Recent content by trilobite

The paper by Soffer and Lynch does make a similar point concerning the alternative of using a logarithmic representation. However, the authors state that this method has "no special physical significance" and should not be "singled out as a preferred physical ... representation" for...

trilobite submitted a new PF Insights post Exploring the Spectral Paradox Continue reading the Original PF Insights Post.

Great question! Unfortunately, I don't know the answer. Every reference I can find simply asserts that there is no elementary formula without giving any justification. If someone can comment with insight into this question, I would definitely be interested to hear it.

Thanks for this interesting remark. My personal bias, for which I have no evidence, is that the "correct" math is continuous, although we use it to model a universe that is likely discrete.

That's an excellent question, but I don't have an answer. It's one thing to live in a physical universe that is hard to understand, but as my article points out, "mysteries" lurk even in the ideal world of rudimentary geometry (squares, circles, ellipses!) It would be "nice" if the square root...

That used to happen to me, too (not that long ago.) For some reason, the feature works for me now. I don't think it has to do with membership level, but I have no idea why this happens.

Thanks for describing your interesting (and ambitious!) project. [By the way, for some reason your post does not appear in "Discuss in the Community", at least not for me. Fortunately, I spotted it in Insights by scrolling down below my article, although usually I can't see any of the comments...

I guess I meant "not easily understandable." But this is not an area I know a whole lot about. I would be interested to see an easily understandable non-computable number, if you have an example. The standard definition is that a number is algebraic if it is the root of a polynomial with...

I believe that a computable number is one that can be computed to any desired number of decimal places by a finite number of operations. Usually, this is expressed in terms of a computer program that accomplishes the required calculation. The interesting thing is that the computable numbers...

Yes, that's a fascinating topic! Thanks for mentioning it.

trilobite submitted a new PF Insights post Simple Geometry, Deep Math Continue reading the Original PF Insights Post.

Hippasus, according to Wikipedia, which says the story may be just legend.

This is just a test comment. If you see it, please ignore. I'm just using it as a sandbox. Now is the time to go to the store and get some... chocolate! $$ \frac 2 3 $$ eek eek eek ## \frac A B ## arg arg arg

Ancient Greek mathematicians freaked out when they discovered that the square root of 2 is not rational. Like Swamp Thing, they were not dummies and realized that the existence of irrational numbers is a fact that is remarkable, deep, and a little scary.

Maybe it's because I recently upgraded to Windows 10. Wouldn't be surprised. :cool: