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Asimov - An Exponentialist View
Bartlett - An Exponentialist View
Darwin - An Exponentialist View
Dawkins - An Exponentialist View
Drexler - An Exponentialist View
Ehrlich - An Exponentialist View
Malthus - An Exponentialist View
Sagan - The Secrets of the Universe
Savage - An Exponentialist View
Turchin - An Exponentialist View
Wallace - An Exponentialist View
Witting - An Exponentialist View

Grey Goo - An Exponentialist Explanation

Population Doubling Mechanism 

New Malthusian Scale 

External Links:
Engines Of Creation - K. Eric Drexler

Nanosystems - K Eric Drexler

There's plenty of room at the bottom - transcript of Richard Feynman's December 1959 talk, provided by Zyvex.

Natural Selection and Differential Reproduction - from Replicators: Evolutionary Powerhouses

K. Eric Drexler - An Exponentialist View

Exponential Growth - "Growth that proceeds in a manner characterized by periodic doublings." (Drexler, 1986)

Unnatural Selection

I use this term to describe the evolutionary process that would apply to any non-biological entity capable of replication

The term Unnatural Selection is probably appropriate given the world-wide reactions of horror to topics such as cloning, genetic modification, genetic testing, artificial intelligence, human-machine interfacing and molecular nanotechnology (MNT). It is as if biological life sees the threat posed by non-biological life, and resists the resultant "struggle for existence". In a sense, it is a struggle between the processes of Natural Selection and Unnatural Selection. In both cases, this struggle is driven by exponential population growth and the principle of differential replication.

True, one must take account of the available resources - the limits to growth. With Natural Selection, those "resources" are often other life-forms and are thus themselves subject to exponential population growth. Any remaining resources are inanimate. Fluctuations in the abundance of inanimate resources are typically driven by the seasons, and a combination of the Earth's orbit and axial tilt. Life then exploits to the full whatever is currently available. In a sense then, who survives and who does not is driven by competition between populations of replicators. 

I will also place the colonisation of space under the heading of Unnatural Selection. True, the current version of humanity might be able to the job. But the technology required will itself be unnatural, and  humanity did not evolve to naturally live in space. Thus, the popular perception is that life on Earth is natural, and life in space would have to unnatural. Really though, the colonisation of space is about extending the arena for Unnatural Selection.

As a caveat, I should add that I use the term Unnatural Selection in recognition of popular perception. However, I do not agree with popular perception, as to an exponentialist there is little difference between a population subject to Natural Selection or Unnatural Selection. Both are subject to the same laws of Nature first revealed by Malthus in 1798. Hence, to an exponentialist, life in the broadest sense means any entity capable of self-replication. This then leads to evolution which is perhaps the key combination that defines what life is (Silver, 1998):

"...it does seem possible to provide a complete definition of life-in-general at the individual level as a product of reproduction and evolution that uses energy to maintain self-defining information and organisation. The inanimate becomes animate only upon achieving the ability to evolve."

In evolutionary terms, as you will see, Drexler is able to argue that life is not wasteful of available resources, that life takes every opportunity to grow exponentially, and that space offers life (human or otherwise) enough resources to allow for practically boundless expansion.

Engines Of Creation

Most people think of the Mad Scientist busily creating a Brave New World, only dimly aware that what he or she is doing may have "unforseen consequences." Such scientists are said to be "playing at God." Drexler is the kind of scientist everyone thinks does not exist! He has a revolutionary idea, he understands the implications (including the ethical implications), and he has opened up the debate to the whole planet at The Foresight Institute and elsewhere. Foresight is a non-profit organisation. Free electronic copies of Engines Of Creation abound. 

The key chapter that relates to exponentialism is Chapter 10 - The Limits To Growth  (available online), particularly from "The Limits To Resources" to "Views Of Limits". 

The other thing to note about Drexler is that, though he clearly understands the negative implications of Malthusian theory, and the limits to growth, he is able to see beyond the approaching Malthusian walls and predict a realistic future for humanity in space which will fill you with hope. Obviously, Drexler pins much of that hope on MNT itself. In the light of the scientific debate so far, this seems reasonable. Nevertheless, it should be realised that we could start on the road to such a space-based future even with today's technology (given the political will, and the economics of scale from commercial rather than government involvement).

Differential Replication

For those with an open mind, there are some vital clues to Natural Selection and Differential Replication  in K. Eric Drexler's book on MNT. These two principles are the cornerstones of evolutionary theory. Like Dawkins, Drexler views evolution from the bottom up (Drexler, 1990):

"In the terminology of Oxford zoologist Richard Dawkins, things that give rise to copies of themselves are called replicators. In this environment, RNA molecules qualify: a single molecule soon becomes two, then four, eight, sixteen, thirty-two, and so forth, multiplying exponentially...."

"Biochemists have found that differing RNA molecules replicate at  differing rates, depending on their lengths and subunit patterns. Descendants of the swifter replicators naturally grow more common.  Indeed, if one kind replicates just 10 percent more rapidly than its  siblings, then after one hundred generations, each of the faster kind gives rise to 1,000 times as many descendants. Small differences in exponential growth pile up exponentially."

If a Population B grows "more rapidly" than Population A then it is more accurate to say that a Population B will reach a certain size in less time, rather than say that Population B will reach a larger size in a set number of generations. However, it would be accurate to state that after a set time Population B will be larger (with no mention of generations at all).

It was Malthus (in 1798) who first modelled exponential growth accurately, and (most significantly) showed how it applied to all populations of replicators. You will not find any examples of exponential growth in Malthus' work that take a generational approach to population modelling. This is for good reason, because the Couttsian Growth Model (a modest refinement of the Malthusian Growth Model) is the only one that works. Yet for over 200 years most people (Darwin, Wallace, Drexler, Dawkins etc) still try to model population growth by taking a generational approach, and virtually nobody ever questions the validity of such an approach. If you take the generational approach, then you must (unrealistically) assume immortal populations if you wish to extend the series 1, 2, 4, 8 etc. 

The (overlooked) genius of Malthus was to then provide a simple and accurate way to demonstrate differential replication, using variable population doubling times (from "A Summary View on The Principle of Population", published in 1830):

"The immediate cause of the increase of population is the excess of the births above deaths; and the rate of increase, or the period of doubling, depends upon the proportion which the excess of the births above the deaths bears to the population."

Here is my own explanation using a Malthusian Growth Model, taking a population of 1 million in each case. Population A grows at 1%, and Population B grows 10% faster (which is 1.1%, not 11%). Just as Malthus would have, I use population doubling times to illustrate exponential population growth and differential replication:

Growth rate 1%
(Doubling time = 70)
70 140 210 280 350
Population A (Millions) 1 2 4 8 16
Growth rate 1.1%
(Doubling time = 64)
64 128 192 256 320
Population B (Millions) 1 2 4 8 16

Table A. Malthusian Growth Model showing Population B 
growing 10% faster than Population A

I base my approximate doubling times based on the Rule of 70 which is accurate enough to prove my point.

So, without any misleading reference to generations, it is possible to clearly demonstrate what Drexler was trying to say. It makes little difference whether Drexler was discussing two human populations, or two populations of RNA molecules - the Malthusian Growth Model still applies, and Table A provides a meaningful description of differential replication for either population. How is this possible? 

It's simple really - for humans, the growth rate is typically expressed as an annual growth rate. For bacteria, and I imagine also for RNA molecules, the growth rate is expressed in time periods of an hour or less. For the sake of argument, let's assume that the growth rate for RNA molecules is expressed as an hourly rate. Hence, if Table A applies to human populations, then Population B reaches 16 million in 320 years, a full 30 years before Population A. Or, if Table A applies to RNA molecule populations, then Population B reaches 16 million in 320 hours, a full 30 hours before Population A.

