An Open Letter to Alain Badiou

Greetings Badiou!

I have recently picked up your book, Being and Event, and I am finding that you and I have been thinking about a number of things in similar ways, though you have been thinking of them in the way you have for the last 20 years or so and I have only been alive a little bit longer than that. It's funny, I keep finding out that everything I might set out to do has already been done in one way or another by somebody else. This is the only way philosophy ever proceeds I suppose, and in fact my current project is in so many ways an attempt to show in fine detail that there really isn't anything new under the sun, at least not anything new that we are inclined to care about: we've all been playing the same game of moving from the 'natural' perspective to the 'philosophical' or 'enlightened' one and it has always had roughly the same rules. They are just really difficult rules to explain to someone who has not yet mastered some of those rules themselves.

In any case I have been thoroughly enjoying your work so far, but there is one little tid-bit that I might pester you about. Much of your system seems to rely on the understanding that the null-set, the void as you call it (or as your translator has you calling it anyway, the logic is clear enough what you mean), is unique. It is the name of being, as you say, and as it can not be differentiated, there can be no difference between one void and another. On this point, sir, I must beg your pardon.

I should point out that I have not finished your work, and I have not taken the trouble to do an exhuastive search of the records, so if this question is answered in some satisfactory way in another place, I do apologize for my own blindness with regard to the vast sea of publications.

In pure set theory, as operated on by mathematicians who are blind to the ontological signifigance of their work, there is no worry about the uniqueness of the empty set. As you point out, it is the axiom of extensionality that actually proves the equality (and therefore replaceability) of any empty set with any other. This is, my friend, a far cry from uniqueness. The problem is one concerning the universe of discourse. In pure set theory, there is no universe of discourse at all. There are ony symbols and rules of symbolic manipulation. Mathematicians (in your understanding of mathematicians, which is just to say the mathematician qua mathematician, no worries about any actual human beings here...) play set theory the same way that a computer plays chess. Just bumping around in the possible manipulations of the various symbols given the rules they have for manipulating them. But when we make the meta-ontological jump, as it were, and start assigning meaning to the symbols in play, now we have a universe of discourse to take into account, and you have been none too explicit about this, which I believe may have you painted into a bit of a corner. You see, given a particular universe of discorse, some set is null with regard to it so long as no element of the universe of discourse is a member of the set. So if we are looking at the set of all vehichles manufactured in the USA and Japan, the set whose members include and are limited to you and I would be null. It would not be absolutely null, of course, but relatively null, with regards to our particular universe of discourse. Within that universe of discourse, many many sets that are not identical could only be treated as identical and as the void itself. This is all well an good, you might say, since you are dealing with the absolutely null. The truely empty set. The set which has no members. And I want to say: under what interpretation, my friend? What is or universe of discourse?
I see two possible answers. The first is that the universe of discourse just is the null set itself. This is not a bad answer: if our universe of discourse is in fact empty, then our set theoretical operations on various permutations of the empty set will be very close to the sort of operations that mathematicians perform. I believe that your answer would almost certainly be something along this line. This gives us an interpretation of the theorems of set theory as operating on that which cannot be presented. The problem is, it does not yet gurantee the uniqueness of the empty set in question. Having our universe of discourse limited absolutely to the empty set itself only locks us into the possibility that our universe of discourse is empty relatively, which would imply the possibility of an alternate interpretation, perhaps inspired by some event (I am actually hoping this is where the book goes, though I am nt sure yet. If it is, you can keep quiet and not spoil the suprise, and I shall turn out delighted if the event is in the end just exactly the finding out that what was termed the void was actually full in some way.... but I have my doubts about you) in which our empty set is only empty relative to some universe of discourse that is not exhaustive of all of being.

I suspect that it might seem that I am missing the point. Ontology presents presentation, and cannot present the unpresentable. Agreed. The unpresentable must be that which ontology operates on, to sho the presentation of the unpresentable in all its unpresentable glory. Doubly agreed. The unpresentable will forever appear within any given interpretation as identical. Thrice I nod. The void is unique. Now we part ways. The only way to gurantee the absolute uniquness of the void is to have it be null, not with regard to some limited universe of discourse, but to be null with regard to the absolute universe of discourse: the multiple of all multiples, the set of all sets. This set is forbidden in set theory, and you follow that forbiddence. I do not blame you. To allow the set of all sets, the multiple of all multiples, is to invite paradox on paradox, contradiction upon contradiction. It is pandoras box, to be sure. But either the null set is only null with regard to some limited universe of discourse and is therefore not necessarily unique, or the null set is the absolute void, in which case our universe of discorse is the set of all sets.

I propose that it must in fact be the case that set theory must operate in this second, terrifying way. Every arrangement of the symbols of set theory that is well formed has the same sort of being as any other, including sets that are 'too large' for set theory to handle, such as the set of all sets that are not members of themselves. Set theory must operate on these sets in one way or another, and the first operation it does on the troublesome ones is to kick them out of the city. To lock them away, hide them from view, and make sure they don't muck up the game we are playing. We play our game of theorem derrivation, of proofs and su-proofs, on a tiny island of logic in a vast sea of chaos, filled to the brim with sets we just cannot bear to bring ourselves to think about. Their very names strike fear in our hearts. Foridding them is akin to forbidding some possible move in a board game. Perhaps some opening always is discovered that always leads to a win, and so we forbid that particular opening in order to continue playing the game in an iteresting way. Forbidding the self contradictory sets is much like that. We could allow them, sure, but our game would be broken, we would no longer have reason to play. So instead we lock them in the mad house, mumble about their madnes here and there, and go about our lives in the walled city, perfectly content that we are protected from their ever ruining our fun. But we can only forbid them in the first place, we can only lock them up because they are there for us to see. Our universe of discourse in any symbolic system is always primarily the set of all possible strings of symbols, from which we then cut out a tiny slice called the set of all well formed formulas, which we then cut down in size, often to as close to nothing as we can get. To a few axioms perhaps. From there we take our building blocks and start to play our game, and if ever we find that we have built a mad-man, we must tinker with our tools so that such a construction is no longer possible, and we must lock him away as an example to those who might forget why our axioms are shaped the way they are.

We must never forget that we built the city we live in, and that no matter how large it grows, there will always be a wilderness outside of it, and within it, there will always be the possibility of mad men. To overcome either of these difficulties entirely, to overtake the wilderness or to lock away every last madman, would be to end the game. It is sometimes the dream of logic to make that final move, but our goal more often is simply to make sure the game stays interesting, and keeping both the threat of the wilderness and the mad alive is a part of keeping the thrill of the game alive.

I look foreward to reading the rest of your book, and perhaps someday its sequal.

Good day!

A Space for Time (I & II & III)

