Kardashev scale

Kardashev scale projections for human civilization ranging from years 1900 to 2030, based on data from the International Energy Agency World Energy Outlook.The Kardashev scale is a method of measuring an advanced civilization's level of technological advancement. The scale is only theoretical 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 Russian astronomer Nikolai Kardashev. The scale has three designated categories called Type I, II, and III. These are based on the amount of usable energy a civilization has at its disposal, and the degree of space colonization. In general terms, a Type I civilization has achieved mastery of the resources of its home planet, Type II of its solar system, and Type III of its galaxy.^[1]

The original and the final draft for this particular scale had energy consumptions ranging so widely from each other, that Kardashev himself revised the scale as to include values between, in hundredths. The human civilization as of 2010 is currently somewhere around 0.72, with calculations suggesting we 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.^[2]

Contents 1 Energy use 2 Current status of human civilization 3 Energy development 4 Civilization implications 5 Extensions to the original scale 6 Examples in science fiction 6.1 Type I 6.2 Type II 6.3 Type III 6.4 Above Type III/ "Type IV" 7 Connections with sociology and anthropology 8 Criticism 9 See also 10 References 11 Further reading 12 External links

Energy use

Energy is a static quantity and is denoted in joules. Power is a measure of energy transfer over time, and is denoted in watts (joules per second). The three levels of the Kardashev Scale can be quantified in units of power (watts) and plotted on an increasing logarithmic scale.

• Type I — a civilization that is able to harness all of the power available on a single planet — has approximately 10¹⁶ or 10¹⁷ W available.^[3] Earth specifically has an available power of 1.74 ×10¹⁷ W (174 peta watts, see Earth's energy budget). Kardashev's original definition was 4 ×10¹² W — a "technological level close to the level presently attained on earth" ("presently" meaning 1964).^[4]
• Type II — a civilization that is able to harness all of the power available from a single star, approximately 4 ×10²⁶ W.^[3] Again, this figure is variable; the Sun outputs approximately 3.86 ×10²⁶ W. Kardashev's original definition was also 4 ×10²⁶ W.^[4]
• Type III — a civilization that is able to harness all of the power available from a single galaxy, approximately 4 ×10³⁷ W.^[3] This figure is extremely variable, since galaxies vary widely in size; the stated figure is the approximate power output of the Milky Way. Kardashev's original definition was also 4 ×10³⁷ W.^[4]

Using nuclear explosion tests as a perspective, Tsar Bomba, the largest nuclear weapon ever detonated, released an estimated 57 megaton yield; a Type I civilization makes use of roughly 25 megatons of TNT equivalent a second, the equivalent of one Tsar Bomba every 2.3 seconds. A Type II civilization controls 4 × 10⁹ times more energy (4 billion hydrogen bombs per second), and a Type III 10¹¹ times more yet.

Current status of human civilization

Further information: World energy resources and consumption

Human civilization is currently somewhere below Type I, as it is able to harness only a portion of the energy that is available on Earth. The current state of human civilization has thus been named Type 0. Although intermediate values were not discussed in Kardashev's original proposal, Carl Sagan argued that they could easily be defined by interpolating and extrapolating the values given above. In 1973, he calculated humanity's civilization type to be 0.7, in relationship to Kardashev's model for Types 0 and I.^[5]
Sagan used the formula

,

where value K is a civilization's Kardashev rating and MW is its power output in megawatts. Sagan used 10 terawatt (TW) as the value W for 1973's humanity, which was somewhat higher than present data suggests.^[6] This overestimation results in a change of 0.01 in the Kardashev value (see table below).
International Energy Agency World Energy Outlook (2005)^[6] and section 7 of Key World Energy Statistics^{[7][dead link]} project values for planetary power utilization yielding these corresponding Kardashev scale estimates:

Year	Energy production				Kardashev rating
	Exajoules/year	Terawatts	Quads/year[8]	Mtoe/year[9]
1900	21	0.67	20	500	0.58
1970	190	6.0	180	4,500	0.67
1973	260	8.2	240	6,200	0.69
1985	290	9.2	270	6,900	0.69
1989	320	10	300	7,600	0.70
1993	340	11	320	8,100	0.70
1995	360	12	340	8,700	0.70
2000	420	13	400	10,000	0.71
2001	420	13	400	10,000	0.71
2002	430	14	410	10,400	0.71
2004	440	14	420	10,600	0.71
2010	510	16	480	12,100	0.72
2030	680	22	650	16,300	0.73

As of 2007, the Kardashev rating is approximately 0.72, calculated using BP's primary energy consumption chart for 2007.^[10] It is important to note that as Sagan's Kardashev rating is base-10-billion logarithmic, a value of 0.72 means we are using approximately 0.16% of the total available planetary energy budget. The baseline value, K = 0, can be imagined as the status of an early civilization with the manual labor of ~10000 adults, or with a team of ~1000 horses (see orders of magnitude).

Energy development

See also: Energy development

Methods by which a civilization could feasibly advance to Type I:

• 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,^[11] 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^[12] in large quantities would have a mechanism to produce power on a scale several factors 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 4 orders of magnitude greater than that from using nuclear fission, and about 2 orders of magnitude greater than the best possible yield from fusion.^[13] The reaction of 1 kg of anti-matter with 1 kg of matter would produce 1.8 × 10¹⁷ J (180 petajoules) of energy.^[14] Although antimatter is sometimes proposed as a source of energy, this is infeasible. Any naturally occurring antimatter would have long annihilated before it could be harvested. Artificially producing antimatter involves first converting energy into mass, so there is no net gain. Antimatter is only usable as a medium of energy storage but not as an energy source.
• Solar 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 utilize 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 civilizations might employ:

• 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 completely enclose a star and capture most or all of its energy output.^[15]
• 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.^[16][17] 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.
• In multiple-star systems of a sufficiently large number of stars, absorbing a small but significant fraction of the output of each individual star.

