Linky goodness from NEDoD

[unixronin]

First, the radial-engined motorcycle built by Jesse James.  What's even cooler-but-crazier, if you read the comments on this article about an alternate take on the radial-engine concept, some guy (see the second comment) is thinking about building a motorcycle with a rotary¹ engine.  Not rotary as in Wankel; rotary as in WW1 rotary aircraft engines, where the entire cylinder array spins around a fixed crankshaft.

And, for a different kind of cool just because it's such outrageous snake oil, check out the miracle hydrogen-power solution to the world's energy needs from the guy who's invented the "very unique¹ elecrolysis process" that turns H2O into the magic wonder-gas HHO.  Just think, if he used his wonder-gas to run a generator to drive his electrolysis machine, he could have a perpetual motion machine!

(....Not.)

[1]  Dammit!  I used the word 'rotary' three times in this post.  And each time, I consistently typo'd it as "rotaty".  And somehow I only spotted ONE of the three typos each time I checked it........ each time I fixed one and glanced at the others to make sure I'd got them right, the others looked OK.

[2]  Last I knew, the formal definition of "unique" was something like "there exists precisely one such".  Does something that's "very unique" use a smaller than usual value of "one"?

Comments

[gdmusumeci.livejournal.com]

To be a little bit more precise (sorry, this is one of my favorite topics). N (the natural numbers), Z (the integers), and Q (the rational numbers) are all the same size (countably infinite, with cardinality aleph₀. R (the real numbers) cannot be put into one-to-one correspondence with any countably infinite set (Cantor originally used N): instead they have cardinality c,¹ the name of which is derived from "continuum."² Note that the set of reals between 0 and 1 -- that is, the open interval set (0,1) -- has the same cardinality as R, which is somewhat interesting. I leave finding a mapping from R to (0,1) to the reader.


1: The Continuum Hypothesis would state that c = aleph₁ = 2^aleph₀.
2: This is how we got into the Continuum Hypothesis and transfinite set theory (which Hilbert called the "paradise of the infinite").

[databeast.livejournal.com]

here's my favorite way to explain infinity to non-mathnerds

You own a hotel
it has infinite rooms
on Day 1, an infinite number of guests check in
your hotel is full
on Day 2, a second batch of an infinite number of guests check in
..you ask all the guests from day 1 to move up to their next even-numbered room
..the new guests check into the odd-numbered room
everyone gets a room
your hotel with infinite rooms and infinite guests is still full.
repeat as neccessary.

granted, that's a purely integer example, but it's a nice way to answer kids who (like we all did) ask questions like 'whats infinity plus one?'

[unixronin.livejournal.com]

Can you really explain infinity to non-mathematicians using infinity in the explanation? Seems to me it'd be a circular-reference problem.

[databeast.livejournal.com]

yes,the example I gave is exactly that, it takes the layman's version of 'infinity' and plays with it to demonstrate the concept.