I understand infinity, but I cannot contemplate it.

Many people stand in awe of the fact that our brain can contemplate, imagine and understand infinity.
My contention is that we do not contemplate nor imagine infinity, but rather that we understand the meaning of the language, or the definition of the concept. Take the sentences:

'For any number you imagine, however great, add one more', or equivalently,
'There is no highest number'.

We are capable of understanding the meaning of the language behind infinity, but we cannot imagine nor grasp an infinite number of things in our head - we always start with finite quantities, and create higher, albeit finite, quantities. To prove my point further, take the sentences:

'There is a certain species of animal which is different from any species of animal you have seen in the past and doesn't share any characteristics with it'.
'A number can be even, odd, or even another one which I have called plath.'
'A tesseract is the representation of a cube in four spatial dimensions'.

We understand the meaning of each of those sentences, in the sense that there is something to be discovered which we have never experienced - but we cannot imagine what it is in our heads. In fact, we can systematize how to build a cube in four-dimensions, yet we do not imagine it as such - if we hadn't come up with a systematic method for lower dimensions, our brains could not, out of thin air, imagine a four-dimensional cube. This is only to show the point that because we understand the meaning of a certain propositions, does not mean we can imagine what it is we are talking about.

Another point to raise is this: you can imagine hybrid animals, and you can imagine many, many different combinations for each species - perhaps one, two, three, or even more with given time. But can you imagine all possible combinations of arms, legs, hair, eyes of animals with the limited, finite number of species you already know in an instant? And if you add the characteristics of plants to the pool? Probably not. If this is true for a finite number of entities that we know (and this number is already an extremely high number), it should be true for an unlimited number of entities, which is the case of numbers, that can be combined to give additional numbers. We are capable of imagining a set of random numbers, however high, but we cannot imagine an infinity of them.

Our brains seem to be limited by empirical input in order to imagine certain things - a new species of animals, four dimensions, a new color. However, some mathematical/abstract concepts, such as infinity, can be understood, but not imagined - how come? My contention (which I am sure is not an original one) is that we understand the meaning of those concepts not from any empirical input, but from the fact that we have a language mechanism inherent to the human being - this language mechanism makes us capable of understanding logical propositions, or general propositions, without us knowing what exactly we are talking about. I will attempt to develop it later on.

Creativity and imagination are still, nevertheless, the features that take us forward - and who knows, some years from now, certain concepts which are so strange for us in the present are nothing short of trivial for future generations.

The World of Abstract Entities II

* is in likeness of polished, clean glass, with a shine of its own; #, on the other hand, presents itself dirty and reckless - guided by its rebellious, random nature, # soils * with suffering and disgust. Pure as it is, * feels ravished, violated, abused; in the end, it realizes that # - frivolous - will not stop and respect purity - the battle between these two abstract identities begins, only to last a few moments in this hypothetical time.

*, exhausted, loses the fight and shatters in the metaphysical walls of this Universe; it can see pieces of itself spread all over the multidimensional space - pieces so dirty they could belong to the opponent. It wishes to have fought more vigorously to maintain its identity, wholeness and purity; it wishes to have battled with fervor and joy worthy of an immaculate concept who knows and values itself.

(Fragments of ideas wither away / abstractions cease to be) and all is silent.
The dark sky has witnessed, an infinite number of times, the death of imagination.

The World of Abstract Entities I

It starts with nothing (0).

0 is broken down into -1 and 1. It is also broken down into two other invented numbers in a number line perpendicular to the first number line, called -2# and 2#; and yet in another perpendicular number line, into -3* and 3*. This process can be repeated ad infinitum, without zero suffering any consequences; nothingness is still there, inventing infinity - relentlessly, tirelessly.

As seen from the eyes of an imagined beholder, the universe of abstract entities is nothing but symmetry aspiring to become anti-symmetric; plus and minus infinity each trying to reach the end of their lines. But it is clear that numbers are just spread bits of nothingness in disguise, attempting to be more than nothing at all.

Emotions I: Problems raised from definitions of emotions

// While an emotion is generally described as a physiological response to an external stimulus (e.g. fear in the face of danger), a feeling is more generally described as a state of consciousness, or an internal, more subjective representation of emotion (http://en.wikipedia.org/wiki/Emotion) - for the purpose of discussion, I will treat them both as being equivalent, in the sense that both are subjective experiences. //

Our individual perception of feelings and emotions towards an object are always true. That is to say, If I am able to perceive my feelings regarding apples, I can know the truth value of the proposition "I like apples", since whatever definition I use for "like" is adequate in the personal realm, whether I consider the proposition to be true or false. What one means by "like", "love" or even "hate" is different from the emotion, or the experience, itself. In fact, at this point, it would be confusing to state that we experience "different emotions", but rather that we experience "emotion" - this definition encompasses all the complex states that an individual might experience, disregarding any labels usually given by us. Although our experience of emotion is, in this sense, absolute and personal, the definitions that we use to describe emotion are not absolute - this raises a problem of subjectivity in describing and communicating our personal experiences to others, and I will try to clarify this issue with an example. If an individual X tells individual Y that he feels love towards individual Z, but Y notices that X is generally aggressive, spiteful, and murderous when he is with individual Z, Y will have a hard time believing that X really loves this individual Z. If the feeling/emotion "love" exists, and X has no doubt that he loves Z, why does Y doubt? That is because what we humans conveniently labelled as "love" is nothing more than an expression of feeling in the form of actions. Even though we perceive and experience emotion, potentially in an unique way which cannot be replicated in other individuals nor completely evaluated, our actions are a function of our subjective experiences - if there is a pattern in the actions taken by a high number of individuals when they experience a certain biological state, then it is convenient to label this biological state. Y will probably not believe that X loves Z because the actions taken by X when he experiences Z do not fall within the set of actions caused by what he previously labeled as "love". To say that a mother loves her child is to say that mothers will generally take certain actions, similar for different mothers, towards each of their child that we therefore label as "love". Even though we cannot access individually the experience of each of these mothers and conclude that these are exactly the same, there is a certain pattern of actions taken on behalf of these emotions that is similar. If a mother states that she loves her child, but abuses, beats down, and violates its own child, most people will not believe her claim - because what we label as "love" is the cause of radically different actions than those taken by this same mother. We are thus at a crossroads: on the one hand, we have the feeling or emotion perceived and experienced by the individual, which is potentially unique; on the other hand, we have the actions taken on behalf of this emotion, which are recognized as a pattern by humans and therefore labeled.

If we wish to systematize and properly define a certain emotion, we are stuck between individuality and actions taken and recognized by others on behalf of emotional states.

Should we walk the long, treacherous path of individual definitions of emotion, or should we simply label it as a pattern, or set, of actions generally observed in individuals? If the former, we probably won't find a satisfying definition that is in accordance with every person and accurately depicts each and every wave in an ocean of sentiments; if the latter, another problem is raised - what if we take no noticeable actions on behalf of the emotions that we feel so that these cannot be evaluated by anyone except ourselves? And if we were mere spectators, how would we be able to distinguish such an individual from an emotionless machine?

I have thought about some possible definitions of emotion that attempt to alleviate some of these problems, but at this time I won't dwell on it. It needs more thought and clarification before it can be presented as something worth considering. Moreover, the future development of science, particularly of the fields of neurology and psychology, might help us establish a link between the personal and the external realm.