70.** Discrete Scale Relativity And SX Phoenicis Variable Star**

*International Journal of Astronomy and Astrophysics*, **1(**2), 38-43, June 2011.

69.** An Infinite Fractal Cosmos**

*Journal of Cosmology* **4**, 674-677, 2009.

68.** Critical Test Of The Self-Similar Cosmological Paradigm: Anomalously Few Planets Orbiting Low-Mass Red Dwarf Stars**

*New Advances in Physics* **3**(2), 55-59, 2009.

The incidence of planetary systems orbiting red dwarf stars with masses < 0.4 M_{¤} provides a crucial observational test for the Self-Similar Cosmological Paradigm. The discrete self-similarity of the paradigm mandates the prediction of anomalously few planets associated with these lowest mass red dwarf stars, in contrast to conventional astrophysical assumptions. Ongoing observational programs are rapidly collecting the data necessary for testing this prediction and preliminary results are highly encouraging.

67.** The Proton As A Kerr-Newman Black Hole**

*Electronic Journal of Theoretical Physics* **6**(22), 167-170, 2009.

The general equation governing the mass, spin and angular momentum of a Kerr-Newman black hole applies equally well to a proton when the gravitational coupling constant predicted by a discrete fractal paradigm is used in the equation, along with the standard mass, spin and angular momentum of the proton.

66.** Meaning of the Fine Structure The Constant**

*Electronic Journal of Theoretical Physics*, submitted, December 2007.

The SSCP’s discrete fractal scaling rules lead to a simple and natural explanation for the 80-year mystery of the meaning of the atomic scale fine structure constant.

65. **Hadrons As Kerr-Newman Black Holes**

*Journal of Cosmology* **6**, 1361-1374, 2010.

Subatomic particles such as the proton and the alpha particle are modeled in terms of black holes. Discrete self-similar scaling indicates that the gravitational interaction within Atomic Scale systems is stronger by a factor of 10^{38} when compared to conventional Stellar Scale gravitational interactions. These ideas are successfully tested by retrodicting the mass of the proton and the radius of the alpha particle.

64.** Discrete Scale Relativity**

*Astrophysics and Space Science*, 311(4), 431-433, December 2007.

The fundamental implications of discrete cosmological self-similarity are considered. In the case of exact self-similarity General Relativity’s Principle of General Covariance must be extended to include covariance with respect to cosmological Scale transformations. A further generalization of Einstein’s relativity program, which incorporates the discrete scale invariance of the SSCP, is proposed.

63.** ZZ Ceti Stars: Fractal Analogues Of Excited He ^{+} Ions?**

IEEE Transactions on Plasma Science

The majority of ZZ Ceti variable stars are identified as discrete self-similar analogues of He^{+} ions oscillating at multiple transition frequencies for states with principal quantum numbers between 2 and 8. A quantitative test comparing observed stellar and atomic oscillation periods provides preliminary support for the discrete fractal analysis.

62.** Discrete Cosmological Self-Similarity And Delta Scuti Stars***
Electronic Journal of Theoretical Physics*,

The masses, pulsation modes and oscillation periods of δ Scuti stars are used to identify their Atomic Scale analogues. The proposed discrete self-similar relationship is quantitatively tested for a specific double-mode δ Scuti variable star.

61.** Discrete Self-Similarity Of RR Lyrae Stars: II. Period Spectrum For A Very Large Sample
**

The discrete cosmological self-similarity demonstrated between RR Lyrae variable stars and excited helium atoms undergoing single-level energy level transitions (see #60) is further tested with a very large and carefully analyzed sample of RR Lyrae stars.

60.** Discrete Self-Similarity Between RR Lyrae Stars And Singly-Excited Helium Atoms***Electronic Journal of Theoretical Physics* **5**(17), 207-214, March 2008*.*

The qualitative and quantitative (masses, radii and oscillation periods) properties of RR Lyrae variable stars are shown to obey a discrete self-similar relationship with the counterpart properties of helium atoms in Rydberg states (n = 7-10) undergoing single-level energy state transitions.

59.** Mass Estimates For Galactic Dark Matter Objects As A Test Of A Fractal ****Cosmological Paradigm**

*Fractals*,** 10**(1), 27-38, March 2002.

An updated review (see #52 for an earlier review) of mass estimates for galactic dark matter objects (MACHOs). The estimates come primarily from gravitational microlensing experiments. The data are consistent with predictions of the Self-Similar Cosmological Paradigm. Trends in the data are discussed, as well as empirical support for a predicted correlation between stellar mass functions and dark matter mass functions.

