Stephen Wolfram - What is Complexity in the Cosmos?

Steve and I like you have had a lifelong passion to understand what the nature of reality is and when we look at reality the first thing we notice is that there is great diversity great complexity so let's focus on that and ask how could such complexity come about well I think it's it's in a sense kind of humiliating for us as humans that if we are presented let's say with two objects and we're told one of them is from nature and one of them is something that we as humans have created that it's a pretty good guess that the one that looks simpler will be the one that we as humans have created and yet with our whole sort of history of civilization and so on somehow we haven't managed to capture the secret that nature seems to have that lets it apparently quite effortlessly create all the kind of complexity that we see so one thing I've been very interested in is to try and sort of homed in on what that secret that nature has is it's kind of a very basic mystery in in science I thought 25 years ago when I started really thinking seriously about this kind of thing that with all of the fantasy physics and mathematics and so on that I knew that this kind of basic mystery of science will be easy to crack but that it would be from my be able to use some mathematical method let's say to be able to say this is how nature manages to do the things it does I didn't manage to do that and I kind of sort of started zooming out to try and see kind of what what could it be about kind of the foundations of the way that I was thinking about things that didn't let me kind of crack what seemed like a very basic scientific question what I realized was was this that if we are to have any theory of this kind of thing it has to be the case that nature follows some kind of definite rules but the issue is have the rules that we have learnt from sort of the development of mathematics and so on are those the rules that nature is really using or is nature using some other kind of rule and what I what I kind of realized is that we have to sort of start thinking about what are all the possible rules that nature might might conceivably use to do what it does they might not happen to be the rules that we as humans have set up in our mathematics and in the development of our science so I kind of started looking at the question of if we look at some all possible rules that nature might be using what can we see out that what can we find in sort of the space of all possible rules I'm not limiting yourself to the traditional mathematics or physics right right and so so in modern times we have kind of a good foundation to think about all possible rules we have computers and computer programs and we can kind of imagine looking at sort of all the possible programs each one corresponding to a different rule for how things get made and we can ask the question in the space of all possible computer programs what's out there and how does it compare with what we see in nature and so I started 25 years ago now to kind of investigate the simplest possible computer program it's kind of a strange thing because we're used to the idea that we make computer programs for particular purposes you know we would make a program to to perform some particular computation that we have in mind a purpose form we don't just think about enumerate all possible programs and just seeing what they do but I decided it would be an important piece of basic science to try and just sort of enumerate the possible programs and see what's out there in the universe of possible programs well my first assumption was that when the program's I was looking at were simple then their behavior would somehow be correspondingly simple that if one wanted to make something complicated that it would necessarily be the case that one had to sort of put something complicated in that one couldn't get complexity out with nothing put in so I was fairly amazed when when I actually did the experiment and found that some of the programs they looked at were very simple they're very simple things but we just started numerating possible programs by the time Europe let's say the 30th program that happens to be one right particularly like you can number these programs this is rule 30 you suddenly see a situation where you can start off from a very simple rule that you can specify in just a few bits of information you say let's start the thing off from let's say one black cell and the kind of ways that the pictures are made and suddenly you see that out of this very simple rule very simple starting condition you get this pattern of great complexity and the this is this is something that certainly I think it's sort of it's it's the single most remarkable thing that I've ever seen what's particularly interesting is that if you look at that rule compared to other rules that look similar you cannot see from the specification of the rule the complexity of one versus the simplicity of the other it's a it's certainly impossible for me yes as I look at them because they seem and sound the same right right but it's sort of what one what one's realizing is that if one goes and explores the sort of computational universe of possible programs there are all kinds of creatures out there some there are some creatures that are very simple they look they look they look very very straightforward there are other creatures that are the most ornate and exotic creatures and there are fundamental things that can be said about there our difficulty in deciding from the rule what which weather will be seeing in our NATO exotic creature for a very simple creature yeah but that's almost the width they always look the same but it's how they perform and what they do that's different yes I mean if I use a metaphor I'd say you know looking at them superficially like you know different kind of wolves or sheeps I'm not not sure what bestnet animal metaphor to use here but when you see the kind of behaviors that they have suddenly there'll be a huge difference between them yes and that's that's that stuff well this is citement I think that the thing that I found most remarkable is that from you know just sort of sampling out in the computational universe one sees this great diversity of behavior some simple some very complex and what what I found remarkable is that this seems to mirror very well what we see in nature I think in a sense that that sort of sampling in the computational universe we get to see the kinds of possible rules that nature can be using when we as humans do kind of engineering we tend to operate under the constraint that we have to readily foresee what the consequences of what we build will be a good point um but nature operates under no such constraints so it gets to kind of sample much more arbitrarily the possible rules and then there's this remarkable sort of fact of basic science that out of all the possible rules many of them have this feature that even from great simplicity the rule the behavior that can be produced can be highly complex let's just take for a moment to define the difference between a behavior that's simple and complex I think we're saying a simple behavior is is repetitive a repetitive pattern that just stays the same forever so to speak and that's a simple pattern and it really has no interest or utilitarian purpose a complex pattern will then have a richness and a story that may go on forever well I think a very practical way to think about this is when you're presented with one of these patterns how easily can you summarize what you see in this pattern if it's just you say a uniform black triangle okay you're done or you say it's a it's