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Revision as of 02:56, 24 December 2012

The Kardashev scale is a method of measuring a civilization's level of technological advancement, based on the amount of energy a civilization is able to utilize. The scale has three designated categories called Type I, II, and III. A Type I civilization uses all available resources impinging on its home planet, Type II harnesses all the energy of its sun, and Type III of its galaxy. The scale is only hypothetical and in terms of an actual civilization, highly speculative; however, it puts energy consumption of an entire civilization in a cosmic perspective. It was first proposed in 1964 by the Soviet astronomer Nikolai Kardashev. Others have extended the scale to even more hypothetical Type IV beings who can control or use the entire universe, or Type V that control collections of universes. Metrics other than pure power usage have also been proposed, such as 'mastery' of a planet, system or galaxy rather than considering energy alone,[1] or considering the amount of information controlled by a civilization rather than the amount of energy.

Definition

In 1964, Kardashev defined three levels of civilizations, based on the order of magnitude of the amount of power available to them:

  • Type I: "Technological level close to the level presently (here referring to 1964) attained on earth, with energy consumption at ≈4×1019 erg/sec[2] (4 × 1012 watts.) Guillermo A. Lemarchand stated this as "A level near contemporary terrestrial civilization with an energy capability equivalent to the solar insolation on Earth, between 1016 and 10 17 watts."[3]
  • Type II: "A civilization capable of harnessing the energy radiated by its own star (for example, the stage of successful construction of a Dyson sphere), with energy consumption at ≈4×1033 erg/sec.[2] Lemarchand stated this as "A civilization capable of utilizing and channeling the entire radiation output of its star. The energy utilization would then be comparable to the luminosity of our Sun, about 4 × 1026 watts."[3]
  • Type III: "A civilization in possession of energy on the scale of its own galaxy, with energy consumption at ≈4×1044 erg/sec."[2] Lemarchand stated this as "A civilization with access to the power comparable to the luminosity of the entire Milky Way galaxy, about 4 × 1037 Watts."[3]

Current status of human civilization

Michio Kaku suggested that humans may attain Type I status in about 100–200 years, Type II status in a few thousand years, and Type III status in about 100,000 to a million years.[4]

Carl Sagan suggested defining intermediate values (not considered in Kardashev's original scale) by interpolating and extrapolating the values given above for types 1, 2 and 3, using the formula

,

where value K is a civilization's Kardashev rating and MW is the power it uses, in megawatts. He calculated humanity's civilization type (in 1973) to be about 0.7, with respect to this extrapolation (apparently using 10 terawatt (TW) as the value for 1970s humanity).[5]

In 2008, total world energy consumption was 474 exajoules (474×1018 J=132,000 TWh), equivalent to an average power consumption of 15 terawatts (1.504×1013 W or 0.7 on the Kardashev scale).[6]

The total photosynthetic productivity of earth is between ~1500–2250 TW, or 47,300–71,000 exajoules per year, making nature a 0.9 Kardashev scale civilization.

Energy development

Type I civilization methods

  • Large-scale application of fusion power. According to mass-energy equivalence, Type I implies the conversion of about 2 kg of matter to energy per second. While there is no known method to convert matter (by itself) completely into energy, an equivalent energy release could theoretically be achieved by fusing approximately 280 kg of hydrogen into helium per second,[7] a rate roughly equivalent to 8.9×109 kg/year. A cubic km of water contains about 1011 kg of hydrogen, and the Earth's oceans contain about 1.3×109 cubic km of water, meaning that this rate of consumption could be sustained over geological time scales.
  • Antimatter[8] in large quantities would have a mechanism to produce power on a scale several magnitudes above our current level of technology. In antimatter-matter collisions, the entire rest mass of the particles is converted to kinetic energy. Their energy density (energy released per mass) is about four orders of magnitude greater than that from using nuclear fission, and about two orders of magnitude greater than the best possible yield from fusion.[9] The reaction of 1 kg of anti-matter with 1 kg of matter would produce 1.8×1017 J (180 petajoules) of energy.[10] Although antimatter is sometimes proposed as a source of energy, this is currently infeasible. Artificially producing antimatter according to current understanding of the laws of physics involves first converting energy into mass, so there is no net gain. Artificially created antimatter is only usable as a medium of energy storage but not as an energy source, unless future technological developments (contrary to the conservation of the baryon number, such as a CP Violation in favour of antimatter) allow the conversion of ordinary matter into anti-matter. There are a number of naturally occurring sources of antimatter [11][12][13] we may theoretically be able to cultivate and harvest in the future.
  • Renewable energy through converting sunlight into electricity by either solar cells and concentrating solar power or indirectly through wind and hydroelectric power. Currently, there is no known way for human civilization to successfully use the equivalent of the Earth's total absorbed solar energy without completely coating the surface with man-made structures, which is presently not feasible. However, if a civilization constructed very large space-based solar power satellites, Type I power levels might be achievable.
Figure of a Dyson swarm surrounding a star

