Living in a simulation

There has been a lot of press lately (summarized here) on the possibility that we are living inside of a computer simulation. Much of the attention has been focused on whether or not you could know if you lived in a simulation. Here, I will focus on what you could know (or compute) if you were running the simulation. Before I proceed, I’ll briefly summarize some points about the theory of computation. I’ve alluded to these ideas in several of my recent posts but have never formally introduced them. Obviously, this is very deep area so I’ll just briefly summarize some important points.

Complexity of the brain

The Kolmogorov complexity of an object is the length of the minimal description of that object. In terms of the brain, it would correspond to the length of the smallest computer program that could reproduce the brain. It could also be thought of as the amount of information necessary to model the brain. Computing the Kolmogorov complexity is not possible since it is an undecidable problem but we can estimate it. If we presume that molecular biology is computable then one estimate of the Kolmogorov complexity of the brain is given by the length of the genome, which is 3 billion base pairs long or 6 billion bits. To be conservative, we could also include the genome of the mother and baby, which implies 12 billion bits. This corresponds to less than two billion bytes and easily fits on a DVD. Hence in principle, we could potentially grow a brain with less than 12 billion bits of information and this is probably an upper bound.

Contrasting worldviews – Part 2

Compared to biologists and mathematicians, physicists are much more uniform in their worldview. There is a central canon of physics that everyone is taught. With respect to how physicists approach biology especially with regards to how many details to include, their ideas are shaped by the concept of universality and the renormalization group, which I will explain below. This is partly what gives physicists the confidence that complex phenomena can have simple explanations although this physics worldview hegemony is starting to break as physicists become more immersed in biology. In fact, I’ve even noticed a backlash of some physicists cum biologists towards their colleagues that espouse the notion that details can be dispensed with. Some physicists are very much of the notion that biologically detailed modeling is necessary to make progress. In this sense, what I’m describing might be more appropriately called the old physics world view.

Contrasting worldviews – Part 1

In my previous post, I talked about how we probably needed a new worldview before we would be prepared to understand the brain. What I thought I would do here is to introduce what I think forms the worldviews of people who do dynamical systems (which forms a sizable contingent of the mathematical neuroscience community) and physics (in particular statistical mechanics and field theory). Having trained in physics and applied mathematics, served on the faculty in a math department and worked on biology, I’ve gotten a chance to see how these different groups view science. The interesting thing is that in many ways biologists and mathematicians can sometimes understand each other better than physicists and mathematicians. I was led to this belief after hearing Alla Borisyuk, who is an applied mathematician, exclaiming at a conference I helped organize in 2000 for young researchers, that she had no trouble talking to biologists but had no idea what the physicists were talking about.