thetwiceler

10 ms·

31.
by thetwiceler 13y ago
Absolutely have to recommend Paul Lockhart's Measurement [1]! Journey Through Genius is a great book as well. [1] http://www.hup.harvard.edu/catalog.php?isbn=9780674057555
32.
by thetwiceler 13y ago
Pictures are worth a thousand words! Now let me put the quadratic formula in disguise as well. Suppose we wish to make a rectangle with a given area and perimeter. This is an interesting problem! Does the number of possible answers depend o
33.
by thetwiceler 13y ago
I think people like to say the prime numbers are the basic building blocks of arithmetic (or numbers), and we say this because of the Fundamental Theorem of Arithmetic (which says that every natural number has a unique factorization of pr
34.
by thetwiceler 13y ago
I agree; it is up to us to decide what constitutes a "clear and present danger." You can always claim anything you want, but you'll have a difficult time convincing me that voicing disapproval of the president constitutes a
35.
by thetwiceler 13y ago
This should not be causing indignation. I think most of you agree with Justice Oliver Wendel Holmes that: The most stringent protection of free speech would not protect a man falsely shouting fire in a theater and causing a panic. [...] Th
36.
by thetwiceler 13y ago
The idea is that the Curry-Howard isomorphism allows you to "play" with constructive mathematics easily. For example, consider the fact that the composition of two functions f and g is continuous if each function is continuous
37.
by thetwiceler 13y ago
As far as I know, Hudak has updated and renamed his book to The Haskell School of Music , and it's available for free from the Yale Haskell Group's website here: http://haskell.cs.yale.edu/?post_type=publication&a
38.
by thetwiceler 13y ago
Here's a really good way to protest security theater (albeit very much at your expense): write SSSS [1] on your boarding pass, and see how you're treated! (Security officers can write SSSS on your boarding pass, so it doesn't
39.
by thetwiceler 13y ago
Yes, a million times! Journey through Genius is an excellent book (I, too, had this book for a History of Math class). It's really appropriate for people of all different levels of mathematical maturity. It's aimed to be read by
40.
by thetwiceler 13y ago
This is by Paul Hudak, one of the creators of Haskell. I took one of his classes that corresponds with this book. This is how I was introduced to Haskell. Now I'm hooked on Haskell! The book is a truly excellent introduction to Haskell
41.
by thetwiceler 13y ago
Sometimes; it depends on the class.
42.
by thetwiceler 13y ago
The first "programming language" that I learned to use was LEGO Mindstorms, when I was around 8 years old. I think that was an absolutely AWESOME way to teach the principles of computer programs to children. (And transferring the
43.
by thetwiceler 13y ago
This is really cool! On a similar note, for those of you who may not be aware, there has also been a human-powered airplane: http://en.wikipedia.org/wiki/Gossamer_Albatross I am totally amazed by the Gossamer Albatross
44.
by thetwiceler 13y ago
If you take this sort-of-stretched case where encryption can be broken, I can explain why this is a problem. Suppose you are using the PRNG to make a stream cipher. Basically, your random key is a seed for the PRNG. You then generate lots o
45.
by thetwiceler 13y ago
Anyone know why "bruising" and "brown spots" are common in the summer? Not as nice as the canonical answer of "ice cream"... http://www.google.com/trends/correlate/search?e=id:UfmYZwmi
46.
by thetwiceler 13y ago
This is false. Think about it this way. A random walk is a martingale - you're expectation of where you'll be in the future is. So you're right that, before you start the walk, they have expectation of being at 0 at any time
47.
by thetwiceler 13y ago
I totally agree. Unless we decide to leave the field of rational numbers (with exponents, trigonometrics or nth roots), there's little reason not to keep the exact rational number around. Fortunately Haskell does this too with Data.Rat
48.
by thetwiceler 13y ago
Once again, don't confuse predictability with ability to understand a system. We actually have a fairly good understanding of weather dynamics and turbulence - and I can give you the formula for both of these - the Navier-Stokes equati
49.
by thetwiceler 13y ago
I think you're just spouting a lot of buzzwords, and you're actually conflating (a) the relevance of chaos theory and (b) criticisms of normal distributions in economics. A major recent criticism is of some economic models which h
50.
by thetwiceler 13y ago
The use of infinitesimals in calculus! Things like integrating against "dx" or taking a derivative of a function "df/dx" make calculus seem like something it's not. Worse, it really introduces a whole new langu
51.
by thetwiceler 13y ago
Yeah, I've literally never seen lower-case pi used as a variable (thank goodness!). tau is a good choice because it looks like pi, and is possible for normal people to write (I would have had a fit if it were lowercase xi!). I like the
52.
by thetwiceler 13y ago
I disagree to an extent. For some classes (it's quite variable), the forums can be of great quality, and it can be greatly enriching to be learning the material (and educational tangents that occur in the forums) along with lots of oth
53.
by thetwiceler 13y ago
Wow this is hilarious. Truly a "manifesto" to set a constant for 2pi. It definitely has a great point, and I totally agree that it's a better constant than pi, but it's not the worst historical accident of mathematics. T
54.
by thetwiceler 13y ago
Actually, this example makes Euclid even more of a logician. Recall that Euclid stated his Fifth Postulate (where his postulates really mean axioms). Geometers for thousands of years afterward, guided by intuition, attempted to prove that i
55.
by thetwiceler 13y ago
http://sciencevsmagic.net/geo/#0A1.0L1.1L2.2A1.1A2.4L0.7A0.9... Ahh! Well you can't say I didn't try. Must have accidentally hit one of the wrong points somewhere in the construction...
56.
by thetwiceler 13y ago
Somebody construct a 17-gon!
57.
by thetwiceler 13y ago
I think this is really hyperbolic. The fact is that Snowden violated the conditions of his Top Secret security clearance, which is a crime that is subject to criminal prosecution. Now, I'd argue the leak that Snowden made was much more
58.
by thetwiceler 14y ago
Proof that Bitcoin is worthless: I set up camp over the Golden Gate Bridge. I ask people if they'd be willing to throw their lunch into the water (use their computer's time/energy/money to mine Bitcoin), with no possibility of retrieving it