Sucking the Blood out of a Mosquito

I considered titling this post ‘On Surrealism’, but ‘Sucking the Blood out of a Mosquito’ sounded less stodgy, so I went with that.  Sorry if it grosses you out a little.  Anyway, here it is:

It was one of the primary goals of the surrealist movement to astonish its audience.  I believe the surrealists have succeeded wonderfully in that regard, but I am not sure to what end.  In terms of the impact, there is little difference between a hare getting a tortoisecut and an apple crawling out of a worm—both are surreal and astonishing, but neither one communicates to us a particular truth or wonder.  It seems that in trying desperately to liberate his expressive palette, the surrealist has actually restricted it and very nearly reduced it to utter meaninglessness.  Instead of reconciling fantasy with reality, he has rejected reality altogether, turning inward to the more vivid but even less satisfying world his of imagination.

Salvador Dalí (1904 – 1989) was a Spanish surrealist painter, and at times, a devout Catholic.  He is probably most famous for painting this:

The_Persistence_of_Memory
The Persistence of Memory

Perhaps, considering how iconoclastic a movement he followed, it might astonish us that Dalí was ever a Catholic.  But I think this only reflects how greatly our modern society tends to misunderstand what it means to be Christian.  Unlike Surrealism, Christianity is an ideology with no preference for either novelty or convention.  The Surrealist movement has existed entirely for the sake of revolution—take away the radicalism and the astonishment dies.  But Christianity makes no comment on either the radical or the obvious, and if it harbours any implicit affiliation with tradition, it is that religious tradition exists for the sake of Christianity and not the other way around.  However, while the novelty of Surrealism then poses no incompatibility in itself, there still seems to be a conflict between the Surrealist movement as it originally began and Christianity.  That conflict is the alleged rejection of reason.

As I’ve argued elsewhere, there really is no such thing as illogical thought.  One can believe in the irrational but not experience it.  And this belief is what fuels conventional surrealist art, while also providing its greatest shortcoming.  What I find so uninteresting about an apple crawling out of a worm is not the situation itself, but its implied context.  Surrealism cannot help but take place in a world with no rules, a world with no limitations or conflicts.  But these adversities are the very things that make earthly life interesting in the first place, and to exclude them from an imitation of nature is to overlook the most beautiful thing on this side of eternity: the resolution of dissonance.  Good art doesn’t astonish merely for the sake of astonishment; instead it imitates nature, and that is astonishing in itself.  Perhaps making that kind of art might entail hares getting tortoisecuts or sucking the blood out of mosquitos, but at the same time, every incongruity ought to be rationally explained, and that will make it all the more beautiful.

Sometimes as Christians we can forget how astonishing the world really is.  We too might think that the only recourse from the dull vexation of this revolving planet under the sun is some kind of escape.  But in actuality, we need no compensation for the truth.  There is in fact nothing more astonishing than the most fundamental reality of our lives:

Dalí's painting of the Passion of Christ.
Dalí’s painting of the Passion of Christ.

 

There is nothing illogical about God’s creation, but everything about it is astonishing.  For we could not imagine something more beautiful or surreal than what Our Saviour has done for us in reality.  And what is the purpose of art or even of fantasy if not to reinvigorate once again our astonishment with that truth?

Incidentally, Dalí was also fascinated with rhinoceroses.

Is Love Irrational?

More specifically, could love be radical without being irrational?

Ever since the mystical romanticism of nineteenth century western culture, it has become fashionable to regard love as an irrational human sentiment.  People seem to like this notion because it gives love a special place in philosophy: love is not the sort of thing you can write a long philosophical treatise on (or can you?), but instead it is a subject for great poems and works of art.  Of course, this understanding completely disregards any art that may be inherent in the genera of boring treatise writing, which is entirely surpassed, it is supposed, by the capacity of an ardent poet.  Indeed, this superior position seems to be where such a notion of love is placed; it is not merely irrational but super-rational, transcending and exceeding the limits of the human intellect into some supposedly higher, metaphysical realm of unintelligible emotion.

