I am working on some very smart things to say here. Really. Meanwhile, there's 
A very limited list of things that nobody knows (as compiled by yours truly, a very limited human). As you may notice, most of the list treads close to things that may be broadly classed as epistemological questions. Do extend it with your own unknowns. There are some other more comprehensive lists: Science Magazine's list from 2005. NY Times list from 2003. A New Scientist list from 2005.
What's the matter with prime numbers. (Reimann Hypothesis)
What are the fundamental constituents of the universe. (see last question)
What is a dimension. How many of it does the universe have.
Can life as we know (so far, it's just on our little planet) make it to The End. Can it make it beyond The End.
Do numbers have a reality of their own. (GH Hardy: I believe that mathematical reality lies outside us)
Is it possible to know what we can and cannot know.
Physical Science
Humanities & Social Science
Comments
hm, to the extend the universe is computable and rich enough to contain arithmetic, a decent argument can be made for answering your last question: namely that we know we cannot know everything, and we can not know what we cannot know.
The second and third question are, in principle, amenable to measurment, and may be known in the near future. The fourth question is, strangely, probably a function of initial cosmological conditions, if restated in terms of cauchy horizons of local volumes and whether there is finite free energy at all times.
It would be nice to know the answer to the first question.
Posted by: Steinn Sigurdsson | September 1, 2009 10:02 AM
Yes. I mean no. I mean I don't know. But that would be the same as no. Ughh. My head hurts.
Posted by: jimspice | September 1, 2009 10:38 AM
"Is it possible to know what we can and cannot know?" That is not merely a central question in Epistemology, but a question about how the nature of the universe and the nature of the human mind are or are not in a deep sense similar in structure or dynamics.
Can we map the borders of what we don't know as the blank space just beyond the edge of what we think that we do know? And what if what we don't know is much bigger than we think it is?
I taught several hundred students, aged 50 to 90, courses including “The Frontiers of Ignorance” from Kuhn’s “Structure of Scientific Revolution.” I’ve taught epistemology, psychology, anthropology, oceanography, sociology, and many other subjects outside my adjunct professorships in Mathematics and in Astronomy. My musings were sparked by that, and my fascination with the topological and categorical questions raised by Zwicky’s Idocosm. Zwicky explored systematically "The Space of All Possible Ideas."
For that matter, attention to the most deeply buried footnotes in science journals make it clear that good scientists admit that their work is on the frontiers of ignorance. Much of what was in textbooks when I was a boy is simply untrue today. And tomorrow...?
Posted by: Jonathan Vos Post | September 1, 2009 1:21 PM
The natural numbers have a reality of their own. Everything else is man-made.
For example, a mathematician says the diagonal of a unit square is an irrational number. But, in reality, one can never measure the diagonal with the degree of accuracy required to say if it is irrational. Therefore, the irrational number is a man-made concept that doesn't correspond to a measure in nature.
Posted by: Robert | September 1, 2009 1:23 PM
It seems to me that these questions come from the fascinating interference pattern that arises when models of reality are laid on top of reality its self. It's that wonderful feedback loop that bootstrapped us up from instinct and being unaware of living in the world, being able to simplify and abstract the world into symbols.
It seems to me to be the difference between a meter stick and the idea of a meter, the chemical formula of water and what we drink. It's a lovely fractal space where how many questions and in what way you ask them determine the answers you get.
It seems to me to be the relationship between the practical and the theoretical.
>Is it possible to know what we can and cannot know.
I'm not sure I understand the question. What is the context? I think it's very important to have something that works, but we don't know precicely how, that there's a level of instability and chance, like breeding crops and livestock, where we just keep what works and discard what does not. An example of the leverage of the blind watchmaker.
Posted by: kleer001 | September 1, 2009 2:43 PM
This is surely one of the silliest lists. Here are the answers:
1. "What's the matter with prime numbers." This question is of interest almost exclusively to mathematicians. Eventually a proof will be found to the Riemanh conjecture.
2. "What are the fundamental constituents of the universe." At any given time, we have a hypothesis of the most fundamental constituent (currently string theory) -- until we find a more fundamental one. This process will continue indefinitely.
3. "What is a dimension. How many of it does the universe have." A dimension is what it is defined as. Again, we currently suspect 11 dimensions, but there is no limit to future discoveries.
4. "Can life as we know (so far, it's just on our little planet) make it to The End. Can it make it beyond The End." There is no "The End". This shows a misunderstanding of the nature of time.
5. "Do numbers have a reality of their own." Of course not, unless you mean reality in the Platonic view. Numbers are no more real than English has a reality outside of English speakers. Numbers are abstract. Most people would not consider Platonic forms to be "reality", however you define that.
6. "Is it possible to know what we can and cannot know." This looks like two questions, but if so, the first one is silly ("Is it possible to know what we can know.) The second one -- is it possible to know what we cannot know -- is well-known to be false. Someone will inevitably provide an answer to any of your questions -- there is no limit to knowledge.
Posted by: Paul Gahlinger, MD, PhD, MPH | September 1, 2009 8:59 PM