# Short: Immortality Math

There are people out there who are quite seriously trying to make human beings immortal. It sounds like something from a bad 1970s pulp comic, but it’s true. Of course, when serious people say “immortal,” they’re not talking Highlander. They’re talking biological immortality, sometimes called by fancy names like “negligible senescence”: the elimination of death by aging. Whether we can (or should) ever achieve biological immortality is a question I’ll leave to people smarter than me, but either way, biological immortality doesn’t mean full immortality. It just means that you can no longer die from, say, a heart attack or cancer or just generally wearing out. You can still quite easily die from things like falls, car accidents, or having Clancy Brown chop your head off with a sword.

There are a number of organisms out there which are either believed or known to be biologically immortal, or at the very least, nearly so. These include interesting but relatively simple organisms like hydras and jellyfish, but also more complex organisms like the bristlecone pine (many living specimens of which are confirmed to be over 1,000 years old, and one of which is over 5,000 years old), and the lobster. (Technically, though, the lobster isn’t really immortal, since they must molt to heal, and each molt takes more energy than the last, until the molts grow so energy-intensive they exhaust the lobster to death.) For the record, the oldest animal for which the age is well-established was a quahog clam named Ming Hafrun, who died at 507 years old when some Icelandic researchers plucked it out of the water.

If a human was made biologically immortal, how long could they expect to live before getting hit by a bus or falling down the stairs (or getting stabbed in the neck by Christopher Lambert)? That’s actually not too hard to estimate. According to the CDC (see Table 18), there were 62.6 injury-related deaths per 100,000 Americans, in 2014. With a bit of naïve math (I’m not adjusting for things like age, which probably inflates that statistic a fair bit, since older people are at a higher risk of falls and similar) that means the probability of death by accident is 0.000626 per year, or roughly 0.06%. Knowing that, it’s almost trivial to compute the probability of surviving X years:

probability of surviving X years = (1 – 0.00626)^X

This formula is based on one of my favorite tricks in probability: to compute the probability of surviving, you do the obvious and convert that to the probability of not-dying. And you can take it one step further. At what age would 90% of a biologically-immortal group still be alive? All you have to do is solve this equation for N:

0.9 = (1- 0.00626)^N

which is no trouble for Wolfram Alpha a math genius like me: a biological immortal would have a 90% chance of surviving 168 years. Here are a few more figures:

• A 75% probability of living up to 459 years.
• A 50% probability of living up to 1,107 years.
• A 25% probability of living up to 2,214 years.
• A 10% probability of living up to 3,677 years.
• A 5% probability of living up to 4,784 years.
• A 1% probability of living up to 7,354 years.
• A one-in-a-thousand chance of living 11,031 years.
• A one-in-a-million chance of living 22,062 years.

For reference, the probability of a member of a population surviving (in the US, in 2012, including death by biological causes) doesn’t drop below 75% until around age 70. To put it in slightly annoying media jargon: if we’re biologically immortal, then 459 is the new 70.

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# Who wants to live forever?

Because you can’t go wrong quoting Queen. Anyway: as I’m writing this, I’ve just turned 26 years old. I remember once when I was 7 or 8 years old there was going to be a birthday party or some other exciting childhood festivity. I asked my mother how long until it started. She said “Nine hours.” I remember thinking “Nine hours??? Holy fuck! That’s almost forever! That’s way too long!” (Okay, I probably didn’t actually think “Holy fuck!” at 8 years old, but seeing as my father taught me to curse in Italian before I knew all my words in English, I wouldn’t rule it out.)

Anybody older than about 20 is probably laughing now. Nine hours? Nine hours is nothing. Hardly enough time to do anything. That’s just one workday. Has anything really significant happened to you in the last nine hours. I don’t mean in the cosmic sense or the Buddhist sense, where everything is significant. I mean has anything happened that felt really significant? If you’re like me, most likely not.

And that (finally) brings us to today’s issue: immortality. Human lifespans are getting longer. Even though my maternal grandmother smoked for much of her life and lived on famously greasy Southern United States food, she lived into her mid-eighties. My paternal great-grandfather lived to 104. Much of this is thanks to modern medicine and sanitation. As Kurt Vonnegut always said, it used to be that pneumonia was “the old person’s friend”: a relatively painless way for an old person to die. Pneumonia still kills lots of old people, but before antibiotics and mechanical ventilation, if you had a weak constitution and you got pneumonia, you were pretty much dead.

