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.

On Aesthetics and Existence

Suppose there were some sort of nonhuman, rational being wandering the earth and observing human life.  This nonhuman, we will call him a ‘metahuman’, has nothing in common with humanity except reason alone.  He doesn’t experience the same desires that we do, nor possess the same needs.  In fact, let us say that he is subject to no desires or needs whatsoever.  As he makes his way through our curious little planet, he encounters a good number of phenomena with which his rationality is perfectly reconciled.  By virtue of being rational, he understands that a being must act in promotion of its own sustainment; this is simply a manifestation of adherence to the core principle of rationality–noncontradiction.  And so it comes as no surprise to him that people eat food.  A quick explanation of the natural science behind the human anatomy allows him to understand this act as rational and noncontradictory to existence.  He is also at ease when he sees people working for money to buy that food, exercising to help maintain the body in other ways, and getting married to help maintain the population.  With all these things, I believe our metahumane friend would be quite satisfied.

There is, however, an aspect of the human experience that I suspect might not sit as well with him.  That aspect is human philocaly, the love of beauty.  Upon extended observation of human living, I believe he might find himself asking, “why do these creatures so fastidiously obsess themselves with matters of absolutely no relevance to their existence?”  “Why,” he might ask, “do the sit for long hours watching the sunrise?  why do they drive themselves mad over the colours of oils on canvases or arrangements of sounds over time?  The time they spend on these things could be better spent working for food, eating food, exercising, or reproducing.” It seems that art is a superfluous facet of human existence.

However, while such an observation might vex our metahuman, if he is capable of being vexed, I do not think that he should outright object to it.  There is, after all, nothing inherently self-contradictory about art.  Art is, by all means, rationally permissible, but what the metahuman would understand, and we must realise, is that, ostensibly, art is rationally unnecessary.

It seems that art neither opposes nor promotes human existence.  And for the metahuman, a being’s existence is the first step in a deductive proof that merits his or her actions.  By taking existence as a given, the metahuman can prove that a human being must eat and exercise and must not undergo self-imposed starvation or deprival of exercise because such do’s and don’t’s are rationally necessary.  All behaviour that a being exhibits is only made possible by his or her existence, and so, in order to be rationally sound, none of such behaviour may oppose that being’s existence, for to do so would be to create, as it were, a contradiction in the normative ‘proof of actions’.  In other words, there is a logical fallacy in a chain of reasoning that reads, “A exists, therefore A acts, therefore A does not exist”*.  Likewise, there are certain actions that a being must take in order to sustain existence, which may be called ‘rationally necessary’.  Obviously, to neglect to do such things is to passively oppose existence and to, therefore, once again create a logical fallacy.  Ergo, all rational beings are demanded, by their reason, to avoid actions that oppose their existence and execute those that promote it.

However, in a sense, art neither promotes nor opposes human existence.  No one has ever starved from musical malnourishment (though I have had nightmares …) nor died of prolonged exposure to oil paintings.  It seems then, at least prima facie, that art has no baring on the metahuman’s proof of actions.  Hence, how it should be handled in the formal proof becomes quite a difficult matter.  Occam’s Razor might suggest that we remove it by default, but this seems a mere ‘easy way out’ of a question that rests on empirical evidence which powerfully suggests alternatives. The very fact that humans do indeed partake in the enjoyment of art seems to suggest that Occam’s Razor cannot be here applicable for one of three reasons: (1) humanity is not rational after all, as demonstrated by her irrational aesthetic passions, (2) art is a necessary part of the proof of actions in some more nuanced way than we have yet understood, or (3) art is necessitated by something other than the ‘primal premise’ in the proof of actions.

(By ‘primal premise,’ I mean existence; the jargon is intended to portray the analogical link between this and the Primal Cause Argument for the existence of God.  It is supposed, under the Primal Cause Argument, that given the existence of the universe and humanity, within the context of causality, a ‘primal cause’ that came first and without a cause of its own is a metaphysical necessity.  Our currant discourse takes the existence of humanity as the ‘primal premise’ in a proof of actions that demonstrates the rational necessity of self-sustainment.  This link will be important later on.)

Of course the first of these three reasons is, in its present form, utterly absurd because it denies the existence of human reason, on which it is dependent, as evidenced by its classification as a ‘reason’.  However, we might refine it a bit to say that, while humanity is capable of being rational, art is an example of her departure from rationality, however exceptional such a behaviour might be for her.  But that is a rather lame explanation of art, especially considering the fact that this blog purposes to demonstrate that beauty is a fractal construct of reason.  Therefore, we will be finding that the better option is either two or three.

In order to consider the reason for human philocaly, we must begin by considering the reason for human philosophy˚.  As it turns out, human philosophy is indeed rationally necessary, however its necessity is less clearly linked to the ‘primal premise’.  If belief is–as many have considered it to be–the act of depending on a supposed truth, then human beings have no choice but to believe in some things and not in others.  By sitting here, typing this post, I am believing that my computer will not explode in my face and kill me.  I am counting on that fact.  If I were to believe that my computer is going to explode, then my act of writing this post would be irrational, as it would be opposing my existence.  Hence, in order to be a rational being, I must believe certain things and not others (which, in this case, means that, given my sitting here typing, I must believe that my computer will not explode and not that it will).  This is because the rationality of an act (i.e. its promotion and non-opposition of existence) is dependent on certain suppositions that surround the act–that is, we must ‘count on’ or ‘believe in’ certain supposed truths in order for the action, or more accurately, the intention behind the action, to be classifiable as an action (or intention) of self-sustainment.  But the only rational way I can arrive at a belief is by way of philosophy.  In other words, it is irrational to count on the veracity of a given supposition without reason to do so.  Hence, the existence of reason (which is simply a more specific facet of the ‘primal premise’) is self-sustained by philosophy.  And so, philosophy is rationally necessary.

Recall from the previous ALUC posts that art, the discourse of emotions, is really an extension of philosophy, the discourse of reason, in that emotions are fractal constructs of rational processes.  Therefore, it seems that art may be necessitated by the mere fact of philosophy’s necessity.  If we are required, by reason, to rationally deliberate truth in order to arrive at rational beliefs, then why would we not also be required to do the same emotionally?  Human engagement in art is, in this sense, simply a way of making use of all methods of discovering truth available to the human.

Now would be a good point in the essay to point out a flaw in our model of reason thus far; I think I’ll do just that: The average Christian or reasonable thinker reading this post has already been quite troubled by the whole idea of self-sustainment.  We Kantian moralists, who make up most of the world, like to think that morality is an extension of rationality, and as such, must be governed by the laws of reason.  Therefore, the idea that reason would incessantly demand our constant attendance to self-sustainment is troubling to the Christian who believes that self-sacrifice is the core principle of all morality.  Hence, it seems our model has been all too simple.

Allow me, therefore, to do a bit of remodelling.  In Computer Science (the science of programming computers) there are conceptual entities called “objects”.  An “object” is something that sits out somewhere in the computer’s memory and can be called to perform tasks or can be acted on by other objects.  The particular tasks that a given object might be able to perform are decided on by the programer, and the possibilities are nearly endless.  However, one task that an object can never perform is self-deletion.  This is because of the logical fallacy that we have been discussing; it simply doesn’t make logical sense for something to destroy itself, and computer science reflects this inescapable normative principle.  However, sometimes, as you might imagine, objects do in fact need to be deleted.  For this task, the system itself must be called.  In other words, to delete an object, we must act not within the object’s personal scope, but within a larger scope that contains the object, which is called the system in the case of computer science.

A very similar phenomenon occurs in life outside of computers.  Sometimes there comes a point when objects need to be deleted, persons need to die.  At such a time, the principle still holds that a moral agent cannot delete himself, but a larger scope must be called on for his deletion.  So far, we have discussed the proof of actions as a self-contained system of rationality—something that is demanded to be non-contradictory with itself.  But if reality is fractal, then this “larger scope” that we are calling on must actually be self-similar; it must be similar to the “proof of actions” construct which it contains.  Hence, the deletion of a person must be appealed to the primal premise not of a proof of actions contained within the person, but of such a proof contained only by the scope of reality itself.

