You can blur the boundary between them. The underlying mathematical reason is that the real unit interval (analogue) is homeomorphic to the Cantor space 2^omega (digital). Which is to say, a real number is essentially the same thing as an infinite bitstream
-
-
Replying to @_julesh_ @oliverbeige
I don't see how that's the underlying reason... I don't think there is a reason, computation deals with numbers that are computable doesn't it, not the unit interval. and I don't think that's really what
@NegarestaniReza is referring to--although I don't know what is1 reply 0 retweets 1 like -
One of the main research directions is models of computation extended with (true) real numbers - motivated exactly because it might be a better model of real life computing than Turing machines are
1 reply 0 retweets 2 likes -
I didn't know that, very interesting!
1 reply 0 retweets 3 likes -
Neural networks are probably the most obvious example. You can (and must) discretise them to run them on a CPU, but that's just an implementation detail - they're ""really"" analogue computation. An implementation as analogue circuits would be impractical, but more "faithful"
3 replies 0 retweets 6 likes -
Replying to @_julesh_ @jancorazza and
I remember this blog post on "Why are eight bits enough for deep neural networks?" (https://petewarden.com/2015/05/23/why-are-eight-bits-enough-for-deep-neural-networks/ …), and more recent this "Ultra-low precision training" https://www.ibm.com/blogs/research/2019/05/ultra-low-precision-training/ … which seem to say that neural nets really are digital computation.
2 replies 0 retweets 3 likes -
Replying to @AlexisToumi @_julesh_ and
Neurons aren't digital. Annealing isn't digital. Radar isn't digital. We need to be careful not to get the simulation confused with the original. That was the key insight of 1986.
1 reply 0 retweets 0 likes -
Replying to @oliverbeige @AlexisToumi and
You seem to use the word digital in a simplistic way like how artists use it. The digital is a logic, numeric-based system with terminating computational functions. All such machines if you call them computers should be isomorphic to the logic of a regular-rule-bound system.
2 replies 0 retweets 2 likes -
Replying to @NegarestaniReza @AlexisToumi and
In case you haven't noticed, this is the boundary I have navigated for a good forty years, so nothing I do here is "simplistic". If you don't stop your attempts at splaining and actually try to offer a counter position, you go on the block.
1 reply 0 retweets 0 likes -
Replying to @oliverbeige @AlexisToumi and
No it was you who was splaining and here is an instance, 'I have worked on this front for 40 years.' Yes good I also wrote my dissertation on these issues 20+ years ago. . Either we begin to look at the fundamental problems calmly or it would be just talking past each other.
2 replies 0 retweets 0 likes
Let's read this together and start from a specific set of questions. The reason I'm suggesting this text is because Ladyman is no bullshiter:https://tinyurl.com/rnwxrf2
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.