Einstein's General Theory of Relativity introduced the world at large to a concept we lovingly (or sometimes terrifyingly) know as Space-Time. This was a fundamental change in our understanding of time, which up until then had largely been thought of in a way that was radically separate from our concept of space. For Kant, for example, Time was the pure form of inner sense, and Space was the pure form of outer sense: the two were entirely separate, divided by a boundary harder than diamond. In our everyday life, space and time seem different enough to warrant such a hard division, though we are all comfortable with metaphors that cross over the line. We think of a long stretch of time for example. Einstein's insight into time as another dimension of space, the fourth dimension in particular, can be thought of as simply taking spacial metaphors for time seriously: no longer is it metaphoric to think of time as a dimension of space, that is the way things really are. The time-line is the most common way of thinking of time as a dimension, and if we have done much graphing in the Cartesian coordinate system, we are used to thinking of the x-coordinate as the dimension of time, and the y-coordinate as a single dimension of space. Most of us have at least dealt with that kind of graphing a little, and so thinking of time as a dimension, thinking of time-lines as a real sort of space, doesn't tend to strike people as quite the crazy idea that Space-Time might have once seemed to be. (Of course, relativity itself is still pretty crazy, but we're not going to worry about any of that right now: We're only concerned with Space-Time here.) The time-line, as a picture of time as a dimension of space, is in particular a picture of Diachronic Time. Paul Ricœur, in his Time and Narrative, makes a distinction between this diachronic time and Synchronic Time, which is what Heidegger called Authentic Time . The distinction between diachronic (or inauthentic) and synchronic (or authentic) time goes something like this: diachronic time fits perfectly well on a time-line, with the present moment as a single point, an instant, somewhere along the smooth and continuous line, with the past stretching out behind and the future stretching out ahead. But synchronic time, which is the lived present, does not fit this picture so well: authentic time has a special privilege of the Now, as a tripartite moment. The Now retains the past within itself, and projects itself into an open future. For synchronic time, the present moment contains the past within itself, and that past moment (as it is present in the current Now) contains the present moment as an empty possibility of the future. There is a similar structure for the future as it presents itself in the present Now, and it lends the present now a character of "being already past" just as it has a character of "having been future". Synchronic time then has a sort of fractal structure to it: The present moment contains within it the full past as a sort of crystalline structure of previous moments, (each of which has a similar structure to the present Now), as well as an opening up to an empty future that is anticipated as having the same temporal structure as the present Now, but not yet being filled. This synchronic, authentic time then is poorly represented by the time-line. The time-line lacks any kind of fractal structure, and points along it are seen as being simply divisible. Spans of time are seen as just collections of instants, and instants are completely unique, separate grains of time.

What I intend to do, in the following little labyrinth of proofs and arguments, is to describe a space that would fit the structure of synchronic time. There are a number of concepts we need to understand in order for the space to make sense, so I will go through those first, and then combine them in such a way as to have a space in which we could imagine synchronic time as spacial, as an authentic space-time.

Part I: Cantor and Infinities Bigger than Infinity

To start with, we're going to go all the way back to Georg Cantor's proof that there are different levels of infinity, or as he called them, different cardinalities. (As it turns out, Cantor is pretty much essential to this whole argument, as he came up with one-to-one correspondence as well as cardinality, and I make some pretty heavy use of both of those concepts here.) First it is clear from the start that there are an infinite number of counting numbers: it is impossible to imagine a number that one counted to that one could not continue counting from. This is a round about way of saying that starting from 1, if you count up by whole numbers, 2, 3, 4, 5 and so on, you'll never reach a stopping point. [The round about phrasing is to avoid the phrasing "it is impossible to imagine a number which could not be counted beyond" as there are in fact infinite numbers, and counting from or to them is impossible, but then we're getting off track.] So we have our first sort of infinity, the infinity of the natural numbers. We can then call this natural or countable infinity, and any infinite set that can be systematically numbered with the counting numbers will be said to be countably infinite.
There are a lot of countably infinite sets of numbers. For example, the even numbers are countably infinite, 2, 4, 6, 8..., as are multiples of three and any other set of multiples. While it might seem at first that there would be fewer multiples of two or three than there are counting numbers in general, it is not terribly hard to see that one can set up a one-to-one correspondence between the counting numbers and any set of multiples of some given counting number, and that given any counting number, one would be able to decide where in a list of all of the numbers you could find its counterpart among the multiples by multiplying by the number in question. For example, if I wanted to know what the 56th even number is, I just multiply 56 by 2, to get 112. So 112 is the 56th even number. This process can also be reversed, and so one can find out which place in line any given even number is in. The same holds for multiples of three or any other countably infinite set.
Now, looking for a set of numbers that is not countably infinite is tricky. We might start by thinking of the integers, because we would be doubling the number of numbers we have. But then just like the even numbers and the counting numbers, it is not hard to line up all of the integers in a row if we only alternate back and forth between positive and negative numbers: 0,1, -1. 2, -2, 3, -3, and so on.
Rational numbers, also might seem to be a set that is bigger than the counting numbers, and it is hard to see how one might go about numbering them all for there are an infinite number of rational numbers between any two counting numbers. So between 1 and 2 there is 1 1/2, 1 1/3, 1 1/4 and so on, and that's just the numbers with a 1 in the numerator. But we can get kind of tricky with how we organize the rational numbers and then we can line them up one-to-one with a list of counting numbers no problem. The way that I have seen this done time and again goes this way:

0 1 2 3 4 5
1 1/1 2/1 3/1 4/1 5/1
2 1/2 2/2 3/2 4/2 5/2
3 1/3 2/3 3/3 4/3 5/3
4 1/4 2/4 3/4 4/4 5/4
5 1/5 2/5 3/5 4/5 5/5

We arrange the rational numbers in a chart like the one above: it shouldn't be too hard to see that this chart can be extended infinitely to include every possible positive rational number, and since we know that adding in the negatives isn't troubling, that's enough for now. Now we just need a way to work through the chart systematically to get all of those rational numbers into a line so we can count them and decide who is first and who is second and so on. We so this by going through in successive diagonals, starting from zero and working our way down. There are a few decisions to make (do we zig zag? Go just one direction over and over? Which direction?) but once we make them we get a nice list of rational numbers that will include them all in a way that lines up with the counting numbers without problem. To demonstrate, we could proceed this way: 0, 1/1, 2/1, 1/2, 3/1, 2/2, 1/3, 4/1, 3/2, 2/3, 1/4.... and so on, each time moving from the top right to bottom left, and proceeding across the top row one number at a time. So even though there are infinite rational numbers between any two counting numbers, we can in fact line up the rational numbers to be counted, so they are countably infinite, of the same cardinality as the counting numbers.

Which brings us to the Reals. Real numbers include numbers like pi, the square root of two, e, and such. They are numbers that are not necessarily representable by a given ratio, but perhaps only by an infinite sum of ratios (this is what the decimal notation of a real number really represents: pi is 3.1415.... which means pi is 3 + 1/10 + 4/100 + 1/1000 + 5/10000 + etc etc). Many many (so, so so many) real numbers then are not yet represented by either the counting numbers or the rational numbers, though those numbers can be included among the reals. It can be troubling to think about numbers that "go on forever", even if we do acknowledge or (dare I say) understand that numbers like pi or the square root of 2 are numbers that are like that, but we can just think of them as being represented by unique sequences of the digits 0-9 that have no termination. This is in fact what Cantor thought about when he did his proof, so it will work well enough for us. Just as it is easy to see that there are an infinity of counting numbers, it should be easy to see that there are an infinity of infinite ordered strings of the digits 0-9. In fact, as a string of numbers gets longer, there are more and more possible strings: for a single digit string, there are 10 possibilities, for two digits 100, for 3 digits 1000 and so on. So if we imagine the set of all possible strings of numbers, including infinite strings, then we are in the same head space as Cantor when he discovered an infinity bigger than infinity. Cantor argued like this:
Say we could make a list of all possible strings of the digits 0-9. Like our list of the rational numbers, this would mean that we would have a complete one to one correspondence with the counting numbers for the set of all strings of numbers. But if such a list existed, it might be possible to construct a string that was not on the list at all, which would mean that the list was incomplete. Cantor's method for constructing such a number works like this: since we (hypothetically) have our list of strings, we just start at the top and work our way down, constructing our string of digits one digit at a time, but making sure each digit that we add is different from at least one digit of at least one string on the list. So we start with our first digit, and we look at the first digit of the first string on the list. Whatever that first digit of that first sting is, we pick a different digit for our magic number. So now we have a one digit string that is different than the first string on the list. Then we look at the second string on the list, but we only look at its second digit, and whatever it is, we pick a different digit for our second digit. Then we have a two digit string that is different from the first and second strings on the list. We move to the third string and look only at its third digit, and so on. This is what is called the diagonalization proof, as we proceed down the list of strings diagonally, differing one digit at a time from every string on the list. We can see that no matter how the list is arranged, it cannot have our number on it, for our number differs in at least one place from every number on the list. So no matter how we arrange a list of all possible infinite strings of digits, we can never complete such a list, and it will never have a one-to-one correspondence with the counting numbers.
This is to say that there is an infinity bigger than infinity. We can see now that while both the counting numbers and the set of all strings of digits are both infinite sets, the second set is bigger than the first, and so we say with Cantor that it is of a higher cardinality.
This is a mind warping concept, and its implications are staggering. But it is also proved beyond the shadow of a doubt given the concepts of number and infinity. And again, so long as we can count, we have both of those concepts. So anyone that can count already has the ingredients in their head for this infinity bigger than infinity. Which is already pretty crazy.

