, I keep my trusty nine in my dresser drawer next to my bed, loaded and ready to go, safety-on of course, and … wait, there are grand-kids in the house…. Skrrrrk.

There’s one simple, central problem with any “intruder came into my house” scenario. The intruder is already prepared for a confrontation. If he’s got a gun, then the gun is out, it’s loaded, and the safety is off. Even if he’s unarmed, he’s keyed up and ready to throw a cell phone at my head and run like hell at the first sign of trouble. By contrast, I’m invariably caught by surprise, because I’m not expecting an intruder. I’m watching television with a beer in one hand and popcorn in the other. I’m sitting at the dinner table. I’m catching up on my bathroom reading. I’m asleep in bed. The gun that I keep for protection is almost certainly out of my immediate reach, maybe in my dresser drawer, probably in a locked drawer or gun cabinet, likely unloaded.

Of course, there are the other nightmare scenarios.

I used to work late on contract down in Boulder, and my boss gave me a key to his house so that I could sleep there rather than making the late-night drive to Fort Collins. One evening, I forgot that he’d told me he had house-guests that weekend. He went home early to entertain them, and promptly forgot that I was working late.

I let myself into his house quietly, well after midnight, set down my things, and padded through the dark house up to the guest room, which was pitch black. I started to undress, when I heard a sudden snore, and someone turned over in the bed I was about to climb into. A big, male snore. I suddenly remembered the house-guests. Crap.

I very quietly slunk out of the room, down the stairs, and out the front door.

As it turns out, the father-in-law was upstairs; he never woke, and never knew I was there. The mother-in-law, however, had not been able to sleep, and had moved down to the couch in the living room. She was still mostly awake when I came in. She saw my dark silhouette enter silently, slink up the stairs, then slink down a few minutes later and vanish. She was too terrified even to scream: she was certain I’d murdered everyone upstairs in their sleep. Then she wondered if she’d been dreaming.

I was the intruder.

My friend said that he had experienced a similar situation, except he was the person at home, and one of his wife’s out-of-state co-workers walked into the house at midnight. She’d forgotten to tell her husband he would be arriving late and spending the night in the guest bedroom.

Or there was the time my sister barged straight into my house, carrying an infant in one arm and a folded crib with the other hand. She just turned the knob and shouldered the door open. No knock, no phone call, no notice at all, and she lived five hours away: the last person in the world I expected to walk through my door.

Of course, there are situations outside the home. A gun seems a little more practical outside the home. After all, you’re going out into that big, bad, scary world full of terrorists and drug dealers and thieves and murderers — you should be frightened, keyed-up, ready to react, right? You can strap on your six-gun and swagger a little, and if it chafes? Well, you can take it off again when you get home. In the meantime, you’ve made the world a little safer for everyone with your public display of lethal armament.

So the NRA argues.

Then I look at cops. They train to deal with physical confrontation. They keep their gun in easy reach, in a holster. They use a target range regularly. They call for backup at the first sign of real trouble.

With all that going for them, they can still die in a shoot-out with a terrified seventeen year old kid. So what chance do I really stand?

I like to play first-person shooter video games. They’ve taught me a valuable lesson: that I die a lot in a firefight. I die even when I know exactly what the other guy is going to do, because I’ve watched him make the same moves each of the fifteen times I’ve already died.

All of those miraculous bits of split-second timing in the movies use the same principle of repetition (plus a big helping of computer graphics): multiple takes of the same scene, over and over, practice makes perfect, until they finally get it right once. Then they cut-and-paste relentlessly until it looks natural.

In real life, muffing the first take means you lose an eye, or an arm, or your life. You don’t get a second take.

We had a tragic real-life situation a number of years back, where a woman, stalked by her psychotic ex-husband, was gunned down on the steps of the police station where she sought sanctuary. Someone wrote a letter to the editor claiming the tragedy would not have occurred if she’d had a gun and “stood up for herself” instead of running to the police.

I thought about that. The police station was diagonally across from the Catholic elementary school playground, and there were children playing there during recess who saw her get shot. I believe the husband was shooting from somewhere between the playground and the police station. Had she pulled out her trusty nine and shot back, she’d have been shooting toward the kids.

Just how good is her aim when her hands are shaking?

Plus, we need more mano a mano shootouts on our public streets? We’re sure the good guy is always the better shot? No one ever misses their target and hits someone in a nearby apartment or house or schoolyard?

The whole concept seems incredibly dim-witted.

Ah, the argument goes, but if everyone had a gun, the bad guys would be too intimidated to use theirs.

I pointed a gun at someone, once, to intimidate him.

It happened like this: I was working at my employer’s house in his extended home office, when he suddenly burst into the room and told me he needed my help. He had a shotgun.

“Jesus!” I said. “What’s going on?”

“Hoodlums,” he said. “They come up on my property and take drugs.”

“You’re going to shoot them?” I asked, appalled.

