Continuous Improvement



When is it adaptive for an organism to be satisfied with what it has?  When does an organism have enough children and enough food?  The answer to the second question, at least, is obviously "never" from an evolutionary standpoint.  The first proposition might be true if the reproductive risks of all available options exceed their reproductive benefits.  In general, though, it is a rare organism in a rare environment whose reproductively optimal strategy is to rest with a smile on its face, feeling happy.

To a first approximation, we might say something like "The evolutionary purpose of emotion is to direct the cognitive processing of the organism toward achievable, reproductively relevant goals".  Achievable goals are usually located in the Future, since you can't affect the Past.  Memory is a useful trick, but learning the lesson of a success or failure isn't the same goal as the original event—and usually the emotions associated with the memory are less intense than those of the original event.

Then the way organisms and brains are built right now, "true happiness" might be a chimera, a carrot dangled in front of us to make us take the next step, and then yanked out of our reach as soon as we achieve our goals.

This hypothesis is known as the hedonic treadmill.

The famous pilot studies in this domain demonstrated e.g. that past lottery winners' stated subjective well-being was not significantly greater than that of an average person, after a few years or even months.  Conversely, accident victims with severed spinal cords were not as happy as before the accident after six months—around 0.75 sd less than control groups—but they'd still adjusted much more than they had expected to adjust.

This being the transhumanist form of Fun Theory, you might perhaps say:  "Let's get rid of this effect.  Just delete the treadmill, at least for positive events."

I'm not entirely sure we can get away with this.  There's the possibility that comparing good events to not-as-good events is what gives them part of their subjective quality.  And on a moral level, it sounds perilously close to tampering with Boredom itself.

So suppose that instead of modifying minds and values, we first ask what we can do by modifying the environment.  Is there enough fun in the universe, sufficiently accessible, for a transhuman to jog off the hedonic treadmill—improve their life continuously, at a sufficient rate to leap to an even higher hedonic level before they had a chance to get bored with the previous one?

This question leads us into great and interesting difficulties.

I had a nice vivid example I wanted to use for this, but unfortunately I couldn't find the exact numbers I needed to illustrate it.  I'd wanted to find a figure for the total mass of the neurotransmitters released in the pleasure centers during an average male or female orgasm, and a figure for the density of those neurotransmitters—density in the sense of mass/volume of the chemicals themselves.  From this I could've calculated how long a period of exponential improvement would be possible—how many years you could have "the best orgasm of your life" by a margin of at least 10%, at least once per year—before your orgasm collapsed into a black hole, the total mass having exceeded the mass of a black hole with the density of the neurotransmitters.

Plugging in some random/Fermi numbers instead:

Assume that a microgram of additional neurotransmitters are released in the pleasure centers during a standard human orgasm.  And assume that neurotransmitters have the same density as water.  Then an orgasm can reach around 108 solar masses before it collapses and forms a black hole, corresponding to 1047 baseline orgasms.  If we assume that a 100mg dose of crack is as pleasurable as 10 standard orgasms, then the street value of your last orgasm is around a hundred billion trillion trillion trillion dollars.

I'm sorry.  I just had to do that calculation.

Anyway... requiring an exponential improvement eats up a factor of 1047 in short order.  Starting from human standard and improving at 10% per year, it would take less than 1,200 years.

Of course you say, "This but shows the folly of brains that use an analog representation of pleasure.  Go digital, young man!"

If you redesigned the brain to represent the intensity of pleasure using IEEE 754 double-precision floating-point numbers, a mere 64 bits would suffice to feel pleasures up to 10^308 hedons...  in, um, whatever base you were using.

This still represents less than 7500 years of 10% annual improvement from a 1-hedon baseline, but after that amount of time, you can switch to larger floats.

Now we have lost a bit of fine-tuning by switching to IEEE-standard hedonics.  The 64-bit double-precision float has an 11-bit exponent and a 52-bit fractional part (and a 1-bit sign).  So we'll only have 52 bits of precision (16 decimal places) with which to represent our pleasures, however great they may be.  An original human's orgasm would soon be lost in the rounding error... which raises the question of how we can experience these invisible hedons, when the finite-precision bits are the whole substance of the pleasure.