So, where do Drexler's "...1,000 times as many descendants." come into the picture? Using my New Malthusian Scale, each row in the table below represents 10 population doublings, with 1024 at the end of one row becoming 1 on the next row. Hence, assuming 100 population doublings rather than 100 generations, Population B will reach 1024 J-Pops in 100 doublings after (100 x 64 hours = 6,400 hours). In the same time, Population A will be between its 91st and 92nd doubling (6,400 / 70 = 91.43), which places them between 2 and 4 J-Pops. This is very close to mathematically proving Drexler's comment regarding 1,000's more descendants (only a couple of population doublings out), and definitely does prove his assertion that "Small differences in exponential growth pile up exponentially." Such populations end up at opposite ends of the same row of the New Malthusian Scale:

A-pops 1 2 4 8 16 32 64 128 256 512 1024
B-pops 1 2 4 8 16 32 64 128 256 512 1024
C-pops 1 2 4 8 16 32 64 128 256 512 1024
D-pops 1 2 4 8 16 32 64 128 256 512 1024
E-pops 1 2 4 8 16 32 64 128 256 512 1024
F-pops 1 2 4 8 16 32 64 128 256 512 1024
G-pops 1 2 4 8 16 32 64 128 256 512 1024
H-pops 1 2 4 8 16 32 64 128 256 512 1024
I-pops 1 2 4 8 16 32 64 128 256 512 1024
J-pops 1 2 4 8 16 32 64 128 256 512 1024

Table B. Population B, growing at a constant 1.1%, reaches 1024 J-Pops in 6,400 hours. 
At the same time, Population A, growing at constant 1%, is in the process of 
doubling from 2 to 4 J-Pops. 

Getting back to Drexler's RNA molecule populations, in exponentialist terms the biochemists that he mentions have merely confirmed a Malthusian Growth Model over 200 years old. As noted in my article on Cell Replicators - An Exponentialist View, reliance on the generational approach to modelling exponential growth is simplistic. In discussing the local doubling of cell generations, Dawkins ("Climbing Mount Improbable", 1996) calls this same approach "unrealistic", and describes such calculations as "naive". 

As the RNA population gets larger and larger, so the definition of a generation gets more and more unwieldy. To continue the series 1, 2, 4, 8 etc (which is what we are expected to do), all the RNA molecules in each successive generation would have to be born at around the same time from their parents (all of whom must survive the full 100 generations). How close must this timing be - a second, a minute or an hour? How much time elapses between generations? 

It is quite likely that the use of the term "generations" isn't meant literally, in which case it needn't be used at all. It is possible that the definition of a generation actually changes during the 100 generation RNA molecule example. At the beginning, a generation is clearly intended to mean the next number in the doubling series 1, 2, 4, 8 etc, and therefore each successive generation is always precisely double the size of the previous generation. Later, I suspect that a generation simply refers to offspring born at around the same time. Hence, successive generations no longer have to be precisely double the size of the preceding generation.

The Malthusian Growth Model is precise, doesn't rely on vaguely defined terms like generation and - modestly extended in the Couttsian Growth Model-  is universal in its application. It doesn't matter how fecund the individual is (how many offspring), you can precisely model the resultant population in the same way that Malthus did back in 1798. 

The Couttsian Growth Model that I have used applies to all populations of replicators, and in its simplest form relies on growth rates and population doubling times. This leads to the principle of differential replication, a principle clearly understood by Malthus (see Malthus - An Exponentialist View for more). Of course, Malthus would never have had any idea of the existence of RNA, or DNA (or MNT). Whilst I'm sure such things would have amazed him, I am also sure that he would have quickly realised that such replicators are subject to his Principle of Population, and the Couttsian Growth Model.

Evolution

Drexler's explanation of "double-negative" evolution is spot on (Drexler, 1990):

"Evolution attributes patterns of success to the elimination of  unsuccessful changes. It thus explains a positive as the result of a double negative- an explanation of a sort that seems slightly difficult to grasp. Worse, it explains something visible (successful, purposeful entities) in terms of something invisible (unsuccessful entities that have vanished). Because only successful beasts have littered the landscape with the bones of their descendants, the malformed failures of the past haven't even left many fossils. The human mind tends to focus on the visible, seeking positive causes for positive results, an ordering force behind orderly results. Yet through reflection we can see that this great principle has changed our past and will shape our future: Evolution proceeds by the variation and selection of replicators."