That’s not to say that life expectancies were ridiculously short in the hunter-gatherer days, some 10,000 years ago. Extrapolating from more modern hunter-gatherers, a sizeable fraction probably made it into their thirties, forties, and even fifties, and some probably reached seventy or eighty. I don’t have a great brain for statistics, but as I understand it, the really low life expectancies you see reported for hunter-gatherers are more an artifact of the way statisticians define “life expectancy”: it’s defined as the number of years a person can be expected to live at birth. Unfortunately, infant mortality was quite high in preagricultural societies (and indeed, depressingly, is still very high throughout much of the world). Every person who dies in infancy pulls down the average life expectancy, because a randomly-selected person is likely not to have many years, because they’re likely to die in infancy. The children who survived that wave of infant mortality probably went on to lead fairly long lives, until an accident, an infection, an attack of cholera, a wild animal, or a disease killed them.

But, statistics aside, life expectancy is getting longer throughout much of the world. Jeanne Calment died at over 122 years old, in 1997. As of this writing (June 2014), Wikipedia lists 73 documented “super-centenarians”: people older than 110 years. If you’re a male, the list is depressing: of those 73, only 2 are men, and they’re both 111 years old, which puts them pretty low on the list.

I keep getting sidetracked because doing random research is one of my questionable hobbies. Better than drug addiction, but not exactly stimulating. To get back on track: life expectancy is increasing. (As I’ve said half a dozen times now.) Gerontologists are beginning to understand more and more of the mechanisms of aging. Through treatments like calorie restriction and genetic modification, organisms like C. elegans nematodes and lab rats have had their lifespans extended by large percentages. In the nematode case, lifespans can sometimes be doubled. And, because deep down, the majority of people aren’t ready to face their deaths, there will always be interest in and support for life-extending medicine. Combined with the advances in cybernetics (isn’t it cool that we live in an age where we can say that there have been “advances in cybernetics”? We’re living in a freakin’ sci-fi novel, and I love it. Except for all the weird privacy-invading stuff. I hope this novel doesn’t turn out to be some miserable dystopian cyberpunk thing.) Ahem. Combined with the advances in cybernetics, it’s not unreasonable to speculate that there are people alive right now (once again, June 2014) who will live to see effective human immortality. Already, peoples’ Facebook profiles and digital footprints are outliving them. Eventually, we’re bound to live on in digital form after biological death, and there’ll probably be ways to prevent biological death in the first place. One more example. I promise I won’t get sidetracked. Before the introduction of the defibrillator, when your heart stopped, you were dead. End of story. Now, people routinely survive cardiac arrests. Sometimes doctors even cause them so they can perform open-heart surgery. It’s not hard to imagine that other illnesses we think of as terminal will be treatable in the near future.

So it’s possible that someday, you’ll be able to live forever. But would you really want to? If you’re like me, that depends on a lot of factors: quality of life, whether there’s anything to live for, and whether I can still get by and survive in a society radically different from the one I was born into. But I would wager that, ultimately, my answer would be “Well, no. Not forever. Maybe a thousand years. No more than that.” I suspect other people who seriously think about it would give similar answers.

There are many problems with living beyond 120. If we assume a utopian future where biological aging stops at 30 (meaning no cognitive decline or physical frailty), you still run into problems if you live long enough. It’s often said that the human brain can’t handle more than 120 years of memories. I don’t know whether I believe that, but there’s certainly no evolutionary reason for the brain to hold much more than that. Very old people do serve an evolutionary purpose: they’re often helpful in maintaining society-stabilizing traditions and passing down lore and stuff like that. (Plus, who would want to live in a world without grandmas and grandpas anyway?) But the brain is an organ of a finite size, and if you live long enough, you’ll hit the limit sooner or later and have to start forgetting shit. And we’re not talking “I forgot to flush that nasty shit I took” or “I forgot the name of my ninth-grade math teacher’s secret lesbian lover.” We’re talking “I forgot everything about my first son.” Serious stuff like that.

But even if memory isn’t an issue, there’s another problem. Since I’ve already quoted one song, why not quote another? This time, it’s Pink Floyd’s Time, from Dark Side of the Moon, which is almost certainly my favorite album of all time. Part of it goes:

And you run and you run to catch up with the sun, but it’s sinking

Racing around to come up behind you again

The sun is the same in a relative way, but you’re older.

Shorter of breath, and one day closer to death.

Every year is getting shorter

Never seem to find the time

[Words I can’t make out because my ears don’t work right.]