Some readers might think this notion is less novel than I have made it out to be, and perhaps a brief look at gothic love poetry—by which the romantics were allegedly inspired—would reveal so much.  But let me respond to all such objectors with the position that the culmination of that poetic school is actually the dolce stil nuovo—a highly rational understanding of love.  Indeed, there is very little mystical about medieval mysticism.  But enough arguing with my imaginary antagonists; let’s look at an early renaissance passage.  This comes from John Milton’s Paradise Lost, wherein Eve has just eaten the forbidden fruit and Adam is now throwing a mild hissy-fit over the matter:

“Should God create another Eve, and I

Another Rib afford, yet loss of thee

Would never from my heart; no, no, I feel

The Link of Nature draw me: Flesh of Flesh,

Bone of my Bone thou art, and from thy State

Mine never shall be parted, bliss or woe.”

(Milton, Paradise Lost IX.911-6)

The last two lines might seem irrational.  Why would Adam ever pursue a state of woe?  That doesn’t make any rational sense; hence, Adam’s love must be irrational.  But such a reading completely overlooks Adam’s own rationale, which he provides quite clearly: ‘I feel the Link of Nature draw me’.  Milton is referring to the classical metaphor for marriage as a chain (people have been complaining about ‘the old ball and chain’ since antiquity).  So entering into a state of woe is something that Adam would do by compulsion, and thus, he violates no rational principles.  But Adam’s first premise is the most puzzling part of his logical argument: ‘Should God create another Eve … loss of thee / Would never from my heart’.  What does that mean?  If God could make another version of the same thing that Adam holds dear, why on earth would Adam pursue the broken one rather than being satisfied with a replacement?

We could easily imagine this question posed in much a more personal way.  Suppose after thirty-five years of marriage, when the children are fully grown and left the cave, Eve turns to Adam in a moment of personal dissatisfaction and asks him that enduring question which has baffled the mind of every lover since the dawn of mankind: ‘why did you choose me?’  Adam would hardly have found himself in a tighter spot if she had instead asked, ‘does this sheep skin make me look fat?’  But he has an easy way out, a simple, rational answer that has been available to no man since: ‘I frankly had no other options.’   However, much to our amazement and stupefaction, Adam utterly refuses this obvious answer and favours a romantic and seemingly mystical one.  He goes out of his way to create a hypothetical situation in which there are other Eves and then still decides to stick with his particular wife.  Why?

But how relevant are the blueberries?

Intellectual reader, I invite you to imagine with me a malleable set of declaratives. By this I mean a set of logically related statements that can be altered for the purposes of experimentation; we can take away, add, or reposition declaratives and observe what becomes of the rest of the set. Our first observation will be the way in which each component part is related to each other. Only two sorts of logical relationships may exist between any given pair of statements, though these relationships may be described multiple ways and are best expressed as magnitudes, not booleans. In other words, it is best to discuss the extent to which a certain relationship exists rather than the fact of its existence or lack thereof.

venn diagram figure 1
Figure 1

We will here only discuss one of the two relationships: that of logical consequence. To describe this relationship, we may refer to declaratives as either “following from” one another or else “being contained” within each other. A concrete example is in order: suppose I held before you a black pen; if I were creative enough, I could talk about the pen forever, because there are infinite truths that may be said of this black pen of mine. But suppose, of all the possibilities, I chose to say to you, “this pen exists”. The use of the demonstrative pronoun ‘this’ brings into language all the infinite qualities that the pen possesses; hence, “this pen is black” follows from, or if your prefer, is contained within “this pen exists” because the former is a subset of all the infinite truths contained within the latter.

Figure 2
Figure 2

So picture the two declaratives as a venn diagram; in this instance, it is not a conventional-looking image (figure 1). But if we were to consider another example, the diagram would look more familiar: suppose instead I said to you, “this pen uses black ink, and all pens that use black ink write clearly”. Now you might reply, being the clever reader you are, with another fact that follows and is contained within the previous two; “if that is so,” you would answer in your decorous manner, “then this pen writes clearly”. Aside from our admiration for what a sensible and insightful logician this response makes you out to be, we are now struck by the complexity of a logical phenomenon. Presently we have two statements that intersect to form a third (figure 2), so “this pen writes clearly” follows from the union of “this pen uses black ink” and “all pens that use black ink write clearly”.

