# ‘The Singularity is Near’ by Ray Kurzweil

2018-03-22

Kurzweil published The Singularity Is Near: When Humans Transcend Biology in 2005 and predicted that human life will be transformed to transcend the current biological limitations from 2045 on. More and more people believe in the technological singularity as artificial intelligence approaches human intelligence. But is his Singularitarianism worth believing? Here I critically examine whether his prediction is correct or not.

## 1 : Why IT evolves exponentially?

Since 1980s Kurzweil[1] has appreciated a belief that “the power of ideas to transform the world is itself accelerating[2]”. Like Moravec[3] he generalizes Moore’s Law and predicts the exponential evolution of information technology in general.

During the 1990s, I gathered empirical data on the apparent acceleration of all information-related technologies and sought to refine the mathematical models underlying these observations. I developed a theory I call the law of accelerating returns, which explains why technology and evolutionary processes in general progress in an exponential fashion.[4]

The law of accelerating returns is based on the positive feedback: “the more capable methods resulting from one stage of evolutionary progress are used to create the next stage.[5].” We can find positive feedback in information-related technologies in general.

Let’s take the invention of letters as an example. Before letters were invented, the future generations often could not succeed it, even if someone made an important invention. Letters have enabled humans to inherit the wisdom of the predecessor effectively without depending on their unreliable memory and utilize it for new inventions. In this sense, the invention of letters was not only a great invention in itself but also an invention that accelerated further inventions. The invention of movable type printing, broadcasting, computers, the Internet, and artificial intelligence are of this kind.

The invention whose positive feedback currently attracts the most attention is artificial intelligence. It was owing to the third “AI summer” beginning in 2006 when Geoff Hinton et al. published the algorithm for deep learning[6] that Kurzweil’s book published in 2005 (still in AI winter) had a strong influence on the world. AI has made a major evolution since then and has now entered a new stage where AI improves itself.

Google Brain team created AI that created its own child. Their approach named AutoML “can design models that achieve accuracies on par with state-of-art models designed by machine learning experts[7].” Thereafter Google DeepMind created AlphaGo Zero, a machine-learning program that plays the board game Go. It teaches itself from scratch without human data, guidance or domain knowledge beyond game rules, and yet won 100–0 against the previously published, champion-defeating AlphaGo that ingested thousands of human example games[8]. Though in a limited field, artificial intelligence has evolved to a new stage where it no longer needs to learn from lower beings like humans.

Kurzweil shows mathematically that the positive feedback results in exponential growth[9]. He supposes the velocity of computation (V measured in calculations per second per unit cost) is proportional to world knowledge (W):

$V = c_{1}W$

where c is a constant. The rate of change of world knowledge is proportional to the velocity of computation:

$\frac{dW}{dt} = c_{2}V$

where t is time. Two equations indicate the positive feedback: the increase in information processing improves knowledge and the improvement in knowledge increases information processing. Substituting Eq.1 into Eq.2 gives:

$\frac{dW}{dt} = c_{1}c_{2}W$

You can apply the method of separation of variables to Eq.3:

$\int \frac{dW}{W} = \int c_{1}c_{2}dt$
$lnW = c_{1}c_{2}t+c_{3}$
$W = e^{c_{1}c_{2}t+c_{3}} =e^{c_{1}c_{2}t} e^{c_{3}} =c_{4}e^{c_{1}c_{2}t}$

If W=W0 when t=0, then we get its particular solution of the differential equation (e is the base of the natural logarithms).

$W = W_{0}\: e^{c_{1}c_{2}t}$

It means that W grows exponentially with time.

## 2 : The exponential growth of the exponent

Kurzweil insists that the rate of exponential growth ― the exponent ― itself grows exponentially if the application range of Moore’s Law of integrated circuits is extended to the earlier signal conversion paradigms, namely electromechanical punched card tabulator, relays, vacuum tubes, and discrete transistors. Although the vertical axis of Fig.0. shows the calculations per second per 1000 dollars on a logarithmic scale, it seems to grow exponentially with time.

If we project these computational performance trends through this next century, we can see in the figure below that an average computer will match the average human brain capability by around 2020 and the entire human brain capability by around the middle of the 21st century.