58.** M-Set As Metaphor**

*Physics Education*, 36(5), 433, September 2001.

The beauty, infinity and mystery of the Mandelbrot Set are discussed, as well as its potential relevance to the physical universe.

57.** An Apparent Gap In Stellar Mass Distributions at ≈ 0.7 M _{¤} And A Possible Explanation**

The Self-Similar Cosmological Paradigm definitively predicts that stellar mass functions have anomalous deficits at about 0.73 M_{¤}. This prediction is based on the fact that there are no atoms with masses of 5 atomic mass units, hence a gap in the atomic mass function. Mass functions for several stellar samples appear to have the predicted deficit. Prospects for further testing of this prediction are considered.

56.** Democritus -- Scientific Wizard Of The 5th Century BC**

*Speculations in **Science and Technology*,** 21**(1), 37-44, 1998.

This essay considers how Democritus, in the 5th century BC, without much help from mathematics or technology, could discover that the world was built up from atoms, that the Sun was a common star, that the Milky Way was made up of unresolved stars, that mass and energy are conserved, etc. The answer: scientific reasoning. It is concluded that the empirical/conceptual approach can be a highly effective complement to the theoretical/mathematical approach in science. What if Democritus’ ideas and methods had caught on immediately, instead of being virtually ignored for 2,000 years?

55.** Morphological Comparison Of Planetary Nebulae And Rydberg Atoms**

Web page, < http://www.amherst.edu/~rloldershaw/stars2/menu.html >.

Planetary nebulae on the stellar scale and electron density functions in atoms share a remarkably similar set of shapes: spheres, ellipsoids, crossed ellipsoids,butterfly-shapes, toroids, propeller-shapes, spheres-within-spheres, etc. This web page demonstrates the isomorphisms pictorially and offers a potential explanation.

54.** Self-Similar Cosmological Paradigm Web Page**, also entitled **Fractal Cosmology**

Web page, < http://www.amherst.edu/~rloldershaw >.

This web page is devoted to the Self-Similar Cosmological Paradigm. The paradigm is described, and some of the papers listed here are included.

53.** Predictions And Observations Relating To The Galactic Dark Matter**

*Sources And Detection Of Dark Matter In The Universe*, edited by D.B. Cline, North-Holland, Amsterdam, 365-368, 1998.

An updated version of #52, which was presented at the “Third International Dark Matter Symposium”, February 1998.

52. **The Galactic Dark Matter: Predictions And Observations**

*Astrophysics **and Space Science*,** 257**(2), 271-278, 1998.

The Self-Similar Cosmological Model’s crucial predictions regarding the masses and physical states of the galactic dark matter objects are shown to agree with available experimental evidence, while the Standard Big Bang Model’s predictions are not supported. Additional SSCM predictions are discussed.

51. **Janus-Faced Cosmology**

*Sky & Telescope*, April, p. 10, 1998.

Discusses the contradiction between the overly optimistic public face of cosmology and the real situation in this field, where we cannot even give a basic description of the cosmos because 90% to 99% of its composition is enigmatic “dark matter”. And that is just for starters.

50.** Common Sense Versus Predictive Power In Cosmology**

*Physics Essays*,**10**(4), 644-645, 1997.

Considers what might happen if a “wrong” idea should uniquely solve a key scientific problem, and uses the Self-Similar Cosmological Model’s successful dark matter predictions as a possible example.

49.** Cold Dark Matter Under Attack**

*Physics World*, March, 1997.

Theoretical cosmologists are touting the CDM hypothesis, while ignoring a considerable amount of observational evidence against the idea.

48.** Successful Prediction Of Three Stellar-Scale Enigmas**

*International Journal **of Theoretical Physics*,** 35**(12), 2475-2481, 1996.

This paper demonstrates the predictive power of the Self-Similar Cosmological Model. Three stellar scale mysteries: (1) an unexpected cutoff in the stellar mass function, (2) the unexpected discovery of planets orbiting neutron stars, and (3) the surprising result that Dark Matter objects of about 0.2 solar masses make up at least 50% of the Galaxy, were predicted by the fractal cosmological paradigm.

47. **Cosmological Candor**

*Apeiron*,** 2**(3), 94, 1995.

A warning against the current trends of over-confidence and complacency in the field of cosmology.

46.** Cosmological Claims**

*Physics Today*, October, 1995.