We also have the odd situation that, starting from 1 hedon, flipping a single bit in your brain can make your life 10154 times more happy.

And Hell forbid you flip the sign bit.  Talk about a need for cosmic ray shielding.

But really—if you're going to go so far as to use imprecise floating-point numbers to represent pleasure, why stop there?  Why not move to Knuth's up-arrow notation?

For that matter, IEEE 754 provides special representations for +/—INF, that is to say, positive and negative infinity.  What happens if a bit flip makes you experience infinite pleasure?  Does that mean you Win The Game?

Now all of these questions I'm asking are in some sense unfair, because right now I don't know exactly what I have to do with any structure of bits in order to turn it into a "subjective experience".  Not that this is the right way to phrase the question.  It's not like there's a ritual that summons some incredible density of positive qualia that could collapse in its own right and form an epiphenomenal black hole.

But don't laugh—or at least, don't only laugh—because in the long run, these are extremely important questions.

To give you some idea of what's at stake here, Robin, in "For Discount Rates", pointed out that an investment earning 2% annual interest for 12,000 years adds up to a googol (10^100) times as much wealth; therefore, "very distant future times are ridiculously easy to help via investment".

I observed that there weren't a googol atoms in the observable universe, let alone within a 12,000-lightyear radius of Earth.

And Robin replied, "I know of no law limiting economic value per atom."

If you've got an increasingly large number of bits—things that can be one or zero—and you're doing a proportional number of computations with them... then how fast can you grow the amount of fun, or pleasure, or value?

This echoes back to the questions in Complex Novelty, which asked how many kinds of problems and novel solutions you could find, and how many deep insights there were to be had.  I argued there that the growth rate is faster than linear in bits, e.g., humans can have much more than four times as much fun as chimpanzees even though our absolute brain volume is only around four times theirs.  But I don't think the growth in "depth of good insights" or "number of unique novel problems" is, um, faster than exponential in the size of the pattern.

Now... it might be that the Law simply permits outright that we can create very large amounts of subjective pleasure, every bit as substantial as the sort of subjective pleasure we get now, by the expedient of writing down very large numbers in a digital pleasure center.  In this case, we have got it made.  Have we ever got it made.

In one sense I can definitely see where Robin is coming from.  Suppose that you had a specification of the first 10,000 Busy Beaver machines—the longest-running Turing machines with 1, 2, 3, 4, 5... states.  This list could easily fit on a small flash memory card, made up of a few measly avogadros of atoms.

And that small flash memory card would be worth...

Well, let me put it this way:  If a mathematician said to me that the value of this memory card, was worth more than the rest of the entire observable universe minus the card...  I wouldn't necessarily agree with him outright.  But I would understand his point of view.

Still, I don't know if you can truly grok the fun contained in that memory card, without an unbounded amount of computing power with which to understand it.  Ultradense information does not give you ultradense economic value or ultradense fun unless you can also use that information in a way that consumes few resources.  Otherwise it's just More Fun Than You Can Handle.

Weber's Law of Just Noticeable Difference says that stimuli with an intensity scale, typically require a fixed fraction of proportional difference, rather than any fixed interval of absolute intensity, in order for the difference to be noticeable to a human or other organism.  In other words, we may demand exponential increases because our imprecise brains can't notice smaller differences.  This would suggest that our existing pleasures might already in effect possess a floating-point representation, with an exponent and a fraction—the army of actual neurons being used only to transmit an analog signal most of whose precision is lost.  So we might be able to get away with using floats, even if we can't get away with using up-arrows.

But suppose that the inscrutable rules governing the substantiality of "subjective" pleasure actually require one neuron per hedon, or something like that.

Or suppose that we only choose to reward ourselves when we find a better solution, and that we don't choose to game the betterness metrics.

And suppose that we don't discard the Weber-Fechner law of "just noticeable difference", but go on demanding percentage annual improvements, year after year.

Or you might need to improve at a fractional rate in order to assimilate your own memories.  Larger brains would lay down larger memories, and hence need to grow exponentially—efficiency improvements suiting to moderate the growth, but not to eliminate the exponent.

If fun or intelligence or value can only grow as fast as the mere cube of the brain size... and yet we demand a 2% improvement every year...

Then 350 years will pass before our resource consumption grows a single order of magnitude.

