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In 1960, the astronomer Frank Drake devised an equation for estimating the number of intelligent civilizations in our galaxy. He did it by breaking down the problem into a hierarchy of various factors.

He suggested that the total number of intelligent civilizations in the Milky Way depends first on the rate of star formation. He culled this number by estimating the fraction of these stars with rocky planets, the fraction of those planets that can and do support life and the fraction of these that go on to support intelligent life capable of communicating with us. The result is this equation:

which is explained in more detail in this Wikipedia entry.

Today, Marcelo Gleiser at Dartmouth College in New Hampshire points out that cosmology has moved on since the 1960s. One of the most provocative new ideas is that the universe we see is one of many, possibly one of an infinite number. One line of thinking is that the laws of physics may be very different in these universes and that carbon-based life could only have arisen in those where conditions were fine-tuned in a particular way. This is the anthropic principle.

Consequently, says Gleiser, the Drake Equation needs updating to take the multiverse and the extra factors it introduces into account.

He begins by considering the total set of universes in the multiverse and defines the subset in which the parameters and fundamental constants are compatible with the anthropic principle. This is the subset {c-cosmo}.

He then considers the subset of these universes in which astrophysical conditions are ripe for star and galaxy formation {c-astro}. Next he looks at the subset of these in which planets form that are capable of harbouring life {c-life}. And finally he defines the subset of these in which complex life actually arises {c-complex life}.

Then the conditions for complex life to emerge in a particular universe in the multiverse must satisfy the statement at the top of this post (where the composition symbol denotes ‘together with’).

But there’s a problem: this is not an equation. To form a true Drake-like argument, Gleiser would need to assign probabilities to each of these sets allowing him to write an equation in which the assigned probabilities multiplied together, on one side of the equation, equal the fraction of universes where complex life emerges on the other side.

Here he comes up against one of the great problems of modern cosmology–that without evidence to back up their veracity, many ideas in modern cosmology are little more than philosophy. So assigning a probability to the fraction of universes in the multiverse in which the fundamental constants and laws satisfy the anthropic principle is not just hard, but almost impossible to formulate at all.

Take {c-cosmo} for example. Gleiser points out a few of the obvious parameters that would need to taken into account in deriving a probability. These are the vacuum energy density, matter-antimatter asymmetry, dark matter density, the couplings of the four fundamental forces and the masses of quarks and leptons so that hadrons and then nuclei can form after electroweak symmetry breaking. Try assigning a probability to that lot.

Neither is it much easier for {c-astro}. This needs to take into account the fact that heavy elements seem to be important for the emergence of life which only seem to occur in galaxies above a certain mass and in stars of a certain type and age. Estimating the probability of these conditions occurring is still beyond astronomers.

At first glance, the third set {c-life} ought to be easier to handle. This must take into account the planetary and chemical constraints on the formation of life. The presence of liquid water and various elements such as carbon, oxygen and nitrogen seem to be important as do more complex molecules. How common these conditions are, we don’t yet know.

Finally there is {c-complex life}, which includes all the planetary factors that must coincide for complex life to emerge. These may include long term orbital stability, the presence of a magnetic field to protect delicate biomolecules, plate tectonics, a large moon and so on. That’s not so easy to estimate either.

Many people have tried to put the numbers into Drake’s equation. The estimates for the number of intelligent civilisations in the Milky Way ranges from one (ours) to countless tens of thousands. Drake himself put the number at 10.

Gleiser’s take on the Drake equation for the Multiverse is an interesting approach. What it tells us, however, is that our limited understanding of the universe today does not allow us to make any reasonable estimate of the number of intelligent lifeforms in the multiverse (more than one). And given the limits on what we can ever know about other universes, it’s likely that we’ll never be able to do much better than that.

Ref: arxiv.org/abs/1002.1651: Drake Equation For the Multiverse: From String Landscape to Complex Life

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