Type III civilizations might use the same techniques employed by a Type II civilization, but applied to all of the stars of one or more galaxies individually.^[18] 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.

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^[19] 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 thanks to 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 sub-Type I state that human civilization currently occupies was not originally included in the Kardashev scale but is now referred to as "Type 0" or by its K value 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).^[20]
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."^[21] 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.^[22]
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 effectively exchange information 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]

Examples in science fiction

Type I

• The humans from Stargate Universe where they use the power of the planet Icarus, with a crust containing massive amounts of a power-generating element, to route enough power to the Stargate to encode or dial the ninth chevron, in contrast to normal intragalactic, seven-chevron addresses and intergalactic eight-chevron addresses. This allowed the gate to open to the Ancient's ship Destiny, which had been travelling for many millennia under solar power and had travelled through hundreds of galaxies other than our own.

Type II

• The territory of Eelong in the Pendragon Series by D. J. MacHale utilizes all power from a belt of suns known as the Skaa.^[23]
• In the Star Trek: The Next Generation episode "Relics", the Enterprise discovers an abandoned Dyson shell, a special case of a Dyson sphere.^{[citation needed]}
• In Bob Shaw's 'Orbitsville', the giant sphere which encases a sun is presumed to have been built by using the output of the star itself. In the sequel, 'Orbitsville Departure', more spheres are confirmed and may escalate the builders to Type III.

Type III

• In Star Maker by Olaf Stapledon. The stellar energy output of the whole galaxy is utilized by the Galactic Community of Worlds.^[24]

Above Type III/ "Type IV"

• 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.^[25]
• 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."^[26]
• The Priors in the House of Suns by Alastair Reynolds could be placed as a Type IV, being surmised by one of the characters for being responsible for the apparent emptiness of the Boötes void some 250 million light years distance.
• The Xeelee in the Xeelee Sequence by Stephen Baxter. They modified their own history and have spread across the universe, typically being concentrated in the heart of galaxies where they use the black holes for their own purposes.^{[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 measure of society advancement he proposed the measure 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.

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.^[27]
On a more direct level, since the Kardashev scale rates a civilization according to how much energy it is capable of harnessing, it "penalizes" a civilization that invents ways of making more efficient use of the energy already available to it, instead of simply harnessing yet more energy. An extremely advanced civilization might also choose to forgo either the projects or the materialistic growth (expansion) humanity associates with high energy demand.
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 the galaxy.^{[citation needed]}

See also

• Astroengineering
• Clarke's three laws
• Drake equation
• World energy resources and consumption
• Orders of magnitude (power)
• Orders of magnitude (energy)
• Sustainability
• Technological singularity

References

1. ^ Zubrin, Robert, 1999, Entering Space — Creating a Spacefaring Civilization
2. ^ Kaku, Michio (2010). "The Physics of Interstellar Travel: To one day, reach the stars.". Retrieved 2010-08-29.
3. ^ ^{a b c} Lemarchand, Guillermo A. Detectability of Extraterrestrial Technological Activities. Coseti.
4. ^ ^{a b c} Kardashev, Nikolai (1964). "Transmission of Information by Extraterrestrial Civilizations" (PDF). Soviet Astronomy 8: 217. Bibcode 1964SvA.....8..217K.
5. ^ ^{a b} Sagan, Carl (October 2000) [1973]. Jerome Agel. ed. Cosmic Connection: An Extraterrestrial Perspective. Freeman J. Dyson, David Morrison. Cambridge Press. ISBN 05-21-7830-38. Retrieved 2008-01-01.
6. ^ ^{a b}  "8" (PDF). World Energy Outlook. Paris, France: International Energy Agency. p. 82. ISBN 92-64-1094-98. Retrieved 2008-01-01.]
7. ^ "Key World Energy Statistics" (PDF). International Energy Agency. 2004. Archived from the original on 2006-05-24. Retrieved 2006-08-10.
8. ^ Quads: 1 quadrillion BTU
9. ^ Mtoes: Million tonnes (metric tons) of oil equivalents
10. ^ BP Primary energy consumption chart for 2007
11. ^ Souers, P. C. (1986). Hydrogen properties for fusion energy. University of California Press. pp. 4. ISBN 978-0520055001.
12. ^ [1]
13. ^ Borowski, Steve K. (1987-07-29). "Comparison of Fusion/Anti-matter Propulsion Systems for Interplanetary Travel" (PDF). Technical Memorandum 107030. San Diego, California, USA: National Aeronautics and Space Administration. pp. 1–3. Retrieved 2008-01-28.
14. ^ By the mass-energy equivalence formula E = mc². See anti-matter as a fuel source for the energy comparisons.
15. ^ Dyson, Freeman J. (1966). "The Search for Extraterrestrial Technology". Perspectives in Modern Physics (New York: John Wiley & Sons).
16. ^ Newman, Phil (2001-10-22). "New Energy Source "Wrings" Power from Black Hole Spin". NASA. Archived from the original on 2008-02-09. Retrieved 2008-02-19.
17. ^ Schutz, Bernard F. (1985). A First Course in General Relativity. New York: Cambridge University Press. pp. 304, 305. ISBN 0521277035.
18. ^ 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.
19. ^ Dyson, Freeman (1960-06-03). "Search for Artificial Stellar Sources of Infrared Radiation". Science (New York: W. A. Benjamin, Inc) 131 (3414): 1667–1668. doi:10.1126/science.131.3414.1667. PMID 17780673. Retrieved 2008-01-30.
20. ^ Galantai, Zoltan (September 7, 2003). "Long Futures and Type IV Civilizations" (PDF). Retrieved 2006-05-26.
21. ^ Milan M. Ćirković (February 2004). "Forecast for the Next Eon : Applied Cosmology and the Long-Term Fate of Intelligent Beings". Foundations of Physics (Springer Netherlands) 34 (2): 239–261. doi:10.1023/B:FOOP.0000019583.67831.60. ISSN (Print) 1572-9516 (Online) 0015-9018 (Print) 1572-9516 (Online).
22. ^ Kaku, Michio (2005). Parallel Worlds: The Science of Alternative Universes and Our Future in the Cosmos. New York: Doubleday. p. 317. ISBN 0713997281.
23. ^ "Afro - Hallawiki". Hallawiki.a.wiki-site.com. Retrieved 2010-09-19.
24. ^ Stapledon, Olaf Last and First Men [ 1931 ] and Star Maker [ 1937 ] New York:1968—Dover Chapters IX through XI Pages 346 to 396
25. ^ Moorcock, Michael: Tales From the End of Time, page 121. Berkley Publishing, 1976.
26. ^ Parkin, Lance (2005). The Gallifrey Chronicles. BBC Books. p. 56. ISBN 0-563-48624-4.
27. ^ Jack Cohen and Ian Stewart: Evolving the Alien: The Science of Extraterrestrial Life, Ebury Press, 2002, ISBN 0-09-187927-2

