1 Charles University (Praha, Czechia)
DOI: https://doi.org/10.29202/phil-cosm/31/10
Received: 21 June 2023 / Accepted: 19 July 2023 / Published: 15 October 2023
View Full-Text Review Reports Cite This Paper
Abstract
Keywords: Albert Einstein, Euler’s identity, God, imagination, Lambert W function, scale factor, spacetime, thought experiment, Universe
References
Banerjee, M., Das, S., Al Mamon, A., Saha, S., & Bamba, K. (2021) Growth of perturbations using Lambert W equation of state. International Journal of Geometric Methods in Modern Physics, 18, 2150139. https://doi.org/10.1142/S0219887821501395
Barbour, J. (1999) The End of Time: The Next Revolution in Physics. Oxford: Oxford University Press.
Bishoff, M. (2022) Can God Be Proved Mathematically? Scientific American, October 4. https://www.scientificamerican.com/article/can-god-be-proved-mathematically/
Bitbol, M., Kerszberg, P., & Petitot, J. (Eds.) (2009) Constituting Objectivity: Transcendental Perspectives on Modern Physics, The Western Ontario Series in Philosophy of Science. Dordrecht: Springer. https://doi.org/10.1007/978-1-4020-9510-8
Bostrom, N. (2003) Are we living in a computer simulation? Philosophical Quarterly, 53(211), 243-255. https://doi.org/10.1111/1467-9213.00309
Boyle, L., Finn, K., & Turok, N. (2022) The Big Bang, CPT, and neutrino dark matter. Annals of Physics, 438, 168767. https://doi.org/10.1016/j.aop.2022.168767
Brito, P.B., Fabiao, F., & Staubyn, A. (2008) Euler, Lambert, and the Lambert W-function today. Mathematical Scientist, 33(2), 127-133.
Brown, B.H. (1942) The Euler-Diderot Anecdote. The American Mathematical Monthly, 49(5), 302-303. https://doi.org/10.2307/2303096
Calinger, R.S. (2016) Leonhard Euler: Mathematical Genius in the Enlightenment. Princeton, NJ: Princeton University Press. https://doi.org/10.2307/j.ctv7h0smb
Calvino, I. (1974) Invisible cities. Weaver, W. (Trans.). New York: Harcourt Brace Jovanovich. (Original published in 1972.)
Carr, P.H. (2004) Does God play dice? Insights from the fractal geometry of nature. Zygon, 39(4), 933-940. https://doi.org/10.1111/j.1467-9744.2004.00629.x
Carter, B. (2006) Who plays dice? Subjective uncertainty in deterministic quantum world. In: Alimi, J.M., Fuzfa, A. (Eds.), Albert Einstein Century International Conference, AIP Conference Proceedings 861. Melville: American Institute of Physics, pp. 73-77.
Corless, R.M., Gonnet, G.H., Hare, D.E.G., Jeffrey, D.J., & Knuth, D.E. (1996) On the LambertW function. Advances in Computational Mathematics, 5(1), 329-359. https://doi.org/10.1007/BF02124750
D’Arcy Kenworthy, W., Scolnic, D., & Riess, A. (2019) The Local Perspective on the Hubble Tension: Local Structure Does Not Impact Measurement of the Hubble Constant. The Astrophysical Journal, 875, 145. https://doi.org/10.3847/1538-4357/ab0ebf
Davis, T.M., Mortsell, E., Sollerman, J., Becker, A.C., Blondin, S., Challis, P., Clocchiatti, A., Filippenko, A.V., Foley, R.J., Garnavich, P.M., Jha, S., Krisciunas, K., Kirshner, R.P., Leibundgut, B., Li, W., Matheson, T., Miknaitis, G., Pignata, G., Rest, A., Riess, A.G., & Schmidt, B.P. (2007) Scrutinizing Exotic Cosmological Models Using ESSENCE Supernova Data Combined with Other Cosmological Probes. The Astrophysical Journal, 666(2), 716-725. https://doi.org/10.1086/519988
Debnath, L. (2009) The Legacy of Leonhard Euler: A Tricentennial Tribute. London: Imperial College Press.
Di Valentino, E., Mena, O., Pan, S., Visinelli, L., Yang, W.Q., Melchiorri, A., Mota, D.F., Riess, A.G., & Silk, J. (2021) In the realm of the Hubble tension-a review of solutions. Classical and Quantum Gravity, 38, 153001. https://doi.org/10.1088/1361-6382/ac086d
Einstein, A. (2005) Albert Einstein to Max Born. Physics Today, 58(5), 16. https://doi.org/10.1063/1.1995729
Einstein, A., Born, M., & Born, H. (2005) The Born-Einstein Letters: Friendship, Politics and Physics in Uncertain Time: Correspondence between Albert Einstein and Max and Hedwig Born from 1916 to 1955 with commentaries by Max Born. Houndmills: Macmillan; New York: Basingstoke, Hampshire, p. 88.
