Karmaclysm

Yes. I took LSD. At a psychedelic trance festival called Karmaclysm. No state of mind like that can be put into words, but I have done my best to describe it. Uploaded as PDF to preserve formatting that I developed in OpenOffice.

karmaclysm

A Paper about Kantian Morality

Sorry I haven’t updated for an extremely long time. Anyway, here is a paper I wrote for my philosophy class comparing Kant to Mill. It’s answering the question of whether moral laws should be absolute or admit of certain exceptions. It was only supposed to be 5 pages long, so I obviously haven’t included all the possible counterarguments.

I’m not sure if I actually believe the entirety of what I wrote, but hey, whatever.

In formulating a morality upon which to base our actions, we will inevitably have to decide upon the level of absoluteness that ought to underly its groundwork. Should our moral laws allow some amount of ambiguity to reside within, or should they command our actions categorically? If the former were the case, we would allow a certain flexibility to permeate the general laws of morality, one that would permit us to under various circumstances deviate from our usual obligations. In the latter case, however, that in which only categorical laws would command us, we could never permit ourselves to find any exception to said laws, that is, we would have to obey them no matter what circumstances arose. Our moral system would consist of an absolute code, one that we could never break while simultaneously considering ourselves to be acting out of morality. The first claim, that moral laws must admit of exceptions, represents a substantial part of John Stuart Mill’s utilitarian view, whereas the second claim, that all of morality ought to be categorical and absolute, characterizes the foundation of Immanuel Kant’s moral framework. Though Mill’s philosophy at first seems to coincide with common perceptions of morality, the non-absoluteness of his moral code undermines the self-consistency in the nature of moral obligation and objectivity; Kant, however, derives his laws on the basis of self-consistency alone, proving that only his morality could actually exist.
If we wish to determine which moral code we ought to let govern our behavior, we must first define what morality means. To begin, let us acknowledge that any set of laws must be inherently self-consistent, for nothing logically contradictory (originally spelled: kantradictory) could ever exist in this universe; all laws, whether scientific or moral, must be non-paradoxical. If we then wish to base our actions upon these moral laws, such a choice obliges us to adhere to their mandates. Simply by definition, morality tells us what we ought to do; it commands the should. If we depart from the dictates of morality (which we as humans have the capability to do), then we can no longer consider our actions moral. Thus, I found this paper on the assumption that we as humans choose to act from morality (the question of whether we ought to make this choice at all is quite interesting, but not relevant to the present subject) and will now attempt to describe at least in part (I could not describe them in full in such a short space) the properties of that morality. Let us begin with Mill.
In Utilitarianism, John Stuart Mill outlines his morality in terms of the greatest happiness principle, in which “actions are right in proportion as they tend to promote happiness; wrong as they tend to produce the reverse of happiness” (Mill 7). As such, he argues, we should always act while considering happiness the ultimate end. Mill defines said happiness as the presence of pleasure and the absence of pain, unhappiness as the reverse (Mill 7). Though his theory resembles classical hedonism in its fundamental nature, with pleasure serving as the ultimate goal, Mill does not treat every pleasure equally, but instead fully acknowledges “the superiority of mental over bodily pleasures” (Mill 8). In other words, Mill applies a strong qualitative filter to the pleasures we seek, enabling us, for example, to distinguish between the pleasure of drunkenness and the pleasure of giving alms.
Avoiding the pitfall of classical hedonism—if we require a standard to compare pleasures, then pleasure is not the ultimate end—Mill argues that the only standard we can employ to differentiate between good pleasures and bad is experience alone. A person who has been both drunk and the leader of a charity (though hopefully not at the same time) will for the most part say that the latter provides more pleasure than the former. Mill then proceeds to detail the ultimate pleasure, that for which we all strive, whether knowingly or not, as that of social expediency (also called social utility), or the advancement of society. The cause of this feeling, the force that drives us to seek this ultimate pleasure, is “the essence of the conscience,” which he describes as “a mass of feeling which must be broken through in order to do what violates our standard of right… a subjective feeling in our own minds” (Mill 29). Describing the conscience as an entity unique to mankind, Mill solidifies the foundation of the moral standard of utilitarianism.
Upon examining some of the general directives of social utility, such as preserving life or keeping promises, one will find that they often coincide with those of Kantian morality (to follow), at least in terms of their consequences. However, as per Mill, social utility is the ultimate end, at times “so important as to overrule any one of the general maxims of justice” (Mill 63). In other words, we can always find exception to any normally followed moral law when we view the situation through a utilitarian lens. For instance, despite the fact that most people consider the act of stealing immoral, if one needed to commit this act in order to save another’s life, Mill’s moral code would allow it, often naming such an act as “not only… allowable, but a duty” (Mill 63). This again arises from the idea of the conscience, that which gives us pleasure for acting out of social expediency, this pleasure being the ultimate end. We can see no moral law as absolute, for each law would yield a number (though few) of particular cases requiring us to break it. Kant, however, argues otherwise.
In Grounding for the Metaphysics of Morals, Immanuel Kant bases his ethics on the idea of the a priori, or deduction based on logic alone. The grounding for a priori reasoning rests on the idea that in order for something to exist, it must be entirely self-consistent. The law of addition, for example, is a priori because it contains no logical contradictions. If, however, a law of mathematics held that 4 + 4 = 8, but 4 + 3 = 9, it could not logically exist, for no standard could explain how both of those equations could ever be in harmony simultaneously. The understanding of self-consistency’s necessity, says Kant, “can admittedly be found only in a rational being insofar as this representation… is the determining ground of the will,” or rather this understanding distinguishes humans as rational beings (Kant 13). Therefore, as human beings, we ought to recognize that if morality exists, it as well must contain no logical inconsistencies.
According to Kant, in order for a moral code to be self-consistent, its laws must be categorical; they must admit of no exceptions. Each law must have as its ultimate property complete universalizability; it can only exist if it “contains in itself its own universal validity for every rational being” (Kant 42). A law requires universalizability, he says, because of a priori reasoning. If a law on occasion allowed exceptions to seep through, then the principle upon which that law was founded would melt away. For example, Kant states as one universal maxim “to be truthful in all declarations is… a sacred and unconditionally commanding law of reason” (Kant 65). In other words, if a universal law permitted one to lie in certain circumstances, the principle of truth-telling would fall apart. We would learn not to expect the truth when asking questions, and when one does not expect truth in the first place, lying can have no function. Thus, if lying had no function, neither would a law that permitted it. Because this is irrational, says Kant, and because rational beings cannot (or at least ought not) will the irrational, “we find that we actually do not will that our maxim should become a universal law” (Kant 32). As such, because of our rationality, we can only truly will a categorical morality, one that holds true without regard for the nature of the situation.
The first qualms with Kant’s moral theory arise when we begin to search for those particular cases which might rightly allow a transgression of our duty to morality. We can first look at the classic example of lying in order to save someone’s life (as per Kant, the preservation of human life is also categorical). If we imagine a situation in which a murderer demands we confess the location of our family in hiding (so that he can murder them), the majority of people would lie in order to protect their family. According to Mill, this act would be exactly in accord with (and for the sake of) social utility, for in no way would society benefit more from the death of an innocent family than from the misleading of a killer. Furthermore, Mill would argue that our conscience, the feeling that is our binding force to social utility, would cause us to feel more pleasure at saving our family than at not. Thus, it seems as if Mill’s theory proves quite successful at both illuminating and solving the obvious inadequacies of Kant’s morality, for who would ever be inclined to sacrifice their family simply in order to uphold a moral law?
According to Kant, however, inclination ought to play no part in morality. Though it may often accompany moral acts, it surely does not define them, as inclinations are subjective by nature. Moral acts instead can only be defined a priori, and they must be categorical in order to be considered moral. As applied to the above example, the act of lying to a killer in fact destroys the self-consistency of the code. If morality permitted not only you, but each person in a similar situation to lie as well, eventually lies would come to be expected, and lying to a murderer would no longer have any functional impact; the “maxim would destroy itself just as soon as it was made a universal law” (Kant 15). In a more general sense, if the code to which we must oblige ourselves in order to be moral allowed for exceptions, if it allowed for people in certain situations to act immorally while others could not, it would destroy the institution upon which it was built. Therefore, we as rational creatures could not consider that code to exist, for it would falter in its consistency. A code that is obligatory in nature by definition cannot acknowledge the existence of any reason for the disregard of its own obligatory power. To be obliged not to be obliged is simply paradoxical (imagine hearing “I order you not to follow this order”). Such a code simply does not exist. In fact, we could only avoid this contradiction by arguing that general rules such as truth-telling and promise-keeping are not moral obligations at all, but instead conform to a still higher standard.
Social utility, says Mill, reigns supreme as “the ultimate sanction of morality.” Furthermore, the existence of this highest standard we suppose through an internal, subjective feeling called the conscience (Mill 29). However, in examining Mill’s philosophy, we cannot forget that though this feeling may exist and may present itself similarly to many people, it is subjective nonetheless. Even Mill admits that often what we as a society consider expedient at one time later “[passes] into the rank of a universally stigmatized injustice and tyranny” (Mill 63). Thus, if the majority of people may at once be universally wrong, why should we base our morality upon their feelings? In fact, basing a moral code on inclinations alone destroys its entire sense of objectivity, a necessary property if it is derived a priori (if it exists). Mill creates his morality from experience, from that which we understand as human nature, from that which is. However, “all imperatives are expressed by an ought,” so we cannot in any way derive a pure morality from that which presently is (Kant 24). Therefore, if morality is an absolute code that tells us what we ought to do, we cannot base it on something as mutable and inconsistent as a personal sentiment, for that would destroy its objective nature entirely. As a final note, even if that sentiment were the highest end, we would still be left with the question as to why we should obey it at all, the debate continuing indefinitely.
As we can now see, only a morality completely free from inconsistencies can ever serve as our governing code. If it exists, it must have the properties of every law of science or mathematics and must conform to no higher standard than itself, for how could there ever be a standard higher than the necessity of self-consistency for existence? A morality as such must be completely categorical; it must admit of no exceptions whatsoever. Morality is the mandate of what we ought to do always, and we can never accept it as moral to disregard it; if we did, we would be basing our lives’ actions on a paradox. Though Mill’s utilitarianism harmonizes often with our instincts of right and wrong, it is not based on that highest principle of self-consistency. It is instead is based upon inconsistent human feelings and sentiments. Both philosophers agree that our feelings are both subjective and variable, so how could we derive from them an objective code of behavior? The only way to skirt around Kant’s morality would be to deny the definition of existence, and to deny that we ought to do what we ought to do. Whether one can actually answer this question, however, I shall decide in my next paper.

