5 ms·

Well, we still don't have the computational power to do things atom-by-atom, even in small things like modeling cells, let alone something like simulating wind

Well, we still don't have the computational power to do things atom-by-atom, even in small things like modeling cells, let alone something like simulating wind shear on a plane or predicting weather patterns. It's not just computational power but memory. There's something like 1E14 atoms in a cell. Storing the x,y,z position with 4 bytes for each dimension (though you'll probably want 8 bytes) comes out to 1.2E15 bytes = 1.2 petabytes of information. Add in more fields for velocity and other pieces of state and you're talking about something that would only fit in working memory in some of our largest machines.

tw1010 9y ago
Sure, but you'd think we would shift our focus to using models explicitly tailored with that aim in mind. Using something that explicitly approximates a desired, precise, foundation. Perhaps parameterized by model accuracy. I would think taking inspiration from approximation algorithms would be a much more appropriate lens with which to model physics.
- auntienomen 9y ago
  In the case of Navier-Stokes, this was done in 1934 by Jean Leray, who showed that the so-called 'weak' solutions always exist. (A weak solution is not a function, but a more general object called a distribution which can be fuzzed out on very short distance scales.) It's a very reasonable idea, and useful enough for computations, but it lacks the essential tension that makes Navier-Stokes a mathematical Everest.
- btilly 9y ago
  The mental model of a bunch of hard little atoms flying around, colliding, rebounding, etc is actually NOT the desired, precise, foundation for understanding how gases behave. The better foundation is quantum mechanics. An example of a macroscopically visible difference between these foundations are the van der Waals forces.
Retric 9y ago
Here is a billion particle model (e9) which is a long way from atomic scale simulation (e14+), but not outside the realm of the possible. https://www.youtube.com/watch?v=B8mP9E75D08 https://www.youtube.com/watch?v=B8mP9E75D08
- openasocket 9y ago
  We are definitely making progress. But another factor to consider, in additional to the number of particles, is the energy of the system. When going through one step of a simulation you have to compute the effects that every particle has on every other particle, but generally a particle only affects the other particles near it. You can take advantage of this fact to speed up computation with the right data structures. However, as particles start moving around faster and faster, the distance they can travel in one time step increases, and the neighborhood of effect increases, limiting the speedup of this optimization. This matters less in larger scale simulations like of weather patterns, because you don't have to worry about air molecules zipping to the other side of the continent in one second. But it matters a lot in small scale simulations, especially in cells. As an example, an average glucose molecule in one of your cells is bouncing around at around 250 miles per hour! That's not 250 miles when scaled up, that's really 250 miles per hour. A molecule in your body is colliding with another billions of times every second. (Source: http://www.righto.com/2011/07/cells-are-very-fast-and-crowded-places.html http://www.righto.com/2011/07/cells-are-very-fast-and-crowde...). At that scale and that level of activity it becomes much harder to simulate each time step.
  - Retric 9y ago
    The other side of this is cells are also really fast. Modeling even 0.01 seconds could be very useful.
    - SAI_Peregrinus 9y ago
      Much of the action inside cells is done via proteins. It's taken a huge amount of distributed computing power just to figure out a reasonable hypothesis for how they fold (only one part of the movement) and €1.22 billion to build the XFEL and have a way to image them on the required timescales: 1-2 femtoseconds. 0.000000000000001 seconds. 0.01 seconds is an eternity, calculating that long would take an utterly enormous amount of computer time.
electricslpnsld 9y ago
> Well, we still don't have the computational power to do things atom-by-atom People do atom-by-atom molecular dynamics simulations of proteins and such.
- openasocket 9y ago
  Certainly, but not at the level of an entire cell
- effie 9y ago
  Yes, but those are simulations of classical mechanics models of molecules which are known to be very limited when it comes to atom-scale objects. We have another model that was much more useful there (Schroedinger's equation) but it is only computationally tractable for systems of few atoms. We do not have the computational power to work out the consequences of the model for proteins.
ctdonath 9y ago
we still don't have the computational power to do things atom-by-atom That's what puzzles me about this discussion. Of course we don't. The goal here is to model more atoms than we have atoms to model with. Until we get to quantum computers that can represent more information per atom, than information per atom we want to represent, it's simply a matter of objectively & obviously inadequate resources. You can't simulate wind shear on a plane when there's more atoms in that wind & plane than there are in the computer simulating them: every single atom being simulated contains the complete information about its state (information independent of any other atom), so simulating it will require at least one atom per atom simulated - if you don't have at least as many atoms to simulate as you are simulating, you can't achieve a complete simulation.
- evandijk70 9y ago
  It is not necessarily the goal to model more atoms than we have atoms to model with. The goal can be, for example, to model a folding protein, which has fewer atoms than a CPU.
  - njarboe 9y ago
    And one might be happy to spend a month computing the folding while in the cell it takes a few seconds.
- pcvarmint 9y ago
  That may be true of digital computers, but it's not necessarily true of analog ones.
RhysU 9y ago
> Well, we still don't have the computational power to do things atom-by-atom... We still don't have the computational power to do certain classes of continuous Navier--Stokes calculations (i.e. not atom based).

