Subhash Kak

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Subhash Kak
Kak vaxjo2.jpg
Subhash Kak at Foundations of Quantum Mechanics Conference, Växjö, Sweden
Alma materNIT Srinagar, IIT Delhi
OccupationComputer Scientist
Known forCryptography, Instantaneously trained neural networks, Kak's three-stage protocol, Quantum information, History of science
Notable credit(s)
Author of In Search of the Cradle of Civilization, The Architecture of Knowledge

Subhash Kak (born 26 March 1947 in Srinagar) is an Indian American computer scientist. He is Regents Professor and a previous Head of Computer Science Department at Oklahoma State University–Stillwater who has made contributions to cryptography, artificial neural networks, and quantum information.

Kak is also notable for his Indological publications on the history of science, the philosophy of science, ancient astronomy, and the history of mathematics.[1] On 28 August 2018, he was appointed member of Indian Prime Minister’s Science, Technology and Innovation Advisory Council (PM-STIAC). [2]


Subhash Kak was born to Ram Nath Kak and Sarojini Kak in Srinagar.[3] He completed his BE from Regional Engineering College, Srinagar (Presently National Institute of Technology, Srinagar)[citation needed] and Ph.D. from Indian Institute of Technology Delhi in 1970, where he was immediately offered a faculty position. During 1975-1976, he was a visiting faculty at Imperial College, London, and a guest researcher at Bell Laboratories, Murray Hill. In 1977, he was a visiting researcher at Tata Institute of Fundamental Research, Bombay.[4] In 1979, he joined Louisiana State University, Baton Rouge, where he was the Donald C. and Elaine T. Delaune Distinguished Professor of Electrical and Computer Engineering. In 2007, he joined the Computer Science department at Oklahoma State University–Stillwater.[5]

He is the author of an autobiography, The Circle of Memory, and several books of poems.[6][7][8] He has also authored scholarly papers on art,[9] architecture[10] and music,[11] and he was the anchor of a documentary on Hindustani classical music.[12]

His brother is the computer scientist Avinash Kak and sister the literary theorist Jaishree Odin.[13]


His research is in the fields of cryptography, random sequences, artificial intelligence, quantum mechanics, and information theory. He proposed a test of algorithmic randomness[14] and a type of instantaneously trained neural networks (INNs) (which he and his students have called "CC4 network" and others have called "Kak neural networks"). He was the first to formulate the discrete and the number theoretic Hilbert transforms.[15][16] He claims to be amongst the first to apply information metrics to quantum systems.[17][18]

He has proposed a hierarchy of languages for communication in biological systems which, in order of increasing complexity, are associative, reorganizational, and quantum.[19][20] He was featured as one of the pioneers of quantum learning in the journal Neuroquantology edited by Cheryl Fricasso and Stanley Krippner,[21] and also featured as one of the interviewees in the area of mathematics and information in the long-standing PBS series Closer to Truth.[22]

Kak proposed a fast matrix multiplication algorithm for cross-wired meshes.[23] He proposed the use of repeating decimals and other random sequences for error correction coding and cryptography.[24][25] He also developed a new way of representation of numbers using unary coding. In cryptography, he has advanced new methods of secret sharing that are of importance in distributed systems such as wireless and sensor networks.[26][27]

In quantum information, he proposed the principle of veiled nonlocality[28] which asserts that although reality is nonlocal a veiling affects not only expectations of experiments but also how the data is analyzed.[29][30] This principle of veiling implies limitations on cognitive processes. Together with Menas Kafatos, he has proposed that veiled nonlocality might be the explanation behind cosmic censorship.[31]

Kak has argued that there are limits to the intelligence machines can have and it cannot equal biological intelligence.[32][33] He asserts that:

...machines fall short on two counts as compared to brains. Firstly, unlike brains, machines do not self-organize in a recursive manner. Secondly, machines are based on classical logic, whereas Nature's intelligence may depend on quantum mechanics.

