Nisan's Shortform

Nisan

Nisan's Shortform

1 min read12th Sep 202111 comments

Crossposted from the AI Alignment Forum. May contain more technical jargon than usual.

This is a special post for quick takes by Nisan. Only they can create top-level comments. Comments here also appear on the Quick Takes page and All Posts page.

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[-]Nisan1y260

Recent interviews with Eliezer:

2023.02.20 Bankless
2023.02.20 Bankless followup
2023.03.11 Japan AI Alignment Conference
2023.03.30 Lex Fridman
2023.04.06 Dwarkesh Patel
2023.04.18 TED talk
2023.04.19 Center for the Future Mind
2023.05.04 Accursed Farms
2023.05.06 Logan Bartlett
2023.05.06 Fox News
2023.05.08 EconTalk
2023.07.02 David Pakman
2023.07.13 AI IRL
2023.07.13 The Spectator (Edited transcript of the full interview)
2023.07.13 Dan Crenshaw
2023.07.28 Coleman Hughes (with Scott Aaronson and Gary Marcus)
2023.08.16 Dwarkesh Patel (with George Hotz)
2023.08.23 One Decision
2023.09.23 Destiny

[-]Nisan6mo190

Hyperbolic growth

The differential equation , for positive $α$ and $b$ , has solution

$y = \frac{1}{(t_{0} - t)^{1 / α}}$

(after changing the units). The Roodman report argues that our economy follows this hyperbolic growth trend, rather than an exponential one.

While exponential growth has a single parameter — the growth rate or interest rate — hyperbolic growth has two parameters: $t_{0}$ is the time until singularity, and $α$ is the "hardness" of the takeoff.

A value of $α$ close to zero gives a "soft" takeoff where the derivative gets high well in advance of the singularity. A large value of $α$ gives a "hard" takeoff, where explosive growth comes all at once right at the singularity. (Paul Christiano calls these "slow" and "fast" takeoff.)

Paul defines "slow takeoff" as "There will be a complete 4 year interval in which world output doubles, before the first 1 year interval in which world output doubles." This corresponds to $α \leq 2$ . (At $α = 2$ , the first four-year doubling starts at $\frac{16}{3}$ and the first one-year doubling starts at $\frac{4}{3}$ years before the singularity.)

So the simple hyperbola $y = 1 / (t_{0} - t)$ with $α = 1$ counts as "slow takeoff". (This is the "naive model" mentioned in footnote 31 of Intelligence Explosion Microeconomics.)

Roodman's estimates of historical $α$ are closer to $0.5$ (see Table 3).

[-]Nisan3y150

People are fond of using the neologism "cruxy", but there's already a word for that: "crucial". Apparently this sense of "crucial" can be traced back to Francis Bacon.

[-]ChristianKl3y40

The point of using a word like this is to point to different habits of thoughts. If you use an existing word that's unlikely to happen in listerners.

If you don't do that you get a lot of motte-and-bailey issues.

[-]Vladimir_Nesov3y40

A cruxy point doesn't have to be important, the whole question being considered doesn't have to be important. This is an unfortunate connotation of "crucial", because when I'm pointing out that the sky is blue, I'm usually not saying that it's important that it's blue, or that it's important for this object level argument to be resolved. It's only important to figure out what caused a simple mistake that's usually reliably avoided, and to keep channeling curiosity to fill out the map, so that it's not just the apparently useful parts that are not wild conjecture.

[-]Dagon3y50

I think it's relative. A crux is crucial to a question, whether the question is crucial to anything else or not. If you're pointing out the sky is blue, that's only a crux if it's important to some misunderstanding or disagreement.

I'm with Nisan. "Crucial" is simply the proper and common term that should be used instead of the backformation "cruxy".

[-]Nisan10moΩ360

Conception is a startup trying to do in vitro gametogenesis for humans!

[-]Nisan4mo40

We can derive Newton's law of cooling from first principles.

Consider an ergodic discrete-time dynamical system and group the microstates into macrostates according to some observable variable . ( $X$ might be the temperature of a subsystem.)

Let's assume that if $X = x$ , then in the next timestep $X$ can be one of the values $x - d x$ , $x$ , or $x + d x$ .

Let's make the further assumption that the transition probabilities for these three possibilities have the same ratio as the number of microstates.

Then it turns out that the rate of change over time $\frac{d X}{d t}$ is proportional to $\frac{d H}{d X}$ , where $H$ is the entropy, which is the logarithm of the number of microstates.

Now suppose our system consists of two interacting subsystems with energies $E_{1}$ and $E_{2}$ . Total energy is conserved. How fast will energy flow from one system to the other? By the above lemma, $\frac{d E_{1}}{d t}$ is proportional to $\frac{d H}{d E_{1}} = \frac{d H_{1}}{d E_{1}} - \frac{d H_{2}}{d E_{2}} = C_{1} - C_{2} = \frac{1}{T_{1}} - \frac{1}{T_{2}}$ .

Here $C_{1}$ and $C_{2}$ are the coldnesses of the subsystems. Coldness is the inverse of temperature, and is more fundamental than temperature.

Note that Newton's law of cooling says that the rate of heat transfer is proportional to $T_{2} - T_{1}$ . For a narrow temperature range this will approximate our result.

[-]Nisan4mo20

I'd love if anyone can point me to anywhere this cooling law (proportional to the difference of coldnesses) has been written up.

Also my assumptions about the dynamical system are kinda ad hoc. I'd like to know assumptions I ought to be using.

[-]Nisan2y40

Agents who model each other can be modeled as programs with access to reflective oracles. I used to think the agents have to use the same oracle. But actually the agents can use different oracles, as long as each oracle can predict all the other oracles. This feels more realistic somehow.

[-]Dagon2y10

I'm not sure there's a functional difference between "same" and "different" oracles at this level of modeling.

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