Fecundity
Most of this essay was written under the conceit of it being a TED Talk
The Axiom of Fecundity:
Every possible event is spontaneously trying to happen right now... and failing mostly.
"Really? That's your Ted Talk thesis?"
Yes, more or less. How's that for a seriously hot take on a seriously cold issue!
My unexpected thesis is, I claim, every bit as true and valid as its more conventional opposite: Nothing happens unless it is caused to do so...except sometimes. What makes the latter believable and the former unbelievable, I think, is merely a matter of our biology, training, and habit rather than a matter of fact. It would hardly be an overstatement to say that our entire Western knowledge system is built around the “nothing” version, so the “everything” version is literally almost unthinkable. My job today is to make it thinkable. You were undoubtedly unaware of having made the choice between the two. But yeah, you have. And if you sit with it for a while, wouldn't you really rather approach the world in a way that emphasizes infinite possibility over dead matter? It's more like the world I see around me for sure. Certainly more like the world of mind where creative possibilities, though sometimes hard to access, are limitless.
Again, my claim is that it is just as valid to say that the universe is absolutely fecund -- an actual plenum of creativity and change -- as to say that it is relatively meek and inert and unfolds only through coercion (i.e. "force"). It is just as valid to say that we must explain why things mostly stay the same as to explain how things sometimes change. Yup, that's my thesis in a nutshell. The facts are these: Things sometimes remain the same and sometimes change. The only question is which of these two conditions is the default circumstance, and which needs to be justified.
Okay, you've got 17 and a half minutes left. Convince them!
Let's bear in mind a few things I'm not saying. I'm not saying that fecundity is true and inertness is false. My belief is merely that the landscape of valid explanatory schemes is broad enough to encompass both approaches. Each can be an axiom -- I like the sound of the Axiom of Fecundity-- in a completely logical descriptive system that will create consistent and comprehensive explanations of a given body of facts. Just don't try to put these contradictory postulates in the same logical system or -- kablooey! -- contradictions everywhere. When I try to picture the explanatory landscapes of the two axioms, I get a Venn diagram with major overlap and major distinctions. With luck, the overlap includes or accounts for all established measurements.
Before we get into it, we probably have to go a bit deeper in the underpinnings first. My deeper claim: The simulated is not the actual. That doesn't sound related to my thesis, but bear with me. We all perpetually confound the map and the territory. The illusion's nearly impossible to overcome and, by the way, it's becoming more and more problematic over recent history as people's experience increasingly comes to involve simulated worlds. That is, if we increasingly spend our mental lives peering at screens, living in simulations that are two steps removed from the territory rather than just the old-fashioned single step away, the territory itself becomes less and less relevant to human thinking and, by extension, scientific thinking. And that's bad! By my way of thinking about it, our thoughts (or mind maps) are just that -- simulations of the real world -- both more and less sophisticated and entrancing than the simulations in the latest computer game. And if those computer simulations get so good that they can't be distinguished from reality, is there still a distinction to be made?
I say "Hell yes!" Turing's famous test kind of says no, but I've never thought that it made much sense. No simulation of say, the law of gravity actually has gravity, and significantly no simulation of a conscious mind actually is a conscious mind. And reality is no video game! It's become a common sci-fi theme to ask if our world is part of a simulation created by some computer programmer of higher consciousness. I don't know if that's feasible, but it seems pretty silly to me, involving a weird sort of humble brag -- God is a geek like me, only with a much better computer. Not to mention the glaring infinite regress which plagues all Godly scenarios. It's a simple map-territory blunder.
But I'm getting way off track here. Reality is radically other than a map, no matter how detailed and excellent the map is. If you can let that thought marinate for a while, it's much easier to contemplate my real takeaway you need here. No single map or set of maps is the right one or the right set. No map is perfect or even best, just more or less useful or enlightening or insightful under the circumstances.
There's more than one way to skin a kumquat
The universe is not only queerer than we suppose but queerer than we can suppose
Let's get down to science for a minute, an area, by the way, in which I have no credentials (duh!). Isn't a law of physics supposed to be some sort of absolute and perfect map? I think that's the original idea -- at least before Kuhn. Well, the best exemplar of a law of physics I can think of -- Newton's law of gravitation -- seems about as perfect and unexceptionable as can be. Two masses are attracted to one another depending precisely and simply on their magnitudes and the distance separating them. The simple equation that most first year algebra students can just about understand offers skilled practitioners the ability to, for example, predict eclipses with extraordinary precision many years in advance. For 200+ years there was little reason to question its absolute correctness; its truth and the validity of the scientific ideal were one and the same. That is, science became science based on the paradigm of this single, simple law. If something as fundamental as gravitation could be perfectly epitomized by an equation, this clockwork view could probably be applied to just about everything. And it has been. And it's all more or less worked too...if you don't mind the myriad messy side effects we call the modern world.