Briefly then before we move into bringing together space and number, we should note that there are a countably infinite number of primes. This is proved by the following: Say there were finite primes, and you knew them all. Multiply them all together, and then add one. You will now have an odd number that is not a multiple of any of the primes in your list. So if there are finite primes, there is at least one more prime. So there are infinite primes. And since the primes are a subset of the counting numbers, and every prime is finite, we know they are countably infinite.

With that, we turn to the application of number to space.

Part II: Numbered Space

A: Squeezing Space Into Space

The Cartesian Coordinate System gives us a way of pairing up numbers (whether just the counting numbers, or the rationals, or all the way up to the reals. We could get real crazy and throw the imaginary numbers and other sets in too, but none of that needs to concern us right now) with points in space so that every single point in a space corresponds to a set of numbers. The most familiar variant of this system is the one with two variables, nearly always referred to as x and y. The x-y plane gives every point of space within an infinite plane (that is oriented about a center we call the origin) a pair of numbers that identify it uniquely (e.g. (0,0) is the origin, (1,1) is a point directly northeast of the origin (at a distance equal to the square toot of 2) and so on) and, when we are working with the reals, there is no point within the plane that does not have its own unique pair of numbers to identify it. The real coordinates completely describe the plane, they match up exactly with every point in the space.

We should pause here and note that Descartes' coordinate system is a monumental achievement in the history of ideas. We have in it a link between space and number. With his system, we can easily translate numerical relationships into spacial ones, and (with somewhat greater difficulty) create numerical relationships that correspond to spacial ones. Descartes' coordinate system allows us to graph, to draw out, to make visible, relationships of number that lie hidden from obvious view in an algebraic system. And it allows us to take spacial relationships and turn them into relationships of number, algebraic equations can be derived from a particular curve, cluing us in to variables, hinges of one sort or another, points of interest or importance that would otherwise be invisible to the naked eye. With Leibniz and Newton's calculi then, we find that the smooth continuity of space can be captured in numerical in numerical relationships. They bring the infinitely divided into the realm of number, and in doing so make it clear just how tightly the realm of number and the realm of space can be. It is by thinking of time as a kind of space that this numeric-spacial system is brought to bear on the world as a whole: modern science consists in large part in fitting numerical and spacial models (which are one and the same thing after Descartes, reinforced by the Calculus) to the data of the natural world. The smooth continuity of the real numbers are brought to bear on the dynamic, temporal relations of the natural world and presented to us in terms of static spacial relations. The arc of a ball thrown into the air becomes a static parabola, its changing speed a simple angular line, and its negative acceleration becomes a constant number which represents the ever present force of gravity that determines its curve through the air.

And here's where the properties of the reals begin to get interesting. Because every point in the plane can be represented by a unique pair of numbers, it is possible to encode the entire, infinite plane within a finite line segment. This can be proved in the following way: say we want to encode an infinite plane of two dimensions within a line segment that consists only of all of the points along the x-axis between x = 0 and x = 1. To accomplish this squeezing of the entire plane into this piece of a line, we need a way to encode the coordinates of each point into a single number. That this can be accomplished is a direct consequence of Descartes' coordinate system. Since every point can be represented by a pair of numbers, we only need to construct a unique real number for each pair of coordinates, and make sure that each number is less than one but more than zero. To do this, we first convert our coordinates into binary. This is non-problematic: any given number can easily be converted from one base to another. 11 in binary is exactly the same thing as 3 in base ten, and it is also the exact some thing as 10 in base three. The base system determines the way we name a given number, but it does not change the number in any way. Decimals and real numbers can be handled just as well in binary as in base ten. So: now every point in our plane is given by a unique pair of real binary numbers.
Now what we do to get those two numbers to become one is interlace their digits. This will best be explained by an example. Say the pair of numbers we want to turn into a single number is the point (1101001.1101, 11011.1). We construct our unique new number by placing each digit of the x-coordinate in a place in our new number that is the next successive even digit, and we place each digit of our y-coordinate in the next successive odd coordinate. So our number will begin this way: 0.11110011010 and then we hit a hitch: we have a decimal in our y-coordinate that needs to be represented somehow. But since our new number does not have to be binary, we can just represent the decimal by the number 2. So then our complete new number to represent this particular point in space will look like this: 0.11110011010211201010010000000000000000.... This is a unique real number that symbolizes a single point in the x-y plane. We can decode this number by pulling out our digits one at a time and placing them in order in the x and then y coordinates, which will get us back to the point we started with. It is also true that if you put an even number of zeros in front of our new number, it will encode the same point (eg. 0.00001111001101021120101001000....), and so there are in fact an infinite number of numbers between one and zero that encode this particular point in the system we have set up. And that is true for every point within the space: any given point that is given by a pair of real numbers (which exhausts the x-y plane) can be encoded in this way to become a unique real number that only encodes a single point. And so we have fit the entire infinite x-y plane into a finite line segment.

In fact, this sort of transformation is a necessary condition for the possibility of computers. We must be able to reduce spacial relations into particular strings of numbers in order to do any sort of computation involving those relationships. The method I have described is not at all like the methods used in actual computing, but we can do a lot of things with computers that are possible only with finite strings of digits, and I am here working outside of the finite realm. I could have made an effort to match in one way or another the sorts of processes that are used in computer science, but so long as my method makes any sense at all it was not necessary that I confine myself to those patterns. There are an infinite number of ways to do the sort of encoding I am discussing here and each of them demonstrates equally well the point I am trying to make: a relation that consists of a set of pairs of numbers can be equally well represented with a set of individual numbers. This is to squeeze a plane, a two dimensional space, into a line, a one dimensional space.

But what if instead of the x-y plane we were dealing with the x-y-z space? Or even some higher space? With a slight modification of this method, we can encode a space of any number of dimensions (even an infinite number of dimensions, though only a countably infinite number). This is possible thanks to the infinity of the primes: rather than giving each digit the evens or the odds, we divide up our digits by prime powers. So for a 3 dimensional plane, we would only use the digits in the places numbered by the powers of 2 (the 2nd digit , 4th digit, 8th digit and so on), the powers of 3 ( 3rd, 9th, 27th...) and the powers of 5 (5th, 25th, 125th...). This will result in a number that consists mostly of zeros, but it will encode any number within the x-y-z space, and will have room for any number of dimensions you want to add into it. This means we can encode infinite space of infinite dimension within the real numbers between one and zero. All Possible Space, in a little line segment. And when you get right down to it, we didn't even use all that much of the space we had.

So this is fine and dandy, but it still leaves something to be desired. A line segment is still a space of its own, so it doesn't seem quite totally ludicrous that we fit all the space in it (not as ludicrous as things are about to get anyway). We can see, even, that it would be possible to fit all of this space in smaller and smaller portions of the line segment: just throw a whole bunch of zeros at the front of every one of your numbers: presto! Now you're in a much smaller space! But then any portion of the line segment, we can see, is infinitely rich. Any portion of the reals has the same sort of cardinality to it as the reals as a whole have. But what about a single point along that line. Would it be possible to encode all of the space that a line segment has within it (which is rich enough to encode all possible space) into a single, solitary point? Into just one real number?

