Infinite Sketchpad / I Am A Strange Loop

I.

"The Emerald Tablet of Hermes"
(Newton Translation)

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II.

∞ ✎ 

In late 2012, I was introduced to Tom Lieber's Infinite Sketchpad (many thanks to Luke Iannini & Mike Rotondo for this!)-- it almost straight-away became one of my very favorite videogames & still is-- 

Get Infinite Sketchpad (∞✎) for iPad HERE. 

Get David Johnston's Infinite Doodle for Windows/XBOX HERE

(very different touch/movement/speed (fast!); mostly same space)

See my drawings HERE.

The ∞✎ space is a visualized Real Number XY Continuum, or 'blank fractal canvas' (the real-number line is a fractal, too, only one of trivial visual interest until we start to fill it in with content). It is a model of Zeno's Playground, that 'flux/motion-disproving' space famously played by Achilles and the Tortoise in defense of Parmenides' eternal/timeless Sphere. "The Continuum Problem" has historically given rise to some huge moments in the history of maths-- from Leibniz/Newton's Calculus, and when re-problematized, to Cantor's Set Theory, and more recently, building from this, as the assumed 'monstrous grain' of the strange infinitely detailed fractal sets described by Mandelbrot's free-scaling geometry.

But none of this history need come up while playing. As described above, Infinite Sketchpad sounds like an esoteric tool, accessible only to mathematician-initiates, opaque to everyone else-- this isn't right, though. In actuality, it's probably much more suited to please the changing whims of irrationalists, luddites, non-gamers than the structured pursuits of formalists... All the ideas are FELT as wonder, it's all,play-- requiring no systems thinking, little design. Just wandering... It is immediate. You need only to play it yourself to meet this quality, its personality, it doesn't require any theory, it barely requires any gaming 'literacy' (drawing-literacy & ipad zooming being the closest it comes).

For my part, it was basically the only videogame that I touched for almost a year...When I first played, I knew very little about the formal concepts of infinities, etc. that composed its conceptual/functional-material-grain, but it was clear that they were there, and it was easy enough to smell out a Borgesian canon-labyrinth of thought surrounding the mechanics and pictures as gradual intuitive understanding developed. It was exciting not knowing (not being able to formulate) things about the space, but still playing it, and coming to know it in a different sense, a non-explicit (non-propositional) kind of knowing/p-o-v.

I started writing notes for a blog-post on it to share my excitement, and soon it grew out of control...

The form is telling-- in the same way that infinite sketchpad allows us to zoom in and out and pan as much as we'd like, the 'blog-post' balloon-zooms in/out/across accordingly, and the ballooning very soon is too much to handle, especially once I start supplementing the canvas-play with external research (which feels necessary from very early on, given the historical-conceptual contexts of the ideas I.S. touches on)… I am learning to compose pictures within this new sort of space, and am writing at the same time-- the sensory-material potentials of the former process are informing the abstract-structural-linguistic potentials of the latter… There is the 'drawing plane' and the 'reading/writing plane' and the project becomes a a matter of seeking and describing a continuity or consistency between the two planes (and between these & the many other planes which are likewise touched).

Finishing the essay becomes a GOAL. When I set out, all I wanted to do was write a little critique of the game, but I kept finding all of this context that the critique seemed to require if it was to be meaningful in the sense that I had felt it to be during my initial encounter.

This goal is still unmet, incomplete. Every time I go through to edit, I want to add more, and when I add more, it's a mess, and I need to edit. There are 'subtractive' and 'additive' methods of composition, and though I've submitted myself at times during this process to both, the growth in its size is proof enough that the latter was a dominant controlling influence. After all, I never really 'delete' things in an Infinite Sketchpad picture. There's always more room! Games teach us how to play within their own frameworks and we carry these 'ways' over to Other games,books,things,life,etc. Living with Infinite Sketchpad cultivated in me a pathological burrowing aesthetic of sorts. This aesthetic seems to have occupied in feeling & intention many similar spaces to those that the 'pathological curves' (proto-fractals, monsters) of the 19th century occupied in mathematical form. 