But let's not forget that Einstein came along eventually, and now gravity ain't what it used to be. Sure Newton's nice equation does a good enough job most the time, but it just plain isn't right. It's main appeal -- simplicity -- is the problematic part. Apparently things are a little more complicated and not at all the same. For one thing, there's no real attraction (something btw Newton himself didn't accept) -- instead masses mysteriously warp space itself so that planets merely travel in "straight" lines. I don't understand the particulars particularly well, but that's okay. That isn't what this talk is about either! A scientist might frame this Newton-Einstein story as one theory being superseded by a better one -- science at its best! But I want to frame it as right answers only being right for particular contexts and inevitably losing their rightness as we try to extend them. The underlying reality is indifferent to theoretical claims.
Right. Enough background. I've chosen one particular seemingly right thing that I want to offer an alternative to.
Nothing happens unless it is caused to do so.
Hmm, again that sounds about right, non? It's practically the definition of causation -- what causation causes is change. A rock is mostly just going to continue on; it won't spontaneously pop out of existence or explode or morph into the Eiffel Tower. Don't bother explaining that. It's natural! The rock only changes when you hit it with a hammer or melt it or slowly erode it away with wind and water, etc.. Likewise my political beliefs or the position of my ear relative to my nose stay pretty much the same unless events cause them to drift a bit to the right or left. There's a kind of natural inertia. Reality seems to need its butt kicked to get moving. This perspective reflects a master-servant relationship between laws and existence. It isn't surprising that it was formulated before egalite was much of a thing, and when social power structures were more top-down.
Sometimes the necessity of causation is a little more subtle than in the case of a rock, however. That is, sometimes it's less obvious that nothing happens unless it is caused to do so. My body will very much change for the worse unless I eat, breathe, etc. Won't it? Causation is required to keep my body or a hurricane as it currently is. That is, I will die and decay without food and elimination, and a hurricane will dissipate into nothingness without something pumping energy into it. And on the flip side, something similar is kind of true even for a rock. Is an extreme temperature that melts rocks less natural than a moderate temperature that leaves them existing? Or more or less natural than a temperature of absolute zero, when matters begins to behave very peculiarly indeed. The persistence of the rock can be said to be caused by moderate conditions which themselves must be caused by something. Still, there's a deep faith that we just need to lower the level of description -- to chemistry maybe -- to see where the degradation of my body without food is caused by something, in the absence of which my body would persist, preserved in amber. Would my political beliefs also be so preserved? Hmmm.
How about the decay of an atom of uranium 238. Current understanding, I am told, suggests this just happens spontaneously and probabilistically -- NOT because something triggers it. Maybe the "nothing happens without cause" approach is worth questioning.
Here's a restatement of the above rule:
In the absence of causes, things stay the same.
This is pretty deep, man. I call the above statement the General Law of Inertia or GLOI, based on its resemblance to Newton's famous law of inertia or LOI (aka the first law of motion):
In the absence of forces, motion stays the same.
You might be more familiar with it in this form:
A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force. (The Wikipedia phrasing.)
A hockey puck or a planet or a speck of dust won't just start moving by itself, and if it is in fact already moving and nothing acts to stop it, it's going to keep going just as it is under its own inertia. Only acceleration (defined as change of motion) is in need of explanation.
This sounds pretty tame and obvious to the ears of modern educated westerners, but back in the day it was utterly revolutionary [and easily contradicted]. Aristotle thought that a thrown stone needed constant impetus to keep moving -- and of course that's kinda right too. A thrown stone, in my experience, will fall to earth, hit the dirt and skid to a stop. No constant motion here.
So that suggests a good first alternative to GLOI: In the absence of causes, change slows down to a stop.
Here are few more alternatives:
2) In the absence of causes, the world ceases to exist. This point of view has been taken up at times -- in Kabbalah e.g. God and human contemplation of God must be ever vigilant lest we puff out into non-existence. "Let there continue to be light." It's worth looking into the religious/philosophical question "Why is there something rather than nothing?" But that's not the topic today either.