If you’re wondering what such a primal premise could possibly be, recall the disgustingly long and tastelessly obtrusive parenthetical element above in which the link between a ‘primal premise’ and a ‘primal cause’ was alluded to.  Herein lies the point: if the self-similar construct that is reality contains moral agents with proofs of actions that are premised on the respective existences of those agents, then reality itself is a massive proof of actions that is premised on its own existence (and since its existence is premised on its primal cause, we may say that this is the primal premise of the universal proof of actions, and consequentially, is the universal analogue of a moral agent’s existence).  Hence, the first line of the universal proof of actions reads: “Reality is.”  And because reality is subject to logic, all following lines must be non-contradictory to the existence of reality—or more specifically, to the existence of the primal cause and its particular nature.

And so, we appeal to this universal proof of actions for the deletion of a person; however, even within this larger scope, the deletions of persons is irrational.  Because reality is fractal, the principle that a moral agent cannot be deleted (which originates within the scope of the agent himself as a principle of self-sustainment) is reconstructed in larger, congruent scopes by necessity, including the scope of reality itself.  So the fact that there come occasions when persons must be deleted poses a serious threat to the logical soundness of the universal system (reality).

However, notice the phrase “a person must be deleted”; this implies that the deletion of the person is logically necessary.  Hence, we have a contradiction.  The principle of non-deletion that is perpetuated up through the self-similar system demands that persons are never deleted, however, sometimes reality demands that they are (e.g. in the case of war).  This tells us that something went wrong earlier in the proof of actions; some phenomenon has opposed reality and defied logic.  We will explore the phenomenon in a later post.  At present, we must merely understand that there is a contradiction, and that the contradiction must be fixed.  Logic demands that something be done in the universal proof of actions in order to correct the error.

So allow me to present the contradiction clearly:  Two moral agents are placed on a metaphysical see-saw, but only one is allowed to step off, leaving the other to go hurling down through the endless abyss of nonexistence (that is, of death or whatever the particular situation calls for).  Each moral agent is demanded to preserve both himself (by his own proof of actions) and the other agent (by a congruent construct of the other agent’s proof of actions).  It’s quite a pickle.  The only rational solution is the beautiful mathematical principle of Substitution.  One of the agents must choose to substitute his own primal premise with that of the other agent; that is, he must value the other agent’s existence in place of his own.  People less esoteric and nerdy than myself call this “love”.

That is exactly what has happened in the case of the universal proof of actions.  As a consequence of some error, humanity got set on a chain of reasoning that leads directly to death, but because it is logically necessary for man to keep on existing, the Primal Cause himself made the Grand Substitution.  The existence of man was substituted for the existence of Reality, causing all the equations to boggle about as reality demanded its own destruction and the very principle that called  for the deletion to be made was set to be deleted, reversing the error and undefying logic.  All this, we know, must have happened for two reasons: (1) it is the only possible solution to the contradiction, and (2) it maintains self-similarity with other proofs of actions (e.g. when a man sacrifices his life for his country).

As a result of all this, Substitution has become a principle of logic.  It logically necessary (and therefore morally right) for persons to sacrifice themselves for others because Reality has sacrificed itself for them.  The principle of Substitution trickles down to latter iterations of the universal fractal in this way.  For that matter, I might point out that logic is simply defined by whatever the Primal Cause does.  In other words, self-sustainment is logically necessary because the Primal Cause exists and continues to exist, and self-sacrifice is logically necessary because the Primal Cause sacrifices itself; every action that the Primal Cause takes is imitated in every smaller scope of reality due to its self-similar structure—that’s what logic is.

So logic is defined by the actions of the Primal Cause.  This might leave us wondering: why does the Primal Cause act in the way it does?  Or to put it more bluntly, what defines the actions of the Primal Cause?  The only answer I have for this is “the Primal Will”.  The “Primal Will” is the end of the line in the determining of actions.  The Primal Cause does what it does simply because that’s the way things Absolutely are.  Christians and non-christians alike might find interesting what the Bible has to say about this.  In Revelations 4: 11, it say, “You are worthy, our Lord and our God, to receive Glory and Honour and Power, because you created all things and through your will they exist and were created”.  Where I have translated “through your will,” the ancient Greek reads “διὰ τὸ θέλημά σου” which we might also translate “because of your pleasure”.  So in one sense, we understand that things are the way they are because they ought to be (because it’s God’s will), but in another sense, they’re just that way for the fun of it (because of God’s pleasure).  Either way, the verse contends that He is to receive glory and honour for this—God’s will or pleasure is absolutely Good.  However, what this means is that as intricate and difficult to decipher as reality is, the fractal is that way in part because that is how it ought to be, but also simply for the mere fun of it.  God choose to create, to love, and to die for that love for the sake of his good pleasure, his θέλημά.

