tag:blogger.com,1999:blog-90857442191101879382014-10-01T21:35:11.813-07:00ARTIS SEQUENTIS PRINCIPIA MATHEMATICATo describe in full and ground in precise <b>mathematical</b> terminology the basic constituents and meanings of commonly-held concepts of sequential art.DrSunshinehttp://www.blogger.com/profile/13446826800939077210noreply@blogger.comBlogger14125tag:blogger.com,1999:blog-9085744219110187938.post-90704984918847030482011-07-19T08:36:00.001-07:002011-07-19T08:46:16.997-07:00Outlines 2Although it is somewhat of a blunt instrument, mathematical logic is the only tool, I feel, that is capable of giving a field which hitherto has not had adequately rigorous theoretical grounding.<br /><br />[...]<br /><br />The thesis of this book boils down to this:<br /><br /><blockquote>(1) "Ordered sequences of images and text consist of a series of assertions about a conceptual world."<br /><br />(1.1) "In order to make sense of the assertions given, there must be a grammar around which a visual language is formed."<br /><br />(1.1.1) "The grammar of this language can be adequately described by first order logic (F.O.L.)."<br /></blockquote><blockquote></blockquote>[...]<br /><br />Descriptive language consists of <span style="font-style: italic;">assertions</span> of the form, "<span style="font-style: italic;">It is the case such that <span style="font-weight: bold;">p</span> is true</span>", or:<br /><ol><li>⊢p</li></ol>DrSunshinehttp://www.blogger.com/profile/13446826800939077210noreply@blogger.com0tag:blogger.com,1999:blog-9085744219110187938.post-38929864601605733172011-07-13T17:17:00.000-07:002011-07-13T17:27:55.423-07:00Let ">" be an asymmetrical two-place predicate such that a is the "predecessor" of b, and b>a is false for ">", if {a, b, c, ...} form a well-ordered set.<br /><br />Let P1 and P2 be any arbitrary sets on L.<br /><br />⊦⌜ a>b⌝ & [a∈P<span style="font-size:78%;">1</span> & b∈P<span style="font-size:78%;">2</span> ] ⊃ ⌜P<span style="font-size:78%;">1</span>>P<span style="font-size:78%;">2</span>⌝DrSunshinehttp://www.blogger.com/profile/13446826800939077210noreply@blogger.com0tag:blogger.com,1999:blog-9085744219110187938.post-40665978344167949022011-02-22T06:17:00.000-08:002011-02-26T19:51:01.586-08:00Part I, Chapter 1: Fundamentals, Section 1.7<span style="font-weight: bold;">§1.7)</span><span style="font-weight: bold;"> Comics as Language, Separate from Art</span><br /><br />Is it possible for pictures to denote logical statements in language? Ordinarily, no. For example, an image of a cat on a mat can certainly be understood, insofar as it can be seen by an entity with visual apparatus compatible with our own, but without the referential concepts of "cat", "mat" and some conceptual understanding of "on", it will appear to that entity as a bundle of shapes and colours. It requires, therefore, the existence of a surrounding linguistic context, which I call "concept-space", to establish the necessary semantic apparatus for pictures to denote statements. This is why abstract art seems confusing to some people, upon first viewing, as they have not entered the concept-space necessary to provide the viewer with a ready supply of concepts to understand the ideas denoted by the visual objects.<br /><br />In the example given earlier, one must already have an idea of what a cat and a mat is, and be able to draw the abstract relation from this concept space to understand what the complex of visual objects in the picture means. It is then understood that the picture contains two certain elements, let us call them "c" for "cat" and "m" for "mat". In addition, the concept-space must also contain a universe of predicate relations, if the viewer is to be able to establish syntactic relations between elements in any given picture. Therefore, the concept of "On", in the example, is a dyadic relation "R" that also exists within the concept-space of the picture.<br /><br />It is only when the concept-space is understood, that we can truly say that the picture of a cat on a mat, denotes the logical statement "cRm".<br /><br /><span jsid="text">This has definite applications to the theory of comics. For one, all comics, I think, draw upon the same concept-space -- that all comics are commonly understood to be attempting to convey a meaningful series of sentences, in visual form. I<span class="text_exposed_hide">...</span><span class="text_exposed_show">t is generally understood that comics will have some distinct sequence of images, and in most cases, text. This distinguishes them from art alone, because while individual artistic pieces draw upon their own individual concept-space, all comics, by virtue of being comics in themselves, must draw from one general concept-space; all comics must in some way show some sequence of events in a world, and must do so in a certain order if the sequence is to be understood.<br /><br />Hence, it is always possible to draw linguistic inferences from objects denoted in a comic layout -- they are, in a sense, always pictures of a state of affairs, a representation of a world of facts, in the Wittgensteinian[1] sense, and whose facts, being the individual elements of a comic layout, are connected by definite syntactic relations. That is to say, while a painting of a cat on a mat may not be equivalent of the sentence "the cat is on the mat", as in the concept space of the painting in question what appears on the painting may be quite different from consensual conceptions of what a cat and a mat are in reality -- that a painting may denote a cat and a mat without being a one-for-one representation of a cat and a mat -- a comic showing a cat on a mat, by virtue of it being a comic, will always have a one-for-one relation to the sentence "the cat is on the mat".<br /><br />This is because, as a sentential representation of some given sequence of events, a comic must establish the semantic correspondence between its images and the desired sentence in language, if there is to be any communication at all.<br /><br /></span></span><span jsid="text">What, then, is the precise difference between an individual piece of art, and a comic?<br /><br />Consider a picture of a vase on a table. A vase on a table in reality is something different from the phrase "a vase on a table", is something different still from a<span class="text_exposed_hide">...</span><span class="text_exposed_show"> picture of a vase on a table. The vase on the table in reality is a pile of atoms, interacting via physical laws, with another pile of atoms. Beyond that, there is nothing we can say. Sam, my artist friend, said that "Of course the vase on the table! I see the vase, and somewhere near the table, and so it's obviously on the table. You'd have to be a very bad artist for it not to have the property of 'on' the table." Herein is a distinction. I separate the linguistic property "on" from that collection of colours on a flat 2-d sheet, which reflect light into my eyes in such a way that my brain connects these shapes to some memory of vases and tables. I also separate the linguistic property "on" from the world of atoms interacting with each other through the physical forces of nature.<br /><br />There is no "on" in nature. You cannot run the Large Hadron Collider high enough to produce evidence for a particle that means the word "on". No matter how deep you dig, how high you fly into the heavens, you will never be able to reach out your hand and isolate so intangible an idea as "on". To propose otherwise is Platonism.