Author’s Note: These are my personal (and sometimes inaccurate) ruminations on the idea of a simulated universe. I don’t claim to know anything about the philosophical treatment this idea has already been given, nor do I know much about any of the arguments. If I’ve stolen someone’s idea, I apologize…I didn’t do it intentionally.
Bob sat on the great stone platform atop the mountain, gazing down over the endless convolutions of the Great Valleys below him. His face bore a look of the most intense concentration. His brow was furrowed, and his eyes were distant and contemplative. It was in this state that Alice found him. She ascended the great staircase and seated herself next to him.
“So there you are.”
“Yes.” It was nothing more than a pleasantry, for Bob was far too lost in thought for any real communication.
“What on Earth could you be thinking about with such intensity?” Bob did not answer, but instead maintained his tense posture for another minute or so, then relaxed, and looked up at Alice.
“I’m sorry, what did you ask?”
“What are you thinking about with such intensity?”
“Oh, well…I’ve just been considering something.”
“Well, what?” A look passed across Bob’s face, and Alice realized with concern that he could very easily lapse back into mute contemplation.
“I’ve just been wondering…it seems to me that we are living in a simulated world?”
“What? What do you mean by that?”
“I simply mean that the Universe that we see is really just an assemblage of data in a computer somewhere, and that the physical laws we observe – and their consequences, such as our own sentience – are simply processes within that computer. You know, program instructions.” Alice rolled her eyes surreptitiously, then crossed her arms.
“Not this subject again!”
“Well, I believe it deserves consideration!”
“Why? It’s an entirely foolish idea!”
“Well, how could we possibly find ourselves in a computerized Universe? No computer could ever manage such a feat of simulation, and even if it could, it wouldn’t be able to produce the robust world we observe!”
“That’s where you’re wrong, I believe.” Bob had now turned fully towards her, and had fixed her with the challenging gaze that was his trademark.
“Oh, really? And have you any evidence of my wrongness?”
“Of course. You know – you should know better than anyone else – that I never make a claim without having a good argument to support it.”
“Okay. Since I am going to base my argument on the idea that a computer likely simulates the universe we live in, I’ll make my argument from a computer-based standpoint, even though essentially any suitable substrate could simulate our Universe. Now, consider a simple electronic circuit.”
“Right. This circuit consists of a small mathematical processor, a few registers for storing data, and all the other necessary equipment for a circuit to work properly.”
“I’m with you so far.”
“Now, say this circuit, on every tick of its internal clock, performed the following calculation: take the value stored in the data registers – call it x – and squared it, then multiplied it by some constant k, then subtracted from the result the value j times x, j being another constant, then stored all of that back in the data registers, and repeated the process ad infinitum.”
“I don’t quite see your point here, Bob. I must confess that I’m rather confused.”
“That is because you’re not thinking about things correctly. Okay, I’ll give you a hint. What would a system such as the one I’ve described represent?”
“Some mathematical function, I think.”
“Go up one more level of abstraction.”
“What do you mean? There are no other levels of abstraction in this system. Either it is a system consisting of electrons darting from atom to atom in a silicon circuit, or it is an abstract mathematical system. There is nothing else!”
“Ah, but you’re wrong on that account! For, think about physical laws!”
“What about physical laws?”
“Are they not just a higher level of abstraction than pure mathematics?”
“Hm…no, I don’t believe they are.”
“I think our definitions of ‘abstraction’ may differ. For now, I’m defining ‘abstraction’ to mean ‘representation,’ or something to that effect.”
“Ah, I see. Well, given that definition, I suppose I’d have to agree: physical laws could be seen as a third level of abstraction.”
“Right. Now, back to my imaginary circuit. Think about what its third level of abstraction would be.”
Alice thought for a moment, and then her face lit up.
“Aha! It seems to be the equations of motion for an accelerating projectile subject to air resistance!”
“But what was the point of the whole exercise?”
“Be patient! I was coming to that! Now, couldn’t one argue – rather convincingly – that in many ways, the creation of this circuit has also brought into existence an accelerating projectile subject to air resistance?”
“No, I don’t think so. The projectile is not real, it’s merely an abstract representation, created by us, its conscious observers.”
“I’ll ignore your little play on the definition of ‘abstraction’ there, for the moment. So, you say that the circuit’s ‘higher-level’ meaning as an accelerating projectile exists only in the minds of us, its conscious observers?”
“Yes, that’s what I said.”
“Well, you’ve stumbled right into my philosophical trap, then! For, is not the mind itself little more than a circuit, similar to (but, of course, infinitely more complicated than) the circuit we are discussing?” Alice looked blindsided for a moment, then recovered.
“The mind is something different. Your little circuit is fixed in time. It cannot observe itself nor rewire itself. The brain can.”
“Ah, yes, but, still, on the cellular level, is not the brain only a ‘system of electrons darting from atom to atom in a biological circuit’, as you said before?” Alice looked as though she had been physically struck.
“Oh, dear…I believe that’s checkmate…Hm…”
“Yes, you see? There can exist such abstractions, the mind being the primary one!” Alice knitted her brow while her toe fidgeted with a pebble.
“Okay, I concede that such abstractions are possible in our Universe. But since our observation is necessary to bring these abstractions – such as the one of the projectile in your nice little argument a moment ago – to light.”
“Ah, I was hoping you’d try to wiggle free in that way, for I have the perfect rebuttal!”
“And what’s that?”
