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

[databeast.livejournal.com]

hrm, good question, if 'infinity approaching everything' has different aspects, what about the 'infinity approaching nothing' version?

yoink!

[radarrider.livejournal.com]

There are actually multiple types of infinity. It's totally an abstract concept but it does play a part in math. Here's an example. There are an infinite number of integers. There are also an infinite number of real numbers, which include all integers and all fractions. For two infinities to be "equivalent" you have to show that there is a one-to-one mapping between them. It can be shown that you can't create such a mapping between the integers and the real numbers. No matter how you try, you will always be able to generate a real number (usually by just adding another digit after the decimal point) that isn't mapped to an integer. In fact, you can generate an infinite number of real numbers for each integer. Thus, there are "more" real numbers than integers even though both are infinities. Integers are an order 1 infinity, real numbers are order 2.

Man, the stuff I remember from college....

[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.