Further reading

• Dyson, Freeman J. Energy in the Universe Article in September 1971 Scientific American magazine (Special September Issue on Energy)
• Rusinek, Marvin (1998). "Energy Consumption of Europe". The Physics Factbook.
• Wind Powering America
• Clean Energy for Planetary Survival: International Development Research Centre
• LBL Scientists Research Global Warming
• E³ Handbook
• Clarke H2 energy systems
• Holdren, John P.; Carl Kaysen (2003). "Environmental Change and the Human Condition" (PDF). Bulletin Fall. pp. 24–31. Retrieved 2006-08-10.
• Dordrecht, D. (1985). "Exponential Expansion: Galactic Destiny or Technological Hubris?". In B. R. Finney, M. D. Papagiannis. The Search for Extraterrestrial Life: Recent Developments. Reidel Publ. Co.. pp. 465–463.
• Shkadov Thruster
• Korotayev, A.; Malkov, A.; Khaltourina, D. (2006). Introduction to Social Macrodynamics: Compact Macromodels of the World System Growth. Moscow: URSS. ISBN 5484004144.
• Kardashev, Nikolai (March 1997). "Cosmology and Civilizations". Astrophysics and Space Science 252.
• Supercivilizations as Possible Products of the Progressive Evolution of Matter: also by Kardashev
• Search for Artificial Stellar Sources of Infrared Radiation, by Freeman J. Dyson
• The Radio Search For Intelligent Extraterrestral Life, by Frank Drake
• Freitas Jr., Robert A.. Energy and Culture (chapter 15).

External links

• Kardashev civilizations
• Detectability of Extraterrestrial Technological Activities
• Flash Animation on Civilizations
• After Kardashev: Farewell to Super Civilizations
• Exotic Civilizations: Beyond Kardashev
• Useful Comparisons of Fictional Works Using the Kardashev Scale

LRO's Crater Science Investigations

If you want to learn more about the history of Earth and other rocky planets in the solar system, craters are a great place to look. Now, thanks to LRO's LROC instrument, we can take a much closer look at Linné Crater on the moon--a pristine crater that's great to use to compare with other craters! See: LRO's Crater Science Investigations

The life cycle of a lunar impact and associated time and special scales. The LCROSS measurement methods are “layered” in response to the rapidly evolving impact environment. See: Impact:Lunar CRater Observation Satellite (LCROSS)

Data from the ultraviolet/visible spectrometer taken shortly after impact showing emission lines (indicated by arrows). These emission lines are diagnostic of compounds in the vapor/debris cloud.
Credit: NASA

LCROSS Impact Data Indicates Water on Moon11.13.09

 ***

 

It is important that we establish an outpost on the moon in order to progress further out into the universe. A lot of work has to be done to venture further out, so that we may explore.

Click on Image

See Also: Plato's Nightlight Mining Company

Geo-neutrinos

The main geophysical and geochemical processes that have driven the evolution of the Earth are strictly bound by the planet̓s energy budget. The current flux of energy entering the Earth’s atmosphere is well known: the main contribution comes from solar radiation (1.4 × 10³ W m^–2), while the energy deposited by cosmic rays is significantly smaller (10^–8 W m^–2). The uncertainties on terrestrial thermal power are larger – although the most quoted models estimate a global heat loss in the range of 40–47 TW, a global power of 30 TW is not excluded. The measurements of the temperature gradient taken from some 4 × 10⁴ drill holes distributed around the world provide a constraint on the Earth’s heat production. Nevertheless, these direct investigations fail near the oceanic ridge, where the mantle content emerges: here hydrothermal circulation is a highly efficient heat-transport mechanism.