[Further], if machines with consciousness are created, they would be living machines, that is, variations on life forms as we know them. Second, the material world is not causally closed, and consciousness influences its evolution. Matter and minds complement each other.[34]

Kak neural network[edit]

The Kak neural network, also called the CC4 network[35] is an instantaneously trained neural network that creates a new "hidden neuron" for each training sample, achieving immediate training for binary data. The training algorithm for binary data creates links to the new hidden node that simply reflects the binary values in the training vector. Hence, no computation is involved.[36] For effective generalization, the network requires unary coding of the input data, and it can be generalized to non-binary inputs as well.[37][38]

This network was used in an intelligent metasearch engine called Anvish, developed in 1999, in which the search results were sorted and checked for relevancy using an instantaneously trained neural network.[39] The technology of Anvish was later incorporated into another metasearch engine called Solosearch.[40]

Kak's three-stage protocol[edit]

Kak's three-stage protocol is a protocol for quantum cryptography suggested by Kak.[41] This method consists of random rotations of the polarization by both parties. In principle, this method can be used for continuous, unbreakable encryption of data if single photons are used.[42] The basic polarization rotation scheme has been implemented.[43] The three-stage protocol has been proposed as a solution to get around the requirement of expensive single-photon sources and receivers in other quantum cryptography protocols.[44]

This protocol has been proposed as a method for secure communication that is entirely quantum unlike quantum key distribution in which the cryptographic transformation uses classical algorithms[45]

History of Science[edit]

Kak has studied the Indus script for its possible connections with the Brahmi script[46][47] and produced a new analysis of the earliest astronomy of India.[48] [49] He has presented new insights into the history of Indian mathematics[50] and its place in the larger history of computation, especially that which is inherent in the grammatical tradition.[51][52] He has examined parallels and differences between Greek and Indian physics[53] and, in particular, done a new translation of Kanada's Vaisheshika Sutra.[54] He has also shown the implication of these insights in the understanding of temple architecture.[55]

He has investigated Mary Boole's assertion that Indian logic played a role in the development of modern logic by her husband George Boole, Augustus de Morgan, and Charles Babbage,[56] as well as the romantic story of the interaction between Nikola Tesla and Vivekananda at the behest of the actress Sarah Bernhardt.[57]

Indological publications[edit]

Kak's writings concerning the astronomy of the Vedic period in his book The Astronomical Code of the Rigveda support the "Indigenous Aryans" theory, questioning mainstream views on the Indo-Aryan migration theory and the nature of early Indian science. While Kak's interpretation has been included in recent overviews of astronomy in the Vedic period in India[58] and the West,[59] his chronology and astronomical calculations have been critiqued by several Indologists, such as Michael Witzel,[60] and Western historians, such as Kim Pfloker.[61] Alan Sokal labeled Kak "one of the leading intellectual luminaries of the Hindu-nationalist diaspora."[62]

Archaeoastronomy - The Astronomical Code of the Rigveda[edit]

The Astronomical Code of the Rigveda,[note 1] which is based on several journal articles and book chapters,[63][64] claims regularities in the organization of the Rigveda, connecting the structure to certain numbers in the astronomy-based ritual of the five-layered vedi (Vedic fire altar). Kak arranges the number of hymns in each book of the Rigveda as follows, and compares the arrangement to the vedi:

RV 10:191 RV 9:114
RV 7 :104 RV 8: 92
RV 5 : 87 RV 6: 75
RV 3 : 62 RV 4: 58
RV 2 : 43 RV 1:191

He then computes various sums and subtractions within the diagram, finding numbers related to the distance between the Earth and the Sun, and the sidereal periods of various planets. Most specifically, he claims that the Vedic astronomers knew that the Sun and the Moon were approximately 108 times their respective diameters from the Earth.[65][66]

Kak's archaeoastronomical claims have the effect of significantly extending the Vedic period, postulating the arrival of Indo-Aryan speakers to the 7th millennium BC. This claim is in contradiction with mainstream Indology and historical linguistics[60] and science historians[61]

