- focused on galaxies rather than quasars In 1971 from redshift quantization G. Paál came up with the idea that the Universe might have nontrivial topological structure. Studies performed in the 1980s and early 1990s produced confirmatory results: In 1989, Martin R. Croasdale reported finding a quantization of redshifts using a different sample of galaxies in increments of 72 km/s or Δz = (where Δz denotes shift in frequency expressed as a proportion of initial frequency). In 1990, Bruce Guthrie and William Napier reported finding a "possible periodicity" of the same magnitude for a slightly larger data set limited to bright spiral galaxies and excluding other types. In 1992, Guthrie and Napier proposed the observation of a different periodicity in increments of Δz = in a sample of 89 galaxies. In 1992, Paal et al. and Holba et al. concluded that there was an unexplained periodicity of redshifts in a reanalysis of a large sample of galaxies. In 1997, Guthrie and Napier concluded the same: "So far the redshifts of over 250 galaxies with high-precision HI profiles have been used in the study. In consistently selected sub-samples of the datasets of sufficient precision examined so far, the redshift distribution has been found to be strongly quantized in the galactocentric frame of reference. ... The formal confidence levels associated with these results are extremely high." Quasar redshifts Most recent discourse has focused upon whether redshift surveys of quasars (QSOs) produce evidence of quantization beyond that explainable by selection effect. This has been assisted by advances in cataloging in the late 1990s that have increased substantially the sample sizes involved in astronomical measurements. Karlsson's formula Historically, K. G. Karlsson and G. R. Burbidge were first to note that quasar redshifts were quantized in accordance with the empirical formula where: refers to the magnitude of redshift (shift in frequency as a proportion of initial frequency); is an integer with values 1, 2, 3, 4 ... This predicts periodic redshift peaks at = 0.061, 0.30, 0.60, 0.96, 1.41, and 1.9, observed originally in a sample of 600 quasars, verified in later early studies. Modern discourse A 2001 study by Burbidge and Napier found the pattern of periodicity predicted by Karlsson's formula to be present at a high confidence level in three new samples of quasars, concluding that their findings are inexplicable by spectroscopic or similar selection effects. In 2002, Hawkins et al. found no