Type II civilization methods

  • A Dyson sphere or Dyson swarm and similar constructs are hypothetical megastructures originally described by Freeman Dyson as a system of orbiting solar power satellites meant to enclose a star completely and capture most or all of its energy output.[14]
  • Perhaps a more exotic means to generate usable energy would be to feed a stellar mass into a black hole, and collect photons emitted by the accretion disc.[15][16] Less exotic would be simply to capture photons already escaping from the accretion disc, reducing a black hole's angular momentum; known as the Penrose process.
  • Star lifting is a process where an advanced civilization could remove a substantial portion of a star's matter in a controlled manner for other uses.
  • Antimatter is likely to be produced as an industrial byproduct of a number of megascale engineering processes (such as the aforementioned star lifting) and therefore could be recycled.
  • In multiple-star systems of a sufficiently large number of stars, absorbing a small but significant fraction of the output of each individual star.
  • White holes, if they exist, theoretically could provide large amounts of energy from collecting the matter propelling outwards.
  • Capturing the energy of gamma-ray bursts is another theoretically possible power source for a highly advanced civilization.

Type III civilization methods

  • Type III civilizations might use the same techniques employed by a Type II civilization, but applied to all possible stars of one or more galaxies individually.[17]
  • They may also be able to tap into the energy released from the supermassive black holes which are believed to exist at the center of most galaxies.
  • The emissions from quasars can be readily compared to those of small active galaxies and could provide a massive power source if collectable.

Civilization implications

There are many historical examples of human civilization undergoing large-scale transitions, such as the Industrial Revolution. The transition between Kardashev scale levels could potentially represent similarly dramatic periods of social upheaval, since they entail surpassing the hard limits of the resources available in a civilization's existing territory. A common speculation[18] suggests that the transition from Type 0 to Type I might carry a strong risk of self-destruction since, in some scenarios, there would no longer be room for further expansion on the civilization's home planet, similar to a Malthusian catastrophe. Excessive use of energy without adequate disposal of heat, for example, could plausibly make the planet of a civilization approaching Type I unsuitable to the biology of the dominant life-forms and their food sources. If Earth is an example, then sea temperatures in excess of 35 °C would jeopardize marine life and make the cooling of mammals to temperatures suitable for their metabolism difficult if not impossible. Of course, these theoretical speculations may not become problems in reality due to evolution or the application of future engineering and technology. Also, by the time a civilization reaches Type I it may have colonized other planets or created O'Neill-type colonies, so the amount of waste heat could be distributed throughout the solar system.

Extensions to the original scale

The state that human civilization currently occupies was originally Type I in the Kardashev scale, but has a K value below 1 using Sagan's logarithmic formula (described above).

Zoltan Galantai has defined a further extrapolation of the scale, a Type IV level which controls the energy output of the visible universe; this is within a few orders of magnitude of 1045 W. Such a civilization approaches or surpasses the limits of speculation based on current scientific understanding, and may not be possible. Frank J. Tipler's Omega point would presumably occupy this level, as would the Biocosm hypothesis. Galantai has argued that such a civilization could not be detected, as its activities would be indistinguishable from the workings of nature (there being nothing to compare them to).[19]

However, Milan M. Ćirković has argued that "Type IV" should instead be used to refer to a civilization that has harnessed the power of its supercluster, or "the largest gravitationally bound structure it originated in."[20] For the Local Supercluster, this would be approximately 1042 W.