3) Heraclitus's formulation: You never go to the same river twice. You and the world are in a constant state of fluctuation and revolution. This is close to my Axiom of Fecundity, but not quite.
And finally:
4) There is never an absence of causes; potential causes are ever-present and plentiful, so everything is trying to happen at once but mostly failing. All changes are the result of successes of that inherent procreation. The generalized law of fecundity or GLOF.
Briefly, the key to making sense of my Axiom of Fecundity is the idea that cancellation of contrary influences keeps things from happening willy-nilly. Yup, that is the topic today -- cancellation. Why didn't I just say so before? I'll trot out some examples shortly. This self-canceling plenum seems more complicated than GLOI, with an infinity of things to keep track of rather than one or a few causes -- but that's really no reason to disbelieve it. Ugh! It's the tyranny of old Occam's Razor, the principle of parsimony. "If two systems equally well explain something, choose the simpler one, stupid!"
Wrong, stupid! Choose an interesting system that leads to further insights. More metaphors bring more insights, at least potentially -- and vastly differing metaphors bring vastly different insights. Don't choose one over the other except as a matter of convenience. In fact, choose both/all in turn for a fuller understanding. Insights brought by analytical thought always involve a trade off between complexity and comprehensibility and thus between accuracy and understanding.... Rather than the simplest theory that accounts for facts, we should instead opt for the most complicated one that we can understand or that can provide the most insight. The assumption-switching process involves a difficult mind trick: sidestepping the law of excluded middle: A and not A can't both be true. I'll address that issue shortly.
Even given the validity of some form of parsimony, one could still argue that GLOF is just as simple as GLOI. It's a clear statement and requires about the same number of words, e.g. It's only the ramifications that quickly overwhelm our poor human minds. It a priori multiplies possibilities rather than narrowing them down. How many things are preventing you from getting a headache right now and how many are trying to give you one? (Is this talk one of them?) Maybe my alternative premise is ill-suited to human brains or to practical engineering. That's a reason for an engineer not to focus on it, but no reason for a seeker of insight to ignore it. It isn't ill-suited to epistemological understanding.
Someone out there is certainly angrily thinking my weird world view contradicts the conservation of energy or other cherished notions. It probably doesn't really if we're clever enough about choosing our other axioms. We can't just flip GLOI for GLOF and leave the rest of the rules the same. The measurable facts will start to get in the way. Remember that we want to account for, or at least be consistent with, the accumulated facts and measurements of science. That will take some major changes to standard procedure. Many will believe that to be an impossible task; I don't think it is. I believe in the power of the patch!
So, the reason that most things are failing to happen right now is that opposite tendencies cancel out. It's important to keep in mind in this regard that cancellation isn't annihilation; waves canceled by your noise-canceling headphones, for example, keep on propagating... Again more later.
As a simple and imperfect illustration of this cancellation model (finally!), imagine a beach ball floating in a circular pool. Around the edge of the pool placed every ten degrees of arc are 36 portable electric fans, each pointed toward the center of the pool. Turn them on. You get the idea, I'm sure. Each fan represents a tendency to move things in a particular direction. Many things are trying to happen. But, in this case, what does happen? Not much, right? You can guess that the beach ball heads toward the center of the pool and more or less stays there, buffeted maybe by turbulent up and down drafts of the crashing streams of air. So... my metaphor suggests that the things that are trying to happen are failing mostly because of cancellation by the myriad efforts of lots of other somewhat contradictory things that are also trying to happen. The beach ball stays the same and doesn't move. Now turn off one of the fans. Something happens. It happens because of an asymmetry. It happens because less is trying to happen. Nanni's First Law: Singularly unopposed or incompletely opposed things happen.
Blocking x facilitates the opposite of x. It's like the judoka who, in fending off an attack, redirects the attackers' energy back at them. My version of an equal and opposite reaction.
