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bigjeff5 comments on Reductionism - Less Wrong

40 Post author: Eliezer_Yudkowsky 16 March 2008 06:26AM

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Comment author: bigjeff5 01 February 2011 08:52:27PM 2 points [-]

I think the point is that the model of four elements we use to describe the CD is also contained within the chromodynamic model - the four elements are a less accurate abstraction of the chromodynamic model, even if we don't recognize it as such when we used the more abstract model.

In the same way, Newtonian Mechanics is a less accurate abstraction of Special Relativity.

Therefore, no matter how precise Newtonian Mechanics is, it does not match up exactly with reality. Because it is an abstraction, it contains inaccuracies. The SR version of the same process will always be more accurate than the NM version, though the SR version is also probably not completely accurate.

A correct lisp would be representable on any compute substrate, from a Mac to a cranks-and-gears Babbage engine.

I don't think that is true. For Lisp to mean anything to any machine, it must first be compiled into the machine language of that particular machine. Because this process is fundamentally different for different types of machines, the way the same Lisp behaves on each machine will be highly dependent on its specific translation into machine language. In other words, the same Lisp code will result in slightly different behavior on a Mac than it would on a Linux machine. The difference may not be enough to take any note of, but it is still there.

This is the similar to calculating the trajectory of an artillery shell with Newtonian Mechanics vs Special Relativity. The difference between the two will be so small that it is almost unmeasurable, but there will definitely be a difference between them.

Comment author: [deleted] 12 January 2012 11:00:32PM 0 points [-]

In other words, the same Lisp code will result in slightly different behavior on a Mac than it would on a Linux machine. The difference may not be enough to take any note of, but it is still there.

I am going to have to disagree here. A given Lisp will require a Bounded-Tape Turing Machine of tape size N and head state count M and symbol table Q. If the ARM processor running Windows NT can supply that, Lisp is possible. If a x86 running Unix can supply that, Lisp is possible. If Lisp behaves differently from the mathematical ideal on any machine, that means the machine is incapable of supplying said turing machine.

"If the Lisp is untrue to the Specification, that is a fact about the Implementation, not the Mathematics behind it."

Comment author: DSimon 17 January 2012 04:28:24AM *  0 points [-]

What about the speed of operation? The specification does not set any requirements for this, and so two different Lisp implementations which differ in that property can both be correct yet produce different output.

Comment author: [deleted] 18 January 2012 12:12:11PM 0 points [-]

Even if it runs at one clock cycle per millenia, it would still theoretically be able to run any given program, and produce exactly the same output. The time function is also external to the LISP implementation; it is a call to the OS, so the output that is printing the current time doesn't count.

Comment author: DSimon 18 January 2012 08:21:43PM 1 point [-]

I think we may have to taboo "output", as the contention seems to be about what is included by that word.

Comment author: [deleted] 18 January 2012 08:41:42PM *  1 point [-]

Given a program P consisting of a linear bit-pattern, that is fed into virtual machine L, and produces a linear bit-pattern B to a section of non-local memory location O. During the runtime of P on L, the only interaction with non-local memory is writing B to O. There is no bits passed from non-local memory to local memory.

For all L If and only if L is true to the specification then for any P there is only one possible B.

  • P is the lisp program source code, which does not read from stdin, keyboard drivers, web sockets or any similar source of external information.
  • L is a LISP (virtual) machine.
  • B is some form of data, such as text, binary data, images, etc.
  • O is some destination could be stdout, screen, speakers, etc.
Comment author: DSimon 18 January 2012 11:07:09PM *  2 points [-]

Ah, ok, I find nothing to disagree with there. Looking back up the conversation, I see that I was responding to the word "behavior". Specifically, bigjeff5 said:

In other words, the same Lisp code will result in slightly different behavior on a Mac than it would on a Linux machine.

To which you responded:

If Lisp behaves differently from the mathematical ideal on any machine, that means the machine is incapable of supplying said turing machine.

So it comes down to: does the "behaviour" of a Lisp implementation include anything besides the output? Which effectively comes down to what question we're trying to answer about Lisp, or computation, or etc.

The original question was about whether a Lisp machine needs to include abstractions for the substrate it's running on. The most direct answer is "No, because the specification doesn't mention anything about the substrate." More generally, if a program needs introspection it can do it with quine trickery, or more realistically just use a system call.

Bigjeff5 responded by pointing out that the choice of substrate can determine whether or not the Lisp implementation is useful to anybody. This is of course correct, but this is a separate issue from whether or not the Lisp abstraction needs to include anything about its own substrate; a Lisp can be fast or slow, useful or useless, regardless of whether or not its internal abstractions include a reference to or description of the device it is running on.