Lost in Math: A Book Review





Anthropic Principle


Beauty is in the Eye of the Beholder




Experiment and Theory







Memorable Quotations








Particles and Interactions




Physics isn’t Math


Quantum Mechanics


Science and the Scientific Method





Standard Model (of particle physics)


String Theory


Triple Threat: Crises in Physics, Astrophysics, and Cosmology?





The book concludes with three appendices:

  • Appendix A: The Standard Model Particles
  • Appendix B: The Trouble with Naturalness
  • Appendix C: What You Can Do To Help


  • As a scientist
  • As a science writer or member of the public



Observation, Theory, and Reality


8.3 Limits of Representation and Knowledge of Reality
It follows…that there are limits to what the scientific method can achieve in explanatory terms.  We need to respect these limits and acknowledge clearly when arguments and conclusions are based on some philosophical stance rather than purely on testable scientific argument.  If we acknowledge this and make that stance explicit, then the bases for different viewpoints are clear and alternatives can be argued about rationally.

We human beings want so badly to be able to explain our existence and existence itself that we tend to “fill in the blanks” and treat speculation (no matter how well reasoned) as if it were something akin to fact.  This is true for both science and religion.  A more reasonable approach, it seems to me, is to reject absolute certainty—especially where physical evidence is sparse or nonexistent—while always striving to deepen our understanding.  That is the scientist’s stock-in-trade—or should be.  Each of us needs to become more aware of the limitations of our understanding!

Thesis F6: Reality is not fully reflected in either observations or theoretical models.
Problems arise from confusion of epistemology (the theory of knowledge) with ontology (the nature of existence): existence is not always manifest clearly in the available evidence.  The theories and models of reality we use as our basis for understanding are necessarily partial and incomplete reflections of the true nature of reality, helpful in many ways but also inevitably misleading in others.  They should not be confused with reality itself!

We humans create our own “realities”, but under the very best of circumstances (science, for example), our “reality” is only an imperfect model of what actually exists.

The confusion of epistemology with ontology occurs all the time, underlying for example the errors of both logical positivism and extreme relativism.  In particular, it is erroneous to assume that lack of evidence for the existence of some entity is proof of its non-existence.  In cosmology it is clear for example that regions may exist from which we can obtain no evidence (because of the existence of horizons); so we can sometimes reasonably deduce the existence of unseen matter or regions from a sound extrapolation of available evidence (no one believes matter ends at or just beyond the visual horizon).  However one must be cautious about the other extreme, assuming existence can always be assumed because some theory says so, regardless of whether there is any evidence of existence or not.  This happens in present day cosmology, for example in presentations of the case for multiverses, even though the underlying physics has not been experimentally confirmed.  It may be suggested that arguments ignoring the need for experimental/observational verification of theories ultimately arise because these theories are being confused with reality, or at least are being taken as completely reliable total representations of reality.

Absence of evidence is not evidence of absence.  But, without evidence, all we have is conjecture, no matter how well informed.  As Carl Sagan once said, “Extraordinary claims require extraordinary evidence.”

No model (literary, intuitive, or scientific) can give a perfect reflection of reality.  Such models are always selective in what they represent and partial in the completeness with which they do so.  The only model that would reflect reality fully is a perfect fully detailed replica of reality itself! This understanding of the limits of models and theories does not diminish the utility of these models; rather it helps us use them in the proper way.  This is particularly relevant when we consider how laws of nature may relate to the origins of the universe itself, and to the existence and nature of life in the expanding universe.  The tendency to rely completely on our theories, even when untested, seems sometimes to arise because we believe they are the same as reality—when at most they are descriptions of reality.

Ellis makes a pretty good case here against dogma.  Though he does not specifically mention religion (and why should he, as the subject at hand is cosmology), I do think these ideas apply to religion as well.

Always a journey, never a destination.


Theory and Observation


Thesis F1: Philosophical choices necessarily underly cosmological theory.
Some cosmologists tend to ignore the philosophical choices underlying their theories; but simplistic or unexamined philosophical standpoints are still philosophical standpoints!

Cosmology, and indeed all human inquiry, is based on (at least) two unproven (though certainly reasonable) assumptions:

  1. The Universe exists.
  2. The human mind is at least to some degree capable of perceiving and understanding the Universe.

Any cosmological theory will have additional foundational unproven assumptions.  These are called axioms.  Ellis admonishes us to at least be aware of them, and to admit to them.

8.1 Criteria for theories
As regards criteria for a good scientific theory, typical would be the following four areas of assessment: (1) Satisfactory structure: (a) internal consistency, (b) simplicity (Ockham’s razor), and (c) aesthetic appeal (‘beauty’ or ‘elegance’); (2) Intrinsic explanatory power: (a) logical tightness, (b) scope of the theory—the ability to unify otherwise separate phenomena, and (c) probability of the theory or model with respect to some well-defined measure; (3) Extrinsic explanatory power, or relatedness: (a) connectedness to the rest of science, (b) extendability—providing a basis for further development; (4) Observational and experimental support, in terms of (a) testability: the ability to make quantitative as well as qualitative predications that can be tested; and (b) confirmation: the extent to which the theory is supported by such tests as have been made.

As you can see, a theory is not an opinion.  It must be well-supported by facts.  It must be internally consistent.  It must have explanatory power.  The Russian physicist A. I. Kitaĭgorodskiĭ (1914-1985) put it succinctly: “A first-rate theory predicts; a second-rate theory forbids, and a
third-rate theory explains after the event.”  Einstein’s special and general relativity are spectacular examples of first-rate theories.  In over 100 years of increasingly rigorous and sophisticated experiments and observations, relativity has never been proven to be incorrect.

Ellis emphasizes the importance of observational and experimental support in any scientific theory.

It is particularly the latter that characterizes a scientific theory, in contrast to other types of theories claiming to explain features of the universe and why things happen as they do.  It should be noted that these criteria are philosophical in nature in that they themselves cannot be proven to be correct by any experiment.  Rather their choice is based on past experience combined with philosophical reflection.  One could attempt to formulate criteria for good criteria for scientific theories, but of course these too would need to be philosophically justified.  The enterprise will end in infinite regress unless it is ended at some stage by a simple acceptance of a specific set of criteria.

So, even our criteria about what makes a good scientific theory rest upon axioms that cannot be proven.  But unlike religion, scientific theories never posit the existence of any supernatural entity.

Thesis F3: Conflicts will inevitably arise in applying criteria for satisfactory cosmological theories.
The thrust of much recent development has been away from observational tests toward strongly theoretically based proposals, indeed sometimes almost discounting observational tests.  At present this is being corrected by a healthy move to detailed observational analysis of the consequences of the proposed theories, marking a maturity of the subject.  However because of all the limitations in terms of observations and testing, in the cosmological context we still have to rely heavily on other criteria, and some criteria that are important in most of science may not really make sense.

String theory? Cosmic inflation?  Multiverse? If a theory is currently neither testable nor directly supported by observations, is it science, or something else?