The generation of the Earth’s magnetic field, its mantle circulation, plate tectonics and secular (i.e. long lasting) cooling are processes that depend on terrestrial heat production and distribution, and on the separate contributions to Earth’s energy supply (radiogenic, gravitational, chemical etc.). An unambiguous and observationally based determination of radiogenic heat production is therefore necessary for understanding the Earth’s energetics. Such an observation requires determining the quantity of long-lived radioactive elements in the Earth. However, the direct geochemical investigations only go as far as the upper portion of the mantle, so all of the geochemical estimates of the global abundances of heat-generating elements depend on the assumption that the composition of meteorites reflects that of the Earth. See:Looking into the Earth’s interior with geo-neutrinos

The Xenon Dark Matter Project

 

Dark Matter Results from 100 Live Days of XENON100 Data

http://www.nytimes.com/2011/04/14/science/space/14dark.html?_r=1&ref=science
http://www.sciencenews.org/view/generic/id/72744/title/XENON100_fails_to_find_dark_matter
http://news.sciencemag.org/sciencenow/2011/04/scienceshot-dark-matter-keep.html
http://www.scientificamerican.com/blog/post.cfm?id=underground-xenon100-experiment-clo-2011-04-14&WT.mc_id=SA_CAT_physics_20110415
http://www.nature.com/news/2011/110414/full/news.2011.235.html
http://www.interactions.org/cms/?pid=1030649
http://www.nsf.gov/news/news_images.jsp?cntn_id=119246&org=NSF
http://www.infn.it/news/news.php?id=609
http://lescienze.espresso.repubblica.it/articolo/titolo/1347477
http://www.abruzzo24ore.tv/news/Xenon-a-caccia-di-materia-oscura-nel-cuore-del-Gran-Sasso/16596.htm
http://www.ilcapoluogo.com/Rubriche/Arte-Cultura-e-Spettacolo/Xenon-fa-luce-sui-misteri-della-materia-oscura-dai-Laboratori-Nazionali-Gran-Sasso-di-Nicola-Facciolini-10971
http://www.cityservices.it/notizia?id=8368
http://www.scienzainrete.it/contenuto/articolo/Dal-Gran-Sasso-novita-sulla-materia-oscura
http://www.laquilaweb.it/news.asp?id=644&cat=4
http://www.abruzzoweb.it/contenuti/laboratori-gran-sasso-primo-identikit-particelle-materia-oscura/23966-4/
http://www.primadanoi.it/modules/articolo/article.php?storyid=5641&com_id=8521&com_rootid=8521&
http://www.agenziastra.it/notizia.php?action=visualizza_notizia&id=74831

See Also: South Dakota's LUX will join the dark matter wars

The Black Swan

"All swans are white" is a falsifiable claim – it could be proven wrong.

Black Swan, Claremont (Cygnus atratus), Tasmania, Australia

Even so, the statement all swans are white is testable by being falsifiable. For, if in testing many swans, the researcher finds a single black swan, then the statement all swans are white would be falsified by the counterexample of the single black swan. See:Inductive categorical inference

The demarcation problem (or boundary problem^[1]) in the philosophy of science is about how and where to draw the lines around science. The boundaries are commonly drawn between science and non-science, between science and pseudoscience, between science and philosophy and between science and religion.^[2] A form of this problem, known as the generalized problem of demarcation subsumes all four cases.
After over a century of dialogue among philosophers of science and scientists in varied fields, and despite broad agreement on the basics of scientific method,^[3] the boundaries between science and non-science continue to be debated.^[4]

Our major conclusion is simply a reaffirmation of the general statement that perceptual organization is powerfully determined by expectations built upon past commerce with the environment. When such expectations are violated by the environment, the perceiver's behavior can be described as resistance to the recognition of the unexpected or incongruous. The resistance manifests itself in subtle and complex but nevertheless distinguishable perceptual responses. Among the perceptual processes which implement this resistance are (1) the dominance of one principle of organization which prevents the appearance of incongruity and (2) a form of "partial assimilation to expectancy" which we have called compromise. When these responses fail and when correct recognition does not occur, what results may best be described as perceptual disruption. Correct [p. 223] recognition itself results when inappropriate expectancies are discarded after failure of confirmation. See:On the Perception of Incongruity: A Paradigm

See Also:

•  Book review: “Thinking, fast and slow” by Daniel Kahneman -

A Point in Space

For Newton the universe lived in an infinite and featureless space.There was no boundary, ad no possibility of conceiving anything outside of it. This was no problem for God, as he was everywhere. For Newton, space was the "sensorium" of God-the medium of his presence in and attachment to the world. The infinity of space was then a necessary reflection of the infinite capacity of God.The Life of the Cosmos By Lee Smolin Oxford University Press; New York, N.Y.: 1997, Page 91-See Also: Configuration Space

Can we be through physicality such a place,  through which  "a point" can be expressed, as the space in which we live?

Three-dimensional space is a geometric model of the physical universe in which we live. The three dimensions are commonly called length, width, and depth (or height), although any three directions can be chosen, provided that they do not lie in the same plane.

In physics and mathematics, a sequence of n numbers can be understood as a location in n-dimensional space. When n = 3, the set of all such locations is called 3-dimensional Euclidean space.

I mean the borders with which perspective is guaranteed is to fill, is to which all life evolves around,  is the perception that is limited to a defined space given through which that point becomes nothing more then the regurgitation of all their own parameters with which the individual builds their own confines? This is what is funneled into their way of thinking, yet out of complexity, such individuality is using the same system with which one can explain universality? How large is your universe?

I presented the idea of Entheorizing as an example of what can be placed over top of Pascal's triangle of possible numbered systems so as to be defined "as a funnel of a parameter spaces" complex and chaotic indeed that can be moved down through a point to a defined position?

Hi Steven,

Yes Pascal has been of quite interest to me as well.

The Galton Box is a interesting correlation in thinking as to outcome? Some might use mountains and pebbles...others still out comes as numbered systems as to the way in which the world expresses itself.