Dr. Michio Kaku has discussed a Type IV civilization, which could harness "extragalactic" energy sources such as dark energy, in his book Parallel Worlds.[21]

In contrast to simply increasing the maximum power level covered by the scale, Carl Sagan suggested adding another dimension: the information available to the civilization. He assigned the letter A to represent 106 unique bits of information (less than any recorded human culture) and each successive letter to represent an order of magnitude increase, so that a level Z civilization would have 1031 bits. In this classification, 1973 Earth is a 0.7 H civilization, with access to 1013 bits of information. Sagan believed that no civilization has yet reached level Z, conjecturing that so much unique information would exceed that of all the intelligent species in a galactic supercluster and observing that the universe is not old enough to exchange information effectively over larger distances. The information and energy axes are not strictly interdependent, so that even a level Z civilization would not need to be Kardashev Type III.[5]

John D. Barrow, going by the fact that humans have found it more cost-effective to extend any abilities to manipulate their environment over increasingly smaller dimensions rather than increasingly larger ones, reverses the classification downward from Type I-minus to Type Omega-minus:

Type I-minus is capable of manipulating objects over the scale of themselves: building structures, mining, joining and breaking solids; Type II-minus is capable of manipulating genes and altering the development of living things, transplanting or replacing parts of themselves, reading and engineering their genetic code; Type Ill-minus is capable of manipulating molecules and molecular bonds, creating new materials; Type IV-minus is capable of manipulating individual atoms, creating nanotechnologies on the atomic scale and creating complex forms of artificial life; Type V-minus is capable of manipulating the atomic nucleus and engineering the nucleons that compose it; Type VI-minus is capable of manipulating the most elementary particles of matter (quarks and leptons) to create organized complexity among populations of elementary particles; culminating in. Type Omega-minus is capable of manipulating the basic structure of space and time.[22]

Examples in science fiction

Type 0

A Type 0 civilization extracts its energy, information, raw-materials from crude organic-based sources (i.e. Food/Wood/Fossil Fuel).

  • Cyberpunk genre (and Post-cyberpunk) is frequently centered on the transitional inter-periods between Type-0 and Type-I status. While frequently focused on how the concepts of "Transhumanism" and "Singularity" will eventually overcome the problems that have, up until now, been endemic to human nature, Cyberpunk subverts this to describe the Dystopian side should a civilization "self-destruct" in the process of achieving Type-I status. In such fiction, most current world problems are local in warfare, local in culture, and usually mono-cultural, and theistic; further aggravated by various groups trying to retain a Type-0 monoculture through existing institutions and opposition to technological progress, and others trying to move forward to a Type-I multicultural, global world though subversion, and revolutionary violence.[23][24][25]

Type I

A Type I civilization is capable of orbital spaceflight and colonization, medical and technological singularity, planetary engineering, trade and defense, and stellar system-scale influence:

Type II

A Type II civilization is capable of interplanetary spaceflight, interplanetary communication, stellar engineering, and star cluster-scale influence:

  • In the Ringworld series by Larry Niven, a ring a million miles wide is built and spun (for gravity) around a star roughly one astronomical unit away. The ring can be viewed as a functional version of a Dyson sphere with the interior surface area of 3 million Earth-sized planets. Because it is only a partial Dyson sphere, it can be viewed as an intermediary between Type I and Type II. Both Dyson spheres and the Ringworld suffer from gravitational instability, however—a major focus of the Ringworld series is coping with this instability in the face of partial collapse of the Ringworld civilization.
  • The territory of Eelong in the Pendragon Series by D. J. MacHale uses all power from a belt of suns known as the Skaa.[27]
  • Stephen Baxter's "Morlock" of The Time Ships occupy a spherical shell around the sun the diameter of earth's orbit, spinning for gravity along one band. The shell's inner surface along this band is inhabited by cultures in many lower stages of development, while the K II Morlock civilization uses the entire structure for power and computation.[citation needed]
  • In the Star Trek: The Next Generation episode "Relics", the Enterprise discovers an abandoned Dyson sphere.[28]
  • In the Halo universe, the United Nations Space Command (UNSC) and the hostile alien society known as the Covenant have both attained type II status. The UNSC is shown to be able to induce a star to go supernova and have a territory consisting of more than 800 planetary systems. [29]
  • In the Mass Effect Universe, according to Michio Kaku[30], Humanity has advanced to a Type II civilization, having colonized several planets and competing with other Type II civilizations (such as the Asari, Salarians, and Turians).[31]

Type III

A Type III civilization is capable of interstellar travel, interstellar communication, galactic engineering and galaxy-scale influence:

