Ghosts
in the model
by
“Benedic,
Domine, Nos et dona tua”. Grace was being read at a formal hall in a
Mark Charlton was
flustered, since he had been running back from his lab. He was a visiting researcher from MIT, the
Massachusetts Institute of Technology, one of the top schools in computing
science in the world. He had grown very
accustomed to the pomp and circumstance of college life in the few months he
had been at
Tonight was a
particularly busy night, with a large presence from the boat club, who had
invited rowers from one of the other colleges.
So far they had a quiet start but that definitely would not last. As Mark had rushed in last in the file of
fellows, he had found himself sitting at the end, next to a woman he had never
met (and seemed to pay him little attention) and Dr Jones, the college chaplain
and lecturer in veterinary science. They
had met many times before, and this time it looked as though they were lumbered
with each other.
“So Mark, succeeded in
playing God yet?” asked Dr Jones. “Getting close.” Mark
was used to skepticism. “No seriously
Mark, is it true that you are creating life?”
“We create large
mathematical models and view emergent behavior.
The one we are looking at at the moment is
Jones asked “how can
you ‘create life’?” Isn’t that a bit
like biology? “Not really. Essentially we are creating an alternative
physics. We use very simple rules to
flip squares on and off. The beauty is
that each square has no idea that is it part of a greater whole, yet we see
some fantastic life-like structures.”
“So you really are
creating life. Are these things alive,
or are they just behaving alive?”
“Well, they replicate
information, mutate, compete with different patterns and spread in their environment. That is a lot like life. The question is why you make the assumption
that life has to be based on carbon?”
“Well, by definition
really.”
“Here is another
definition.”
Celery
and stilton soup.
“But surely you can’t
create a mind in such a model” asked Jones.
“Well, some of our ‘organisms’ have developed some very complex
responses to their environments. We
could even go as far as calling it a “brain”, though I
agree, ‘mind’ is quite far-fetched at the moment.”
“How can something in
a deterministic model ever have a ‘mind’?
There is just no freedom for the mind to think, since the ‘thinking’ is
done by the computer, which by definition is not thinking.”
“The
cells/atoms/whatever in your brain don’t think individually, and don’t know
that they are part of a bigger whole.
Yet still we think. It is exactly
the same with cellular automata. Each
cell doesn’t know it is part of a bigger whole, yet when you put the whole
system together, fantastic emergent behavior can result.”
“Including thought I
suppose?” added Jones. “Again, you may
get things that look like they are thinking, but are they actually
thinking? Are they conscious?”
“That is a good
question” conceded Mark Charlton. “Maybe
if they act as though they have minds, then they really do. Even in the real world, how can the mind
affect the body? Either the brain does
it all itself via emergent behavior, or the mind is capable of somehow directing
the neurons in the brain. My money is on
emergent behavior – I mean why devise a convoluted hypothesis of a mind
interfering with physics when such a mechanism isn’t necessary?”
Jones grunted. He was interested in people and didn’t see
what if anything tinkering with artificial models could ever say about the real
world.
The meal continued
cordially. Coffee was served, but Mark
was anxious to get back to his lab for another couple of hours. Mark ate up and rushed across the
mathematical bridge and back to his department.
Back in his office his
colleague David Hardy had some very exciting news. “I think we’ve done it!” The new algorithms work amazingly and have
given us a million time speed increase.
Mark couldn’t believe it. This
alone was worth another publication.
They both looked at
the model. It was bigger than anything
they had ever done before. The patterns
appeared to have organized themselves into two tribes and seemed to be
communicating complex strategies to defeat the other side.
The year was 2008.
* * *
“We are all inhabitants of a mathematical soup” began the teacher. The year was 5020 AD (the age of discovery), and the classroom was filled with a small group of eight-year-olds. The children were strong, healthy, and already had wisdom in their eyes. The person they were looking at was their astrometrics teacher. In previous years he had taught them mechanics, calculus and quantum theory. This was their fourth year of physics, and these children were in the top set of their school.
The teacher continued, and the children were obediently watching and learning. “As you know, all matter obeys fixed laws. Everything we see behaves within strict parameters, which we can model exactly. In this first class we will model the simplest universe which spontaneously generates intelligent life – namely our own.”
“The first simulation was performed in Oxford in 2010 when two scientists, Green and Derek, ran what was then a large simulation of Conway’s ‘Game of Life.’ Of course, they needed to seed the Game of Life in the right way, since life does not spontaneously arise in that system. Nevertheless, the point had been proven – thinking was virtual, a subjective experience of the inhabitants of the model, and could be created from nothing.”
“Over the next century, available computing power carried on increasing exponentially, and universe models became more and more refined. Sagan cracked the big one in 2072. By applying multi-domain topology to regression field theory, he simplified and discretised the underlying equations of our universe and derived from first principles how our universe is constructed. To date, nearly three thousand years later, these equations have stood up to every single experiment with the most extreme energies from the collision of artificial black holes. The model has been completely accurate every time. We can only conclude that the Sagan equations represent some kind of ‘truth’, and are what underpins our universe.”
