The discussion of the idea of a computational universe is a religious one as of now, because we don't yet know of a way to prove or disprove it. I realize that to talk about this in such a literal way is to postulate God, but however far we go back, once we realize that time existed before the big bang, we never reach the answer of "why?". As a scientifically minded person, I don't demand this answer, like most religious people do, because I realize that it cannot be answered, and therefore is impractical to ask. But I also don't wish do sweep it under the table, because it is the most important question we can ask, regardless that the only answers we can generate are postulations. This is all, of course, postulation - is the universe a computer?
1. Computation can be viewed as providing a small number of inputs to generate a large number of outputs, such as the fundamental force(s) and energy (although even the separation between these two things might in fact be superficial) generating the complexity that we are today.
2. The universe is a fabric of individual quanta of information, which communicate the nature of themselves to every other part of the universe, and manipulate the performance of these other universal constituents.
3. We see in our modern world a doubly exponential rate of expansion of computational power. We have moved through paradigms of computation, from electromechanical calculators, to relay based computers, to vacuum tubes, to discrete transistors, to integrated circuits, which is where we find ourselves (in the common public) today. The scale that we're moving to now is to nanoscale computation with the same fundamental properties we see in computers now, but with much smaller proportions. Also in successful development is self-assembling computation, using the inherent structure and behavior of things like DNA and other complex molecules to generate computational results (software) and small physical structures (hardware, like cell phones or smiley faces). After that, we will be in the atom and quantum scales. In fact, many great strides have already been made in this field lately. The types of computation that we will be doing in 100,000 years or so, if we project these trends, might look something like the universe we live in.
4. If time is infinite, the probability of life being created in the past who create these profound types of computational devices that we foresee in our own future are also infinite. Of course, I'm talking about a multiverse, or whatever; not simply the universe that we can see within the cosmological horizon of our light sphere. Big bang theory is said to form time as well as matter and energy as we know it, but this is all based on equations that are based within relativity theory. There are a host of quantum principles that would prevent matter from, as the most strict big band theorists say, condensing into an infinitely small point, in which nothing exists, including time. Many cosmologists agree with this, and it is bringing back the old "bounce" theory of a local universe that expands and contracts forever.
5. The only constant we find in the universe around us on all scales is information. Everything contains information that is used to communicate to, and manipulate, everything else. The most straightforward example is DNA, which uses a single language of four letters to create all forms of life that exist on our planet. But this property of information-based manipulation is shared by everything that has mass, and therefor has gravity, as I will discuss later.
6. If the fabric of the universe that we are a participating part of is computational in its most perceivably fundamental nature, then we can never, ever, become aware in a positive way that we are part of a computational system. Even if we find something of a drastically different nature, the only way we could perceive it is if it were of the same nature as us, and we could never know whether or not it is also part of the computer.
Of course, I realize that to postulate a final cause of our existence as the products of previously existing, information-seeking entities results in the logical fallacy of infinite regress, but this is no worse than the situation we find ourselves in now. With infinite time, there will have to be infinite regress in any question with the form, "But how were the creators created?" On some of the grandest scales, I am hooked on Lee Smolin's idea that our universe is a product of many, many generations of other universes that reproduce through black holes, and thereby exist in an environment of natural selection that is created by the tendency for universes that have more progeny, or offspring, to tend to win in selective competition. That is, the universes that create the most black holes tend to continue their line of descent, while the universes that create less black holes due to mutations of their physical laws, have less progeny to continue their "genetic" line, and the landscape becomes overwhelmed by those universes that can create more progeny.
But this still does not give us an answer to "Why?" Why was this chain of evolving universes composed of ingredients that gave rise to something like matter, or physical structure, rather than something else, or nothing at all? This is where the infinite regress comes in - something needs to be the cause of this initial cause, and so on. So, I acknowledge the possibility of conscious creation of physical properties causing this cycle, and the possibility of the conscious creators of those creators. And at those types of scales, science has no ideas, doesn't and shouldn't consider, and even scoffs at, ideas like this. And they should, because there is absolutely no way to know.
So, perhaps the final cause of physical structure and organization is computation itself. Computation, creating more sophisticated computation, and so on, ad infinitum.
Certainly, in our universe, I can imagine no other future than one dominated by conscious beings, who understand how to manipulate their physical environment to increasingly minute degrees. This, I believe, is the cosmic arena of evolution. Forms of life on an individual planet will be eventually dominated by those who can understand and manipulate their environments in the most creative ways. These are the forms of life that reach out into the rest of the universe outside of their planet, and eventually, out of their local solar system. Eventually, these beings interact with each other, communicating and sharing knowledge and resources, creating more and more sentient beings who embody more fundamentally and minutely the informational potential of the universe, and make increasingly wise and powerful choices in their interactions and communications.
When we do approach the ultimate limit of computation, I think that we will be trying to emulate the best software platform we see in the world around us - gravity.
Einstein gives us a picture in which gravity is the shape of space-time produced by the organization of energy in our universe. It can be viewed this way, but another hypothesis is that it is a particle. This is one avenue that people take towards finding a unifying theory of physics between relativity and gravity.
But however we view it, it is clear that, although gravity is taken for granted by most of us, it is truly profound. It communicates infinitely (infinitely, you guys!!!!!!) between everything (you guys!!!!!) all the time, at the fastest possible speed (the speed of light). Everything that has mass communicates this force to everything else that has mass in an unfathomably precise way. This universally attractive force is truly the only real necessity for creating great organization in the universe, on all scales. (Of course, repulsive forces are necessary on small scales, which is what we find in our universe). We know that our universe expanded from an extremely dense point, and that the unimaginably minute inhomogeneities within this early universe were the seeds of gravitational condensation that were the cause of the large-scale structure of our universe.
If we could detect gravity (and the other forces) on the smallest theoretically minute scales, we could note the position, size, shape, and movement of everything in the universe. I cannot stress that this information is being communicated to and from everything that exists, to extreme precision, and that this information results in an extremely precise manipulation of the discreet constituents that receive this information. The universe is the perfect computer because there is absolutely no separation between its hardware and its software (which is the direction that we see computation going down today) and because its most basic platform (the laws of physics) are extremely simple and universally communicative, while resulting in unimaginably complex and cohesive products.