Euler, L. (1783) De serie Lambertina, plurimisque eius insignibus proprietatibus. Acta Academiae Scientiarum Imperialis Petropolitanae [pro Anno MDCCLXXIX Pars Posterior : Acta Acad. Imp. Sc. Tom. III, P. II. : Mathematica], 3(2), 29-51.
Evangelidis, B. (2018) Space and Time as Relations: The Theoretical Approach of Leibniz. Philosophies, 3, 9. https://doi.org/10.3390/philosophies3020009
Farid al-Din ‘Attar (2017) The Conference of the Birds. Wolpé, S. (Trans.). New York: W. W. Norton & Company. (Original completed around 1187.)
Freedman, W.L. (2021) Measurements of the Hubble Constant: Tensions in Perspective. The Astrophysical Journal, 919, 16. https://doi.org/10.3847/1538-4357/ac0e95
Fugate, C.D. (2019) Kant’s Cosmology, Miracles and the Autonomy of Reason. In: Fugate, C.D. (Ed.), Kant’s Lectures on Metaphysics: A Critical Guide. Cambridge UK: Cambridge University Press, pp. 122-155. https://doi.org/10.1017/9781316819142
Gillings, R.J. (1954) The So-Called Euler-Diderot Incident. The American Mathematical Monthly, 61(2), 77-80. https://doi.org/10.2307/2307789
Grin, A.S. (1924) Blistayushchiy mir. [The Shining World]. Moskva: Zemlya i Fabrika.
Grin, A. (1975) Zárivý svet; Královna vln. [Blistayushchiy mir (The Shining World); Begushchaya po volnam (She Who Runs on the Waves)]. Psutková, Z. (Trans.). Praha: Odeon, p. 27. (Original published in 1956.)
Hoffmann, M.H.G. (2019) Transcendental Arguments in Scientific Reasoning. Erkenntnis, 84(6), 1387-1407. https://doi.org/10.1007/s10670-018-0013-9
Holmyard, E.J. (1923) The Emerald Table. Nature, 112(2814), 525-526. https://doi.org/10.1038/112525a0
Krishnan, C., Mohayaee, R., Colgain, E.O., Sheikh-Jabbari, M.M., & Yin, L. (2021) Does Hubble tension signal a breakdown in FLRW cosmology? Classical and Quantum Gravity, 38, 184001. https://doi.org/10.1088/1361-6382/ac1a81
Lambert, J.H. (1758) Observationes variae in Mathesin puram. Acta Helvetica, Physico-Mathematico-Anatomico-Botanico-Medica, 3, 128-168.
Lane, W.C. (2021) Living God Pandeism: Evidential Support. Zygon, 56(3), 566-590. https://doi.org/10.1111/zygo.12704
Leibniz, G. W. (1996) New Essays on Human Understanding. Remnant P. and Bennett J. (Trans.). Cambridge UK: Cambridge University Press, p. 473. (Original published in 1765.)
Lincoln, D. (2017) God’s Thoughts: Practical Steps Toward a Theory of Everything. Physics Teacher, 55(4), 204-209. https://doi.org/10.1119/1.4978713
Mandal, S., Bhattacharjee, S., Pacif, S.K.J., & Sahoo, P.K. (2020) Accelerating universe in hybrid and logarithmic teleparallel gravity. Physics of the Dark Universe, 28, 100551. https://doi.org/10.1016/j.dark.2020.100551
Martinez, V.J., & Trimble, V. (2009) Cosmologists in the Dark. In: Rubino-Martin, J.A., Belmonte, J.A., Prada, F., Alberdi, A. (Eds.), Cosmology Across Cultures: An International Conference on the Impact of the Study of the Universe in Human Thinking, ASP Conference Series 409. San Francisco: Astronomical Society of the Pacific, pp. 47-56.
Mezo, I. (2022) The Lambert W function: its generalizations and applications. Boca Raton, Florida: CRC Press. https://doi.org/10.1201/9781003168102
Mezo, I., and Baricz, A. (2017) On the generalization of the Lambert W function. Transactions of the American Mathematical Society, 369(11), 7917-7934. https://doi.org/10.1090/tran/6911
Musser, G. (2015) Is the Cosmos Random? Einstein’s assertion that God does not play dice with the universe has been misinterpreted. Scientific American, 313(3), 88-93. https://doi.org/10.1038/scientificamerican0915-88
Nabokov, V. (1992) The Real Life of Sebastian Knight. New York: Vintage International, p. 64.
Neben, A.R., & Turner, M.S. (2013) Beyond H0 and q0: Cosmology Is No Longer Just Two Numbers. The Astrophysical Journal, 769, 133. https://doi.org/10.1088/0004-637X/769/2/133
Nojiri, S., Odintsov, S.D., & Oikonomou, V.K. (2017) Modified gravity theories on a nutshell: Inflation, bounce and late-time evolution. Physics Reports, 692, 1-104. https://doi.org/10.1016/j.physrep.2017.06.001
Norton, J.D. (2013) Chasing the Light: Einstein’s Most Famous Thought Experiment. In: Frappier, M., Meynell, L., Brown, J.R. (Eds.), Thought Experiments in Philosophy, Science and the Arts. New York: Routledge, pp. 123-140.