Now that was a pretty long tangent.  Remember, this post is about philocaly.  And so I ask what is art if not the highest form of Substitution available to man?  Art is the surrendering of one’s self to beauty, the giving of one’s soul to all of humanity.  An artist is demanded to be courageous and bold; he must wildly surrender everything with which his creator has endowed him to the creation of something beautiful—a love letter to humanity.  When he performs this creative task, he is acting rationally and in congruity with his maker’s primal act of creation and self-sacrifice, which was conducted under the Καλός Θέλημά (Good Will or Beautiful Pleasure, Καλός being the word from whence we get ‘philocaly’ – the love of beauty; the love of good).

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* Obviously an application of the transitive property to this statement makes it read “A exists, therefore A does not exist,” which, needless to say, is utter nonsense.

˚Just when you thought those ivory towers couldn’t grow any higher and the thinkers inside them couldn’t become anymore distanced from the real world, the philosophers start philosophising about philosophy.

So Just How Many Cookies did Jimmy Have?

If Jimmy has negative seven cookies and eats the square root of them, does he have more than zero left?

This question was, of course, primarily designed to make fun of the limited number of applications that exist for some of the most interesting pieces of mathematics.  Even the few applications that do exist for imaginary numbers are rather esoteric and obscure.  But it is no surprise that departure from real numbers makes applicability in the real world sparse.

However, for those of you quixotics who, like me, don’t care so much about the real world, I have decided to write a brief discussion of the topic.  The question is: Is i root seven positive or negative?  Most people will want to say it is positive, but consider the following:

i=-iThe fact that = –might leave some readers confused.  There are many ways of looking at this, but here’s the one that I prefer:  is neither negative nor positive, it is imaginary, and only real numbers can be compared with zero.  When we say “negative i,” what we really mean is “times negative one”.  can have a real coefficient, but, being imaginary, has no sign.  Therefore, the number of cookies Jimmy had is a truly matter of philosophical inquiry.

A friend of mine put it well: “He has something other than zero cookies, but really, he has nothing–except in his imagination”.

Therefore, the answer to the question posed earlier (Is i root seven positive or negative?) is no.

Why I am not an Evolutionist

Unlike many, I see no incompatibility between Christian doctrines and the Theory of Evolution.  I don’t think that Christianity is meant to explain all of science for us; instead, I am quite compelled to think the opposite.  The Holy Bible uses the language it uses not to explain the laws of physics to us or tell us how old the earth is, but to explain that which lies beyond the capacity of human finding.  Turning once more to the model presented in “La cima del purgatorio,” one might say that the Bible was written to explain to us all the things that Virgil is incapable of discovering for himself.

With that in place, it quickly becomes clear that any references to “science” that we find in the Bible are not the ultimate intent of their associated rhetoric, but are themselves rhetorical devices being used for the communication of something much more important.  To differentiate between the makeup of a rhetorical strategy and the intention of the rhetoric, consider the case of Larry the Cucumber’s infamous water buffalo song.  Here we have a vacuous vegetable going on with a rather silly song only to be interrupted by some scrupulous other who objects to a discrepancy of complete irrelevance.  The situation is almost comical.  Actually, I think it is comical, maybe even silly.  But I hold it as no less silly to object to a passage in the Bible because it makes allusion to the earth being flat (or something of that sort).  Indeed, at the time the Bible was written, the earth was thought to be flat, and we should hardly expect the text to have gone so far out of its way as to first explain all of science to its readers before making any allusion to the physical universe–that’s just silly!  Instead, the best rhetorical strategy God could have chosen would be to speak of the world in the vernacular of the people he was working through, which happened to include some irrelevant misunderstandings about the physical universe.  This indeed seems to be the strategy He has taken.