To explain the exponential growth of the exponent, Kurzweil includes the fact that the resources deployed for computation, N, are also growing exponentially:

$N=c_{5}e^{c_{6}t}$

The rate of change of world knowledge is now proportional to the product of the velocity of computation and the deployed resources:

$\frac{dW}{dt} = c_{2}NV$

Substituting Eq.8 and Eq.1 into Eq.9 we get:

$\frac{dW}{dt} = c_{1}c_{2}c_{5}e^{c_{6}t}W$

You can apply the method of separation of variables to Eq.10:

$\int \frac{dW}{W} = \int c_{1}c_{2}c_{5}e^{c_{6}t}dt$
$lnW = \frac{c_{1}c_{2}c_{5}}{c_{6}}e^{c_{6}t}+c_{7}$
$W = e^{\frac{c_{1}c_{2}c_{5}}{c_{6}}e^{c_{6}t}+c_{7}} =e^{c_{8}e^{c_{6}t}} e^{c_{7}}=c_{9}\: e^{c_{8}e^{c_{6}t}}$

This solution[12] indicates that world knowledge accumulates at a double exponential rate with time. Factoring in this rate Kurzweil predicts “that nonbiological intelligence will be billions of times more powerful than biological intelligence before the middle of the century[13]”. That is why he proclaims that the singularity is near (around 2045).

According to him the singularity is “a future period during which the pace of technological change will be so rapid, its impact so deep, that human life will be irreversibly transformed.[14]” Is his definition appropriate? In the next section, we will examine the original definition of the term to verify it.

## 3 : What is the original definition of the singularity?

Kurzweil owes the concept “singularity” to Vinge[15]'s 1993 essay “The Coming Technological Singularity[16]." In this essay, Vinge expected the technological singularity where the creation of entities with greater than human intelligence would bring about the physical extinction of the human race. As for this term, he mentions John von Neumann’s usage in the 1950s.

One conversation centered on the ever accelerating progress of technology and changes in the mode of human life, which gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue.[17]

Although von Neumann did not mean “singularity” as the creation of superhuman intellect, he as well as Vinge rightly regarded the singularity as an undesirable end of their days.

The term singularity in mathematics, as Kurzweil admits, means a point where a function has an undefined (infinite or not differentiable) value in mathematics.

“Singularity” is an English word meaning a unique event with, well, singular implications. The word was adopted by mathematicians to denote a value that transcends any finite limitation, such as the explosion of magnitude that results when dividing a constant by a number that gets closer and closer to zero. Consider, for example, the simple function y=1/x. As the value of x approaches zero, the value of the function (y) explodes to larger and larger values.[18]

To be sure, as the value of x approaches zero, the value of y explosively increases. It is, however, not a singularity, no matter how large it is, if it is a finite value. It can be a singularity only when x=0. Kurzweil sets the date for the Singularity as 2045 by which one thousand dollars’ worth of computation will be equal to 1026 cps (calculations per second) and the intelligence created per year will be about one billion times more powerful than all human intelligence today[19]. The figures are huge but limited. The year 2045 would, as he predicts, bring about a profound and disruptive transformation in human capability, but it is not the mathematically defined singularity.

As the exponential functions Eq.7 and Eq.13 output no infinite values if t is a finite argument, Kurzweil plays shrewd tricks on the differential equation of the growth rate of world knowledge to make its solution output a mathematical singularity[20]. For example, he devises a new form of the growth rate of W (C > 1):

$\frac{dW}{dt} = C^{W}$

He claims that the solution should be

$W=\frac{1}{lnC}ln\left ( \frac{1}{1-tlnC} \right )$

which explodes close to the singularity at t=1/lnC. Another form is:

$\frac{dW}{dt} = W^{a}$

where a > 1. He insists that it should lead to a solution:

$W=W_{0}\: \frac{1}{\left (T-t \right )^{\frac{1}{a-1}}}$

which results in a singularity when t=T. These hypotheses and solutions are doubtful and I think they are false.

It is probably because Kurzweil regards the technological singularity as an epoch-making event symbolizing the dramatic progress in technology that he is trying to devise solutions that output the mathematical singularity. However, such a positive evaluation of the singularity is different from the general perception by scientists.

A theory of physics is considered to be a failure when it results in a singularity. For example, Newton’s law of universal gravitation

$F= G \frac{M m}{r^2}$

entails a singularity, when r, the distance between two centers of the masses, M, m, becomes zero and thus F, the force between them, becomes infinite. Fortunately for physicists, it does not really happen so long as bodies are not geometrically defined points.

In physics “singularity” theoretically refers to a point of zero size with infinite density of mass and therefore infinite gravity. But because of quantum uncertainty there is no actual point of infinite density, and indeed quantum mechanics disallows infinite values.[21]

The density of matter was thought to become infinite at the center of a black hole or at the big bang forming a gravitational singularity, which physicists are now trying to eliminate applying a string theory.

A singularity is a disease that an empirical science must cure to be consistent and non-contradictory. Strangely, however, the singularity for Kurzweil is not a disease to cure but a goal to aim for. His usage of the singularity is obviously different from the traditional usage by scientists.

