by Ray Kurzweil
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.
In addition, Church and Turing also advanced, independently, an assertion that has become known as the Church-Turing thesis. This thesis has both weak and strong interpretations. The weak interpretation is that if a problem that can be presented to a Turing machine is not solvable by one, then it is not solvable by any machine. This conclusion follows from Turing’s demonstration that the Turing machine could model any algorithmic process. It is only a small step from there to describe the behavior of a machine as following an algorithm.
The strong interpretation is that problems that are not solvable on a Turing machine cannot be solved by human thought, either. The basis of this thesis is that human thought is performed by the human brain (with some influence by the body), that the human brain (and body) comprises matter and energy, that matter and energy follow natural laws, that these laws are describable in mathematical terms, and that mathematics can be simulated to any degree of precision by algorithms. Therefore there exist algorithms that can simulate human thought. The strong version of the Church-Turing thesis postulates an essential equivalence between what a human can think or know and what is computable.
It is important to note that although the existence of Turing’s unsolvable problems is a mathematical certainty, the Church-Turing thesis is not a mathematical proposition at all. It is, rather, a conjecture that, in various disguises, is at the heart of some of our most profound debates in the philosophy of mind.30
The criticism of strong AI based on the Church-Turing thesis argues the following: since there are clear limitations to the types of problems that a computer can solve, yet humans are capable of solving these problems, machines will never emulate the full range of human intelligence. This conclusion, however, is not warranted. Humans are no more capable of universally solving such “unsolvable” problems than machines are. We can make educated guesses to solutions in certain instances and can apply heuristic methods (procedures that attempt to solve problems but that are not guaranteed to work) that succeed on occasion. But both these approaches are also algorithmically based processes, which means that machines are also capable of doing them. Indeed, machines can often search for solutions with far greater speed and thoroughness than humans can.
The strong formulation of the Church-Turing thesis implies that biological brains and machines are equally subject to the laws of physics, and therefore mathematics can model and simulate them equally. We’ve already demonstrated the ability to model and simulate the function of neurons, so why not a system of a hundred billion neurons? Such a system would display the same complexity and lack of predictability as human intelligence. Indeed, we already have computer algorithms (for example, genetic algorithms) with results that are complex and unpredictable and that provide intelligent solutions to problems. If anything, the Church-Turing thesis implies that brains and machines are essentially equivalent.
To see machines’ ability to use heuristic methods, consider one of the most interesting of the unsolvable problems, the “busy beaver” problem, formulated by Tibor Rado in 1962.31 Each Turing machine has a certain number of states that its internal program can be in, which correspond to the number of steps in its internal program. There are a number of different 4-state Turing machines that are possible, a certain number of 5-state machines, and so on. In the “busy beaver” problem, given a positive integer n, we construct all the Turing machines that have n states. The number of such machines will always be finite. Next we eliminate those n-state machines that get into an infinite loop (that is, never halt). Finally, we select the machine (one that does halt) that writes the largest number of 1s on its tape. The number of 1s that this Turing machine writes is called the busy beaver of n. Rado showed that there is no algorithm—that is, no Turing machine—that can compute this function for all ns. The crux of the problem is sorting out those n-state machines that get into infinite loops. If we program a Turing machine to generate and simulate all possible n-state Turing machines, this simulator itself gets into an infinite loop when it attempts to simulate one of the n-state machines that gets into an infinite loop.
Despite its status as an unsolvable problem (and one of the most famous), we can determine the busy-beaver function for some ns. (Interestingly, it i
s also an unsolvable problem to separate those ns for which we can determine the busy beaver of n from those for which we cannot.) For example, the busy beaver of 6 is easily determined to be 35. With seven states, a Turing machine can multiply, so the busy beaver of 7 is much bigger: 22,961. With eight states, a Turing machine can compute exponentials, so the busy beaver of 8 is even bigger: approximately 1043. We can see that this is an “intelligent” function, in that it requires greater intelligence to solve for larger ns.
By the time we get to 10, a Turing machine can perform types of calculations that are impossible for a human to follow (without help from a computer). So we were able to determine the busy beaver of 10 only with a computer’s assistance. The answer requires an exotic notation to write down, in which we have a stack of exponents, the height of which is determined by another stack of exponents, the height of which is determined by another stack of exponents, and so on. Because a computer can keep track of such complex numbers, whereas the human brain cannot, it appears that computers will prove more capable of solving unsolvable problems than humans will.
The Criticism from Failure Rates
Jaron Lanier, Thomas Ray, and other observers all cite high failure rates of technology as a barrier to its continued exponential growth. For example, Ray writes:
The most complex of our creations are showing alarming failure rates. Orbiting satellites and telescopes, space shuttles, interplanetary probes, the Pentium chip, computer operating systems, all seem to be pushing the limits of what we can effectively design and build through conventional approaches. . . . Our most complex software (operating systems and telecommunications control systems) already contains tens of millions of lines of code. At present it seems unlikely that we can produce and manage software with hundreds of millions or billions of lines of code.32
First, we might ask what alarming failure rates Ray is referring to. As mentioned earlier, computerized systems of significant sophistication routinely fly and land our airplanes automatically and monitor intensive care units in hospitals, yet almost never malfunction. If alarming failure rates are of concern, they’re more often attributable to human error. Ray alludes to problems with Intel microprocessor chips, but these problems have been extremely subtle, have caused almost no repercussions, and have quickly been rectified.