For those of you Christians who do not agree with me on this, consider 1 Kings 7:23 which reads, “And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and its height was five cubits: and a line of thirty cubits did compass it round about” (KJV).  If we do some algebra:

d = 10 cubits

r = 5 cubits

c = 30 cubits = 2 π r

2 * 5 cubits * π = 30

π = 3

We get a mathematical statement that I have disproven more times than I can possibly count.  But I do not hold the exact value of π as being any more relevant to the salvation of souls than the ownership of water buffaloes is to the enjoyment of a humorous little song.  And so it seems to me to be of equally little importance whether or not God created humanity through a long, many-yeared process or a six-day one.  All I care, with regard to the literal facts, is that He created us and did so according to the normative principles that have elsewhere been established as necessary prerequisites to our existence.

One brief side note before I turn directly to the science of evolution: All the inaccuracies that have hitherto been mentioned are perhaps not even as dramatic or detrimental to the purely literal bible as we might make them out to be.  Consider the following points:

  • Three is less than five percent different from π, which actually makes it an accurate estimate of the irrational number when we account for significant figures.
  • The earth cannot be proven to revolve around the sun, and we indeed have no conclusive evidence that it does.
  • The earth, being roughly egg-shaped, does not really form any exact geometric shape at all, and therefore, to say whether it is flat or round is somewhat subjective.  Parts of it are flat, and other parts are round, but no part of it is perfectly flat or perfectly round.†
  • The order of the creation of species described in Genesis is roughly the same order science is uncovering, and the word that is translated to “day” could also be translated to “period.”  Therefore, the book might be saying that God created the universe in six time periods which are in the same order as science supposes them to be.

However, as I have said, I find all this argument about the physical universe to be largely irrelevant.  Now to evolution:

I find no theoretical inconsistency with the theory of evolution, but I find it hard to accept as a respectable scientific theory on the grounds of plausibility.  Having relatively little knowledge of biology, I will find it useful to comment on the theory from a statistical perspective rather than an empirical one.

Your DNA is made up of approximately six billion (6,000,000,000) genetic base pairs, each of which are in one of four possible arrangements (assuming that mismatches of nucleotides are negligible).  This means that according to Carl Haub’s estimate for the total number of people that have ever lived, there is less than a one in 3 * 10 ^ 1,800,000,000 chance that you would exist right now, assuming that there cannot be two people with exactly identical DNA, which would further decrease the probability.˚  This number completely excludes the probability of the human race existing, which is dependent on all physical factors that were necessary for its genesis–if there are such identifiable factors–as well as all those which are necessary for its continued prosperity.*

Furthermore, in the world of statistics, if we suppose that apes have DNA that is different from humans by two percent, and humans and apes together have an average of four point two billion base pairs (still using that six billion from earlier, and averaging it with the two point four billion ape base pairs), then forty-two million base pairs had to randomly mutate in order for either species to evolve from their ideal common ancestor (this being one percent of the aforementioned average), and twice that number in order for the whole process to occur.  Hence, the chance of the human race evolving from a common ancestor to apes is less than one in roughly 2 * 10 ^ 25200001 for every four point two billion mutations that occur.  We do not currently have any conclusive figure describing the mutation rate of humans or apes (that I know of), but it is thought to be very low.  Hence, if I were to take a single atom off the tip of your nose and throw it randomly into the universe, this single evolutionary step in what is thought to be an immense chain reaction of similar processes is less probable than you finding your missing nose piece without searching for it (based on the current estimates of the number of atoms in the universe).

It is imperative that you understand that these numbers are incomprehensible (uh … yes … that’s supposed to be funny).

Of course all this work is very rough and dependent much more on statistics than science, but the math certainly shows that biologists have some serious explaining to do, if nothing more.  I fear that because many believe that evolution is so relevant arguments against theism, they have shaded the public’s view of the theory.  Indeed, public perception is so misguided on this matter that people who know nothing about the subject hold it as solid fact.  In reality, it seems that it is very shaky theory, and if the evolutionist don’t have some clever reason that statistics are irrelevant to the plausibility of the theory, then we will all be compelled to call the Theory of Macroevolution “pseudoscience.”  I do, of course, understand that it is a very useful model that can be stimulating to research and organisation of data, and for that reason would not propose to throw it out all together, but would suggest to stop preaching it so religiously as fact–because it is clearly not true.

What bothers me about this situation, and has led me to blog about it, is a concern not with theistic and atheistic argument, but with academic honesty and sincere truth-seeking.  It seems that the voice of those who would point out that the emperor has no cloths has been buried in the overpowering assertiveness of those who would not.  Science has effectively lied to us, and that bothers me for science’s sake as well as for the sake of all academia.