On Solipsism

At some point in life, we all stop and wonder if all of our surroundings are just illusions created within own minds, if we have so far only been dreaming up all that we consider as reality. Are we really just imagining it all? This idea, called solipsism, though not often taken seriously, is often used as a philosophical example when playing devil’s advocate in certain debates. For instance, when pondering what all in the universe we can really be sure of, a common counterpoint says that we can never really be sure of anything but our own existence, for how could we ever prove that the physical world around us really exists? After all, it has been shown scientifically that many diseases, and even dreams can trick each and every one of our senses into believing in a false reality. People see things that aren’t there and hear voices that don’t exist, yet often they still appear to be so real. So, can solipsism actually be disproved, and furthermore does it make any difference at all?

Solipsism cannot be disproved in the conventional, scientific manner, by collecting mounds of evidence and looking for inconsistencies. This is because, if solipsism is true, then all of that evidence would be imaginary as well, and thus we would have not advanced at all in our proof. However, I believe that we may disprove solipsism if we analyze reality itself through a thought experiment. It should be noted that much of the following is derived from the work of theoretical physicist David Deutsch.

The basis of this attempt to disprove solipsism relies on not only on our definition of reality, but our ability to define it. If solipsism is untrue, then reality is simply the universe around us and all is well, there are no paradoxes related to our perception. If solipsism is true, however, then the universe around us, everything that we see and smell and hear and touch and taste, is false, just an illusion caused by our own minds. In this latter case, despite everything being false, we would all argue that what we see certainly acts as realistically. People respond when you speak to them, and if you put your hand on an oven burner, you will certainly get hurt. As per Deutsch, if something acts real, we might as well just name it real. There is no purpose in believing in solipsism, for it only adds another complexity in our understanding the universe. Rather, we have much more reason to believe that the universe is real than that it is not, and without rationale and explanation, we really have no logical basis for presenting any theory as probably true, especially something as odd as solipsism.

If solipsism is true, then there is something rather peculiar that we must note. If everything we see and experience is a result of no more than our own imagination, then every bit of knowledge we encounter and every complex calculation is also a result of our imagination. Complicated mathematical proofs and all theories of physics, chemistry, psychology, and the like are all completely self-created. Each one of us has all of the knowledge of Einstein, the creativity and eloquence of Shakespeare, and the computational ability of the most powerful super computers. That seems pretty special. Unfortunately, it also seems pretty unlikely. But of course, things seeming pretty unlikely has never been the basis for any logical proof, so let me continue.