“All of this you covered in cosmology last term. But it doesn’t end there. The Sagan equations are one of a family, where Sagan’s original is the simplest. The proof of this will not be covered this year. There are other models which would take the lifetime of our own universe to compute a single step. But for practical reasons we shall not investigate these either.”
A hand shot up at the back of the class. “Yes Peter”. “How could people make sense of the world before the Sagan equations?” “Do you mean, how did people make sense of the world, or how did scientists understand the world? Remember that back then, not everyone was a scientist, and many people didn’t even understand quantum fields, and some could barely count without a computer, I mean abacus.” “I mean”, said Peter, “without knowing the fundamentals, how could they know that anything they said was true?”
“Interesting question Peter. Intellectually and technologically mankind had not really left the dark ages by 2072. It was only by uncovering the fundamentals that everything could fall into place. Back then there was a lot of room for doubt. Even after the Sagan equations, there was still a period of scrutiny and disbelief. Sure people thought had certainties, but it was not backed up with centuries of evidence as it is today. Most of the population was still gripped by the haze of religion, and still held firm their superstitious beliefs.”
The class sniggered. It was easy to look back at the foolish notions of Zeus and Yahweh, but when all you have is straws, they are all you can clutch. Peter did not even understand death, since he knew he would live forever, and couldn’t imagine anything else. You had to pity their attempts to cheat death through faith.
The class was used to Peter interrupting but they didn’t mind. The teacher continued. “In the first practical I want you all to set up a Sagan system from scratch.” The children rushed to start their assignments, and the teacher left them alone for ten minutes to grade their previous week’s homework.
He saw how they were getting on, by viewing each student’s workspace in turn. Out of politeness, his avatar always met them in their workspace, though there were many teachers who did not extend them the courtesy, and would peer into their workspaces as they worked. He always thought that students had a right to privacy.
Each student worked in a virtual workspace, which was an enhanced reality, and could instantly move into or out from it. Their spinal nerves were monitored and could directly manipulate virtual objects in the workspace. Optic and sensory nerves were also intercepted and appropriate images, sounds and smells were suitably inserted. This arrangement has not changed for a long time, and it was deemed too invasive to manipulate nerves inside the brain itself, yet the interface was much more convenient and immersive than physical screens and input devices. The computing power for all this was hosted somewhere inside the school, though many students also had a computer at home.
In a workspace, you could do anything and you really were a god.
Several of the students had created Big Bangs by now, and were watching their universes unfold, each one of them different. Nicola’s seemed to run backwards, whilst Janus’s always seemed to destabilise after a few milliseconds. The teacher remembered fondly his own first attempts to start a universe, which had managed to twist itself into a knot and eventually collapse under its own gravity.
Many of them had now succeeded, and were now back from their workspaces and in the classroom.
Peter meantime had started to explore his universe. He couldn’t help but marvel at the stars, how they were so like his own, yet so different. He found planets, he fast-forwarded, and he found a planet rather like earth. A city with a river. Tall spires in beautiful masonry. Humanoids walking, and talking in strange tongues. He knew he had just used a huge amount of computer power to do this but he didn’t care.
He saw some people sitting in a dining hall. They were wearing black gowns with their heads bowed, and one of them was talking. The talking stopped, and chatter resumed. Peter paused his universe and saved it.
* * *
By next week, Peter had all but forgotten the dining hall. This lesson was about determinism.
“Last week” began the teacher, “we recreated the very first experiment performed by Sagan in 2072. Of course now we can do this with considerably more ease, and computers and interfaces are nothing like as primitive. As you all saw, some of you created universes successfully, some of you did not. Some were stable, and some were not. With a bit of practise, you will all be able to create stable universes every time.”
“You may wonder why it is that these systems evolve differently each time. The reason is because there is choice inherent in the Sagan equations. There are multiple solutions. What you have done is followed one choice over another – we don’t have the computing power in this school to take all choices simultaneously – but that is what happens in practise. We are only here by the anthropic principle – our universe must have taken fortuitous choices – otherwise we would not be observing them.”
“What you see is a possibility, and you must select certain outcomes by setting up your models correctly. You also have the benefit of accelerating time since we don’t actually need to model every uniton in order to see the universe evolve, we can compute on the fly as we explore. But here is a question. Which of these outcomes is the real one?”
Nicola put her hand up. “Surely it is whichever one you find yourself in.” The teacher smiled. “That is a very self-centred view. It is like saying that you are more real than me, or that now is more real than tomorrow.” Nicola looked puzzled. “While you can take the view that you are special, this is a science class not a philosophy class! Here we deal with the outside world, not the internal world in your mind. Equations do not give us a privileged place.” Nicola looked like she understood, so the teacher continued.
