Ray Kurzweil foresees a future of Artificial General Intelligence (AGI) — the topic of this series at Evolution News — in which we achieve immortality by shedding our human bodies and becoming fully digital. This prospect is the most wonderful thing he can imagine. Yet a reality check is in order: Just how great is such digital immortality and how does it compare with traditional immortality? As we’ll see, good old-fashioned immortality has advantages that digital immorality cannot hope to rival.

Let’s start with traditional immortality. Traditional immortality sees finite humans sharing eternity with an infinite God. This God is an actual or realized infinity, and not just a potential infinity in the sense of the natural numbers, for which there’s always a bigger number given any finite set of numbers. Indeed, it makes little sense to think of a God who inhabits eternity and whose mind can grasp all of mathematics (certainly divine omniscience encompasses mathematics) as having considered only those natural numbers from 0 to some big number N, as though God had yet to consider N+1, N+2, etc. 

When the mathematician Georg Cantor, who was a Christian and was deeply influenced by Augustine, proposed his theory of sets, it was precisely to capture in mathematics God’s actual infinity. For him the natural numbers were not a potential infinity. It wasn’t, in his view, that we just kept approximating infinity by continually adding the number 1 to existing numbers. No, the natural numbers could be considered as a totality, namely, as the set of all natural numbers. As such, the natural numbers were an actual, and not merely a potential, infinity. Appropriately, the premier mathematician of the time, David Hilbert, described Cantor’s set theory as a “paradise” out of which mathematics would never be driven. 

Our Status as Finite Creatures

Now here’s the point about our status as finite creatures inhabiting eternity with an actually infinite God: We never achieve infinity as such in our own essence, but we can experience infinite progress toward union with God, much like an asymptote in mathematics comes ever closer to a line without ever touching it. The theologian who developed this idea at length was Gregory of Nyssa (ca. 335 – ca. 395, pictured above). Gregory taught that eternity for humanity is an unending progression in the knowledge of God. Humans have an unlimited capacity for spiritual growth and connection with God. What underwrites this capacity is that humans, alone among physical creatures, are created in the image of God, having free will and thus a capacity to participate in the divine nature (2 Peter 1:4). 

Gregory expounded these theological ideas in On the Making of Man and The Life of Moses. In these writings, he describes the human soul’s journey toward God as an infinite process. The process is infinite because the divine is inexhaustible and the human understanding of God is therefore never complete. At the same time, God created humans with the capacity to grow without limit. In this way, we become potential infinities that ever strive after God’s actual infinity. Yes, there is a potential infinity, but it is on our end. And yes, there is an actual infinity, but it is on God’s end.

This conception of eternal life as eternal growth under the aegis of an actually infinite God has implications for mathematics and computation, which is the realm of digital immortality. As an actual infinity, God can perform any computation, finite or infinite. Think of it this way: God has infinite memory and infinite computational power. The great statistician David Blackwell is said to have mused about a “super supercomputer” that performs its first computational step in half a second, its next in a quarter of a second, its next in an eight of a second, and so on. Given that the infinite series 1/2 + 1/4 + 1/8 + … + 1/2^n + … equals 1, such a computer could perform a countably infinite number of computational steps in 1 second. But note, such computations are beyond the reach of conventional algorithms, which can only perform a finite number of steps. 

As it is, an actually infinite God could do even better than Blackwell’s super supercomputer, performing all such computations instantly (and if God is outside time, timelessly). With such computational power, God could determine whether any proposition or its negation is provable from any countably infinite set of axioms: for the first n axioms determine all propositions provable from those axioms in n steps. Do that for all n and do that both for the proposition as well as its negation. In this way, God could instantly prove all mathematical truths that are provable. Contrast this to humans, for whom it is hit-or-miss whether they can prove a given mathematical proposition even if it is in principle provable.