a pattern that is you know nested in some some way but you can sort of specify the nesting and and you say you have a quick description that kind of gets you the the complete specification of the pattern when we say that things are when we see things as complex what's really going on is that we as human analyzers of what we're seeing don't get very far we we can't sort of crush the thing we're seeing as some simple description right we're just stuck with saying well it is what it is and we may be able to give some ornate description of what's there but we don't get to sort of summarize everything in a matter of a sentence or two and that's I think the sort of the operational definition of complexity right and there's a fundamental question of sort of how can it be that these very simple underlying rules make something that we as humans are kind of unable to decode I mean it could be you know our basic sort of intuition about things tends to be when we see something complex we assume that its cause must be somehow correspondingly complex because that's been our experience with with the things that we build for example but that that intuition is the thing that to my great surprise I discovered is fundamentally not correct that out in the sort of computational universe it doesn't work that way instead in the cutout in the computational universe there are many instances where even though the underlying rules are extremely simple but behavior that emerges is highly complex and radically different from a similar rule yes and in principle do you think you will ever you will ever be able to determine from the simple rule certain characteristics that could predict or must--you the only way you can find out if you develop a simple or complex pattern is through testing it there's an and it's in principle you can't tell well this is that this is sort of a fundamental scientific fact that there's a there's a whole bunch of development that that goes into showing that this has to be the case that's the sort of phenomenon that I call computational irreducibility that kind of shows one that from the description there is sort of an irreducible amount of computational work that has to go on to find out what consequences this this simple description will have so that means in principle you can never be able to differentiate from those original simple rules which will generate the complex rich patterns and which will generate just the simple repetition yes that's true I mean there are certain cases in which you can say this particular one has some particular simplifying feature whether it makes it kind of completely incapable of doing anything interesting but that's that's kind of the exception we have complexity I understand but complexity doesn't mean meaningfulness we can have many things very complex completely devoid of meaning although many things that have great meeting are very complex so how do we then go from complexity to something meaningful that's a that's there's quite a lot of layers they want us to peel off to understand by the answer to that I so when once presented with something and once asked is this was the set up for a purpose for example there's a there's a sort of a this question of Cameron infer whether something was made for a purpose for example let's say one might think that if one saw something that was very simple that one would immediately know that it was not made for a purpose that's probably not correct one of my favorite kind of parables about this is something I think due to Immanuel Kant he said if we see a hexagon drawn in the sand we know that it must have been put for a purpose now what one then in modern times it's it's people have noticed that there these patterns of stones for example that arrange themselves in perfect hexagons and do so bye-bye as the results of sort of physical processes of wind and these sorts of things so this kind of gives gives a lie to what-what Canton said about this idea that you know if you if you see this hexagon drawing in the sand it must have been been put there for a purpose but this question of how do you how do you recognize purpose in things it's a it's a really interesting question and it kind of it's also complicating arrested in the in a sense when when we when we try to look at the natural world one of the things that we in our civilization have done is to try and sort of mine the natural world for things that we can use for technology we've tried to take things from the natural world and apply them to our particular human purposes and that's something that has been done with lots of materials and things like that what I think is an important phase in the future of technology will be mining the computational universe will be mining sort of the space of all possible rules for making things and finding which of those rules are relevant for particular human purposes in the history of our engineering so far we've tended to follow some very definite motifs we've got the idea of sort of rotary motion levers things like this these are very particular kinds of developments that have happened historically there's a whole sort of vast computational universe of possible rules possible ways to make things out there and the the I think in the in the future of technology will see increasing use of these kind of more diverse ways to make things and our our intuition about when something has been created for a purpose versus not will probably change as a result of us being quite familiar with technology that's been created in a quite different way than it's created today I actually think one thing one can do one one thinks sort of scientifically and mathematically one thinks about sort of the limits of things and will you think about sort of the mathematical limit of infinitely sophisticated technology kind of an interesting thing to imagine and I think in sort of that limit what we perhaps might imagine is that every purpose that we have would be achieved in the most efficient most optimal possible way now as a matter of basic science we can investigate right now what are the most optimal most efficient ways to achieve particular kinds of simple purposes so for example one thing that I've done is to kind of search the computational universe for optimal ways to perform particular computational tasks actually in in our software Mathematica we we routinely use this kind of technique to find sort of the optimal algorithms for things they're not algorithms that any human would ever have created as a piece of engineering their algorithms sort of plucked mind from the computational universe that are sort of optimal for their particular purposes the remarkable thing is that those algorithms often look to sort of to us as humans they look bizarre alien highly complex yet they happen to achieve their purpose in sort of the optimal way and I think that's a sort of in the in the limit of infinitely sophisticated technology we'll see a lot more of these kinds of things where we can identify purpose by the fact that the thing that we're seeing is the thing that achieves what it achieves in kind of the most efficient possible way it's a it's a you know as we try and dig into sort of what the what this idea of purpose is not in the limit of infinitely sophisticated technology we're kind of led to this whole chain of taking a thing and asking how it sort of fits into our whole cultural history

Channel: Closer To Truth

Views: 22,660

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Keywords: Stephen Wolfram, Closer To Truth, Cosmos, Cosmology, Complexity, Life, Physics, Intelligence

Id: xrXEQlvUpYI

Length: 14min 57sec (897 seconds)

Published: Mon Feb 26 2018