jbrot

I guess that makes sense since the Earth’s radius is around 6400km so from 400 to 1400km is really a change from 6800 to 7800km which is proportionally similar to a change from 90 to 110 minutes.

Edit: I just looked up the formula for orbital period and it turns out period is proportional to radius^(3/2) (See: https://en.m.wikipedia.org/wiki/Orbital_period)

A related concept I’ve read about is the “Schelling Coin,” where a crypto contract accepts community input and then pays out to everyone who submitted the most popular answer. The idea being that you label the contract with something like “temperature in Chicago” which causes the actual temperature in Chicago to be the only value everyone is likely to agree on (i.e., the real value becomes the Schelling point)—thereby allowing for decentralized embedding of real world information into the block chain.

I’m unclear if this mechanism is actually in use, though, and I’ve seen a convincing attack proposed which might explain why Schelling coins don’t seem to be in widespread use.

Could you clarify why you think placing crypto rigs in space is a good idea? To run a crypto rig, you need to provide a lot of power and have a mechanism to keep the processors cool. Being in space seems to make both of these substantially more difficult (especially cooling the electronics). It seems highly implausible to me that crypto will be the “killer app” of space.

These algorithms all reduce the division problem into some fixed range. For instance, in the case of 3, we are able to reduce the divisibility of an arbitrary integer by 3 into the divisibility of a single digit number by 3. In the 13 case described in the article, we reduce the problem to a 3 digit number. The base case can then just be a lookup table.

As for how to generate the base table, recall that we say a divides n provided there exists some b such that ab = n. In this case we're talking about integers, although this is the definition for any ring.

Therefore, proving 3 divides 9 is as simple as noting that 3 * 3 = 9, and likewise we can prove 3 divides 6 by noting that 3 * 2 is 6.

Proving a lack of divisibilty is a little bit trickier. For this, you'll want to first prove the division algorithm which, in the case of the integers, says that for any two integers a and n, there exists unique integers b and r with abs(r) < abs(a) such that ab + r = n.

Given this, we can then note that, for instance, 7 = 3 * 2 + 1. Therefore 7 cannot be divisible by 3 as that would imply there exists some other integer b such that 7 = 3 * b + 0 contradicting that the integers from the division algorithm are unique.

You might then wonder: well, how do we know 3 * 2 is 6? Well, to stop these questions from recursing endlessly, we need to define the integers. One reasonable definition is "the initial element in the ring category" which gives us that the integers are a ring by definition. As such, we have axiomatically that there are integers 0 and 1, a commutative operation + with identity 0 that is closed under inverses, an associative operation * with identity 1, and that * distributes over +. If we then define 2 to be 1 + 1, 3 to be 1 + 1 + 1, and 6 to be 1 + 1 + 1 + 1 + 1 + 1, we can use distributivity to prove that 3 * 2 = 3 * (1 + 1) = (3 * 1) + (3 * 1) = 3 + 3 = 6.

I watched the interview with the artist at the bottom of the article, and apparently the sculptures have been lost.

Hurwitz received the sculptures in the U.K. from the lab in Germany on a slab of glass. Hurwitz then found a local electron microscope operator so he could look at them. After getting an initial set of images, the owner of the microscope accidentally put his finger on the glass when adjusting it’s angle in the microscope—losing the sculptures.

Hurwitz says, “the sculptures have been lost and in their place is a story.”

As a corollary all of the pictures of the sculptures not on a blank background must therefore be overlays (or possibly renders?)