That last line is worth repeating:

"...Evolution proceeds by the variation and selection of replicators."

This eloquent phrase neatly states the exponentialist view. The "variation" is usually attributed to Natural Selection, but the Exponentialist view is that Malthusian Selection, Unnatural Selection and Artificial Selection all contribute to the resulting rate of differential replication. See the introductory Exponentialist page for more.

Molecular Nanotechnology (MNT)

Engines Of Creation is a book about MNT. I do not intend to go into MNT in any great detail here, and recommend that you buy the book or read the freely available copy online. The Holy Grail of MNT is the universal assembler, capable of self-replication and assembly of any object. Here are a couple of fundamental principles (Drexler, 1990):

"How fast these replicators can replicate will depend on their assembly speed and their size."

"The speed of replication will depend also on the total size of the system to be built."

Drexler gives due consideration to the misuse and abuse of MNT in a scenario popularly known as the Grey Goo scenario (see Grey Goo - An Exponentialist Explanation for more).

However, for proponents of MNT, the message is an optimistic one. We can and we will colonise space (Drexler, 1990):

"For a long time to come, however, the solar system can provide room enough."

"This will open room enough for an era of growth and prosperity far beyond any precedent. Yet the solar system itself is finite, and the stars are distant."

Drexler then sounds a note of caution for the over enthusiastic space cadet (Drexler, 1990):

"Concern about population and resources will remain important because the exponential growth of  replicators (such as people) can eventually overrun any finite resource base"

This is pretty much the same message that Malthus gave us over 200 years ago.

Kardashev

As Drexler himself points out, The Club Of Rome ("Limits To Growth" 1972) made the same mistake as Malthus in assuming that humanity was incapable of increasing its food supply to match the rate of population growth.

Drexler recognises that exploitation of solar energy is the key source of energy for the foreseeable future (Drexler, 1990): 

"Today Earth has begun to seem small, arousing concerns that we may deplete its resources. Yet the energy we use totals less than 1/10,000 of the solar energy striking Earth; we worry not about the supply of energy as such, but about the supply of convenient gas and oil."

Drexler does not directly refer to Nikolai Kardashev and his definition (in 1964) of the future limits to growth - home planet, home solar system. home galaxy. Nevertheless, Drexler clearly recognises the same limits as Kardashev (Drexler, 1990):

"Yet Earth is but a speck. ...The resources of the solar system are truly vast, making the resources of Earth seem insignificant by comparison.

Yet the solar system is but a speck. ...The resources of our galaxy make even our solar system seem insignificant by comparison.

Yet our galaxy is but a speck. ...The resources of the visible universe make even our galaxy seem insignificant by comparison."

Once again, Drexler is optimistic about our future (Drexler, 1990):

"The solar system seems answer enough to Earth's limits - and if the rest of the universe remains unclaimed by others, then our prospects for expansion boggle the mind several times over. Does this mean that replicating assemblers and cheap spaceflight will end our resource worries?

Once again Drexler wisely cautions against unfettered optimism (Drexler, 1990):

In a sense, opening space will burst our limits to growth, since we know of no end to the universe. Nevertheless, Malthus was essentially right."

Malthus

I find it quite telling that Drexler, in writing about a technology as revolutionary as MNT (and also about our colonisation of the solar system and beyond) is able to recognise the contribution made by Malthus so long ago (Drexler, 1990):

"In his 1798 Essay on the Principle of Population, Thomas Robert Malthus, an English clergyman, presented the ancestor of all modern limits-to-growth arguments. He noted that freely growing populations tend to double periodically, thus expanding exponentially. This makes sense: since all organisms are descended from successful replicators, they tend to replicate when given a chance. For the sake of argument, Malthus assumed that resources - the food supply - could increase by a fixed amount per year (a process called linear growth, since it plots as a line on a graph). Since mathematics shows that any fixed rate of exponential growth will eventually outstrip any fixed rate of linear growth, Malthus argued that population growth, if unchecked, would eventually outrun food production.