“Nah,” he said. “It’s not loaded. But I don’t want them to run off while I call the police.” He cracked it open and showed me — it was a simple, single-load shotgun, a bare metal pipe, and I could look down the barrel and see daylight.

I followed him outside, and he confronted two teen-aged kids sitting in a grove of trees just on his side of the property line. On the other side was a railroad right-of-way, and beyond that, a Wal-Mart parking lot. I couldn’t read the kids very well — they were probably pretty high on pot, so they were too mellow to react much, but I think they were also terrified and trying to cover it up. They just sat there with defeated “oh shit” expressions on their faces. I felt sorry for them.

“Here,” my boss said, and shoved the shotgun into my hands. “You keep an eye on these two while I call the cops.” He took a few steps away, turned his back, and pulled out his cell phone.

I stood with the gun pointed at the ground in the kids’ general direction and wondered how many laws I was breaking at the moment.

I’ve thought about that situation on and off over the last sixteen years, and in hindsight, I wish I’d handled it differently. While the boss was looking the other way, arguing with the dispatcher — he argued with everyone — I think I’d have pointed the gun away from the kids, and quietly gestured for them to beat feet and get out of there. The point had already been made: this is bad property to trespass, the guy who lives here is crazy and he has a gun.

Had our roles been fully reversed — had it been my property — I think I’d have handled it very differently. On the one hand, I’d probably have ignored it. Kids grow up and move on: the problem solves itself. On the other hand, there’s a reason these kids decided to light up right there and not somewhere else — probably convenience, and that will be the same for the next batch of kids, year after year — and there’s always the risk of a “tradition” forming around the spot. So if it really bothered me, I’d likely have walked up to them, hunkered down, maybe bummed a toke off them, and talked. I don’t personally care for cannabis, but there are proprieties to be observed when approaching members of a foreign and potentially hostile tribe. If you approach with respect, you’re generally okay.

I learned this from a different girlfriend — long blond hair, sexy, beautiful — who had once lived in one of the roughest neighborhoods of a big city. She didn’t have a gun. She didn’t need a gun. She had bikers. She befriended those rough, tough bastards who surrounded her, and they treated her like a favorite kid sister. Had anyone raised a finger against her, he’d have been hunted.

All it required from her was a little respect.

I think I could have reached a workable deal with the kids. Who knows — maybe a tiny touch of respect would have turned their lives around in a good way. Probably not. But being sucked up into the legal system as enemy combatants in the Drug War had zero potential for helping them in any way.

I’ve often thought about how dangerous my boss’s action was. The gun wasn’t loaded; even if it had been, it was a single-loader, and there were two kids. Suppose they had been armed? Supposed they had been jacked up on something crazy-making? Suppose they were as crazy and suicidal as the two kids at Columbine? Or the Sandy Hook shooter? What my boss did was classic escalation of threat of violence, simply assuming it would overwhelm these two kids and make them fearful and compliant. That’s not a reasonable assumption.

There’s an old saying: if you’re going to hunt bear, for God’s sake, use enough gun. If you’re going to threaten another person with deadly force, you need to be willing to use deadly force and then, for God’s sake, use enough gun. An unloaded single-shell shotgun pointed at two potential threats is not enough gun.

What I can say with absolute personal certainty is that pointing an unloaded shotgun at two teen-agers to bluff them into not running did not feel good, and it isn’t something I’d ever want to do again.

I can’t leave this topic without at least a mention of the paranoid, delusional “defending our nation against tyranny” argument for private ownership of assault weapons, which is basically an argument that owning a machine-gun with hollow-point rounds is a patriotic duty.

For those of you who aren’t familiar with this idea, it’s based on the belief that The Real Enemy is Government: specifically the United States Federal Government. It claims the Second Amendment to the Constitution as the basis for our right to bear arms against our own government, should it get too uppity.

Well, that’s not what the Second Amendment is about. Truth is, they don’t teach what the Second Amendment is about in the schools, because it’s part of our shameful past as a nation.

The Second Amendment is about preserving slavery. Read this article — it’s an eye-opener. In a nutshell: the slave states had what they called “militias,” also known as “slave patrols.” White men in the slave states were required by state law to serve in the patrols — it was their duty, just like jury duty. Their job was to keep the African slaves under control, and to do so effectively, the militias needed to be armed. The slave-states feared that the wording of the Constitution was such that the federal government could disarm (and therefore abolish) their militias, thus destroying their ability to keep their African slaves, so they insisted on the Second Amendment as a condition to signing the Constitution.

We no longer have “militias” of this sort, because slavery is now illegal. The Thirteenth Amendment abolished the principle reason for the Second Amendment.

That isn’t to say that States could not organize militias against internal threats other than slave revolts, but the idea of “well-regulated” means that they are organized under and subject to state law, and are therefore subject to federal law as well. The State Highway Patrol could be considered a “well-regulated militia” organized under the Second Amendment.