“Imagine a computer, a huge computer. As big as the Earth, if you like, or bigger. It has memory cells for the storage of data, and processors for the computation of the effects of physical laws. Now, furthermore, let’s say that this computer is running a program that simulates the interaction of a huge number of elementary particles, based on physical laws that are the same as those in this Universe.”
“All right, I follow you so far.”
“Right. Now, let’s further suppose that this computer was allowed to run long enough that the Computed Universe experienced the Big Bang, the formation of ‘normal’ matter, the coalescence of stars and galaxies, and the formation of planets, and all the requisite molecules of life. And then, let’s assume that life does indeed begin in this Computed Universe, and that it evolves to the point where it has developed something like a complex nervous system – what resemblance it actually bears to a nervous system is immaterial, it just must fulfill a very similar function. Then, through the slings and arrows of Darwinian evolution – you don’t disagree that Darwinian evolution would necessarily take place, do you?” Alice shook her head. She knew that evolution was a principle based merely on the idea that the more fit an organism is for its environment, the more likely it will be to be represented in the next generation, and this principle is completely ignorant of the material composition of what is actually evolving. “Good. Then, we have Darwinian evolution, and let’s assume that it produces self-aware organisms. Now, do we not have that ‘secret ingredient’ necessary to allow the universe to be viewed in an abstract way?” Alice was at a loss for words, and she had to work to keep her mouth from falling agape.”
“Oh dear…I seem to have argued myself into a corner…if I allow for the existence of conscious minds, then it seems that I must inevitably fall to your argument…” Bob looked rather satisfied with himself, but then Alice took on a very resolute expression. “Wait! Would not this giant computer still require the observation of its operators in order to see the abstract things – the conscious observers – that it represents?” Bob smiled knowingly, and Alice realized that he would soon deliver his finishing blow.
“No more than our Universe requires a godlike figure to observe it in order for ourselves to exist.” Alice nearly fell off the rock. Then, she steadied herself, and a smile crossed her lips.
“Ah, but you have forgotten your original claim! How can you claim that we live in a simulated Universe? All you have done is to prove that it is possible that we might be, not that it is inevitable, or even likely!” It was Bob’s turn to grin.
“I was waiting for you to recover, so that I could philosophically knock you down once more.” Alice feigned offense.
“Oh, you philosophical sadist!” They both had a good laugh, then Bob suddenly grew serious.
“Now, for the final blow!”
“Let’s assume that some species in some Universe – simulated or not – created a computer simulation of a Universe. Suppose furthermore that that simulation was rich enough that observers – conscious entities – could arise within it. Then suppose that these Computed Observers created their own Computed Universes – for it seems inevitable that any such Universe-Computing race would compute more than one Universe – and within these Computed Computed Universes, Thrice-Computed Universes arose. This would continue until the ‘Nth-Time-Computed Universes’ became too small – for any Computed Universe must necessarily be smaller than the Universe in which it is computed – for conscious observers to arise. Despite this limitation, is it not obvious that there would be an immense hierarchy of simulated Universes for every ‘real’ Universe?” Alice nodded gravely, her defeat seeming imminent. “So, given the laws of probability, since there is such a hugely larger number of Computed Universes, compared to the original few ‘real’ ones, isn’t it much more likely that we find ourselves in a Computed Universe.” Alice sighed loudly, but then a glimmer of hope touched her countenance. After a few moments’ introspection, she smiled.
“Unless, of course, some of the current findings of cosmology prove true, and there is an infinite number of ‘real’ Universes!”
“I don’t follow.”
“Well, consider it! If there is an infinite number of ‘starter’ Universes – that is, ones that are not simulated – there would then be an infinity of Computed Universes, too, but only an infinity, since the mathematical laws of infinite numbers are so slippery. Then, the probability that we find ourselves in a Computed Universe is only one-half, since there is an equal number of both.” Bob looked flabbergasted.
“Oh, dear! I hadn’t even considered that! Excellent riposte, Alice!”
“But, wait! Suppose that instead of a finite hierarchy of Computed Universes, the hierarchy was infinite!”
“How would that even be possible.”
“Well, suppose that the infinite ‘starter set’ of Universes was itself simulated, and the Universe in which they were simulated was also simulated, and so on out to infinity!” Alice laughed. It was now her turn to be sadistic.
“But, Cantor showed that an infinity is an infinity. Even if an infinity of initial universes produced an infinity of simulated ones, their numbers would still be equal!” Bob seemed almost to deflate.
“Well, one could get around that by supposing that there is only a single Universe.”
“Not really.” Alice was now philosophizing at full steam, ready to make the kill. “Since, in an infinite Universe – which ours appears to be, based on telescopic observations – there will be regions too far apart to communicate, which are separated by the insurmountability of the speed of light, so that no information can ever pass between them. These regions might as well be separate Universes. This position would only be strengthened if the physical laws could vary from one such region to the next. No matter what you do, unless the Universe is closed and finite – which seems unlikely given the data – then we only have a fifty-percent chance of finding ourselves in a Computed Universe after all!”
Bob was silent for a long time, his head bowed. Then, he began to emit a peculiar rhythmic sound, a little repetitive squeaking. Concerned that he might actually be weeping, Alice leaned in to comfort him, but then the squeaking erupted into chuckling, then into uproarious laughter. Alice was confused.
“What’s so amusing?” Bob stopped laughing, shot her an impish grin, and extended his hand. In his palm was a coin. Alice joined in his laughter, and said, “If it comes up heads, we’re living in a real Universe…otherwise…”