I tried abstractly to show that from symmetry(where is this?) has an asymmetrical relation as to the bean, as if, the energy enters into expression at the peak and arrives somewhere at it's based? Yes pyramidal:)

Space

Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction.^[1] Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of the boundless four-dimensional continuum known as spacetime. In mathematics one examines 'spaces' with different numbers of dimensions and with different underlying structures. The concept of space is considered to be of fundamental importance to an understanding of the physical universe although disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework.

Debates concerning the nature, essence and the mode of existence of space date back to antiquity; namely, to treatises like the Timaeus of Plato, in his reflections on what the Greeks called: chora / Khora (i.e. 'space'), or in the Physics of Aristotle (Book IV, Delta) in the definition of topos (i.e. place), or even in the later 'geometrical conception of place' as 'space qua extension' in the Discourse on Place (Qawl fi al-makan) of the 11th century Arab polymath Ibn al-Haytham (Alhazen).^[2] Many of these classical philosophical questions were discussed in the Renaissance and then reformulated in the 17th century, particularly during the early development of classical mechanics. In Isaac Newton's view, space was absolute - in the sense that it existed permanently and independently of whether there were any matter in the space.^[3]

Other natural philosophers, notably Gottfried Leibniz, thought instead that space was a collection of relations between objects, given by their distance and direction from one another. In the 18th century, the philosopher and theologian George Berkely attempted to refute the 'visibility of spatial depth' in his Essay Towards a New Theory of Vision. Later, the great metaphysician Immanuel Kant described space and time as elements of a systematic framework that humans use to structure their experience; he referred to 'space' in his Critique of Pure Reason as being: a subjective 'pure a priori form of intuition', hence that its existence depends on our human faculties.

In the 19th and 20th centuries mathematicians began to examine non-Euclidean geometries, in which space can be said to be curved, rather than flat. According to Albert Einstein's theory of general relativity, space around gravitational fields deviates from Euclidean space.^[4] Experimental tests of general relativity have confirmed that non-Euclidean space provides a better model for the shape of space.

Contents 1 Philosophy of space 1.1 Leibniz and Newton 1.2 Kant 1.3 Non-Euclidean geometry 1.4 Gauss and Poincaré 1.5 Einstein 2 Mathematics 3 Physics 3.1 Classical mechanics 3.2 Astronomy 3.3 Relativity 3.4 Cosmology 4 Spatial measurement 5 Geographical space 6 In psychology 7 See also 8 References

Philosophy of space

Leibniz and Newton

Gottfried Leibniz

 

In the seventeenth century, the philosophy of space and time emerged as a central issue in epistemology and metaphysics. At its heart, Gottfried Leibniz, the German philosopher-mathematician, and Isaac Newton, the English physicist-mathematician, set out two opposing theories of what space is. Rather than being an entity that independently exists over and above other matter, Leibniz held that space is no more than the collection of spatial relations between objects in the world: "space is that which results from places taken together".^[5] Unoccupied regions are those that could have objects in them, and thus spatial relations with other places. For Leibniz, then, space was an idealised abstraction from the relations between individual entities or their possible locations and therefore could not be continuous but must be discrete.^[6] Space could be thought of in a similar way to the relations between family members. Although people in the family are related to one another, the relations do not exist independently of the people.^[7] Leibniz argued that space could not exist independently of objects in the world because that implies a difference between two universes exactly alike except for the location of the material world in each universe. But since there would be no observational way of telling these universes apart then, according to the identity of indiscernibles, there would be no real difference between them. According to the principle of sufficient reason, any theory of space that implied that there could be these two possible universes, must therefore be wrong.^[8]

Isaac Newton

 

Newton took space to be more than relations between material objects and based his position on observation and experimentation. For a relationist there can be no real difference between inertial motion, in which the object travels with constant velocity, and non-inertial motion, in which the velocity changes with time, since all spatial measurements are relative to other objects and their motions. But Newton argued that since non-inertial motion generates forces, it must be absolute.^[9] He used the example of water in a spinning bucket to demonstrate his argument. Water in a bucket is hung from a rope and set to spin, starts with a flat surface. After a while, as the bucket continues to spin, the surface of the water becomes concave. If the bucket's spinning is stopped then the surface of the water remains concave as it continues to spin. The concave surface is therefore apparently not the result of relative motion between the bucket and the water.^[10] Instead, Newton argued, it must be a result of non-inertial motion relative to space itself. For several centuries the bucket argument was decisive in showing that space must exist independently of matter.

Kant

Immanuel Kant

 

In the eighteenth century the German philosopher Immanuel Kant developed a theory of knowledge in which knowledge about space can be both a priori and synthetic.^[11] According to Kant, knowledge about space is synthetic, in that statements about space are not simply true by virtue of the meaning of the words in the statement. In his work, Kant rejected the view that space must be either a substance or relation. Instead he came to the conclusion that space and time are not discovered by humans to be objective features of the world, but are part of an unavoidable systematic framework for organizing our experiences.^[12]

Non-Euclidean geometry

Spherical geometry is similar to elliptical geometry. On the surface of a sphere there are no parallel lines.

 

Euclid's Elements contained five postulates that form the basis for Euclidean geometry. One of these, the parallel postulate has been the subject of debate among mathematicians for many centuries. It states that on any plane on which there is a straight line L₁ and a point P not on L₁, there is only one straight line L₂ on the plane that passes through the point P and is parallel to the straight line L₁. Until the 19th century, few doubted the truth of the postulate; instead debate centered over whether it was necessary as an axiom, or whether it was a theory that could be derived from the other axioms.^[13] Around 1830 though, the Hungarian János Bolyai and the Russian Nikolai Ivanovich Lobachevsky separately published treatises on a type of geometry that does not include the parallel postulate, called hyperbolic geometry. In this geometry, an infinite number of parallel lines pass through the point P. Consequently the sum of angles in a triangle is less than 180^o and the ratio of a circle's circumference to its diameter is greater than pi. In the 1850s, Bernhard Riemann developed an equivalent theory of elliptical geometry, in which no parallel lines pass through P. In this geometry, triangles have more than 180^o and circles have a ratio of circumference-to-diameter that is less than pi.

