The paradox of self-replicating machines - An OcUK theorem

[rubberduck]

Had a few beers and was pondering...

I think self replicating machines of any significant complexity must be paradoxical which disproves the whole von neumann probes theory of why the universe should be teaming with life... the great silence.... kardashev scales etc. you name it, it is gone!

Lets break it down... If we can define the complexity of a machine by its abilites such as the following list (for example). Obviously the more features the greater the complexity sum if you will.

Propulsion and navigation
Sensing/resoruce hunting
Descision making
Material and Energy Extraction

(to name but a few)

Lets say we add all of these together and gain a combined complexity of U+V+W+X=Z.... But now we have to incorporate the self replicating parameter... The lay person may think ok, just add Y in so the total complexity now becomes U+V+W+X+Y=Z+Y... Simple right? Well no because the paradox states that the fundamental need need to make something self-replicating will influence every parameter.... So maybe we should say (U+Z1)+(V+Z2)+(W+Z3)+(X+Z4)=Z+Z1+Z2+Z3+Z4+Z5.... And now we have the paradox because we also need to include the added complexity of self replication to the basic self replication complexity.... and then we just get complexity that equates to a sum to infinity (by definition).

In simple terms the added complexity of self replication of various abilities adds an ever growing level of complexity that must then be self replicable... and so on and so on..

Did a quick google but didnt hit any citations for self-replicating machine paradoxes so I think I must be on to something... I haven't fully thought this through and I am sure the maths is a little sketchy but I really believe I have come up with a unique bit of academic work here. Is anyone on here willing to help me flesh this out and perhaps we can look to publish a peer-reviewed journal paper? Would be pretty cool if we could list OcUK in the acknowledgements section - maybe we get some free stuff?

 

[rubberduck]

The terms are not independent so do not sum to infinity. Trivial counterexample - life is a self replicating machine.

I did think about this and it was something I would have to explain to advance the theorem... I think it comes down to thermodynamics and entropy. You may say the formation of life goes against entropy as all things should tend to a more disorder state right? Of course that is only for closed systems and as we have sun constantly feeding us/our planet energy then we cant consider ourselves a closed system.... A self replicating machines will not have this this phenomena in place... But it could harvest more energy than it actually needs to cover self replication right? Well in that case the very act of energy harvesting is inherently tending things to a more ordered state... So a machine can only self replicate if something else in the galaxy is inherently becoming more disordered like a planets energy storage.... I dont think planets are close to self replication so there is your answer.

 

[rubberduck]

Unfortunately the Mrs has told me I need to go to bed.... I should be allowed a few pints of Ruddles again on Friday so hopefully can invest some more time in my pondering... In the meantime hopefully others can advance the theorem further. Don't worry I will put all those will decent input as co-authors on the paper.

 

[rubberduck]

Dont worry I havent abandoned this.... I have worked on the theory a bit more... I need to put the Maths together but I can give you a basic explanation.

Machine need to make drill bit (for example), (let's call it part C)... Machine needs to use part A + part B in order to make part C... Machine now able to make part C... Machine need to make part A incase it breaks during making of part C.... Machines need to make part D in order to make Part A...... Machine need to make part E in order to make part D... And so on and so forth... We havent even considered making part B... But what if part A + part B where actually part(100) We have to consider 100 parts!!!... SO! Not only do we have a paradox we also have the fact that what happens if as part of the self replicating machine fails during replication... Machine basically screwed right? If we include a breakage kernel in our equations we essentially consign self replucation to the galactic dustbin. Bye Bye von neumann indeed! It's like playing Ultima Online on Siege Perilous server but the odds are stacked against you with it being impossible to mine more material that it takes to replace your tools before they break...

And that is for basic tools... With self replication you have the additional math that I have thrown in... Seriously I think I am on to something here... We can prove it and get a journal article in Nature etc if we can get the maths together. What do you reckon.

PS I have been drinking Gin tonight as opposed to beer, I think it has given me more insight. Would love to hear your opinion.

 

[rubberduck]

Thanks for the feedback, will do some further pondering tonight. Unfortunately I only have a 4 pack of McEwan's export to get the creative juices flowing so don't expect any miracles.

 

[rubberduck]

Have still been thinking about this. Doesn't self replication break the laws of entropy in terms of the natural decay of the universe to disorder? The principle doesn't apply to humans as despite being a highly ordered structure, over our lifetimes by living we naturally create a net overall contribution of disorder to the universe. That is fine, but if you take it to Von neumann levels of a locust like plague of infinitely growing self replicating machines utilising all mass and energy in the universe... Guess what? The universe will push back.

I think this postulation strengthens my theorem.