The Singularity Is Near: When Humans Transcend Biology (83 page)

The point here is that a simple design rule can create a lot of apparent complexity. Stephen Wolfram makes a similar point using simple rules on cellular automata (see
chapter 2
). This insight holds true for the brain’s design. As I’ve discussed, the compressed genome is a relatively compact design, smaller than some contemporary software programs. As Bell points out, the actual implementation of the brain appears far more complex than this. Just as with the
Mandelbrot set, as we look at finer and finer features of the brain, we continue to see apparent complexity at each level. At a macro level the pattern of connections looks complicated, and at a micro level so does the design of a single portion of a neuron such as a dendrite. I’ve mentioned that it would take at least thousands of trillions of bytes to characterize the state of a human brain, but the design is only tens of millions of bytes. So the ratio of the apparent complexity of the brain to the design information is at least one hundred million to one. The brain’s information starts out as largely random information, but as the brain interacts with a complex environment (that is, as the person learns and matures), that information becomes meaningful.

The actual design complexity is governed by the compressed information in the design (that is, the genome and supporting molecules), not by the patterns created through the iterative application of the design rules. I would agree that the roughly thirty to one hundred million bytes of information in the genome do not represent a simple design (certainly far more complex than the six characters in the definition of the Mandelbrot set), but it is a level of complexity that we can already manage with our technology. Many observers are confused by the apparent complexity in the brain’s physical instantiation, failing to recognize that the fractal nature of the design means that the actual design information is far simpler than what we see in the brain.

I also mentioned in
chapter 2
that the design information in the genome is a probabilistic fractal, meaning that the rules are applied with a certain amount of randomness each time a rule is iterated. There is, for example, very little information in the genome describing the wiring pattern for the cerebellum, which comprises more than half the neurons in the brain. A small number of genes describe the basic pattern of the four cell types in the cerebellum and then say in essence, “Repeat this pattern several billion times with some random variation in each repetition.” The result may look very complicated, but the design information is relatively compact.

Bell is correct that trying to compare the brain’s design to a conventional computer would be frustrating. The brain does not follow a typical top-down (modular) design. It uses its probabilistic fractal type of organization to create processes that are chaotic—that is, not fully predictable. There is a well-developed body of mathematics devoted to modeling and simulating chaotic systems, which are used to understand phenomena such as weather patterns and financial markets, that is also applicable to the brain.

Bell makes no mention of this approach. He argues why the brain is dramatically different from conventional logic gates and conventional software design, which leads to his unwarranted conclusion that the brain is not a
machine and cannot be modeled by a machine. While he is correct that standard logic gates and the organization of conventional modular software are not the appropriate way to think about the brain, that does not mean that we are unable to simulate the brain on a computer. Because we can describe the brain’s principles of operation in mathematical terms, and since we can model any mathematical process (including chaotic ones) on a computer, we are able to implement these types of simulations. Indeed, we’re making solid and accelerating progress in doing so.

Despite his skepticism Bell expresses cautious confidence that we will understand our biology and brains well enough to improve on them. He writes: “Will there be a transhuman age? For this there is a strong biological precedent in the two major steps in biological evolution. The first, the incorporation into eukaryotic bacteria of prokaryotic symbiotes, and the second, the emergence of multicellular life-forms from colonies of eukaryotes. . . . I believe that something like [a transhumanist age] may happen.”

The Criticism from Microtubules and Quantum Computing

Quantum mechanics is mysterious, and consciousness is mysterious.
Q.E.D.: Quantum mechanics and consciousness must be related.

                   —C
HRISTOF
K
OCH, MOCKING
R
OGER PENROSE’S THEORY OF QUANTUM COMPUTING IN NEURON TUBULES AS THE SOURCE OF HUMAN CONSCIOUSNESS
²¹

Over the past decade Roger Penrose, a noted physicist and philosopher, in conjunction with Stuart Hameroff, an anesthesiologist, has suggested that fine structures in the neurons called microtubules perform an exotic form of computation called “quantum computing.” As I discussed, quantum computing is computing using what are called qubits, which take on all possible combinations of solutions simultaneously. The method can be considered to be an extreme form of parallel processing (because every combination of values of the qubits is tested simultaneously). Penrose suggests that the microtubules and their quantum-computing capabilities complicate the concept of re-creating neurons and reinstantiating mind files.
²²
He also hypothesizes that the brain’s quantum computing is responsible for consciousness and that systems, biological or otherwise, cannot be conscious without quantum computing.

Although some scientists have claimed to detect quantum wave collapse (resolution of ambiguous quantum properties such as position, spin, and
velocity) in the brain, no one has suggested that human capabilities actually require a capacity for quantum computing. Physicist Seth Lloyd said:

I think that it is incorrect that microtubules perform computing tasks in the brain, in the way that [Penrose] and Hameroff have proposed. The brain is a hot, wet place. It is not a very favorable environment for exploiting quantum coherence. The kinds of superpositions and assembly/disassembly of microtubules for which they search do not seem to exhibit quantum entanglement. . . . The brain clearly isn’t a classical, digital computer by any means. But my guess is that it performs most of its tasks in a “classical” manner. If you were to take a large enough computer, and model all of the neurons, dendrites, synapses, and such, [then] you could probably get the thing to do most of the tasks that brains perform. I don’t think that the brain is exploiting any quantum dynamics to perform tasks.
²³

Anthony Bell also remarks that “there is no evidence that large-scale macroscopic quantum coherences, such as those in superfluids and superconductors, occur in the brain.”
²⁴

However, even if the brain does do quantum computing, this does not significantly change the outlook for human-level computing (and beyond), nor does it suggest that brain uploading is infeasible. First of all, if the brain does do quantum computing this would only verify that quantum computing is feasible. There would be nothing in such a finding to suggest that quantum computing is restricted to biological mechanisms. Biological quantum-computing mechanisms, if they exist, could be replicated. Indeed, recent experiments with small-scale quantum computers appear to be successful. Even the conventional transistor relies on the quantum effect of electron tunneling.