B: Squeezing Space Into Number

Yes. Well a single point anyway. Though our number might not be a regular real one. It looks like we're going to have to take another step into the wide wide world of numbers and use a hyper-real, or an infinitesimal. A hyper-real is a number that is bigger than infinity. And infinitesimal is what you get when you divide one by a hyper real. As it turns out every infinitesimal is 'very close' to some particular real number, so in what we're about to do I like to imagine that we are working with a particular infinitesimal number, which would then be a given point along the number line. This point will be located in a one dimensional space then, but the point itself, as a particular number, will be of zero dimensionality. We are going to be thinking a lot about the numerical expansion of this particular infinitesimal, and we should not confuse the numeral with the number, but we should remember also that the numeral corresponds to a particular number. There will be some discussion of complications surrounding these issues at the end of the section.

What we are going to do here is look at a construction of an infinite series of digits, but the way that series of digits is arranged necessitates that we have an uncountably infinite number of digits. This sounds kind of crazy, but so long as we keep things well ordered then it won't be so crazy as to be meaningless as we will retain the ability to differentiate our number from another. The important thing is to get every single infinite string of digits that would serve to represent a real number between zero and one into a single well ordered string of infinite digits. If we do that then we have a single string of digits (which then has the same sort of being as a real number, even if it doesn't quite qualify as one) that includes within it a representation of every real number (we're just going to deal with reals between zero and one, but that's just as many as all of them, thanks to the craziness of infinity) and so then based on what we've said above this string of digits could encode for every possible space of countably infinite dimension. This can be done.

We can show this by the following: we are going to start, much like Cantor did with his list of all the reals, by assuming that we have a representation this number already. We (hypothetically) know that we are looking at it, and we are going to refer to this behemoth of a number by the symbol B. Now we just need to show that there is a way to find within our numerical representation of B, which is an infinite string of digits, a representation of any given real number. To do this, we need to know some properties of B:
First: the numerical representation of B that we are dealing with consists only of the digits 0,1,2, and 3.
Second: Every real has been encoded only in binary: just using the digits 0 and 1. When we look at B, any place we see 0's and 1's is a particular real being encoded.
Third: the 2's and 3's in B are called signposts and are a kind of guide. They are to be understood as a second kind of binary in which a 2 is a zero and a 3 is a one. So for example the number three (normally 11 in binary) would be represented by 33, the number eight (normally 1000 in binary) would be 3222 and the number zero would be a single solitary 2.
Fourth: Each signpost number is surrounded to the left and to the right by a unique infinite sequence of 1's and 0's
Fifth: The solitary 2 representing zero in our secondary type of binary occurs only once within B. Thus out of the possible sequences 121, 120, 021, or 020, only one of the four can be found in B, but one of the four must be found.
Sixth: to the left of the 2 that is zero there is exactly one occurrence within B of the solitary symbol 3 bordered by 1's and zeros. So either 131, 130, 031 or 030 occurs just once to the left of the 2 that is zero. The same is true to the right: the solitary 3 occurs just once to the right side of the 2 that is zero.
Seventh: Now, counting upwards in signposts, our binary made of 2's and 3's, we find to the left and to the right of each signpost an instance of the next higher number that can be found without moving past any signpost of lower significance (from the right hand 3 for instance, there are two instances of the symbol 32 to the left, but only one of those is to the right of the 2 that is zero; the other is the 32 that is to the right of the left hand 3).

We can get an idea of the organization of B by looking at this fractal:



Looking at this picture, we can think of this fractal structure governing the construction of B. If we were to draw a horizontal line across the centers of the circles and then think of that line as the numerical representation of B, each place where a circle intersected the line would be the location of a signpost number consisting of 2's and 3's, and and space between would be filled with 1's and 0's encoding our real numbers.

Now: we find any given real between 0 and 1 (encoded in the binary of 1's and 0s) in the following fashion: Let 1 signify the left, and 0 signify the right. Starting with the first digit of the real in question, we ask: is this digit a one or a zero? Now, from the 2 that is zero, we make a decision about which signpost to traverse to based on that first digit, if it is a 1, left, if it is a 0, right. At each signpost we arrive at, we check the sequence of 1's and 0's to the left and to the right of the signpost we have just arrived at. That sequence will begin (from the signpost, reading to the right as normal on the right, but reading to the left if not) with the sequence we have used to decide our course so far. If either of those sequences is the real we are looking for, then our journey is complete, otherwise, we look to the second digit to decide which direction to move in to navigate to our next signpost.

Looking at the fractal image above as a symbol of B, we can think of ourselves as a traveler in a branching tunnel. We have in our hands a particular real that we are looking for, and it serves as its own address within B. It is a map to its own house, in a way. The series of digits in the real we are looking for guides us through the tunnels until we arrive finally (perhaps after an infinite number of choices) at exactly the real we were seeking.

So then: B is a string of digits that can be found in a representation of a hyper-real number (since a given hyper-real has an infinite number of digits) and which contains all possible reals.

C: Wait, really?

This should strike us as immediately problematic, since a given real can only have a countably infinite number of digits, and it is clear that B must have an uncountable infinity of digits. But: the place within B that we find any given real will not be given by a digit that can be counted to, since there are an infinite number of digits between any two signposts within B. And so we are dealing with an uncountably infinite strings of digits. If we were to attempt this sort of trick with a normal real number, we would have to start from the beginning of its numerical representation and just count out to the right until we find the real we are looking for which would be impossible even if the reals were countable: we would never get past the first real number we got to. B then cannot be located within itself, as it cannot be given (as the reals we are used to can be given) starting with its first digit and moving one digit at a time to the right until all its digits are accounted for. B contains a real infinity (rather than a countable infinity) of digits. B should be considered to be a hyper-real, or an infinitesimal rather than a real. In either case, its numerical representation is a well-ordered infinite sequence of the digits 0, 1, 2, and 3 and so should be considered the representation of a unique, particular number without any more qualms than the numerical expression for square root of two or pi or any other real is considered to correspond to a number. That our normal system of naming reals is inadequate to name B is no surprise: there are even an infinite number of reals that can not be indicated in any finite way. Certain reals, the ones we are familiar with, like pi, e, the square roots of non-square numbers and such, are special and interesting because they are real numbers that seem to contain infinite information, but can be indicated precisely with a finite, ordered symbolic sequence. Or a picture of a particular spacial ratio, more often than not. But besides these reals that can be easily indicated in any number of ways by a finite sequence of symbols or a picture of some particular spacial ratio, there are an infinite number of reals that cannot be so indicated in their particularity, but only suggested by a sequence of digits understood to go on forever. The number 5.829864321987653287432873487653932083.... cannot be said to have been given in its entirety, and indeed, if that is to be understood as a particular real, it implicates in fact an infinite field of possible reals, even if we only mean by it a single number from within that field.

There is no systematic way to name every real. And while every real can in fact be symbolized by an infinite sequence of digits, that in no way guarantees a finite symbolic pattern that will identify any particular real: in fact if there were for every real a single finite symbol sequence that could name it in particular, we would have a situation similar to Cantor's diagonalization proof, unless by some strange magic we managed to have a symbol set that was as rich as the reals. Such a symbol set can be imagined, perhaps, but to decide from a given symbol from it into the real it corresponded to would take an infinite amount of information: such an alphabet would be entirely unreadable. And so B is just a particular number (or if we want to be quite careful, B as described could be any one of an entire class of numbers) that fits the description above. It is the case that there are a number of arbitrary choices that had to be made in our construction of B: each of these choices could be made differently, resulting in other numbers that share the wonderful property of B of encoding every real between zero and one and thus encoding in turn every point in an infinite space of countably infinite dimension. There is a real infinity of such numbers, and numbers that fit our description of B represent only the tiniest slice of them.

B can then be thought of as a single point of zero dimension (to be found in a one dimensional space), just as much as any single number is without dimension, that encodes the full richness of the reals, which then in turn encodes the full richness of infinite space of infinite dimension.