Describes two cases wherein cosmologists bent the rules of science in support of fashionable models

45.** Book Review Of Progress In New Cosmologies**

A review of a book presenting unorthodox cosmological ideas.

44.** Keeping Physics On Track**

*Apeiron*,** 1**(20), 32-36, 1994.

A discussion of problematic trends in the “New Physics”, citing specific examples. Includes suggestions for improving the situation.

43.** Dark Matter Predictions**

*Speculations in Science and Technology*,** 17**(4), 315-316, 1994.

Presents the definitive predictions of the Self-Similar Cosmological Model regarding the Dark Matter problem, then shows that these predictions are consistent with the results of recent DM experiments.

42. **Zwicky’s Last Puzzle: What’s Dark And Rules The Universe?**

*American **Journal of Physics*,** 62**(2), 106, 1994.

*AJP*’s editor lamented that there were no major unsolved conjecture’s in physics, like Fermat’s Last Theorem in mathematics. This essay points out that the Dark Matter Enigma, first posed by Fritz Zwicky early in the 20th century, is such an unsolved conjecture.

41. **Prediction Of Pulsar-Planet Systems By The Self-Similar Cosmological ****Model**

*Speculations in Science and Technology*,** 16**(4), 319-320, 1993.

In the early 1990s, astronomers were shocked to discover planets orbiting pulsars (pulsating neutron stars). This paper documents the fact that the Self-Similar Cosmological Model predicted the existence of planets orbiting neutron stars before they were discovered.

40.** Book Review of Clifford Pickover’s Computers And Imagination**

A book review, requested by the journal’s editor.

39.** A Cosmological Reckoning***
Meta Research Bulletin*,

Criticism of overly optimistic speculation in the field of cosmology in the early 1990s.

38.** Hierarchical Cosmology**

*Astrophysics and Space Science*,** 189**, 163-168, 1992.

In 1970 the eminent astrophysicist G. De Vaucouleurs published an important paper in the journal, *Science*, which argued that a hierarchical cosmological paradigm appeared to be superior to the standard Big Bang paradigm. The present paper looks at the evidence gathered between 1970 and 1992, and comes to the same conclusion.

37.** Discrete Self-Similarity Between Period-Radius Relations For Variable ****Stars And Rydberg Atoms**

*Speculations in Science and Technology*,** 14**(3), 193-202, 1991.

Period-radius relationships for variable stars and Rydberg atoms are analogous, as expected in the Self-Similar Cosmological Paradigm. Quantitative scaling for the relationships is also in agreement with the scale transformation rules of the SSCP.

36.** What’s Wrong With The New Physics?**

*New Scientist*,** 128**(1748/9), 56-59, 1990.

Commentary on “The New Physics”, e.g., inflation, QCD, string theory, etc. The basic thesis is that these are very speculative ideas, but they are discussed in the scientific literature as if they are well-supported by observations, which is not the case.

35.** Cosmology Theory Compromised**

*Nature*,** 346**, 800, 1990.

Three examples of increasing tensions between expectations of the standard cosmological model and unexpected observational findings are discussed. The three cited inconsistencies involve (1) the cosmological density parameter, (2) dark matter results and (3) periodic clustering of galaxies.

34.** Mathematics And Natural Philosophy**

*Mathematics And Science*, ed. by Ronald E. Mickens, World Scientific Publishing Co., 136-153, 1990.

Commissioned essay for a book exploring the relationships between mathematics and science, asking questions like “What is mathematics?, Is mathematics a language?, and Why is mathematics so effective in scientific applications?

33. **Is Strict Reductionism The Only Viable Alternative?**

*Speculations in **Science and Technology*,** 13**(3), 224-225, 1990.

Argues that fractal models, especially those with infinite levels of self-similar structure, offer a radically different understanding of nature, when compared to the usual reductionist approach.

32.** The Self-Similar Cosmological Model: Technical Details, Predictions, ****Unresolved Issues, And Implications**

*International Journal of Theoretical **Physics*,** 28**(12), 1503-1532, 1989.

Part 2 of an introductory review of the Self-Similar Cosmological Model, emphasizing details, predictions and problems.

31.** The Self-Similar Cosmological Model: Introduction And Empirical ****Tests**

*International Journal of Theoretical Physics*,** 28**(6), 669-694, 1989.

Part 1 of an introductory review of the Self-Similar Cosmological Model, emphasizing the basic ideas and many retrodictive tests.

