The sicence behind 1 to 4 to 9 precision (2001 a Space Odyssey)

[Darnok]

On 2.03.2016 at 1:04 AM, softweir said:

Pi is universal in any time-space which is sufficiently flat enough that circles can exist. Some races may use tau instead of pi, but if they do use pi and calculate it then they will get the same answer we do. And if they use tau and calculate it they will get twice the value we use for pi.

Incidentally, tau is a better value than pi. And as for comparison with e, tau turns up in all sorts of weird places you wouldn't expect it either.

Where?

On 1.03.2016 at 9:08 PM, Kerbart said:

Aside from the incredible difficulties base-pi would impose on day-to-day arithmetic, as a "universal" base it would fail as pi is not a very universal number.

Why would you use π on day-to-day arithmetic? It would be very wrong, for every day use you have integer based system.

[Kerbart]

3 hours ago, Darnok said:

Where?

Why would you use π on day-to-day arithmetic? It would be very wrong, for every day use you have integer based system.

Which is why I say that it's very hard to use on a day-to-day basis.

 

[cantab]

If I may get back to the original topic. I don't think the 1:4:9 ratio has any great significance - it's a nice integer sequence but there are plenty of other nice integer sequences.

What I feel does have significance isn't even remarked on in the book - that the sides are at right angles. It seems trivial, obvious even, but I see importance in extending to higher dimensions.

You may be familiar with the Platonic solids, and how there are five and only five. In four dimensions there are six regular "polytopes", but beyond that there are just three series that work for any number of dimensions. One are the hypercubes, and they can be seen in a way as the units of space - at each vertex the edges all meet at right angles. The hypercubes can tessellate space, and for example could be combined to make a 1:4:9:16:25:... ratio Monolith (at least conceptually); I think the hypercubes might be the only family of regular polytopes that can fill space.

To get into more familiar terms, suppose instead that the "Monolith" had been an icosahedron. In three dimensions that would be no less perfect than the cuboid, in fact arguably more perfect. But it doesn't extend into higher dimensions. There's no 4D polytope made of icosahedra. A dodecahedron would extend to 4 dimensions, making a polytope called the 120-cell, but no further.

So really, the Monolith had to be a cuboid.