<br /><br />Here is a painting. It is a collection of shapes and textures, on canvas. The paints have colours, and are arranged in all sorts of ways. Human beings with eyes can see this painting and connect the shapes it makes in certain ways to things in their experience. But what meaning exists in the paint itself? If there were no humans to see it, would the artist's concept of whatever he painted still be inscribed in the painting, embedded into the world as if he had plucked the concept out of his brain and put it into a jar of formaldehyde? This is patently ludicrous.<br /><br />Draw back from the world of just paintings, to the world of "art" in general. Consider a Ming vase, a 20,000 year old Aboriginal cliff drawing, the pattern on a Zulu shield, a Navajo blanket, "Fountain" by Marcel Duchamp, and Da Vinci's fresco of the Last Supper. What do these all have in common, if art is to be some kind of "language"? They express a thing, so far as they are made to evoke some kind of memory, feeling, or image in the minds of humans. But what is this thing? Does the structure of the "thing" evoked by any of these items bear any resemblance to the structure of the "thing" evoked by any other? Is the African mask really saying something in the same way as my saying "Hi there everyone, I'm Anh-vu and I am arguing with you!" Any individual work of art can mean something different, evoke something different, in each person who sees it. Certainly the sense-data are similar insofar as we are all "seeing" it, but how do these sense-data assemble to make sense in our minds? Regularly or irregularly? If it is regular, then it is linguistic; if it is irregular then it is not.<br /><br />Why is it that we can have disputes about what a painting "means", about what an artist was trying to "express", when we do not have disputes over what I mean when I say "two plus two equals four"? One is a statement of language, the other is an argument over differing opinions. Certainly one can quibble over the semantics of what Samuel Taylor Coleridge was really "symbolizing" when he wrote Kubla-Khan, but we would not quibble over the way in which he delivered those words.<br /><br />When Coleridge writes:<br /><br />"In Xanadu did Kubla-Khan,<br />A stately pleasure-dome decree".<br /><br />We can ask "What did he mean to symbolize by this?" But two people won't read this same sentence, and the one says:<br /><br />Anh-vu: I read it and what he wrote was "Goobla moobla boopity boo"<br /><br />While the other says:<br /><br />Sam: You're mistaken. What he wrote was "Paffle faffle naffle waffle".<br /><br />When we are confronted with Duchamp's "Fountain", what kind of statement comes into mind? Do all people come to the same statement, or is each statement different depending on the viewer? One man says "Duchamp was saying that all of art is now in the toilet." Another says "Duchamp needed to go to the bathroom." Another says "Everything in the world is now art." Another says "Nothing is art." Just by looking at the same painting, multiple people may conclude, if asked what the artist was trying to "say", an infinite multitude of different statements. When one is confronted with a statement of language, there is only the one statement. What it is is clear. Coleridge said: "In Xanadu..." and not anything else. What he was symbolizing by it is a question of a higher order. But it's obvious that when a sentence of language says a thing, it says only that thing, nothing else.<br /><br />Consider the African mask. What does it "say"? "I am strong"? "I am wise"? "I am fearsome"? "God is dead"? What? We can read a multitude of different statements just from the same object.<br /><br />Return to the vase upon the table.<br /><br />One person, when asked, "What does the painting say?" Replies, "It's a memoir of the artist's grandmother". Another: "The old vase is on the dirty table". Another: "The vase on the table bore telltale signs of years of neglect". Another: "I'm bored and there's nothing else in the room to paint." Another: "My vase is old, and I should clean my table".<br /><br />These are all different statements, even if they can refer to the same sorts of objects. From the same painting bursts a multitude of different phrasings, interpretations, predicates. One can read the "statement" made by the painting of the vase on the table any number of ways. The form of the statement is nebulous, not specific.</span></span> Such sentential notions are unique to language, not works of art.<br /><br />Yet sentential notions <span style="font-style: italic;">do</span> exist in comics. We perceive art pieces as making statements any number of ways, but given a certain sequence of sequential art, one will always interpret that sequence in the same way; in a sense, if one is to understand the meaning of the events portrayed in the sequence at all, one must submit to the general concept-space which defines sequential art. There can be <span style="font-style: italic;">only one</span> statement derivable from any given sequence of sequential art, and this statement, being a statement of logical facts, must be <span style="font-style: italic;">form-independent</span>.DrSunshinehttp://www.blogger.com/profile/13446826800939077210noreply@blogger.com2tag:blogger.com,1999:blog-9085744219110187938.post-14814303842006578162010-12-28T09:44:00.000-08:002010-12-28T10:15:37.825-08:00Part I, Chapter 1: Fundamentals, Section 1.6<span style="font-weight: bold;">§1.6) Elemental Semantics</span><br /><br /><div style="text-align: center; font-style: italic;">From §1.1 we have a set of axioms for the further construction of the theorem of formal logic in sequential art. However, the practical meaning of the concept of "element" remains undefined. In this section, we shall define elements and provide intuitive examples of the way in which elements in a layout combine to create the formal semantics of sequential art as a language.<br /></div><br />1.6.1) In axiomatic sequential art, as illustrated in previous sections, elements <span style="font-weight: bold;">e<span style="font-size:78%;">t</span></span> in a layout <span style="font-style: italic;">L</span> are considered to be atomic propositions. In formal logic, an atomic proposition is a statement of fact that can take either a value of "true" or "false", and which cannot be broken down further into smaller statements. For example, the statement "Socrates is a man" is an atomic proposition. In axiomatic sequential art, the <span style="font-style: italic;">illustrations of the objects themselves</span> are considered atomic propositions. For example, if I were to draw a dog, it would be the equivalent of the written statement "There is a dog", or more simply - DOG.<br /><br />Sequential art builds meaning out of assemblages of the elements in the same way that logic assembles atomic propositions with logical connectives such as AND, OR, NOT, and IF-THEN. These are called "molecular propositions". For example, the statement "Socrates is a man AND he is mortal". The logic of sequential art, similarly, composes elements into a larger semantic context. Imagine if I drew a dog in a running pose and drew movement-lines behind it. This would be equivalent to the molecular proposition: "There is a dog AND it is running", or more simply [DOG & RUNNING]. Adding on successive numbers of elements increases the complexity of each statement in the layout. For example, if one added a third element to the scene of the running dog - that of a sky in the background with no visible ground underneath, for example, a bank of clouds or a bird - then the context would increase in complexity and the statement would become [DOG & ( RUNNING & SKY ) ], and therefore "There is a dog and it is running in the sky". This is why, for brevity and simplicity of interpretation, the practice of dividing scenes into <span style="font-style: italic;">panels</span> was born, which reduces the number of statements the reader must deal with in any given scene.