If solipsism is true, then by definition, we would have to say that the universe we experience is something other than reality. We would thus be completely unable to ever experience true reality, as everything we could experience would be a construct of our own mind. Furthermore, everything we could imagine, because it would be necessarily influenced by the false universe we experience, would also be a product of no more than our own thinking. Thus, simply because of how solipsism defines itself, we would have no manner at all of imagining or defining true reality. The closest we could ever come to pinning down exactly what “real” reality is would be to construct it in terms of the experiential “false” reality.

So, in order for us to say that the universe in which we live is not real, we would have to define what “real” means and what “not real” means. However, given a state of affairs in which we blind ourselves from reality, we could not possibly define either “real” or “not real.” The only way we could define “real” would be if the universe around it were real. Therefore, if we are able to define “real,” then the universe we experience must be the one that actually exists. QED ■

An Addendum to On Art

Previously I discussed the value of various forms of art and the idea that no interpretation is uniquely correct, that works of art in nature are no more significant than the works of great painters in terms of how they relate to our lives. I have recently come to the further conclusion that although a piece of art may not carry any single meaning, it may carry a specific set of meanings. Of course, the number of meanings within this set is infinite, but the variations are still contained within a unique set (just as there are infinitely many numbers between 1 and 2, yet none of them is 3). Of course, despite being unique, this set is undefinable in mere words.

As a result, each piece of art likely has indeed an objective meaning, but not in the sense that it can be scribbled down on a napkin or in an essay or in a thousand volumes. Rather, the meaning is objective in the sense that it is the summation of every possible interpretation of the work of art. Therefore, we do not come closer to understanding a piece of art by narrowing down our views on it and rigidly defining our personal interpretation. We come closer to understanding it by seeing it from as many perspectives as possible, by looking at every interpretation anyone may devised. We ought not dismiss a single one, for each is indeed part–as small a part as some may be–of the whole, of the objective nature, and the more that we can add together in our summation, the closer we come to understanding that objective nature.

If we were to graph each interpretation of the objective meaning, our graph would not only have infinitely many points, but would extend in infinitely many dimensions. It’s easier to visualize, however, in just two.

Two-dimensional representation of infinitely-dimensioned objective meaning:

On Black Holes

Ever since the hypothesis that entities known as “black holes” existed in our universe, scientists have been struggling to understand them. According to current knowledge, a black hole is an infinitesimally small point containing an enormous amount of matter, such that its own gravity causes it to collapse in on itself forever. Because the gravity is so strong, not even light can escape a black hole’s pull within a certain radius (known as the event horizon). Thus, there is no possible way for anyone to “see” the inner workings of a black hole, without actually going inside one. This presents the grandest of problems to physicists, for black holes, being both significantly massive as well as significantly small, ought to simultaneously obey both the laws of general relativity and quantum mechanics, the two contrasting theories of fundamental physics. As of now, no solutions have been proposed.

The purpose of this post is to redefine the problem and from doing so to perhaps pull out even more peculiar understandings of the real goings-on. First of all, a black hole is typically formed from the collapse of a star. As the star collapses, its density increases, and thus its gravitational field increases as well. General relativity dictates that near massive objects, time actually slows down from a foreign perspective. For example, if we on Earth were to watch an atomic clock attached to the surface of a very dense star, we would see it tick maybe half as slowly as an equivalent clock on Earth. If that star were to then start collapsing and becoming more dense, we would see its clock tick even more slowly. This phenomena is not just about clocks but about time itself. From our perspective, the star is actually collapsing more slowly than non-relativistic equations would predict. Now, if this star were of the black-hole-forming variety, as its size shrunk we would see it collapse more and more slowly, until eventually, when its radius reached the radius of its event horizon, we would “see” it freeze all together. Its time would stop from our perspective, it would forever maintain the size of its event horizon. Thus, it would never in fact shrink to an infinitesimally small point from our perspective, except given an infinite time (which is silly). So, from our perspective–which as per general relativity is no less favored than any other, i.e. the perspective of the black hole–we have no paradoxes.

Of course our goal now is to disprove paradoxes from inside the perspective of a black hole. This feat could amount to anything, perhaps even to changing/expanding the laws of physics inside a black hole. Maybe in there nothing would be the same because of all the gravity. Maybe acceleration wouldn’t be distance per time squared, maybe 1+1 wouldn’t equal 2. Maybe everyone wouldn’t be so obsessed with joining fraternities.

On Free Will

Since the dawn of consciousness, humans have not only questioned their own existence, but they have driven themselves mad trying to understand the choices they make. Countless thinkers and theorists have spent decades solely searching for either a confirmation or refutation of the existence of so-called “free will.” At times, free will seemed like a paramount part of existence, an idea with which society could not at all function without. One interesting argument stated that whether or not free will existed, all civilized people must have believed in it, for otherwise society would crumble. Without a belief in free will, no one would have any sense of moral responsibility, as each could simply blame his actions on the inability to change that which was bound to happen anyway. And so it went. The existence of free will no longer mattered, all that was important was that which people believed.

Of course, on the contrary, a theory arose called determinism, which essentially stated that every action, while not necessarily predictable through human means, was inevitable. Someone or something had written all the pages in the book of time and people were simply flipping through them one by one. The emergence of various scientific discoveries further aided in the evolution of determinism. With the advent of classical physics, a fundamental science to which theoretically every other science could be reduced, it seemed that if one could potentially know the position and momentum of every particle in the universe, one could predict exactly the state of the universe at any other time in either future or past. This became the crux of classical mechanics. Experiments with the same initial conditions would always yield the same results, and everything in the universe seemed utterly deterministic.

These two theories presented somewhat of a paradox. Even though classical physics easily proved the determinism of the universe, and science dictated that humans were indeed a part of the universe–though a very complex part, at that–human minds still conformed to thinking that their actions were their own and not at all predictable by mere calculation, and society still stood firmly upon its moral ground.

Many years later, in the middle of the 20th century, a science known as quantum mechanics arose, one of the most bizarre and non-intuitive branches of human thought in all of history. When scientists began to peer deeply into the inner workings of atomic and subatomic particles, they saw that these “particles” neither acted nor were anything at all like the macroscopic entities of the everyday world. In reality, their very existence could not even be defined. Scientists could only describe particles or energy patterns as having tendencies to exists, or tendencies to perform certain actions. Each possible future of a “particle” carried only a certain probability; however, it was uncertainty, a game of quantum chance, that ruled the playing field. These discoveries completely uprooted the determinism of classical physics and once again made philosophers reconsider their feelings towards that elusive free will. The problem now was not between free will and determinism, but between free will and complete unpredictability, between conscious choices and paths undefinable even by infinite calculation.

And as such remains the problem today. Do we control our own actions or are they determined by quantum randomness? In order to tackle this question we must, as per usual, define it and analyze it in its most fundamental state before beginning to search for an answer. This almost algorithmic approach to any philosophical problem is highly necessary, for at times, it even may yield a refutation of the logic of the question itself. In fact, that is what I hope to do in the following explanation.

The latter part of our question is relatively straightforward, basically stating the possibility that we have no way of influencing the quantum probabilities governing the actions of the atoms and molecules of which we and the world are comprised. The former part, however, requires much digestion in order to understand its true nature. “Do we control our own actions?” leaves much unexplained. Foremost, what does “we” mean in its most fundamental sense, and how is that related to freedom of choice?

Most people, myself included, imagine the essence of themselves to be well within their body, most often within their head, within their brain. So if we ask what it means to make a “free” decision, we might say that a “free” decision is one in which our brain processes certain information and decides upon a route of action, executing that action through the neurological connections to the rest of the body. Fair as this may be, however, it brings us to another question. If the brain is where the decision-making power of the body lies, then wherein lies the decision-making power of the brain? Although I am not well versed in either neuroscience or psychological phenomena, I assume that some spots within the brain can be identified as wielding less of this power and some spots as wielding more of this power. Ergo, each action we perform is controlled by our body, which is controlled by our brain, which is controlled by certain neural centers. Again, we must now define the construction of each of these decision-making neural centers. Certainly there must be a process within each one that relays information and assists us in our decision-making ability (of course, each one could not stand alone, as their interrelatedness is necessary; that, however, doesn’t affect this point). Something must have some kind of control over even these sites within us. And thus the search continues.

