Tue, Dec 18, 2007 Permanent linkWhen that day comes, when people try to handle problems that cannot be solved by throwing hardware at them, algorithms will be only relevant factor. As more and more jobs become automated, but NP-complete tasks like Theorem Proving remain intractable for computers, the discovery of new algorithms will be a central task for human beings.
I think NP-complete problems are really interesting, because by definition they are all reducible to the same problem. (Formal definition here.) So, if a polynomial time algorithm is found for any NP-complete problem, then in theory an algorithm has been found for all the others.
However, a lot of NP-complete problems are not so hard for humans to figure out in specific cases. Sudoku puzzles are a good example of this—it's pretty easy to solve a Sudoku puzzle, but so far it has been impossible to find an algorithm for solving Sudoku problems in general in polynomial time. The reason for this is that we humans use a sort heuristic-based reasoning where we use some broadly applicable (but not universally applicable) "rules of thumb" to attack these problems in a sort of non-algorithmic way. This approach involves leaving out a lot of irrelevant information and getting straight to the crux of the problem at hand—something that can only be done in specific cases and not in general to NP-hard problems.
So, our best hope, in my opinion, for solving NP-hard problems is to take a more cognitive approach. That is, I think that we should model our algorithms for certain tasks that are well-suited to human brains after the strategies we use to solve them ourselves.
I haven't read Eric Baum's book which you mentioned, but I think that one of his claims is that humans are so successful at thinking because they leave out all the irrelevant possibilities just by the nature of how they evolved—they evolved in such a way that only the important possibilities are addressed in cognitive functioning.
Thus, I think that the algorithm design of the future should take into account traditionally "non-algorithmic" problem-solving strategies like the sort of probabilistic ones humans use in order to perform more efficiently. However, these new "algorithms" will not necessarily be provable to solve a problem, even if they can solve a certain class of problems most of the time. Hence, the way of gaining efficiency in this way will be sacrificing universal applicability in order to simplify the problem.
Tue, Dec 18, 2007 Permanent linkEnjoyed reading this post, your comments on the future of human thought and potentially increasing its potential through art and music reminded me of a 2005 article in the Guardian on autistic savant Daniel Tammet who can perform mind-boggling mathematical calculations at breakneck speeds. This is perhaps not unique among autistic savants, but here is the beauty of this particular case:
Tammet is calculating 377 multiplied by 795. Actually, he isn't "calculating": there is nothing conscious about what he is doing. He arrives at the answer instantly. Since his epileptic fit, he has been able to see numbers as shapes, colours and textures. The number two, for instance, is a motion, and five is a clap of thunder. "When I multiply numbers together, I see two shapes. The image starts to change and evolve, and a third shape emerges. That's the answer. It's mental imagery. It's like maths without having to think."
Seeing "numbers as shapes, colours and textures" and the fact that Tammet is actually performing these tasks makes me wonder what kind of "algorithms" lie at the basis of his mathematical artform and if there could be any hope of decoding these into states that might be reproduced.
Full article: A genius eplains
I wonder what these shapes might look like in his mind, I like to imagine them looking like Richard "dr." Baily's Spore experiments, and of course it helps his site is called Image Savant...
Imagine the following images as "solutions" to mathematical problems:
· Wikipedia page on Daniel Tammet
· link to the Guardian article
· more of Richard Bailey's work at imagesavant.com
Wed, Dec 19, 2007 Permanent linkThis makes me think of a few things at once. some of which may be very tangential.
#1
algorithms as being key to the future of everything including digital warfare and the ability to move freely through whatever barriers are posed in digital space. algorithms are key to grasping the immaterial which makes them as or more powerful than agents that allow us to transform the material world, like corrosive liquids or chain saws.
#2
it seems logical to me that the 'algoritm' that produces human thought must have, throughout the course of our evolution, discarded anything that wasn't important to us leaving us with a specfici set of parameters for perceiving and existing in the world. The limits of sensory perception are definitely part of the equation, although we are doing out best to get beyond those.
