Viewing a single comment thread. View all comments

space_troubadour t1_j8dav3e wrote

Isn’t that just what exponentials do…

171

sprucenoose t1_j8dzbqs wrote

He just paraphrased the long-established definition of the singularity, but made it confusing and wrong.

59

jamesj t1_j8f8w5x wrote

What did he get wrong? He's saying the rate of exponential change is increasing, which I think is true. Like, the doubling rate is getting shorter with time.

10

sprucenoose t1_j8jfprm wrote

>What did he get wrong? He's saying the rate of exponential change is increasing, which I think is true. Like, the doubling rate is getting shorter with time.

Even doubling, meaning a relatively small exponent of 2, quickly results in a graph with an effectively vertical rate of change and increasingly astronomical numbers. A higher exponent, like 10 or 1,000,000 or whatever, results in the same vertical line even more quickly, and an even higher exponent becomes vertical even more quickly, ad infinitum.

That is what exponential equations do - increasingly graph to vertical, ever more sharply with ever higher exponents. Even an exponent to the power of an exponent multiplies the powers together to provide a higher exponent. A "compounding" exponential equation can only do the same thing - increasingly graph vertical. It's not helpful.

0

Biuku t1_j8g2auk wrote

He described the curve from inside it. Like the Milky Way.

3

fool_on_a_hill t1_j8havtu wrote

I can't stand how he's trying to claim this as an original thought that his sweet lil brain came up with all on it's own! Thanks Jack, yeah buddy we're gonna put it right here on the fridge!

3

just_thisGuy t1_j8edpr1 wrote

No, there are degrees of exponential https://en.m.wikipedia.org/wiki/Degree_of_a_polynomial and if you start with one does not mean you are always using the same degree. The point he is making is the degree is increasing.

25

CellWithoutCulture t1_j8fgbpg wrote

I think he mean it's now super-exponential. It's rising faster than an exponential curve.

4

fairly_low t1_j8e1v2y wrote

I think what he is trying to phrase is the Ackermann function. (Up-arrow etc)

2

SoylentRox t1_j8e8c8p wrote

Can you go into more detail?

In this case, there is more than 1 input that causes acceleration.

Set 1:

(1) more compute
(2) more investor money
(3) more people working on it

Set 2:

(A) existing AI making better designs of compute

(B) existing AI making money directly (see chatGPT premium)

(C) existing AI substituting for people by being usable to write code and research AI

​

Set 1 existed in the 2010-2020 era. AI wasn't good enough to really contribute to set 2, and is only now becoming good enough.

So you have 2 separate sets of effects leading to an exponential amount of progress. How do you represent this mathematically? This looks like you need several functions.

7

human_alias t1_j8gfcbk wrote

No, the exponential distribution is memoryless meaning it should look exponential in every frame

1