I stand, stare at the Cantor dust of stars,
Stand alone in the open field of grass
That glows in the silver of the moon brass
And dark emerald under a rising Mars.
I wage a silent war within my mind
As I wait in vain for a happiness
These stars cannot bring me. My loneliness
Soaks into the ground to be left behind.
I turn away from Mars and search the sky –
The false-star Venus must be out among
The stars and darkness, a beacon for me
To connect my life to, so I can fly
And leave this lonely-soaked ground a far-flung
Memory. I want to love and to be.
Wednesday, August 11, 2004
I stand, stare at the Cantor dust of stars,
When people want to defend a transcendental world view (particularly against science), they often bring up mathematics.
"How can you scientifically prove that two plus two equals four?" they ask. Since you cannot, mathematics must be transcendentally true. However, this shows a misunderstanding of how one can use science to understand aspects of philosophy. Using the scientific method is not the only way of using scientific knowledge to prove something is factual ("true" in Nietzsche’s "uninteresting" sense in his "Truth and Lies in a Nonmoral Sense"). If we can show that it is natural for the brain to process the world in such a way that we can make statements such as 2+2=4, then we have a science-based (though not "proven" scientifically per se) explanation for math, meaning we do not need a transcendental explanation for it.
Math is the abstract expression of relationships in nature. Words are sounds representing conceptual categories, which are derived by observing many objects and placing those objects with certain similarities into categories. Take the Bactrian camel. We categorize camels as either Bactrians or Dromedaries, because the Bactrians have two humps, and the dromedaries have one. All the Bactrian camels more closely resemble each other than any one resembles a dromedary, or any other animal, for that
matter. So we categorize two-humped camels as Bactrian. But are Bactrians in fact identical? No, each one is different – we erase the differences so we do not have to create a different category for each individual object in the world, which would be very cumbersome (this, despite the fact that we do oftentimes give an individual it’s own category, as when we name our pet dogs and cats, because we become so familiar with them that they become more individuated in our eyes). Our brains, to be more efficient, conceptualize. If brains did not do that, the owner of the brain would not recognize that the cat that ate a member of the group was similar enough to the approaching cat that it would be prudent to try to escape. This is why and how vervet monkeys can have a different call meaning 1) big cat, 2) eagle, and 3) snake, which each result in different responses. The same is true of the one who needs to eat: one must be able to recognize what is not-food and what is food. To eat, one cannot have to relearn this information each time. Life was much simpler for one-celled predators: eat anything that moves (or, more accurately, whatever binds to the outside of the cell, meaning there is a kind of conceptualization even at the chemical level in the surface proteins). Those who could not make these judgements about the world and create concepts such as these would have died either from eating something poisonous or from being eaten. Any animal that could not make proper judgments regarding the reality of the world they were in would not have been able to survive. Those who were better able to make those judgements would be able to survive even better. I give as evidence a human population of over 6 billion people at present.
Due to the complexity of our brains and our use of language, humans are able to create more conceptual categories than any other animal. Further, those categories can overlap, and they can exist in nested hierarchies. The Bactrian camel is simultaneously a camel, in the camel family (which includes the humpless llama and its relatives in South America), an herbivore, a mammal, a vertebrate, an animal, and alive. Thus a Bactrian camel shares similarities with other herbivores – elephants, rabbits, buffalo, manatees, etc. – in that they all only eat vegetation. We call it a mammal because it has hair, is warm-blooded, and feeds its young milk, just like platypuses, whales, koalas, and leopards. It is a vertebrate because it has a backbone and an internalized skeleton, like fish, birds, reptiles, and amphibians.
And what of math? "Two" is a conceptual category. It is necessary to keep track of group members (we are a social species after all), and to make proper divisions in a group (as chimpanzees share meat from a kill). It would also be useful information to share if one is hunting or gathering. "Yes, there are two of them. We need more hunters." "Two" is a conceptual category in the same way as "Bactrian camel" is. If we have tow humps on two different camels on two mountains with two rivers flowing from the two mountains, then the relationship among humps, camels, mountains, and rivers is "twoness" – a conceptual category we designate by using the word "two". The sound "two" may be an arbitrarily chosen sound to represent this concept, but the concept, and the fact that a word exists to represent it, are not arbitrary.
