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0 pointsConst-me9y ago0 comments

> one of those is what actually happens

No it’s not. If the heads aren’t moving in lockstep, what actually happens is you’ll extremely rarely have a moment of time when both locations are whole numbers.

At one moment you have { head1loc=0, head2loc=4.17 }, head #1 reached the cell position on the tape, head #2 is still moving. After a while, you’ll have { head1loc=0.872, head2loc=5}, head #1 is on its way, head #2 reached the cell position.

Looks like for a Turing machine with two asynchronously moving heads, there’s no usable concept of “state” at all. That’s very close to what happens when doing actual parallel programming on real hardware.

Good luck applying your idea of computation as a sequence of state transitions to that.

0 comments

arielb19y ago

Pick a reference frame. Sample the state of each CPU on its clock edge. Now you have a sequence of transitions.

The sequence is heavily non-deterministic, but that's life in a concurrent universe.

Const-meOP9y ago

A non-deterministic sequence ain’t a sequence.

The thing is called “partially ordered set”: https://en.wikipedia.org/wiki/Partially_ordered_set

argv_empty9y ago

I'm not sure it's useful to try to discuss concurrency with someone who refuses to believe that a group of machines can be in a state (which is really the point of the article).

argv_empty9y ago

Even if a Turing machine were a physical object (I had thought you would be aware that it's not), either one of those moves completes before the other, or both complete simultaneously.

Const-meOP9y ago

Sure, it’s an abstract machine invented to research mathematical model of computation.

I’d like to point out, the very moment you hooked second asynchronously moving head to the machine, the abstraction leaked spectacularly. With two asynchronous heads, the machine no longer has state; suddenly we need to consider physical time, not just count steps; and so on.

Turing machine is useful abstraction for sequential computing, but nearly useless to research parallel computing problems. The same happens with many other abstractions and approaches when going parallel.

> either one of those moves completes before the other

Yeah, but in parallel computing, we don’t know that order, and have no way of knowing. Meaning the “sequence of state transitions” idea is IMO nearly useless.

dogecoinbase9y ago

if a Turing machine were a physical object ... either one of those moves completes before the other, or both complete simultaneously.

...depending on how fast you're moving relative to the machine heads and in what direction. Simultaneity does not exist in the real world.

argv_empty9y ago

We use the tape's reference frame, of course! Looking at data stored on some particular device in the physical system is going to force a particular reference frame, where you will have a defined simultaneity. A global definition of simultaneity is only really needed if your system promises to provide sequential consistency.

j / k navigate · click thread line to collapse

0 pointsConst-me9y ago0 comments

> one of those is what actually happens

No it’s not. If the heads aren’t moving in lockstep, what actually happens is you’ll extremely rarely have a moment of time when both locations are whole numbers.

Good luck applying your idea of computation as a sequence of state transitions to that.

0 comments

arielb19y ago

Pick a reference frame. Sample the state of each CPU on its clock edge. Now you have a sequence of transitions.

The sequence is heavily non-deterministic, but that's life in a concurrent universe.

Const-meOP9y ago

A non-deterministic sequence ain’t a sequence.

The thing is called “partially ordered set”: https://en.wikipedia.org/wiki/Partially_ordered_set

argv_empty9y ago

I'm not sure it's useful to try to discuss concurrency with someone who refuses to believe that a group of machines can be in a state (which is really the point of the article).

argv_empty9y ago

Even if a Turing machine were a physical object (I had thought you would be aware that it's not), either one of those moves completes before the other, or both complete simultaneously.

Const-meOP9y ago

Sure, it’s an abstract machine invented to research mathematical model of computation.

> either one of those moves completes before the other

Yeah, but in parallel computing, we don’t know that order, and have no way of knowing. Meaning the “sequence of state transitions” idea is IMO nearly useless.

dogecoinbase9y ago

if a Turing machine were a physical object ... either one of those moves completes before the other, or both complete simultaneously.

...depending on how fast you're moving relative to the machine heads and in what direction. Simultaneity does not exist in the real world.

argv_empty9y ago

j / k navigate · click thread line to collapse