While Klaus Klostermaier has stated that "Subhash Kak, with his 'decoding of the Rigveda' has opened up an entirely new approach to the study of Vedic cosmology from an empirical astronomical/mathematical viewpoint,"[67] other scholars like Meera Nanda have said that Kak's "method is breathtakingly ad hoc and reads like numerology 101."[68] Kak's method depends on the structure of the Rigveda as redacted by the shakhas in the late Brahmana period, well within the Indian Iron Age, when it was organized into mandalas ("books"). According to Witzel, this leaves Kak's approach attempt to date the text flawed, because this process of redaction took place long after the composition of the individual hymns during the samhita prose period.[60]

Kak prepared the section on archaeoastronomical sites in India for the thematic study on Heritage Sites of Astronomy and Archaeoastronomy in the context of the UNESCO World Heritage Convention prepared for UNESCO by the International Council on Monuments and Sites (ICOMOS) and the International Astronomical Union (IAU).[69]

In Search of the Cradle of Civilization[edit]

Kak co-authored In Search of the Cradle of Civilization (1995) participating in the controversy in the politics of India around the "indigenous Aryans" theory.[70] The chronology espoused in this book is based on the archaeoastronomical readings obtained by correlating textual references and archaeological remains.


Kak's book The Asvamedha: The Rite and Its Logic (2002) provides an interpretation of the Vedic aśvamedhá (horse sacrifice) rite.[71] He argues that the details of this rite are connected to the Agnicayana ritual.

Temple architecture[edit]

Kak has argued that the form of the Hindu temple and its iconography are a natural expansion of Vedic ideology related to recursion, change and equivalence.[72] It codes the equivalence of the macrocosm and the microcosm by astronomical numbers, and by "specific alignments related to the geography of the place and the presumed linkages of the deity and the patron". [73]. He argues that this is consistent with other representations of triple-knowledge (trayi-vidya) that show the relationships between the outer and the inner worlds.[74][75]


In the books The Nature of Physical Reality and Mind and Self and other publications,[76] Kak argues that there are limits to the extent the world is computable. His "philosophy of recursionism" is expounded in his books The Gods Within, The Architecture of Knowledge, and The Prajna Sutra.

Kak claimed to be the first to have used the term "quantum neural computing",[77] taking a Quantum mind position. He sees the brain as a machine that reduces the infinite possibilities of a "quantum-like universal consciousness", which is a consequence of the "recursive nature of reality".[78]

In The Architecture of Knowledge, Kak talks about quantum mechanics, neuroscience, computers, and consciousness. The book is one of the twenty planned monographs in the multi-volume series on the Project of History of Indian Science, Philosophy and Culture under the general editorship of Professor D. P. Chattopadhyaya. The book provides philosophical connections to contemporary science that reach back not only to the Greek but also to the Indian tradition.

The book seeks to find a consistent framework for knowledge in logic, purpose, and awareness, and sees science as representation and transformation of machines, of reality, and of life. Reality is seen in different layers, and

with the dual aspects of purposive and reflexive behaviour in each layer, we see parallels in the structures in quantum theory, neuroscience, and computers. The overarching unity is provided by human consciousness. As conscious subjects, we examine the universe through the agency of our minds. In our strivings to describe the outer world using formal knowledge, shadows of the architecture of the inner world are also unveiled.[79]

More recently, he has spoken of two kinds of consciousness that he calls big-C and little-C, where big-C represents phenomenal consciousness associated with awareness, whereas little-C are those aspects of consciousness that relate to cognitive tasks.[80] He has argued that machines will be able to emulate little-C quite effectively.[33][81]



