124 reputation
7
bio website movingsql.com
location New Jersey
age 57
visits member for 3 years, 10 months
seen Nov 24 at 18:38
coder & programmer of many defunct languages...

Sep
25
comment Is it true to say that “it's not logically possible to prove something can't be done”?
This is just a slightly smartened up version of the inane truism "You can't prove a Negative." Obviously not true in mathematics and formal system, but less obviously, not true in any common reasoning system that has a notion of "proof". What's really meant is "You can't prove a Universal.", at least not empirically. Scott Adams is brilliant, but he's definitely wrong on this one. Saying that you can't prove that anything can't be done is effectively equivalent to saying that you can't disprove anything.
Jul
28
revised Interview puzzle with a deck of cards, some cards upside-down
correcting opposite of upside down. (keep missing pieces)
Jul
28
suggested suggested edit on Interview puzzle with a deck of cards, some cards upside-down
Jul
20
comment Elementary theorems with several proofs?
This probably should be a community wiki, since it does not have a single correct answer.
Apr
14
comment Limit is found using polar coordinates but it is not supposed to exist.
OMG, I will upvote you just for the images if you'll tell us what you used to make them...
Mar
30
comment Why would you expand a square wave in a Fourier series?
All modern digital audio uses the Fourier Transforms extensively, so knowing a square wave's Fourier series can be very helpful to understanding why, say, a hi or lo-pass filter changes its shape in various ways. learnabout-electronics.org/ac_theory/filters84.php
Mar
21
comment Why is $\sin^2x + \cos^2x = 1$ important?
$\sin^2x + \cos^2x = 1$ is basically just the Pythagorean identity ($a^2 + b^2 = c^2$) expressed in Trigonometric terms instead of Algebraic terms. And that's important because the Pythagorean theorem is the basis for almost all trigonometry.
Mar
18
revised If the infinite cardinals aleph-null, aleph-two, etc. continue indefinitely, is there any meaning in the idea of aleph-aleph-null?
Included theactual question into the body of the post.
Mar
18
comment If the infinite cardinals aleph-null, aleph-two, etc. continue indefinitely, is there any meaning in the idea of aleph-aleph-null?
FYI: make sure that your actual question is in the body of your post. It's confusing to have it only in the title.
Mar
18
suggested suggested edit on If the infinite cardinals aleph-null, aleph-two, etc. continue indefinitely, is there any meaning in the idea of aleph-aleph-null?
Mar
8
comment What is exponentiation?
Exponentiation in the complex plane is a chiral operator. You cannot possibly have an intuitive or natural understanding of it without first grasping that. And the rest naturally follows from that.
Feb
14
comment Very probable event occuring at least once during $n$ trials
Assuming that they are independent events (and/or that subsequent probabilities for the events are unaffected by prior ones). This was never actually stated in the question.
Feb
5
comment Why are there so few Euclidean geometry problems that remain unsolved?
After some research I am no longer confident that my earlier statement about being resolvable in O(n) is correct. I had forgotten a few things (such as recursive enumeration, and that linear optimization problems can be restated as a problem of planar inequality bounding maximums), and now believe that I may have misunderstood the potential complexity of the transformation procedure.
Feb
4
comment Why are there so few Euclidean geometry problems that remain unsolved?
@WillieWong Yeah, but its been 35 years since I worked on any of this. I am having a lot of trouble finding the references, or even recalling the proper mathematical terms to search for. :-( I'll try though.
Feb
4
comment Why are there so few Euclidean geometry problems that remain unsolved?
@vonbrand Yes, unlike formalized Euclidian Geometry modern "interesting" branches of geometry, such as Projective Geometry, etc. extend (and/or modify) the Euclidian concepts a great deal and are not deductively complete and thus still fall into the realm of exponential proof searches.
Feb
4
comment Why are there so few Euclidean geometry problems that remain unsolved?
@JasonDeVito No, by Godel's theorem and subsequent work any deductively complete formal system like EG (Euclidian Geomtery) has a lexical truth function that given any syntactically valid statement in the formal system, transforms it into an arithmetical expression that always returns 0/1 based on the truth of the statement. Both the transform and the expression are closed and so run in O(n) steps where 'n' is the length of the statement. I believe that EG's function was demonstrated back in the early 60's. As such, EG will never again have an unsolved problem, and is thus "uninteresting".
Feb
3
comment Why are so many of the oldest unsolved problems in mathematics about number theory?
For some reason, I cannot get the pasted link to work correctly. Google works though ...
Feb
3
comment Why are so many of the oldest unsolved problems in mathematics about number theory?
@twirlobite Gödel's Theorem (see here: http://en.wikipedia.org/wiki/…)
Feb
3
comment Why is the notation for differentiation like this?
"..if we take $x$ to mean $\Delta x$ in a loose sense." I think that it would be more accurate to say "..take $dx$ to mean $\Delta x$ in a loose sense." because loosely, $dx$ is $\Delta x$ as it approaches zero. Also, the implicit assumption in $dy/dx$ is that as $\Delta x$ approaches zero, then so does $\Delta f(x)$. Otherwise it wouldn't be differentiable.
Feb
3
comment Why are so many of the oldest unsolved problems in mathematics about number theory?
@DavidH The answer is simple, unlike Number Theory (and almost all other branches of mathematics) Euclidean Geometry turned out to be deductively Complete. Thus all syntactically valid statements in it are either provable or disprovable within it. Formal systems that are "deductively complete" are also called "uninteresting" because of how easy it turns out to be to prove/disprove all statements once you know this.