Introduction

Vernor Steffen Vinge suggested that there will be a 'singularity' event in the future where it will no longer be possible to predict the future evolution of technology because computers will start designing themselves. Typically, works with this thesis extrapolate Moore's law curves to a point where the number of transistors per commercial microprocessor die reaches the same number as neurons in the brain. Such crossings are typically found to occur in 10 or 20 years.

I have used this metric for measuring intelligence in talks of my own. I used the dendrite equivalence to a transistor rather than neuron equivalence and calculated a crossing in the year 2042, but I question the accuracy of jumping from transistor counts per die to brain power, as discussed below. I also disagree that there exists such a time as the singularity. In this paper, I suggest a different and more colorful future for computing machinery than a singularity, that of encapsulating the apotheosis of mankind.

What is a Singularity?

A singularity is a point in a coordinate system where axes cross. For example, on the sphere of the earth, there are singularities at the poles. Coordinate singularities create mathematical 'features' at positions that may not otherwise be special. In this sense, they may be artificial. Consider, for example, the latitude and longitude lines used for navigation over the earth. The earth happens to be rotating so the singularities appear to have meaning when placed at the ends of this axis of rotation. This aligns the coordinate artifacts with a physical feature. But this is an arbitrary choice for a physical feature. Why not, for example, place the singularities at the magnetic north and south poles? This would have the advantage of making compasses more accurate. If a large rock flew in from space, the axis of rotation could change in a short period of time; chances are we would leave the orthonormal longitude and latitude lines where they are. For purposes of correlating position points on maps, we could have just as easily placed the singularities on what is now the equator. In fact, the coordinate singularity distracts from the fact that all locations on a sphere are indistinguishable against many familiar metrics and thus can be seen as an inconvenient and undesirable artifact of the math.

It is common to use a grid of orthotropic lines in a wireframe to illustrate curvature of space-time in general relativity theory. This makes gravity wells look like hoops descending down into a hole. There is a singularity at the center of the black hole. Because of the math, the term 'singularity' became a colloquial term for a black hole. Our early understanding of black holes was lacking, and that vacuum left space for the imagination. This is still the case today, but not as much so as 20 years ago.

Human beings will not fall down a black hole the day a robot designs another; the axis of the earth will not change location. I argue further below that technology curves such as Moore's law will not even have discontinuities.

Moore's Law and Intelligence

Because Moore's law is exponential, small multiplying factors do not affect the results of crossing a particular threshold by much. For example, if the transistor count was off by a factor of 2, that would affect the time axis by only 18 months. An error factor of 1024 in count would shift the time axis by 180 months, or 15 years.

So what can be done for an intelligence test? The Turing Test is an intelligence parity test, but it is anecdotal rather than scientific. No underlying model exists to justify it. The suggested metric in this case is to look at a computer designed by another computer, and to see if it is better than the original, but again, by what metric? For that matter, we don't really even know how to define intelligence for humans. Without the bridge from transistor count to intelligence, we really don't know the meaning of a crossing between neuron and transistor counts.

Transistors surely have something to do with artificial intelligence; at the least, we might say that Moore's law is modeling the facilitation of artificial intelligence rather than modeling intelligence itself. There is a lot of missing science between having a platform that is even speculated to theoretically facilitate human-like intelligence and having that intelligence. In addition, there is no reason to expect that even if this facilitated intelligence existed, it would be helped by the number of transistors available. We can observe today even with simple computer programs many cases where putting more transistors in the processor does not make a program faster or more efficient. For example, there are quickly diminishing returns when expanding cache memory.

On the human side, today we have only a vague idea of how the brain works. We don't know if neuron counts are related to intelligence or are even atomic computation units. It is likely that single neuron computation exists both in the dendritic connections and in the soma. It is possible that the neuron itself is a brain, and what we witness when looking at an individual action potential propagating down an axon is more akin to a vote than the output from a switching transistor.

If the crossing point with transistor counts happens to have meaning, but we count dendritic connections rather than neurons, we must multiply the transistor count before a crossing by around 10,000. If the neuron is in fact or sort of a voting brain, then one must roughly square the count. Being off in the 'count' by a factor of 4 billion on Moore's curve would be 32 doubling cycles, or about 50 years.