POST WORD:

Here is a program that shows how a geocentric theory of the solar system is just as plausible (but less practical perhaps) as the current heliocentric theory.

And here is a “Super Calculator” that I created with the hope of using it to compute those ridiculous figures I’ve included in this post.  Much to my chagrin, I found that, even as efficient as it is, the program would take many years to arrive at those numbers (that’s how absurd they are!), and was compelled instead to turn to more theoretical methods of “Discrete Mathematics.”  But if you think that a super calculator is the sort of thing you’d like to have floating around on your hard drive, click the link.

(Technically, every word in this article is a “post” word.)

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† As the currant theory stands, it is a fractal.  Of course I have stepped outside the scope of the question once I turn to such a theory, but so have the people who proposed the question in the first place.

˚ We shall ignore the negligible probability of two individuals having the same DNA by chance or in the case of identical twins.  This makes the math easier and has little effect on the estimate.

* I realize that this statistic is not all that relevant to evolution, but consider it an interesting prelude to the more relevant information found in the subsequent paragraph.

Ref #2: What’s a Fractal

Draw your own fractals with my fractal drawing software, TWM Fractals.  With the new “Animate” feature, you can watch as your fractals iterate before your very eyes!  (It’s quite entertaining.)  Click the link to download.  (It requires java JRE.  I’m not really sure which version, but as long as it’s not super old, it should work.)

In geometry, a fractal is the infinite iteration of a recursively defined figure.  That is, it is a figure whose sides are defined recursively and iterated to infinity.  A simple example of a fractal it Koch’s Snowflake .  Koch’s Snowflake is a geometric fractal based around an equilateral triangle.

The algorithm for turning such a triangle into a fractal is as follows:  subdivide each side into four equal parts such that, in the middle of each side, a triangle protrudes that is similar to the original, only missing one side. It will look like this:

Once this is completed, the figure is said to have undergone one iteration.  Now we repeat the process for each side, include those newly formed sides:


and so on to infinity…

Once the figure has been iterated to infinity, it is considered a fractal.  This means that every part of its perimeter has the exact same structure (while some parts are smaller and others larger).  Fractals are often considered to be fraction-dimensional figures.  This is because, in any integer dimension, an infinite sum of infinitesimal parts (that is, 0over0) is an integral, which always has a finite solution.  But in the case of a fractal, we have an infinite sum of infinitesimal parts (still 0over0) that has an infinite solution.  This means that the perimeter of Koch’s flake has an infinite length (as each iteration increases the length by a factor of 4/3).  This is because the order of infinity that describes the number of sides is higher than the order of inverse infinity that describes the length of each side.  It is often thought of as a paradox that a figure, such as a fractal, can have a finite area but infinite perimeter and an infinite perimeter made only of infinitesimals.

Theology of Nonbeing

A friend of mine was recently discussing hell with me, a delightful subject, and we came to the issue of being and nonbeing.  I realise I can often sound kind of crazy when I present one of my models on just about anything, so I thought I’d post about it in the hopes of straightening things out a bit.  If I do not achieve that end, at least the rest of the public will be able to benefit from the entertainment.  Everyone loves a good crazy-man-ramble; that’s why Shakespeare is so full of them!

I think that’s the first exclamation mark I’ve used in this entire blog!

So, to be clear, the question I will intend to address is: what does the Bible tell us that hell is?

In quantum physics, there is a theoretical phenomenon called quantum superposition.  In summary (and, if you’re a physics person reading this, forgive me for not explaining this well), it states that a physical system exists, in part, in each of its possible states or configurations at the same time, though when measured, results will only suggest one particular state.  It is my understanding, though I am much more a calculus person than a physics person, that there is not currently a satisfying model as to how this is possible, only a mathematical model for how physical systems behave under this theory, and the probability of a given measurement returning a given result.  The phenomenon is often likened to some sort of analogy, a common example being that of “Schrödinger’s Cat,” which goes as follows: a cat is placed in a box where it cannot be seen along with a lethal vial of poison that will automatically be broken after an unknown, finite duration of time, killing the cat.  While the box is closed, the cat is therefore considered to be both dead and alive (‘superpositioned’ in these two states simultaneously).  It is not until the box is open that a measurement reports a single one of these states.

