4 ms·

The thing about conversion from analog to binary is that it's a one-time-cost only. With analog computation, you pay for every single computation/conversion ste

The thing about conversion from analog to binary is that it's a one-time-cost only. With analog computation, you pay for every single computation/conversion step with increased noise, even if each operation theoretically provides more precision than the binary equivalent. There's just no equivalent to the noise-resiliency of binary compute.

jhayward 8y ago
On the contrary, every single digital floating point operation has the inherent capacity to add noise. To make things worse, the noise depends very much on order of operations, relative magnitudes of operands, and other algorithmic aspects of what is usual an estimation method for solving equations. Estimating accumulated error in floating-point calculations is an extremely difficult science. On the other hand, a simple circuit that solves an ODE in an analog computer can be analyzed rather easily.
- jonfw 8y ago
  So don't use floating points? You can use arbitrary precision math libraries. If you devote enough memory, you can be much more precise with continuous values than an analog computer could ever hope to be. Frankly it wouldn't take much memory at all by modern standards though.
  - jhayward 8y ago
    Arbitrary precision doesn't help with irrational numbers. You may be thinking of the "just use enough bits so you're sure the accumulated error isn't significant" approach, which is essentially what modern floating-point attempts to do. There are still some pitfalls though, around doing an analysis that proves the bounds of said error in a given algorithm and data set. You might be interested in the concepts used in interval arithmetic [1] and specifically the work of Gustafson in designing some models for using those in scientific computing hardware. [1] https://en.wikipedia.org/wiki/Interval_arithmetic https://en.wikipedia.org/wiki/Interval_arithmetic

jhayward 8y ago

On the contrary, every single digital floating point operation has the inherent capacity to add noise. To make things worse, the noise depends very much on order of operations, relative magnitudes of operands, and other algorithmic aspects of what is usual an estimation method for solving equations. Estimating accumulated error in floating-point calculations is an extremely difficult science. On the other hand, a simple circuit that solves an ODE in an analog computer can be analyzed rather easily.

jonfw 8y ago
So don't use floating points? You can use arbitrary precision math libraries. If you devote enough memory, you can be much more precise with continuous values than an analog computer could ever hope to be. Frankly it wouldn't take much memory at all by modern standards though.
- jhayward 8y ago
  Arbitrary precision doesn't help with irrational numbers. You may be thinking of the "just use enough bits so you're sure the accumulated error isn't significant" approach, which is essentially what modern floating-point attempts to do. There are still some pitfalls though, around doing an analysis that proves the bounds of said error in a given algorithm and data set. You might be interested in the concepts used in interval arithmetic [1] and specifically the work of Gustafson in designing some models for using those in scientific computing hardware. [1] https://en.wikipedia.org/wiki/Interval_arithmetic https://en.wikipedia.org/wiki/Interval_arithmetic