Physicist Max Tegmark has identified 32 dimensionless ratios that are basic properties of reality in his though-provoking book, Our Mathematical Universe: My Quest for the Ultimate Nature of Reality. These are 32 pure numbers from which every other fundamental constant of nature can be theoretically derived.

In this illustration I depicted these parameters and added the missing on/off switch, bringing the grand total of controls needed to mathematically define a universe up to the magic 33.

33 controls must be tuned to create our universe

33 controls must be tuned to create our universe

These knobs must be so incredibly finely-tuned to create a universe, let alone a universe capable of supporting life, that we have truly won the cosmic lottery. Tegmark explains:

“How far could you rotate the dark-energy knob before the “Oops!” moment? The current setting of the knob, corresponding to the dark-energy density we’ve actually measured, is about 10−27 kilograms per cubic meter, which is almost ridiculously close to zero compared to the available range: the natural maximum value for the dial is a dark-energy density around 1097 kilograms per cubic meter, which is when the quantum fluctuations fill space with tiny black holes, and the minimum value is the same with a minus sign in front. If rotating the dark-energy knob…by a full turn would vary the density across the full range, then the actual knob setting for our Universe is about 10−123 of a turn away from the halfway point. That means that if you want to tune the knob to allow galaxies to form, you have to get the angle by which you rotate it right to 123 decimal places!

That’s interesting also because of the parallel with the game of Chess. Louis Victor Allis, a Dutch computer scientist working in the artificial intelligence field, has calculated that there are at least 10^123 games of Chess that can possibly be played. That means that the probability that our universe contains galaxies is akin to exactly 1 game of chess in 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 games. Unlikely doesn’t even begin to describe these odds. There are “only” 10^81 atoms in the observable universe, after all.


Tegmark continues:

…if the electromagnetic force were weakened by a mere 4%, then the Sun would immediately explode as its hydrogen fused into so-called diprotons, an otherwise nonexistent kind of neutron-free helium. If it were significantly strengthened, previously stable atoms such as carbon and oxygen would radioactively decay away.

If the so-called weak nuclear force were substantially weaker, there would be no hydrogen around, since it would all have been converted to helium shortly after our Big Bang. If it were either much stronger or much weaker, the neutrinos from a supernova explosion would fail to blow away the outer parts of the star, and it’s doubtful whether life-supporting heavier elements such as iron would ever be able to leave the stars where they were produced and end up in planets such as Earth.

If electrons were much lighter, there could be no stable stars, and if they were much heavier, there could be no ordered structures such as crystals and DNA molecules. If protons were 0.2% heavier, they’d decay into neutrons unable to hold on to electrons, so there would be no atoms. If they were instead much lighter, then neutrons inside of atoms would decay into protons, so there would be no stable atoms except for hydrogen. Indeed, the proton mass depends on another knob that has a very wide range of variation and needs to be fine-tuned to thirty-three decimal places to get any stable atoms other than hydrogen.

Many of these fine-tuning examples were discovered in the seventies and eighties by Paul Davies, Brandon Carter, Bernard Carr, Martin Rees, John Barrow, Frank Tipler, Steven Weinberg and other physicists. And more examples just kept turning up.”

The Moon and the Sun constitute further proof we passengers on spaceship Earth are winners. There is nothing in physics that says the Moon and Sun must appear the same size in our skies. In fact our Moon is the only satellite in our system that even comes close to doing this. It is truly amazing that the Moon and Sun discs match up—and they won’t forever as the Moon is slowly moving away from the Earth. We won the cosmic lottery again!

A look at any total solar eclipse is proof of the astronomically unlikely situation that the Sun is 400 times larger than the Moon and 400 times father away from Earth than the Moon.

Luc Viatour / CC-BY-SA-3.0

Luc Viatour / CC-BY-SA-3.0

I discovered another such symmetry in the orbital dynamics of Moon and Earth.

During one orbit around the Sun, Earth actually rotates about its own axis 366.3 times. The Moon orbits the Earth in 27.3 days. Of course a day is one Earth rotation on its own axis.

366.3 x 27.3 = 9999.99

At the same time, the Earth is 366.3% the diameter of the Moon and the Moon is 27.3% the diameter of Earth.



To better understand why the Earth rotates more times than there are days in the year, watch this clear explanation:

How can it be that the Earth and Moon are in a reciprocal mathematical relationship in terms of number of rotations and in the pure ratios of diameters? Nothing in physics says this need be so. It is far too perfect and we won the cosmic lottery yet again!


The following equation also reveals something about the unexpected perfection of the Earth-Moon system:


The combined diameter of all the planets in our solar system is 10 times greater than the Earth’s circumference. This has astonishingly high accuracy at 99.99%. As we don’t know the combined diameters of all the planets with more than 99.99% accuracy this relationship might in fact be exact. It is a powerful argument for the primacy of base 10.

“It is the mark of an instructed mind to rest satisfied with the degree of precision which the nature of the subject admits and not to seek exactness when only an approximation of the truth is possible.” -Aristotle


We won the cosmic lottery yet again, against astronomical odds! What are we not understanding?

God, Aliens, Conspiracy, Randomness and/or Triviality are unsatisfying explanations to me. These major secrets placed so obviously in plain sight make me feel like humanity is destined to understand the deeper implications.

Many more such symmetries and wonderment are in my most recent book, The Divine Proportion.