<br /><br />Fundamental to the nature of sequential art is the concept of <span style="font-style: italic;">sequentiality</span> - that of a passage of time. This is, essentially, equivalent to the IF-THEN statement of logic. In static art, scenes depicted are of a "snapshot" of a single image. In the context of sequential art there is the implication of a time-interval between individual elements. Here is the fundamental difference between static art and sequential art. The contextualization of a sequence of events relies necessarily on the viewer filling in the essential logical step of "if there is this set of elements, then there will be this next set of elements."<br /><br />Imagine if I drew the running dog in the previous example and then followed it by an image of the dog licking a man. The semantics of sequential art means that the following statement was produced: "If there is a dog and it was running, then it ran to a man and licked him," or rather: "A dog ran to a man and licked him." Symbolically: [ DOG & RUNNING ] -> [ DOG & (LICKING & MAN) ]. <br /><br />Therefore, one can build statements equivalent to written propositions visually, through the formal logic of sequential art.DrSunshinehttp://www.blogger.com/profile/13446826800939077210noreply@blogger.com0tag:blogger.com,1999:blog-9085744219110187938.post-38299391499850181082010-11-28T12:37:00.000-08:002011-01-04T17:56:26.449-08:00Part I, Chapter 1: Fundamentals, Section 1.5<span style="font-weight: bold;">§1.5) Definition of Panel as an Operator</span><br /><br /><div style="text-align: center;"><span style="font-style: italic;">In order to develop a comprehensive theory of the mechanics of</span><br /><span style="font-style: italic;">sequential art, we must necessarily come to a functionally robust,</span><br /><span style="font-style: italic;">yet adequately general definition for what it means for an object</span><br /><span style="font-style: italic;">to be "inside" or "outside" of a panel. This section develops the idea</span><br /><span style="font-style: italic;">of a panel as a binary relation that maps objects from the space of</span><br /><span style="font-style: italic;">elements <span style="font-weight: bold;">E</span> to the spaces defined by a set of borders <span style="font-weight: bold;">G</span>. We develop</span><br /><span style="font-style: italic;">notation for the operator as P<span style="font-size:78%;">m</span>{E,G,k}.</span><br /></div><br />1.5.1) Logical Definition of Panel:<br /><br />Let P<span style="font-size:78%;">m</span>(x) be a predicate consisting of the statement "is contained within a border G", and x be any element of <span style="font-weight: bold;">E</span> or any <span style="font-style: italic;">n</span>-tuple of elements selected therefrom. This predicate is true for all x, and is false for no x, <span style="font-style: italic;">e.g</span>. for things not included in the <span style="font-style: italic;">universe of discourse.</span><br /><br /><blockquote>(∀x∈<span style="font-weight: bold;">E</span>).P<span style="font-size:78%;">m</span>(x)<span style="color: rgb(255, 255, 255);">...............</span>Df.<br />(∀~x∈<span style="font-weight: bold;">E</span>).P<span style="font-size:78%;">m</span>(x) ⊃ <span style="font-style: italic;">f</span><span style="color: rgb(255, 255, 255);">........</span>Df.<br /></blockquote><br />1.5.2) Functional Definition of Panel:<br /><br />With the logical description in hand, we now expand the definition into its full functional form.<br /><br />Define: P<span style="font-size:78%;">m</span>{<span style="font-weight: bold;">E,G</span>,<span style="font-style: italic;">k</span>}: <span style="font-weight: bold;">E→G</span> under <span style="font-style: italic;">k</span>.<br /><br />Where <span style="font-weight: bold;">E</span> is the tuple consisting of all elements in the layout L, and G is the set of all finite, simply-connected borders in L, such that E=(e<span style="font-size:78%;">1</span>, e<span style="font-size:78%;">2</span>, ..., e<span style="font-size:78%;">t</span>) and G={G<span style="font-size:78%;">1</span>, G<span style="font-size:78%;">2</span>, ...G<span style="font-size:78%;">m</span>}. Here, k is an index containing entries {σ<span style="font-size:78%;">1</span>, σ<span style="font-size:78%;">2</span>,..., σ<span style="font-size:78%;">m</span>}, where σ is some positive integer satisfying Σσ<span style="font-size:78%;">m</span> = t.<br /><br />Then P<span style="font-size:78%;">m</span> is defined as the mapping which associates a certain sequence of elements out of <span style="font-weight: bold;">E</span>, specified by <span style="font-style: italic;">k</span>, to a specific <span style="font-weight: bold;">G</span>.<br /><br />Thus:<br /><br />P<span style="font-size:78%;">m</span>{<span style="font-weight: bold;">E,G</span>,<span style="font-style: italic;">k</span>} :=<br /><br /><blockquote>G<span style="font-size:78%;">1</span> = (e<span style="font-size:78%;">1</span>, e<span style="font-size:78%;">2</span>, ..., e<span style="font-size:78%;">(σ1)</span>) : k= σ<span style="font-size:78%;">1</span><br />G<span style="font-size:78%;">2</span> = (e<span style="font-size:78%;">(σ1) +1</span>,e<span style="font-size:78%;">(σ1) +2</span>, ..., e<span style="font-size:78%;">(σ1)+(σ2)</span>) : k= σ<span style="font-size:78%;">2</span><br />...<br />G<span style="font-size:78%;">m</span> = (e<span style="font-size:78%;">(σt-m)</span>, ..., e<span style="font-size:78%;">t</span>) : k= σ<span style="font-size:78%;">m</span><span class="Unicode"></span></blockquote><span class="Unicode"> 1.5.3) Some Properties of the Panel Operator:<br /><br />P<span style="font-size:78%;">m</span>{<span style="font-weight: bold;">E</span>,<span style="font-weight: bold;">G</span>,<span style="font-style: italic;">k</span>} is useful insofar as several interesting properties can be derived from this definition. These properties are analogous to the basic operations of arithmetic. They are: Union (Adding panels to each other) and Disjunction (Breaking panels up).<br /><br /><span style="font-style: italic;">Union of adjacent Borders</span>: ... G<span style="font-size:78%;">n-1 </span></span>∪ <span class="Unicode">G<span style="font-size:78%;">n</span> </span>∪ G<span style="font-size:78%;">n+1</span> ...