His Singularitarianism is comprehensible not as science, but as religion. In fact, he says, “we need a new religion[22].” Religion will favorably affirm a miracle as such, while science will try to explain what seems to be a miracle in terms of non-miracle laws. Similarly, Kurzweil favorably affirms the singularity that scientists try to avoid. Maybe he means the singularity as eschatological transcendence and reunion with God. In this sense, Singularitarianism may well be “a religious rather than a scientific vision[23]” or “an apocalyptic cult masquerading as science[24].”

## 4 : Did Kurzweil’s predictions come true?

As of March 2018, more than 12 years have passed since The Singularity Is Near was first published. We can now verify some of Kurzweil’s predictions. He said supercomputers would have the same computing power as human brains by 2010.

We will have the requisite hardware to emulate human intelligence with supercomputers by the end of this decade and with personal-computer-size devices by the end of the following decade. We will have effective software models of human intelligence by the mid-2020s.[25]

Dharmendra Modha, director of cognitive computing at the IBM Almaden Research Center, estimated a computer comparable to the human brain to be able to perform more than 38 petaflops (PFlop/s) of processing power[26]. The figure below shows that the top supercomputer of the world (brown triangles) did not attain this goal by 2010.

The figure also indicates the growth of the top supercomputing power was not more than exponential as Kurzweil expected, but less from 2013 on.

What about the following 2010 scenario?

Computers arriving at the beginning of the next decade will become essentially invisible: woven into our clothing, embedded in our furniture and environment. […] Displays will be built into our eyeglasses and contact lenses and images projected directly onto our retinas.[28]

As he predicted, some attempted to disseminate wearable computers. For example, Google where he belongs publicly announced Google Glass, eyeglasses with an optical head-mounted display and camera, in April 2012[29]. As of 2018, however, it is not widespread among consumers except Google Glass Enterprise Edition, a workplace-focused assistive device, which is deployed across many factories in the United States[30]. Smart contact lenses are still in development stage[31]. Retinal projectors, such as Intel’s Vaunt[32] or QD Laser’s RETISSA Display[33] are yet to be produced on a commercial basis. I do not dismiss the downsizing trend of computers to be as small as wearable in the future, but the downsizing trend is not so explosively accelerated as Kurzweil expected.

My current interim assessment of his prediction is that he was wrong in expecting the improvement in computing performance to be more than exponential. So, there will be no mathematically defined singularity except that God performs a miracle. Some even throw doubt on the simple exponential growth like Moore’s Law.

## 5 : How can we exceed the limit of Moore’s Law?

Moore’s Law is named after Gordon Moore who said in 1965, “The complexity for minimum component costs has increased at a rate of roughly a factor of two per year[34].” Moore himself did not advocate the so-called “Moore’s Law" which is now taken for a law vaguely meaning that semiconductors improve their performance per cost exponentially.

Moore predicted that the miniaturization and integration of semiconductor’s components would continue at least till 1975, but the trend had continued since then thanks to Dennard scaling: transistors were reduced in size, while their power density stayed constant. This trend, however, hit the ceiling around 2006, namely, after Kurzweil published The Singularity Is Near. The nanoscale miniaturization resulted in the quantum tunneling leakage current through the dielectric between the gate and the channel, leading to increased static power consumption and heat production that might trigger off thermal runaway. Thus, CPU manufacturers came to rely on multicore processors as an alternative way to improve CPU performance.

On January 2, 2018, The Register, British tech website, publicly reported that modern Intel CPUs have a “design flaw" later named Meltdown and Spectre vulnerabilities[35]. The security patches to fix the bugs reduce the responsiveness of the latest CPUs (7th or 8th generation processors) by 12-14% and older ones (6th generation processors) by 21% on Windows 10 PCs[36]. The Register that claims remediating Meltdown should impose as much as a 30% performance penalty published a “death notice” of Moore’s Law in the month, announcing “From the age of fifty, Moore’s Law began to age rapidly, passing into senescence and then, at the beginning of this month, into oblivion[37]."

As the Spectre vulnerability can affect not only Intel but also AMD, ARM, and IBM processors, the performance of all computers will more or less go backward in the short term. In the long term, however, physical limits are more serious for the improvement in a semiconductor. Kurzweil expected that Moore’s Law would reach the end of its sigmoid curve before 2020. But he insisted that the exponential growth should continue with three-dimensional molecular computing, which would constitute the sixth paradigm succeeding to electromechanical punched card tabulator, relays, vacuum tubes, discrete transistors, and integrated circuits[38].

As the figure below shows, a new paradigm can start a new S-curve.

In accordance with the law of accelerating returns, paradigm shift (also called innovation) turns the S-curve of any specific paradigm into a continuing exponential. A new paradigm, such as three-dimensional circuits, takes over when the old paradigm approaches its natural limit, which has already happened at least four times in the history of computation.[40]

To be sure, some developers are trying to stack silicon wafers or dies and interconnect them vertically to improve IC performance, but is this 3D IC worth the name of a paradigm shift? It seems to me a mere puzzle-solving for IC improvement rather than an innovation that replaces the current IC paradigm.

What about molecular computing? As Kurzweil recognizes, “We already have proofs of concept for all of the major requirements for three-dimensional molecular computing: single-molecule transistors, memory cells based on atoms, nanowires, and methods to self-assemble and self-diagnose the trillions (potentially trillions of trillions) of components[41].” A molecular computer can be a new paradigm if it utilizes biologically derived molecules instead of silicon, though the idea itself has been around for more than 40 years.

Today, the most promising candidate for the “three-dimensional molecular computer" is DNA computer. DNA (Deoxyribonucleic acid) that life has used to preserve its genetic information is superior to conventional computer media for its high density and long durability. The big challenges to deploying DNA data storage are “cost and speed[42].” Microsoft Research has formalized a goal of having an operational storage system based on DNA by 2020[43]. The goal is, however, difficult to reach because the cost of DNA storage needs to fall by a factor of 10,000 and the rate of moving data into DNA needs to be speeded up by a factor of 262,000 before it becomes widely adopted.

DNA molecules are expected to act as parallel processors[44], while the most popular candidate for parallel computing is quantum computers. But Kurzweil is skeptical about quantum computers.

The ultimate role of quantum computing remains unresolved. But even if a quantum computer with hundreds of entangled qubits proves feasible, it will remain a special-purpose device, although one with remarkable capabilities that cannot be emulated in any other way.[45]

On May 11, 2011, D-Wave Systems announced the world’s first commercially available quantum computer that can solve certain classes of hard combinatorial optimization problems through a process called quantum annealing[46]. This is “a special-purpose device,” but now IBM[47], Google[48], Microsoft[49] and many other companies are developing general-purpose quantum computers.

Though quantum computers are susceptible to errors than classical computers owing to decoherence, they are suitable for fault-tolerant deep learning. In the age of machine learning, GPU will play a more important role than CPU and the massively parallel quantum computing on GPU is expected to improve the performance of computers. As the lifetime of quantum memory is short (up to 8 hours as of 2018[50]), quantum bits can be converted into classical bits and stored in DNA. This combination of classical, quantum and DNA computers can maintain the exponential growth of the calculations per second per cost beyond the classical limit of Moore’s Law.

## 6 : Can we upload our brains to computers?

If the performance of computers continues to improve exponentially in the future, it will exceed the performance of human brains and the significance of our existence will be questioned. This is what Neo-Luddites are concerned about. But if “Uploading the Human Brain[51]”, that is to say, “scanning all the salient details of a human brain and then reinstantiating those details into a suitably powerful computational substrate[52]” will be possible, we will not only be able to live forever but also keep the master position of civilization, making exponential progress in step with computers. The problem is whether it is possible or not.

Researchers engaged in the OpenWorm project mapped all the connections between the neurons of a roundworm (Caenorhabditis elegans), simulated them in software, and made it drive a Lego[53] or an Arduino[54] robot body. As the movie below shows, the worm’s virtual brain controlled the robot without any additional programmed instruction as if it were a worm’s body.

We can also reverse-engineer the human brain, simulate it in artificial intelligence, and make it control a robot in the future. Such a project, however, just copies the pattern of a human brain. It never uploads it. As Kurzweil acknowledges, copy and transference are completely different.

Although the copy shares my pattern, it would be hard to say that the copy is me because I would ― or could ― still be here. You could even scan and copy me while I was sleeping. If you come to me in the morning and say, “Good news, Ray, we’ve successfully reinstantiated you into a more durable substrate, so we won’t be needing your old body and brain anymore,” I may beg to differ.[56]

So, Kurzweil thinks of maintaining his self-identity by gradually replacing his body parts with machines. The next generation computer for him is, as we have already recognized, the three-dimensional molecular computers. If computers and robots are reduced to a molecular, namely, nanoscale size, they can take the place of the molecules constituting the human body. He calls these nanoscale robots “nanobots".