It is true that B does not encode itself, or any other hyper-real or infinitesimal. Three brief notes before we move on any further:

1) That a coordinate system with real numbers exhausts every bit of space that can be meaningful might not necessarily mean that it exhausts every bit of space. Thinking about hyper-reals and infinitesimals can sometimes appear to be the same sort of thinking involved in trying to answer the question, "How many primes are blue?" Since the real number system is already beyond sufficient for any possible science (since we can only ever deal with finite representations of numbers, the rationals will do just fine, thanks, and anyway it's looking more and more like we live in a pixelated universe, so let's just cut the worry about smoothness and continuity right?) it seems to be worthless to explore any sort of number that might still lie outside of that system, and indeed I have known a professor or two that was unwilling even to admit the reals themselves as legitimate numbers. Wittgenstein himself felt that set theory had just pretty much rotted everyone's head it wriggled into (though he never said it quite like that, his feelings on the matter were strong enough). But the fact of the matter is that these sorts of consequences are necessary conclusions of some very simple assumptions that we just don't want to abandon under any circumstances. Such as 'there is no biggest number'. And we could try to avoid any direct reference to infinity, but we would have to give up calculus or start thinking of it as just a fancy method of estimation, and you're going to have whole leagues of scientists and engineers up in arms if you try to send them back to the dark dark days before Leibniz and Newton came along and treated infinity as unproblematic.

2) Whether or not you want to run with me on this whole B is a number thing, it should at least be clear that whatever you can fit in a line, which can only be understood through a synthesis of all of the individual points in the line, can be gotten out of a single point understood in the proper way. It's not so much that it has to be a special sort of point as that we have to have a special sort of way of looking at it. The way we name it (the way its numerical expression is organized) and the relationships we look for in its name are choices we make, but the possibility of making those choices, e.g. the logical space necessary for encoding an infinite field of infinite dimension, is already given by the simplest assumptions about the relationships of space and number if we are only willing to follow out the consequences of those relationships.

3) As Godel's famous theorem also shows, things that represent systems of number will always be in some way inadequate of completely representing themselves. The field of number swallows up any unification made of its field into an even greater field not yet represented. But any field of number that cannot in fact be completely explored within a particular representation of natural numbers (say the real numbers or the hyper-reals for instance) can be indicated within that system with finite strings of natural numbers just as much as it can be represented within natural language or natural minds. What I mean is this: B cannot encode itself in the same way that it encodes the reals, but so far as everything I have typed here is captured by a string of data that consists of 1's and 0's, B will contain a representation of everything said here, and moreover, so far as a logical language can be represented by numerical relationships, and so far as numerical relationships can be represented by logical relationships, and so far as any logical argument or proof will always be given in a finite sequence of steps (even steps involving the idea of infinity), every logical relationship, every truth of mathematics can be encoded within a number like B, including a rigorous proof that B cannot contain a complete representation of itself. Laws of infinity can be given within finite symbolic strings. A proof of the infinity of the primes, for example, or the infinity of the natural numbers, does not require infinite steps. Infinity is a completely negative property, it is established by the absence of walls, rather than the positive being of anything in particular. And so while B cannot represent itself, or other numbers of its class, with the same completeness with which it represents the reals, it does capture every truth about itself that can be gotten at in a finite way, and a number of things that can only be gotten at in infinite ways.


We should also, finally, note that if we look only at finite strings of binary data (and living in the digital world we all are well aware of the enormous power of finite strings of binary data) it would be sufficient to construct a single real number to contain every possible sequence of 1's and 0's of finite length. This could be accomplished by simply counting in binary. 0.011011100101110111... A number of this type already contains within it every possible string of 1's and 0's that is not infinite, and is a definite real number located on the number line just as much as pi is. Such a number, thanks to our understanding of encoding information in binary data, contains within itself every book that could ever be written, every photograph that could ever be taken with a digital camera, every piece of music that could make its way onto a digital music player, every film that could ever be shown on a digital projector, any conceivable computer program, including incidentally a number of programs that would only function with an infinite number of lines of code, so long as those lines of code could be generated by some finite algorithm. If we were content with discreet data, and unconcerned with the smooth and continuous, such a number would do just fine for our purposes, and those of you feeling woozy about B can just imagine everything I say from here on out just deals with this one little real number rather than the whole lot of them. Many of the consequences remain the same, though we lose out on the sort of overwhelming quality of B's unfathomable infinity. The infinity of a real number, just a countable infinity mind you, is already stupendously, wonderfully, inconceivably large, but it can be almost easy to forget that sometime, having seen so many infinite sequences truncated after the 7th or 8th member. And so B both gives us the wonder of the smooth and continuous, and it also overwhelms. These two aspects I find stylistically important for what is to follow. But if you're just not going to stand for such ridiculousness, I hope you will at least grant me the real number which contains every finite binary sequence. With that we should be able to at least make due.

It is my intent now to show that synchronic time requires a space that is something more like B than like the number line.
We will examine that and some other possible weirdness indicated by the existence of B in Part III.

Part III: Moments of Time

So now that we've slogged through all that, we can come back to the question I opened all of this up with, the search for a space for synchronic time. My claim at this point is that it makes a certain sort of sense (the same sort of sense as thinking of a timeline as diachronic time) to think of B as a particular moment of synchronic time. The immediate temptation is to think of the 2 at the center of B as the present, with the past stretching out in one direction and the future stretching out in another, but then we would be left in exactly the same sort of position we are in with the timeline, albeit with the present moment having the special quality of being in the center. But that isn't really all that interesting. We could have just had a timeline with NOW at the center and that would have done just fine. No, the special thing about B is that it exists in a sort of crystalline state, without change, all of it at once, its complete ridiculous massive infinity. And that all at once contains within it the full possibility of every spacial relationship that can be captured by ordered sets of real numbers. If you arn't terribly into science that might not sound like all that much, but if you stick with me we might get somewhere. That every point within any given space of countably infinite dimension can be found within B also means that every relationship of points with such a space can be found. A sort of Kantian way of saying this would be that B contains within it all possible pure forms. Relationship of any sort is can be found with B.

To make sure we don't get too starry eyed: To get any particular relationship out of B one needs to have a way of translating B from numerals into whatever sort of matter you're interested in. Say you're wanting to look for color relationships, so you're going to be navigating the three dimensional field of color, and then maybe you will be wanting to put pixels of color in a two dimensional grid. To put pixels of color in a two dimensional plane requires 5 coordinates per pixel: one for each of three dimensions of color and one for each of two spacial dimensions. Looking at B then we could pull out particular reals and think of them as giving us ordered quintuplets in one way or another or we could pull a single real out and think of it as giving us a string of ordered quintuplets. By doing this we could create full color pictures by pulling out and translating reals that we find in B. In this way, because B contains every real between zero and one, we would be able to find every possible image that can be represented by pixels of color in a two dimensional plane. If we remember that software and data are digitally stored in binary, we could also see that every possible bit of software as well as every possible bit of data can also be found in B, we just need a Turing machine of some sort (a computer) to turn our 1's and 0's into something that means something. Once we start thinking about data and the vast capabilities of digital storage, we can start to think about how whole worlds could be found in B. And that's when we might start getting starry eyed to some degree if we forget that any way of translating the reals into this sort of data is going to produce almost exclusively nonsense. We find ourselves in a circumstance similar to Borges' Library of Babel, in which one can find every possible book that is 400 pages long and consists of the letters of the alphabet, commas and periods. In such a library there must exist a book that explains in detail the library itself and all its contents, but that book will only be one of countless volumes that claim to do so, and those volumes in turn will only make up a tiny slice of the vast library which consists almost entirely of completely nonsensical works. We should remember that for every world that might make sense that is contained in B there are an unfathomable number of worlds that are utter chaos, completely devoid of any possible meaning. Such is the full realm of form.

To think of B as the full repository of all form is not quite right: it only contains those forms that are representable within the reals, which is quite a lot, considering the smoothness and continuity they are so famous for, but B remains a particular representation of all the reals, of which there are infinitely many that cannot be represented within B. This is just to say that B does not contain itself, nor any number quite like it. So B is a particular arrangement of the field of smooth and continuous form. A static, unchanging being that represents countless types of change, so far as that change can be represented.