Needless to say, writing & drawing has felt something like the beginnings of a potentially infinite project, paralleling the structure of the game.. Fully submerging myself in that process for even another month is not something I'm interested in giving myself over to, as the endless tunnel of research has proven to keep me from other interests and work and from the joy of completing small projects. I was not prepared for the gravity what I embarked on, and though I'm very happy with the time I've spent on it, it's time to PAUSE or ESC the game for the time being (hopefully to return to finish the final chapter, at least, but we'll see...).

I've loosely tightened the essay up these last weeks, clipped off (some) rough ends, and have made it available as a first complete draft, which may or may not be a final draft, depending on how I'm feeling in the future:

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III.
Structure & Alchemy in
New Fractal Playspaces, v 0.6

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These essays are personal notes, a year or so of what might have served as Content on this blog, hoarded, cut, and re-composed in a single document instead. I have tried to be as truthful as possible. I have sampled many sources, some uncredited, usually on account of lazy book-keeping. Any of the writing's formal integrity is thanks to the bevy of samples of Pseudo-Hermes Huvanistagg-Ludistagg's work, an old ludic realist-materialist who I've given primary authorial credit to, though the less refined passages throughout are always my own…. Pseudo-Hermes is presumably named after Hermes Trisgmegistus, the first alchemist (with P.H. adopting the medieval scholastic naming convention, a la Pseudo-Dionysus, Pseudo-Aristotle, et al). The essay's historical ambitions, guided by P.H.H.L's alternate 'play canon', plateau at a still massively underdeveloped reevaluation of the epoch which immediately preceded our own 'scientific modernity'-- one in which Galileo, Newton, etc must be revisited & re-considered just as much as practitioners of intuitive magics (alchemy, astrology, qabbalah, etc.), as practitioners of the strict 'rationalism' we know them for today. At this pre-modern moment, the object of scientific inquiry is not separate from the subject of personal inquiry, feeling, affect-- speculative interest.. this is the meaning of magic.. It is my belief that videogames are irreducibly pseudoscientific, being composed of such subject-object dissolves, and that failing to account for their status as such will only serve to cut off those speculative possibilities best prepared to advance the medium. Hermes is a line back to the time and ethos of the protosciences ('pseudoscience' was first used to refer to alchemy)-- the conditions of modern science -- the primordial soup from which the functions and concepts of which we are so proud and confident were given their first breath of life. Modern science, proud as it is, must give due thanks-- it did not birth itself but is rather a child of the magicians.

I can't say any longer that the essay's purpose is simply to celebrate/critique Infinite Sketchpad (though I hope it opens a way of thinking that could be more readily excited by the possibilities that I.S. presents). Instead, while Infinite Sketchpad serves as a materialized (vibrating) model of the spaces discussed throughout, the topic of the essay has rather undergone a massive zoom-out to the point of being concerned with the infinite macrocosmic canvas of Games as a Whole, their playings microcosmically represented by 'paths' walked through infinite sketchpad-- infinitely scalable approaches to the questions of what games are, what they've always been, what they might be… these are the 'boring' questions of last year, 'What are game?' etc, but the battle over the use of these terms is by no means complete.. The relations between gamefulness and artfulness and playfulness are by no means well understood, and the prophetic power of the notgames idea has not at all been exhausted. Notgames have their formal structures, too, and I am interested in exploring them. Why? I often do not enjoy games that present me with an explicit goal. I like to wander with whatever it is I am doing, to shift the goal. I like to lose if this allows me to shift-- I like even to spoil a game for others, to grief, for this same reason (I apologize!). I have on many occasions found looking at a picture to be a better Game than most videogames. For me, games are all about touching, affecting, but the eyes can touch, too. 