<br /><br />Which can be represented by the operator as the following, given <span style="font-weight: bold;">u</span>, <span style="font-weight: bold;">v, w</span> ∈ E; G<span style="font-size:78%;">n</span>, G<span style="font-size:78%;">n-1</span>, G<span style="font-size:78%;">n+1</span> ∈ <span style="font-weight: bold;">G</span>, σ<span style="font-size:78%;">n, </span>σ<span style="font-size:78%;">n-1, </span>σ<span style="font-size:78%;">n+1</span> ∈ k:<br /><br /><ol><li><span class="Unicode">G<span style="font-size:78%;">n-1</span> </span>∪ <span class="Unicode">G<span style="font-size:78%;">n</span>: </span>P<span style="font-size:78%;">m</span>{E, G<span style="font-size:78%;">n-1</span> + G<span style="font-size:78%;">n</span>, k}= P<span style="font-size:78%;">m</span>{<span style="font-weight: bold;">u</span>+<span style="font-weight: bold;">v</span>, G<span style="font-size:78%;">n-1</span>+G<span style="font-size:78%;">n</span>, σ<span style="font-size:78%;">n-1 <span style="font-size:100%;">+</span></span> σ<span style="font-size:78%;">n</span>}</li><li><span class="Unicode">G<span style="font-size:78%;">n</span> </span>∪ <span class="Unicode">G<span style="font-size:78%;">n+1</span>: </span>P<span style="font-size:78%;">m</span>{E, G<span style="font-size:78%;">n</span> + G<span style="font-size:78%;">n+1</span>, k}= P<span style="font-size:78%;">m</span>{<span style="font-weight: bold;">v+w</span>, G<span style="font-size:78%;">n</span>+G<span style="font-size:78%;">n+1</span>, σ<span style="font-size:78%;">n <span style="font-size:100%;">+</span> </span>σ<span style="font-size:78%;">n+1</span>}</li><li><span class="Unicode">G<span style="font-size:78%;">n-1</span> </span>∪ <span class="Unicode">G<span style="font-size:78%;">n</span></span>∪ <span class="Unicode">G<span style="font-size:78%;">n+1</span>: </span>P<span style="font-size:78%;">m</span>{E, G<span style="font-size:78%;">n-1</span> + G<span style="font-size:78%;">n</span> + G<span style="font-size:78%;">n+1</span>, k}= P<span style="font-size:78%;">m</span>{<span style="font-weight: bold;">u+v+w</span>, G<span style="font-size:78%;">n-1</span>+G<span style="font-size:78%;">n</span>+G<span style="font-size:78%;">n+1</span>, σ<span style="font-size:78%;">n-1 <span style="font-size:100%;">+ </span></span>σ<span style="font-size:78%;">n <span style="font-size:100%;">+</span> </span>σ<span style="font-size:78%;">n+1</span>}</li></ol><br />Since <span style="font-weight: bold;">E</span> is well-ordered, we can write <span style="font-weight: bold;">u+v+w</span>=<span style="font-weight: bold;">x</span>, G<span style="font-size:78%;">n-1</span>+G<span style="font-size:78%;">n</span>+G<span style="font-size:78%;">n+1 <span style="font-size:100%;">= G', </span></span>σ<span style="font-size:78%;">n-1 <span style="font-size:100%;">+ </span></span>σ<span style="font-size:78%;">n <span style="font-size:100%;">+</span> </span>σ<span style="font-size:78%;">n+1</span> = σ'. Thus:<br /><blockquote>P<span style="font-size:78%;">m</span>{<span class="Unicode"><span style="font-weight: bold;">E</span>, G<span style="font-size:78%;">n-1 </span></span>∪ <span class="Unicode">G<span style="font-size:78%;">n</span> </span>∪ G<span style="font-size:78%;">n+1, <span style="font-size:100%;"><span style="font-style: italic;">k</span>}</span> </span>= P<span style="font-size:78%;">m</span>{<span style="font-weight: bold;">x</span>, G', σ'} .</blockquote><span style="font-style: italic;">Corollary</span>: L = <b>Σ G</b>. <span class="Unicode">∎</span><br /><br />However, this only makes sense for consecutive panels. We can run this oppositely to get disjunctions.DrSunshinehttp://www.blogger.com/profile/13446826800939077210noreply@blogger.com0tag:blogger.com,1999:blog-9085744219110187938.post-68951460771367347212010-11-21T13:11:00.000-08:002011-01-04T06:48:24.157-08:00Part I, Chapter 1: Fundamentals, Section 1.4<span style="font-weight: bold;">§ 1.4) Elements as Atomic Propositions</span><br /><br /><div style="text-align: center;"><span style="font-style: italic;">So far our discussion has built up several of the necessary truths<br />of sequential art that have heretofore been taken for granted, or<br />left undefined. However, a necessary concept - that of the "element"-<br />has not yet been defined. This is because ASPM treats all sequential<br />art layouts as being comprised of these fundamental entities, whose<br />nature cannot be further defined. They are, therefore, "atomic".<br /></span></div><br /><br />1.4.1) Sequential Art As Logic:<br /><br />Russell and Whitehead write in <span style="font-style: italic;">Principia Mathematica</span>:<br /><blockquote><br /><div style="text-align: left;">"Atomic propositions may be defined negatively as propositions containing no parts that are propositions, and not containing the notions 'all' or 'some'. Thus 'this is red', 'this is earlier than that,' are atomic propositions." [1]<br /></div></blockquote><div style="text-align: left;">We apply this definition in our treatment of sequential art. Just as in statements of logic there are fundamental propositions which cannot be split up into smaller propositions, there are objects in sequential art that cannot be split up into further objects. For example, the image of a man, as a symbol, is a single element. If one imagines a stick figure standing in an empty white box, the stick figure would be an element, and one could imagine equating the figure in the language of sequential art, with an equally valid statement in writing: "There is a figure".<br /><br />Given the Panel Sequence Theorem (<span style="font-weight: bold;">§</span><span style="font-weight: bold;">1.2</span>), if we draw two panels, we have set up a sequence. And this is the same as saying "If A (panel 1) then B (panel 2)". The act of demarcating some arbitrary number of elements in sequence equates to creating a linear chain of inference.<br /><br />Hence, an element is defined as any object depicted in a layout that cannot be broken down into further qualifications. In practice, of course, it may be difficult or impossible to precisely point to every single element in a layout, but since the object of our task is to achieve a perfectly idealized mathematical model that can serve as a Platonic ideal for all sequential art works, for our purposes we shall treat elements as discrete objects.<br /><br />1.4.2) Sequential Art As Language:<br /><br />As McCloud writes in <span style="font-style: italic;">Making Comics</span>:<br /><br /><blockquote>"Comics is a <span style="font-style: italic;">secret language</span> all its own, and <span style="font-style: italic;">mastering</span> it poses challenges unlike any faced by prose writers, illustrators or any other creative professionals." [2]<br /></blockquote>This statement is true. As mentioned in the introduction, sequential art is a framework built upon writing and art, and exists at the unification of the two disciplines. From this union, and from the special demands imposed on art and writing by the demands of presentation of a visual story on the page, comes a unique grammatical structure built to convey meaning effectively. To that end, insofar as it is, in fact, an orderly system of meaning, sequential art yields useful insights when subjected to analysis by reductionistic logic.<br /><br />This is to say, in general, that, as a<span style="font-style: italic;"> language</span> unto itself, sequential art is by definition an ordered system. One can imagine that, just as the statements of formal language are ordered by the structure of grammar, so too are the statements of sequential art are ordered by a unique form "grammar". Whereas in language, statements such as "If given X, P(x) implies Y; X is true, therefore Y" exist and can be written down, so too does the language of sequential art possess a similar if-then structure, conveyed visually by elements on the page. The fact that there are elements, and that they are encoded by a formal logic, implies a sequentiality similar to that possessed by elements of a language. One can imagine a set of elements in a given layout is in many ways "meant" to be ordered in a given sequence - otherwise, insofar as it as a work of sequential art, the layout would be meaningless. Similarly, a sentence in written language without the structure of grammar, is also meaningless.