Now I can’t speak to the broader question of whether or when we’ll need to throw off an oppressive Federal Government, a la The Hunger Games. But it’s quite clear that it isn’t legal to do this now, and isn’t going to be legal to do so then, with or without the Second Amendment. Furthermore, we come back to the earlier notion that if you’re going to hunt bear, for God’s sake, use enough gun.

A rabble of disgruntled citizens armed with assault weapons isn’t even close to enough gun for the job of overthrowing an oppressive national government. The only gun big enough for that job is a citizenry that is substantially willing to die rather than submit to continued oppression.

Such a citizenry doesn’t need guns to overthrow the government.

So how do I come down on the moral issue of owning guns for safety?

I have no idea: I can’t get that far. I can’t get past the practical issues.

When it comes to promoting safety, guns simply don’t work.

What guns provide is a means of projecting lethal force with great accuracy over a relatively long distance. They do that quite well, but that’s all they do. There are certainly times when that is appropriate. But it is lethal force. If you’ve used enough gun for the job, it will kill your target. If you don’t intend to kill your target, you’re using entirely the wrong tool.

Using a gun for intimidation does not promote safety: it is one of the riskiest things you can do. You rely upon the other person being afraid of death, and willing to stand down in the face of your threat of force. But the only thing you know about their mental state is that they are already outside the bounds of civil behavior: they’re in your house without permission, or they’re stalking you on the street, or they’re robbing a convenience store with a gun of their own. They’re a little bit crazy at the moment. How will they react if they see you pull out a gun?

You have absolutely no idea how they will react. No one does.

Maybe, like in the movies, they’ll suddenly come to their senses, and they’ll put down their weapon and meekly submit to being tied up with a convenient bit of rope lying nearby, so you can call the police and have them “taken away” to wherever the police take the bad guys when they tidy up.

And maybe Gwyneth Paltrow really will step out of her hiding place behind the Coke machine and smother you with kisses.

Maybe.

I sure wouldn’t bet my life on it.

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## More on Cold Fusion

Cold fusion seems to be picking up steam.

A NASA scientist has now weighed in on this, Dennis Bushnell of Langley Research Center, and he seems to think there’s something to it.

There’s even a first theoretical framework for it, called the Widom-Larsen theory. It’s similar to what I outlined in general terms in a previous post, but with a small twist. Instead of needing to overcome the Coulomb barrier and jam a proton (hydrogen nucleus) directly into a nickel nucleus, this proposes that the hydrogen atom itself collapses into a neutron, which — lacking any electrical charge — effectively gets sucked straight into the nickel nucleus to produce an unstable isotope of nickel. The nickel then decays by emitting an electron and a gamma ray, converting it to copper.

From the outside, it looks exactly the same: same energy yields, same gamma rays, same everything. However, this mechanism is much more energetically plausible.

I find the signs of retrenchment even more interesting. I commented in my earlier post on how this is no longer called “cold fusion,” but instead “low-energy nuclear reaction” or “lattice-assisted nuclear reaction” (LENR or LANR, respectively). Dr. Bushnell had this to say:

The Strong Force Particle physicists have evidently been correct all along. “Cold Fusion” is not possible. However, via collective effects/ condensed matter quantum nuclear physics, LENR is allowable without any “miracles.”

The distinction here has to do with the “strong” nuclear force versus the “weak” nuclear force. Dr. Bushnell is doing some face-saving redefinition here, by making sure that “cold fusion” is directly tied to “miraculous” claims about the strong nuclear force, while what is actually happening is probably a result of the weak nuclear force. As it turns out, the strong force has been studied extensively, because it allows us to make big bombs. The weak force has received relatively little attention over the past century, because there was no obvious way to use it to make things blow up.

What Bushnell is really saying here is, “All right, we physicists were dead wrong about cold fusion, and we collectively and very publicly destroyed two scientific careers, as well as suppressing an entire field of research for twenty years. But you see, we weren’t really wrong at all, because it isn’t ‘Cold Fusion’ — it’s LANR, which is something we’ve just never looked at.”

It’s traditional face-saving, and while I’m going to point it out, I’m not going to pick it up and force him to eat it. What’s done is done.

What I find interesting is that this retrenchment indicates a radical shift in the politics of physics. This is covering fire to allow future research to reach some safe harbor of respectability, yet without requiring recantation or apology from any of the still-living and influential physicists who called cold fusion a load of bunk. Neatly done.

The fact that face-saving has begun indicates, to my mind, a very high degree of interest.

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## The Educated Palate, Or the Aesthetics of Ick

Women. They are always so damned pragmatic.

By women, I mean my wife, Marta. By always I mean “any time we are in disagreement about anything.” And by pragmatic, of course, I mean “right.”

The other day, while I was taste-testing the Australian Liverwurst, I wanted a second opinion, so I asked Marta to taste it. Mind you, this was after I had thoroughly aerated the wine, and had written in My Blog about the “finish of sour cherries” and let it off the hook with the self-deprecating “too tart for my taste buds.” Meaning, I’m obviously just a wimp. After all, a real man would take it that tart, and like it.