The essay has become an anti-formalist formalism in a way, an attempt to defend the irrational, the inconsistent as manifest in games-without-goals (which really have many goals rather than none), and in the sensuous/haptic aspects of games, which some are inclined to consider 'less intelligent', but which are rather simply irrational in something very much like the numerical sense, in that these are the games that exist between the members of the infinitesimal series of rational numbers/rational games, which condition our reality at every moment even as we 'hop' from one rational game to the next (as we lose, grief, etc.).… This is to say that it is possible to play even a rational game irrationally (as is the nature of 'non-optimal' play). This capacity of the player is what I am most interested in, which puts me at odds with the conventional computer game-formalisms, from what I understand. I'd been calling Infinite Sketchpad a game, and I still do, but it can be considered as such only if irrational games are allowed to exist. Needless to say, the Pythagoreans were not pleased by Hippasus' discovery of irrational numbers, and despite a handful of exceptions to the contrary, it seems that the mechanisms of Game Culture are not liable to be pleased by an insistence of the material primacy of irrational games, or by the corresponding principles of ludic realism that parallel the pathological realism of the Real number continuum--

That there are indeed infinitely many rational games, but that in between each of these games, there are infinitely MORE games which are irrational. That almost all games are irrational. 

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IV.
Atalanta Fugiens 1 -18

V.
8 Theses on ∞ ✎ 

Since I realize that very few readers will click through to read more than a few pages of the essay and that fewer still will read the whole, AND since even in its finished state the essay gets carried away with itself and the applications of infinite sketchpad gets lost in the mess of things…-- I'd like to present just a few numbered theses here which are directly related to the game itself, not drifting away from it so much as the essay does, but rather summarizing some of the key ideas that I have arrived at while playing/writing, as a standalone mini-essay and preview of the larger project. 

The full essay is a piece of 'game criticism' on Infinite Sketchpad only by an analogical leap/stretch of the imagination-- the below points more clearly so.

1. Properly acknowledging the nature of scaling relations in Infinite Sketchpad drawings warrants a re-evaluation of fractals such that the category is opened to include not only scaling objects generated by algorithms, but also scaling objects generated by a constant stream of finite PLAYED material actualities the sources (players) of which are potentially non-computable. Such an inclusion allows for the completion of Mandelbrot's Naturalistic project

The calculation of Mandelbrot's variable D, the fractal dimension, operates on the assumption that a scaling self-similarity will cascade into further detail infinitely, it supposes a wholly abstract image of space which does not fully correspond with out own. But this has not stopped Mandelbrot from applying this abstract model to concrete-finite actualities in nature, art etc. D is already famously applied to finite-natural pseudo-fractals like the British Coastline, which was not generated by an algorithm, but rather by the MATERIAL PLAY of waves, of tectonic movements, etc. His whole book The Fractal Geometry of Nature, is concerned with other non-algorithmic fractalish things which were played by nature, and then abstracted & modeled algorithmically. 

The fractal geometry of nature points the way toward a new class of proudly finite fractals. Natural fractals are all finite. What there is of the infinite is to be found within the finite. And insofar as an artwork can be considered an extension of nature (the player or artist and her environment is the system of waves shaping the shoreline), it only makes sense to apply Mandelbrot's mathematics to pictures such as these. Mandelbrot was already onto this idea, as his paper "Scaling and Scalebound structure: A useful distinction in the visual arts" can attest to. In Infinite Skethpad, we may not have strict self-similarity, depending on what the player chooses to draw, but similarity and difference are BROAD categories, and it ought to be possible to delineate scaling relations between, as it were, pattern and entropy, as regards whatever information we're presented with.

2. Infinite Sketchpad is both the most radical and most intuitive dimension-shifting game that has been made. [a] It is the most radical because it is concerned with surfing a continuum of floating point/irrational dimensions, as opposed to 'snapping' between integer dimensions (as per #2); [b] it is the most intuitive because it manages to shift dimensionality all while remaining a strict 'virtual parallelism' to the 2-dimensional material of the screen itself-

Charles Sirato's 1936 "Dimensionist Manifesto" might provide a fitting generic term for games of wonky shifting dimensionalities-- Fez's move from 2 to 3 to a different 2. Miegakure's move from 2.5(ish) to 4(ish) (ostensibly a movement from 3 to 4). Etc. Braid moving from 2-D space + 1-D time where time is one-directional, to 2-directional 3-D spacetime.  

If we follow the logic of the classic dimensionist book Flatland, in which a sphere penetrating the 2-D plane is perceived by locals as a a circle which grows from small (at contact) to large (at sphere mid-slice), then it would suggest that games in which scaling objects are prominent characters could likewise be considered 'dimensionist' games-- for instance, Katamari Damacy, Scale (forthcoming), Within A Star-Filled Sky, Maquette, Gorgoa, Google Earth, etc. Each of these games is a game of N-dimensions penetrated by objects of dimension N+1 projected downward onto the lower plane. 