“Every year is getting shorter.” Once I got old enough to think back more than a year or two, I started noticing that phenomenon myself. I think everybody notices it sooner or later. No matter how interesting or exciting your life, it just seems like time speeds up no matter what you do. It speeds up for some people more than for others, but it speeds up for all of us. Part of this is biological: dying neurons and falling levels of neurotransmitters mean the brain’s clock doesn’t run as well the older you get, and it means that you process information slower, and therefore miss more of what happens around you. But beyond the biological decay (which, in our hypothetical scenario, has been eliminated), there’s an essential, inescapable, mathematical reason that time seems to speed up: novelty.

Let’s say each year of your life contains N units of novelty. They consist of significant events like learning to walk, falling in love, breaking a leg, winning an argument in a YouTube comment section, stuff like that. Let’s assume that novel events happen at random intervals, so that they’re spread evenly throughout your life. Therefore, let’s instead say that each year is worth 1 Value Unit, which is equivalent to N novelty units. You’re likely to have years valued at higher than 1 and years valued at lower than 1, but let’s say it averages out over time, so that we can say each year is worth 1 VU.

But not all value units are equally valuable. Your first year of life contributes 1 VU, increasing your fund of novelty from 0 to 1. If you do the math naively, the increase in novelty is ∞%. Everything is new. From age 1 to age 2, you acquire another 1 VU. You go from a stockpile of 1 VU to 2 VU, an increase of 100%. If I was your boss and told you I was giving you a 100% raise, everybody would think I was crazy, but I’m sure you would be pretty damn happy. I know I would be. From age 2 to age 3, you gain 1 more VU, going from 2 to 3. That’s an increase of 33.33%, which ain’t bad at all.

But by the time you go from age 9 to age 10, the pattern starts becoming clear. On my 10th birthday, even though we had the Slip’n’slide set up and I’d just gotten a Nintendo 64 and Starfox 64 (which is still one of my favorite video games), I remember saying “Everything feels so old.” Well, by age 9, I’d accumulated 9 VU, and the extra VU I got when I turned 10 only added 11.11% to my fund. This is inflation at work. It’s the same reason you can’t stimulate an economy by printing a bunch of \$20 bills: when everybody has more to spend, retailers can charge more without seeming like crooks, and so prices go up, and the value of a \$20 bill goes down. In that same way, the value of a year goes down, even if each year adds a constant 1 VU.

When I turned 26, I only increased my stock of novelty by 4%. To put it in less mathematical terms, even though, from that cosmic perspective I mentioned, the novel events that happened between age 25 and age 26 were of the same value as the novel events that happened between, say, age 9 and age 10, they’re worth less to me because I’ve seen so many novel events. One of the fundamental properties of novelty is that it wears off. I like chocolate. If I went five years without having any chocolate, and somebody gave me a Dairymilk bar, I’d be very happy, and I’d really enjoy it. If, on the other hand, some creepy scientist decided to test my willpower and give me a supply of 10 Dairymilk bars per day, eventually I wouldn’t end up eating 10 per day, even if you factor out the inevitable ballooning of my waistline. After a while, you get sick of chocolate. It’s the same reason people get addicted to drugs like cocaine and heroin: when the brain is in a state of intense pleasure long enough, it re-calibrates its pleasure scale so that a syringe of heroin brings the user orgasmic pleasure at the start, but six months later, isn’t even enough to get them through the day.

Novelty seems to run on similar rules, except that unlike heroin or Dairymilk bars, you can’t stop experiencing time. Forrest Gump was full of shit. Life isn’t like a box of chocolates. Life is like being force-fed a box of chocolates every day of your life. And you can etch that on my tombstone. (And teenagers will come by and say “Jesus. Here lies an emo prick.” But oh well.)

We can actually turn that progression of percentages from a few paragraphs ago into an equation. If, instead, we measure time in seconds instead of years and adjust our value-unit accordingly, the math is still the same: when you go from 1 to 2 seconds old, you’ve increased your time lived (and therefore your novelty experienced) by 100%. When you go from 9 seconds to 10 seconds old, that second is only worth 11% of what it once was. When you go from 31,535,999 seconds old to 31,536,000 seconds old (when you reach 1 year old), each second is worth 0.000031%. That’s not a lot, but there are a lot of seconds (86,400 in every single day), so they keep adding up. My point is that, even as you make your time units smaller and smaller, the same math holds. Therefore, you can create an equation that measures the value of arbitrarily small time units as you age. The function is beautifully simple: 1 / t, where t is the number of time units that have passed. For me, at 26, my graph thus far looks like this:

(Graph courtesy of Fooplot.com, which is a nifty online function grapher, if you happen to need that kind of thing. Like I do.)