Billions of nanobots will travel through the bloodstream in our bodies and brains. In our bodies, they will destroy pathogens, correct DNA errors, eliminate toxins, and perform many other tasks to enhance our physical well-being. As a result, we will be able to live indefinitely without aging. In our brains, the massively distributed nanobots will interact with our biological neurons. This will provide full-immersion virtual reality incorporating all of the senses, as well as neurological correlates of our emotions, from within the nervous system. More important, this intimate connection between our biological thinking and the nonbiological intelligence we are creating will profoundly expand human intelligence.[57]

Kurzweil predicted that the nanobot era would arrive around 2025 and strong AI would emerge around 2029[58]. To be sure, scientists are developing medical nanobots that can complement the function of immune cells. In February 2018, for example, Arizona State University scientists have successfully programmed nanorobots to shrink tumors by cutting off their blood supply[59]. According to Kurzweil, nanobots will also complement the function of the brain.

The use of nanobots as brain extenders will be a significant improvement over surgically installed neural implants, which are beginning to be used today. Nanobots will be introduced without surgery, through the bloodstream, and if necessary can all be directed to leave, so the process is easily reversible.[60]

He thinks that the gradual replacement of the brain with nanobots will eventually result in uploading the brain to the machine with the personal self-identity maintained.

Consider replacing a tiny portion of my brain with its neuromorphic equivalent. Okay, I’m still here: the operation was successful (incidentally, nanobots will eventually do this without surgery). We know people like this already, such as those with cochlear implants, implants for Parkinson’s disease, and others. Now replace another portion of my brain: okay, I’m still here . . . and again. . . . At the end of the process, I’m still myself. There never was an “old Ray” and a “new Ray.” I’m the same as I was before. No one ever missed me, including me. The gradual replacement of Ray results in Ray, so consciousness and identity appear to have been preserved.[61]

The gradual replacement of my brain with machines, however, might result in the gradual disappearance of my consciousness rather than its gradual transference to machines. I would gradually disappear and die like an Alzheimer’s disease patient whose brain suffers gradual atrophy, even if computers compensate for the loss of neurons and synapses, making believe that I still persist.

What on earth is the essence of me then? Why is my copy different from myself, no matter how it resembles me? The problem of the self-identity of consciousness that philosophers have tackled through the ages is yet to be solved. But I can form a physical hypothesis. According to the Quantum Brain Hypothesis, consciousness is a quantum state of the brain and the quantum state cannot be copied on account of the quantum no-cloning theorem. Therefore, my consciousness cannot be copied exactly without destroying my self-identity.

While there are many versions of the Quantum Brain Hypotheses, the most famous is Roger Penrose’s[62]. Kurzweil criticizes Penrose’s argument as follows.

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.[63]

Although Kurzweil seems to believe that the quantum no-cloning theorem makes the perfect downloading impossible, it actually enables rather than disables us to transfer the personality by means of the quantum teleportation. This is a method of simultaneously transmitting the quantum state in my brain to a quantum computer utilizing an EPR pair in a Bell state (the simplest form of quantum entanglement) without the quantum state being measured or observed. Owing to the theorem my consciousness disappears in my old body while it can reappear in a new artificial body maintaining the same quantum state of consciousness.

Some may suspect that the Quantum Brain Hypothesis that I presuppose is wrong. In fact, when Penrose published The Emperor’s New Mind in 1989, his proposal that quantum effects in “microtubules” play a role in human consciousness was dismissed as an occult idea.

The main arguments which are raised against the quantum brain hypothesis are the following two:

1. Maintaining quantum coherence in the noisy, wet and warm environment like our brain for a long period is impossible.
2. Neuronal systems in our brain are too large for quantum phenomena to play a significant role in their functioning.

However, a growing body of empirical evidence is refuting these counterarguments.

1. The Posner molecule, Ca9(PO4)6is identified as the unique molecule that can protect the coherence of neural qubits in the noisy, wet and warm environment on very long times, and thereby serve as a working quantum-memory[64].
2. Non-linear chaotic dynamics in our brain can amplify lowest-level quantum fluctuations upward, modulating even larger-scale mesoscopic and maybe also macroscopic neuronal activity as a butterfly effect[65].

Not all of the information processing is quantum computing that can neither 1 nor 0. We often make a digital judgment that can be either true (1) or false (0) like a classical computer. As Kurzweil says, “the human brain uses digital-controlled analog methods[66]” because “the firing of a neuron can be considered a digital event whereas neurotransmitter levels in the synapse can be considered analog values[67].” The combination of quantum computer GPU and classical computer CPU that I proposed reflects the combination of analog intuition and digital concept that constitute our mind.

Kurzweil, who thinks lightly of quantum computers, also makes light of analog aspect of our recognition and attempts to convert it all to a digital equivalent.