Kindly notice that each bubble in the diagrams above may vary in size, depending on what order of infinity it represents. Notice further that, in our second example, A and B share certain common facts, which set of declaratives we call C, but also have some differences. So how closely related are A and B? The answer is a simple measure of area, and it describes a notion that I will call ‘gravity’. To express the formula for gravity, I will refer to the area of a statement X with the symbolic convention, ∫X. So the gravity between A and B in our example is Γ = ∫C / (∫A + ∫B).

This expression solves two important problems. The first is that of defining a scope, a sector of reality that is coherent. Consider an example: you tell a friend that, on theological grounds, you believe it was immoral for him to steal blueberries from Mr. Dimmesdale, and in his contemplative manner, he says, “but ‘God works all things together for the good of those who love Him’, so my deed will ultimately come to good”. You are both right, but he has misapplied a teleological perspective to an analysis of the action itself. The fact that he brought up exists in a larger scope than the matter you are discussing. And defining a scope is no subjective matter, to express it mathematically, we must first make one more definition: a “gravitational average” is the average gravity that one statement bears on each other member of a set. With that in place, a scope is any set of declaratives that exists such that each member has an equivalent gravitational average.

The second issue that gravity solves is that of distinguishing normal functioning from dissociative functioning. Dissociative functioning is a section of a proof of actions on which an alternative declarative bears greater gravity than the primal premise. For a more in-depth discussion of this, see Is Hypnosis Self-Evident? A Concise Philosophical Inquiry, in which post I describe the concept of gravity in different terms that nonetheless mean the same thing.

It seems prudent to define one last term: the Quantum Model of Reality. If we picture reality as a black-board with an infinite area, on which each infinitesimal point represents a fact (and those combine to from larger facts), by the Quantum Model of Reality, we are able to draw lines on the board to sector it off into quantum regions contained within one another; in other words, we can draw a larger circle around a smaller one ad infinitum, where each circle represents a valid scope that is defined in terms of a gravitational average. This is why, elsewhere on this blog, we have referred to reality existing in ‘levels’. In practical application, “God works all things together for the good of those who love Him” can only be discussed in relation to other notions of equal size, and Mr. Dimmesdale’s blueberries still ought be returned.

The Nature of Causality in the Logical Scope

if a then b => if !b then !a

Doesn’t that make sense? Why do people act like it doesn’t?

Causality is such a difficult phenomenon to isolate. This is a large part of what makes tragic plays so stimulating–we can argue for hours about what really caused all the dead bodies to pile up at the end; was it Hamlet’s slowness to act? his uncle’s murder? or perhaps Polonius’ regulation of his daughter? The best answer is generally something along the lines of, “it was all these things and more”. For maybe if Hamlet weren’t so prone to depression, if Laertes hadn’t come from France, or the dang Dane, Hamlet the late, had just decided to take his nap somewhere else or a little later in the afternoon, the whole catastrophe could have been avoided. This brings up the whole discussion of chaotic theory on a sociological level. Because perhaps even smaller changes could have been made to the history than the ones I have mentioned if they were made earlier on. Maybe if Hamlet the late had gone to bed earlier the night before, he wouldn’t have needed to take a nap˚. And maybe he would have gone to bed earlier if he weren’t busy doing such and such, and perhaps such and such wouldn’t have had to be done if… We could, theoretically trace the whole history back to the beginning of time; at which point, if a single molecule, floating in space, had been displaced by a fraction of a micrometer, Gertrude might never have married, Hamlet might have never been born, and perhaps even Denmark might never have become a nation.

