The Table of Contents below is too long to display fully. If you click to the right of these Lessons,you'll see the primary source documents displayed under each. These original sessions are a world treasure.
1c Images & Attributions (in order of appearance)
1. Banner: Rhiannon C. 2016
a) Albion Glyph: William Blake, "Glad Day" or "The Dance of Albion," c.1794
https://upload.wikimedia.org/wikipedia/commons/thumb/4/47/William_Blake_-_Albion_Rose_- _from_A_Large_Book_of_Designs_1793-6.jpg
2. "Möbius II" as ∞, M.C. Escher (request for permission to use image submitted & pending)
3. Portrait of Immanuel Kant https://upload.wikimedia.org/wikipedia/commons/0/0a/Kant_foto.jpg
4. Photo of π (highlighting groups of the same numerals)
https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Pi_tau_digit_runs.svg/512px Pi_tau_digit_runs.svg.png
5. "Möbius II" as ∞, M.C. Escher (request for permission to use image submitted & pending)
An illustration perhaps? Let’s start simply, with something we know to be infinite. I’m sure you know a bit about irrational numbers—π, for instance, or the square root of 2. Irrational numbers are real numbers that cannot be expressed as a fraction of two integers or, in decimal form, decimals which go on forever without repeating. The number π has been calculated to many million places [now trillions (see above)], and within these million digits there exists no discernible pattern whatsoever. Undoubtedly π—and remember π is a real number in our real world everywhere around you—every single phone number in the world appears in order as it would be listed in a world phone book. Every phone number also appears in the reverse order. Somewhere else in π is every phone number in its proper order with the single exception of your own ten-digit number, while elsewhere your number is repeated a quadrillion times. Somewhere in π, in fact, is π itself (minus the decimal point) to more decimal places than any being ever could calculate. And each of these numeric sequences occurs not just once, but an infinite number of times.
And that’s just π. Within the square root of 2 or the cube root of your phone number you will find exactly the same orders and numbers, as well as every other possible sequence of numerals you could ever conceive. (And, for your information, the set of irrational numbers is an order of infinity much larger even than the already-infinite set of rational numbers; some infinities are just bigger than others.) And that’s just the simplest illustration of infinity.
Here’s another: Suppose, contrary to scientific opinion, the universe is infinitely large. If so, then elsewhere in the universe the matter and energy which define our world are exactly duplicated (down to the last atom & photon), creating an infinite number of worlds identical to this one. Right now, for instance, an infinite number of Phus are reading an infinite number of letters identical to this one. In a moment these same Phus, upon finishing their identical letters & thinking identical thoughts, will rise from where they are seated to go to the bathroom, to eat a bowl of cereal, or attend their middle school science class, exactly as our own Phu chooses in this world.
Of course among these infinite identical worlds few (an infinite subset) remain identical to ours for long; random chance & human choice conspire to create points of divergence, trees & branches everywhere imaginable. Many of these worlds differ from our own in ways wholly imperceptible to us: A single electron in a carbon atom fails on another Earth to match the random location of its counterpart here. The result: A grass fire in the Australian bush releases one less CO2 molecule into the atmosphere; and, given time, this small detail may or may not multiply into differences which sharply distinguish our respective planets (no doubt you’ve heard of the “butterfly effect”). Still other worlds, which appear at first glance most familiar to us, may on close inspection reveal subtle, perhaps disturbing differences: On one such world, for example, everything seems identical to our own, except there is no Phu (alas, a victim of spontaneous human combustion). On another world the United States Constitution has been amended solely so that one thirteen-year-old Phu can become President.
It’s easy to see then how a universe that is spatially infinite is, in human terms, no different from one that allows for time travel & parallel existences. One need not travel into another dimension to meet oneself, for instance; there are plenty of Phus to be had in this one (if you can get there). For not only do your clones exist in infinite number elsewhere, but so also exist Phus whose respective worlds are just like our own except they’re one day older—or one day younger, or a year, or a thousand years. To travel to these worlds in space is as good as traveling to the past or future. (But which past? Whose future?)
While such improbable worlds are often fun to imagine, it seems almost absurd actually to believe in them. Nevertheless, when we assume the universe to be infinite, we have no choice but to acknowledge the literal existence of all possible worlds. (Only the purely impossible may be excluded.) For this reason believing in infinity—even trying the belief on for size—is very hard to do honestly. And what makes infinity still harder to grasp are the innumerable paradoxes & contradictions which arise within it. Another example: Suppose again the universe is infinite in space, but let’s assume now that it’s infinite in time as well—it has neither a beginning nor an end. (I further assume that life on this planet is not the unique creation of one God.) From these premises the following paradox arises:
albionspeak: a draught of language (1.3)
Letter to Phu – On Infinity
November 1996
The following letter, “To Phu,” marks a brief departure from my sequence of Letters in that Phu is not (assumed to be) a member of the Jewel Net. As I know him, Phu is a thirteen-year-old boy of recent Vietnamese-immigrant descent, who, for the second straight year, is a student in my wife’s science class. [My wife] tells me Phu is a nice boy: intelligent, mature (for thirteen), and quite isolated from his family & classmates for his passionate interests in physics and science fiction. He loves Star Trek, knows the biographies of everyone who worked on the Hubble Space Telescope, and is already laboring toward his goal of attending Cal Tech. When [my wife] mentioned her husband shares some of these interests, Phu sent me a typed four-page letter regarding his speculations on infinity & alternate universes. I never met Phu.