  • The Galactic Empire in the Star Wars series extends throughout most of its galaxy.[citation needed]
  • In Star Maker by Olaf Stapledon. The stellar energy output of the whole galaxy is used by the Galactic Community of Worlds.[32]
  • In the Halo universe, The Forerunners attained type III status; the species had the ability to manipulate gravitational force, create AI with full sentience, fabricate super-dense materials, perform super-accurate slipspace navigation, the ability to create life, and the ability to create worlds. [33]
  • In the Mass Effect universe, an advanced race of sentient machines exists known as the Reapers. In "cycles" of roughly 50,000 years, the Reapers return to the Milky Way to destroy any civilizations that have reached a certain level of technological advancement, then return to intergalactic space and await the next cycle. Reapers possess highly powerful sources of energy and can communicate across distances of thousands of light years in real time.
  • While not much is known about them, the Ancient Humanoids from Star Trek have manipulated the course of biological evolution across the entire galaxy billions of years ago. As a result, the vast majority of species in the Milky Way is humanoid, and possess a secret code embedded in their DNA. [34]

Type IV

A Type IV civilization is capable of intergalactic travel, intergalactic communication, and universal-scale influence:

  • The backstory of The Dancers at the End of Time series by Michael Moorcock describes a civilization which consumed all the energy in all the stars in the universe, save Earth's own sun, in order to fuel an existence in which the inheritors of Earth lived as near omnipotent gods.[35]
  • In a rare mention of the scale within a work of fiction, the Doctor Who novel The Gallifrey Chronicles, a Time Lord named Marnal asserts that "the Time Lords were the Type-4 civilization. We had no equals. We controlled the fundamental forces of the entire universe. Nothing could communicate with us on our level."[36]
  • Michio Kaku, in a lecture, said that in Star Trek: The Next Generation, the god-like Q Continuum could be considered above Type IV, drawing their energy from outside the universe.
  • The Players of The New Cosmogony, a fictional Nobel Prize oration in A Perfect Vacuum by Stanisław Lem, are altering the laws of physics for their own purposes.[37]
  • In Lexx a character named Mantrid uses exponential growth to make copies upon copies of his constructor arms called "Mantrid drones", eventually using all the matter in the light universe, which ends up destroying the universe when too much matter accumulates in one place, "unbalancing" it.
  • In The Gods Themselves by Isaac Asimov, a sentient species from another universe reaches Type I in conjunction with humanity, by developing a technique of exchanging electrons and protons across universes. To combat the flux of energy, humans reach Type IV by developing a technique of harvesting the energy from yet another universe, which exists in a pre-big-bang state, or a "Cosmic Egg" state.[citation needed]
  • In the Bionicle universe, the Great Beings attained this type. While they haven't been shown travelling through space, they have shown to be capable of constructing a 40 million foot high sentient robot that is capable of moving planets, and capable of creating fully sentient and synthetic cyborg civilisations. They have the ability to genetically engineer creatures to give them superpowers. Amongst their notable achievements are objects capable of manipulating fundamental forces of the universe, such as the Mask of Life and the Mask of Creation. They also possess the ability to travel between dimensions and even universes.[citation needed]
  • The immortal "Guardians of the Universe", creators of the Green Lantern Corps (DC Comics), have manipulated events on an intergalactic scale for three billion years.
  • The Xeelee from Stephen Baxters Xeelee Sequence are present through the universe, have instantaneous communication and constructed an artefact 10 million light year across, using the material of many galaxies. They possess time travel capabilities which they use to construct closed timelike curves in which they modified their own evolution, becoming the most advanced barionic civilization.
  • The "Ancients" from the multiple Stargate series. The building of wormhole travel devices, time travel devices as well as the potential to bridge parallel universes for the purpose of travel and energy production classify these as a class IV civilisation. The Stargate Atlantis series is based with technology hundreds of thousands of years beyond that of space travel on a universal scale, as shown in the Stargate Universe series, potentially classifying them as class V, but with no proof.

Type V, and beyond

Such hypothetical civilizations have either transcended their universe of origin or arose within a multiverse or other higher-order membrane of existence, and are capable of universe-scale manipulation of individual discrete universes from an external frame of reference. In fiction, their artifacts or endowed abilities find their way into the hands of relatively juvenile civilizations, such as humanity:

  • The 2011 God and the Universe episode of the American History Channel television series The Universe explored the possibility of sufficiently advanced civilizations custom-building new universes.[38]
  • The organization known as the Infinite Consortium from Magic: the Gathering stretches between the planes of existence throughout the multiverse.[citation needed]
  • The Downstreamers from Manifold: Time, after completely controlling their universe, used time travel to induce the creation of a multiverse.[citation needed]
  • In the collection of Science Fiction Short Stories 'Ancient Tales from the Distant Future', Author Nicholas Mustelin partially describes an entity, given in English the name The Jovian Collective (they do not use a name for themselves as their mode of communication differs from speech and could considered as pure thought) , a race of omnipotent beings capable of entering in between individual 'time-frames' of the time-space continuum. The Jovian Collective is an entity that stems from The Collective, an ancient race that is one of the three first civilizations that emerged: The Firstborn (as described by Sir Arthur C. Clarke in his Space Odyssey series and other works, see 2001: A Space Odyssey above), The Collective which are slightly younger than The Firstborn and consist of Hive Minds or groups of smaller components, and The Experimentals, who, among other things – in cooperation with The Firstborn and The Collective – create, assist and guide emerging cultures, such as Humanity. The Jovian Collective consists of three basic elements: A) The Translucents who are born from certain chemical reactions and radiation processes in the atmosphere of certain types of gas-giant planets, in this case Jupiter; however they are not indigenous to this particular planet. The main function of The Translucents is to gather information and investigate all matter and phenomena, conveying that information to The Solids and The Omnis. B) One Solid is created through a complicated synthesis and merging of three (or occasionally more) compatible Translucents who have completed their cycle and concluded their other tasks. The Solids are the builders, constructors, engineers and architects of The Jovian Collective. When a large number of Solids (usually 250 or more units) at the end of their life-cycle merge in a process that lasts for several weeks, Earth time, they form one Omni through a certain type of a complicated guided fusion. C) The Omni, who are very few in number but much more powerful than The Translucents and The Solids, have the ability to visit all spatial coordinates in the Universe in one single point, and all points in time – past, present and future – in one moment. Thus they can enter in between the individual 'time-frames' of the time-space continuum, as described in the Short Stories 'Freeze!' and 'Good Morning?' in the above mentioned collection 'Ancient Tales from the Distant Future' by Nicholas Mustelin. The Omni are also capable of creating, manipulating and destroying cosmic objects such as stars, planets and black holes. The Translucents, Solids and Omni are all connected through a neural network and communicate instantly and directly and without effort or intent, much like the cells in a human body, for example. Through their combined efforts and capabilities, The Jovian Collective could be considered as a Type V civilization or above on the Kardashev scale, although the method of classification is somewhat inappropriate due to the abilities of The Jovian Collective – and The Collective in general – not described in this method of classification. Like The Firstborn, their civilization may be thought of as one that surpasses those which can be easily classified on the Kardashev scale. A more detailed description of The Jovian Collective will be included in the second volume of 'Collected Tales from the Future' will be introduced in the collection of SF Short Stories 'More Ancient Tales from the Distant Future' (name pending) that will be published in 2013.[citation needed]

Connections with sociology and anthropology

Kardashev's theory can be viewed as the expansion of some social theories, especially from social evolutionism. It is close to the theory of Leslie White, author of The Evolution of Culture: The Development of Civilization to the Fall of Rome (1959). White attempted to create a theory explaining the entire history of humanity. The most important factor in his theory is technology: Social systems are determined by technological systems, wrote White in his book, echoing the earlier theory of Lewis Henry Morgan. As a measure of society advancement, he proposed the measure of energy consumption of a given society (thus his theory is known as the energy theory of cultural evolution). He differentiates between five stages of human development. In the first stage, people use energy of their own muscles. In the second stage, they use energy of domesticated animals. In the third stage, they use the energy of plants (which White refers to as agricultural revolution). In the fourth stage, they learn to use the energy of natural resources—such as coal, oil, and gas. Finally, in the fifth stage, they harness nuclear energy. White introduced a formula P=E×T, where P measures the advancement of the culture, E is a measure of energy consumed, and T is the measure of efficiency of technical factors utilizing the energy.[citation needed]

Criticism

It has been argued that, because we cannot understand advanced civilizations, we cannot predict their behavior; thus, Kardashev's visualization may not reflect what will actually occur for an advanced civilization. This central argument is found in the book Evolving the Alien: The Science of Extraterrestrial Life.[39]

Robert Zubrin uses the terms to refer to how widespread a civilization is in space, rather than to its energy use. In other words, a Type I civilization has spread across its planet, a Type II has extensive colonies in its respective stellar system, and a Type III has colonized its galaxy.[citation needed]