Authors have repeated variations on this idea ever since, in books like The Population Bomb and Famine - 1975!, yet food production has kept pace with population. Outside Africa, it has even pulled ahead. Was Malthus wrong?

This is the key question which everyone asks, though not all recognise that Malthus was basically right (Drexler, 1990):

Not fundamentally: he was wrong chiefly about timing and details. Growth on Earth does face limits, since Earth has limited room, whether for farming or anything else. Malthus failed to predict when limits would pinch us chiefly because he failed to anticipate breakthroughs in farm equipment, crop genetics, and fertilizers.

It is curious to reflect that Malthus knew that his Principle of Population applied to all life, and so all populations of life-forms tend to grow exponentially. Malthus also realised that Man is special because Man is able to encourage and harness such exponential growth. Hence, as all human food is derived from other life-forms, Malthus should have realised that food supply does not increase arithmetically as he asserted. Another significant breakthrough which Malthus failed to anticipate is vaccination, which started with Jenner (vaccinating against smallpox) in the same year that Malthus wrote his essay! Of course, it is easy to criticise with hindsight, and forget that Malthus had the genius to be the first to recognise that all populations of replicators are subject to his Principle of Population, and grow exponentially at varying rates (leading the principle of differential replication).

Drexler thus focuses on the part that Malthus clearly got right, and extends Malthusian thinking beyond the Earth and into space (Drexler, 1990):

Some people now note that exponential growth will overrun the fixed stock of Earth's resources, a simpler argument than the one Malthus made. Though space technology will break this limit, it will not break all limits. Even if the universe were infinitely large, we still could not travel infinitely fast. The laws of nature will limit the rate of growth: Earth's life will spread no faster than light.

Drexler again tempers optimism with caution, and the reality of the distribution of resources in space (Drexler, 1990):

Steady expansion will open new resources at a rate that will increase as the frontier spreads deeper and wider into space. This will result not in linear growth, but in cubic growth. Yet Malthus was essentially right: exponential growth will outrun cubic growth as easily as it would linear. Calculations show that unchecked population growth, with or without long life, would overrun available resources in about one or two thousand years at most. Unlimited exponential growth remains a fantasy, even in space."


In summary then, modern Malthusians recognise the Kardashev levels as the true limits to growth. Each planet, each solar system, and each galaxy thus present their own limits to any replicators clever enough to colonise space. This is also the exponentialist view. 

It is important to think about such matters now, because the future of Unnatural Selection (which includes Drexler's own MNT replicators and potential new life-forms) poses a very real threat to the future of humanity. As a human exponentialist, I am in favour of extending the duration of our human species. I also believe that it is Drexler's position. However, unless we fight for our human future in space now, evolution may well favour non-human intelligences of our own creation over us. 

Although Drexler's MNT might entail our destruction, it could also transform us without having to lose our humanity. It could also transform our ability to live, as humans, in space. The question nobody is able to answer is: what level of population could be supported on Earth, or in our solar system, with MNT? I compare the coming MNT revolution to a combination of the agricultural revolution and the industrial revolution all rolled into one, starting in as little as 2 or 3 decades and changing everything we know within perhaps just a few more decades after it starts. Of course, it could take longer to start, but the effect when it does start will be the same. Everything changes.

And yet, nothing changes. Malthusian principles are universal in their application. No matter what comes, all replicator populations will be subject to those principles:

Malthus, also famous as an economist, would no doubt have envisaged supply and demand still driving price. Even in a MNT future, someone has to provide the raw materials to satisfy the demand of an ever expanding population of human replicators. 

Everything changes, and nothing changes.

Is there anybody out there?

Drexler's pragmatic realism also extends to the issue of alien life-forms (Drexler, 1990):

"If extraterrestrial civilizations exist, and if even a small fraction were to behave as all life on Earth does, then they should by now have spread across space."

