Embracing Chaos

One of the reasons I chose not to pursue a career in science was a feeling that all the interesting problems of physics have been solved.  In a sense I still believe this — I don’t see the current line of pursuit bearing much fruit.  But I do see two really important questions that physics hasn’t answered.  What makes them especially interesting is that most of the scientific establishment doesn’t even recognize them as valid questions.

Ever since Maxwell unified the theories of electricity and magnetism in
1864, physicists have been working towards a single model that can explain all observed forces.  It took another hundred years or so for
us to understand how the electromagnetic and weak nuclear forces are really the same thing, and a grand unified theory is close to merging in quantum chromodynamics (QCD) and the strong nuclear force.  The only thing left now is to merge in gravity.  String theory is a popular contender for a so-called “theory of everything” which explains quantum gravity. Progress here is slow, but finding a theory which combines general relativity and quantum mechanics is widely regarded as one of the big unanswered questions in physics.  Personally, I’m not all that excited by it.  I think we have bigger fish to fry.

Let’s say we find a Theory of Everything that explains quantum gravity in addition to merging electricity, magnetism and the strong and weak nuclear forces.  What changes when we figure this out?  Of course, we
can’t really know until we have the answer.  But consider the merging
of the electromagnetic force and the weak magnetic force into the
electro-weak force.  They look different under just about every condition we will ever encounter.  It’s only when the temperature exceeds about 10^15 Kelvin that they start to look the same.  For comparison, the middle of the sun is relatively frigid at 10^7 degrees.  So my guess is that when we figure this out, it isn’t going to lead to any new
practical understandings about the world around us.

The theoretical basis for most everything that we experience on a daily basis was figured out in the early 20th century with quantum mechanics.  It provides a theoretical foundation which reduces essentially all of chemistry to solving mathematical equations.  Admittedly these are horrendously difficult equations that even modern computers can only approximate for relatively small molecules.  But the theory is there.  And with chemistry solved, we have a theoretical basis for all of biology, and everything to do with life.  Not to say there aren’t interesting problems to solve there and plenty we don’t understand, but on some level, it’s all applications of an understood theory.

I completely realize this is a simplification of the state of science,
but this is what I thought when I was an undergrad.  This realization
and disillusionment drove me away from science towards my career in
software, which I love because of its ability to directly improve people’s lives on a massive scale.

But now as I write about things like the fate of humanity, the nature of consciousness and how to save the world, I see two huge gaps in what science can explain.  For context, here’s a quote that I love:

The most exciting phrase to hear in science, the one that heralds new discoveries, is not ‘Eureka!’ (I found it!) but ‘That’s funny …’

Whoever finds the Higgs Boson, or explains quantum gravity will yell “Eureka!” at the top of their lungs.  Two things that make me say “that’s funny” about about how physics explains the world today are:

• quantum randomness
• the big bang

I’ll spare the details for now and write more on each of these later.  (I’ve written some about quantum randomness and the nature of free will before.)  But for now I’ll summarize by saying these are a couple of areas where the standard explanation really doesn’t sit well with me.  Moreover, I think a better understanding of these issues would do a lot to answer questions that have troubled humanity since the birth of consciousness.

There’s been a lot of fuss lately about Nick Bostrom’s ideas that we live in a simulation as a result of an article in the New York Times.  Here I’ll provide some analysis of Bostrom’s bold claim, including a proposed mechanism to explain my grandfather’s assertion that mathematical simplicity and beauty were indicators of underlying truth.  I’ll also explore the implications of this possibility to our daily lives, and show why this is another reason to follow Transhuman Morality.

Simplified Simulation or Complete, Accurate Model?

The simulations Bostrom describes would not be precise to the subatomic level, but rather use abstractions to simplify the computation.  Instead of simulating every electron, proton, neutron, quark, etc in each person’s body and everything around us, it might only simulate synapses and neurons in our brains.  Such short-cuts would be extremely useful to accomplish the goals he describes of virtually resurrecting ancestors.  (A convenient version of heaven.)  Just simulating the brains of the inhabitants of a virtual world is drastically easier than accurately simulating an entire universe down to the subatomic level.  For many purposes, including the ones we are likely to engage in anytime soon, it is sufficient. 