Here's a more detailed cancellation image to think about: Suppose you found yourself in the exact center of a mostly hollowed out spherical planet. Take a second. How does it feel? What sort of gravitational tugs are you subject to from the mass of that planet? Every point on that sphere is yelling "come here." By the symmetry of all the mass surrounding you, however, all of those calls in all of the directions would be equal and thus effectively cancel out. It's the electric fan situation again -- or maybe more like a circle of vacuum cleaners; you would be weightless. Weird. Already we have an infinity of actions trying to happen, but they all cancel. Now imagine drifting say northward toward the north pole in this enormous interior. The northerly parts of the globe are now nearer to you so pull harder (according to the inverse square rule), but the parts that are more southerly, though more distant, are growing more numerous. Newton's famous shell theorem proved that the total of gravitational tugs still cancels perfectly. That is, you remain weightless everywhere in the interior of the hollowed out planet. Wow. Why isn't this mentioned in every elementary school! It sets my imagination to buzzing! It might be enough to make you think that cancellation is a common and important aspect of how things work! In particular, notice that when you place an object at a particular spot it just sits -- not by inertia but by perfectly balanced cancellation.
Once you cross the threshold to the exterior of the shell, of course, things go back to normal-- that's the more famous part of the shell theorem. Since nonhollow planets like our own can be thought of as made of layers of shells (like a jawbreaker or an onion) that each produces this cancellation, the rule applies to actual Earth situations. If one were able to make and survive the trip halfway to the center of the Earth, for example, and ignoring the changing density as we approach the center, one would actually weigh only half as much, since the effect of all the outer shells wouldn't have any effect. (For those checking the math, 1/8 of the mass is attracting you but you're twice as close so that means half as much force is produced). Wow again. The part of the Earth further from the center than you are have no net influence because they're pulling equally in every directions, but the part closer to the center than you are all pulling in the same direction, so you feel it. One last image in this thought experiment. If there were a sizeable hole in the north pole and nowhere else, you would slowly accelerate to the south pole. Singularly unopposed things happen, and blocking x facilitates the opposite of x.
Aside from supporting GLOF, the point of these cancellation examples is to spur creative insights, so here's one. Maybe it's just me, but this hollow planet reminds me of how time and memory work. Think of time and space as a nesting of 3-D surfaces (spheres) in 4-D reality, where one such surface is the moment in time in which you find yourself. The interior of that spherical surface is the past and the exterior is the future. We feel and remember the influence of the past but not the future because the influence of one is unopposed and the influence of the other is opposed, except maybe sometimes.
In the hollow planet example, the cancellation is perfect and geometrical. In real world cases, however, the cancellation is a statistical and happenstance, so little bits of everything trying to happen leaks out less than fully cancelled. That is, some special stuff manages to happen.
Okay, if that silly notion hasn't already gotten me banned from TED, here's something that definitely will: Experiments consistently show that ESP is real! And materialists equally consistently deny it and say that every single one of the hundreds of studies showing, for example, clairvoyance are poorly designed or fraudulent. Ugh. Sounds like a bunch of poor sports. Unfortunately for the true-believers in ESP or the Men Who Stare at Goats, the effects are really small and thus neither particularly useful, glaring, or convincing. That is, it's a statistical fact that people have very small but nonzero ability to predict the future among other things. Well, of course, if the influence of the future isn't perfectly canceled, little bits of it leak into the present for us to (somehow perhaps) perceive. I'm not saying how one might perceive them... Remembering the future, maybe?
The idea that massive cancellation is part of the story of reality is nothing new. The basic computations of quantum mechanics involve enormous cancellations. In Richard Feynman's delightful book "QED," he gives a quantum description of light reflecting off a mirror. The familiar notion that angle of incidence equals angle of reflection holds in the end but not in the simple way that we imagine for billiard balls bouncing off cushions. According to quantum electrodynamics, any given photon from source S could reflect from any point on the mirror in almost any direction and be detected by observer O. That is, the observer would see the dot of light at different places in the mirror or all over the place rather than one place. Each of the infinitely many possible paths from S to the mirror and off to O is associated with a different probability vector of a certain amplitude. The remarkable thing is that those vectors are different lengths and point in different directions and so tend to cancel each other out; the sum of those vectors that reflect off an "incorrect" point to O is always virtually zero. So the likelihood of detecting a photon from S that reflected off a point other than the preferred point A is near zero. Only the vectors from S to O passing through "correct" point A reinforce each other rather than pointing in contrary directions. Singularly unopposed things happen. If you think this might be some false hocus pocus, Feynman describes how the idea can be tested. If many well-placed scratches are made in the silvering of the mirror, the perfect cancellation of the wrong paths can be disrupted. Glare and hilarity ensues. The mirror no longer acts as a mirror. That's queerer than I can imagine! I obviously haven't done this example justice in these few moments. I urge you check out Feynman's detailed but non-technical description.