#3
it also reminds me of the conversation ensuing on al's infinity post, where someone said we weren't necessarily built to perceive infinity, and likewise, the difficulty posed by the human brain trying to understand itself is, if nothing else, amusing. And it seems like so much of what human beings have put into the world, including computers and computer simulations, have been in the service of understanding ourselves by projecting into the outside world and looking back.
#4
At one point i thought this was leading up to the inevitable creation of intelligent machines who were like us. We would only finally understand ourselves when we'd superceeded ourselves. I'll refrain from being super rational about that hypotehsis and leave it at that.
Wed, Dec 19, 2007 Permanent linkGreat post but I believe its really important to look at the social implications your thoughts and the rise in importance of "algorithmic arts." As a starting point one might look at this line:
This seems to be a utopian vision of human purpose in an era of automated abundance. Now I have no problem with utopian visions, they are crucial to reflecting on current social problems that need fixing and planning for a better future, but one must look at the assumptions that predict an era of automated super abundance. This might be one of those assumptions:
automation will be global and benefit all humanity.
I'm skeptical, automation will not in itself end human stake holder politics and the divide between haves and have-nots (for example, the species has had the ability to feed everyone on the planet since sometime in the 19th century, yet we have not). With that in mind a better way to phrase the quote above might be, "As more and more jobs become automated in the developed world... the discovery of new algorithms will be a central task for human beings in the information economy.
The social implications of this aren't great. It would increase the digital divide between the haves and have-nots (as the haves will have better algorithms) and reinforce the status of a scientific elite.
Now before people start calling me a luddite let me outline the two points i trying to make:
(1) I believe in the beauty of a society who celebrates scientific (and algorithmic) discovery but we must ask how to bring this about with equity, social justice and sustainability. Automation is not an answer in and of itself. We must work to make technological develop benefit all so everyone could have a place in humanities central tasks, whether they be algorithmic discovery or something else completely.
(2) when making predictions about futurity, assumptions could lead to unexpected social problems as people work towards the predictions they like best
To end I really do love the post and believe that algorithms will play an important (and wonderful) role in future creativity but we have to look more closely at the social vectors that might get us there.
Wed, Dec 19, 2007 Permanent linkLess interested in responding to your post, Render, than I am in responding to chr15's comment:
Do you not think it's true that throughout history we humans have had a problem with the separation of creation with dealing with the aftermath of it? Scientists run around creating, discovering, and only later does society try to clean up the aftermath of it.
ex. industrial revolution created pollution, increased poverty-wealthy gap in the world
I am not saying that this is a done-deal. If anything, I feel as if this is something we need to correct.
Do you have any ideas for solutions to this? I am very interested in hearing any ideas about how to better connect the social science and science spheres, the intellectual and practical worlds; figuring out ways to merge the theoretical with the reality. But less abstractly, how can we continue to grow without killing ourselves in the mean time?
How can we do this?
Wed, Dec 19, 2007 Permanent linkhi embeezee, these are great question which i'm not sure i can even begin to answer. But i feel they deserve there own space and started a new thread to address them.
thanks, -c
Wed, Dec 26, 2007 Permanent linkI can't believe nobody mentioned this yet :)
What about algorithms simulating a human brain?
Seems to me that we're getting there.
excellent questions and well thought out. I don't know the answer either, but I cannot help but to look at what the right brain does in creating worlds uttered forth from the greath depths of neurochemistry - that is in fact - art. We know art like we know rocket science. Yet within art are defining truths like a red circle is a red circle. in some cases it offers a sublime redefinition of existence.
As technology improves our ability to map algorithms of thought, it's output is essentially one that's processed by the very same technology. This function is one of countless many that can map nature in some way. All are facets that all together elude the essential nature of understanding thought as a human experience.
This is where art comes into play. I'm speaking about creativity in a broader sense. There's Thought on paper painted with a brush stroke or revealed from marble.
Not to hiack the conversation away from your questions, but I think as we strive to hear and see big numbers dance and breathe in some algorithmic swarm, the swarm has also been witnessed through the expression of art itself.