The software to run a simplified simulation like this would put its designer in an interesting predicament whenever the simulatees decide to build a new particle accelerator or perform some other experiment that pushes the limits of their understanding of fundamental physics.  Would a dialog box appear on the simulation screen asking the designer to make decisions about how to treat a new class of quark that had never been observed?  Then once the designer answers this question the simulation moves on?  Moreover, so many trappings of modern life are the result of applications of scientific breakthroughs like this?  For example, we could have never built semiconductors and thus computers without a solid understanding of quantum mechanics since they take advantage of quantum effects.  So closing the dialog box would require not only require describing the results of this experiment, but also coding up a bunch of new high-level abstractions that represent things like semi-conductors.  The simulation would need to know when it could use the molecular mechanics model, and when it would have to substitute a more detailed model or a coding abstraction that simplifies the results of more base laws.

If we lived in such a simplified simulation, it seems likely that chinks in the armor of reality would periodically appear.  Modern science has few inconsistencies like this.  (The big bang and quantum randomness being the two biggest two exceptions IMHO.)  I would wager that if we live in a simulation it is a completely accurate physical model that started with the big bang and covers the entire universe including our own evolution from primordial soup.  It’s not clear to me whether or not our universe has enough matter/energy to build a computer powerful enough to run such a simulation.  I should dig up my notes from Yael Maguire’s excellent talk at Foo Camp on the fundamental limits of computation to be sure, but I know it would chew through at least solar systems worth of our universe if not galaxies or more to simulate a comparable universe.  It seems more likely to me that if our world is simulated then the “host world” is governed by a different set of physical laws.  This point is debatable and important, but I’ll assume from here that the host world is governed by different laws.

Motivations of the Simulation Designers and Implications for Personal Morality

As the NY Times article points out, the simulators might just be bored, doing the equivalent of playing video games with us.  Or they might be scientific researchers investigating how changes to fundamental laws affect how worlds evolve.  Whatever their goals are in running a simulation of this scale, they are almost certainly interested in the complexity that we are creating here and now.  But how should we behave?

Robin Hanson suggests that as individuals living in a simulation we should try to lead the most interesting, impactful lives that we can.  This goal attempts to optimize for the case that the simulators will pick individuals from this simulated society to do something special with.  I think it extremely unlikely that the designers care about individuals at all.  If they’re looking at anything, I’d bet it’s entire societies.  So, if we are living in a simulation, I argue that we should do our best to advance technology as an insurance policy against extinction.  I have written a fair bit about the transhuman morals that such a guiding principal implies, but basically it boils down to being a geek and/or a hippie – advance technology as fast as possible and conserve natural resources so that the world doesn’t end before we reach the next level of technology.  Thinking that somebody might hit the “stop” button on the entire simulation puts a new twist on the idea of the world ending because as a society we failed to reach a certain level of technological sophistication.

A Simulation Argument for Truth in Mathematical Beauty and Simplicity

If our world is a simulation running inside a massive computing device, then something must have programmed this simulation.  The programmers of the simulation chose the physical laws that we live by, perhaps to see what would happen.  This puts an interesting spin on evaluating fundamental physical laws.  Which of these two equations below is more likely to be an accurate representation of the way the simulation designer wrote the code?  These are two different mathematical representations of P.A.M. Dirac’s eponymous equation, which is AFAIK believed to be a completely accurate representation of our physical world.

By this logic, the second one is almost certainly closer to how the simulation programmer understood the concept.  This perspective puts an interesting twist on Occam’s razor – the principal that the simpler explanation is probably true.  My grandfather believed that the simpler a physical law was, the more likely it was to be correct.  In this way he saw a certain beauty in math and physics.  If our world exists only as a simulation, then the simpler a physical law is, the more likely it is to be an accurate representation of the way the simulation was coded.

In this essay, I’m going to explore the question "If the human brain is Turing complete, what does that imply about the existence of free will?"  And moreover, what does that mean about the ability to upload our consciousness into computers?