Outside simple examples from physics, how might one demonstrate things happening or failing to happen by cancellation? How about this. In reductionist determinist thinking, there's never such a thing as a new creation or idea -- just fortuitous recombinations of old things or ideas that haven't come up before. What could cause true novelty? This sort of thing rubs most laypeople the wrong way. GLOF may or may not be consistent with true novelty, but it at least gives us a more favorable approach to the issue. Creativity is baked into the axiom.
Well, you probably aren't convinced that everything's trying to happen at once, but maybe you're at least a tad intrigued. The thing is, this isn't in itself something to argue for; it's something to be assumed. I've developed a whole system I call Assumption Switching, the point of which is to call old assumptions into question with the hopes of leading to new insights into our world while promoting a kind of open-mindedness.
You might well ask what sort of universe we live in if the coercion assumption has the same status as the fecundity assumption. Answer: a world that cares not for assumptions. Human thinking seems to be bound by foregrounds and backgrounds, insides and outsides, subjectivity and objectivity, yin and yang, my way or the highway, but in the deepest reality no such distinctions hold. If maps always contain these dichotomies like foregrounds and backgrounds then the world isn't fundamentally mappable no matter how subtle the map. What is is mysteriously, tantalizingly situated in the space between the between of the between of our maps (see the both and neither diagram).
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My little "between the between of the between" phraseology isn't quite as poetical or whimsical or random as it might at first seem. The idea comes from another one of my favorite math metaphors that also includes a kind of cancellation. You must know that people love the number pi -- the ratio of the circumference of any circle to its diameter. Since going around a circle is about 3 times as far as going across a circle, pi is about 3. Mathematicians have known for a long time that there are equations that can approximate pi as accurately as you please if you are willing to calculate for a long time. They also know that there is no way to calculate an exact decimal value of pi in a finite number of steps. The algorithm may be brief but the steps go on forever. The first of the great pi equations is:
pi = 4 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 ...
That's thrilling to contemplate. What do the odd reciprocals of the integers have to do with circles? Hell if I know.
The good news is that we know the equation is true -- after alternate steps we get a quantity too big then one too small, constantly over-correcting (the cancellation part) and the approximation gets better and better forever. The bad news is that it zeroes in on pi agonizingly slowly.
And here's good news again! There's a very simple way to speed it up that I call finding "the between of the between of the between."
Let's see if we can get there in just a few explanatory steps. First, I want to replace this series of individual terms with a sequence of running totals:
4 (4 - 4/3 = 8/3) (8/3 + 4/5 = 52/15) (52/15 - 4/7 = 304/105) ...
For comprehensibility, let's use decimal representations for this never-ending sequence (truncated at an arbitrary point):
4 2.666666666 3.466666666 2.895238095 3.339682539 2.976046176 3.283738483 3.017071817 3.252365934 3.041839618 ...
Heading to 3.14159265 maybe, but too slow, right?
The neat fact is that this sequence goes up and down in such an interesting and particular way that a new sequence made from averaging consecutive terms above will also approach pi, but a bit faster. We'll call this row of averages the second row.
3.333333333 3.066666666 3.180952380 3.117460317 3.157864357 3.129892329 3.150405150 3.134718875 3.147102776 3.137077714 ...
Well, that's the first "between" and the results are a bit more like it: the averages are "better" than the original list of running totals (partial sums, as they're called)
You may have already guessed that we can just keep doing this. Take the previously created sequence and replace it with averages of consecutive terms again, and so on. In each new sequence of averages, the result heads toward pi even faster. Here's the tenth row:
3.141686658 3.141581088 3.141594858 3.141592104 3.141592818 3.141592596 3.141592675 3.141592644 3.141592657 3.141592651 ...
and the 20th row:
3.141592688358 3.141592651252 3.141592653841 3.141592653553 3.141592653596 3.141592653588 3.141592653590 3.141592653589 3.141592653589 3.141592653589 ...
So, in my funny way of putting it, pi is between the between of the between of the original terms of the simple sequence. A simple scheme plus a bit of complexification leads to dramatic accuracy
Anyway, by metaphorical extension of this betweenness business, I want to say that actual territory is always between the between of the between of formal (or informal) maps inherent in various sets of assumptions.