Type of geometry	Number of parallels	Sum of angles in a triangle	Ratio of circumference to diameter of circle	Measure of curvature
Hyperbolic	Infinite	< 180o	> π	< 0
Euclidean	1	180o	π	0
Elliptical	0	> 180o	< π	> 0

Gauss and Poincaré

Carl Friedrich Gauss

 

Henri Poincaré

 

Although there was a prevailing Kantian consensus at the time, once non-Euclidean geometries had been formalised, some began to wonder whether or not physical space is curved. Carl Friedrich Gauss, a German mathematician, was the first to consider an empirical investigation of the geometrical structure of space. He thought of making a test of the sum of the angles of an enormous stellar triangle and there are reports he actually carried out a test, on a small scale, by triangulating mountain tops in Germany.^[14]

Henri Poincaré, a French mathematician and physicist of the late 19th century introduced an important insight in which he attempted to demonstrate the futility of any attempt to discover which geometry applies to space by experiment.^[15] He considered the predicament that would face scientists if they were confined to the surface of an imaginary large sphere with particular properties, known as a sphere-world. In this world, the temperature is taken to vary in such a way that all objects expand and contract in similar proportions in different places on the sphere. With a suitable falloff in temperature, if the scientists try to use measuring rods to determine the sum of the angles in a triangle, they can be deceived into thinking that they inhabit a plane, rather than a spherical surface.^[16] In fact, the scientists cannot in principle determine whether they inhabit a plane or sphere and, Poincaré argued, the same is true for the debate over whether real space is Euclidean or not. For him, which geometry was used to describe space, was a matter of convention.^[17] Since Euclidean geometry is simpler than non-Euclidean geometry, he assumed the former would always be used to describe the 'true' geometry of the world.^[18]

Einstein

Albert Einstein

 

In 1905, Albert Einstein published a paper on a special theory of relativity, in which he proposed that space and time be combined into a single construct known as spacetime. In this theory, the speed of light in a vacuum is the same for all observers—which has the result that two events that appear simultaneous to one particular observer will not be simultaneous to another observer if the observers are moving with respect to one another. Moreover, an observer will measure a moving clock to tick more slowly than one that is stationary with respect to them; and objects are measured to be shortened in the direction that they are moving with respect to the observer.

Over the following ten years Einstein worked on a general theory of relativity, which is a theory of how gravity interacts with spacetime. Instead of viewing gravity as a force field acting in spacetime, Einstein suggested that it modifies the geometric structure of spacetime itself.^[19] According to the general theory, time goes more slowly at places with lower gravitational potentials and rays of light bend in the presence of a gravitational field. Scientists have studied the behaviour of binary pulsars, confirming the predictions of Einstein's theories and Non-Euclidean geometry is usually used to describe spacetime.

Mathematics

In modern mathematics spaces are defined as sets with some added structure. They are frequently described as different types of manifolds, which are spaces that locally approximate to Euclidean space, and where the properties are defined largely on local connectedness of points that lie on the manifold. There are however, many diverse mathematical objects that are called spaces. For example, vector spaces such as function spaces may have infinite numbers of independent dimensions and a notion of distance very different to Euclidean space, and topological spaces replace the concept of distance with a more abstract idea of nearness.

Physics

Classical mechanics

Classical mechanics

Newton's Second Law

History of classical mechanics · Timeline of classical mechanics [show]Branches [show]Formulations [hide]Fundamental concepts Space · Time · Velocity · Speed · Mass · Acceleration · Gravity · Force · Impulse · Torque / Moment / Couple · Momentum · Angular momentum · Inertia · Moment of inertia · Reference frame · Energy · Kinetic energy · Potential energy · Mechanical work · Virtual work · D'Alembert's principle [show]Core topics [show]Scientists

v · d · e

Space is one of the few fundamental quantities in physics, meaning that it cannot be defined via other quantities because nothing more fundamental is known at the present. On the other hand, it can be related to other fundamental quantities. Thus, similar to other fundamental quantities (like time and mass), space can be explored via measurement and experiment.

Astronomy

Main article: Astronomy

 

Astronomy is the science involved with the observation, explanation and measuring of objects in outer space.

Relativity

Main article: Theory of relativity

 

Before Einstein's work on relativistic physics, time and space were viewed as independent dimensions. Einstein's discoveries showed that due to relativity of motion our space and time can be mathematically combined into one object — spacetime. It turns out that distances in space or in time separately are not invariant with respect to Lorentz coordinate transformations, but distances in Minkowski space-time along space-time intervals are—which justifies the name.
In addition, time and space dimensions should not be viewed as exactly equivalent in Minkowski space-time. One can freely move in space but not in time. Thus, time and space coordinates are treated differently both in special relativity (where time is sometimes considered an imaginary coordinate) and in general relativity (where different signs are assigned to time and space components of spacetime metric).

Furthermore, in Einstein's general theory of relativity, it is postulated that space-time is geometrically distorted- curved -near to gravitationally significant masses.^[20]

Experiments are ongoing to attempt to directly measure gravitational waves. This is essentially solutions to the equations of general relativity, which describe moving ripples of spacetime. Indirect evidence for this has been found in the motions of the Hulse-Taylor binary system.