The rest of the equation is relationships. Relationships are inherent in nature. Math describes nature so well because all of nature is relationships, each object has and is in a relationship with other objects (objects here including pure, substanceless energy). "Equals" is such a relationship. If there are a number of objects that we call (in English) "two", and we have another number of similar objects that we would also call "two" due to the number of objects being equivalent, then we have a number of objects that we designate in our language as "four". If "four" represents this many objects: * * * * , and two represents this many objects: * * , and 2=2, then 2+2=4. A transcendental explanation is not needed in the least. All we need is a proper understanding of how concepts are formed in the brain, and we can learn that through cognitive psychology, which is science. Thus, while science cannot prove using the scientific method that2+2=4, while 2+2 cannot equal 5, and never can as long as we use the language and notation as we presently do, I have shown that a proper understanding of science can help us use philosophy to understand the source of mathematical statements as non-transcendental.
Posted by Troy Camplin at 9:13 PM
Tuesday, August 10, 2004
I have been reading Stuart Kauffman's new book, Investigations. I have been thinking about the same problem of the source of the complexity of the universe in light of the current 3 laws of thermodynamics. If the universe had its origins in the breaking of the perfect symmetry (nothing) that gave rise to the big bang, then symmetry-breaking would in fact be the primary law of the universe, giving rise to all the other laws of the universe, which evolved as the universe emerged. This is suggested by the equations in Kauffman's The Origins of Order, which I have shown in my dissertation "Evolutionary Aesthetics" could show how 10-11 dimentional strings could be derived from nothing, with D=0 giving rise to D=1, or the singularity that exploded into the universe. This initial symmetry-breaking becomes then a fundamental aspect of the universe, giving rise to the complexity of the universe, with its plurality unified into a hierarchy of complex systems. Thus I propose as a law of physics the tendency of the universe to break symmetries to create more diversity in the universe.
Posted by Troy Camplin at 10:09 PM
Monday, August 09, 2004
My true concern is for your health
In asking you to share my bed –
I only wish to share the wealth
Of benefits that have been wed
By all the doctors of the day
To the one thing you’ve kept at bay.
Why would you miss this exercise,
So pleasant, easy when you’re prone?
How can you say that it is wise
To miss out on the firm and tone
Muscles that can make you sure,
With head held high through good posture?
Your lovely skin and thick, dark hair
Will turn much shiner and smooth –
Your loveliness will be more fair;
And it is said that this can sooth
Your headaches and your every stress –
And all you have to say is "Yes."
No better drug could lift you up
Than those you’ll brew up in this bed;
No pharmacist could yet brew up
A medicine to clear your head,
So every flower smells more sweet –
Just climb in here under the sheet.
Relaxed, you’ll get much better sleep
Than any that you’ve ever had –
With brighter light this tiny leap
Will open you and make you glad
You changed your mind and joined me here
So that same mind becomes more clear.
A longer life is here for you,
And much more slowly you will age;
You’ll be less sick – yes, it is true –
What arguments must I still wage?
My proof, at least, you must agree,
Is stronger proof than is a flea.
When the sun dapples through the trees’ leaves
And the world becomes a familiar stranger
In the wild and growing tapestry it weaves,
We’ll be in danger
Of finding flowers in reds and indigos
Sprouting up to fill the new open spaces
Once filled by the brush we’ve cleared with our woes,
Lost love’s embraces.
Pain breaks the chains we had while down in the cave,
Its deadly fires purify our perceptions,
Cleans them for the very few who can be brave –
Be gone, deceptions!
Be gone and let us see the world in color,
In resolution sharper than quarks can give us,
Sharper than old photos with their tin color
Most still use to truss
Up the prejudices and preconceptions
They hold, too terrified to question a thing
That they believe. Can we know what receptions
Deep knowledge could bring?
In the unbelievable and unknown –
In the unrefined and those without thought –
In the unremarkable and unwise –
We find our leaders
We find our heroes
We find our artists
I see it – there is a sun on the horizon –
The rosy fingers of an ancient dawn –
A rebirth of everything from everything we have torn apart –
A world in fragments – no longer a world –
Fragments gathered up –
A world reborn from the fragments –
A world reborn from the past, the ancients –
Greeks, Romans, Chinese, Africans, Arabs, Indians, and aborigines –
I am not a postmodernist
And I am not a classicist
And I am not a romantic
And I am not a modernist
And I am not a naturalist
I am each of these – and none
I am the moon and the sun
I am the earth and the sea
I am woman and man
Seriousness and fun
Fragments and unity
Plurality and one