15 ms·

Exponential curves look really boring, until they aren't.

by adamsmith143 4y ago

mdorazio 4y ago
Can you show us this exponential curve?
- Eddy_Viscosity2 4y ago
  https://en.wikipedia.org/wiki/Exponential_growth https://en.wikipedia.org/wiki/Exponential_growth
  - dekhn 4y ago
    that's just a sigmoid where you haven't reached the upper asymptote yet
    - polynomial 4y ago
      All exponential growth is periodic?
    - adamsmith143 4y ago
      Do people really think quantum computing improvement is already on the asymptote of a sigmoid?
      - pclmulqdq 4y ago
        No, but a lot of us think it's on the exponential-looking part of a sigmoid that will hit its asymptote lower than other people think. At least this quantum computing technology is.
      - dekhn 4y ago
        Well, much of the current field is about increasing the number of high fidelity q-bits. With the idea being that interesting problems will finally occur (IE, a slam-dunk, yes that was useful to know, sort of result that couldn't possibly be done with classical computers) when some qbit threshold is achieved.
- adamsmith143 4y ago
  https://s3.amazonaws.com/cbi-research-portal-uploads/2019/01/14180930/quantum-computing-qubit-timeline.png https://s3.amazonaws.com/cbi-research-portal-uploads/2019/01...
pclmulqdq 4y ago
Every growth function looks exponential until it's not. Most things in science and technology aren't exponential, though. Computers have been (through force of will by many physicists and engineers), and if we think they are the model for everything, I give you the airplane and the car as counterexamples. As far as quantum computing goes, IBM and Google were promising us exponential growth in quantum chip size, but what we have actually seen so far is exponentially faster decoherence that comes with size.
- marcosdumay 4y ago
  > Every growth function looks exponential until it's not. What is this about? Discovering the shape of a curve near the origin is one of the oldest and most mature estimation techniques people have. It has been done for centuries, and it's pretty trivial to differentiate exponential curves from other common shapes. Anyway, IBM and Google have been delivering exponential growth in quantum chip size with faster (but really doesn't look exponential) decoherence each time. Any promises are irrelevant.
  - pclmulqdq 4y ago
    Are you sure you aren't looking at the bottom of an S curve? Extrapolation is a dangerous thing to engage in, particularly from the nascent forms of a technology. Many technologies hit walls early on in their lives and are discovered to be infeasible or not useful. Also, differentiating an exponential from even a low-order polynomial is not trivial at all given only a few points (we have <10) and a lot of noise. However, the trajectory of each is markedly different when you extrapolate.
    - marcosdumay 4y ago
      Of course it's the bottom of an S curve. Anybody that talks about exponential growth on the real world is talking about the bottom of an S curve. What is your point? That the curve will inflect soon? Also, about the "differentiating an exponential from even a low-order polynomial is not trivial at all given only a few points" part. Well, if you want to propose that the curve is a low-order superlinear polynomial, the onus is on you to propose a mechanism or show some analysis. That's not a very ordinary way for things to behave on practice.

Exponential curves look really boring, until they aren't.

mdorazio 4y ago

Can you show us this exponential curve?

Eddy_Viscosity2 4y ago
https://en.wikipedia.org/wiki/Exponential_growth https://en.wikipedia.org/wiki/Exponential_growth
- dekhn 4y ago
  that's just a sigmoid where you haven't reached the upper asymptote yet
  - polynomial 4y ago
    All exponential growth is periodic?
  - adamsmith143 4y ago
    Do people really think quantum computing improvement is already on the asymptote of a sigmoid?
    - pclmulqdq 4y ago
      No, but a lot of us think it's on the exponential-looking part of a sigmoid that will hit its asymptote lower than other people think. At least this quantum computing technology is.
    - dekhn 4y ago
      Well, much of the current field is about increasing the number of high fidelity q-bits. With the idea being that interesting problems will finally occur (IE, a slam-dunk, yes that was useful to know, sort of result that couldn't possibly be done with classical computers) when some qbit threshold is achieved.
adamsmith143 4y ago
https://s3.amazonaws.com/cbi-research-portal-uploads/2019/01/14180930/quantum-computing-qubit-timeline.png https://s3.amazonaws.com/cbi-research-portal-uploads/2019/01...

pclmulqdq 4y ago

Every growth function looks exponential until it's not. Most things in science and technology aren't exponential, though. Computers have been (through force of will by many physicists and engineers), and if we think they are the model for everything, I give you the airplane and the car as counterexamples. As far as quantum computing goes, IBM and Google were promising us exponential growth in quantum chip size, but what we have actually seen so far is exponentially faster decoherence that comes with size.

marcosdumay 4y ago
> Every growth function looks exponential until it's not. What is this about? Discovering the shape of a curve near the origin is one of the oldest and most mature estimation techniques people have. It has been done for centuries, and it's pretty trivial to differentiate exponential curves from other common shapes. Anyway, IBM and Google have been delivering exponential growth in quantum chip size with faster (but really doesn't look exponential) decoherence each time. Any promises are irrelevant.
- pclmulqdq 4y ago
  Are you sure you aren't looking at the bottom of an S curve? Extrapolation is a dangerous thing to engage in, particularly from the nascent forms of a technology. Many technologies hit walls early on in their lives and are discovered to be infeasible or not useful. Also, differentiating an exponential from even a low-order polynomial is not trivial at all given only a few points (we have <10) and a lot of noise. However, the trajectory of each is markedly different when you extrapolate.
  - marcosdumay 4y ago
    Of course it's the bottom of an S curve. Anybody that talks about exponential growth on the real world is talking about the bottom of an S curve. What is your point? That the curve will inflect soon? Also, about the "differentiating an exponential from even a low-order polynomial is not trivial at all given only a few points" part. Well, if you want to propose that the curve is a low-order superlinear polynomial, the onus is on you to propose a mechanism or show some analysis. That's not a very ordinary way for things to behave on practice.