Cosmology

Main article: Shape of the universe

 

Relativity theory leads to the cosmological question of what shape the universe is, and where space came from. It appears that space was created in the Big Bang, 13.7 billion years ago and has been expanding ever since. The overall shape of space is not known, but space is known to be expanding very rapidly due to the Cosmic Inflation.

Spatial measurement

Main article: Measurement

 

The measurement of physical space has long been important. Although earlier societies had developed measuring systems, the International System of Units, (SI), is now the most common system of units used in the measuring of space, and is almost universally used.

Currently, the standard space interval, called a standard meter or simply meter, is defined as the distance traveled by light in a vacuum during a time interval of exactly 1/299,792,458 of a second. This definition coupled with present definition of the second is based on the special theory of relativity in which the speed of light plays the role of a fundamental constant of nature.

Geographical space

Geography is the branch of science concerned with identifying and describing the Earth, utilizing spatial awareness to try and understand why things exist in specific locations. Cartography is the mapping of spaces to allow better navigation, for visualization purposes and to act as a locational device. Geostatistics apply statistical concepts to collected spatial data to create an estimate for unobserved phenomena.

Geographical space is often considered as land, and can have a relation to ownership usage (in which space is seen as property or territory). While some cultures assert the rights of the individual in terms of ownership, other cultures will identify with a communal approach to land ownership, while still other cultures such as Australian Aboriginals, rather than asserting ownership rights to land, invert the relationship and consider that they are in fact owned by the land. Spatial planning is a method of regulating the use of space at land-level, with decisions made at regional, national and international levels. Space can also impact on human and cultural behavior, being an important factor in architecture, where it will impact on the design of buildings and structures, and on farming.

Ownership of space is not restricted to land. Ownership of airspace and of waters is decided internationally. Other forms of ownership have been recently asserted to other spaces — for example to the radio bands of the electromagnetic spectrum or to cyberspace.

Public space is a term used to define areas of land as collectively owned by the community, and managed in their name by delegated bodies; such spaces are open to all. While private property is the land culturally owned by an individual or company, for their own use and pleasure.

Abstract space is a term used in geography to refer to a hypothetical space characterized by complete homogeneity. When modeling activity or behavior, it is a conceptual tool used to limit extraneous variables such as terrain.

In psychology

Psychologists first began to study the way space is perceived in the middle of the 19th century. Those now concerned with such studies regard it as a distinct branch of psychology. Psychologists analyzing the perception of space are concerned with how recognition of an object's physical appearance or its interactions are perceived.

Other, more specialized topics studied include amodal perception and object permanence. The perception of surroundings is important due to its necessary relevance to survival, especially with regards to hunting and self preservation as well as simply one's idea of personal space.

Several space-related phobias have been identified, including agoraphobia (the fear of open spaces), astrophobia (the fear of celestial space) and claustrophobia (the fear of enclosed spaces).

See also

	Book: Space
Wikipedia Books are collections of articles that can be downloaded or ordered in print.

Wikiquote has a collection of quotations related to: Space

Look up space in Wiktionary, the free dictionary.

• Aether theories
• Cosmology
• General relativity
• Personal space
• Shape of the universe
• Space exploration
• Spatial analysis
• Absolute space and time

References

1. ^ Britannica Online Encyclopedia: Space
2. ^ Refer to Plato's Timaeus in the Loeb Classical Library, Harvard University, and to his reflections on: Chora / Khora. See also Aristotle's Physics, Book IV, Chapter 5, on the definition of topos. Concerning Ibn al-Haytham's 11th century conception of 'geometrical place' as 'spatial extension', which is akin to Descartes' and Leibniz's 17th century notions of extensio and analysis situs, and his own mathematical refutation of Aristotle's definition of topos in natural philosophy, refer to: Nader El-Bizri, 'In Defence of the Sovereignty of Philosophy: al-Baghdadi's Critique of Ibn al-Haytham's Geometrisation of Place', Arabic Sciences and Philosophy: A Historical Journal (Cambridge University Press), Vol.17 (2007), pp. 57-80.
3. ^ French and Ebison, Classical Mechanics, p. 1
4. ^ Carnap, R. An introduction to the Philosophy of Science
5. ^ Leibniz, Fifth letter to Samuel Clarke
6. ^ Vailati, E, Leibniz & Clarke: A Study of Their Correspondence p. 115
7. ^ Sklar, L, Philosophy of Physics, p. 20
8. ^ Sklar, L, Philosophy of Physics, p. 21
9. ^ Sklar, L, Philosophy of Physics, p. 22
10. ^ Newton's bucket
11. ^ Carnap, R, An introduction to the philosophy of science, p. 177-178
12. ^ Lucas, John Randolph. Space, Time and Causality. p. 149. ISBN 0198750579.
13. ^ Carnap, R, An introduction to the philosophy of science, p. 126
14. ^ Carnap, R, An introduction to the philosophy of science, p. 134-136
15. ^ Jammer, M, Concepts of Space, p. 165
16. ^ A medium with a variable index of refraction could also be used to bend the path of light and again deceive the scientists if they attempt to use light to map out their geometry
17. ^ Carnap, R, An introduction to the philosophy of science, p. 148
18. ^ Sklar, L, Philosophy of Physics, p. 57
19. ^ Sklar, L, Philsosophy of Physics, p. 43
20. ^ chapters 8 and 9- John A. Wheeler "A Journey Into Gravity and Spacetime" Scientific American ISBN 0-7167-6034-7

Entheorizing

LEONARD SUSSKIND:

And I fiddled with it, I monkeyed with it. I sat in my attic, I think for two months on and off. But the first thing I could see in it, it was describing some kind of particles which had internal structure which could vibrate, which could do things, which wasn't just a point particle. And I began to realize that what was being described here was a string, an elastic string, like a rubber band, or like a rubber band cut in half. And this rubber band could not only stretch and contract, but wiggle. And marvel of marvels, it exactly agreed with this formula.