She swirled the glass. She sniffed.

“Ick,” she said.

She touched the wine to her lips and drew a tiny mouthful. She let the flavors blossom on her palate. Her eyes screwed up tight, and her lips puckered.

“Ick,” she said, and handed back the glass with her eyes tight-shut, as if to say, “Take this out of my sight. Better yet, get it out of my house.”

There really should be a revered position in the academic study of Aesthetics for the word, “Ick.” It cuts directly through all the geometric misdirection of ellipses, parables, and hyperbole, instantly resolves the ambiguity of simile and metaphor, transcends all fable, lore, and myth, and lays waste to paradigms, philosophies, creeds, and Schools of Thought.

Ick.

I’m even willing to wager a fair sum that it translates directly and without ambiguity into every language known to humankind, past, present, and future.

Ick is a valuable corrective to pretensions.

You see, there is this concept of the educated palate, which is somehow able to relish the subtleties that the uneducated palate cannot, and which presumably vastly expands the field of what is pleasurable to the taste. Indeed, it creates the entire hypothetical class of tastes which are “accessible” only to the educated palate. By the usual and ever-popular application of the Fallacy of the Inverse (or Denying the Antecedent) we arrive at the idea that therefore, if you find the taste inaccessible, you must not have an educated palate. You are a Philistine.

I’m hardly an accomplished oenologist, but I am a musician with a highly trained musical ear, and exactly the same fraud has been going on in the world of music for at least a century. Most music composed in the 20th century — apart from “pop” music and movie scores — is “inaccessible” to any but the most rarified of educated musical ears. If you don’t like Bartok, you are by definition a Musical Philistine.

I remember once commenting, shortly out of college, that Dmitri Shostakovich was a talentless hack, and being told in response that I was the “most arrogant man in the world.”

It was a strange insult. After all, if it were true, it would be a compliment. It’s only an insult if it isn’t true, which takes all the sting out of it. Furthermore, although Donald Trump had not yet intruded on the national scene, I had already conclusively theorized his existence, so I knew I could not possibly be the most arrogant man in the world.

Arrogant or not, the fact remains that most of Shostakovich’s music evokes an instant response of Ick.

By contrast, the second movement of Beethoven’s seventh symphony has never, to my knowledge, resulted in Ick. To the contrary, the first audiences stomped their feet until the balcony swayed, and ceased only when the conductor returned to the stage and performed it again. Nor does The Moldau, by Bedrich Smetana, ever invoke Ick: indeed, that one is enough to get you laid, if you play your cards right (I speak from personal experience).

The educated ear lets me enter into the joy of music more fully, yes. And it can occasionally — occasionally — take me past a visceral Ick into an appreciation of something playful or haunting, such as certain passages from Sergei Prokofiev’s two violin concerti. But it also makes me more aware of the Ick, not less.

An educated palate should not draw me away from a good wine, which I consider one which a dinner party of my friends will clamor for a second (or third) bottle to be opened, though hopefully they will refrain from stomping their feet until the balcony rattles. It should also lead me to appreciate a great wine, which is not one which I must struggle to get past the Ick through aeration of the wine and proper preparation of the senses: it is a wine that begins at good and then carries my educated palate into ecstasy.

Even if I’m belching garlic after a liverwurst sandwich on rye.

So back to women. And their damned pragmatism.

After we exchanged a few animated presentations of Various Points of View, Marta took the pragmatic stance of saying she would be picking wines from here on out. Like it’s that easy. Fine. We’ll just see how that goes.

So we came back from Wilbur’s with a box full of under-$10 wines. Yesterday, Marta’s son and our grandson came up to spend the night — mom is in DC at a scientific conference — and I opened a BV Coastal Estates 2011 Zinfandel that Marta picked out. Under$10. Cheap, factory-bottled California swill. Marta had a glass, and made only faces of delight. Her son — a sparing drinker even on his wild nights — said, “Say, I’ll have another glass of that.”

And you know, it brought me all the way back to earth. Is it a great wine? Probably not. It’s a run-of-the-mill good wine, drinkable straight out of the bottle with no aeration, no special crackers or food pairings, and no fancy discussion of nose or legs or bloom or finish. It smells good, and it tastes good.

I think I’ll have another glass, too.

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## Chasing the Exponent

Today is fun with LaTeX!

No, not rubber gloves, you naughty person. LaTeX, the mathematics formatting program.

But we can’t do math without a math problem, right? So let’s ask a math question: what does 2% annual growth of the GDP (Gross Domestic Product) mean? Is this a good growth rate, or is it bad? Is it better than 1% growth? Is it worse than 5% growth?

As it turns out, all of these rates are catastrophic. But not in the way most would think.

