life would not arise otherwise. Various authors have introduced new sets of numbers into the original "coincidence" considered by Dirac and his contemporaries, thus broadening or even departing from Dirac's own conclusions. Jordan (1947) noted that the mass ratio for a typical star (specifically, a star of the Chandrasekhar mass, itself a constant of nature, approx. 1.44 solar masses) and an electron approximates to 1060, an interesting variation on the 1040 and 1080 that are typically associated with Dirac and Eddington respectively. (The physics defining the Chandrasekhar mass produces a ratio that is the −3/2 power of the gravitational fine-structure constant, 10−40.) Modern studies Several authors have recently identified and pondered the significance of yet another large number, approximately 120 orders of magnitude. This is for example the ratio of the theoretical and observational estimates of the energy density of the vacuum, which Nottale (1993) and Matthews (1997) associated in an LNH context with a scaling law for the cosmological constant. Carl Friedrich von Weizsäcker identified 10120 with the ratio of the universe's volume to the volume of a typical nucleon bounded by its Compton wavelength, and he identified this ratio with the sum of elementary events or bits of information in the universe. Valev (2019) found equation connecting cosmological parameters (for example density of the universe) and Planck units (for example Planck density). This ratio of densities, and other ratios (using four fundamental constants: speed of light in vacuum c, Newtonian constant of gravity G, reduced Planck constant ℏ, and Hubble constant H) computes to an exact number, . This provides evidence of the Dirac large numbers hypothesis by connecting the macro-world and the micro-world. See also Dimensionless physical constant Naturalness (physics) Time-variation of fundamental constants References Further reading External links Audio of Dirac talking about the large numbers hypothesis Full transcript of Dirac's speech. Robert Matthews: Dirac's coincidences sixty years on The Mysterious Eddington–Dirac Number Physical cosmology Obsolete scientific theories Large Numbers Hypothesis Astronomical hypotheses 1937 introductions Coincidence