30.** Particle Physics Programme**

*Nature*,** 332**, 106, 1988.

A critique of practices and attitudes among the particle physics elite, as well as the status of their models. This essay was prompted by a Stephen Weinberg article suggesting that particle physics was “in absolute terms quite deep, perhaps close to the final source”. Examples are given to show that we are still very far from a “theory of everything”.

29.** Two New Tests Of The Self-Similar Cosmological Paradigm**

*Speculations **in Science and Technology*,** 12**(2), 135-137, 1989.

As predicted, the oscillation periods of neutron stars and white dwarf stars are related to their atomic scale counterparts in atomic nuclei and helium atoms by the scale transformation equations of the Self-Similar Cosmological Model.

28.** The New Physics - Physical Or Mathematical Science?**

*American Journal of **Physics*,** 56**(12), 1075-1081, 1988.

As creators of “the new physics” have proposed increasingly abstract descriptions of nature, the possibility of testing their theoretical constructs experimentally has markedly declined. This situation has been exacerbated by incongruously strong confidence in the standard paradigms of particle physics and cosmology. Numerous examples from these fields are cited, and the implications are discussed

27.** Rydberg Atoms, Variable Stars, Kepler’s Third Law and E=hv**

*International Journal of General Systems*,** 14**(1), 77-84, 1988.

Observed radii and oscillation periods of variable stars are correlated in a manner analogous to the correlations between radii and oscillation periods of atoms. In both cases the form of the correlations is that of Kepler’s Third Law, wherein R^{3} = K_{i}P^{2}. The constants K_{atom} and K_{star} are shown to be related by the scale transformation equations of the Self-Similar Cosmological Model. The idea of discrete energy levels for variable stars is explored.

26.** The Self-Similar Cosmological Paradigm: A New Test And Two New ****Predictions**

*Astrophysical Journal*,** 322**(1), 34-36, 1987.

The magnetic dipole moments of atomic nuclei and neutron stars are shown to be quantitatively related the manner predicted by the scaling equations of the Self-Similar Cosmological Model. Definitive predictions regarding the structure of the electron and the nature of the dark matter are presented.

25.** Possible Evidence For Projection Effect Bars In Sc Galaxies**

*Astrophysics and Space Science*,** 133**, 183-187, 1987.

The distribution of axial ratios (ellipticity) of barred Sc galaxies is skewed in a manner that is consistent with predictions of the author’s Projection Effect Model for barred spiral galaxies.

24.** Cosmological Self-Similarity And The Principle Of Scale Covariance**

*Astrophysics and Space Science*,** 128**(2), 449-453, 1986.

The question of why the cosmos should be organized in a discrete self-similar hierarchy, is explored. The possibility that General Relativity’s fundamental Principle of Covariance needs to be extended to include Scale, well as time, location, orientation and state of motion, is suggested.

23.** The Self-Similar Hierarchical Paradigm: Galactic Scale Phenomena And ****The Dark Matter**

*International Journal of General Systems*,** 13**(1), 67-82, 1986.

Radii and spin periods of galaxies are shown to obey the self-similar scaling equations of the SSHP. The “peculiar velocities” of galaxies and the global expansion on the galactic scale are reinterpreted within the context of a self-similar cosmos. A solution to the Dark Matter Problem is presented, along with definitive predictions for the masses of the dark matter objects.

22.** Cosmological Self-Similarity**

*Astrophysics and Space Science*,** 126**(1), 203-206, 1986.

Self-similar scaling relationships are noted for six fundamental parameters of atomic scale systems and their six stellar scale counterparts. Extension of the scaling rules to the galactic scale and a decisive prediction are discussed.

21.** Self-Similar Scaling And Angular Momentum Relationships In Stellar And ****Atomic Systems**

*Astrophysics and Space Science*,**126**(1), 199-201, 1986.

Two types of angular momentum relationships shared by both atomic and stellar systems suggest self-similarity between analogues on different cosmological scales.

20.** Comparison Of The Effects Of 1,25 Dehydroxyvitamin D(3) On T Lymphocyte ****Subpopulations. **

Did Cytofluorograph work for this immunology study. First author was Dr. William Rigby; I was third author. Not sure where it was published.

19.** Quantitative Scaling For The Self-Similar Hierarchical Cosmology**

*International **Journal of General Systems*,** 12**(2) 137-148, 1986.

Scale transformation equations are derived from empirical results and theoretical considerations. The introduction of quantitative scaling relationships allows one to make definitive predictions by which the SSHC can be unambiguously tested.