Two percent growth means that at the end of the year, you have two percent more than you started with, or 102% of what you started with. “Percent” stands for “per centum” which is Latin for “in every one hundred.” So one percent is “one in every one hundred,” while two percent is “two in every one hundred.” So:

$102\%&space;=&space;\frac{102}{100}&space;=&space;1.02$

Percentage growth is also called “proportional” growth, because the growth is a proportion of what you started with. You can calculate it by simply multiplying the original amount by the proportion of growth, as follows:

$GDP_1&space;=&space;GDP_0&space;\times&space;1.02$

If you keep growing at two percent each year, then at the end of the second year you have two percent more than you had at the end of the first year, which was already two percent more than you started with. So it looks like this:

$GDP_2&space;=&space;GDP_1&space;\times&space;1.02&space;=&space;(GDP_0&space;\times&space;1.02)&space;\times&space;1.02&space;=&space;GDP_0&space;\times&space;(1.02&space;\times&space;1.02)$

At the end of the third year, you have:

$GDP_3&space;=&space;((GDP_0&space;\times&space;1.02)&space;\times&space;1.02)&space;\times&space;1.02&space;=&space;GDP_0&space;\times&space;(1.02&space;\times&space;1.02&space;\times&space;1.02)$

At the end of ten years, you have:

$GDP_{10}&space;=&space;GDP_0&space;\times&space;(1.02&space;\times&space;1.02&space;\times&space;\cdots&space;\times&space;1.02)&space;=&space;GDP_0&space;\times&space;(1.02)^{10}$

This notation, the “exponential” notation, indicates that you multiply 1.02 times itself ten times. This is why proportional growth is also known as exponential growth.

You can do this pretty easily on a calculator by entering 1.02, then hitting the times button twice. Now, every time you hit the equals button, it multiplies the result by 1.02. The result on my little four-banger after hitting the equals button nine times is 1.21899…, or about 1.22 (note that you hit equals once less than the number of years you want, because the first time you hit equals, you get the total at the end of the second year.) That means after ten years, this modest little growth of two percent every year has become twenty-two percent total growth.

We can play with this a little more to bring out an interesting feature of exponential growth. First, I need to point out a property of logarithms, which I won’t bother to prove, as follows:

$\ln(a^b)&space;=&space;b&space;\times&space;ln(a)$

This turns out to be very useful in this next bit of reasoning.

IF

$x&space;=&space;(1.02)^{n}$

THEN

$\ln(x)&space;=&space;\ln((1.02)^{n})&space;=&space;n&space;\times&space;\ln(1.02)&space;=&space;n&space;\times&space;\ln(1.02)&space;\times&space;\frac{\ln(2)}{\ln(2)}&space;\\&space;\medskip&space;\hspace*{0.6in}&space;=&space;n&space;\times&space;\frac{\ln(1.02)}{\ln(2)}&space;\times&space;\ln(2)&space;=&space;\left(&space;\frac{\ln(1.02)}{\ln(2)}&space;\times&space;n&space;\right&space;)&space;\times&space;\ln(2)&space;\\&space;\medskip&space;\hspace*{0.6in}&space;=&space;\ln&space;\left&space;(&space;2^{\frac{\ln(1.02)}{\ln(2)}&space;n}&space;\right&space;)$

THEREFORE

$x&space;=&space;(1.02)^n&space;=&space;(2)^{\frac{\ln(1.02)}{\ln(2)}&space;n}$

What does this nonsense mean? It means that raising a small percentage growth (like two percent) to some exponent is exactly the same as raising the value two to some different exponent. And two means doubling. In other words:

$GDP&space;\times&space;(1.02)^{n}&space;=&space;GDP&space;\times&space;(2)^{\frac{\ln(1.02)}{\ln(2)}n}$

The magic value of ln(2)/ln(1.02) is the doubling time for two percent annual growth. When n (in years) reaches the value of ln(2)/ln(1.02) = 35.003, the GDP will double:

$GDP_{35}&space;=&space;GDP_0&space;\times&space;(2)^{\frac{\ln(1.02)}{\ln(2)}&space;\times&space;\frac{\ln(2)}{\ln(1.02)}}&space;=&space;GDP_0&space;\times&space;(2)^{1}&space;=&space;GDP_0&space;\times&space;2$

A two percent annual growth means the GDP doubles every thirty-five years. In seventy years, it will double again, and will be four times its original value. In a little over a century, it will be eight times its original value.

proportional growth = exponential growth = doubling growth

This is simply mathematics.