Odintsov, S.D., Oikonomou, V. K., Timoshkin, A.V., Saridakis, E.N., & Myrzakulov, R. (2018) Cosmological fluids with logarithmic equation of state. Annals of Physics, 398, 238-253. https://doi.org/10.1016/j.aop.2018.09.015
Rameez, M., and Sarkar, S. (2021) Is there really a Hubble tension? Classical and Quantum Gravity, 38, 154005. https://doi.org/10.1088/1361-6382/ac0f39
Rani, N., Jain, D., Mahajn, S., Mukherjee, A., & Pires, N. (2015) Transition redshift: new constraints from parametric and nonparametric methods. Journal of Cosmology and Astroparticle Physics, 2015, 045. https://doi.org/10.1088/1475-7516/2015/12/045
Reiner, L. & Reiner, W. (1990) The Blind Man Who Could See. In: Mathematicians Are People, Too: Stories From the Lives of Great Mathematicians: Volume 1. Palo Alto, CA: Dale Seymour Publications, pp. 72-81.
Riess, A.G., Filippenko, A.V., Challis, P., Clocchiatti, A., Diercks, A., Garnavich, P.M., Gilliland, R.L., Hogan, C.J., Jha, S., Kirshner, R.P., Leibundgut, B., Phillips, M. M., Reiss, D., Schmidt, B.P., Schommer, R.A., Smith, R.C., Spyromilio, J., Stubbs, C., Suntzeff, N.B., & Tonry, J. (1998) Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant. The Astronomical Journal, 116(3), 1009-1038. https://doi.org/10.1086/300499
Ritchie, S.J., Cox, S.R., Shen, X.Y., Lombardo, M.V., Reus, L.M., Alloza, C., Harris, M.A., Alderson, H.L., Hunter, S., Neilson, E., Liewald, D.C.M., Auyeung, B., Whalley, H.C., Lawrie, S.M., Gale, C.R., Bastin, M.E., McIntosh, A.M., & Deary, I. J. (2018) Sex Differences in the Adult Human Brain: Evidence from 5216 UK Biobank Participants. Cerebral Cortex, 28(8), 2959-2975. https://doi.org/10.1093/cercor/bhy109
Robertson, R. (1996) Euler’s identity; a mathematical proof for the existence of God? Psychological Perspectives, 34(1), 62-75. https://doi.org/10.1080/00332929608405751
Rovelli, C. (2018a) The Order of time. Segre, E. and Carnell, S. (Trans.). New York: Riverhead Books, p. 48. (Original published in 2017.)
Rovelli, C. (2018b) Ibid., p. 110.
Saha, S., and Bamba, K. (2020) The Lambert W Function: A Newcomer in the Cosmology Class? Zeitschrift für Naturforschung A – Physical Sciences, 75(1), 23-27. https://doi.org/10.1515/zna-2019-0240
Sandage, A.R. (1970) Cosmology: A search for two numbers. Physics Today, 23(2), 34-41. https://doi.org/10.1063/1.3021960
Scott, T., Mann, R., & Martinez II, R. (2006) General relativity and quantum mechanics: towards a generalization of the Lambert W function – A Generalization of the Lambert W Function. Applicable Algebra in Engineering, Communication and Computing, 17(1), 41-47. https://doi.org/10.1007/s00200-006-0196-1
Silagadze, Z.K. (2010) Citation entropy and research impact estimation. Acta Physica Polonica B, 41(11), 2325-2333.
Simpson, A., & Visser, M. (2020) Regular Black Holes with Asymptotically Minkowski Cores. Universe, 6, 8. https://doi.org/10.3390/universe6010008
Struik, D.J. (1967) A Concise History of Mathematics. New York: Dover Publications, p.129.
Tadevosyan, M. (2005) The ‘Road to Nowhere’, a road to ‘Glory’: Vladimir Nabokov and Aleksandr Grin. Modern Language Review, 100(2), 429-443.
Tobar, G., & Costa, F. (2020) Reversible dynamics with closed time-like curves and freedom of choice. Classical and Quantum Gravity, 37, 205011. https://doi.org/10.1088/1361-6382/aba4bc
Toro, R., Perron, M., Pike, B., Richer, L., Veillette, S., Pausova, Z., & Paus, T. (2008) Brain size and folding of the human cerebral cortex. Cerebral cortex, 18(10), 2352–2357. https://doi.org/10.1093/cercor/bhm261
Ursic, M. (2006) Einstein on religion and science. Synthesis Philosophica, 42(2), 267-283.
Vazza, F., and Feletti, A. (2020) The Quantitative Comparison Between the Neuronal Network and the Cosmic Web. Frontiers in Physics, 8, 525731. https://doi.org/10.3389/fphy.2020.525731
