In summary, there are two key points to take away: The External Reality Hypothesis implies that a “theory of everything” (a complete description of our external physical reality) has no baggage, and something that has a complete baggage-free description is precisely a mathematical structure. Taken together, this implies the Mathematical Universe Hypothesis, i.e., that the external physical reality described by the theory of everything is a mathematical structure. So the bottom line is that if you believe in an external reality independent of humans, then you must also believe that our physical reality is a mathematical structure. Everything in our world is purely mathematical – including you. ...Yes it is a crazy idea. A much more sensible SciAm reader comments:

This crazy-sounding belief of mine that our physical world not only is described by mathematics, but that it is mathematics, makes us self-aware parts of a giant mathematical object. As I describe in the book, this ultimately demotes familiar notions such as randomness, complexity and even change to the status of illusions; it also implies a new and ultimate collection of parallel universes so vast and exotic that all the above-mentioned bizarreness pales in comparison, forcing us to relinquish many of our most deeply ingrained notions of reality.

Confusing mathematics with physical reality (extreme Platonism) has a long and undistinguished history going back to a few ancient Greek philosophers.He is right -- the junk-bond physics has grown even more prolific and exotic than ever. I explained Tegmark's errors in my FQXi essay.

No one doubts that mathematics is an effective way to describe the physical world, but to give mathematics some sort of physical substance, or to say there is no physical substance - it's just math, is a fairly bizarre way to understand nature.

Could this conjecture be tested? I doubt it.

Is it science? Not by my definition.

A more sensible view of mathematics is that it is a very effective, but artificial and invented language we use to model nature.

Further, all mathematical models are approximations to physical reality, and thus subject to change and evolution.

The extreme Platonists like Tegmark are true believers who want to lead us into the completely abstract and unscientific world of fantasy, and define it as "reality".

We do not have to follow. ...

Michael S. Turner said in the late 1990s that the "go-go junk bond days of physics were over".

That may have been wishful thinking, or maybe it was just what was PC at the moment, but the fact is that junk-bond physics has grown even more prolific and exotic since then.

Tegmark replies:

Thanks Robert for raising these important issues! I discuss them extensively in the book, exploring the full spectrum of views.So he blames SciAm for this choice? Tegmark has spent much of his career promoting the math (multi) universe. See his 2003 SciAm cover story on

Like you and Popper, I view untestable theories as unscientific.

Please beware that parallel universes are not a theory, merely a prediction of certain mathematical theories (such as cosmological inflation and unitary quantum mechanics), which have in turn passed some experimental tests (hence their popularity) but may be ruled out during new experiments in coming years. ...

You asked for more detailed material: you'll find a sample on http://mathematicaluniverse.org (click either "Popular" or "Technical" depending on your taste), and please feel free to ask me direct questions on Facebook as well. The book is of course mainly on uncontroversial but fascinating recent discoveries in modern physics, from cosmology to particle physics, but Scientific American predictably chose to highlight some of the most controversial material.

Parallel Universes - Not just a staple of science fiction, other universes are a direct implication of cosmological observations and his defense to criticisms, The Multiverse Strikes Back. His own web site says:

Those articles are titled, "Everything in the Universe Is Made of Math – Including You" and "Is the Universe Actually Made of Math? Cosmologist Max Tegmark says mathematical formulas create reality." So yes, the SciAm excerpt on the "key idea" from the book.Articles about the book

- Discover magazine, December 2013 issue (excerpts from Chapter 10; paywall disappears December 3 2013)

- Discover magazine (interview with me about a key idea from the book)

His proposal is silly because no one has ever reduced any physical object to math, not even a photon or electron. By his own admission, he needs to assume that randomness, complexity, and change (over time) are just illusions. These are philosophical issues that were debated by the ancient Greeks. His position is no stronger today than it was 2300 years ago.

Update: Woit reviews Tegmark.

I’m still though left without an answer to the question of why the scientific community tolerates if not encourages all this. Why does Nature review this kind of thing favorably? Why does this book come with a blurb from Edward Witten? I’m mystified.

It is incredibly refreshing to see I'm not alone in my opinion that mathematical Platonism is utter garbage as far science is concerned. I think math and physics majors must skip logic, philosophy and English courses else they would recognize Platonism when they encountered it, or realize that concepts and abstractions (including all math) are not actual existent material entities, and can not exchange places with matter and energy or time except in the imagination and fiction, as much as they would wish otherwise. I can appreciate flights of fantasy in its muse like ability to inspire the human spirit and provoke the imagination, but I don't call this science, or confuse it with reality.

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