We should keep in mind, as well, that digital computing can be functionally equivalent to analog computing ― that is, we can perform all of the functions of a hybrid digital-analog network with an all-digital computer.[68]

To be sure we can make a digital copy that is exactly like the analog original but we should keep in mind, as well, that the digital copying throws away something. If Kurzweil admits that his digital copy is not himself no matter how it resembles him, he should notice that a digital classical computer cannot transfer his personality.

## 7 : Does the Universe wake up in the future?

Kurzweil conceptualizes the history of evolution from the Big Bang to the future as occurring in six epochs, where “the Singularity will begin with Epoch Five and will spread from Earth to the rest of the universe in Epoch Six[69].”

According to Kurzweil, “As intelligence saturates the matter and energy available to it, it turns dumb matter into smart matter[71]” and the expansion of the saturation wakes up the universe.

Seth Lloyd estimates there are about 1080 particles in the universe, with a theoretical maximum capacity of about 1090 cps. In other words, a universe-scale computer would be able to compute at 1090 cps. To arrive at those estimates, Lloyd took the observed density of matter ― about one hydrogen atom per cubic meter ― and from this figure computed the total energy in the universe. Dividing this energy figure by the Planck constant, he got about 1090 cps.[72]

Lloyd’s article Kurzweil cites in this quoted passage draws the following conclusion.

If, as seems highly unlikely, it is possible to extrapolate the exponential progress of Moore’s law into the future, then it will only take two hundred and fifty years to make up the forty orders of magnitude in performance between current computers that perform 1010 operations per second on 1010 bits and our one kilogram ultimate laptop that performs 1051 operations per second on 1031 bits.[73]

Such a one-kilogram computer might be produced in 250 years, but it is impossible to make the universe a computer using all its matter and energy because the complexity of matter per se is not information and not all energy can be used for information processing.

Kurzweil takes up an ordinary rock as an example of turning dumb matter into smart matter. According to him a one-kilogram (2.2-pound) rock which has 1025 atoms represent at least 1027 bits of memory.

In terms of computation, and just considering the electromagnetic interactions, there are at least 1015 changes in state per bit per second going on inside a 2.2-pound rock, which effectively represents about 1042 (a million trillion trillion trillion) calculations per second. Yet the rock requires no energy input and generates no appreciable heat.[74]

Here complexity is confused with information. While admitting “the concept of complexity is complex.[75],” Kurzweil says, “One concept of complexity is the minimum amount of meaningful, non-random, but unpredictable information needed to characterize a system or process[76].” The confusion results in the contradictory expression: “non-random, but unpredictable." While information must be non-random, complexity must be unpredictable.

This is common confusion, and in fact, people regard the bit, a unit of complexity, as a unit representing the size of information. Let me explain in a simple example that complexity is not information.

Compare the following two propositions.

1. Tomorrow’s weather is whether sunny or not, whether hot or not and whether windy or not.
2. Tomorrow’s weather is sunny, hot and windy.

The first proposition shows the possibility of 23=8 bits with respect to tomorrow’s weather. In other words, the complexity is 8 bits, but this proposition does not provide any information about tomorrow’s weather. On the other hand, the second proposition reduces the complexity, providing some information on tomorrow’s weather. The logarithm of complexity is called entropy, and if the base is 2, the entropy of the first proposition is 3, while the entropy of the second is 0. As Shannon recognized[77], information is negative entropy. In this case, the negative entropy -3 provides information.

Whether the rock is to be used for storing or processing information, the entropy of the rock must be reduced. For this purpose, the low entropy energy should be charged and high entropy heat should be exhausted in accordance with the second law of thermodynamics. Not all of the energy in the universe can be used for this purpose. Owing to the two constraints of the environment and the resource it is thermodynamically impossible for the whole universe to become a computer and wake up.

Wakening universe is a religious rather than a scientific idea. The idea that when human spirit rises to the level of God, it will saturate the universe so ubiquitously that the universe wakes up is also seen in Hegel’s philosophy[78], which further traces back to the Christian eschatology.

Once we saturate the matter and energy in the universe with intelligence, it will “wake up,” be conscious, and sublimely intelligent. That’s about as close to God as I can imagine.[79]

Judging from this passage, Kurzweil’s Singularitarianism sounds like a religious belief. Believers in the prophet Kurzweil are called “Singularitarians." This is a strange name. Taking the original definition of the singularity into consideration, it sounds like “a person whose mind is blown off" (and actually they are regarded as such). I do not deny the future possibilities of the continued exponential evolution of information technology, the mind uploading, and the diffusion of humans, but I will not declare along with Kurzweil, “Ich bin ein Singularitarian[80].”