"By now, after hundreds of millions of years, even widely scattered civilizations would have spread far enough to meet each other, dividing all of space among them."

Drexler touches on an area which is key to understanding the nature of life. Life does not waste resources, and every solar system contains resources on a scale that dwarfs our own current resource usage. For those fans of science-fiction who dream of galactic empires soon after we colonise the Moon or Mars, I urge you to reconsider. The full colonisation of our solar system is the logical next step for whichever Earth life-form gets there first. Anything else is inefficient and wasteful, and any Earth species which fails to recognise that will not be able to compete on the galactic evolutionary stage should they have to, in fact, compete with other space-faring species (Drexler, 1990):

"If these civilizations are indeed everywhere, then they have shown great restraint and hidden themselves well. They would have controlled the resources of whole galaxies for many millions of years, and faced limits to growth on a cosmic scale. An advanced civilization pushing its ecological limits would, almost by definition, not waste both matter and energy. Yet we see such waste in all directions, as far as we can see spiral galaxies: their spiral arms hold dust clouds made of wasted matter, backlit by wasted starlight."

I take my hat off to Drexler for his consistently realistic and practical views, and his optimism. Even without the MNT content, "Engines Of Creation" should be recognised as contributing to evolutionary theory (or at least presenting a neat synthesis of existing concepts). With MNT, "Engines Of Creation" and the more technical "Nano Systems" deserve to be recognised as helping define the future course of evolution. Whereas Darwin deserves recognition for explaining the puzzle of the geological record and the living world, Drexler is one of a few who dare to look forward. Drexler's arguments for MNT replicators apply equally well to von Neumann machines (with or without AI), and any genetic creations of the future. They are all replicators, they are all subject to Malthus' Principle Of Population (particularly exponential growth), all will compete within the principle of differential replication, and all would have to face the Kardashev-Malthus limits to growth should they make it that far.

I find it fascinating that, once again, Malthus is a key figure in the thinking on evolution (as he was for Darwin and Wallace).

Our future, our choice

The following passage from Drexler's 1990 book puts me in mind of Dawkins' later reflections on the "replication bomb" of life "reverberating through deep space" - see Dawkins - An Exponentialist View for more (Drexler, 1990):

"Although endless exponential growth remains a fantasy, the spread of life and civilization faces no fixed bound. Expansion will proceed, if we survive, because we are part of a living system and life tends to spread."

This is the exponentialist view of life. Life does tend to spread. Civilization, and knowledge, are precious. Civilization is also the key to the spreading of life beyond the Earth. In a sense, that is the unintentional "purpose" of any space-faring civilization. Humanity could make it an intentional purpose, and redress the harm done so far to Earth life.

Drexler then re-states the Fermi Paradox  "Where are they?" (Drexler, 1990):

"We know that competing replicators tend to expand toward their ecological limits, and that resources are nonetheless wasted throughout the universe."

From this observation Drexler, like Savage after him (see Marshall T. Savage - An Exponentialist View) concludes that we are effectively alone. Yet the message is a positive one (Drexler, 1990):

"Thus for now, and perhaps forever, we can make plans for our future without concern for limits imposed by other civilizations."

I'll second that!

Addendum.

Does Drexler have Exponentialist views? Apparently so!

"Eric Drexler's exponentialist views on molecular nanotechnology, explained in his book Engines Of Creation and popularly misrepresented as the grey goo scenario"

This is from The Discontinuity Guide: The New Series. The Doctor Dances - 28th May 2005. Writer: Steven Moffat, Director: James Hawes.

http://www.whoniverse.org/discontinuity/9J.php

As far as I am aware, this is the first independently published referenced to my usage of the word "Exponentialist" as an adjective.

David Coutts - 24th January, 2006.

 

References

Drexler, K. Eric. Engines Of Creation - The Coming Era of Nanotechnology. Online Glossary  (website accessed 15th September 2009). 1986.

Drexler, K. Eric. Engines Of Creation - The Coming Era of Nanotechnology. Oxford University Press. 1990.

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Last modified: 23 August, 2012