Alright: With the timeline, we have a particular form, the line, which we apply to time as its matter. The parts that make up the line, points, we think of as points of time. Now: B itself we are thinking of as a form made up of forms. It is a complete compendium of all spacial forms that can be represented by relationships of real numbers. It is only one particular complete representation of that field, of which there are infinitely many, none of which are entirely represented by B, but many of which (all those that can be) are indicated so far as they can be indicated within a logical system consisting of strings of symbols. So if we are going to think of B as a moment of time, that moment of time contains within it, in a complete, simultaneous way, all possible spacial forms arranged in a particular way. It does not contain every moment of time, as other moments of time would be things of the same sort. So it does not contain itself, nor any other complete moment of time. It contains representations, forms. But so far as time can be understood as a spacial dimension, and so far as qualities can be represented as spacial relations, this moment of time we are calling B contains within it representations of every possible (and impossible, and nonsensical, and contradictory, etc etc) spacial relation. So as a moment of time it would contain within it representations of moments of time as thought of diachronically, but it could only indicate moments of time thought of synchronically (similar to B itself) through symbolic manipulation: no moment of synchronic time could be represented in full as each is of the same order of complexity as B itself, but every arrangement of diachronic time (sensible or not) could be found within it.

Ok: That leaves us saying that this single point, this number that is represented by the uncountably infinite string of digits arranged in a fractal pattern such that every real gets its own place can be thought of as representing a particular arrangement of all possible forms, and that such an arrangement can be thought of as a unique moment of time, where another moment of time would be a different arrangement of all possible smooth and continuous spacial forms. If we're Kantians, we are going to want to say, ok, you've got the form maybe, if I allow all this craziness, but what about the matter?

What about the matter indeed. For a good Kantian, by the way, Form is a unity, a particular relationship, while Matter is a part considered as a part. If we stick with the Kantian division of Form and Matter (and I don't see any reason not to) every bit of matter is in turn a particular form. This is of course how we understand matter in the sciences at this stage: each bit of stuff can be thought of as a particular relationship of smaller bits of stuff, and it's turtles all the way down, or it's chaos at some point. But that chaos is just a formal relationship that is unpredictable, and therefore unresolvable into specific matters. We have maintained the Kantian division, and it seems to be working just dandy, so I don't see any reason to be afraid of it. Especially since it seems then that one of its consequences is that form is primary, matter is just an aspect of form, a placeholder that has not yet been resolved into pure relationship. And so far as the world can be resolved into formal relationships, it is comprehensible and intelligible, and so far as it can't, it is unintelligible and incomprehensible. If we accept then that matter either resolves further into form or that matter is merely a symbolic placeholder at bottom that only exists as a formal relation to other parts of some whole, then the world resolves into a super-complex form. So far as that form has a simultaneous existence, it can be thought of as a particular possible moment of time, or as a particular possible arrangement of forms, either of all possible forms or of some sub-set. And so the world a a simultaneous temporal totality has a form similar to B.

The question then becomes: in what way can a particular arrangement of all possible form, all possible relationship, be thought of as a moment of time? So glad you asked: within such a moment of time one will find the particular set of formal relationships that makes up your present condition, so far as that condition can be represented by formal relationships. Unless we've somehow exploded Kant's castle, the knowable universe at any given point of time has exactly this sort of being-for-us. A Heideggerian might want to stop the show here. 'Relations of Being cannot be reduced to purely formal relationships,' they might say. Well alright, perhaps that is the case, but if so I'm willing to take a step back and say that I'm not aiming at capturing anything about Being in particular, but only about our representations of Being. 'Now, haven't we found all kinds of problems with representations? And don't we want to move on from representational thinking?' Oh sure we have, and sure we do, but let's take things one step at a time shall we? We have to understand what representation is if we are going to avoid it, and there's no harm in fleshing out just one more big representation for us to avoid thinking about later on if that's what we're into. Leave me alone would you? 'But what about being-in-the-world? What about care? What about temporality? What does this have to do with facing up to your death? Didn't you mention Heidegger way back at the start? I thought this was supposed to have something to do with authentic temporality!' Alright, you've got me. I'm arguing here that even Heidegger's authentic temporality can be captured by a certain sort of representation. And it happens just when all of being shows up as having the possibility of being nothing at all. Of not-being-anything. Death for Heidegger is the ever present possibility of our own non-being. It looms. And so does B, in its way: B is a certain sort of nothing that the world turns out to be if you look at the world in a funny sort of way. All of a sudden you are reduced to a purely formal relation in a field of mostly meaningless purely formal relations that in the end are really nothing at all. Suddenly your normal understanding of time is just one representation among many. And here you are, hearing the call of conscience, your own being-here calling you through its peculiar silence. Which is the sort of way that infinity calls. By just not being anything at all. By not showing up. Infinity is a sort of absence that contains all presence. And a moment of time is a sort of particular relationship of infinite relationships. Its form is settled, we are thrown into something without having given it shape, but it is being revealed and there is always more out ahead that we have to project ourselves out into.

Let's take all of this from the perspective of a given individual: Being-here on this view turns out to be a particular arrangement of forms within a totality of possible forms arranged in some way. Either Being-here is made up of forms that can be represented by finite relationships (even an infinity of them) and can therefore be represented by a single real, or Being-here can only be represented by an infinity of infinite relationships, in which case a particular Being-here (so far as Being-here could be particular in this case...) will be made up of a number of reals that are in some sort of relation to one another. This moment of time will then be, for this particular Being-here we are considering, made up of forms that are revealed and forms that are concealed. The revealed forms, those that Being-here is made up of (Being-in-the-world here is being made up of forms, not so much being presented forms, which is more Heideggerian than say Kantian: we don't have an abstract subject presented with forms, but merely an arrangement of the world that happens to be such that it can be thought of as Being-here from our outside perspective) are arranged in a particular way such that they make up a particular being here: there is the situation, given as pre-existing, the throwness of Being-here; then there are the projects, those forms given as open possibilities that Being-here can participate in. These forms are,primordially and for the most part, arranged in such a way that they do not reveal themselves as being so arranged: Being-here is just casually involved in day to day goings on, living in thein-authenticity of the they-self (which isn't so much bad as it is incomplete). In this first and for the most part, Being-here takes for granted the forms it is presented as being something other than Being-here itself. In this mode, the forms that represent the timeline are taken to be the time that Being-here finds itself in. But, given a proper re-arrangement of things, in a certain sort of moment, Being-here can find itself presented with Being-here itself: we come to find ourselves as the particular situation we find ourselves is, thrown into a world we did not choose and opened up to a field of possible projects, including the ever looming possibility of our own non-being, death. This particular arrangement of forms is the call of conscience, in which Being-here is called by Being-here's own silence to simply be what it is. Suddenly the normal understanding of time as a timelineindependent of Being-here's existence is shown to be a mere shadow, a false appearance. Time shows up as a pure moment of unfolding, unconcealing existence. In this moment, we can imagine something like B being presented within B itself. Not of course the full numerical representation of B, but perhaps a sudden realisation of the in-finity of possible presentation. A revelation of the absolute relativity of all Being-here, as only a tiny slice of the unconcealed, very nearly nothing at all. This could take many many different forms, most of which would have almost no direct relation to B as I have presented it here, but all bearing on the looming possibility of being-nothing-at-all.

To see the way in which the call of conscience necessarily takes place as a particular arrangement of forms that shows the presentational nature of presentation is to see the way in which B can be thought of as a space for lived time. This is mired in my own take on Heidegger and so it may look at first like a bunch of gobbledygook. That's understandable. Being and Time often looks that way, and I am building weird on top of weird here. The key point is this though:

Being-here is always a particular arrangement of forms. Sometimes that arrangement of forms reveals itself as an arrangement of forms.

