Human beings like to think of themselves as being superior to (other) animals. How so? Some will say that we are blessed with consciousness whereas "lower" animals don't. I can't help settle this question: I've never been inside the mind of a cow. But it may be helpful to look at the evolutionary endpoints.
At the primitive endpoint of evolution we find single-cell bacteria; the thought that bacteria have consciousness is rather disturbing so let's assume that they don't. At the other endpoint, the sophisticated one, we find humans, who, in general, are endowed with consciousness. This begs the Darwinian question, at what point in the progression of evolution was consciousness introduced, and how exactly did that happen?
Or perhaps one of our assumptions is wrong?
Zzzzz...
[Homage to the Intermediate Value Theorem]
Showing posts with label evolution. Show all posts
Showing posts with label evolution. Show all posts
Thursday, April 23, 2009
Monday, February 16, 2009
Meta-morphosis
There is a cute mathematical paradox that goes as follows:
The vocabulary of the English language, while undoubtedly vast, has finitely many words; hundreds of thousands perhaps, but still only finitely many. The number of English phrases with less than seventeen words is therefore finite as well. But there are infinitely many natural numbers (i.e. numbers of the type 0, 1, 2, 3, 4, ...) so not all of them can be described by English phrases of less than seventeen words. Some can be --- e.g. 6 can be described by the phrase "six" or by the short phrase "one plus five" --- but some just can't. The principle of mathematical induction tells us then that among all the natural numbers which cannot be expressed in less than seventeen words there is one which is the smallest. That is, there is the smallest natural number which cannot be described by English phrases of less than seventeen words. But wait! Hold on... Counting the words in italics we see that we just managed to describe that number in sixteen words!
How did that happen? The culprits here are the manners in which we used the English language. Indeed, "manners" in plural because we used English in two ways: in a low-level to talk about numbers and in a higher meta-level to discuss the system of numbers.
Other mathematical paradoxes (e.g. Russell's famous paradox) stem from similar dual usage of languages, in low- and meta-levels.
Mankind has long ceased to participate passively in the process of evolution. We have been breeding dogs, genetically modifying plants, transplanting hearts, and much more. Our reach is no longer confined to within the bounds of the evolution system; we have increasingly been manipulating the evolution system itself.
I don't know about you but I hear the music of paradoxes. And at least in Math this music rings trouble.
Zzzzz...
The vocabulary of the English language, while undoubtedly vast, has finitely many words; hundreds of thousands perhaps, but still only finitely many. The number of English phrases with less than seventeen words is therefore finite as well. But there are infinitely many natural numbers (i.e. numbers of the type 0, 1, 2, 3, 4, ...) so not all of them can be described by English phrases of less than seventeen words. Some can be --- e.g. 6 can be described by the phrase "six" or by the short phrase "one plus five" --- but some just can't. The principle of mathematical induction tells us then that among all the natural numbers which cannot be expressed in less than seventeen words there is one which is the smallest. That is, there is the smallest natural number which cannot be described by English phrases of less than seventeen words. But wait! Hold on... Counting the words in italics we see that we just managed to describe that number in sixteen words!
How did that happen? The culprits here are the manners in which we used the English language. Indeed, "manners" in plural because we used English in two ways: in a low-level to talk about numbers and in a higher meta-level to discuss the system of numbers.
Other mathematical paradoxes (e.g. Russell's famous paradox) stem from similar dual usage of languages, in low- and meta-levels.
Mankind has long ceased to participate passively in the process of evolution. We have been breeding dogs, genetically modifying plants, transplanting hearts, and much more. Our reach is no longer confined to within the bounds of the evolution system; we have increasingly been manipulating the evolution system itself.
I don't know about you but I hear the music of paradoxes. And at least in Math this music rings trouble.
Zzzzz...
Tuesday, January 6, 2009
A Pinch Of Humility
When was the last time you headed out with nothing but cloths on you?
I can't recall the last time I did; too many years have passed since. Nowadays when I get out I always carry something on me --- at the very least a key, to make sure I would be able to get back in. My iPhone and wallet almost always join along too (in that order); the laptop when I head to work; sunglasses when I need to look particularly cool; several Kleenex tissues never hurt; a pen could come in handy; a water bottle in prudent moments. And the list grows...
How do we shuttle all these items around? We can hold them in our hands, or attempt to balance them on our heads, but these methods are somewhat limited and restrictive. Instead we typically resort to employing portable storage accessories such as pockets, pouches, purses, backpacks, and their like.
In contrast some Australian species (marsupials) don't require external storage accessories: they are naturally born equipt with built-in pouches.
You see, even this silly aspect of day to day life begs the question: is homo sapiens really the pinnacle of evolution?
Zzzzz...
I can't recall the last time I did; too many years have passed since. Nowadays when I get out I always carry something on me --- at the very least a key, to make sure I would be able to get back in. My iPhone and wallet almost always join along too (in that order); the laptop when I head to work; sunglasses when I need to look particularly cool; several Kleenex tissues never hurt; a pen could come in handy; a water bottle in prudent moments. And the list grows...
How do we shuttle all these items around? We can hold them in our hands, or attempt to balance them on our heads, but these methods are somewhat limited and restrictive. Instead we typically resort to employing portable storage accessories such as pockets, pouches, purses, backpacks, and their like.
In contrast some Australian species (marsupials) don't require external storage accessories: they are naturally born equipt with built-in pouches.
You see, even this silly aspect of day to day life begs the question: is homo sapiens really the pinnacle of evolution?
Zzzzz...
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