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        riddles >> easy >> Living Machines "Paradox"
        
(Message started by: william wu on Nov 15^th, 2003, 12:56pm)

Title: Living Machines "Paradox"
Post by william wu on Nov 15^th, 2003, 12:56pm

1. Living things are machines.
2. Living things can reproduce.
3. Machines cannot reproduce.

Each of these statements is justified for reasons given in the next paragraph. However, when these statements are considered together, we get a paradox. How can this be? Explain what is wrong.

Justifications of Statements

1. This is a tenet of modern biology. We believe organisms operate in a mechanistic way.

2. The ability to self-reproduce is one of the essential criteria for being a living thing.

3. For this statement, consider the following argument that machines cannot self-reproduce. Consider a machine that constructs ther machines, such as an automated factory that produces cars. Raw materials go in at one end, the manufacturing robots follow a set of instructions, and then completed vehicles come out the other end. We claim the factory must be more complex than the cars produced, in the sense that designing the factory would be more difficult than designing a car. This claim must be true because the factory itself has the car's design within it, in addition to the design of all the manufacturing robots. The same reasoning applies to any machine A that constructs a machine B: A must be more complex than B. But a machine cannot be more complex than itself. Consequently, no machine can construct itself, and thus self-reproduction is impossible.

- Source: Introduction to the Theory of Computation, by Michael Sipser.

Title: Re: Living Machines Paradox
Post by TimMann on Nov 15^th, 2003, 1:36pm

3 is just a lot of handwaving, and is wrong for any number of reasons.

Title: Re: Living Machines Paradox
Post by Icarus on Nov 15^th, 2003, 3:13pm

I agree. I would say the 3 sounds reasonable until you examine it closely, but quite frankly, this is not true. Statement 3 did not sound reasonable to me even on a first reading.

While not exactly easy, it seems to me that it would be a straight-forward task to build a robot which when given the appropriate raw materials would create an identical robot. The final step would be to download the controlling program - including the design information. The problem only becomes complicated when you must also have the robot go out and obtain the raw materials itself. However, this is a problem only in the complexity of the given task - not a fundamental limitation.

Title: Re: Living Machines "Paradox"
Post by Eigenray on Nov 16^th, 2003, 3:54am

The simplest resolution to this paradox is to just accept the fact that there are no living things. And you can't prove me wrong, because you don't exist. Further, I can't be proven wrong because I don't exist.

But the argument in (3) could be used to "prove" that quines (http://www.nyx.net/~gthompso/quine.htm) are impossible: the source code must be more complex than its output, after all. And yet, far from being impossible, quines must exist in any Turing complete language!

Title: Re: Living Machines "Paradox"
Post by towr on Nov 16^th, 2003, 7:59am

Obviously 3 is wrong.. Here's yet another reason.
Even if one machine could not reproduce itself, many machines together may still reproduce..
That's exactly how we get ever increasingly complex machines. Other machines each design/build parts and put it together to form more complex ones..
Note also that many living beings (though a minority) can also not reproduce singularly, for them (including us) it takes two. And two is more complex than one.

[e]NB, looking a bit closer at the first post there's another problem. A jump is made from reproduction in the first three statements to self-reproduction in 'justifications' 2 and 3.
Many organisms can't self-reproduce (i.e. as a singular individual without any 'assistance' from another individual of unspecified species.). We humans still can't, though maybe in the future..[/e]

Title: Re: Living Machines "Paradox"
Post by Dudidu on Nov 16^th, 2003, 11:57pm

Another reasoning that the 3^rd statment is wrong is simply recursion... (think about it).
A a nice example of this idea from CS studies is computer viruses... (think about this to) :o

Title: Re: Living Machines "Paradox"
Post by towr on Nov 17^th, 2003, 12:35am

A computer virus isn't really a machine though, and it needs a machine (an active computer) to copy itself..
Just like biological virusses can't copy themselves without a living host. And normal virusses are generally not considered living either.

Title: Re: Living Machines "Paradox"
Post by Speaker on Nov 17^th, 2003, 1:03am

What struck me as wrong with item three is that is tries to eliminate the machines because the building machine has greater complexity than the offspring machine.

That doesn't seem to be a limiting factor. As long as the offspring machines can eventually grow in complexity until they reach a stage where they can reproduce. But, I wonder if that is a prerequisite of life. Aren't there some living things that are born from a complex system, but do not attain a level of complexity high enough to reproduce.

How about bees. Anyone would say that a drone bee is a form of life, but it cannot reproduce. Therefore if you had a large factory that could produce many less complex robots that would be a form of life similar to bees. The robots could then wander off and build another queen bee factory and start over again. They would all carry they machine equivalent of DNA: Memory. That way every robot would have the potential to reproduce.

Finally, I was reading it and kept thinking of infants. They are not sufficiently complex to survive and reproduce. Infants require all sorts of auxiliary stuff.

Title: Re: Living Machines "Paradox"
Post by James Fingas on Nov 17^th, 2003, 11:02am

Guys, all this discussion misses the point. The problem with this question is that we change the definition of "machines" half-way through.

If we consider "machines" to refer to human-engineered machines at the current state of the art, then statement 1 is just a metaphor (and thus is not strictly true).

If we consider "machines" to refer to living things plus human-engineered machines, then statement 3 is false.

Besides, statement 2 is false, if you want to get nitpicky...

Title: Re: Living Machines "Paradox"
Post by towr on Nov 17^th, 2003, 1:06pm

I don't think it's necessary to assume the notion of machines used changes halfway through.
Statement 3 is false either way..

Title: Re: Living Machines "Paradox"
Post by Lightboxes on Nov 18^th, 2003, 6:07pm

This paradox reminds me of a false statement (proof) I made up.
NOTE: Ignore if a soul may exist or not to simplify the argument.
You are you.
You are made up of 50% from the environment and 50% from genetic material, so therefore you are not really you but made up of other things.

But the problem lies in the definition of you, as it changes from the first to the last.
Anyway, what's wrong with this statement:

Not all poor people
commit crimes.
Not all crimes are committed
by poor people.
Therefore, poverty doesn't cause crime.

Title: Re: Living Machines "Paradox"
Post by rmsgrey on Nov 22^nd, 2003, 8:25pm

"This statement is more complicated than itself" seems to follow from the same argument as 3...

Depending upon how you define or measure complexity, it may well be true that any process must be at least as complex as its output, but that doesn't mean it must be strictly more complex. And the question of how you measure complexity is one without an easy answer - which is more complex "50 Ls" or "LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL"? Both express exactly the same concept, but one requires much less space to do so (though I suspect an appropriate compression algorithm would store each of them in exactly the same amount of space).

As to "poverty doesn't cause crime", it is, for a sufficiently pedantic interpretation, true. "Poverty and other factors, in conjunction, cause crime" is true. Poverty, in isolation, is neither necessary nor sufficient for crime. Strictly, "X causes Y" only applies if X is a sufficient precondition for Y (and not always then - for instance, if Z causes both X and Y, but always causes X first), so "not all crimes are committed by poor people" is a non sequitur anyway - only if the claim were "Poverty is the sole cause of crime" would the existence of rich criminals be relevant.