See also

References

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  10. ^ By the mass-energy equivalence formula E = mc². See anti-matter as a fuel source for the energy comparisons.
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  16. ^ Schutz, Bernard F. (1985). A First Course in General Relativity. New York: Cambridge University Press. pp. 304, 305. ISBN 0-521-27703-5. {{cite book}}: Cite has empty unknown parameter: |coauthors= (help)
  17. ^ Kardashev, Nikolai. "On the Inevitability and the Possible Structures of Supercivilizations", The search for extraterrestrial life: Recent developments; Proceedings of the Symposium, Boston, MA, June 18–21, 1984 (A86-38126 17-88). Dordrecht, D. Reidel Publishing Co., 1985, p. 497–504.
  18. ^ Dyson, Freeman (1960-06-03). "Search for Artificial Stellar Sources of Infrared Radiation". Science. 131 (3414). New York: W. A. Benjamin, Inc: 1667–1668. Bibcode:1960Sci...131.1667D. doi:10.1126/science.131.3414.1667. PMID 17780673. Retrieved 2008-01-30. {{cite journal}}: Cite has empty unknown parameter: |coauthors= (help)
  19. ^ Galantai, Zoltan (September 7, 2003). "Long Futures and Type IV Civilizations" (PDF). Retrieved 2006-05-26.
  20. ^ Milan M. Ćirković (2004). "Forecast for the Next Eon : Applied Cosmology and the Long-Term Fate of Intelligent Beings". Foundations of Physics. 34 (2). Springer Netherlands: 239–261. arXiv:astro-ph/0211414. Bibcode:2004FoPh...34..239C. doi:10.1023/B:FOOP.0000019583.67831.60. ISSN (Print) 1572-9516 (Online) 0015-9018 (Print) 1572-9516 (Online). {{cite journal}}: Check |issn= value (help); Unknown parameter |month= ignored (help)
  21. ^ Kaku, Michio (2005). Parallel Worlds: The Science of Alternative Universes and Our Future in the Cosmos. New York: Doubleday. p. 317. ISBN 0-7139-9728-1. {{cite book}}: Cite has empty unknown parameter: |coauthors= (help)
  22. ^ Barrow, John (1998). Impossibility: Limits of Science and the Science of Limits. Oxford: Oxford University Press. p. 133. ISBN 0-09-977211-6. {{cite book}}: Cite has empty unknown parameter: |coauthors= (help)
  23. ^ "Type 0 Civilization".
  24. ^ "Transitioning from Type 0 oil dependency to a Type 1 civilization & ET/UFO disclosure".
  25. ^ "Type 1, 2, & 3 Civilizations".
  26. ^ "Cory Doctorow: Down and Out in the Magic Kingdom".
  27. ^ "Afro — Hallawiki". Hallawiki.a.wiki-site.com. Retrieved 2010-09-19.
  28. ^ "Star Trek: The Next Generation Relics (TV episode 1992) - IMDb". IMDB. Retrieved 2011-11-21.
  29. ^ "Technological Achievement Tiers".
  30. ^ "The Science of Mass Effect 2", at Gametrailers.com, interview with Michio Kaku
  31. ^ "Science of Mass Effect by Dr. Michio Kaku". TheClark501. Retrieved Feb 13, 2012.
  32. ^ Stapledon, Olaf Last and First Men [ 1931 ] and Star Maker [ 1937 ] New York:1968—Dover Chapters IX through XI Pages 346 to 396
  33. ^ "Technological Achievement Tiers".
  34. ^ "The Chase". The Next Generation. {{cite episode}}: |access-date= requires |url= (help); Check date values in: |accessdate= (help); Unknown parameter |Episode= ignored (help); Unknown parameter |Season= ignored (|season= suggested) (help)
  35. ^ Moorcock, Michael: Tales From the End of Time, page 121. Berkley Publishing, 1976.
  36. ^ Parkin, Lance (2005). The Gallifrey Chronicles. BBC Books. p. 56. ISBN 0-563-48624-4.
  37. ^ Swirski, Peter (2006). The art and science of Stanislaw Lem. McGill-Queen's Press. p. 147. ISBN 0-7735-3046-0.
  38. ^ | God and the Universe.
  39. ^ Jack Cohen and Ian Stewart: Evolving the Alien: The Science of Extraterrestrial Life, Ebury Press, 2002, ISBN 0-09-187927-2

Further reading

[[fr:Échelle de Kardashev]