Infinite Sketchpad is quite strange in that the spaces we draw in it are always effectively BETWEEN 2 and 3 dimensions-- but unlike the above-mentioned scaling games, I.S.'s spaces dimensionalities are in constant flux, the value of D is constantly changing-- e.g. 2.1, 2.2, 2.23, 2.8… Detail which doesn't tunnel into further detail is representative of the side of the continuum nearer D=2, while detail which tunnels deeply into further detail is representative of the side of the continuum nearer D=3. The fractal dimension D on this plane is always 2 < D < 3. The zoom characterizes the possibility and actualization of an infinite line on a finite plane such that the (2D) surface is effectively becoming (limit 3D) volume.

3. Following from its capacity to freely navigate the strange dimensional continuum between D=2 and D=3, something very much like Infinite Sketchpad will be an invaluable aid in prototyping any future-videogame ideas of sufficient free-scaling complexity.

If more games (software-spaces in general) are to made where objects contain entire spaces, and where spaces can be fully encapsulated as objects, and where there is to be a potentially infinite cascade of such zooms in and out-- planning & playing in a tool like Infinite Sketchpad will be essential. Such a tool can (and will) be amplified by new Forms of Life, no doubt, but the basic idea of freely composing a Great Chain of parts and wholes irrespective of an algorithmic top-down will prove powerful in the years to come, if the intuitive bottom-up is to be joined with the Universalizing potentials of speculative abstraction. 

Infinite Sketchpad allows such abstraction to be explored smoothly. Smooth like pen wandering on paper. Smooth like pressing into butter, or some other 'spreadable' sensitive substance. Smooth like smooth functions. Smoothness is Realistic. Continuity is realistic. This is part of why Half-Life is so beautiful. It is a continuous stream of synthetic consciousness, straight-up. You start on the tram, and everything follows from what precedes it without gaps, there are no substantial 'edges' to take into consideration. Life is continuous (save sleep, hypnosis, and other strange edge-states). To create a smooth scaling space where objects are always spaces and spaces are always objects is merely to take this principle of 3D spacetime realism and amplify it. The capacity for smoothness in a scaling space allows that part/whole object-relations need not be overly simplified-- it is possible to draw cascades of entangled objects in Infinite Sketchpad of the sort that it is difficult to say where one ends and where the other begins. Object-hyper-object-hyperhyperobject-hyjectperobbbb,he etc... The 'count as one' replaced, as often as possible, with the 'count as what?' (inconsistent multiplicity). 

4. The depth of scale and the scaling drift required to 'visit' (in time) all of an I.S.-picture complicates the as-yet little interrogated 'edge' between videogames and pictures. Pictures in I.S. are undoubtedly pictures, but they also seem to be little adventure games, too, explorations, as deserving of that title as any other… Videogames and drawings/paintings/images-in-general must be considered as existing together on a continuum with their distinction characterized by a difference of degree, rather than one of kind.

These are drawings, but they are shifting possibility spaces (or games) just the same, in our experience and in their material constitution. Pictures, of course, have always been shifting possibility spaces in our experience, but a new material principle of relativity is introduced here, whereby the whole and parts are more distanced from one another than they have ever been.

Following up on the implications of the picture-game continuum requires stepping outside of Infinite Sketchpad, and revisiting wholly 'static-flat' drawings with the new sense of possibility that I.S. has instilled in us. Now, there is a clear sense of preparing to zoom into, e.g. Kandinsky's free-scaling Compositions. Clumpings of details function as attractors for our attention. Our eye follows details, and enters new (faster) rhythmic spaces in those detail-basins which feature objects more densely packed together. Infinite Sketchpad automates the possibility of tunneling endlessly into such detail basins, allows K's Compositions to unfold. Paul Klee's Notebook's will be a good place to steal game mechanics from, once we are comfortable abandoning representational design in favor of pure concreteness / synthetic-vibrational player-materiality. 

5. The shift of scale initiates rhythmic-musical flows as much as it does drifting-ludic flows, and thus infinite sketchpad must exist on a continuum with other music objects as much as it does on that with other picture objects.

