The Fermi Parameter
Life on planet Earth has taken many millions of years to evolve to the complex life-forms that characterise Homo sapiens with all its intelligence and associated technological tools. Yet, for centuries, astronomers have speculated that it may be possible that intelligent life exists elsewhere, and this search has informed some of the motivations for our national space programs. Life may have evolved from the same primordial soup and simply been transmitted from one world to another, such as during planetary collisions during the early stages of the Solar System formation, or it may have separate points of evolution that are independent from each other. A discovery of life representative of a separate biogenesis from Earth would be one of the most profound moments in the history of the scientific endeavour.
This search has become more poignant in recent years since the discovery of thousands of exoplanets around other stars thanks to amazing astronomical observatories like the Hubble Space Telescope, the Kepler Space Telescope and the James Webb Space Telescope. These observatories and others that succeed them are sure to change our perspectives on models of planets, stars and life in the Universe as their sensitivity and resolution improves with each decade of technological development. In our search for planets around other stars we have discovered Hot Jupiter’s, Super Earth’s, tidally locked planets and they range in compositions from mostly iron to mostly water. It seems only a matter of time where instruments like this will be able to directly image exoplanets around other stars and fully characterise their atmospheric composition and possible evidence of technological industrialisation.
Fundamental to the arguments regarding life visiting our solar system is the Fermi paradox, which asserts that there is a contradiction between our theoretical expectations for intelligent life emerging in the Universe and our apparent lack of observations to confirm it has indeed done so. The calculation for such a prediction is based on the number of galaxies, stars, and planets, their measured ages and spectral types when compared to the solar system from which we originate. From a statistical basis, a calculation of probability suggests that we are not special but perhaps typical of an average system that might evolve.
It is perhaps constructive to consider the Fermi Paradox in terms of two factors so that any paradox is quantified numerically. There is a measurement M. Then there is a Theoretical estimate T. We can define both M and T as the measured or predicted number of independent intelligent civilisations to exist within 100 LY/1 million years, or a similar sort of scaling. We can then define the Paradox as a ratio between these two factors in what we may define as a Fermi Parameter
F = M / T (1)
This then presents three possible scenarios. When M > T, then F > 1 and in this scenario, there would be more ETI civilisations observed than we expected from theoretical predictions. When M = T, then F = 1, and there is no paradox since the number of observed civilisations is consistent with our theoretical predictions. However, when M < T, F < 1, this is when the number of measured ETI civilisations is less than expected from theoretical predictions. This is in fact the current paradigm accepted by mainstream science, in that it is the position we have only observed one intelligent civilisation (humanity on Earth) and yet estimates of our theoretical predictions (such as using the Drake equation) suggest there should be more. In fact, one might go further and argue that according to the current paradigm M << T, and so F << 1.
Yet we can take this a step further and consider the addition of uncertainties associated with both the measured and theoretical parameters in our attempt at quantification. There is a measurement M which has an uncertainty δm. Then there is a Theoretical estimate T which has an uncertainty δT. Then rewriting the Fermi Parameter to include the uncertainties we get the following
F = (M +/- δm) / (T +/- δt) (2)
To make any analysis simple, we can take the special case of values for M, T, δm, δt close to unity and not large deviations thereof. This is done to facilitate the visualisation of the potential solution space. For the scenario of the currently accepted particular paradigm M = 1, but we are attempting to look at the more general case here.
To illustrate with an example. Imagine that the measured was determined to be M = 5 but with an uncertainty of δm = ± 2. Now imagine that the theoretical was determined to be T = 10, but with an uncertainty of δt = ±1. In this scenario M < T and δm > δt. Then calculating
F = (5 +/- 2) / (10 +/- 1) = (3 < F < 7) / (9 < F < 11) ==> 3/7, 3/9, 7/9, 7/11 (3)
We note that in all these solutions F < 1, since the number of measured ETI civilisations would be less than what our theories predict. This is a hypothetical scenario since in reality once we discovered other civilisations this would lead to a revision of our theoretical models to bring them into parity. However, we must consider here that T is a theoretical model prior to the latest measurement.
The figure below shows the different models that can arise from this sort of thinking, where the Measurement M is plotted against the Theoretical prediction T, but both with uncertainty error bars on the prediction.
The figure below shows a summary of the possible solutions and how they compare to each other. The point of presenting this data is to illustrate the different solutions and that to narrow the solutions it would be constructive to focus on the quantification of our theoretical predictions and our measurements, so that this may lead towards a narrower range of solutions that we may focus on. The uncertainties may be systematic or random in form.
In terms of the measurements, the nature of the uncertainties is the limitations on the detecting equipment, what data they are filtering and how it is being processed. Whether scientists are even looking at the right type of data, or neglecting others. Therefore, the main uncertainties are likely to be physics and engineering based. In terms of our theoretical predictions, the nature of the uncertainties is in our definitions for life and intelligence and what we understand about systems that can organise. Therefore, the main uncertainties are likely to be biologically based.
For both the measured and theoretical uncertainties they will be informed by our prior expectations and if it is the case that M ≠ T, then it is likely that to close this one of our prior expectations must be revised. In particular, a prudent strategy would be to broaden our measurement range outside of the current domains of observations, but also to broaden our definitions for life and intelligence. Yet, there appears to be resistance to doing either.
One example of an alternative idea to definitions of life originated in 1944 with the physicist Erwin Schrödinger who wrote in his book ‘What is Life?’: “living matter, while not eluding the laws of physics as established up to date, is likely to involve other laws of physics hitherto unknown which however once they have been revealed will form just as integral a part of science as the former….life can be defined by the process of resisting the decay to thermodynamic equilibrium”..
A sensible strategy would be to list the source of uncertainties within the measurements and theoretical predictions and then attempt to quantify them. Through using normalised units, it would then be possible to state them relative to a unity value and so then the source of the Fermi Paradox could be identified as dominated by measurements or theoretical models. This would then promote research in these two areas and therefore close the gap.
If over time the uncertainties in the measurements can be minimised to a negligible value, then this would imply a major rethink on our theoretical models, such as definitions for life and how it may form in different types of environments. If instead the uncertainties in the theoretical models can be minimised to a negligible value, then this would imply a rethink on the sorts of measurements we conduct with our experimental detectors that allows us to rule out the existence of ETI. From this author’s perspective, it is curious that this attempt to close the Fermi Paradox through the quantification of uncertainties has not been pursued previously and is suggested as the subject of a major research effort.