The complexity of computerized systems has indeed been scaling up, as we have seen, and moreover the cutting edge of our efforts to emulate human intelligence will utilize the self-organizing paradigms that we find in the human brain. As we continue our progress in reverse engineering the human brain, we will add new self-organizing methods to our pattern recognition and AI toolkit. As I have discussed, self-organizing methods help to alleviate the need for unmanageable levels of complexity. As I pointed out earlier, we will not need systems with “billions of lines of code” to emulate human intelligence.
It is also important to point out that imperfection is an inherent feature of any complex process, and that certainly includes human intelligence.
The Criticism from “Lock-In”
Jaron Lanier and other critics have cited the prospect of a “lock-in,” a situation in which old technologies resist displacement because of the large investment in the infrastructure supporting them. They argue that pervasive and complex support systems have blocked innovation in such fields as transportation, which have not seen the rapid development that we’ve seen in computation.33
The concept of lock-in is not the primary obstacle to advancing transportation. If the existence of a complex support system necessarily caused lock-in, then why don’t we see this phenomenon affecting the expansion of every aspect of the Internet? After all, the Internet certainly requires an enormous and complex infrastructure. Because it is specifically the processing and movement of information that is growing exponentially, however, one reason that an area such as transportation has reached a plateau (that is, resting at the top of an S-curve) is that many if not most of its purposes have been satisfied by exponentially growing communication technologies. My own organization, for example, has colleagues in different parts of the country, and most of our needs that in times past would have required a person or a package to be transported can be met through the increasingly viable virtual meetings (and electronic distribution of documents and other intellectual creations) made possible by a panoply of communication technologies, some of which Lanier himself is working to advance. More important, we will see advances in transportation facilitated by the nanotechnology-based energy technologies I discussed in chapter 5. However, with increasingly realistic, high-resolution full-immersion forms of virtual reality continuing to emerge, our needs to be together will increasingly be met through computation and communication.
As I discussed in chapter 5, the full advent of MNT-based manufacturing will bring the law of accelerating returns to such areas as energy and transportation. Once we can create virtually any physical product from information and very inexpensive raw materials, these traditionally slow-moving industries will see the same kind of annual doubling of price-performance and capacity that we see in information technologies. Energy and transportation will effectively become information technologies.
We will see the advent of nanotechnology-based solar panels that are efficient, lightweight, and inexpensive, as well as comparably powerful fuel cells and other technologies to store and distribute that energy. Inexpensive energy will in turn transform transportation. Energy obtained from nanoengineered solar cells and other renewable technologies and stored in nanoengineered fuel cells will provide clean and inexpensive energy for every type of transportation. In addition, we will be able to manufacture devices—including flying machines of varying sizes—for almost no cost, other than the cost of the design (which needs to be amortized only once). It will be feasible, therefore, to build inexpensive small flying devices that can transport a package directly to your destination in a matter of hours without going through intermediaries such as shipping companies. Larger but still inexpensive vehicles will be able to fly people from place to place with nanoengineered microwings.
Information technologies are already deeply influential in every industry. With the full realization of the GNR revolutions in a few decades, every area of human endeavor will essentially comprise information technologies and thus will directly benefit from the law of accelerating returns.
The Criticism from Ontology: Can a Computer Be Conscious?
Because we do not understand the brain very well we are constantly tempted to use the latest technology as a model for trying to understand it. In my childhood we were always assured that the brain was a telephone switchboard. (“What else could it be?”) I was amused to see that Sherrington, the great British neuroscientist, thought that the brain worked like a telegraph system. Freud often compared the brain to hydraulic and electromagnetic systems. Leibniz compared it to a mill, and I am told some of the ancient Greeks thought the brain functions like a catapult. At present, obviously, the metaphor is the digital computer.
—JOHN R. SEARLE, “MINDS, BRAINS, AND SCIENCE”
Can a computer—a nonbiological intelligence—be conscious? We have first, of course, to agree on what the question means. As I discussed earlier, there are conflicting perspectives on what may at first appear to be a straightforward issue. Regardless of how we attempt to define the concept, however, we must acknowledge that consciousness is widely regarded as a crucial, if not essential, attribute of being human.34
John Searle, distinguished philosopher at the University of California at Berkeley, is popular among his followers for what they believe is a staunch defense of the deep mystery of human consciousness against trivialization by strong-AI “reductionists” like Ray Kurzweil. And even though I have always found Searle’s logic in his celebrated Chinese Room argument to be tautological, I had expected an elevating treatise on the paradoxes of consciousness. Thus it is with some surprise that I find Searle writing statements such as,
“human
brains cause consciousness by a series of specific neurobiological processes in the brain”;
“The essential thing is to recognize that consciousness is a biological process like digestion, lactation, photosynthesis, or mitosis”;
“The brain is a machine, a biological machine to be sure, but a machine all the same. So the first step is to figure out how the brain does it and then build an artificial machine that has an equally effective mechanism for causing consciousness”; and