I’m calling into question the coherency of your argument.
I think iamnotbatman has already said this, but, for a more intuitive understanding, take a look at the concept of the information content of a message. Intuitively, the possible information that can be transferred with a message rises with the complexity of the message – a simple message, like ‘yes’ or ‘no’, only transfers one bit of information, while more complex messages – more complex strings of symbols – may transfer more than that (such as, hopefully, this post).
Now let’s look at a situation in which I can transfer to you messages from a fixed and, for the sake of simplicity, finite ‘pool’ of messages. Say they’re all messages about the composition of a certain object, by listing its properties. One such message might be: ‘it’s round, larger than a mouse, pink, and weighs twenty pounds’. This obviously does not describe the object completely, but it serves to constrain the set of objects that may fit that descriptions. All black objects are out, as well as all rectangular ones, etc. All the messages I can transfer to you contain a similar amount of information about the object – i.e. serve similarly to constrain the set of possible objects.
But what happens if I transfer more than one message to you? Two messages may be composed into one message using the logical ‘or’: ‘it’s round, larger than a mouse, pink, and weighs twenty pounds or it’s triangular, mouse-sized, black and weightless’. But now, despite having received a naively ‘more complex’ message, you actually have less information about the object than before! So if you want to measure the complexity of a message by the amount of information it transfers, you are forced to admit a measure of complexity that can actually decrease through adjoining more elements. This goes to the extreme: if I simply transmit you the set of all possible messages, you will learn nothing at all – the set is of zero complexity, even though it contains many subsets of non-vanishing complexity.
This carries over to the notion of ‘algorithmic’ or ‘description-length’ complexity. For instance, the set of all binary strings has a very small (asymptotically zero) complexity – I have just completely described it, using only the words ‘the set of all binary strings’. But any given binary string will typically not admit a description much shorter than it itself is (except for very special ones, such as 111111… or 1010101… etc.), and consequently, have quite a high complexity. But, to the extent that one can say that the set of all binary strings is composed of binary strings, which are thus its ‘parts’, this is a concrete example where the parts are more complex than the whole.
This isn’t just idle semantics – one can devise quite concrete examples in ‘the real world’. Indeed, take a block of concrete, a cube of one m edge length. I’ve just completely described it, so its complexity isn’t all that high. But now break it into parts – typically, these will assume quite complicated shapes, each much harder to describe than the original cube was; nevertheless, from those parts, the cube can be uniquely reconstructed, so in that sense, the set of all parts contains the same ‘information’ the cube previously did.
What we’re essentially looking at here is a consequence of the fact that a sub-set of a set contains the same information as its complement – i.e. the set that remains when you take the original set out of the total set. So one way to specify a set is ‘constructive’: you can give a direct description of the set. But another is just to specify the whole set, and the complement. Say the whole set is ‘the alphabet’, and you want to specify a set in which one letter is missing. You could laboriously specify all the other letters, or just say (A-Z)/E, for example. Since this specifies the set you’re interested in completely, it is just as complex – it contains the same information, even though naively the string ABCDFGHIJKLMNOPQRSTUVWXYZ may look more complex.
So it’s not a given that the whole must be more complex than any of its parts.
This is a tangent, but something that always bugs me about statements like this about message complexity is that the message is relative to the receiver.
For example:
11111111111111
could be much more complex than
10101110101010
depending on who/what the interpreter is.
My argument, if you want to call it that, is: To the question “Is the human brain the most complex object in the universe?” the answer is “No.”.
Jragon defined"human brain" as that which only controls “my mental faculties, and not yours and everyone else’s”.
“complex” is not yet defined.
“object” is not yet defined.
You defined “universe” as the “universe of possible universes”.
You are making the argument, so you define the terms. We’re waiting. It’s impossible to argue coherently with you until firmly embed the goalposts in stable ground.
TimeWinder was right:
Certainly – it depends on the architecture, the programming language, etc. But I’m hoping that Mangetout and I share enough of a common conceptual basis to neglect this difference; and in the limit, the algorithmic measure of complexity is wholly machine-independent, so that the qualitative statements hold even in the face of different implementations. (The reason for this is computational universality: for any universal machine with respect to which the complexity of a certain string is defined, there exists with respect to another universal machine a program ‘simulating’ the first one, such that the complexity of the string with respect to the second machine differs from the complexity with respect to the first machine by at most a fixed constant, the complexity of the program simulating the first machine on the second. In the limit of complex strings, this constant will be vanishingly small, and thus, the notion of complexity is asymptotically independent of the implementation – this is known as the ‘invariance theorem’ in algorithmic complexity.)
That is nowhere near a definition I think is appropriate for the context of the question in the OP. If you change the goal posts to “all possible universes”, then obviously I doubt the brain is the most complex. The answer to your question is rendered trivial for such choices of definitions.
That defintion is appropriate for the context of the question, “Is the human brain the most complex object in the universe?”. However, that defintion is not appropriate for the context of the question, “Is the human brain the most complex object on earth?” the answer of which is “Yes.”.
In other words, you still got nuttin’.
What do you mean?
I make the argument; you define the terms. And who’s waiting?
I, for one, am waiting for you or Jragon to define “complex”.
You are going in circles because you won’t define your terms.
I make the argument; you define the terms. And who’s waiting?
I, for one, am waiting for you or Jragon to define “complex”.
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Again, your argument, you define the terms. This ain’t rocket surgery.
“human brain”: that which only controls “my mental faculties, and not yours and everyone else’s” Defined by Jragon.
“universe”: “universe of possible universes” Defined by iamnotbatman.
Why should I define “complex” and “object” when iamnotbatman is arguing over the defintion of “universe”?
Grin! And I’m still quibbling over the definition of “object.”
For instance: is a galaxy an object? I can think of reasons to say yes…and reasons to say no!
If you’ve defined ‘universe’ already you can ignore iamnotbatman, or change your definition based on his argument. And you can go ahead and pick definitions for ‘object’ and ‘complex’ based on the arguments presented, or something you just make up. So quit playing games and state your argument using unambiguous terms so I can explain why you are wrong.
Define it however the hell you want. Just be clear about it. Write it down, rather referring to it misleadingly by “iamnotbatman defined it”, when all I did was mention in passing a possible definition one might use if we were to be having a totally different discussion from the one I thought I was engaged in. If you want to define “universe” as “all possible universes” then so be it; say so. Just beware how imprecise and misleasing the title of the OP is (especially in the context of the quote), and how vague and confusing you are being in addressing such an obvious point of confusion.
Yes! That is what I want for the terms “human brain”, “complex”, “object”, and “universe” - a possible defintion one might use. I got a possible defintion one might use for “human brain” and I accepted it. I got a possible defintion one might use for “universe” and I accepted it. I am waiting for a possible definition one might use for “complex”. I am waiting for a possible definition one might use for “object”.
I accept “all possible universes” as the defintion of “universe”. I accept that which only controls “my mental faculties, and not yours and everyone else’s” as the definition for “human brain”.
How about a definition of ‘object’ as something that resembles a bucket of fried chicken? I like the crispy kind, but not that fast food stuff. I can’t find good old southern fried chicken anywhere anymore, I just have to make it myself or it will be really dry.
So now you just have to work out a definition of ‘complex’.
That’s ok. Just as long as you don’t call into question the coherency of the definitions.