  • The Nature of Physical Reality, Peter Lang Pub Inc, 1986, ISBN 0-8204-0310-5; Third Edition, Mount Meru Publishing, Mississauga, Ontario, 2016, ISBN 978-1-988207-08-7
  • The Loom of Time (2016), DKPrintworld, New Delhi ISBN 8124608741
  • The Circle of Memory: An Autobiography (2016), Mount Meru Publishing, Mississauga, Ontario, ISBN 978-1-988207-17-9
  • Matter and Mind (2016), Mount Meru Publishing, Mississauga, Ontario, ISBN 978-1-988207-13-1
  • Mind and Self (2016), Mount Meru Publishing, Mississauga, Ontario, ISBN 978-1-988207-06-3
  • India at Century's End, South Asia Books / Voice of India, (1994) ISBN 81-85990-14-X
  • Georg Feuerstein, Subhash Kak, David Frawley, In Search of the Cradle of Civilization, Ill: Quest Books, (1995, 2001) ISBN 0-8356-0741-0.
  • The Astronomical Code of the Rigveda (Third Edition) Aditya Prakashan (2016), ISBN 978-8177421590
  • Computing Science in Ancient India; Munshiram Manoharlal Publishers Pvt. Ltd (2001)
  • The Wishing Tree: Presence and Promise of India (Third Edition) Aditya Prakashan (2015), ISBN 978-8177421538
  • The Gods Within: Mind, Consciousness and the Vedic Tradition, Munshiram Manoharlal Publishers Pvt. Ltd (2002) ISBN 81-215-1063-5
  • The Asvamedha: The Rite and Its Logic, Motilal Banarsidass Publishers, (2002) ISBN 81-208-1877-6
  • The Prajna Sutra: Aphorisms of Intuition, DK Printworld, 2007. ISBN 81-246-0410-X
  • The Architecture of Knowledge: Quantum Mechanics, Neuroscience, Computers and Consciousness, Motilal Banarsidass, 2004, ISBN 81-87586-12-5
  • "Recursionism and Reality: Representing and Understanding the World", 2005.
  • Advances in Communications and Signal Processing, Springer-Verlag, 1989. (with W.A. Porter).
  • Advances in Computing and Control, Springer-Verlag, 1989. (with W.A. Porter and J.L. Aravena).
  • Consciousness and the universe : quantum physics, evolution, brain & mind, Cosmology Science Publishers, 2011. (with Roger Penrose and Stuart Hameroff) ISBN 9780982955208, ISBN 0982955200



  • Arrival and Exile: Selected Poems (2016), Mount Meru Publishing, Mississauga, Ontario, ISBN 978-1-988207-15-5
  • The Conductor of the Dead, Writers Workshop (1973) ASIN: B0007AGFHA
  • The London Bridge, Writers Workshop, Kolkata, 1977.
  • The secrets of Ishbar: Poems on Kashmir and other landscapes, Vitasta (1996) ISBN 81-86588-02-7
  • "Ek Taal, Ek Darpan" (Hindi), Raka, Allahabad, 1999.
  • "The Chinar Garden", 2002.
  • "Mitti ka Anuraag" (Hindi), 2007.[12]

See also[edit]


  1. ^ New Delhi: Aditya Prakashan, 1994; revised and enlarged edition, New Delhi: Munshiram Manoharlal, 2000; second revised edition 2016


