## A (final) speculation from “The Hidden Reality”

I have just finished Brian Greene’s The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos, so want to take this opportunity to once again endorse it and also to restate or reprise one of his speculations in the book: this time one grounded firmly in computing rather than string theory or conventional cosmology.

The key question at the heart of this speculation is this: do you think that, given we have seen computational power double every 18 – 24 months or so for around a century now, we will reach the point where we will be able to convince computer-based agents that they are in a physically real world when they are, in fact, in a computer-based simulation?

And if you answer yes to that question, do you realise that you are more or less forced to accept that you are one such agent and what you see around you as real is, in fact, a computer-generated “virtual reality”?

The reasoning is simple: once the technology to build a sufficiently convincing virtual world exists then such worlds are likely to rapidly grow in number and there will be far many more ‘people’ who are agents than people who are physically real. By simple averaging you and I are far more likely to be such agents than to be real.

It’s a truly mind-bending thought.

Saying ‘no’ to the question requires putting a hard limit on human progress in the field of computation. How can that accord with our experience of ever faster, more powerful and ubiquitous computing?

Well, there are some reasons – but even they are open to attack.

Reality appears smooth and continuous, but smooth and continuous numbers are not computable. Computable numbers are of finite extent – as otherwise the computer would never finish computing them. For instance no computer can ever compute $\pi$, only render an approximation. Indeed most numbers are “transcendental numbers” and inherently not computable.

But this argument – which sounds like a sure-fire winner for knocking down the idea that our reality is, in fact, a simulation, has a weakness: we cannot measure smoothness either. Our measurements are discrete and while it appears to us that the world is smooth and continuous, maybe it is not – it is just that the computed approximation is beyond our ability to (presently) measure it.

If, at some point in the future, we discovered a finite limit to measurement that was beyond physical explanation it would surely confirm we were in a simulation.

## “Basically, you would be able to compute anything you wanted”

The quote that forms the title here comes from Lance Fortnow, a computer scientist at Northwestern University, in an article (here – subscription required) in the current edition of the New Scientist on the $P = NP$ question.

It’s an odd statement for a computer scientist to make – most numbers are transcendental numbers and so are fundamentally incomputable: for instance there are $\aleph_{0}$ (aleph null – the smallest of Cantor’s hypothesised infinities) transcendental numbers between 0 and 1 (or between any range of integers).

But besides that oddity it is actually a very good article – calling the world where $P = NP$ Algorithmica – “the computing nirvana”.

I have written before of how much I hope we do live in Algorithmica, though the consensus is we live in a world of NDAlgorithmica (ND for non-deterministic).

The article’s beauty is that it also examines the states between the two: what if, for instance, we discovered that the class of $P$ problems were identical to the class of $NP$ problems but that we could not find the $P$ algorithm, or that the $P$ algorithm was of such a degree of complexity it “would not amount to a hill of beans”?