## 8 : References

1. Raymond “Ray" Kurzweil (born February 12, 1948) is an American computer scientist and inventor in the fields of recognition technology and artificial intelligence.
2. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 352.
3. Hans Moravec. “When will computer hardware match the human brain?.” Journal of evolution and technology 1.1 (1998): 10. Hans Peter Moravec (born November 30, 1948, Kautzen, Austria) is a futurist focusing on transhumanism.
4. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 356.
5. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 1,029.
6. “We show how to use “complementary priors” to eliminate the explaining-away effects that make inference difficult in densely connected belief nets that have many hidden layers. Using complementary priors, we derive a fast, greedy algorithm that can learn deep, directed belief networks one layer at a time, provided the top two layers form an undirected associative memory.” Hinton, Geoffrey E., Simon Osindero, and Yee-Whye Teh. “A fast learning algorithm for deep belief nets." Neural computation 18.7 (2006): 1527-1554.
7. Quoc Le & Barret Zoph, Research Scientists, Google Brain team. “Using Machine Learning to Explore Neural Network Architecture.” Research Blog. Wednesday, May 17, 2017.
8. Silver, David, et al. “Mastering the game of go without human knowledge." Nature 550.7676 (2017): 354-359.
9. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 9,627.
10. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 1,352.
11. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 1,373.
12. Let W=W0=c9ec8 when t=0.
13. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 9,666.
14. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 408.
15. Vernor Steffen Vinge (born October 2, 1944) is an American science fiction author and computer scientist.
16. Vernor Vinge. “The Coming Technological Singularity: How to Survive in the Post-Human Era”. In Vision 21: Interdisciplinary Science and Engineering in the Era of Cyberspace. Sponsored by NASA Lewis Research Center and the Ohio Aerospace Institute, March 30-31, 1993. Vernor Steffen Vinge (born October 2, 1944) is an American science fiction author and retired professor of mathematics and computer science at San Diego State University.
17. Ulam, S., “John von Neumann, 1903-1957.” in Tribute to John von Neumann. Bulletin of the American Mathematical Society. vol 64, nr 3, part 2, May 1958. p.5.
18. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 654.
19. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 2,428.
20. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 9,671.
21. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 9,574.
22. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 7,279.
23. John Horgan. “The Consciousness Conundrum.” Special Report: The Singularity.
24. NEWSWEEK STAFF. “RAY KURZWEIL’S SCIENCE CULT.” 5/17/09 AT 8:00 PM.
25. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 710.
26. Larry Greenemeier. “Computers have a lot to learn from the human brain, engineers say.” Scientific American Blog Network. March 10, 2009. FLOPS stands for floating-point operations per second, a common benchmark measurement for rating the speed of microprocessors. PFlop/s is equivalent to thousand trillion operations per second.
27. TOP500 Supercomputer Sites. “PERFORMANCE DEVELOPMENT.” Accessed 2018/02/04.
28. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 6,009.
29. Trefis Team. “Google Glasses Sound As Crazy As Smartphones And Tablets Once Did.” Forbes. APR 5, 2012 @ 11:17 AM.
30. Vlad Savov. “Google Glass gets a second chance in factories, where it’s likely to remain.” The Verge. Jul 18, 2017, 8:17am EDT.
31. Jennifer Birch. “What Happened to the Plans for a Smart Contact Lens for Diabetics?.” Labiotech.eu. 25/01/2018.
32. Dieter Bohn. “Exclusive: Intel’s new Vaunt smart glasses actually look good.” The Verge. Feb 5, 2018, 8:00am EST.
33. 株式会社QDレーザ. 「網膜走査型レーザアイウェア RETISSA® Display を今夏発売」2018年1月4日. Cf. “QD Laser Eyewear.”
34. Moore, Gordon E. “Cramming more components onto integrated circuits." Proceedings of the IEEE 86.1 (1998). p.83.
35. John Leyden, Chris Williams. “Kernel-memory-leaking Intel processor design flaw forces Linux, Windows redesign.” The Register. 2 Jan 2018 at 19:29.
36. Adarsh Verma. “How Much Slower Will My PC Become After Meltdown And Spectre Patches?.” Fossbytes. January 12, 2018.
37. Mark Pesce. “Death notice: Moore’s Law. 19 April 1965 – 2 January 2018.” The Register. 24 Jan 2018 at 07:03.
38. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 1,355.
39. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 1075.
40. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 1,399.
41. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 2,143.