  1. ^ Akella, Usha (21 December 2013). "The Renaissance man". Retrieved 2 December 2018.
  2. ^ "New committee formed to advise PM on science, tech-related policy issues". Retrieved 2 December 2018.
  3. ^ Kak, S. The Circle of Memory. Mississauga, 2016
  4. ^ "Short Biography" (PDF). Retrieved 3 December 2018.
  5. ^ "Kak, Subhash, Ph.D. - School of Electrical and Computer Engineering". Retrieved 2 December 2018.
  6. ^ [1][dead link]
  7. ^ "Archived copy". Archived from the original on 18 January 2015. Retrieved 18 January 2015.CS1 maint: Archived copy as title (link)
  8. ^ Akella, U. "Archived copy". Archived from the original on 18 January 2015. Retrieved 18 January 2015.CS1 maint: Archived copy as title (link)
  9. ^ "Kak, S. Art and Cosmology of India, 2006" (PDF). Retrieved 2 December 2018.
  10. ^ Kak, S. Space and order in Prambanan. In Manju Shree (ed.) From Beyond The Eastern Horizon: Essays In Honour Of Professor Lokesh Chandra. Aditya Prakashan, Delhi, 2011. [2]
  11. ^ "Kak, S. Early Indian music, 2002" (PDF). Retrieved 2 December 2018.
  12. ^ "Review of Raga Unveiled: India's Voice [Interview With Gita Desai.]". Retrieved 2 December 2018.
  13. ^ Kak, Ram Nath. Autumn Leaves. Vitasta, 1995.
  14. ^ "Randomness Tests: A Literature Survey". Retrieved 2 December 2018.
  15. ^ Kak, S. The discrete Hilbert transform. Proc. IEEE, vol. 58, pp. 585-586, April 1970.
  16. ^ Kak, S.The number theoretic Hilbert transform. Circuits, Systems and Signal Processing, vol. 33, pp. 2539-2548, 2014.
  17. ^ Kak, S. "On quantum numbers and uncertainty," Nuovo Cimento, 34B, 530-534, 1976.
  18. ^ Kak, S. On information associated with an object. Proceedings Indian National Science Academy, vol. 50, pp. 386-396, 1984.
  19. ^ Kak, S. The three languages of the brain: quantum, reorganizational, and associative. In Learning as Self-Organization, Karl Pribram and J. King (editors). Lawrence Erlbaum Associates, Mahwah, NJ, 185-219, 1996.
  20. ^ Kak, S. Communication languages and agents in biological systems. In: Biocommunication: Sign-Mediated Interactions between Cells and Organisms. Eds.: J. Seckbach & R. Gordon. London, World Scientific Publishing: 203-226, 2016.
  21. ^ Fracasso, Cheryl; Krippner, Stanley (11 September 2011). "Pioneers Who Have Changed the Face of Science and Those That Have Been Mentored By Them". NeuroQuantology. 9 (3). doi:10.14704/nq.2011.9.3.446. Retrieved 2 December 2018.
  22. ^ "Mathematics & Information - Our Contributors - Closer To Truth". Retrieved 2 December 2018.
  23. ^ Kak, S. A two-layered mesh array for matrix multiplication. Parallel Computing, vol. 6, pp. 383-385, 1988.
  24. ^ Kak, S. Encryption and error-correction coding using D sequences. IEEE Transactions on Computers, C-34: 803-809, 1985. Watermarking using decimal sequences
  25. ^ Kak, S. Goldbach partitions and sequences. Resonance, vol. 19, pp. 1028-1037, November 2014.
  26. ^ Parakh, A. and S. Kak, Online data storage using implicit security. Information Sciences, vol. 179, pp. 3323-3331, 2009.
  27. ^ Parakh, A. and S. Kak, Space efficient secret sharing for implicit data security. Information Sciences, vol. 181, pp. 335-341, 2011.
  28. ^ Kak, S. (2016) The Nature of Physical Reality. Mt. Meru.
  29. ^ Kak S. (2014). "From the no-signaling theorem to veiled non-locality". NeuroQuantology. 12: 12–20.
  30. ^ Kak, S. (2016) "Communication languages and agents in biological systems".] In: Biocommunication: Sign-Mediated Interactions between Cells and Organisms. Eds.: J. Seckbach & R. Gordon. London, World Scientific Publishing: 203-226
