3 ms·

can someone provide an ELI5 for this critique?

by fierro 7y ago

neel_k 7y ago
The "normal" physical systems we build (say houses and hydraulic systems) are mostly "continuous". This means small changes in the inputs generally result in small changes in the behaviour of the system. So, for example, if the screws on your kitchen cabinet doors are not tightened quite enough, the cabinet doors might wobble a little -- that is, a small change resulted in a small change. On the other hand, systems based on digital logic are very "discontinuous". A small changes in an input can result in the system behaving vastly different. A single-bit error in a computer program can result in an if-then-else switching from the true branch to the false branch, and thereby running an entirely different piece of code. So your computer is a single bit flip away from fintech entrepreneurs using your entire bank account to rent AWS time to mine Bitcoin. In general, we are drawn to discrete logic because it's easy to write programs to do different things based on different inputs. However, von Neumann was worried about this, because no machine works perfectly -- every computer runs with a certain probability of error, and computers run fast enough that even a low probability of error can compounds very quickly. And if a single small error can result in radically different results, how can you trust the result of a computer program? In this note, written in 1947, he expressed the hope that if you could make computers behave continuously, you could not worry about small errors, because they would only have a small impact on the result. However, a few years later von Neumann ALSO invented the alternative, modern way of handling these issues! In his 1956 paper _The Synthesis of Reliable Organisms from Unreliable Parts_, he proved that it was possible to use redundancy in a way to drive the error probability arbitrarily low, enough that you COULD trust the output of a computation.
- avinium 7y ago
  Great summary.

can someone provide an ELI5 for this critique?

by fierro 7y ago

can someone provide an ELI5 for this critique?

The "normal" physical systems we build (say houses and hydraulic systems) are mostly "continuous". This means small changes in the inputs generally result in small changes in the behaviour of the system. So, for example, if the screws on your kitchen cabinet doors are not tightened quite enough, the cabinet doors might wobble a little -- that is, a small change resulted in a small change. On the other hand, systems based on digital logic are very "discontinuous". A small changes in an input can result in the system behaving vastly different. A single-bit error in a computer program can result in an if-then-else switching from the true branch to the false branch, and thereby running an entirely different piece of code. So your computer is a single bit flip away from fintech entrepreneurs using your entire bank account to rent AWS time to mine Bitcoin. In general, we are drawn to discrete logic because it's easy to write programs to do different things based on different inputs. However, von Neumann was worried about this, because no machine works perfectly -- every computer runs with a certain probability of error, and computers run fast enough that even a low probability of error can compounds very quickly. And if a single small error can result in radically different results, how can you trust the result of a computer program? In this note, written in 1947, he expressed the hope that if you could make computers behave continuously, you could not worry about small errors, because they would only have a small impact on the result. However, a few years later von Neumann ALSO invented the alternative, modern way of handling these issues! In his 1956 paper _The Synthesis of Reliable Organisms from Unreliable Parts_, he proved that it was possible to use redundancy in a way to drive the error probability arbitrarily low, enough that you COULD trust the output of a computation.

avinium 7y ago
Great summary.