Given infinite computational firepower, God can resolve the halting problem, which is central to computation. The halting problem is to show that as a computer program is executed, it either stops or goes on forever. God’s ability to solve the halting problem does not contradict that the halting problem is unresolvable with conventional computation. That’s because conventional computation cannot execute an infinite number of steps. In effect, God resolves the halting problem for programs that do not halt in a finite number of steps by running them an infinite number of steps and noting that the program did not halt in any finite number of steps. 

Obviously, an infinite God could instantly solve any finite problem solvable in a finite number of steps (however large the problem and however computationally intensive its solution). A case in point would be the traveling salesman problem, which consists of finitely many nodes connected by edges marking various distances between nodes. The problem is solved by finding the shortest path among edges connecting all nodes. An exact solution of the traveling salesman problem in general, when the number of nodes gets large (greater than 1,000), is beyond the computational resources of the known physical universe. Yet the solution would be trivial to an infinite God.

Given this backdrop of divine infinity, let’s now turn to digital immortality. As we’ll see, it is a dim reflection of traditional immortality. Alan Turing was one of the first to moot digital immortality. His high school friend Christopher Morcom died unexpectedly when they were teenagers. Turing, with his invention of a theoretical computational device now known as the Turing machine, distinguished software (the configured state of the machine) from hardware (the mechanism that runs the software, in Turing’s case an infinite tape with a reader for each slot on the tape). Because the software could be realized on different hardware devices (multiple realizability), the “software” that comprised Morcom’s identity might thus be moved from his disease-prone physical body to a more reliable hardware device. In this way, Morcom could achieve immortality.

Running with the Idea

Current AGI fans such as Ray Kurzweil and Nick Bostrom have run with this idea. To set the stage for their approach, let me back up to 2002. That year I was at the World Skeptics Conference in Burbank, California, to defend intelligent design. At the conference was MIT’s Marvin Minsky, known among other things for his statement “the human brain is just a computer that happens to be made out of meat.” He was there to receive the Committee for Skeptical Inquiry’s 2002 In Praise of Reason Award. In his acceptance talk, he described his desire to have another 500 years of life to engage in scientific research. As I listened to him, it struck me that his creative output had considerably lessened over the years (he was 74 when I heard him), and that another 500 years might provide no guarantee of ongoing fruitful research. Most mathematicians, after all, do their best work in their 20s.

Now for supporters of digital immortality, an additional 500 years of life is setting the bar way too low. Thus for Kurzweil, given sufficiently advanced technology, Minsky could be uploaded onto a computer and then continue doing research indefinitely, with far more computational firepower than available from his paltry “computer made of meat.” But what would this digital immortality actually look like? It would be one thing if the universe were infinite and matter could change states instantly, with the transmission of signals occurring not at the (slow) speed of light but at infinite speed. We tend to think of the speed of light as fast because it is so much faster than the speeds in our ordinary experience, such as walking, driving, or flying. But even with digital products, we still experience considerable lags because computation times are limited by the signal propagation speed of electrons. Now granted, the speed of electrons can approach the speed of light, but that only confirms that the speed of light is not all that fast. 

So how much computational firepower is available to Kurzweil’s digital immortality? Right now, computer scientists are oohing and aahing about computations at the exaflop level (10^18 floating point operations per second). The currently fastest computer is Oak Ridge National Lab’s HPE Cray EX235a supercomputer, which operates at 1.686 exaflops. Tesla’s Dojo computer, to make fully automated self-driving possible, aspires to that same level of computational speed. Speeds like this are needed to drive current artificial intelligence research forward. But they are hardly enough for digital immortality.

The problem with digital immortality is that the known physical universe only allows so much computation, no more. Quantum computational theorist Seth Lloyd has calculated the ultimate limits of computation. For what he calls the ideal laptop, consisting of one liter of matter, he calculates 10^81 bit operations per second. For the universe as a whole over its entire history, he calculates 10^210 bit operations, or possibly 10^240 if gravitational degrees of freedom are factored in. (For Lloyd’s calculations, see the second edition of The Design Inference, section 4.3.) Now granted, these numbers far exceed the 10^18 operations of current supercomputers, even allowing that floating-point operations are richer than bit operations. But the point to recognize is that these numbers are still very finite. 

