Benoit_Essiambre
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Benoit_Essiambre has not written any posts yet.
Lucretius' On the Nature of Things (http://en.wikipedia.org/wiki/On_the_Nature_of_Things) is considered one of the most beautiful epic poem ever written and the subject can be summed up as the rejection of religion in favor of the physical sciences. Written before Christianity even existed, Lucretius describes atoms, the movement of mass, the infinite nature of the universe, and the materialistic nature of the soul. Beautiful indeed.
"It was previously pointed out to me that I might be losing some of my readers with the long essays"
I for one find the long mathematical bayesian proselytizing some of your most fascinating posts. I can't wait for the next ones.
art is a piece of temporary entropic order, the kind that appears extraordinarily from time to time in a universe subject to the second law of thermodynamics.
What's interesting about "Thingspace" (I sometimes call it "orderspace") is that it flattens out all the different combinations of properties into a mutually exclusive space of points. An observable "thing" in the universe can't be classified in two different points in Thingspace. Yes you can have a range in Thingspace representing your uncertainty about the classification (If you're a mere mortal you always have this error bar) but the piece-of-universe-order you are trying to classify is in ideal terms only one point in the space.
IMO this could explain the way we deal with causality. Why do we say effects have only one cause? Where does the Principle of Sufficient Reason come from?... (read more)
Well, for example, the fact that two different real represent the same point. 2.00... 1.99... , the fact that they are not computable in a finite amount of time. pi and e are quite representable within a computable number system otherwise we couldn't reliably use pi and e on computers!
Benquo, I see two possible reasons:
1) '2' leads to confusion as to whether we are representing a real or a natural number. That is, whether we are counting discrete items or we are representing a value on a continuum. If we are counting items then '2' is correct.
2) If it is clear that we are representing numbers on a continuum, I could see the number of significant digits used as an indication of the amount of uncertainty in the value. For any real problem there is always uncertainty caused by A) the measuring instrument and B) the representation system itself such as the computable numbers which are limited by a finite amount... (read more)
James, I share your feelings of uneasiness about infinite digits, as you said, the problem is not that these numbers will not represent the same points at the limit but that they shouldn't be taken to the limit so readily as this doesn't seem to add anything to mathematics but confusion.
Thanks g for the tip about computable numbers, that's pretty much what I had in mind. I didn't quite get from the wikipedia article if these numbers could or could not replace the reals for all of useful mathematics but it's interesting indeed.
I agree that infinity is an abstraction. What I'm trying to say is that this concept is often abused when it is taken as implicit in real numbers.
"We can only "count" because our physical world is a quantum world. We have units because the basic elements are units, like elementary particles. If the real world were a continuum, there would be no arithmetic."
I don't see it that way. In Euclid's book, variables are assigned to segment lengths and other geometries that tie algebra to geometric interpretations. IMO, when mathematics stray away from something that can be interpreted physically it leads to confusion and errors.
What I'd like to see is a definition of... (read more)
Reading Lucretius made me realize how long the science vs religion debate has been going on. I was introduced to Lucretius through reading George Santayana, the American Philosopher of aesthetics in particular of literature and poetry. I discovered Santayana at about the same time I discovered E.T. Jaynes which is an weird coincidence since they both seem to base their doctrine on untangling the confusion of the mind projection fallacy. They both argue at length that humans attribute too much of what goes in their head to the real world. Santayana used it to argue that religion is poetry and it is an error to believe it speaks of the real universe... (read 536 more words →)