  31. ^ Kafatos, M.C. and Kak, S. (2015) "Veiled nonlocality, cosmic censorship, and local observations". Physics Essays, vol. 28, pp. 182-187
  32. ^ Kak, S. Active agents, intelligence and quantum computing. Information Sciences, vol. 128, 1-17, 2000.
  33. ^ a b Kak, Subhash. "Will artificial intelligence become conscious?". Retrieved 2 December 2018.
  34. ^ "ACM Ubiquity". Retrieved 2 December 2018.
  35. ^ Shortt, A.; et al. (2005). "Optical implementation of the Kak neural network". Information Sciences. 171 (1–3): 273–287. doi:10.1016/j.ins.2004.02.028.CS1 maint: Explicit use of et al. (link)
  36. ^ Kak, S. New algorithms for training feedforward neural networks. Pattern Recognition Letters 15, 1994, pp. 295-298; Kak, S. On generalization by neural networks. Information Sciences 111, 1998, pp. 293-302. "Archived copy". Archived from the original on 2005-07-17. Retrieved 2005-12-16.CS1 maint: Archived copy as title (link)[3][4]
  37. ^ Tang, K.W. and Kak, S. Fast classification networks for signal processing. Circuits, Systems, Signal Processing 21, 2002, pp. 207-224.
  38. ^ Kak, S. Learning Based on CC1 and CC4 Neural Networks. 2017. [5]
  39. ^ Shu, B and Kak, S. A neural network based intelligent metasearch engine. Information Sciences 120, pages 1-11, 1999.
  40. ^ Kak, S. Better Web searches and prediction with instantaneously trained neural networks. IEEE Intelligent Systems, November/December 1999.
  41. ^ Kak, S. A Three-Stage Quantum Cryptography Protocol. Foundations of Physics Letters 19 (2006), 293-296. Trusted certificates in quantum cryptography
  42. ^ Chen, Y. et al, Embedded security framework for integrated classical and quantum cryptography in optical burst switching networks. Security and Communication Networks. 2 (2009) 546-554.
  43. ^ "Multi-photon approach in quantum cryptography implemented". Retrieved 2 December 2018.
  44. ^ Zhang, L. et al. Universal optimal estimation of the polarization of light with arbitrary photon statistics. Physical Review A 93 (2016) 032137
  45. ^ Thapliyal, K. and Pathak, A. Kak’s three-stage protocol of secure quantum communication revisited. Quantum Information Processing, vol. 17, 2018[6]
  46. ^ Kak, S. (1994), The evolution of early writing in India, Indian Journal of History of Science, 28: 375–388
  47. ^ Patel, P.G., Pandey, P., Rajgor, D. (2007) The Indic Scripts: Palaeographic and Linguistic Perspectives. D.K. Print world.
  48. ^ Kak, S. (1995) Astronomy of the age of geometric altars. Quarterly Journal of the Royal Astronomical Society, vol. 36.
  49. ^ Kak, S. (1996) Knowledge of Planets in the Third Millennium BC. Quarterly Journal of the Royal Astronomical Society, Vol. 37.
  50. ^ Pearce, I.G. Indian Mathematics: Redressing the balance. [7]
  51. ^ Kak, S. The Paninian approach to natural language processing. International Journal of Approximate Reasoning, vol. 1, 1987, pp. 117- 130.
  52. ^ Bhate, S. and Kak, S. Panini and Computer Science. Annals of the Bhandarkar Oriental Research Institute, vol. 72, 1993, pp. 79-94.
  53. ^ Kak, S. (2005). Greek and Indian Cosmology: Review of Early History. History of Science, Philosophy & Culture in Indian Civilization, vol. 1, part 4 (A Golden Chain, G.C. Pande, ed.), pp. 871-894 [8]
  54. ^ Kak, S. (2016)n 'Matter and Mind: The Vaisheshika Sutra of Kanada', Mount Meru Publishing, Mississauga, Ontario, ISBN 978-1-988207-13-1.
  55. ^ Kak, S. (2009). Time, space and structure in ancient India. Conference on Sindhu-Sarasvati Valley Civilization: A Reappraisal, Loyola Marymount University, Los Angeles, February 21 & 22, 2009 [9]