In some ways, these sorts of theories seem to me like the attempts of physicists to jam together a whole lot of facts that we just can’t seem to make proper sense of, but in other ways, they seem to make perfect sense based on the empirical information we have and the accompanying math.  I suppose the theories can be described in both those ways at the same time.

I bring this up because my model of hell is very similar in nature to these sorts of theories.  There is a conflict in a lot of the most essential writings of theology and Christian literature (and even an implied conflict in the Bible) between hell being a real place that God sustains for the continued punishment of evil and hell being the conceptual place of nonexistence.  Let us call the first of these the “classical” theory and the second the “annihilationist” theory.  There seems to be particular issues with each of these models: in the classical theory, we have two main issues (1) how could a loving God be so mean as to actively torture his own creation? (2) how could any place be a hell if God himself is sustaining it? wouldn’t his very presence make it a heaven?  And in the annihilationist theory, we have two main doctrinal issues: (1) how is it justice if the unsaved just cease to exist? it seems like they got away with it. (2) what about the lake of fire and all that? doesn’t the Bible Itself completely debunk this theory?

I shall discuss each of these issues before arriving at my model.

As for the first issue of the classical theory; that is, how could a loving God be so mean as to actively torture his own creation?  Most doctrines suggest that God is not doing anything of the sort.  Those who are damned are simply allowed to do as they chose, and however painful such a choice may be, they much prefer it over having to answer to a Higher Authority˚.  Of course, this presents a problem, because it is impossible to not answer to God, as He is the very definition of Reality, so part of hell is irrationality.  There is no logical way for one to justify one’s own damnation, therefore one turns to the illogical.  This is one of the many things that Milton portrays so well in his Paradise Lost.  In the second book, when the demons are holding council, after having been damned to hell, to determine a course of action, Mammon (one of the demons) says this: “Let us not then pursue / By force impossible … our [former] state / Of splendid vassalage [under God in Heaven], but rather seek / Our own good from ourselves, and from our own / Live to ourselves, though in this vast recess [that is hell], / Free, and to none accountable, preferring / Hard [or painful] liberty before the easy yoke / Of servile Pomp” (Milton II.249-257).  Of course this is completely irrational, as there is no joy to be found in hell, and to be confined to flames is certainly not freedom, but hell is a matter of illogical rhetoric, and the demons are good at this.  Even a parting from reason is an abolition of freedom, for as the classical model of the soul suggests, a will is not free without reason.  Logic is what makes the act of willing pointed.  Without it, a will is just a random decision maker; there is no point to willing something if one does not do so for a reason.  (What’s the difference between saying “I had a point in doing it” and “I did it for a reason”?)

But I digress, the point is, hell is a place of reversals; what seems to be freedom is oppression, and what seems to be oppressive torture by God is really just free choice by man.

As for the second of the classical issues (how could any place be a hell if God sustains it?):  Somehow, God must create a distance between Himself and that evil, for it is an Omnipotent impossibility (Absolute Nonsense) for God to be united with evil.  Therefore, God must be entirely absent from hell.  But how can something exist  apart from God?  For “without Him, nothing was made that has been made,” and in a timeless reality, as we are lead to believe eternity exists, to be made must really be the same as to exist.  Thus it seems that nothing should exist without Him, and indeed it is commonly excepted doctrine that without God, we would cease to exist.  So how can hell exist where God is absent?  This issue seems to confirm that our model is required to contain some element of annihilationism.

The two issues with the annihilationist theory do not bring up anything of significance themselves other than that our model must include some element of the classical theory.  However one piece of evidence directly in favour of the annihilationist theory is Jesus’ repeated reference to the saved being blessed with “eternal life” (ex. John 17), the implication that the damned to not receive this.