Let’s do a little more advanced exploration of this exponential growth concept. There’s a common technique used in math called functional expansion. It lets you express a complicated function as a collection of simpler functions, typically a sum of simple functions. In particular, let’s do a conversion as follows, to make this a little easier:

$x&space;=&space;(1.02)^{n}&space;=&space;(2)^{\frac{\ln(1.02)}{\ln(2)}n}&space;=&space;e^{\frac{\ln(1.02)}{\ln(e)}n}&space;=&space;e^{\ln(1.02)n}&space;=&space;e^{kn}$

The letter e represents a magic number, like π. It has a value approximately equal to 2.71828…. It’s a useful number, like π, which I won’t go into right now. This is the so-called standard exponential function, and k is just a constant number based on the growth rate of two percent, while n is the number of years. Let’s do a functional expansion of the standard exponential function using something called a Taylor expansion:

$e^{kn}&space;=&space;\sum_{i=0}^{\infty&space;}\frac{(kn)^i}{i!}&space;=1&space;+&space;\frac{(kn)}{1}&space;+&space;\frac{(kn)^2}{2}&space;+&space;\frac{(kn)^3}{6}&space;+&space;\frac{(kn)^4}{24}&space;+&space;\cdots$

Why is this important?

It has to do with how fast things grow. We refer to the speed of growth as the order of the equation, such as $O(logN)$ or $O(N)$ or $O(N^2)$. It’s traditional to use a capital N in this expression, but it means the same as the small n in this case. The reason this is important is that as n (or N) gets larger — as time passes — the maximum order of the growth starts to dominate everything. For instance, some quantity might grow like this:

$Growth&space;=&space;a&space;+&space;bn&space;+&space;cn^2&space;+&space;dn^3$

where a, b, c, and d are constant values, and n is the number of years. Even if a, b, and c are very large, and d is very small, after enough time has passed, the dn3 starts to take over. This is because ngrows much faster than n2 or n. So we would call this $O(N^3)$ growth, or cubic growth, even though there are some other things going on.

In fact, a, b, and c could all be negative numbers: they could represent shrinkage, rather than growth. But if d is positive, no matter how small, this equation will eventually show cubic growth, and all of the shrinkage will become negligible.

Going back to our original economic question, let’s say we have a fixed amount of wealth that we keep in a cave, like a dragon’s hoard. This is proportional to the first term in our standard exponential equation:

$1$

That is, it’s a fixed constant. It may not be one, but it never grows, and it never shrinks, no matter how many years we keep it in the cave.

Now let’s assume we decide to walk around and pick up things we find along the path — shiny rocks, seashells, fruit that has fallen from the trees, that sort of thing. We can only walk so far in a given day, and can only pick up things that are within reach of whatever path we walk, so we can only add to our store of wealth a certain fixed amount — on the average — every year. That’s proportional to the second term in our equation:

$\frac{(kn)}{1}$

Now let’s assume that we begin to have children, and that we start expanding across the surface of the earth at a steady rate from our original village. Let’s say we raise just exactly enough children to keep the population density constant as we take up more and more land. Every person walks about the same distance each year, but every year we have more people to cover more area, so our wealth increases as the size of the area. Areas are proportional to the square of the distance from the center, so this is proportional to the third term in our equation:

$\frac{(kn)^2}{2}$

Obviously, we’re going to face a problem once we’ve covered the surface of the earth and can’t expand any more. But by then, they tell us, we’ll have space travel! So now we can expand into the third dimension, sending out space ships that move at a steady rate away from our original Earth. Every year we have more people colonizing more worlds and walking new paths within the volume of space we fill, which is proportional to the cube of the distance from the center. Thus, this is proportional to the fourth term in our equation:

$\frac{(kn)^3}{6}$

I think the problem is pretty clear. To sustain exponential growth of wealth, we still have an infinite number of terms left to cover, and I’m pretty well out of ideas as to how we’d get to even the fifth term, let alone the thirty-seventh. After the thirty-seventh, there is still an infinite number of terms left.

Exponential growth is $O(expN)$, which is faster — much faster — than populating outer space at the speed of light, which is only a paltry $O(N^3)$ .

There’s one more important characteristic of exponential growth. Chris Martenson over on his Crash Course in Peak Economics site gave a wonderful visual image of how exponential growth behaves, involving filling Fenway Stadium in Boston with water. To give a brief reprise, you find yourself handcuffed to the railing in the top row of seats at Fenway Stadium. A water main breaks right underneath the pitcher’s mound. It starts out leaking just one drop of water per minute, but every minute, that rate doubles: two drops, four drops, eight drops…. The two questions are:

1. How long does it take Fenway Stadium to fill completely with water, drowning you?
2. From the moment you notice that the stadium is beginning to flood, how much time do you have to get out of the handcuffs and escape to safety?

The answer (as I recall, and I haven’t checked his numbers) is that it takes something like 24 hours for the stadium to fill, but you won’t even be able to see the water from the top row until the last forty-five minutes.

Throughout his course he refers to the “hockey stick” shape of an exponential curve, meaning that it creeps along slowly and then — BANG — shoots through the roof. As it turns out, this is mathematically not quite correct, but it does give voice to something important about exponential curves. It has to do with how these higher-order terms start to dominate the equations. This is easier to show than to describe.

Here is an exponential curve seen from time 0.0 to time 1.0. At time zero, the function has a value of 1.00, and at time one, it has a value of about 2.72. In this range, we see only a gentle bend to an otherwise straight line.