“The fact is that none of these is more real than any other universe, and as you see there are an unlimited number of variations. What is real is a subject for philosophy, but in my opinion they are all on an equal footing. Today we will be modelling the equations in reverse, and asking ourselves what is the difference between past and future. Then we shall see modal logic working in practise.”
The students were running the Sagan equations forwards and backwards, observing the differences.
Peter ran the equations forwards and backwards, but got quickly bored. He picked up his universe from the previous week. The humanoids were still sitting at the table, heads bowed in religious ritual. He started it up again, and ran in real time.
Idly, Peter started manipulating things in his universe. This was strictly not part of the model but what harm could it do? Everyone in the hall started looking around in a very startled manner, and started to run towards the doors and hide under the tables. He had done the same in some computer games but this was much more fun since it was so unexpected! Peter stopped.
* * *
The lesson the following week was once again about the direction of time, and Peter was once again feeling quite fidgety. He remembered the previous lesson, and was definitely looking forward to spending some more time with his universe. He had been thinking about this a little, and decided that he could actually write a program that would project his avatar into his universe. It was not enough to actually see the structure of his world, he actually wanted to be there. What a shock these people would get!
Peter paused his universe and earnestly wrote a program to project himself into it. It was certainly advanced for an eight-year-old, but essentially involved connecting his workspace to the Sagan model directly. Peter rewound the model to before he had started messing with it, and inserted his avatar.
Peter found himself walking around a
Men with torches in bowler hats came out of a door and started to look around the small wood. A vehicle with flashing blue lights pulled up by some gates.
His teacher appeared, and looked very unamused. “Come out of here at once!” said the teacher. He and the teacher returned to the classroom.
* * *
After falling over, Mark Charlton picked himself up and looked back at the boy. He had run into the Grove and was presumably up to no good. Mark carried on walking back to his lab. It was going to be another long evening.
* * *
Peter paused his universe.
* * *
Mark Charlton carried on walking to his lab.
* * *
“Peter, I thought I told everyone to delete their universe and start afresh”. “Yes teacher” replied Peter. Peter tossed his virtual universe into his virtual trashcan, which made a scrunching sound as it gobbled it up.
* * *
Mark Charlton reached his lab and met with his colleague David Hardy.
* * *
The following week Peter asked his teacher “what happened to all the people in the hall.” “Oh I expect they’re still going about their usual business.” Peter didn’t understand. “B, but didn’t we just delete them and put them into the trash?”
“Yes Peter, but remember that their time is not the same as our time. What we can simulate in 5 minutes takes them 15 billion years. If we pause them for a bit, and they don’t notice since it’s not their time we pause, it is our time.”
Peter looked perplexed. “But you still killed them? We can never get them back.”
“No Peter. We killed a model of them. Mathematics is not about creating new things, it is about discovering existing things. They would be there even if nobody had modelled them. Our model allows us to see them, but they were there all along. If the model goes away, the mathematics is still there.”
“That makes no sense- how do we know that they are there all along? If nobody has ever seen them before, then how do we know they exist?”
“That is a principle of science. We have to assume that certain things happen
even when we don’t watch them every minute.
Before any life existed, the mathematics was there. Before we knew
Peter still didn’t get it. “But we switched them off!! Prove to me that they still exist.”
The teacher sighed. Clearly this was going to take some direct evidence. He looked back at the homework of three weeks ago and took Peter’s starting parameters. The teacher fed it into the Sagan simulation and watched the Big Bang unfold. Where did you say they were? The teacher looked into Peter’s logs and saw where the dinner had been taking place. The model repeated itself. Fellows shuffling into a large hall, one latecomer rushing behind. Peter breathed a sigh of relief. The teacher let the model run. The fellows came out of formal hall and one of them crossed the wooden bridge and carried on to his lab.
“Yes” agreed, Peter, they are still there. “But that doesn’t prove that when you switch it off a second time, the people don’t just die.”
“Yes it does. For the same reason that when you close your eyes the world does not disappear. The people in the model have no idea they are in a model. It doesn’t matter if you model them today, tomorrow, or whether you pause it or run it backwards. To them time just carries on at its own pace, and they certainly don’t care if they are modelled in my computer or yours. If we repeat the model two, three or four different times, they will still only experience one timeline. It’s all the same to them.”
“So what you’re saying” said Peter, “is that these people would exist even if we didn’t model them.”
“Exactly, in the same way that the number 12345 existed before people could count. Have you ever wondered what it really means that 18237462 + 973645253 = 991882715? Have you any idea how amazing that is? Two people doing this sum would always get the same number (try it). It proves that mathematics is real and transcends reality. It proves that mathematics runs far deeper than we first suspected.”
“So who models us?” asked Peter.
“Nobody. That’s the thing, we don’t need a modeller. We are just mathematics that woke up.”