At the smallest scale

How does our world appear at the smallest scale? Is it point particles, strings, twistors or something else? If it is point particles without any special features, then I would suggest that it is necessary for our universe to have a lot more than the four dimensions that we often speak of. If it were only a point in four dimensional space; how would it know how to react to the forces of nature, how could it remember its velocity and direction at any given time, where would all this information be stored? No, I would guess that it would require at least 10 dimensions for point particles to work.
The recent discoveries in string theory (or more correct; M-theory) suggests that it would be necessary for the universe to have 11 dimensions, which I find is a very interesting result.
Note that I'm referring to either internal dimensions or spatial dimensions here. I reckon that it doesn't matter that much of which form the extra dimensions are, you could probably not find "shortcuts" from two widely separated locations in 4D-space by moving in the extra dimensions anyway. But the exact number of dimensions is interesting in finding out how to mathematically represent elementary forms; be it complex numbers, quaternions or octonions (for example).

Quantum theory explains that you cannot know everything in detail about extremely small bits of matter and energy. If we stick with the point particle view of the world for now, the theory says that whenever a particle is not observed it can be described more like a wave function of probabilities. It is at first when we want to observe the particle that it chooses one of the many positions it could have had.

What causes the wave function to collapse?

I find it more likely to be due to one of the following two explanations: The last point of view has many resemblances with the theory of mind and matter that the Buddhist tradition has investigated for over 2500 years. In fact, this is the last thing that still leaves the door open to living entities having a free will. If the hidden variables view is true, then everything would be deterministic and we could not move beyond what's dictated by the mathematics of the fundamental forces.

Stepping away from our time's local maxima

The possible synergy between thousands of years of research by the Buddhists and modern Quantum Gravity is enticing. The view that nothing exists and that consciousness is fundamental and in turn creates matter and energy will, I hope, inspire some theoretical physiscists to make another lateral leap from where we stand now. The current standings seems like we're about to reach a local maxima very soon where we can't move on and make any progress from. Much like the situation in the late 19th century. Scientists claimed that "soon we know all there is to know". But then there came some new groundbreaking ideas from outstanding persons, most notably perhaps is Albert Einstein. With his totally lateral steps from the old ideas, new progress emerged like wild flowers. But perhaps we're about to reach another local maxima soon and new lateral steps has to be made.

Is it possible to simulate human behaviour by a deterministic machine?

I would say that if it's possible to simulate the human consciousness with only the help of a modern computer (although: NOT a quantum computer) then the view that consciousness would be fundamental must be thrown away.
Chances are that if we do not succeed in mimicing consciousness with traditional computers, then we might succeed with quantum computers. With quantum computers we would have the opportunity to tap information from whatever lies behind the collapse of the wave function.
In particular one leading scientist, Roger Penrose, claims that consciousness involves non-computational parts. Theses non-computational parts would have their origin in microtubules within brain cells. These microtubules would tap the quantum field on information, possibly amplify the effects of the quantum world to make input to the computational brain.
Currently I myself is doing a lot of work, research and thinking on this matter. I've developed some simulations of very primitive robots that evolve during generations. The motor behind each robot, that does all the thinking, is one or several interconnected Spiking Neural Nets. The aim is to be able to create a thinking entity from just pure deterministic calculations. However, just a single neuron in the brain is very complex and no one completely understands the full workings of a single neuron as of today. To create a thinking entity from the simplified leaky-fire-and-integrate neuron model is not perhaps very realistic. But it is good for zombie-like tasks, like "must have food", "must not be eaten" etc.

Spiking Neural Networks

One of the latest and most interesting models of parts of the brain is the Spiking Neural Net. The brain consists of about 200 billions of spiking neurons, connected to each other in various complex patterns. Not all of the 200 billion neurons are connected to each other, but groups of hundreds to millions of neurons forms different centers of the brain. These centers are then connected to other centers on electrical highways. Much like people living together in cities, and the cities are connected to each other forming countries. The countries are then connected to each other forming the global perspective. In this analogy you might argue that our planet would be a thinking entity! I myself find that thought very thoughtful...
The leaky fire-and-integrate neuron model I mentioned above works as follows; each neuron has thousands of input wires from other neurons. When a sufficiently large number of the neurons on the input wires fires, the neuron that gets the impulses also fires. This is spatial integration. If not all input neurons fire at the same time, but a sufficiently large number of neurons fire over time, the neuron will also fire. This is temporal integration.
The model thus becomes sensitive to actions taking place in the room (many neurons firing at the same time) and over time (many neurons firing after each other). This is very important in forming short term memory.
For details on how to implement a Spiking Neural Network in a computer program, have a look at The Spiking Neural Net Tutorial.

How to make the neural network learn anything?

This is my most current research project. I haven't so far been able to construct a theoretical model on how learning works. The robots I mentioned earlier have simply competed against each other, and when it is time for mating season, only the most fitted robots will be parents. The offspring is then a combination of its parents' genes, possibly slightly mutated. After a number of generations, a more and more fitted individual will take form.
But this behaviour isn't any good for one robot learning of its own mistakes.
And the mathematical function you create to measure an individual's fitness becomes all too important. Often the entities that evolve finds a very low energy solution to the fitness function, like just spinning in circles at the place they're standing at.
So how to learn a network something?
I guess we must take something for granted. I would think that certain input (for example too much pressure on the nervecells under the skin) maps directly to negative behaviour. And this would be hardcoded in each individual. Perhaps certain chemical substances are released when the signal "negative behaviour" is triggered. Maybe these substances alters or in some way interacts with the most recent active signals sent between neurons. Like a pair of neurons remembering that they have communicated for an amount of milliseconds after the actual communication. And if the negative signal occurs within this period, the communication ability is slightly decreased. So the next time a similiar behaviour occurs the chance is lower of the result being negative again.