tw1010 9y ago

Sure, but you'd think we would shift our focus to using models explicitly tailored with that aim in mind. Using something that explicitly approximates a desired, precise, foundation. Perhaps parameterized by model accuracy. I would think taking inspiration from approximation algorithms would be a much more appropriate lens with which to model physics.

auntienomen 9y ago
In the case of Navier-Stokes, this was done in 1934 by Jean Leray, who showed that the so-called 'weak' solutions always exist. (A weak solution is not a function, but a more general object called a distribution which can be fuzzed out on very short distance scales.) It's a very reasonable idea, and useful enough for computations, but it lacks the essential tension that makes Navier-Stokes a mathematical Everest.
btilly 9y ago
The mental model of a bunch of hard little atoms flying around, colliding, rebounding, etc is actually NOT the desired, precise, foundation for understanding how gases behave. The better foundation is quantum mechanics. An example of a macroscopically visible difference between these foundations are the van der Waals forces.

Retric 9y ago

Here is a billion particle model (e9) which is a long way from atomic scale simulation (e14+), but not outside the realm of the possible. https://www.youtube.com/watch?v=B8mP9E75D08 https://www.youtube.com/watch?v=B8mP9E75D08

openasocket 9y ago
We are definitely making progress. But another factor to consider, in additional to the number of particles, is the energy of the system. When going through one step of a simulation you have to compute the effects that every particle has on every other particle, but generally a particle only affects the other particles near it. You can take advantage of this fact to speed up computation with the right data structures. However, as particles start moving around faster and faster, the distance they can travel in one time step increases, and the neighborhood of effect increases, limiting the speedup of this optimization. This matters less in larger scale simulations like of weather patterns, because you don't have to worry about air molecules zipping to the other side of the continent in one second. But it matters a lot in small scale simulations, especially in cells. As an example, an average glucose molecule in one of your cells is bouncing around at around 250 miles per hour! That's not 250 miles when scaled up, that's really 250 miles per hour. A molecule in your body is colliding with another billions of times every second. (Source: http://www.righto.com/2011/07/cells-are-very-fast-and-crowded-places.html http://www.righto.com/2011/07/cells-are-very-fast-and-crowde...). At that scale and that level of activity it becomes much harder to simulate each time step.
- Retric 9y ago
  The other side of this is cells are also really fast. Modeling even 0.01 seconds could be very useful.
  - SAI_Peregrinus 9y ago
    Much of the action inside cells is done via proteins. It's taken a huge amount of distributed computing power just to figure out a reasonable hypothesis for how they fold (only one part of the movement) and €1.22 billion to build the XFEL and have a way to image them on the required timescales: 1-2 femtoseconds. 0.000000000000001 seconds. 0.01 seconds is an eternity, calculating that long would take an utterly enormous amount of computer time.

electricslpnsld 9y ago

> Well, we still don't have the computational power to do things atom-by-atom People do atom-by-atom molecular dynamics simulations of proteins and such.

openasocket 9y ago
Certainly, but not at the level of an entire cell
effie 9y ago
Yes, but those are simulations of classical mechanics models of molecules which are known to be very limited when it comes to atom-scale objects. We have another model that was much more useful there (Schroedinger's equation) but it is only computationally tractable for systems of few atoms. We do not have the computational power to work out the consequences of the model for proteins.

ctdonath 9y ago

we still don't have the computational power to do things atom-by-atom That's what puzzles me about this discussion. Of course we don't. The goal here is to model more atoms than we have atoms to model with. Until we get to quantum computers that can represent more information per atom, than information per atom we want to represent, it's simply a matter of objectively & obviously inadequate resources. You can't simulate wind shear on a plane when there's more atoms in that wind & plane than there are in the computer simulating them: every single atom being simulated contains the complete information about its state (information independent of any other atom), so simulating it will require at least one atom per atom simulated - if you don't have at least as many atoms to simulate as you are simulating, you can't achieve a complete simulation.

evandijk70 9y ago
It is not necessarily the goal to model more atoms than we have atoms to model with. The goal can be, for example, to model a folding protein, which has fewer atoms than a CPU.
- njarboe 9y ago
  And one might be happy to spend a month computing the folding while in the cell it takes a few seconds.
pcvarmint 9y ago
That may be true of digital computers, but it's not necessarily true of analog ones.

RhysU 9y ago

> Well, we still don't have the computational power to do things atom-by-atom... We still don't have the computational power to do certain classes of continuous Navier--Stokes calculations (i.e. not atom based).