First, a little computer science background.  Turing completeness is the idea that a computing system has the same capabilities as a universal Turing machine.  This theoretical machine moves along a long tape which has various symbols on it that the machine can read and write.  The machine itself is always in one internal state, but will change to different states based on its programming and input.  It is programmed by a huge state transition table which says "if you’re in state X, and you’re reading symbol Y, then write symbol Z, move left n spaces, and switch to state W" for all possible states and symbols.  It turns out that with a long enough tape and enough states this device can do just about anything you think of a computer being able to do.  In fact, computer scientists have shown that every modern computer system is functionally equivalent to a Turing machine.  That is to say all modern computers are Turing complete.  It’s useful because it’s simple enough to prove theorems about.  Some important things we know about Turing machines and anything which is functionally equivalent to one:

• Turing machines are deterministic — given a set of inputs they’ll always reach the same output.
• It’s impossible to reliably predict whether or not a program on a Turing machine will ever finish.

I see two ways to interpret the question of whether or not a human brain is Turing complete.  The first one is "Can a human brain perform the same functions as a Turing machine?"  I think that given a pen, paper, and enough patience the answer is clearly yes.  But that’s not the question that interests me.

As a transhumanist, the interesting question for me is "Can a Turing-complete computer perform the same functions as a human brain?"  This question is important to me because if the answer is yes, then it is possible for a computer to simulate a human personality.  That is to say uploading of a human consciousness into a computer is possible.  I’m going to dodge the detailed analysis of this question today, and get back to it in a later article.  For now, let’s assume the answer is "Yes" and see what that implies about free will.

Remember that theorem that says Turing machines are deterministic?  That is, once you start it going with a given set of inputs, that it’s always going to reach the same answer?  If this were true for us as humans, then we would have no free will — our actions would be entirely determined by our current state and our surroundings.  We might think we are making choices, but in fact a fast computer could run the same calculation and tell us what our answer would be before we thought we had decided.  So by this logic if uploading is possible, then humans have no free will.  Troubling, eh?

Fortunately, I think the above analysis has a flaw.  Let’s dive down a little deeper into neurochemistry.  Neurons fire as a result of electro-chemical processes.  Basic chemistry tells us that the rates of chemical reactions are deterministic based on concentrations of the relevant input chemicals.  But if you took stat-mech then you learned that these predicted rates are actually just statistical averages and that they’re only accurate if the brazillions of molecules involved happen to collide with each other at a constant frequency as they randomly bounce around in solution.  And quantum mechanics tells us that this apparently random bouncing around is in fact, to Einstein’s chagrin, truly random — god does play dice with the universe.  (I’m not sure I completely buy this, but I’ll have to save that for another article too.  Yes, I know that the Bell inequalities were experimentally observed in the 1980’s but it still sits funny with me.  Sorry grandpa.  More on this later.)  Because of this randomness, the instantaneous rate of any chemical reaction will vary randomly, while still averaging around the classically predicted rate.  So the upshot is that neurons don’t behave completely deterministically, but that the exact timing of neurons firing has a truly (quantum) random component to it.

Now this implies quite firmly that our brains cannot be simulated by a Turing machine since Turing machines can’t act randomly, and thus wouldn’t be able to properly simulate the randomness of neurons firing.  But if we modify a Turing machine slightly so that a spot on its tape read a different random symbol each time you check, I think we’re good.  Given this, it seems reasonable that a modern computer that has a source of truly random data could simulate a brain.  Some have argued that we need quantum computers to simulate consciousness, but I don’t think so.  (Again, more on this later.)

Computers are pretty good at generating psuedo-random data internally, and by listening to the outside world (hard drive vibration, microphones, etc) can generate what is probably actually random data.  If true randomness is really important, we can build small accessory cards that sample thermal noise on
a resistor and produce large volumes of truly (quantum) random data.  Some advanced cryptographic systems do this today.  So it’s totally possible today to build this modified Turing machine that also incorporates random input.

Now our transhuman dilemma is solved.  The essence of free will lies in the quantum randomness of electro-chemical processes in our brain.  Moreover, it will be possible to upload our personalities into computers, complete with our free wills in tact, by incorporating random processes into the hardware that simulates our brains.  If the computers we upload into are only psuedo-random (as almost all software is today), we will appear to have free will, in fact we will believe that we have it, but we will in fact be total robots.  Now, who can come up with a Turing test for free will?

[[Thanks to Barry Brummit.  This article is a rehash of a couple good conversations we had over New Year's and this morning after yoga practice.]]