I was pretty sure at that time that I was the only one in the world who knew this.

Thoughts cross my mind as it did with Susskind's journey into the understanding of how something like a rubber band could have helped him made sense of anything. Just as with Einstein, and how it finally came to him in the understanding of the geometry Grossmann had presented to him?

It was Grossmann who emphasized the importance of a non-Euclidean geometry called elliptic geometry to Einstein, which was a necessary step in the development of Einstein's general theory of relativity. Abraham Pais's book on Einstein suggests that Grossman mentored Einstein in tensor theory as well.

That intuitive leap is an important one in my view when it has been understood that all the data had been gone through, and ultimately, as if resting in some state of equilibrium( it should be understood that QGP and Lagrangian numbers provide such places in my mind), it was fortunate for an access to potential was realized by working to arrive at such a point.

If you picture probabilistic valuation as a link between such a funnel pointing toward the tip of Pascal's triangle, then what fills that funnel(potential) and what comes out of Pascal's triangle? What s the nature of that numbered system. Choose one?

If you can funnel such potential through a point it is more then the constraint with which others may see this proverbial struggle as to identify it as a koan, but more to realize that such potential is the very essence of accessing such a point and allowing the solution toward materialism, which was logically conducive to combing all that data.

So the idea here is that such a heat death could have happened within any mind that the very essence of such a QGP was to realize that it provide for such "a mean" in which transference of information could take place? So how can any mind ever go there?:)

I mean for sure, not only was I concerned about finding this place inside each of our selves and the truth seeking that goes on, but also toward understanding that this was a cosmological process about which sustenance of the universe could have ever been measured in it's "status quo?"




The shaky game: Einstein, realism, and the quantum theory By Arthur Fine

4 Arthur Fine (1986) characterizes such a move, this not the only instance in Einstein's thinking, as the "entheorizing" of a methodological principle in the form of a physical postulate. Fine, however, argues that determinism is, for Einstein, the entheorized version of realism.

Stanford Encyclopedia of Philosophy Notes to Einstein's Philosophy of Science-Citation Information Don A. Howard

It is most certainly important for myself to maintain some thread of consistency in regard to how we look at reality and how one theorizes about it. So sure... what was Einstein's Realism all about?

So you have to follow that line of thinking?

It still is about truth. About looking to understand it, and being able to know when you have come across it. Does it sound right to you, and does it ring at the very basis of your being when you recognize it?

***

Einstein and the Development of Twentieth-Century

Philosophy of Science
Don Howard
University of Notre Dame

And in a 28 November 1944 letter to Robert Thornton he echoed those words of nearly thirty years earlier:

I fully agree with you about the significance and educational value of methodology as well as history and philosophy of science. So many people today—and even professional scientists—seem to me like somebody who has seen thousands of trees but has never seen a forest. A knowledge of the historic and philosophical background gives that kind of independence from prejudices of his generation from which most scientists are suffering.
This independence created by philosophical insight is—in my opinion—the mark of distinction between a mere artisan or specialist and a real seeker after truth. (Einstein to
Thornton, 7 December 1944, EA 61-574)

Triangle of Thoughts

Triangle of Thought by Alain Connes, Andre Lichnerowicz, Marcel Paul Schutzenberger

Conversations on Mind, Matter, and Mathematics

 

The original Socratic dialogues were artificially constructed to present a coherent view. The dialogue between Connes and Changeux is quite different. It is the recording of real-life arguments where the speakers are frequently at cross-purposes and operate in different planes. For the reader this can be irritating but it also encourages him to become involved and frame his own answers. . . . -- Sir Michael Atiyah, The Times Higher Education Supplement

See:Conversations on Mind, Matter, and Mathematics Jean-Pierre Changeux (Author), Alain Connes (Author), M. B. DeBevoise (Translator)

***

Do numbers and the other objects of mathematics enjoy a timeless existence independent of human minds, or are they the products of cerebral invention? Do we discover them, as Plato supposed and many others have believed since, or do we construct them? Does mathematics constitute a universal language that in principle would permit human beings to communicate with extraterrestrial civilizations elsewhere in the universe, or is it merely an earthly language that owes its accidental existence to the peculiar evolution of neuronal networks in our brains? Does the physical world actually obey mathematical laws, or does it seem to conform to them simply because physicists have increasingly been able to make mathematical sense of it? Jean-Pierre Changeux, an internationally renowned neurobiologist, and Alain Connes, one of the most eminent living mathematicians, find themselves deeply divided by these questions.

The problematic status of mathematical objects leads Changeux and Connes to the organization and function of the brain, the ways in which its embryonic and post-natal development influences the unfolding of mathematical reasoning and other kinds of thinking, and whether human intelligence can be simulated, modeled,--or actually reproduced-- by mechanical means. The two men go on to pose ethical questions, inquiring into the natural foundations of morality and the possibility that it may have a neural basis underlying its social manifestations. This vivid record of profound disagreement and, at the same time, sincere search for mutual understanding, follows in the tradition of Poincaré, Hadamard, and von Neumann in probing the limits of human experience and intellectual possibility. Why order should exist in the world at all, and why it should be comprehensible to human beings, is the question that lies at the heart of these remarkable dialogues. From Princeton University Press

 ***

See Also: Remarks on Jean-Pierre Changeux & Alain Connes Conversations on Mind, Matter, and Mathematics by Jean Petitot