<br /><br />Thus, by <span style="font-style: italic;">definition</span>, sequential art, in order to be considered sequential art at all, must needs possess an underlying orderliness. It is from orderly, sequential placement of the elements, structured by the grammatical logic of sequential art, that it derives meaning.<br /><br />1.4.3) Logic and Language Imply Atomic Truths<br /><br />Given 1.41 and 1.42, we come to the conclusion that, to gain meaning as a language, sequential art employs elements that are fundamental, and place them in sequence. Therefore, it is meaningful to write statements such as<span style="font-weight: bold;"> e<span style="font-size:78%;">1</span> </span>⊃<span style="font-weight: bold;"> e<span style="font-size:78%;">2</span> </span>⊃<span style="font-weight: bold;"> ... </span>⊃<span style="font-weight: bold;">e<span style="font-size:78%;">m-1</span><span style="font-size:130%;">.</span> ⊢ e<span style="font-size:78%;">m</span></span>, or molecular propositions <span style="font-weight: bold;">e<span style="font-size:78%;">m</span> </span>⊃<span style="font-weight: bold;"> ~e<span style="font-size:78%;">m+1</span></span><span style="font-size:78%;"> </span>because the elements can be treated as ordered sets of atomic propositions. Since sequential art possesses a unique grammar and structure, many aspects are therefore amenable to the same forms of mathematical treatment as logic. Concepts such as design, emotional affect, aesthetics, symbolism, metaphor and so on, are, however, philosophical in nature, and not within the scope of logical sequential art as treated by ASPM. ▮<br /><br />1.4.4) References:<br /><br /><ul><li>[1] Whitehead, A. N. & Russell, B., <span style="font-style: italic;">Principia Mathematica to *56, </span>Second Edition, Cambridge at the University Press, 1964, p. xv</li><li>[2] McCloud, S., <span style="font-style: italic;">Making Comics</span>, Harper-Collins, 2006, p. 2<br /></li></ul></div>DrSunshinehttp://www.blogger.com/profile/13446826800939077210noreply@blogger.com2tag:blogger.com,1999:blog-9085744219110187938.post-33719274058848333002010-11-19T23:01:00.001-08:002010-11-20T12:59:07.284-08:00Part I, Chapter 1: Fundamentals, Section 1.3<span style="font-weight: bold;font-family:georgia;font-size:100%;" >§ 1.3) Uniqueness Theorem</span><br /><br /><div style="text-align: center;"><span style="font-style: italic;"> The Uniqueness Theorem states that any given element <span style="font-weight: bold;">e<span style="font-size:78%;">t </span></span></span><span style="font-style: italic;font-size:100%;" >must</span><span style="font-style: italic;"> absolutely<br />choose to belong to one panel and no others. </span><span style="font-style: italic;">Therefore, the set</span><br /><span style="font-style: italic;">0f elements </span><span style="font-weight: bold; font-style: italic;">e</span><span style="font-weight: bold; font-style: italic;font-size:78%;" >t</span><span style="font-style: italic;"> belonging to Pn is the set of those objects with the property</span><br /><span style="font-style: italic;"> of not belonging to any prior or subsequent panels.</span></div><br />1.3.1) Plain language proof:<br /><br />Given the Axiom of Panels and its corollary, let us define a panel <span class="Unicode">ϕ</span>(x) with the property of being the set of all elements contained in both P<span style="font-size:78%;">n</span> and P<span style="font-size:78%;">n+1</span>. Now every x that is an element of <span class="Unicode">ϕ</span>(x) will have the following properties:<br /><ol><li>It belongs to neither P<span style="font-size:78%;">n-1</span>, nor P<span style="font-size:78%;">n+1</span> .<br /></li><li>It belongs to neither P<span style="font-size:78%;">n</span>, nor P<span style="font-size:78%;">n+2</span>.</li></ol> In terms of predicate logic for a two-valued function <span class="Unicode">ϕ</span>(x,y) where x=y.<br /><br />(x,y)<span class="Unicode">ϕ</span>(x,y): ~x ^ x<br />(x,y)<span class="Unicode">ϕ</span>(x,y): y ^ ~y<br /><br />Using a truth table we can compute the value for these statements.<br /><br />~x ^ x<br />F F T<br />F F T<br />T F F<br />T F T<br /><br />y ^ ~y<br />T F F<br />T F F<br />F F T<br />F F T<br /><br />And, since both statements are equally false, the statement ~x^x = y^~y is true for all cases. Substituting y=x for y, we get ~x^x = x^~x. Being true in all cases, then, means that we can say without a doubt that the statement (x, ...)<span class="Unicode">ϕ</span>(x,...):{x NOT in P<span style="font-size:78%;">n-1</span>, x NOT in P<span style="font-size:78%;">n</span>, x NOT in P<span style="font-size:78%;">n+1</span>, x NOT in P<span style="font-size:78%;">n+2</span>, ...} is always false for any given set of x's, since by mathematical induction, we can see that the proof works for the n+1 case as well. Therefore, by induction, we conclude that because <span class="Unicode">ϕ</span>(x) contains all the elements x that do not belong to any union of spaces P<span style="font-size:78%;">n</span> U P<span style="font-size:78%;">n+1</span>, it is therefore equal to the empty set. Therefore, any element <span style="font-weight: bold;">e<span style="font-size:78%;">t</span></span> must belong to one and only one P<span style="font-size:78%;">n</span>. <span class="Unicode">▮</span><span style="font-style: italic;">.<br /><br /></span><span>1.3.2)</span><span style="font-style: italic;"> </span><span>Proof in Symbolic Logic<span style="font-style: italic;">.</span></span><span style="font-style: italic;"><br /><br /></span><div style="text-align: center;"><span style="font-style: italic;">A proof in symbolic logic will follow.</span><br /><br /><div style="text-align: left;"><span style="font-weight: bold;">NB</span>: Bear in mind that these assertions make no statement on the movement of the eye over the design. At this stage, we are merely trying to build up precise definitions for concepts such as "belonging to" or "exists".<br /><br />1.3.3) Implications of the Uniqueness Theorem.<br /><br />The Uniqueness Theorem implies that, whatever their position in space related to the layout, an element will belong to that panel where it was first read. Imagine if each panel were on its own unique layer, and whatever arrangement of elements was free to exist either within or outside the panel boundaries. By the Uniqueness Theorem, all elements first encountered within those panels will belong strictly to those panels and those alone, since each dwells within its own unique space.<br /></div></div>DrSunshinehttp://www.blogger.com/profile/13446826800939077210noreply@blogger.com0tag:blogger.com,1999:blog-9085744219110187938.post-32397761310214359152010-11-18T09:03:00.001-08:002011-01-04T21:01:11.097-08:00Part I, Chapter 1: Fundamentals, Section 1.2<span style="font-weight: bold;">§ 1.2) Panel Sequence Theorem</span><br /><br /><div style="text-align: center; font-style: italic;">It is now possible to define our first theorem. Panel P<span style="font-size:78%;">1</span> containing a finite<br />subset of elements e<span style="font-size:78%;">1</span>...e<span style="font-size:78%;">t</span>, 1≤t≤m, implies a final panel P<span style="font-size:78%;">m</span>.