Here’s that same curve seen from time 0.0 to time 5.0. At time zero, it has a value of 1.00, as before, while at time five, it has a value of about 148. Notice the small box showing the curve from 0.0 to 1.0 from the previous chart, and how sharply the curve bends upward after that.

Here’s that same curve seen from time 0.0 to time 10.0. At time zero, it has a value of 1.00, as before, while at time ten, it has a value of around 22,000. Notice again how much sharper the curve becomes after time 5.0.  The higher-order terms are beginning to dominate strongly now, and the curve is getting very steep indeed.

The point here is that exponential curves start out innocently. They look a lot like linear growth, as we see in the first chart. But as time passes, they accelerate. And accelerate. And accelerate. The acceleration never stops, and the curve grows impossibly steep.

But this idea of a “hockey stick” shape actually obscures the more important feature of exponential curves, illustrated below:

${\color{DarkRed}&space;y&space;=&space;\left&space;(&space;e^{x+0}&space;-&space;e^0\right&space;)&space;\left(&space;\frac{e^1&space;-&space;e^0}{e^1&space;-&space;e^0}\right&space;)&space;+&space;0.00}$

${\color{DarkBlue}&space;y&space;=&space;\left&space;(&space;e^{x+1}&space;-&space;e^1\right&space;)&space;\left&space;(\frac{e^1&space;-&space;e^0}{e^2&space;-&space;e^1}&space;\right&space;)+&space;0.01}$

${\color{DarkGreen}&space;y&space;=&space;\left&space;(&space;e^{x+2}&space;-&space;e^2&space;\right&space;)&space;\left&space;(&space;\frac{e^1&space;-&space;e^0}{e^3&space;-&space;e^2}&space;\right&space;)&space;+&space;0.02}$

So what is this all about? Well, let’s take it in pieces.

First, note that the X-axis runs from zero to one for all three curves.

So the first equation is simply ex from 0.0 to 1.0 — this is the very first chart we saw above, the one that looks almost like a straight line. We’ve subtracted its starting value from the result to shift it down so it starts at (0,0). We’ve then multiplied that by a constant which, if you look at it closely, is equal to one. Then we’ve added zero to it. Whoopee.

The second equation is a bit more interesting. The function is still ex, but because we’re adding one to x, this is ex  seen from 1.0 to 2.0: it’s where we see the curve getting steeper in the second graph. In this case, we again subtract its starting value (e1), divide it by its total height (e2 – e1), and then multiply by the total height from time 0.0 to 1.0 (e- e0), so that this new function fits on the y-axis of the old graph. Finally, we’ve added a smidge (0.01) to push it up a bit, so we can see the curve.

Just to make sure, we did this one more time, this time looking at ex from 2.0 to 3.0, again scaling it so it fits on the same chart with the original curve, and adding a smidge more to separate the lines.

The curves are identical in shape.

What does this mean? It means that over any fixed range of time (in this case, one unit of time), regardless of where it is located in the curve, the curve is “scale-invariant” — it is exactly the same curve, just viewed at a different scale. The “hockey stick” shape is an illusion of scale.

This is what really underlies what is happening in the Fenway Stadium Drowning Incident.

Exponential curves move through different scales of magnitude at a constant rate. When the water main leak starts, it is of concern only to microbes handcuffed to the top row of a thimble. It is far beneath our human “scale of relevance.” It is unimportant to us.

But the problem doesn’t merely get bigger, like a single dripping faucet that eventually fills the basement. The problem keeps changing scale, and then doing exactly the same thing all over again at the new scale: that is precisely what “scale-invariance” means. After it has drowned the microbes, it starts to drown larger creatures, like ants, in exactly the same way. Then rats. Then cats. Then big dogs. Then people. Then elephants. Then giants. Then mountains. Then continents. Then planets.

An exponential water leak in Fenway Park, could its growth be sustained, would drown the entire universe in a finite amount of time. And at that point it would only be getting warmed up for the real work.

As humans, we have a fixed scale of relevance. The flooding of an anthill is of little concern to us. The flooding of a continent — or a solar system — is too big for us to cope with, almost too big to imagine. There’s just this narrow range of scales that’s important to us. Something on the order of yards, and pounds, and gallons, and years. That’s the human scale.

Exponential curves aren’t like that at all. All scales are relevant to them, sooner or later. They methodically plod through them all, taking successively bigger and bigger steps.

So the issue we have with exponential curves as humans is that it takes astonishingly little time for them to pass straight through our scale of relevance, from “negligibly small” to “intractably huge.” The reason we have only forty-five minutes to get out of our handcuffs, rather than the full twenty-four hours after the problem started, is because the exponential growth of water didn’t intrude on our scale of relevance for twenty-three hours and fifteen minutes. And then, in forty-five minutes, it ripped right through our entire scale of concern, from “puddle” to “catastrophe.”