Personally, I find this is fascinating. It certainly says something about the nature of causality. Every little, fractal detail of the cause has a profound impact on the effect. This is an even bigger deal when it comes to a consideration of the Omnipotent, for He is the beginning of time and the root cause of all reality. I’ve included a definition of the rule of modus tollens at the beginning of this post, with whatever disregard of formal symbols, for this reason. Many a tricky relativist likes to try to weasel his way around causality, often suggesting that every event and quality of reality is the result of nothing and our minds are merely erring in seeking out patterns and reasons for things to result from other things. As far as I’m concerned, that’s fine; if a person doesn’t believe in reality, then I should even less expect him or her to believe in the causal nature of reality. But what doesn’t work, by my assessment, is the attempt to separate causality from the logical scope. Logic, by definition, assumes the principles of modus ponens and modus tollens, or more simply, the concept of an “if then”. Therefore, it seems to be quite impossible to have logic without having causality. For logic assumes that the validity of a premise determines, or causes, the validity of a conclusion.

Within the absolutist scope, metaphysical reality is assumed to be, to some extend, comprehensible via the normative reasoning of the human mind. In a way, reason is the only metaphysical entity that we are undeniably conscious of (if you will pardon my casual use of the term metaphysical). Though reason is expressed as physical phenomena in the brain, the pure properties of logic, that express themselves in the mind, must be considered metaphysical, or as I am using the word, real but not tangible. Because of this, there is a sense in which reason must dictate our beliefs as to the qualities of reality as it exists beyond the purely physical. Just as we assume physical reality to have the qualities which are perceived by our five sense, we must also assume metaphysical reality to have the qualities perceived by our sixth sense–our mind. If the fact that we see in colour leads us to believe that the universe is colourful, then the fact that we reason causally must lead us to believe that the normative is causal. And if we believe there is anything beyond the physical–which we must believe, for by the very act of thinking logically, we are engaging such a realm–then we must believe that reality is ultimately beyond the physical†. Therefore, in the same sense of the word, “reality” is ultimately causal in nature.

This being established, we must consider the nature of causality as it exists in reality to be the same as the nature of causality as it exists in reason. Let us consider what this nature is.

It may be useful here for us to rethink the conventional concept of a logical proof. Proof is commonly thought of as a sort of sequence of steps that lead from a given to a conclusion. This is all fine and well, but let us consider what it really means. If the rules of logic are universal, then a proof is not the act of taking one thing and transforming it into another, but rather the human explanation of why one thing is also another. Take a mathematical proof for instance. If we want to prove that 0over0 equals one in the context of “limit x–> 0 f(x) = sin(x) / x”, we take the function and limit as a given, go through a series of steps, and show why it equals one. But we have not in fact converted one concept into another. We have merely shown that by logic, the one concept is the other, for at the end of the proof, we realise that the given expression is equivalent to the concluded one. There is no conversion process from premise to conclusion; proofs only serve to show us that a premise is the same thing as a conclusion.

In the same sense, we must also consider causality to be, like proofs, a human way of understanding that a cause is, normatively, the same thing as its effect. Therefore, returning to the Omnipotent, He must in this same sense be, as the primal cause, the same thing as His effect. This is why I so often write that He is reality. And thus, if He is everything that is Real, He must possess every quality that is Real. Therefore, if we assume that our reason is Real, then we must believe Him to be rational. To me this is the easy part of the argument. It is self-evident that the cause of all Reality would have to be rational if there is such a thing as reason. Reason must be linked, by causality, all the way to the beginning of existence, the primal cause. And only things that are not real in some sense* may posses “qualities” not possessed by the Omnipotent (see “Theology of Non-being”)˚. All this follows from (or is) what is written above.

And now a point of interest: What also “follows” from above is that the Omnipotent is very large. Certainly, we already knew He was infinite and we are “finite,” but the Hamlet example can give a very good explanation for this. If every effect is affected by smaller and smaller details of its cause the further along the chain of causality that it gets from that cause, then with the Omnipotent having existed eternally before time began, we must believe that we are the effects of his infinitesimals. That is, if the Omnipotent is a giant fractal at the beginning of reality (and really making up all of reality), then we, being effects that exist some infinite distance along His causal chain, must be caused by the smallest possible details of Him, and therefore, are the smallest possible details of Him. However, it is important to note that, with Him being the highest possible order of infinity–paradox that that is–even his infinitesimals must be infinite, and therefore, while He is infinitely greater than us, we are still, in this sense, infinite ourselves, so long as we actually exist.