Hofstadter's 'Strange Loop', if one is familiar with it, could be worth thinking about here. We find ourselves finding ourselves: representation can never be fully represented as such (the seeing eye can never see its own seeing) but it can be symbolized in such a way as to reveal itself as representational. In the language of Sartre's Transcendence of the Ego, we can indicate consciousness, we can symbolize it, but it can never be a proper object of consciousness. Consciousness can not become a proper object of consciousness. There are many many ways of formulating this same idea, each of which coming down to the impossibility of a true self-representation, but the inevitability of at least some partial self-presentation. For Kant, it is the necessary possibility of the addition of 'I think' to any of our presentations. Consciousness is always consciousness-of something: it is intentional. Being-here is always situated in a world. But there are special moments in which consciousness reflects, turns back on itself, and in one way or another catches a glimpse of its own un-representationality. That particular moment, that particular arrangement of forms, is when the synchronic nature of time shows up as such. It is for that reason why a timeline is incomplete: it takes for granted the structure of moments of time in order to give their arrangement relative to one another. But the arrangement of a moment of time is of the utmost importance for understanding what we are, if it means anything to ask the question, 'what am I?'

I have an awful lot more explaining to do, to be sure, and to that end we're going to turn to Borges in the next couple parts, specifically to his stories "The Aleph" and "The Zahir", to show ways we can go about thinking about something like B, and ways that maybe we should be real careful to avoid. After some of that we will look at some of the really interesting consequences of smoothness and continuity and the various ways that they affect our thinking when we are careful about them.

Another Incarnation

So I'm reading Portrait of the Artist as a Young Man, and I've been thinking about the Dalai Lama, and the two things in my headspace have produced some interesting ideas about reincarnation.

The thing about the Dalai Lama is that reincarnation is a project that is accomplished through years of study. After being picked as the new incarnation, a Lama goes through years of study of the lives of the previous Lamas, learning just what it is he's been up to all these generations (14 now, which is quite a lot of years of history and memories to absorb while also living your own life). Whatever the case is for the infant chosen, the Dalai Lama becomes the Dalai Lama by reading his history as his own history. By appropriating the lives of those who have come before as his own previous lives, the Dalai Lama actually becomes a part of that liniage, and is in fact a continuation of a single entity. If a nation can exist for thousands of years through the lives of many generations, if a nation is a real entity, and hey, if you can exist for decades though the lives of many generations of your own cells, which exist through generations of various molocules, the Dalai Lama is a person that has lived for 14 generations now. In this sense, he is really re-incarnated. Which is knd of neat, really.

Where Joyce comes in is that his novels are such rich pictures of Joyce himself that reading them seems to me to be a little like studying up on the previous Dalai Lama. By reading his novels, we become, bit by bit, a re-incarnation of Joyce. He lives on through our absorption of his thoughts into our own. But this isn't true of just Joyce, he's just what got me thinking about it. It's true of everyone we read, and the music we listen to, and the movies we watch, and the people we interact with, and (Joyce illustrates this wonderfully) this is true for those things as well: they are conglomoratrions, tapestries woven from so many lives that came before them, intermingled with the lives that directly motivated their creation, intermingled with the lives of their viewers and listeners.

The mad man who believes himself to be Napolean Bonaparte is only mad because he thinks that he is more Napolean than anyone else. We are interpenetrated by thousands of lives of other people, living and dead, who were in turn blended with so many lives themselves. We are made of other people and we make up other people.

This also got me thinking that our creations really are our children in a similar way. What we make takes on a life of its own (as a re-incarnation of us, seperate but not seperate as the case might be) as it moves through one mind and into another, bouncing through so many heads as it changes and grows and echos again.



We are the things we create, we are the things we consume, we are the people we know, we are the places we go, we are the movements and the gestures, we are the raindrops on our face and the stars and the ocean and so many sunrises and sunsets, we are our dreams and we are the stories we tell, we are a history, we are a world.

We are another incarnation of so many things.
And so many things are another incarnation of us.

mmhmm.

more it plan

which would seem ungrammatical. But really.
Here's more of the planning for It (the first third)


it

What is?

Pitfalls:
**None/Some** Thing Thing Being Is fuckall.
right: lets not got too far there, differance and all that

WE"RE MODEL MAKING HERE, NO NEED TO WORRY ABOUT WHAT REALLY IS THE CASE THANKS!
Also: There is a science o the human mind specifically, and there are lots of people making models of it of various sorts. Their work is all well and good and I'm not out to say they're wrong. This is about figuring out what a mind can be. What are the elements required for a self to emerge. We must keep our eye on that

Simple/Complex
-the single simple
(parmenides)
LETS NOT THINK THESE THINGS: But: the single is really Some rather than None
And: The impossibility of simples (from the but: the simple is a complex of none and some)
LETS JUST NOTE: IT CANNOT BE A MIND
why:
Change. The end.
So we have two options:
-plural simples: complex of simples
(still one, sort of)
we have to get at least somewhat away from the simples themselves to have anything we're going to call a mind here
AND, we only technically have bottom plurality:
complexes are impossible to concretely distinguish
so they arn't really things-plural, though we can make arbitrary distinctions that work to some degree
-the single complex: complex of complex
(only sort of single, as its divisible)
And specifically a fractal one, something we can get a grip on. Normally this will imply elements, but they might never show up at any level of zoom (we can have infinite complexity down and up, just for arguments sake) Otherwise we've got mush.
every level of zoom is the same, sort of.
from any level we see simpler below (as here is composed of those) and more complex above

Only with simples do we start with many.
We don't start with simples
We don't start with many
We start with much

Much/One/Many/One
what's much? (why is that not one yet?)
So then one of much
then many one
which can be one

((We play this game here so to know what we are playing with))

{{Chaos/Order}}
[at the lowest level of zoom (at our pixels) we will have mystery as there will be no detail, hense random at that level, but order will emerge from there: random random random means pattern pattern pattern]
Unstable/Stable
this is assuming time. but we're in third person land so we get to do that.
if stable then no change
Oh! unstable then
if no stable, then just constant, ABSOLUTE (otherwise we have a gauge) change, which is ridiculous.
we need grey to make this interesting
So balance of stable from unstable
Evolution!
every system with this balance of stable and unstable (which is no archemedian point) will evolve.
simple(r) stables interact to make complexer things, etc
Village - > child
we need a lot of the same sort of simple(r)s in the same place to get complexs of them
Environment tends towards complexity
The vast proliferation of mind.
MIND: a kind of semi-stable structure (complex in nature)
that: reacts to environment
by: signals (not quite symbols, but close)
basically if-then structure of sufficient complexity to warrant treating it as such (my threshold is low, but it needent be for there to be fireworks)
any two minds that interact are a mind (by this deffinition of mind)
Symbols as complexes of signals
structure strcture makes it go
The Self-symbol is the complex of signals that react directly to the mind in which it is a symbol
so a model of the mind
so some brief implications about simplicity/complexity thereof
The rise/myth of individuals
Minds with parts that take care of themselves (and are minds too) Succeed!
individuals plural, not the topmost level, minds that deal with minds
all interactions thereof are of a bigger mind
/are signals
/are parts of symbols
yay evolve go (implications of all kinds)
As mind evolves its parts become more mindlike (towards complexity)
Culture/individual
the signal-set and hense symbol set comes from enviroment
when enviroment is a mind, the symbol set then is a gift of the enviroment and of that mind
as in, is given by it as a whole
any part of a mind is also a signal/symbol
The self symbol can be generated spontaneously, but it can be encouraged to
or prepared for
The nature/nurture debate is silly: the nurture has been determined by the nature has been determined by the
to see the way its silly is to know what I mean here
Public/Private
witt arguments about language
how deep that goes?
everything is interaction with the mind that you are made by
so. Deep.

Someone else

I kind of feel like I've been saying this stuff for a while now.
But apparently so has Kevin Kelly.
And I read WIRED and he edits it so maybe that has something to do with it and maybe not.
But either way, the guy knows what's up.

And he's worth a look:

Read my right hip

I don't do drugs.
I am drugs

~Salvador Dali


The man may have been more right than he knew. Or he may just have known more than I knew he knew. Or he might have been more right than I knew he knew, but still even more right than he could know.
Enough of that.