The X axis is time in years. The Y axis is the value of each microscopic parcel of time. For convenience, I’m saying that, when my clock reached age 1, the new time unit had a value of 100%, or 1.0. The graph looks the same as long as your units are something small, like seconds or days.

Notice the sharp drop. Throughout my childhood, even though there were fewer new things to do, there were still plenty of opportunities for exploration. Every birthday party was celebrated with gusto. The first few times I went driving with my new driver’s license (at age 16) were ecstatic. Graduating from high school (age 18) was a great feeling. But when I graduated from college, I didn’t even bother to go to the ceremony. I just had them mail me the diploma.

Now, I’m an extreme case. I’m what you call “a miserable gloomy bastard,” so I tend to under-value new events. But even so, the math and the principle holds for pretty much everyone. It seems to be a result of the way the brain evaluates value. It’s also built into the numbers themselves. There are other important factors not included in this math. For one thing, the brain becomes less plastic as we age, and therefore, it gets stuck in ruts more easily and has difficulty adapting to novel situations and therefore appreciating their novelty. So that means the real graph would actually fall towards zero a little faster after age 18 than the one above. But the graph above is a useful upper bound: mathematically speaking, unless you do something that alters your emotions or your ability to appreciate novelty, your graph is going to be at least as bleak as that.

Which is no reason to be miserable. Me, I’m miserable by temperament, but there are plenty of people who realize in their thirties that they’re having more fun than they had in high school, and there are people who start having more fun at 50 than they did in the 49.9 years before that. And you don’t see a lot of people committing suicide and saying “It’s because value = 1 / time.” That’s not a good reason. But it is a reason you might be less inclined to choose immortality. Here’s what the graph looks like at age 122:

By age 122, the value of a year has fallen to 0.82%. Not only that, but the value of a year has been below 10% for 90% of that time, which is to say for 112 years.

To put it simply: no matter what, if you live long enough, you’re going to run out of shit to do. You’re going to start getting bored.

In the culture I grew up in, being 18 years old is a big deal. You’re legally considered an adult, and there’s a lot of novelty around that age. Most people lose their virginity somewhere around 18, with a margin of a few years either way. Like I mentioned, most people learn to drive at age 16 or after, and you start gaining more control over the course your life takes around this time. A lot of cool stuff happens around 18 (even if you’re a miserable, neurotic nerd like me). So let’s use age 18 as a benchmark. Age 18 is a time when many people feel good, a time when the world still feels new and exciting to them. According to my formula, the value of a year at age 18 is 5.56%, or, to be more scientific (and to round to nine significant digits, which I do just because I’m obsessed with numerical accuracy), 0.055555556.

Returning to our scenario where you can take a pill or get an implant and stop biological aging, by the time your 200th birthday comes along, the value of your time has dropped to 0.005000000, or half a percent. If we assume future psychology doesn’t invent a way to help people appreciate everyday things more, then that means your time is worth almost ten times less at 200 than it was at 18. Imagine a demon appears before you and says “Starting tomorrow, for the rest of your life, your maximum possible happiness will be lowered to 10% of its current maximum.” I would not be happy about that. I don’t think I’m alone in that.

It just gets worse the longer you live (although, because of the way math works, it gets worse slower and slower). At 1,000 years old, your time is worth 0.001000000, or one fiftieth of what it was worth at 18. Now the demon’s really being a dickhead (as demons are wont to do). He’s saying “Your maximum happiness has now been reduced to 2% of its former level.” Imagine trying to get by on 2% of your current income. Not fun. Now, imagine it’s like that, but about everything. (To quote Allie Brosh of Hyperbole and a Half.) It’s going to get hard to get interested in things at 1,000 years old. The plots of all the movies are going to start to seem the same. You’re going to run out of new foods to try and new sex positions. If you took one vacation to a new country every decade, you’d run through the current catalogue of UN members (193 countries, with South Sudan being the newest member, added in 2011, which is fun to think about) in 1,930 years. I don’t know that I’d like to go 10 years between vacations.