  56. ^ Kak, S. (2018) George Boole’s Laws of Thought and Indian logic. Current Science, vol. 114, 2570-2573
  57. ^ Kak, S. (2017) Tesla, wireless energy transmission and Vivekananda. Current Science, vol. 113, 2207-2210.
  58. ^ In Govind Chandra Pande, "The Dawn of Indian Civilization". CSC, New Delhi, 2000.
  59. ^ In S. Wolpert (ed.), "Encyclopedia of India." Scribner's, 2005.
  60. ^ a b c Witzel, Michael (2001), "Autochthonous Aryans? The Evidence from Old Indian and Iranian Texts" (PDF), Electronic Journal of Vedic Studies, 7 (3), 70-71, archived from the original (PDF) on 2013-05-23, retrieved 13 Feb 2013
  61. ^ a b "Archived copy". Archived from the original on 2007-10-23. Retrieved 2007-02-11.CS1 maint: Archived copy as title (link)Kim Plofker, Review of Kak (1994), Centaurus 38 (1996), 362-364 Archived 2007-10-23 at the Wayback Machine
  62. ^ Sokal, Alan (2006). "Pseudoscience and Postmodernism: Antagonists or Fellow-Travelers?". In Garrett G. Fagan (ed.). Archaeological fantasies: how pseudoarchaeology misrepresents the past and misleads the public. Routledge. p. 317. ISBN 978-0-415-30593-8.CS1 maint: Uses editors parameter (link)
  63. ^ Kak, S. (1992) The astronomy of the Vedic altars and the Rgveda. Mankind Quarterly 33: 43-55
  64. ^ Kak, S. (1994/5) The Astronomical Code of the Rigveda. Puratattva: Bulletin of the Indian Archaeological Society 25: 1-30.
  65. ^ Kak, S. (1993) Astronomy of the Vedic altars. Vistas in Astronomy, 36: 117-140
  66. ^ Kak S. (2000) Birth and Early Development of Indian Astronomy. In: Selin H., Xiaochun S. (eds) Astronomy Across Cultures. Science Across Cultures: The History of Non-Western Science, vol 1. Springer, Dordrecht
  67. ^ Klaus Klostermaier, A Survey of Hinduism, Second Edition. State University of New York Press, 1995, pp. 129.
  68. ^ Nanda, Meera (2003). Prophets facing backward: postmodern critiques of science and Hindu nationalism in India. Rutgers University Press. p. 112. ISBN 978-0-8135-3358-2.
  69. ^ Kak, Subhash (2010), "India", in Ruggles, Clive; Cotte, Michel, Heritage Sites of Astronomy and Archaeoastronomy in the context of the UNESCO World Heritage Convention: A Thematic Study, Paris: ICOMOS / IAU, pp. 99–107, ISBN 978-2-918086-07-9
  70. ^ Edwin Bryant, The Quest for the Origins of Vedic Culture: The Indo-Aryan Migration Debate. Oxford University Press, 2001.
  71. ^ The Asvamedha: The Rite and Its Logic, Motilal Banarsidass Publishers, (2002) ISBN 81-208-1877-6.
  72. ^ Kak, S. Early Indian architecture and art. Migration and Diffusion. vol.6, pp. 6-27 (2005)
  73. ^ Kak, S. The axis and the perimeter of the temple. Kannada Vrinda Seminar Sangama 2005 held at Loyola Marymount University in Los Angeles on November 19, 2005.
  74. ^ Kak, S. Time, space and structure in ancient India. Conference on Sindhu-Sarasvati Valley Civilization: A Reappraisal, Loyola Marymount University, Los Angeles, February 21 & 22, 2009.[10]
  75. ^ Kak, S. (2016) The Loom of Time, DKPrintworld, New Delhi ISBN 8124608741
  76. ^ Kak, S. Observability and computability in physics. Quantum Matter 3: 172-176 (2014)
  77. ^ In Advances in Imaging and Electron Physics 94: 259-313 (1995)
  78. ^ Karl H. Pribram and Robert King (eds.), Learning and Self-Organization, Lawrence Erlbaum Associates, 1996, 185-219.
  79. ^ The Architecture of Knowledge(2004), ISBN 81-87586-12-5 (page 299)
  80. ^ Kak, Subhash (2017). "Kak, S. The Limits of Machine Consciousness. 2017". arXiv:1707.06257 [cs.OH].
  81. ^ Neelakandan, A. "C" is for consciousness. Swarajya, February 2019.[11]

External links[edit]