There is no sound attached to these rhythms, so we are still dealing with strictly visual music. Rhythm exists even in classical pictures, but now there is a new physical time element (this, despite the 'static' form of the pictures), whereby the density of objects dispersed around a basin of attraction creates relative pulses, where higher density is faster, and lower density is slower. Size itself is rhythm.

There are many scaling aspects in music. The classic example is a pulsing rhythm which, when sped up beyond a certain threshold, we begin to perceive as a tone. 2:1 is octave & boom-chick-boom-chick both. 3:2 is fifth and duple-triple polyrhythm. We can imagine (and maybe it has been done) a space which plays with e.g. duple-triple rhythms using tones that have been generating by speeding up this rhythm itself. And this is to list only the first 2 pitch-rhythm members of the harmonic series of integer relations, which continues scaling up (in frequency), down (in wavelength/time), etc… All of this is ancient-- there are more modern, computational devices, too-- Granular synthesis comes to mind. The shepard tone comes to mind. These & other musical-mechanical devices could be used to produce wildly dynamic soundtracks for new games which use free-scaling mechanics. And to this end, it will be as much a matter of developing a taste for these new sound-worlds as it will be one of actively designing with them. 

It is not clear exactly what the relation between scaling musics and scaling pictures might be, but the 'continuum' of musical form outlined in scaling theoretical works such as Adam Harper's Infinite Music, James Tenney's Meta-Hodos, Erik Christiansen's The Musical Timespace, Curtis Roads' Microsounds etc will be of great use in exploring the possibilities...

6. Infinite sketchpad's emergent relations between parts and wholes ties the 'problematic' of drawing/composing in an infinite space to some of the classical problems of metaphysics.

Metaphysics seems to deal with games played collaboratively by a relatively small list of 'conceptual personae', several of which are key 'mechanical personae' in Infinite Sketchpad-- Parts and Wholes, the One and the Many, Process & Object... These concepts are all unavoidable in any attempt to describe what something is, what it is becoming... (etc!). Metaphysics is a 'gateway drug' to mathematics. These Problems more or less all follow from the play of Zeno's paradox, the famous formulation of the "Problem of the Continuum", which is reducibly mathematical-technical in one sense, and irreducibly metaphysical in another. Is there flux-becoming or is the form-being? And what is the relation between such pairs? Leibniz' work on the 'labyrinth of the composition of the continuum' produced the infinitesimal calculus alongside Newton's. The continuum is a labyrinth precisely because no matter how much you divide and divide into infinity, you are still only producing rational numbers. Between each pair of infinitely small rational units, there are infinitely many irrational numbers which have still not been touched. These irrationals are the seat of the proper smoothness or continuity of the continuum. Calculus does not solve Zeno's paradox, it merely asks it again, and makes something useful from the question. Over a century later, Georg Cantor's study of irrational numbers develops into his transfinite theory of infinities (irrationals requiring infinite calculation to describe), which describes the split between countable-digital infinite (rationals) and the uncountable infinite (irrationals and beyond-- approaching--> Absolute/Inconsistent Infinite--God). These studies were also the beginning of his set theory (which is the count of a Many into a One). Meanwhile formal logic (non-electronic videogames) is being stratified by Frege, next Whitehead & Russell will attempt to map maths on logic onto one another and Gödel follows up eventually with his incompleteness theorem, with its discoveries surrounding inconsistency and this is Hofstadter's pet project, the Strange Loop, the tangled hierarchy, the part that contains the whole. This looping form, snake eating its tail, has also been called the Ouroboros by the alchemists. 

Inconsistency. Irrationality. Infinity. THESE mathematical qualities which are, at some value-limits, NOT computable-- the problem of the continuum sheds light on them, and Infinite Sketchpad sheds light on the problem of the continuum.  