And yet there are only around 1080 atoms in the observable universe.

Do the math.

(It works out to a lifespan of around 28,000 years.)

Now... before everyone gets all depressed about this...

We can still hold out a fraction of hope for real immortality, aka "emortality".  As Greg Egan put it, "Not dying after a very long time.  Just not dying, period."

The laws of physics as we know them prohibit emortality on multiple grounds.  It is a fair historical observation that, over the course of previous centuries, civilizations have become able to do things that previous civilizations called "physically impossible".  This reflects a change in knowledge about the laws of physics, not a change in the actual laws; and we cannot do everything once thought to be impossible.  We violate Newton's version of gravitation, but not conservation of energy.  It's a good historical bet that the future will be able to do at least one thing our physicists would call impossible.  But you can't bank on being able to violate any particular "law of physics" in the future.

There is just... a shred of reasonable hope, that our physics might be much more incomplete than we realize, or that we are wrong in exactly the right way, or that anthropic points I don't understand might come to our rescue and let us escape these physics (also a la Greg Egan).

So I haven't lost hope.  But I haven't lost despair, either; that would be faith.

In the case where our resources really are limited and there is no way around it...

...the question of how fast a rate of continuous improvement you demand for an acceptable quality of life—an annual percentage increase, or a fixed added amount—and the question of how much improvement you can pack into patterns of linearly increasing size—adding up to the fun-theoretic question of how fast you have to expand your resource usage over time to lead a life worth living...

...determines the maximum lifespan of sentient beings.

If you can get by with increasing the size in bits of your mind at a linear rate, then you can last for quite a while.  Until the end of the universe, in many versions of cosmology.  And you can have a child (or two parents can have two children), and the children can have children.  Linear brain size growth * linear population growth = quadratic growth, and cubic growth at lightspeed should be physically permissible.

But if you have to grow exponentially, in order for your ever-larger mind and its ever-larger memories not to end up uncomfortably squashed into too small a brain—squashed down to a point, to the point of it being pointless—then a transhuman's life is measured in subjective eons at best, and more likely subjective millennia.  Though it would be a merry life indeed.

My own eye has trouble enough looking ahead a mere century or two of growth.  It's not like I can imagine any sort of me the size of a galaxy.  I just want to live one more day, and tomorrow I will still want to live one more day.  The part about "wanting to live forever" is just an induction on the positive integers, not an instantaneous vision whose desire spans eternity.

If I can see to the fulfillment of all my present self's goals that I can concretely envision, shouldn't that be enough for me?  And my century-older self will also be able to see that far ahead.  And so on through thousands of generations of selfhood until some distant figure the size of a galaxy has to depart the physics we know, one way or the other...  Should that be scary?

Yeah, I hope like hell that emortality is possible.

Failing that, I'd at least like to find out one way or the other, so I can get on with my life instead of having that lingering uncertainty.

For now, one of the reasons I care about people alive today is the thought that if creating new people just divides up a finite pool of resource available here, but we live in a Big World where there are plenty of people elsewhere with their own resources... then we might not want to create so many new people here.  Six billion now, six trillion at the end of time?  Though this is more an idiom of linear growth than exponential—with exponential growth, a factor of 10 fewer people just buys you another 350 years of lifespan per person, or whatever.

But I do hope for emortality.  Odd, isn't it?  How abstract should a hope or fear have to be, before a human can stop thinking about it?

Oh, and finally—there's an idea in the literature of hedonic psychology called the "hedonic set point", based on identical twin studies showing that identical twins raised apart have highly similar happiness levels, more so than fraternal twins raised together, people in similar life circumstances, etcetera.  There are things that do seem to shift your set point, but not much (and permanent downward shift happens more easily than permanent upward shift, what a surprise).  Some studies have suggested that up to 80% of the variance in happiness is due to genes, or something shared between identical twins in different environments at any rate.

If no environmental improvement ever has much effect on subjective well-being, the way you are now, because you've got a more or less genetically set level of happiness that you drift back to, then...

Well, my usual heuristic is to imagine messing with environments before I imagine messing with minds.

But in this case?  Screw that.  That's just stupid.  Delete it without a qualm.


Part of The Fun Theory Sequence

Next post: "Sensual Experience"

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