<br /></div><br />1.2.1) Proof:<br /><br />By the Axiom of Extension (§ 1.1.4) we have a set of elements defined by the property that each <span style="font-weight: bold;">e</span><span style="font-weight: bold;font-size:78%;" >n+1</span> follows sequentially from <span style="font-weight: bold;">e</span><span style="font-size:78%;"><span style="font-weight: bold;">n</span></span>, where 1≤n≤t, on the set of well-formed formulae <span style="font-weight: bold;">e</span><span style="font-weight: bold;font-size:78%;" >1</span> to<span style="font-weight: bold;"> e<span style="font-size:78%;">t</span></span>.<br /><br /><span style="font-weight: bold;">Lemma 1:</span><br /><br /><ol><li> Given <span style="font-weight: bold;">e<span style="font-size:78%;">1</span></span>, and <span style="font-weight: bold;">e<span style="font-size:78%;">1</span></span> ⊃ <span style="font-weight: bold;">e<span style="font-size:78%;">2</span></span>, therefore <span style="font-weight: bold;">e<span style="font-size:78%;">2</span></span>. (<span style="font-style: italic;">modus ponens</span>)</li><li> <span style="font-weight: bold;">e<span style="font-size:78%;">n-1</span></span> ⊃ <span style="font-weight: bold;">e<span style="font-size:78%;">n</span></span></li><li> <span style="font-weight: bold;">e<span style="font-size:78%;">t</span></span> ⊃ <span style="font-weight: bold;">e<span style="font-size:78%;">t+1</span></span></li><li> <span style="font-weight: bold;">e<span style="font-size:78%;">1</span>, e<span style="font-size:78%;">2</span>, ..., e<span style="font-size:78%;">t</span>, e<span style="font-size:78%;">t+1</span>,...,e<span style="font-size:78%;">m-1</span> ⊢ e<span style="font-size:78%;">m</span></span> ▮.</li></ol>This is true by the Deduction Theorem of the propositional calculus.<br /><br />Now, given P<span style="font-size:78%;">n</span> = {<span style="font-weight: bold;">e</span><span style="font-weight: bold;font-size:78%;" >1</span><span style="font-weight: bold;">, e<span style="font-size:78%;">2</span>, ..., e<span style="font-size:78%;">t</span></span>}, let us define P<span style="font-size:78%;">n+1</span> = {<span style="font-weight: bold;">e<span style="font-size:78%;">t+1</span>, e<span style="font-size:78%;">t+2</span>, ..., e<span style="font-size:78%;">s</span></span>}, s ≤ m-1.<br /><br />Let us write x as a variable that takes on values <span style="font-weight: bold;">e<span style="font-size:78%;">1</span>,..., e<span style="font-size:78%;">t</span></span> and satisfies the conditions for P<span style="font-size:78%;">n</span>. Then the definition of P<span style="font-size:78%;">n</span> becomes a predicate P<span style="font-size:78%;">n</span>(x) and all <span style="font-weight: bold;">e<span style="font-size:78%;">t</span></span> in P<span style="font-size:78%;">n</span> can be written as the statement: ∀xP<span style="font-size:78%;">n</span>(x).<br /><br />Now, given Lemma 1:<br /><ol><li>P<span style="font-size:78%;">n</span>(<span style="font-weight: bold;">e<span style="font-size:78%;">t</span></span>) ⊃ P<span style="font-size:78%;">n+1</span>(<span style="font-weight: bold;">e<span style="font-size:78%;">t+1</span></span>)<br /></li></ol>So:<br /><ol><li>∀x<span style="font-size:78%;">1</span>P<span style="font-size:78%;">n</span>(x<span style="font-size:78%;">1</span>) ⊃ ∀x<span style="font-size:78%;">2</span>P<span style="font-size:78%;">n+1</span>(x<span style="font-size:78%;">2</span>); x<span style="font-size:78%;">2</span> = {<span style="font-weight: bold;">e<span style="font-size:78%;">t+1</span>, e<span style="font-size:78%;">t+2</span>, ..., e<span style="font-size:78%;">s</span></span>}</li><li>∴ P<span style="font-size:78%;">n</span>(x<span style="font-size:78%;">1</span>) ⊃ P<span style="font-size:78%;">n+1</span>(x<span style="font-size:78%;">2</span>)</li><li>∴ P<span style="font-size:78%;">n</span>(x<span style="font-size:78%;">1</span>) ⊃ P<span style="font-size:78%;">n+1</span>(x<span style="font-size:78%;">2</span>) ⊃... Pm-1(x<span style="font-size:78%;">m-1</span>) ⊢ P<span style="font-size:78%;">m</span>(x<span style="font-size:78%;">m</span>) ▮.</li></ol><br />1.2.2) Corollary to the Panel Sequence Theorem.<br /><br /><div style="text-align: center; font-style: italic;">Given t=m, the Axiom of Completion implies P<span style="font-size:78%;">1</span> = P<span style="font-size:78%;">m</span>.<br />That is, the panel containing all elements e1...em contained within L is<br />the the only and final panel. Let us call this the Identity Panel P<span style="font-size:78%;">I</span>.<br /><br /></div>1.2.2.1) Proof:<br /><ol><li>∀x<span style="font-size:78%;">1</span>P<span style="font-size:78%;">1</span>(x<span style="font-size:78%;">1</span>) ⊃ ∀x<span style="font-size:78%;">2</span>P<span style="font-size:78%;">n+1</span>(x<span style="font-size:78%;">2</span>)</li><li>x<span style="font-size:78%;">1</span>= <span style="font-weight: bold;">e<span style="font-size:78%;">1</span>, e<span style="font-size:78%;">2</span>..., e<span style="font-size:78%;">m</span></span> = x<span style="font-size:78%;">m</span><br /></li><li>∀x<span style="font-size:78%;">m</span>P<span style="font-size:78%;">1</span>(x<span style="font-size:78%;">m</span>) ⊃ ∀x<span style="font-size:78%;">m</span>P<span style="font-size:78%;">2</span>(x<span style="font-size:78%;">m+1</span>) . ⊃ <span style="font-weight: bold;">f </span><span>(</span><span>Axiom of Completion, </span>§1.1.5<span>)</span><span style="font-weight: bold;"><br /></span></li><li>∀x<span style="font-size:78%;">m</span>P<span style="font-size:78%;">1</span>(x<span style="font-size:78%;">m</span>) ⊃ ∀x<span style="font-size:78%;">m</span>P<span style="font-size:78%;">2</span>(x<span style="font-size:78%;">m+1</span>) . ⊃ <span style="font-weight: bold;">f </span><span>.</span><span style="font-weight: bold;"> </span>⊃<span style="font-weight: bold;"> </span>∀x<span style="font-size:78%;">m</span>P<span style="font-size:78%;">1</span>(x<span style="font-size:78%;">m</span>) = ∀x<span style="font-size:78%;">m</span>P<span style="font-size:78%;">m</span>(x<span style="font-size:78%;">m</span>)</li><li>∴ P<span style="font-size:78%;">1</span>=P<span style="font-size:78%;">m</span> </li><li>⊢P<span style="font-size:78%;">1</span>(x<span style="font-size:78%;">m</span>) : P<span style="font-size:78%;">I</span> ▮.</li></ol>1.2.3) Summary<br /><br />Having proved that P<span style="font-size:78%;">n+1</span> necessarily follows from P<span style="font-size:78%;">n</span>, we arrive at the logical conclusion that if we are to assume that the set of <span style="font-weight: bold;">et </span>is orderly, then having exhausted all <span style="font-weight: bold;">e<span style="font-size:78%;">1</span>...e<span style="font-size:78%;">t</span></span> within P<span style="font-size:78%;">n</span>, one must continue on to P<span style="font-size:78%;">n+1</span> until one has reached P<span style="font-size:78%;">m</span>. Essentially, if the elements are finite and ordered, then the panels must also be finite and ordered.DrSunshinehttp://www.blogger.com/profile/13446826800939077210noreply@blogger.com1tag:blogger.com,1999:blog-9085744219110187938.post-46531493373058466172010-11-17T14:38:00.000-08:002011-02-24T22:16:02.936-08:00Part I, Chapter 1: Fundamentals, Section 1.1<span style="font-weight: bold;">1) Axiomatization of Fundamental Truths of Sequential Art</span><br /><br /><div style="text-align: center;"><span style="font-style: italic;">By developing a sufficiently rich language to describe sequential art,<br />it is possible to make powerful, general statements that are true of all<br />works of sequential art, irregardless of their individual differences.