42. “The big challenges to deploying DNA data storage are cost and speed. For archival storage, magnetic tape is still the most cost-effective data storage medium, and although slower than flash memory it is still able to transfer hundreds of megabytes per second. That would be equivalent to reading and writing 1 billion DNA bases per second, something that could only be achieved with new chemistry in a massively parallel system.” Mark Peplow. “Rebooting the molecular computer.” Chemical & Engineering News. Volume 95. Issue 4. p.23-25. Issue Date: January 23, 2017.
43. Antonio Regalado. “Microsoft Has a Plan to Add DNA Data Storage to Its Cloud.” MIT Technology Review. May 22, 2017.
44. “While conventional computers attack problems via mind-numbingly large calculations in series, properly encoded ‘molecular computers’ might quickly solve the same problems by simultaneously carrying out billions of operations in parallel.” Rozen, Daniel E., Steve McGrew, and Andrew D. Ellington. “Molecular computing: Does DNA compute?" Current Biology 6.3 (1996): 254-257.
45. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 2,139.
46. Johnson, M. W., et al. “Quantum Annealing with Manufactured Spins.” Nature, vol. 473, no. 7346, May 2011, pp. 194–98.
47. Christine Vu. “IBM Announces Advances to IBM Quantum Systems & Ecosystem.” IBM News room, United States. 10 Nov 2017.
48. Julian Kelly. “Research Blog: A Preview of Bristlecone, Google’s New Quantum Processor.” Google Research Blog. Monday, March 05, 2018.
49. Allison Linn. “With new Microsoft breakthroughs, general purpose quantum computing moves closer to reality.” Microsoft news, features, events, and press materials. 25 September 2017.
50. Astner, Thomas, Johannes Gugler, Andreas Angerer, Sebastian Wald, Stefan Putz, Norbert J. Mauser, Michael Trupke et al. “Solid-state electron spin lifetime limited by phononic vacuum modes." Nature materials (2018): 1.
51. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 3,642.
52. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 3,647.
53. Lucy Black. “A Worm’s Mind In A Lego Body.” I Programmer. Sunday, 16 November 2014.
54. Mike James. “A Worm’s Mind In An Arduino Body.” I Programmer. Wednesday, 04 October 2017.
55. OpenWorm. “Worm Robot Sneak peek.” YouTube. Published on Jul 21, 2017.
56. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 7,498.
57. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 5,741.
58. “I do expect that full MNT will emerge prior to strong AI, but only by a few years (around 2025 for nanotechnology, around 2029 for strong AI).” Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 4,970; “Once the nanobot era arrives in the 2020s we will be able to observe all of the relevant features of neural performance with very high resolution from inside the brain itself.” Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 3,619.
59. Li, Suping, et al. “A DNA Nanorobot Functions as a Cancer Therapeutic in Response to a Molecular Trigger in Vivo.” Nature Biotechnology, Feb. 2018.
60. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 6,114.
61. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 7,511.
62. Roger Penrose. The Emperor’s New Mind. Oxford University Press (November 9, 1989).
63. Kurzweil, Ray. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 8,886.
64. Fisher, Matthew PA. “Quantum cognition: the possibility of processing with nuclear spins in the brain." Annals of Physics 362 (2015): 593-602.
65. Jedlicka, Peter. “Revisiting the Quantum Brain Hypothesis: Toward Quantum (Neuro)Biology?Frontiers in Molecular Neuroscience 10 (2017).
66. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 8,443.
67. “the firing of a neuron can be considered a digital event whereas neurotransmitter levels in the synapse can be considered analog values” Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 2,678.
68. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 2,726.
69. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 548.
70. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 552.
71. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 7069.
72. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 7080-7084.
73. Lloyd, Seth. “Ultimate physical limits to computation." Nature 406, no. 6799 (2000): 1047. p.17
74. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 2,329.
75. “Not surprisingly, the concept of complexity is complex.” Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 938.
76. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 965.
77. Shannon, C. E. “The mathematical theory of communication." The Bell System Technical Journal, Vol. 27, pp. 379–423, 623–656, July, October, 1948.
78. Georg Wilhelm Friedrich Hegel (August 27, 1770 – November 14, 1831) is a German philosopher. According to him the absolute spirit overcoming the conflict between the subjective spirit and the objective spirit reaches God’s height.
79. Ray Kurzweil. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 7,298.
80. “Ich bin ein Singularitarian.” Kurzweil, Ray. The Singularity Is Near: When Humans Transcend Biology. Kindle edition. Penguin Books; 1st edition (September 22, 2005). Location. 7,159. This is, of course, a parody of the speech by U.S. President John F. Kennedy in West Berlin on June 26, 1963, “Ich bin ein Berliner."