3 ms·

This is also a good intuition for why Brownian motion (frequently used to model stock prices) does not have a derivative! If you imagine zooming in on a stock p

This is also a good intuition for why Brownian motion (frequently used to model stock prices) does not have a derivative! If you imagine zooming in on a stock price, with each successive zoom closer it remains self similar, looking perpetually like a noisy stock chart. One of the basic assumptions of derivatives is that as we zoom in on a smooth curve the more that curve resembles a straight line. This doesn't hold true for fractal structures like the coast of Britain and stock prices.

nordsieck 6y ago
> If you imagine zooming in on a stock price, with each successive zoom closer it remains self similar, looking perpetually like a noisy stock chart. Unless some exchange has allowed traders to infinitely divide currency, that's doesn't seem like it could be true.
- baron_harkonnen 6y ago
  Likewise you could argue that the coastline problem is limited to at most the Planck length. Most models of stock movement are modeled mathematically with Brownian motion which is by definition a continuous time process. You can even more trivially show that stocks are non-differentiable if you want to argue that they are fundamentally discrete time processes, in which, by definition, they are not continuous, differentiable functions. But the argument of about "what does continuous even mean when we talk about physical systems" is another and older argument altogether.
  - pdonis 6y ago
    > you could argue that the coastline problem is limited to at most the Planck length Only if the Planck length were really a minimum possible length. But it might not be; even in a theory of quantum gravity, it might not be, since what is quantized in quantum gravity does not have to be lengths and times.
manfredo 6y ago
Stock prices have discrete changes, though, in the form of individual transactions. Zoom in far enough that your graph is entirely occupied by the time between two transactions and you have a straight line.
- jlawson 6y ago
  But you don't really have a straight line. You have an instantaneous step change. Of course, when you're zoomed in that much the concept of 'price' becomes a lot more complex. You need to distinguish between bid, ask, and last transaction price. So the whole mental model kind of falls apart.
- littlestymaar 6y ago
  But it's modeled as a continuous function of time, because then you can use calculus on it. We do the same all the time in physics too: since quantum mechanics became a thing, we know that at a microscopic level, many things are discrete and not continuous (energy levels for instance), yet macroscopic physics use continues function to model it, because we have powerful tool we can use on them (and derivation is one of those).
andbberger 6y ago
edit: removed dumb false statement. had misconception that brownian motion couldn't be non-differentiable because that's non-physical.
- littlestymaar 6y ago
  It's funny because even the Wikipedia links you posted explicitly mention Brownian motion modeling as the first practical use of such curve…
  - andbberger 6y ago
    ok rip me i'm dumb

nordsieck 6y ago

> If you imagine zooming in on a stock price, with each successive zoom closer it remains self similar, looking perpetually like a noisy stock chart. Unless some exchange has allowed traders to infinitely divide currency, that's doesn't seem like it could be true.

baron_harkonnen 6y ago
Likewise you could argue that the coastline problem is limited to at most the Planck length. Most models of stock movement are modeled mathematically with Brownian motion which is by definition a continuous time process. You can even more trivially show that stocks are non-differentiable if you want to argue that they are fundamentally discrete time processes, in which, by definition, they are not continuous, differentiable functions. But the argument of about "what does continuous even mean when we talk about physical systems" is another and older argument altogether.
- pdonis 6y ago
  > you could argue that the coastline problem is limited to at most the Planck length Only if the Planck length were really a minimum possible length. But it might not be; even in a theory of quantum gravity, it might not be, since what is quantized in quantum gravity does not have to be lengths and times.

manfredo 6y ago

Stock prices have discrete changes, though, in the form of individual transactions. Zoom in far enough that your graph is entirely occupied by the time between two transactions and you have a straight line.

jlawson 6y ago
But you don't really have a straight line. You have an instantaneous step change. Of course, when you're zoomed in that much the concept of 'price' becomes a lot more complex. You need to distinguish between bid, ask, and last transaction price. So the whole mental model kind of falls apart.
littlestymaar 6y ago
But it's modeled as a continuous function of time, because then you can use calculus on it. We do the same all the time in physics too: since quantum mechanics became a thing, we know that at a microscopic level, many things are discrete and not continuous (energy levels for instance), yet macroscopic physics use continues function to model it, because we have powerful tool we can use on them (and derivation is one of those).

andbberger 6y ago

edit: removed dumb false statement. had misconception that brownian motion couldn't be non-differentiable because that's non-physical.

littlestymaar 6y ago
It's funny because even the Wikipedia links you posted explicitly mention Brownian motion modeling as the first practical use of such curve…
- andbberger 6y ago
  ok rip me i'm dumb