From an architectural point of view, we see that human architecture is unchanging. It is determined by the same DNA today as 10,000 years ago. The DNA itself encapsulates interspecies learning gathered over generations affected by selection from the environment. Thus, the neural circuits are metadesigned by evolution to perform types of functions. Today we can only broadly classify these as brain regions.

Computer architecture also carries a weighty history, though one of decades rather than of epochs, but these circuits are being created by brains, and in a fashion reflect the brain architecture. Computer architecture is becoming more like brain architecture. It is little wonder that the most recent theory of how the brain works in psychology often comes from computer science. This might indicate that the missing science that would provide a bridge from transistor counts through architecture and to intelligence might be coming into view.

There does exist a parallel accelerated development of transistor counts per die and the rest of the technology fabric. People are making steady progress on discovering missing pieces to the puzzle. Also, 60 years instead of 10 years does not push the problem into the territory of unimaginable. So from an intuitive point of view while looking at all the work and progress being done, with Moore's law holding up as an example of such progress, it does appear that someday there will be computers that have such human-like intelligence that they can design computers. I don't know when but it seems likely that at least our grandchildren will see it happen.

Apotheosis

The apotheosis is the time when humans reach divinity. This is a better term for the time when computers reach a level of intelligence comparable to that of humans for a number of reasons.

Firstly, one has to ask, "so what?" We already have nearly 7 billion brains on the planet, soon to be more. There is no shortage of 'human-like' brainpower. Our problem in society is not the availability of brains, rather it is in providing existing people an education and 'enlightenment' to have the desire to be constructive, and to provide people with education and the resources required to make life for the lot of us better. It may in fact be more important to develop an understanding of this 'enlightenment' than to put more transistors on a die should we want computer intelligence to participate in creating a better world.

Secondly, computers already contribute to the design of computers. Some science fiction writers would probably be surprised to find out the extent of this. It is already a large part of what is driving Moore's law. CAD tools, design synthesis, mathematical modeling of physics - these are a large part of all technology development in the first place. Hence, it is not clear if the concept of an inflection point is valid. It appears more likely that this effect of better computers will continue to be an important contributor to maintaining the current exponential rate of advance in many fields of endeavor with no discontinuity in the curves measuring technological achievement.

It follows that it is not the case that all ability to predict the future gets sucked down a black hole when computers can design computers. Rather we can expect to continue to achieve solutions to our problems today in modeling and controlling the weather; in providing energy to our homes, cities, and industry; in continued exploration of space and understanding of the cosmos; in creating an efficient economy, etc. Our problems will neither disappear immediately nor remain unsolved; rather there will continue to be incremental advance as today.

Thirdly, human intelligence is not a constant. The human mind cannot be considered to be limited to the boundaries of the skull. Human intelligence spans society, and due to exosomatic memory such as books and computer data, it extends over time as well. Intelligence is like the surface area of a crystal: the more knowledge we develop, the more knowledge we are capable of. The more philosophy that exists, the more advanced philosophy can become, etc. Improvements in techniques in education have brought the level of knowledge adults were capable of gaining in a lifetime in the past to the children of today.

Descartes's analytical geometry, which was advanced degree study, is now taught to 7^th graders. The limit to this trend is being removed by the creation of the computer. What we are doing is passing the flame given to us by Prometheus to the next generation of intelligence. Among our children to be taught in the future will be ones who have brains of a different substrate, and like our children now, their minds will absorb knowledge like a sponge absorbs water. However, rather than the geometry of Descartes being parochial, these children will start with a database that contains all human knowledge and then work forward from there. They will be the children of the human apotheosis.

As many writers have pointed out, the substrate of the children of the apotheosis will have many advantages. Because they will not have to eat organic bulk nor breathe oxygen in quantity, they will be able to continue the trend of populating this planet, and other parts of the solar system. Due to data backups and part replacements, their life spans will be without physical bound. Due to networking and complete ability to communicate, they will exist more as a hive than humans do now. All current trends continue their natural course.