But there’s a lot to do within each country. So, because I am so very immature, let’s say that, instead of just visiting countries, you make the purpose of your immortal life having sex with as many people as possible. Forget sexual orientation or physical attractiveness–let’s say you’re getting so bored you’ll fuck absolutely anybody (of consenting age, of course). And let’s say you’ve got nothing to do but fuck, so that, every 30 days, you pick a new sex partner and have wild and crazy sex with them every day that month. Now that‘s living the dream. If you started this lunatic sex-spree at age 18, by age 912,617, you’d have had sex with 10 billion different people. There are only 7 billion people on Earth today, so in a way, this sex-tour would be the same as a much friendlier demon appearing before you right this moment and saying “I will now teleport you to your soul mate, who is currently extremely horny and desperate to fall in love.” After you’ve climbed Everest, the other mountains lose a lot of their appeal (so to speak). No matter what, you’re going to run out of things to do.

Here’s another example: according to IMDB, there have been 310,270 feature films released since 1874. Most of those were made between 1920 and 2014, which comes out to about 3,300 movies a year. You could watch 10 movies a day and not run out. But then you have to consider how many of those movies are either going to be similar to previous movies you’ve seen (think of all the cookie-cutter romantic comedies that come out), or are going to be so awful you wouldn’t want to see them (I’m thinking about Gerry, Thankskilling, and Solyaris here), you’re going to run through the list in a few centuries. And when you think about it, this list contains every feature film ever made by a human being. That is the very definition of inclusive.

By now, you might be wondering what the fuck I’m talking about. Am I trying to depress you? Am I pretending to be an existentialist philosopher and advocating rational suicide? Am I rambling on without knowing what the fuck I’m talking about? Well, no. None of those things. (Okay, maybe some of that last one…) What I’m saying is that, as our lifespans get longer and things like the Internet give us more opportunities to experience novelty, we have to be careful. We have to make finding joy and value in our lives a top priority. The Universe is huge, even for a modern-day human mind turned immortal and given an infinite capacity for new memories. But as (if) we begin to expand into that universe, we’re going to have to take care not to grow numb to it.

I’m really showing my age this article, but when I was a kid, there was no Internet. There was Usenet and stuff like that, but only the tech-savvy had it. Having access to the Internet when I was a kid was like having Google Glass is today (except less creepy and less silly-looking). You were modern. Now, my Internet connection, shitty as it is, is so fast that it loads YouTube videos faster than my first Internet connection could load still pictures. And, much as I hate to admit it, I take that connectivity for granted. I have access to a larger portion of human thought and knowledge than my 10-year-old self ever dreamed of, and compared to even the best scholars of 1800, I have thousands of times as much information available.

But, Internet aside (a disturbingly large proportion of that great library of knowledge consists of articles that begin with “1 Weird Trick to Increase the Size of Your…”), we really ought to stop and pay attention more often. Empty out our dizzy brains and look around. Before I stop my rambling for today, I want you to do something for me. If you’ve got any other browser tabs open, close them. If you’ve got music playing in the background, pause it. Stop thinking about what you’re going to eat for dinner or breakfast, or who you’re going to have sex with tomorrow, or whether your aluminum hat is thick enough to keep out the insectoids’ mind-control rays, or whether you fed the snails, or whether Kiro’s meningitis will clear up. Just sit there for a moment with nothing on your mind. Just concentrate.

It’s just you and me now. You’ve taken a moment to read a bunch of words that I stuck together. I could get all modern-metaphysical and talk about the miracle of electronics that transmitted those words from me to you, but I won’t. Just think about this: you’ve read what I’ve written, and that makes me happy. Right now, at this very moment, I am imagining you. I’m sitting here with my coffee cup and my slice of watermelon. The house is quiet. Everything is peaceful. I’m wondering what it’s like where you are. I’m wondering whether there’s a naked woman sleeping in your bed (Don’t worry, I wonder that about everybody.) I’m wondering how many lights are on in your room, whether it’s bright and cheerful or dark and secretive.

As I’m writing this, it’s early in the morning on June 28th, 2014. June 28th, 2014 will last 24 hours, and then will be gone. I will see things today that I have never seen before, and have experiences that are different from any experiences I’ve had before. I may not notice the differences, but they will be there, and with practice, maybe I’ll learn to notice them.

I don’t know whether my hypothetical immortal utopia will ever happen. I’m going to be pessimistic and assume I’ll be dead by age 65. But, as is the case for everybody, if I learn to appreciate that time, and pay attention to it, and not go numb or take it for granted, then, whether I live 39 more years or six more days, and maybe if I live ten thousand more years, I’ll still be able to enjoy it.

Stay groovy out there.

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