Imagine thousands, millions, or even billions of humans uploading themselves digitally, and let’s be generous that among themselves they get to share 10^240 computational steps (the very upper limit of what the universe can offer computationally). There are only about 10^90 elementary particles, so any memory will have to be shared among those particles. And presumably there will be communication among the digitally uploaded erstwhile humans. As our “lived experience” of digital immortality unfolds, we will be going from one of finitely many states to another. Presumably, we’re going to want to remember what we experienced, which means much of the “server space of the universe” will have to be dedicated to such memory. 

Reciting Words from a Dictionary

Moreover, given the pigeonhole principle of mathematics, which here applies to a fixed number of states evolving over a far greater number of state changes (infinitely many, in fact, if digital immortality really means immortality), our digital identity will necessarily have to revisit the same states over and over again. It’s like reciting words from a dictionary: if there are only a fixed number of words and you say enough words, eventually you’ll have to repeat the same word. Only with digital immortality, you’ll be repeating the same life. 

To illustrate what’s at stake, consider a scene from the 1970s program The Six Million Dollar Man in an episode titled “Day of the Robot.” In that episode, a robot impersonates a friend of Steve Austin. Austin is the protagonist, played by Lee Majors. Suspicious that something is up with his friend, Austin asks a question and then deliberately repeats the question. The robot, rather than responding “Hey, you just asked that,” repeats exactly the same answer as before. That’s the problem with digital immortality: it reduces immortal life to rinse and repeat. 

Digital immortality is therefore a case of Nietzschean eternal recurrence. Such recurrence will entail a dissolution and reconstruction of past memories, which is to say that our entire history and personal identity will (at best) be repeated over and over again. The very term “digital immortality” is something of a misnomer. Our best physical understanding of the universe is that we won’t even get eternal recurrence. Indeed, the known physical universe does not seem to allow for an unending stable physical existence of agents, whether organismal or computational. Entropy being what it is, the matter that could support an organismal or digital life will eventually be so dissipated and so energetically weak as to dissolve every conceivable life form (unless life, as in traditional immortality, can be translated to a new indestructible state of being). 

Worry and Despair

Bertrand Russell, in an earlier generation, captured the underlying worry and despair about the evanescence of any life based purely on our material constitution. As he remarked:

Man is the product of causes which had no prevision of the end they were achieving. His origin, his growth, his hopes and fears, his loves and his beliefs, are but the outcome of accidental collocations of atoms. No fire, no heroism, no intensity of thought and feeling, can preserve an individual life beyond the grave. All the labours of the ages, all the devotion, all the inspiration, all the noonday brightness of human genius, are destined to extinction in the vast death of the solar system, and that the whole temple of Man’s achievement must inevitably be buried beneath the debris of a universe in ruins — all these things, if not quite beyond dispute, are yet so nearly certain, that no philosophy which rejects them can hope to stand. 

Bertrand Russell, Logic and Mysticism

Now it might be argued that Russell would have been more sanguine if he had but read Ray Kurzweil and could appreciate the full promise of digital immortality. But at best Kurzweil adds a few zeros to the span of human lives once those lives are digitally uploaded. But Russell’s point about humans being “destined to extinction in the vast death of the solar system” holds with but slight modification for digitally uploaded humans. Instead, we are destined to extinction in the vast entropic death of the universe. And if for some reason we think that the universe will not expand indefinitely in an entropic dissolution (leading to a loss of all computationally useful energy) but contract to a singularity that results in a big bounce and thus an oscillating universe, all the information needed to ensure personal identity of digitally immortal beings will be lost in that big bounce. Digital immortality is thus misnamed. It is at best digital life extension. But the bigger question is whether it is life at all.

Next, “Artificial General Intelligence: Machines vs. Organisms.”

Editor’s note: This article appeared originally at BillDembski.com.