So it seems hell must be a place where God is entirely absent, and evil suffers from the very nature of being evil (for to be evil is to suffer).  Thus we have two elements of the model that need to be jammed together like the quantum physics model discussed earlier.  And thus, hell is a place where the nonbeings exist–the failed creations, those who were given the option to be a part of the Body of Christ, to live eternally, and chose not to.  Clearly there is a sense in which, while Heaven is everlasting life, hell is well thought of as everlasting death*.  Thus it is described as an abyss (Revelation 9), or a bottomless pit (Revelation 20) where one may not rest (Isaiah 57), and evil is often associated with falling (Proverbs 24:16).  All seems to invoke a sense of infinite nothingness, and this is indeed what one should mathematically expect it to be like, for since there is such a thing as infinite somethingness, anything aside from that somethingness must be infinitely nothingness.  Another common biblical image is the likening of evil to darkness and Good to light.  Darkness is nothing in itself, but is the absence of light.  In this way, we can imagine something outside of God which, while it is nothingness because it is apart from God, still exists relative to God, and is thus neither self-sustaining nor nonexistent, just as darkness could be said to be sustained, as an independent entity (or non-entity), by the existence of light while it is still nothingness.  One thing worth noting with this analogy is that just as light and darkness, Good may exist without there existing evil but evil may not exist without there existing Good, for darkness is only defined relative to light (it is the absence of light), but light is a thing in itself†.

So there we have a good chunk of the biblical basis of the model, but let us continue to develop images for it, now secular ones, in order to better isolate it.

There’s always calculus to do this for us.  Let us imagine and infinite God that creates a finite being which of its own free will, chose to part from its maker.  Thus, the finite being can be represented by lim x->∞ 1/x.  And thus, it can be said both to exist and not exist in the same way that the limit is always zero but the function never is.  This relates nicely to the image of constant falling in a bottomless pit˚.

Lastly, let us consider an image for you folks that don’t care so much for math and technicality.  A story:  Once upon a time, there was a boy named Jimmy.  Jimmy loved to smoke, eat fries, and listen to a single rap song, which he played very loudly.  All these things were, for him, the greatest joys in life, and he did all he possibly could just to get more of them.  Then, one day, Jimmy suddenly broke down; he couldn’t stand his life any longer and he didn’t know why.  At therapy, he was introduced to classical music and forced to start eating better and stop smoking.  Suddenly, he realised that he had never known pleasure till that day, but had always been in a lot of pain.  It was as if his life had changed from black and white to colour. He no longer enjoyed smoking or eating junk, nor did he consider that rap song to be music.  Thus, there was some sort of paradox between the existence of pleasure in those activities and the absence.  It seems that they are existing pleasures, but whence one compares them to something much greater, their value completely vanishes.  So may it be with Heaven and hell.  Hell may exist, and creatures damned to it may consider it to constitute as existence (though, unlike in our story, they will find it very painful), but if they were to be graced by but a single delicate ray of Heaven, they would blaspheme their very beings and call it death.  It is clear which of the perspectives is the most correct one.  God is Reality, and since everything exists relative to Reality, that is, to the Absolute Truth, Heaven must have the final say.

Like much of my writing, this may just seem like a whole lot of work over something trivial, after all, all we really need to know about hell is that it’s a place we don’t want to end up, but this could perhaps help some people reconcile the mystery of infinite love and divine justice (two elements that Christianity is the only religion I know of to sufficiently address, and does so primarily through its unique doctrine of Redemption), but the main point of this theorising is to create functional models that may be used in other circumstances for the accomplishment of more practical ends.

I do anticipate mathematics catching up to this concept in the future; it’s a wonder we don’t already have numbers that are simultaneously entirely real and entirely imaginary.

__________________________

˚ Conceptually, there is a difference between God creating and sustaining a place of torture away from Himself to which all are given the option to go, and Him actively torturing them.

* Thus Milton also writes “Then who can create thee lamenting learn / When who can uncreate thee thou shalt know” (Milton V.894-95), and thus revelations talks of damnation as the “second death.”

† An interesting aside is how this relates to eastern philosophy.  It upholds the idea of nonbeing, or whatever they prefer to call it, but refutes the idea of Yin and Yang, because while nonbeing is dependent on being, being is not dependent on nonbeing, and thus the one is evil and the other Good.  There is, therefore, an essential difference between the two that results from logical necessity.

˚ It is interesting to note, however, in this case we are literally plugging in infinity for x, and therefore we arrive at an absolute infinitesimal (that is one for which, like a recursively defined infinitesimal, rate of change is irrelevant), and in calculus, we like to say that infinitesimals are both nonzero and zero quantities.

Please note: on further examination, it was found that there had actually been twenty-five other exclamation marks on this blog preceding the ones above, so I was a little off; I didn’t realise I was such an exciting writer!