<br /><br /></span></div><span style="font-weight: bold;">§ 1.1) Formalization of First-Order Mathematical Sequential Art</span><br /><br /><div style="text-align: center;"><span style="font-style: italic;">To adequately ground mathematical Sequential Art in firmly logical<br />foundations necessitates the creation of a precise, logical language by<br /> which all theorems of Sequential Art can be derived. What follows are<br />the axioms and formation rules necessary for first-order mathematical<br />sequential art.<br /></span></div><br /><span style="font-weight: bold;">1.1.1) Definitions</span><br /><br />1.1.1.1) <span style="font-style: italic;">The Layout. </span>The layout<span style="font-style: italic;"> </span>L ⊆ ℝ<span style="font-size:78%;">2</span> bounded by a finite, simply-connected border <span style="font-weight: bold;">B</span>. All objects so bounded are considered part of the <span style="font-style: italic;">Universe of Discourse. </span>Any element or subset of L has a positive truth value, any element or subset not in the Universe of Discourse has a negative truth value.<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://2.bp.blogspot.com/_wSw3FwgsD2U/TORde7dAvxI/AAAAAAAAACk/BaJa8ToRjas/s1600/2.png"><br /></a><br />1.1.1.2) <span style="font-style: italic;">Elements. </span><span style="font-weight: bold;">E</span> is the <span style="font-style: italic;">t</span>-tuple consisting of all elements <span style="font-weight: bold;">e<span style="font-size:78%;">t</span> </span>in<span style="font-weight: bold;"> </span>L.<span style="font-weight: bold;"> </span><span>An element is an object in the Universe of Discourse.</span><span style="font-weight: bold;"><br /><br /></span><span>1.1.1.3) <span style="font-style: italic;">Relations. </span>Define the dyadic relation > where<span style="font-style: italic;"></span> </span><span style="font-weight: bold;">e<span style="font-size:78%;">n-1</span></span> > <span style="font-weight: bold;">e</span><span style="font-weight: bold;font-size:78%;" >n</span> for 1<span class="huge">≤n</span><span class="huge">≤t. Let </span><span style="font-weight: bold;">e<span style="font-size:78%;">n-1</span></span> be defined as the <span style="font-style: italic;">predecessor</span> and <span style="font-weight: bold;">e</span><span style="font-weight: bold;font-size:78%;" >n</span> be defined as the <span style="font-style: italic;">successor</span>.<br /><span style="text-decoration: underline;"><br /></span><span style="font-weight: bold;">1.1.2) Formation Rules</span><br /><br />1.1.2.1) <span style="font-style: italic;">Modus Ponens</span>. From <span style="font-weight: bold;">e<span style="font-size:78%;">n-1</span></span> > <span style="font-weight: bold;">e</span><span style="font-weight: bold;font-size:78%;" >n</span> and given <span style="font-weight: bold;">e<span style="font-size:78%;">n-1</span></span> to imply <span style="font-weight: bold;">e</span><span style="font-weight: bold;font-size:78%;" >n</span> . In logical notation:<span><blockquote></blockquote></span><blockquote><span>[[</span><span style="font-weight: bold;">e<span style="font-size:78%;">n-1</span></span> > <span style="font-weight: bold;">e</span><span style="font-weight: bold;font-size:78%;" >n</span>] & [ <span style="font-weight: bold;">e<span style="font-size:78%;">n-1 </span></span>]] ⊃ <span style="font-weight: bold;">e</span><span style="font-weight: bold;font-size:78%;" >n</span>. Df.<br /></blockquote><span style="font-weight: bold;">1.1.3) Axioms</span><br /><br />1.1.3.1) <span style="font-style: italic;">Axiom of Enclosure</span>. Within L, we may draw any number of finite, simply-connected borders enclosing some grouping of elements, subset of <span style="font-weight: bold;">E</span>. Every border is a member of the set of borders <span style="font-weight: bold;">G</span>.<br /><br />1.1.3.2) <span style="font-style: italic;">Axiom of Sequence</span>. The relation > will apply to every pair of elements in E.DrSunshinehttp://www.blogger.com/profile/13446826800939077210noreply@blogger.com3tag:blogger.com,1999:blog-9085744219110187938.post-17652132766751942132010-11-17T14:11:00.000-08:002011-01-04T06:40:40.010-08:00Table of Contents<span style="font-weight: bold;">Part I: Diagnostics</span><br /><br />Chapter 1: Axioms of Mathematical Sequential Art<br /><br />Chapter 2: Formal Semantics<br /><br />...<br /><br /><span style="font-weight: bold;">Part II: Prognostics</span>DrSunshinehttp://www.blogger.com/profile/13446826800939077210noreply@blogger.com0tag:blogger.com,1999:blog-9085744219110187938.post-65238595959258523492010-11-17T14:10:00.000-08:002010-11-21T13:04:13.876-08:00<div style="text-align: center;"><span style="font-size:180%;"><span style="font-weight: bold;">PART I</span></span><br /><br /><br /><br /><span style="font-size:100%;"><span style="font-style: italic;"><span style="font-size:130%;">Diagnostics</span><br /><br /><br /><br /><br /><br /><br /><span><br />Mathematics is the dream,<br />Physics is the reality.<br /></span></span><span style="font-weight: bold;"></span></span></div>DrSunshinehttp://www.blogger.com/profile/13446826800939077210noreply@blogger.com0tag:blogger.com,1999:blog-9085744219110187938.post-16914658299950448332010-11-17T14:00:00.000-08:002010-11-20T12:56:57.030-08:00Outline of the BookThe agenda of this book will be to provide precise, mathematical descriptions for every aspect of sequential art, and to derive theorems based on these axioms proving commonly-held notions about sequential art. The goal of this exercise is essentially to prove that these commonly-held notions consist of an independent, consistent logical framework that obeys certain properties; and, having a fundamental basis in logical operations, to be able to make broad, general statements that are true for all sequential art. To that end, we will develop a calculus for determining an abstract, general system of sequential art that exists entirely in the world of mathematics, but whose properties can be specified or modified to apply to any real work of sequential art.<br /><br />The ability to make precise statements about any particular system governed by a certain set of axioms, is a fundamental step towards a comprehensive understanding of all systems governed by the same axioms. This is analogous to how a fundamental knowledge of physics is essential for making precise statements necessary for engineering and building specific machinery. A broad, fundamental understanding of the basic principles underlying <span style="font-style: italic;">all</span> sequential art, then, is imperative for the growth and development of the field.<br /><br />Thus, this book will be divided into two main parts: Part One will deal exclusively with the establishment of axioms, theorems, and precise definitions for the common tools and systems found within sequential art; while Part Two will deal with the material implications of these axioms and theorems. A substantial goal of Part One will be to develop the mathematical machinery necessary for describing the concept of <span style="font-style: italic;">flow</span> through a sequential art layout, a precise, mathematical description of which will be the primary subject of Part Two.