This means that the Omnipotent is capable of considering us infinitely, while at the same time conceiving an infinite universe, and for that matter making an infinite number of other infinite creations all of which He plans for and cares about infinitely. This seems to present a reasonable rebuttal to the objection that there cannot be a personal God because the universe is so large.

Such is one of the arguments that Richard Feynman brings up in the following video. He doesn’t really focus exclusively on that topic, but he says some other interesting things as well, which I thought made the video worth posting:

____________________

˚ Okay, I suppose it was “his custom always in the afternoon”, but still, would he have upheld that custom even if he wasn’t tired? Of course there is no definitive answer to such a question, but that’s my point: the causality is hard to isolate.

† For it is only beyond the physical that we are ultimately able to say that something exists, as the very notion of existence is a normative principle, and all the qualities of reality are normative, because, while we might describe a physical object as having “physical qualities” those qualities themselves are concepts (ex. an apple is red, but redness is a concept). This might just sound like a word game to many, and I realise that I may be over simplifying a much larger issue–and one that is largely disagreed about–but consider it as this: Somewhere in your mind, you differentiate between the way you view and understand the physical and the conceptual. You, by your very nature as a human, attach to those to realms particular values. That is, each of them means something different. Whether you want to call the one or the other “more real” doesn’t really matter much to this argument, so long as you realise that when I discuss reality, I will be referring to the conceptual or normative, and not just as it exists in our minds, but as it actually exists, even beyond them. For I am assuming–the absolutist that I am–that two plus to actually equals four, not that it just happens to in our minds. Without this sort of assumption, there is no actual point in thinking at all (in the same sense of the word “actual”).

* As darkness can be said to be a thing, but is really nothingness, it is the absence of something, so can there be things that are defined by their lacking of realness, they are the absence of realness.

˚ Here is another way of looking at the irrationality of evil discussed in “Theology of Non-being.” Irrationality is allowed to exist in evil, though it is not a quality possessed by the Omnipotent, because evil is, in a sense, “unreal”.

Ref #1: What’s Recursion

It was recently brought to my attention, thanks to the much appreciated input of a commenter that not everyone reading this blog knows what a fractal is.  As I began to think about how to explain the concept, I started to realize that there may be many such topic that I frequent in my writings that readers are unfamiliar with.  Although I try to give enough background information within each post, perhaps that is not always entirely sufficient.  Therefore, I have decided to create a series of “reference posts” explaining various such things for the sake of increasing the overall accessibility of this site.

Recursion: see recursion.

On its basic level, a recursive algorithm is an algorithm that is somehow defined relative to the same system it is creating.  For example, one might define a geometric sequence recursively as follows:

A1 = 2

An = A(n-1) * 2

This definition would produce the following sequence:

2, 4, 8, 16, 32, 64 … 2^n

In this sequence, I have defined each term relative to the term before it with the exception of the first term which I have given a set starting point.  Since each term is found by doubling the previous term, the overall sequence can be said to be recursive because each part of the sequence is defined relative to another part of the same sequence, and so, more generally, the sequence is defined relative to itself.

Recursion is, however, a broader concept than this and can extend beyond the world of simple algebra.  In fact, recursion can be found all over nature.  A simple example is when two mirrors are held so that they reflect each other.  One ends up with the image of a mirror inside a mirror inside … This is because the image on the mirror is defined relative to itself.

Another simple example of recursion is proof by induction.  In a proof by induction, one proves that an algebraic expression of n is equivalent to each respective term of a sequence by plugging it in recursively.  I will use the same geometric sequence above as an example:

Prove: if   A1 = 2  &  An = A(n-1) * 2  then  An = 2^n

2, 4, … A(n-1) * 2 = An

Assume: An = 2^n

2, 4, … A(n-1) * 2 = 2^n

∵  (2^n) * 2 = 2^(n + 1)     ! plug-in 2^n for the sequence on the left and apply the algorithm

!of multiplying by two to find the next term.  See if that is equal

!to the definition one the right incremented by one.

(2^n) * (2^1) = 2^(n + 1)

2^(n + 1) =  2^(n + 1)

Q.E.D.