Dear Phu,
Congratulations! You’ve started thinking about INFINITY. There’s good news & bad news. First the bad news: You’ll never figure it out. Now the good news: You’ll never figure it out.
That infinity is a mystery absolutely unattainable to mortal man (or, for that matter, immortal man) makes it one of the great concepts worth thinking about. The philosopher Immanuel Kant said there are only four categories of experience which cannot be grasped solely within the context of our rational lives: time, space, God, and infinity. Simply put, nothing in our set of personal experiences can equip us to understand these ideas, so, says Kant, any knowledge we might possess must have come to us a priori, meaning prior to our experience—that is, knowledge we’re born with. It stands to reason then, Phu, that on some deep biological level, you already possess—if not the racial memory—at least a genetic intuition of infinity. Perhaps you’ve caught it glimmering, like a star, beyond the boundaries of your own mind. And maybe you suspect it is drawing you toward it—unavoidably, like a magnetic attractor or black hole. Nevertheless (& despite feeling that others might label you “crazy”) you’ve chosen to brave the consequences & have laid in an intercept course. Should you pursue infinity, Phu, it will change you and will, in your language, “blow you away”; yet maybe, if your intuition proves true, you might rank among a fortunate few, for perhaps indeed it is a star worth pursuing. Still, you’ll never figure it out.
Now about your current thoughts: First, I think you make one critical error of assumption. I don’t at all believe that “at any given point there are an infinite number of [future] possibilities.” Your “tree & branches” graph is certainly accurate, more accurate, I feel, than your assumption. The number of possibilities may indeed be truly huge, and no doubt increases exponentially with time (at least); but this is not even close to infinite. (There is no such thing, in fact, as “close to infinite.”) Actually, at any given moment one’s options are pretty limited: Even on the molecular level there are only so many different things that can happen; and, of course, most of these minor events have little affect on the actions one may or may not ultimately choose. But just because the number of possibilities is totally beyond our puny cranial cavities, this doesn’t mean the universe is infinite.
I do not mean to discourage you by pointing out these walls (nor do I mean to patronize, for I, too, am struggling). On the contrary, I wish to highlight the same road signs that are described throughout the human world in religion, mythology, and literature. We are not alone, and the path, though arduous, has been traveled by many. (Indeed, once you start looking for it, it’s everywhere.) I also have another reason for pointing out the walls: The walls are not final barriers. While you cannot scale them or get around them with your reason alone (as Kant illustrated), absorbing & embracing them on a deep personal level can eventually help them to dissolve, perhaps disappear altogether. You may already know this intellectually; but unfortunately, because it takes time & much effort to know one’s self-limitations, this process generally involves some years of frustration. A friend, who is both a guide & oracle to me, once advised me in my own pursuit of infinity. He wrote simply, “Be patient and discover your finity.”
And the end? The Final Frontier? I really don’t know yet, but I can volunteer a little of what I personally believe: I feel strongly that the first wall can be breached by means of the imagination. If we discipline ourselves, we can travel anywhere we want in our minds. The second wall, as I’ve already illustrated, involves choice, involves our free will. Thus, while few people possess the method or strength of will for such travel, even fewer have the wisdom to know how to choose. Perhaps once you have considered all of this deeply, you will understand that within infinity every choice you make fundamentally is a moral act—that to consider infinity is ultimately to consider the nature of the Good.
Good luck on your journey, and remember patience…
Hail aliah
§
a slice of π
Mobius II
M.C. Escher
∞!
Henceforth, let this symbol highlight any discussion of Infinity (this whole letter) or point in a discussion requiring extra caution, due to encroaching infinities.
Immanuel Kant
1724 - 1804
alert
1) Life must exist elsewhere.
2) Some of this life is intelligent, including life forms much
smarter & more advanced than our own.
3) Of these, some must possess technologies which can build
spacecraft (light speed may or may not be a barrier).
4) Some of these advanced life forms (fortunately very rare) are,
for reasons better left unsaid, bent on the destruction of
all other life. They speed away from their planet in various
deliberate & random directions to seek out new life, solely
that they might “blow it away.”
5) Thus, there are an infinite number of aliens coming at us
right now who are going to kill us.
6) The problem is they’ve already been coming at us since the
dawn of history—indeed, an eternity prior to that—but
we’re not dead yet.
7) So somewhere, indeed everywhere, there must be an infinite
number of good aliens preventing the bad ones from
getting here.
8) Such a line of defense is only possible, however, if Good
always triumphs over Evil; since if Evil were even to
win a single battle out of a billion, there would still be an
infinite number of bad aliens that would get through, and
we should be dead.
9) And so on…
All this leads us to your ultimate conjecture, “Everything that can happen has happened,” which though quite profound, is, I’m afraid, only a start. (Actually there are at least several models of reality which fit this assertion, although few satisfy me and none of them is easy.) If, as is likely the case, your conjecture is derived from a belief in infinity, then it is also likely you will, in your relentless pursuit, hit two separate & inevitable walls, both of which result from simple human limitation. The first is a problem of means: So what if a billion zillion future Phus dangle like apples from the tree & branches of the universe, ripe for the picking? If you can’t reach them, they’re irrelevant. The second problem is actually harder, for it involves discrimination: Suppose you do find a way to hit any (but not all) of these parallel worlds. Which ones do you visit? How do you know, for example, that the future world you visit holds the same future you’d find back on this one? What can you bring back from your travels? Do you bother to come back at all?