Here’s the part that Chris didn’t talk about. Should the leak continue to grow at an exponential rate, it won’t matter whether you get out of your handcuffs. In a matter of minutes after the stadium floods, all of Boston will be awash in a tidal gusher fountaining from the pitcher’s mound. Some minutes after that, the entire United States will be underwater, with a gravity-distorting tidal wave of water rushing toward Europe and Asia. Within a few hours or days, water will fill the entire Solar System and will put out the sun.

By the time this exponentially growing watery menace intrudes on the scale of relevance for the Galactic Federation of Planets, they will have about forty-five minutes to save the entire galaxy.

Now, if this seems to be getting silly, it is.

It’s silly because nothing in nature can sustain exponential growth.

In nature you’ll see brief spurts of exponential growth, as when yeast cells divide in a vat of beer wort, or as when a new product is first introduced to the marketplace. After that, the exponential growth scales back until it reaches no-growth. Then it reverses, declines, and is recycled to make room for the next wave of growth for something else.

Nature may abhor a vacuum, but it simply will not tolerate sustained exponential growth.

So let’s go back, now, to that original economic question. What is the appropriate growth rate for the GDP? Five percent? Two percent? One percent?

The correct answer is zero percent. The economy cannot sustain exponential growth at any rate.

At this point, you may be suffering a little bit of cognitive dissonance. After all, the news is constantly yammering about how the GDP grew two percent this year, or a disappointing one percent, and how growth is necessary for a “healthy economy.” And what about investment income? People get a percentage return on CDs, and savings accounts, to say nothing of stocks, bonds, and futures. It’s how the economy works.

Right?

Wrong. This takes us right into the heart of the shell game that is our modern economy.

Rather than trying to summarize this, I’ll refer you to Chris’s excellent Crash Course, as well as John William’s Shadowstats site.

Physical reality trumps economic theory. Nothing in nature can sustain exponential growth. So if economic theory is reporting exponential growth, there is a big mistake in the theory.

The presenting symptom of this big mistake is inflation. Chronic inflation is a symptom of faulty economics and a broken economy.

Monetary inflation is simply a matter of the money supply increasing in excess of the real economy the money is used to facilitate.

If there’s one chicken left in a village, there will be a bidding war for the chicken, and whoever has the most money will get the chicken. Let’s say that’s $10. Now, let’s give everyone in the village an extra$10. There’s still only one chicken, so now the bidding war will end at $20 instead of$10, and the same person goes home with the chicken.

The chicken is the real economy. Adding money to the village doesn’t change anything but the price of the chicken. The same is true of any other good or service in the village: all the prices rise as you pour in money, because everyone has more money, but no more goods or services to trade. This is monetary inflation.

The proper reason to increase the money supply is to match a growing real economy, to keep prices stable. Otherwise the money itself grows scarce, and you see monetary deflation.

Consider doubling the size of the village, and the number of chickens (and everything else) but leaving the amount of money the same. The original inhabitants all have money, but the newcomers are flat broke and can buy nothing. Over time, that money will disperse to everyone, but on the average, people will have only half as much money — the same total amount, spread out over twice as many people. If they eat all the chickens but one, the bidding war will only be able to go up to $5. Prices fall. When money deflates, people start to hoard it as precious in its own right, and then trade breaks down. So it’s important to pump more money into the village so that prices go back up to$10 and stay there as the real economy grows.

But if you pump too much money into the village, prices will rise above $10 through monetary inflation. When inflation keeps happening, year after year, you have a chronic problem with your money supply. When the inflation rate is exponential, you have an exponential problem. If you browse the Internet for old product catalogues, it doesn’t take long to realize how far things have gone. In 1960, a new sedan, straight off the showroom floor, sold for about$2500. A new pair of jeans cost about $1.50. A simple meal in a diner cost$1.00. My father bought a new house in the suburbs for $16,000. Gasoline cost$0.35/gallon. Penny candy cost a penny.

Just shift that decimal point over, and you’re looking at today’s prices for the same kinds of goods, with remarkably few exceptions (like computers). When computers finally reach the end of their run with Moore’s Law — they’re getting close — you’ll start to see them subject to the same inflation as everything else. We’ve seen an average of about 5% per year between 1960 and 2006, just based on the 10-fold increase in prices over that forty-six-year period. The annual rates have varied — I remember it going up to around 13% in the late 1970′s, and some years have had lower inflation rates.

But overall, the US dollar is being exponentially eroded by inflation. And remember how exponential problems rip through our scale of relevance. What we see in our economic system right now is the puddle on the pitcher’s mound. The problem is changing scales even as I write.

Chris and John can take you on a tour of exactly how this all operates: GDP and CPI, hedonics and weighting and chaining and more tricks and traps for your edification and amusement. All a collection of desperate contortions to deny that there’s a problem, because we won’t (or can’t) get out of the handcuffs.

It’s quite a ride.

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