Another example of recursion is the algorithm used by a scientific calculator to parse a formula into a computable expression.  That is, if I enter the expression

3 *2+4*3*2 +2

into a scientific calculator, it solves it recursively.  It might, for example, have an evaluate method that takes the first number and applies to it the solution of the rest of the expression (which it finds using the same evaluate method) using the given operation.  If you are familiar with computer science, the code might look something like this (in summary):

double evaluate(String expression){

if(getFirstOperation(expression) == MULTIPLICATION)

return getFirstNumber(expression) *  evaluate(getRestOfExpression(expression))

+ evaluate(getExpressionAfterFirstPlus(expression));

else if(getFirstOperation(expression) == ADDITION)

return getFirstNumber(expression);

//the code would be written a little differently

//inorder to accommodate for other cases

// this is merely an example that would solve

//the above problem

}

Recursion can also be thought of more generally as any process that references itself.  For example, phycology might be considered recursive because it is using the mind to study itself.  Recursion occurs in levels (see “Levels of Recursion”) or iterations.  Every time a recursive algorithm is completed, the system is said to have undergone one iteration or advanced one level of recursion.

Google has a pretty funny joke about recursion.

A Singular Application of Levels of Recursion

A friend of mine recently showed me the following question which I believe can be found online somewhere (besides here):

If an answer to this question is chosen at random, what is the percent chance that it will be the correct answer?

A. 25%

B. 15%

C. 50%

D. 25%

There is actually nothing wrong with this question.  If one looks at it at the trivial case level, it actually doesn’t have an answer, and therefore, an answer must be assigned arbitrarily in order to see the rest of the system work its way out, thus any answer given is ultimately arbitrary.  The question is, in this sense, like asking “What is the correct answer to this question?” which is really just nonsense.  However, ignoring that, lets suppose we assigned our trivial case the answer “B. 15%.”

This selection, while creating an arbitrary answer on this level, the trivial case, causes a relative correct answer of A or D on the next, lets call it the second, level of recursion.  There being two correct answers on the second level of recursion makes C the right answer on the third level, and thus on the fourth level we are back to A or D.

This is not a paradox, it is just a matter of an indeterminate level of recursion, which I find, as you probably could have deduced from the title of this website, quite fascinating.

Of course, the absolute answer to this question is that is does not have an intelligible answer anymore than does the aforementioned question, “What is the correct answer to this question?”  However, if we assume the trivial case for no reason (i. e. we chose it trivially˚), then I think the most convincing answer would be the “infiniteth” level of recursion, which, because the system has no limit, no end behavior, would be best put into the words “none of the above.”

In a later post, I might well invent a less trivial application or come across it by necessity; I just found this one interesting.

__________________________________

˚ O dear.  I’m really not that funny am I.

Levels of Recursion

Haskell Curry’s paradox, titled “Curry’s paradox,” is often stated in formal logic as follows:

let A = (A–>B)          ! A is a boolean assigned the value “if A then B,” in words this means that “A is true if A’s being true means that B is true”

A –> A

A –> (A–>B)             ! Substitution

A && A –> B

A –> B

A                                      ! Substitution

B                                       ! modus ponens

The logical error lie in the ignorance of levels of recursion.  In reality, there is no such thing as letting A1 = (A1–>B), because that is an in equality.  A1 does not equal A1–>B, it equals A1.  The algebraic analog of this principle would be something like “x=x+1” for which there is no real solution, and seeing as there is no such thing as imaginary logic, at least not yet (though there should be), the expression is utter nonsense in logic.  The first statement can remain in the syntax that it is currently in; however, it should be realized that what that statement implies is “Let A1 = (A2–>B).”  Thus the recession in logic works just the same as it does in algebraic recursive sequences (i.e. we never define “a sub n” in terms of “a sub n” but rather in terms of “a sub n plus or minus some integer value”).

Thus the proof is disproven as follows:

let A1 = (A2–>B)

A1 –> A1

A1 –> (A2–>B)

A1 && A2 –> B              ! This simplifies no further.

This understanding is essential to the functionality of logic and is very relevant allover the place.