If we continue breaking down this human decision-making ability into more and more fundamental parts, eventually we arrive at the interactions and workings of the various so-called “elementary particles” that comprise every little piece of our body. Now here, if we assume that nothing more exists than the uncertain quantum peculiarity of the subatomic world and its butterfly effects on the macroscopic universe, we may stop, and assume that the latter part of our original question is true, that we have no free will, that our actions are unpredictable and unchosen, dictated only by some fundamental laws of quantum mechanics. However, we do have another option that we may examine. Let us say, simply for the sake of argument, that there does indeed exist some kind of “soul,” some entity within us that is immeasurable by scientific devices, a reality undetectable when filtered through our five senses. Let us thus assume that this “soul” further governs the quantum randomness of the particles in our neurons. In other words, something else exists other than just these packets of energy bouncing around within us, something that indeed provides some kind of “free” control. Despite this entity being unquantifiable and undetectable, if it exists, its actions must further be governed by something else. However, the only two “patterns” capable of governing any system are order and disorder, almost by definition. If this “soul” of ours is governed by the latter, then we have consequently disproved free will. If it is governed by the former, per contra, then we return to the exact same question at which we were stuck beforehand. What governs this deeper order, order or disorder? And such, if we keep choosing order as our governing process, we become stuck in an infinitely long chain of control, one from which we can never derive any sort of freedom, as there always exists a “higher power,” if you like, a deeper level of control. If we ever then diverge from this infinite chain and choose disorder as a governing power, then we again have disproved free will.

All in all, that we have “free will” is a statement neither true nor false, but one that is illogical and undefinable simply by its own wording. The concept of “free will,” when analyzed, proves an almost paradoxical one, for how could any choice truly be free? There always exists a superior authority beyond each level of decision-making. Of course, we still find ourselves necessarily believing in this odd, undefinable concept, as society stands, and most people are at least convinced of their own moral responsibility, even if they are unable to define it by any familiar terms. Thus, the entire idea of free will ought to evaporate, for even the best argument could only either disprove it or become stuck climbing down an infinite ladder. We all believe in free will, but we can never logically admit it.

Side Blog: My Quest for Lucidity

Hi all,

I’ve started a side blog to document my quest of honing my ability to lucid dream, to achieve one of the most peculiar states of consciousness, tantamount only to those brought on by strong doses of psychedelic chemicals. This is all natural, though, and revolves around trying to gain conscious control of the pineal gland’s release of the substance DMT (N-dimethyltryptamine). The blog is located at http://questforlucidity.wordpress.com. I will return to my usual posts hopefully tomorrow after my chemistry exam is over. Tentative topic: free will.

On Spectra: Part II

The one-dimensionality of our thought is not solely evident in the immediate and concrete world that we walk through, but it also projects itself dutifully onto to the abstract aspects of our lives. This may well be related to a fundamental limitation in our thinking, perhaps the limitation that maybe we can only think in a linear manner in this stage of our evolution, that all of our thought processes must progress down a narrow path, but that is for later discussion. More importantly, one-dimensionality exposes itself most blatantly in society’s thinking when we use the concept of spectra to analyze complex issues.

Take, for example, the political arena. Although I am not at all well-versed in politics, and surely have no right to speak authoritatively regarding any of the bigger controversies, the one thing that I can point out is the almost constant reference to the political spectrum. This spectrum consists a single line, just a segment marked down in one stroke by a pen upon a sheet of paper. Upon this line, we find ourselves describing all of politics. We find ourselves attempting to describe every person, every party, every group of individuals that give themselves a title, via the use of this spectrum. By standard convention, we speak of the left end being more “liberal” and of the right end being more “conservative.” But again, this is just convention, something only necessary when comparing one’s own opinions to the opinions of others.

But still, where we suffer is not in where we place each person or party, or how far one is to the “right” or “left.” We lack in that we plot an entire universe of differentiated thought onto a single pen-stroke. This whole idea actually reverts back to one of the simplest mathematical ideas in set theory, that of mapping. Mapping is defined as the comparison of the elements of two different sets of data, and is used almost constantly in daily life. In linear algebra, it shows its importance when mapping one set of higher dimensional vectors onto a second set of lower dimensional vectors. For example, we might map an arrow pointing up and to the northwest onto a flat plane below it. The best representation of the arrow that we could draw on the plane would just be an arrow pointing northwest. By mapping that three-dimensional arrow onto a two-dimensional plane, we lose crucial information about it, and our drawing becomes only an approximation of the real arrow. From the two-dimensional perspective of the plane, not only would we not know if the arrow had been pointing up or down, but we would have no concept of up and down at all. No matter how hard we tried, we would have no way of accurately describing what up and down even meant. To take it one step further, imagine mapping this arrow not onto a plane, but onto a single north-pointing line. In this case, we would remove both the up and westward components, losing even more information about the true nature of the line. However, were we actually confined to this one-dimensional perspective, our drawing of the northward component would still be the best approximation we could make, even though it may well be a very poor one.