Penrose’s position has been interpreted to imply that it is impossible to perfectly replicate a set of quantum states, so therefore perfect downloading is impossible. Well, how perfect does a download have to be? If we develop downloading technology to the point where the “copies” are as close to the original as the original person is to him- or herself over the course of one minute, that would be good enough for any conceivable purpose yet would not require copying quantum states. As the technology improves, the accuracy of the copy could become as close as the original to within ever briefer periods of time (one second, one millisecond, one microsecond).

When it was pointed out to Penrose that neurons (and even neural connections) were too big for quantum computing, he came up with the tubule theory
as a possible mechanism for neural quantum computing. If one is searching for barriers to replicating brain function it is an ingenious theory, but it fails to introduce any genuine barriers. However, there is little evidence to suggest that microtubules, which provide structural integrity to the neural cells, perform quantum computing and that this capability contributes to the thinking process. Even generous models of human knowledge and potential are more than accounted for by current estimates of brain size, based on contemporary models of neuron functioning that do not include microtubule-based quantum computing. Recent experiments showing that hybrid biological/nonbiological networks perform similarly to all-biological networks, while not definitive, are strongly suggestive that our microtubuleless models of neuron functioning are adequate. Lloyd Watts’s software simulation of his intricate model of human auditory processing uses orders of magnitude less computation than the networks of neurons he is simulating, and again there is no suggestion that quantum computing is needed. I reviewed other ongoing efforts to model and simulate brain regions in
chapter 4
, while in
chapter 3
I discussed estimates of the amount of computation necessary to simulate all regions of the brain based on functionally equivalent simulations of different regions. None of these analyses demonstrates the necessity for quantum computing in order to achieve human-level performance.

Some detailed models of neurons (in particular those by Penrose and Hameroff) do assign a role to the microtubules in the functioning and growth of dendrites and axons. However, successful neuromorphic models of neural regions do not appear to require microtubule components. For neuron models that do consider microtubules, results appear to be satisfactory by modeling their overall chaotic behavior without modeling each microtubule filament individually. However, even if the Penrose-Hameroff tubules are an important factor, accounting for them doesn’t change the projections I have discussed above to any significant degree. According to my model of computational growth, if the tubules multiplied neuron complexity by even a factor of one thousand (and keep in mind that our current tubuleless neuron models are already complex, including on the order of one thousand connections per neuron, multiple nonlinearities, and other details), this would delay our reaching brain capacity by only about nine years. If we’re off by a factor of one million, that’s still a delay of only seventeen years. A factor of a billion is around twenty-four years (recall that computation is growing by a double exponential).
²⁵

The Criticism from the Church-Turing Thesis

Early in the twentieth century mathematicians Alfred North Whitehead and Bertrand Russell published their seminal work,
Principia Mathematica
, which sought to determine axioms that could serve as the basis for all of mathematics.
²⁶
However, they were unable to prove conclusively that an axiomatic system that can generate the natural numbers (the positive integers or counting numbers) would not give rise to contradictions. It was assumed that such a proof would be found sooner or later, but in the 1930s a young Czech mathematician, Kurt Gödel, stunned the mathematical world by proving that within such a system there inevitably exist propositions that can be neither proved nor disproved. It was later shown that such unprovable propositions are as common as provable ones. Gödel’s incompleteness theorem, which is fundamentally a proof demonstrating that there are definite limits to what logic, mathematics, and by extension computation can do, has been called the most important in all mathematics, and its implications are still being debated.
²⁷

A similar conclusion was reached by Alan Turing in the context of understanding the nature of computation. When in 1936 Turing presented the Turing machine (described in
chapter 2
) as a theoretical model of a computer, which continues today to form the basis of modern computational theory, he reported an unexpected discovery similar to Gödel’s.
²⁸
In his paper that year he described the concept of unsolvable problems—that is, problems that are well defined, with unique answers that can be shown to exist, but that we can also show can never be computed by a Turing machine.

The fact that there are problems that cannot be solved by this particular theoretical machine may not seem particularly startling until you consider the other conclusion of Turing’s paper: that the Turing machine can model any computational process. Turing showed that there are as many unsolvable problems as solvable ones, the number of each being the lowest order of infinity, the so-called countable infinity (that is, counting the number of integers). Turing also demonstrated that the problem of determining the truth or falsity of any logical proposition in an arbitrary system of logic powerful enough to represent the natural numbers was one example of an unsolved problem, a result similar to Gödel’s. (In other words, there is no procedure guaranteed to answer this question for all such propositions.)

Around the same time Alonzo Church, an American mathematician and philosopher, published a theorem that examined a similar question in the context of arithmetic. Church independently came to the same conclusion as Turing.
²⁹
Taken together, the works of Turing, Church, and Gödel were the first
formal proofs that there are definite limits to what logic, mathematics, and computation can do.