What I realized was this: drugs are compounds that alter minds in interesting ways. If human culture comprises a big mind (and if you haven't noticed, it does) than there are some people that alter reality as it is perceived by that mind. Dali was most certainly one of those folks. Duchamp probably was even more so. Along with a lot of other artists, musicians, novelists, poets, and other creative people who get digested by the collective unconsciousness (and the collective consciousness too), but not just the overtly creative people. Major thinkers are some pretty potent drugs (we ae still working on our Aristotle hangover, and we're just coming down from our Cartesian high), but the most powerful drug of all is almost certainly the enlightened ones.
Yeah thats right, the short list: Buddha, Lao Tsu, Moses (and a number of other old testament guys. I want to see the Dali quote above attributed to Ezekiel, but it might take some fancy translation), Jesus, Mohammad. Those are the psychotropics that we have not come down from yet. (That list could be a lot longer, but a lot of the names that should be on it are lost to history, and a lot of the effects of those other drugs have been destroyed by some of these ones (Jesus and Mohammad have both had that effect to some degree).
Theres sort of a butterfly effect that happens with a psychotropic of that potency, but for the most part, at the core, each of them has done wonders for our headspace. Sure, the mental digestion (is there a better word for that?) of the ideas that these guys are have created some confusion, but it's also given us glimpses of how really great things might be.
People are wont to naysay, but theres no reason we can't all be enlightened ones. And how great would that be? (SO MUCH, that is how great.)

Theres a sanskrit word for the sort of awesome glimpse the enlightened ones offer: Bodhi. It's something that happens (constantly, in the background) during meditation (see: being aware [also known as being alive]) and it's sort of like a supernova of joy, a radiant explosion of goodness and love and blissfull connectedness. With the right sort of awareness, you can find it happening deep inside yourself, basically powering your very being.

It's neat.

And it's infectious. But as it spreads through the collective mind, it fades out some, we come down. Slowly, for sure, and theres constantly the possibility of becoming a booster shot of the most powerful anti-depressant in the known universe.

Somehow, somewhere along the way, I got branded with an effect of this ongoing bodhi-psychotropic meme plague, a flash of bodhi that hit someone else before it bounced into my skull (over the phone first, but later though my eyes and ears) and made its way down onto my right hip where it's inked in a copy of a copy of sharpie on paper:
HAPPIES WILL SET YOU FREE.
It's been said a lot of different ways, before and since, but I can't thank Sean enough for letting me have his sentence. It's exactly the sort of thing the world needs.
Some people have problems with "happies" not being a word. But lots of things are happies: soap bubbles and caterpillars and flying kites and riding bikes and taking walks and house plants and long walks and frisbee on the beach and fetch with a dog or catch in the yard or jumping in puddles or crayons and blocks and grass in your toes and fizz in your nose. There's millions of them. And it just takes some awareness of how much they pervade existence to really start feeling excited about being alive.

Things are great. Theres lot's of great things. And there's no reason not to enjoy them.

So maybe I'm drugs too, and probably you are too.

Isn't this world amazing?

Om

All this is full, all that is full.
From fullness fullness comes.

We are not two we are one

I've been reading the Upanishads
at work. It's been nice. But then it was pretty crazy that you were listening to music from a movie about India, and then so was I, but by accident (it was in a car I was in).
And the song kept saying
We are not two we are one
Which is what I was writing last night.

Which is all pretty crazy.

I will probably forget about today in the long run.

I will only remember today as a border of yesterday, maybe (who knows what will happen) as a border of tomorrow. But not for itself. Today was just another day. And considering today is day TWO of the great adventure, that's pretty encouraging.

I have focused a lot of my energy into making this change into something that is more like a change in key, more like a change in rhythm than a change in band, a change in genre. The song that we sing, I want to keep singing. And I know that there needs to be a tempo change, and maybe a key change, and maybe some instruments rotated in or out. But this is all still one song for me. One song that includes cow jokes and line walking and string tears and a bucketful of magical realism.

I've been thinking a lot about HoL and how that book is a lot about the language that develops between two people that are deeply connected, how that is the only code that is unbreakable.

A pair of people can be just as solipsistic as a single person, but its way more fun with two people than it ever could be with one.

Another 10 hour day tomorrow. Goodness me.
It's kind of fun knowing that I am the equivalent of a nerve repairman. But the job is less glorious than it could be. I guess platelets don't exactly live a live of glamor. But my job, replacing broken cell phones, is more like a nerve cell cluster that controls the re-growth of nerve connections, so thats at least somewhat more complicated than just being a platelet.
Not to be down on those guys: they did their job in Windsor when the tornado hit.

Yeah. I am talking in code that only two or maybe three people understand. It is time for rest.
I think.

But.
We are not two we are one
Goodness that's important.
So Much.
So much.
We are not two we are one.




We are not two we are one

Loose ends

After finishing Hofstadter's book, I felt that I was a little harsh, but not too much. The man is convinced that a single adult human mind is the top level of consciousness. And frankly that's crazy. He flirts with the idea that two people might form something more than a single individual, but he shies away from the idea as fast as he approaches it. At one point, while he is thinking about video cameras pointed at the TV that displays what the video camera sees (making a little strange loop, like at target or best buy when they have the TVs set up so that you can play with their video cameras and you point the camera at the TV; you get a sort of grey tunnel hall of mirrors effect.), he thinks about two such cameras situated so that they can see each other's displays.
This is sort of a complicated situation.
With one camera pointed at its own screen, you get a sort of infinite tunnel, like when two mirrors face each other. But because of the time delay in the camera, if you add any input (like waving your hand in front of the camera) you get a cascading pulsating image, which Dougie is pretty excited about, mostly because he has played with it a decent amount, and feels like it's something he has explored more than other people.
But things get much more interesting with two cameras and two TVs. Good ol' Dougie just points out that each camera still has the specific TV tied to its own input, and so two individual strange loops exist, but he completely misses the existence of the big strange loop made up of the whole system, two cameras and two TVs.
The same problem happens with people. He's so worried about losing his own ego that he just won't acknowledge the entity that consists of himself AND his wife, and their awareness of each other. Again, he flirts with the idea, but only enough to infuriate me.
We are two. And we are one. And I am many, and you are many (there are so many ways to carve up Reality). But the One is just as important as the many. No more, no less.

What I'm getting at is this:
A mind is made up of subsystems that share information (experiences, emotions, moments, sights, sounds, tastes, conversations, touches, kisses, movements, etc). Any two minds that have flow of information between each other ( see above ) compose a single, greater mind.
Once you have a physical understanding of the mental, this is an undeniable fact.

When we are together, we build a communal headspace. Our minds are like houseboats. When they float near one another, we build bridges between them. Then, when the bridges are stable, we begin to build rooms and extensions to our individual houseboats. I add to your boat and you add to mine, we both add to the space between. The entire constructed entity, this big bunch of two houseboats and the bridges and rooms between them, the links that tie it together make it into one houseboat.

[Metaphorical thinking: helpful?]

As we interact, our two individual minds comprise one greater mind. Your brain has two hemispheres that cannot communicate everything that happens between themselves. But they can communicate, and it is their communication that is YOUR MIND. Our communication is OUR MIND. Yours AND mine. Just because minds are physical and so are we.

This might all sound crazy, but it's just true.
If we spend some time thinking about the physical nature of our minds, and abhor mysticism with a proper carefulness, we must come to the conclusion that any pair (or greater number) of minds in communicative community will comprise a single greater mind.
The End.


The thing that is important is the life of this entity that is made up of you and me.
With a brain, you can separate the two hemispheres, so long as you maintain the informational connections. The connection can be stretched over any given distance (with little radios, or fiber optics, or quantum strangeness, or what have you). This will change the rhythm of the complete brain, but not its function.
Any distance between two people works the same.
The rhythm will change, but not the function. Not the existence of this greater whole that we are a part of. And that's what's amazing about being here together.
Here can be very, VERY big.
And we only have to stretch it a little to get a taste of that.

Nighty night.