Blog Post

Invariants

While cleaning out my files--digital files, of course--I found an old presentation on the Euler Characteristic that I gave in Differential Geometry. This element is called an invariant, and it happens to be the most fundamental link between topology, geometry, and analysis.

Indeed, in mathematics it seems as though the invariants are the most beautiful and elegant constructs. Invariants are unchanging by definition, and descriptive by nature, but most importantly they are the twisting trunks of magnificent trees from which all of mathematics can blossom forth. (Poetry aside, it's quite true how all fields of mathematics always tend to boil down to the same few invariants. Similarly, these invariants, although often hidden, always reappear in calculations or theoretical deconstructions.)

Are there invariants for humans?

Perhaps intelligence. My intelligence characteristic might be different than yours, everyone has a constant one, and it separates each of us into classes (figuratively and otherwise).

Perhaps beauty. This innate quality uniquely defines each and every human, yet it also stratifies and lends itself to further analysis.

Perhaps personality. While some are sharp with their tongues, others are sharp with their wits. Some are quick to assault, others are quick to resolve. However each and every person has a personality which defines him, and so it too may be an invariant.

I disagree.

What makes us human is the lack of invariance. While mathematics has order and structure, it is the organic nature of humanity which precludes any sort of regularity and begs for variance.

If mathematics is the massive, gnarled oak, humanity is the field of wildflowers.

And then does it follow that there is no invariant in the world of Web 2.0? Currently, I'm on a sort of crusade to find one. Any one have any ideas?

109

3 comments

 

"If mathematics is the massive, gnarled oak, humanity is the field of wildflowers."   This is a beautiful post, Matt. 

 

Of course you know my answer, that humanity lacks invariance, that the human brain and human society are constantly being rewired by everything and everyone we encounter, and that, if we manage it right, keep it open, and understand the responsibilities and possibilities of openness, we can magnify not only how large that field of wildflowers might be, but even sow new ones where, before, we just saw concrete or blight or desert.  

 

Thank you for such a deep and moving post! 

136

Hi Matt,

Great post. I'd offer up the idea that consciousness is the human invariant. Personality can change, as can intelligence and beauty. All three of those things change as we age, and radically in some cases. The one aspect of humanity that doesn't change is consciousness. Jung had quite a bit to say about this. And mystics from all religions do as well.

 

101

Anonymous (not verified)

According to your article i want to add that one things what is invariant for every person is lot.It is lot what is constant creator and we just lead our life in accordance with creator's written lot.Besides, Pi is a mathematical invariant which existance everywhere and in every creation.But its hidden.when we start to experimant on it,we will get existance of this miracle number.I am really astonished when I knew the existence of pi in butterfly wings. i think there are also so many invariant in this universe what is full of diversity.

97