The ideas related to mapping that I’ve just described are all well when speaking in mathematical terms, but they sadly actually “map” themselves onto abstract real-life situations quite frequently. Again returning to the example of the political spectrum, what we are essentially doing here is projecting a subject of infinite complexity and relatively high dimensionality onto a single, one-dimensional, unbending line. This is an act we choose to do, not one that we are forced to do. Unfortunately, in our linear laziness, we prevent an enormous amount of information from reaching through to our consciousness and understanding. Even with the addition of another single dimension to “the political spectrum” (thus, of course, destroying the spectrum) we would gain an enormous amount of comprehension of such a detailed and complex problem. Imagine comparing three candidates or parties or ideas not on a simple line, but on a graph with two defined axes. Even this simple expansion of our descriptive ability would tremendously augment our awareness of the nature of politics.

Of course, politics is but an example of a matter that we imprison to the spectrum. There exist countless other areas that we as humans feel inclined to illustrate through the use of a single line, such as philosophical beliefs, religious practices, and emotions, for example. Why we do such a peculiar thing I do not know. Perhaps this thought process was the one that survived after millions of years of evolution. But the evolution of the human race has become obsolete. No longer do our traits and behaviors significantly determine whether we survive and pass on our genes. Thus, we do have the ability to revert from our instinct of linear-thinking and to begin seeing the world, the universe, the ocean of possibilities and ideas, in a multi-dimensional manner. True, some things may be of infinite complexity, of infinite dimensionality, if you like, and they be unreachable in their absolute form. However, if we continue to add dimensions to our thinking, even though we may never be able to perceive the true and unmasked nature of certain things, we can always come closer in our understanding, and that is what is most important.

Proof of Multiple Universes

I went to a cosmology lecture a few days ago, and that inspired me to revise an idea I had last year about proving the existence of universes other than our own. I thought it ought to have a webpage of its own, so take a look if you’re curious: http://www.nosmalltalk.org/proofs/proof.html. Soon I will return to writing on the various way spectra have limited our conscious capabilities.

On Spectra: Part I

Despite the human mind’s astounding capability to think abstractly and analyze the universe through infinite perspectives, societal trends and cultural evolution have driven us towards thinking only one-dimensionally. The whole emphasis of the line, of the spectrum, in modern day society has cleaved off the most creative part of our analytical ability. The idea of mapping concepts onto one-dimensional spectra arises in nearly every aspect of life, from walking down the street to political forecasting.

Most people most of the time walk in order to get from one place to another. In the first scenario, we spend the entire walk consciously or subconsciously measuring the distance from our destination. In our minds, we draw a straight line (or several straight line segments, if a direct path is impractical) in between our starting and ending point and calculate or estimate our progress along it as we go. Mind you, this is a fairly pragmatic thing to do, as it allows us to reach our final destination relatively efficiently. However, this innate practice subtly yet powerfully shapes the way we view the rest of the world. As we travel from one point to another, we map our incredible three dimensional (or more!) universe onto the simplest possible route (vectorspace), that which happens to be no more than a line. In doing so, we neglect to realize that the other dimensions exist at all, and sadly confine ourselves to a linear, conventional, and uncreative mindset.

Of course, most people can certainly say that they’ve taken a walk at some point in their lives just for the sake of taking a walk, or of clearing their thoughts, perhaps, or of really soaking in that beautiful three-dimensional world (though they probably wouldn’t say it in those exact words). This is a marvelous regression towards our primal instincts of simply appreciating the world’s beauty on the most fundamental level, without need to constantly adapt our interpretations to fit societal standards. Only through this regression to the most basic plateau of understanding can we truly think of the universe through original and creative perspectives. However, and alas, the two different types of walking through this world divorce themselves so mercilessly that only very seldom do any of us find ourselves walking both with destination and appreciation in mind. This world presents to us such incredible marvel each time we walk down the street, and to simply pass it by because it doesn’t lie exactly on our line of travel is heartbreaking.