<br /><br />Hence, one could broadly describe the two parts as largely being divided into, for part one, a treatment of "statics", of building up an analytic model for the base, logical machinery that govern the operations of sequential art; and for part two, a development of "dynamics", of creating a prognostic model using that machinery to create a deterministic system for governing flow. Necessarily, then, the first part will rely heavily on mathematical logic, set theory, and abstract algebra; while the second part will rely heavily on systems analysis, differential equations, and multivariable calculus.<br /><br />It is assumed by the author that the reader is at least generally familiar with these mathematical tools and can follow a cogent mathematical argument. Arguments will be done in the traditional theorem-proof structure, building conclusions based on logical deductions from the basic axioms, then using theorems to prove further theorems. Where necessary, simple diagrams will be provided.DrSunshinehttp://www.blogger.com/profile/13446826800939077210noreply@blogger.com0tag:blogger.com,1999:blog-9085744219110187938.post-80050528156065477472010-11-17T13:00:00.000-08:002010-11-20T11:55:59.765-08:00Acknowledgments<div style="text-align: center;"><span style="font-style: italic;">Special thanks go to Eric Gerlach, my</span><br /><span style="font-style: italic;">philosophy professor at Berkeley City College,</span><br /><span style="font-style: italic;">for his excellent course in logic, that</span><br /><span style="font-style: italic;">turned me on to concepts such as syllogisms,</span><br /> <span style="font-style: italic;">mathematical logic, and truth tables. I would<br />not have known about these interesting<br />systems had it not been for this course and<br />his clear and effective presentations.<br /></span></div>DrSunshinehttp://www.blogger.com/profile/13446826800939077210noreply@blogger.com0tag:blogger.com,1999:blog-9085744219110187938.post-37238207275266417512010-11-17T12:52:00.000-08:002010-11-20T11:43:28.523-08:00IntroductionThis is a declaration of war.<br /><br />This is the response of the natural scientist, who knows the world empirically, based on reason and sound logic, to those who claim to know nothing. This is a rejection of negative, skeptical philosophies who reject the axioms of true, physical reality, in favor of unprovable, unknowable claims about the unreality of nature and the uncertainty of knowledge that are beyond proof and evidence; and an affirmation of empirical truths that appeal to common sense and logical deductions based on sound axioms.<br /><br />The natural scientist embraces the future and values forward progress and knowledge; the skeptic claims that history is a circle and points to the past. The past is dead, a rotten framework built of driftwood and twigs, around a termite-hollowed core; it is in the future that promise and progress lie.<br /><br />Thus spoken we turn to the aim of this book: the axiomatization and empiricization of a realm that which was once thought of as the domain of only the philosopher, the artist, and the writer. Here I speak of the world of <span style="font-style: italic;">sequential art</span>.<br /><br />Let me address the question of <span style="font-style: italic;">why</span><span> we must axiomatize sequential art. The world of sequential art is a type of <span style="font-style: italic;">craft</span>, hence it lies at the intersection of art and writing, the boundary inhabited by design and technical illustration. Art without writing is static, is frozen: a statue has no movement, a painting has form but does not change in time; writing without art is invulnerable to physical analysis, trapped within a world of symbols, metaphor, language and grammar. Taken alone, each are equally timeless and resistant to analytical techniques, but the demands of <span style="font-style: italic;">craft</span>, when taken together, bring them down to a zone where they are amenable to logical treatment.<br /><br />Yet in the history of analysis of sequential art, all treatises on the subject have been written exclusively by artists, not engineers nor scientists, and are necessarily comparative, inductive rather than deductive, without the technical vocabulary to <span style="font-style: italic;">precisely define</span> the concepts of which they speak. McCloud comes closest to this, but even he fails at giving a <span style="font-style: italic;">totally empirical definition</span> of the mechanisms which animate comics, and is forced to reason by means of analogies and vague pictures and symbols. The same has happened time and time again in every area of human knowledge.<br /><br />Like DaVinci, Galileo, and Kepler of the past, the world of physics fully explored the myriad descriptive methods available to science of the time until it ran up against the boundaries of what was possible with their paradigm. With the coming of Newton's <span style="font-style: italic;">Philosophiae Naturalis Principia Mathematica</span> the world of physics was transformed with a new paradigm; it was given new life and animation by the development of Newton's calculus, which axiomatized the principles of planetary motion and the movements of objects in space, generalizing and abstracting the inductive, empirical knowledge of before with deductive logic. Having the new paradigm of Newton's logic, science explored every avenue of research until it reached its limit in the early twentieth century, where again its boundaries were expanded and generalized further with the quantum theory and Einstein's general relativity.<br /><br />Likewise, all theoretical developments in any area of human knowledge will explore every possibility, every method of analysis, until they reach the boundaries posed by their current methodological paradigm, at which point progress is impossible without forcing open those boundaries with a new concept, and establishing a new paradigm. And at the core of each new paradigm is a further abstraction, a further generalization, an expansion of the view to encompass larger principles and a more concrete description of the concepts of the previous.<br /></span><br />Therefore the agenda of this book is <span style="font-style: italic;">revolutionary</span>. We have currently reached the limit of where earlier theorists have explored and if we are to progress further we must discover new principles. Our aim is therefore to axiomatize the rules-of-thumb that describe the principles of sequential art, outlined by predecessors such as McCloud and Eisner, and create a paradigm where sequential art is enriched by <span style="font-style: italic;">precise definitions</span> and refined by <span style="font-style: italic;">exact, deterministic analytical tools</span>. <span></span><br /><br />And at the core of this agenda, is logic. We will use logic as a hammer to smash down the hand-waving, flimsy architecture of those who came before; we will use our hammer of logic and the raw firmament of the past furnished by this demolition to build a new system on stronger foundations than ever before.<br /><br /><span style="font-style: italic;">ATD, 2010</span>DrSunshinehttp://www.blogger.com/profile/13446826800939077210noreply@blogger.com1