18.** Warped Galactic Disks And Optical Projection Effects**

*Astrophysics and Space **Science*,** 121**, 273-281, 1986.

A review of the Projection Effect Model for barred spiral galaxies.

17.** A Conventional Explanation For The Axial Ratio Anomalies Of Bar-Within-Ring ****Galaxies**

*Astrophysics and Space Science*,** 115**,195-196, 1985.

An erratum to numbers 15 and 16.

16.** Inner Rings of Barred Spiral Galaxies**

*Astronomy and Astrophysics*,** 149**, 221-223, 1985.

Statistics of inner rings are compared with predictions of the Projection Effect Model.

15.** Unusual Properties Of Bar-Within-Ring Galaxies And The Projection Effect ****Model For Barred Spiral Galaxies
**

Further comparisons of predictions of the Projection Effect Model with observed characteristics of bar-within-ring-galaxies.

14.** Set Theory Applied To The Self-Similar Hierarchical Cosmology**

*International **Journal of General Systems*,** 10**, 235-255, 1984.

The SSHC is described in the language of set theory.

13. **A New Model For Barred Spiral Galaxies***
Astrophysics and Space Science*,

Computer simulations demonstrate that warped spirals can produce bar and bar-within-ring shapes as projection effects.

12.** The Continuing Case For A Hierarchical Cosmology**

*Astrophysics and Space **Science*,** 92**(2), 347-358, 1983.

An update on de Vaucouleurs’ original discussion of the Big Bang versus the Hierarchical cosmological paradigms, emphasizing the empirical discoveries of the last decade.

11.** New Evidence For The Principle Of Self-Similarity**

International Journal of General *Systems*,** 9**(1), 37-42, 1982.

Defines the Principle of Self-Similarity and presents further empirical and theoretical support for it.

10.** The Preferred Pitch Angle Of Spiral Galaxies**

*Monthly Notices of the Astronomical **Society of South Africa*,** 41**(5+6), 42-46, 1982.

This paper offers a brief answer to the question of why spiral galaxies tend to have arm pitch angles of about 73°. This is the pitch angle of the unique “Golden Spiral” (same shape at all scales of magnification), which is well-known in mathematics. Also included is a discussion of self-similarity between stellar and galactic systems.

9.** Empirical And Theoretical Support For Self-Similarity Between Atomic And ****Stellar Systems***
International Journal of General Systems*,

Various types of evidence for isomorphisms and self-similarity among stellar and atomic systems are presented.

8. **Gravity and Levity**

*Bulletin of the Atomic Scientists*,** 37**(7), 53-54, 1981.

An essay on Einstein’s use of humor.

7.** A discussion Of Beer’s Comments On Astrophysical Spirals**

*Speculations in Science **and Technology*,** 4**(3), 307-309, 1981.

Rebuttal of criticism concerning stellar-galactic isomorphism.

6.** On The Number Of Levels In The Self-Similar Hierarchical Cosmology**

*International Journal of General Systems*,** 7**(2), 159-163, 1981.

The SSHC is discussed in terms of set theory. Set theoretical arguments link the number of cosmological scales to the degree of self-similarity between analogue systems of neighboring scales.

5.** Conceptual Foundations Of The Self-Similar Hierarchical Cosmology**

*International **Journal of General Systems*,** 7**(2), 151-157, 1981.

A general introduction to the new paradigm of discrete cosmological self-similarity.

4.** Faraday, Maxwell, Einstein And Epistemology**

*Nature and System*,** 3**, 99-108, 1981.

This paper explores and evaluates the conceptual/empirical approach versus analytical/mathematical approach in understanding nature.

3.** Hierarchical Modeling In The Sciences**

*Nature and System*,** 2**, 189-197, 1980.

Applications of hierarchy theory in mathematics, cosmology, physics, biology and political science are reviewed.

2.** The Atomic Scale In The Self-Similar Hierarchical Cosmology**

*Speculations in Science and Technology*,** 2**, 161-171, 1979.

Isomorphisms among atomic and stellar systems are presented. Eight predictions of the SSHC model are cited.

1.** On The Morphology And Dynamics Of Galaxies**

*Speculations in Science and **Technology*,** 1**, 477-482, 1978.

This paper considers isomorphism between stellar and galactic systems. It also identifies the properties of the primary systems defining the fundamental scales of nature’s discrete self-similar hierarchy.