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.