I ran into this little bit from Raph Koster: "It may be that games are all about math. And I think that sucks." But this sort of sentiment is a shame! Why does this suck? The thinking, I imagine, is that if games are all about math, they can't be all about Art, but to hold to this is to think too little of math and art both. Freely allow mathematics to breathe metaphysics. Is it, has it ever been, anything more, or less? Attempting to allow a maximally intensified/living Art to coexist (become One with?) a maximally intensified/living Maths is the most promising project of videogames, as far as I'm concerned. A new kind of Hippasusian-Pythagorean approach is wanting, where we DO NOT think that it sucks for games to be all about math, because math is not regarded as over-rational reductionism but is rather, as it has always been, the formalization of the players of metaphysics itself, the One, the Many, the parts and the wholes, the rationals and irrationals, and their relations and inconsistencies-- the games that they play.

7. Building from #s 3-5, It follows that software structures ought to be thinkable as elements existing on a continuum which likewise contains metaphysical structures, musical structures, pictorial structures, etc. This is maybe something akin to what Deleuze calls the Virtual Continuum.

There exists some sort of vast N-dimensional Real continuum that can count games, pictures, music, and philosophy all together, each freely able to appropriate structural 'tactics' from the next. The way Herman Hesse described his imagined "Glass Bead Game" plays out similarly. And though this continuum counts the supreme consistency of software and its wholly rational numerical composition as part of its ranks, it reaches beyond the computable, too, touching the inconsistent, the irrational, the infinite-- this is no different from the Real number continuum itself! And this is the space (to descend fully into pseudo-science), between each of infinitesimals, which the language of the arts might operate in, such that the meaning of a picture, a game, a piece of music, a concept-- this meaning will both touch (being conditioned by) and be inconsistent with (being unbounded by) the information structures of software itself. 

8. Since 'ideas' of some sort (Whitehead's 'eternal objects' reduced to structural consistencies) can exist as structure encoded in the computational material and outer flesh of the software as much as in our nervous system/human brain, and since it is possible to learn from the software as teacher, the relationship between mind, body, and world is immediately complicated, where each seems to be implicated in the next, where Mind can and does exist in the world just as much as in the body.

But this is not so simple as to say that we ARE computers. That thesis is up for grabs... this is rather to say that we live WITH computers. And that we think with and in many ways are what we live with. Tool-Being. Mind is distributed across the environment. 

"Radical embodied cognitive science" is probably the discipline these days which is doing the most to shed light on this point of view. It is, as it were, a borderline alchemical mix of eco-psychological behaviorism and cognitive representationalism via Merleau-Ponty body-phenomenology..

This thesis that Mind exists dispersed throughout the whole environment, of course, can be applied across the board to any and all videogames, insofar as we enter the game and the game enters us, but I have found infinite sketchpad to be a particularly good example, partly because of the grandeur of the ideas which it touches on, and partly because I spent so much time following trails it seemed to lay out for me to learn from. I went to school with this Mind.. 

In Jung's description of alchemy, the individual's Mind is 'projected into the materials' -- Radical embodied theories might allow for an understanding of such 'projections' that they are not ego-centric 'illusions,' but rather Real bonds of relation, World-Mind, connections in aesthetics and causality. 

The alchemist's Art of Memory (see Francis Yeates) does not discriminate between matter and memory. Matter outside the body is just descriptive of memory structures (RAM) as is matter inside the body is (Brain), . Memory, and mind in general, permeate the environment, chaos-cosmos.  The contemporary obsession with Enlightenment materialism and its metaphysics which is at all times wholly reducible to quantified observation has proven itself powerful. But it did not grow itself. "In order to understand our situation today we must understand that in the sixteenth and seventeenth centuries the educated section of wester Europe inherited the results of about five centuries of intense speculative activity" (Whitehead, The Function of Reason). The question-- do we proceed with this 'objectivity' that seems to have been won from the Game of the proto-sciences which culminated in the proud, modern discoveries and systems of Galileo, Copernicus, Newton, etc? Or do we go back and figure out what games were played for those five centuries that allowed the conditions of such wins to be possible in the first place. As happens again and again, the Problem loops back to the question of whether to prioritize the Object, or the Process. The revisitation of history will be an invaluable tool in reclaiming faith in a self-destabilizing object-Idea of irreducible Process itself.

If Infinite Sketchpad is not composed of some kind of Mental Stuff, then it seems to me that whatever mental stuff actually is composed of perhaps ought not hold such a tight monopoly on the 'limits' of thought and experience as we are so often inclined to think.