It's not that F(N)=1/N "stops working", it's just that there are real numbers between 0 and 1 that won't be the output of that function for any value of N. You don't even have to use the diagonal method to show it in this case—for instance, 2/3 is between 0 and 1, yet there is no positive integer N you can choose such…

He's talking about an arbitrary function that, when fed an integer as an input, returns a real number between (and including) 0 and 1 as an output. A very simple example of such a function would be F(N)=1/N, so F(1) = 1, F(2)=1/2, F(3)=1/3, F(4)=1/4, etc. You don't even have to imagine a function that follows a…

If you jump diagonally you will experience zero-G while away from the floor, but then you'll eventually collide with a different part of the floor and then start experiencing G-forces again...that's also exactly what happens if you jump sideways on Earth! Another part of the equivalence principle is that anyone free…

See my comment here. According to Einstein's equivalence principle, the distinction you're making isn't so clear-cut.

Depends what you mean. According to Einstein's equivalence principle, "gravity" in the sense of G-forces really has exactly the same cause on Earth and accelerating in space. Only in terms of the gravitational effects known as "tidal forces" (differing gravitational pulls on different parts of the system in question),…

Well, the author of this page says iron is abundant, but there are some other elements that he says would be needed to build a mass driver that are hard to come by on the moon and would probably need to be shipped:

And meanwhile, transporting large quantities of Helium-3 back to Earth will be another problem. A spacecraft would likely be able to only carry a few tons of Helium-3 as payload, necessitating a revolving door of shuttles to supply enough Helium-3 to care for the Earth's energy needs.

all I'm saying is that you reviewed the film as if it was one of the worst films of the year, whereas it's simply mediocre

The science fiction writer Charles Stross had a really interesting article about the kind of changes to society this sort of technology could lead to as data storage and recording becomes better and better: [www.antipope.org]

I believe "witch" isn't just talking of the supernatural but as the writer put it, it is a sassy woman who "stirs the pot". The "witch" type, from this perspective, is any woman who is a form of unbridled energy that acts as, while maybe not a direct-antagonist, at least causes trouble where she goes. She has her hand…

He freaks out in an aggressive or a laughing-maniacally type of way, not a frightened or meek way which is what is usually meant by skittish—again, his freakouts are more like those of the Joker (who is also an outcast in the sense that most of mainstream society doesn't like him, at least until he hands out money).…

Beetlejuice isn't really a skittish outcast, he's a totally confident sociopath who most people would fear as much as they dislike him, more like the Joker in Batman. Similarly, it's a bit of a stretch to call The Red Queen or Catwoman "the witch" when neither have any witchy powers, and The Red Queen is a powerful…

True, but the quotes from the original story don't seem to say anything about "space", that's just part of a misleading headline on the io9 article debunking it.

If you read the end of the story, you see that the part about it being crewed was a lie anyway.

Most likely the "34th century" part is an error, looking at the samples of the book on amazon they say the year is "T8975" and the narrator is told that "a period of some twelve thousand years has passed since your craft left the Sol system", and the beginning of chapter 8 recalls an event from the narrator's life…

I think the end of the article is implying that the quote about going 32,000 feet up was fabricated anyway (see my question in the comment above), but you're right, 32,000 feet is about 9 km while "space" is usually defined to be about 100 km up (32,000 feet is around the typical cruising altitude of a commercial…

A clue as to what started the entire manned rocket story might be found in the name Nebel had given his test rocket. It was called the "Magdeburg Pilot Rocket". An over-enthusiastic reporter had misunderstood the use of the word "pilot" and had run with it.

Although this thing is almost certainly pseudoscience, the whole premise of this post is confused—with "ionic cleansing" in the name they are presumably talking about ions (atoms or molecules with electrons subtracted or added), not ordinary "steam". In fact if you read the description of an ion cleanse here it…

Nope, just another stupid conversion: