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The Alien Equation

May 8, 2021

Throughout history, humanity’s view of the universe has changed drastically. For a long time, people believed that the Earth was all there was, with a dome high above it that had pinpricks they called stars. Later, they believed the solar system was the extent of the universe. Then that view expanded to the galaxy as we realized the pinpricks were actually other suns. Now, we believe there is a universe beyond even what we can observe, with other galaxies than our own populating space. When our understanding of the universe allowed us to understand that other stars exist, there began to be questions of extraterrestrial life around other stars and whether we on earth could somehow communicate with it. In the 1960’s, a man named Frank Drake wrote a book exploring the chances of life on other planets that was intelligent and capable of communicating with Earth in our galaxy. The book lead to an equation that expresses this chance numerically:

N = R * f(g) * f(p) * n(e) * f(l) * f(i) * f(c) * L

This equation has many terms that are not able to be calculated exactly, but they do lay extremely good groundwork for an estimate of intelligent, communicative life. This equation got experts talking about what they thought the odds for life in the universe could be and helped encourage the search for extraterrestrial life. This equation is also really easy to use to develop your own guess on the chances of extraterrestrial life. Breaking down this equation, there are three categories the values can be put into based on what factors they relate to. 

 

Astronomically Based Values

The first three values in the equation are values that are gained from observing the galaxy. They are astrophysical values that, with our current scientific capabilities, are reasonable to calculate somewhat accurately. The first value, R, is the rate of star formation in the galaxy. It can alternatively be the number of stars estimated to be in the galaxy. It is the starting point of the equation, as most of the other terms are fractions that whittle this value smaller and smaller as the criteria gets more specific. The current estimate of stars in the galaxy is between 100 and 400 billion stars. The second value, f(g), is an estimate of how many stars in the galaxy are suitable for hosting planets with life. Stars that can host planets with life must be long living and steady stars and they cannot have large fluctuations in temperatures and intensity. This value is currently estimated to be between 5 and 10 percent, meaning .05 to .1 for use in the equation The third value, f(p), is a measure of how many of those suitable stars actually have planetary systems. For example, stars that are in binary systems are thought to very rarely host planetary systems. This value is often estimated at about .5, as about 50% of star systems are binaries or multistar systems and the other 50% are single stars. 

 

Biologically Based Values

The next three values of the Drake equation are based on biological factors with life. The first one, n(e), is how many planets per star system are suitable for life. This mainly means how many planets are in the habitable zone of a star. The habitable zone is the distance from a star where planets can have water in all three phases, solid, liquid, and gas. The value to plug into the question can be found by taking your estimate of the number of planets in the habitable zone and dividing it by the estimated total number of planets in the system. For a system like our solar system, this would be .125. The next value, f(l), is the fraction of planets in the habitable zone that will actually have life form. This is where the values in the equation begin to vary greatly from person to person. Some people argue that if life can form it will and put this value at 1. Others argue that life is extremely rare to happen, putting the value closer to .001, or even smaller. Since we have so little understanding of how life started on Earth, it is hard to estimate its rarity in other places.  The final value, f(i), is the fraction of cases in which life develops intelligence. Once again, this is a controversial value to choose. Currently, we don’t know if life always evolves to intelligence. It can be argued that we did, so why wouldn’t other planets? However there have also been millions of species on our planet, and only one has evolved to our level of intelligence: humans. With those odds, intelligence seems rare. 

 

Sociological Based Values

The last two values of the Drake equation are sociological factors. The first one, f(c), is the number of intelligent races that have the technological capability and desire to try and communicate with other species. An example of this coming into play may be with an intelligent species that lives underwater. It would be difficult, if not impossible, for them to invent electronic devices like ours, and things like radio telescopes to communicate with might never be designed by them. Experts tend to estimate this as a fairly large value because it is thought by many that upon developing intelligence, a species will continually improve their technology. This is believed to always lead to communication technology in the process. The exception to this are species that face rare environmental factors that dissuade the invention of specific types of technologies, such as the underwater species example. The last value, L, is the lifetime of a civilization. This is as simple as it sounds. This value is necessary because we live so far from other planets that it would take a very long time to communicate with them. The very long time it takes to send a message means there needs to be long standing civilizations to continue any conversations, otherwise they would not be able to truly communicate with us. This value is often estimated to be between 1,000 and 100,000,000 years. 

 

Concluding Thoughts

Current estimates of the value calculated from the Drake equation range from as low as .00000000000091 to 15,600,000 planets that host intelligent, communicative life. The value can be much larger or lower than this as well, but there is no “correct” answer. You can find your own solution by plugging in values that you think are true. All you have to do is start with the number of stars in the galaxy and fill in what fractions you believe fit for the other values, and choose a lifetime to use. If your answer is greater than 1, your chosen parameters suggest that life exists elsewhere in our galaxy. However, if your answer is less than 1, your parameters suggest that we are likely alone in the galaxy. As long as you can give a reason for the values you chose, you have created your own theory for life in the universe.

Burchell, M. (2006). W(h)ither the Drake equation? International Journal of Astrobiology, 5(3), 243-250. doi:10.1017/S1473550406003107

Drake, F.; Sobel, D. (1992). Is Anyone Out There? The Scientific Search for Extraterrestrial Intelligence. Delta. pp. 55–62. ISBN 0-385-31122-2.

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About Author

Alyssa is a first year physics major at Georgia Tech. She is planning to go into astrophysics or astronomy and loves giving tours of the night sky. She also enjoys horseback riding, painting, and playing board games.

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  Timothy Durham was convicted of rape when a test showed his DNA genotype matched the DNA recovered from the crime scene. Eye witnesses testified that Durham was in a different state at the time of the incident, but he wasn’t exonerated from his 3000 year sentence until follow up DNA analysis showed that the preliminary forensic analysis used in the trial was misinterpreted (Thomas et al.). DNA testing serves an invaluable part in our criminal justice system, but it comes with complications and bias that can lead to wrongful convictions and misinformed juries.  

Background:

Forensic genetics aims to identify the origin of a biological sample. It can be traced back to Karl Landsteiner who discovered human ABO blood groups. With blood groups, suspects could be eliminated based on their blood type. For example, if a suspect had type A blood and there was type B blood left at the scene by the perpetrator, the investigators could rule out the suspect. Unfortunately, the reverse didn’t work. If the suspect and perpetrator both had the same blood type, it can’t be concluded that the suspect was guilty. Blood identifiers evolved into 8 distinct categories which improved the ability to eliminate suspects, but could only conclude that (if the system matched) it might be the perpetrator or this person might be related to the perpetrator (Jobling and Gill). The field evolved in the 1980s with the discovery of Minisatellites, lines of repetitive DNA that don’t encode proteins. Minisatellite patterns in DNA create what we know today as the DNA fingerprint, and it has a much higher accuracy rate than previous methods (Augustyn et al.). Around the same time, a breakthrough for victims of sexual assault was discovered. In the case of assault, bodily fluids of both the victim and the assaulter can get mixed. A process called differential lysis was created which could selectively increase the concentration of sperm in a fluid sample thereby allowing for accurate DNA testing (Jobling and Gill). Forensics evolved to use single-locus probe testing after several years because of its ease of interpretation. It looked at specific minisatellites that had high variability between subjects. This was the first DNA-based method to be used in a criminal investigation. Two murder homicides from several years apart were connected using DNA evidence. The evidence was then used to exonerate an innocent man, and the guilty party was found when he tried to evade mandatory DNA testing for all men in the small town. His guilt was then reinforced when the DNA profiles matched, and he gave a confession (Jobling and Gill). Finding DNA at a crime scene doesn’t guarantee that you’ll find a murderer. There are issues with non-pure samples and limited samples that make DNA work difficult, and accreditation of facilities and new techniques and take time (Jobling and Gill).  

Subjectivity of DNA Interpretation:

In a 2009 publication, the National Academy of Science discusses the possibility for subjective influence in lab based forensics. The interpretation bias happens in complex cases where, for example, there could be a mixture of DNA. A study published in 2011 looked specifically at this issue. A gang rape happened in Georgia, and the mixture in DNA from the case was used to prosecute one suspect after another suspect took a plea bargain to testify against him. With DNA mixtures, there are three possible conclusions: suspect excluded, suspect cannot be excluded, and inconclusive. If the suspect is excluded, it means that there’s little to no possibility that his DNA is part of the sample. If the suspect cannot be excluded, it means that there’s a possibility that his DNA is part of the sample. In the trial, the DNA examiners who knew the context of the case concluded that the suspect being prosecuted could not be excluded. The 2011 study gave the DNA evidence from this case and the DNA profiles of the suspects to 17 forensic examiners. These examiners had no context of the case, and they all worked independently. Of the 17, only 1 came to the same conclusion (suspect cannot be excluded) as the examiners who knew the context of the case. Twelve of the 17 concluded that the suspect who was prosecuted and convicted had no relation to the DNA found in the sample. Not only does this show that subjectivity occurs due to the context of the case, but the 17 examiners came up with different findings based on their past experiences meaning that not all DNA analysis is objective. Some organizations like the Scientific Working Group on DNA Analysis Methods say that quantitative statistical evidence should be presented with every categorical conclusion, but the US doesn’t require this (Dror and Hampikian).

False Positives:

There are two categories that cause wrongful identification in a DNA report: coincidental matches and false positives. Coincidental matches are DNA matches between two unrelated people. The probability of these matches is about 1 to 500,000 for white individuals and about 1 to 350,000 for black individuals. This small probability of coincidental matches makes people feel confident in DNA evidence. False positives, on the other hand, are matches between DNA and test DNA that result from issues in the forensics lab. There have been multiple cases of forensics labs accidentally switching victim and suspected rapist DNA which lead to convictions that were later overturned when the lab realized the error. There are also cases of misreading or misunderstanding a sample. In a case from 1993, a man was convicted of rape because someone interpreted a mixed sample of victim and perpetrator DNA as an individual sample. The conviction was again overturned. To prevent false convictions, retesting DNA is allowed, but it’s not an efficient solution. Many people are pushing for statistical information on the probability of false positives, so that the jurors can make accurate judgements based on DNA evidence (Thomas et al.).  

Conclusion:

DNA analysis is a useful tool for the criminal justice system, but subjectivity can be an issue in forensic testing. To combat wrongful convictions, there are organizations like The Innocence Project who use DNA testing to free the innocent, but reformed forensic testing standards should be put in place to prevent subjectivity and to ensure juries are correctly informed during trials. https://www.innocenceproject.org/    

Citation:

Augustyn , Adam, et al. “DNA Finerprinting.” Encyclopedia Britannica , 26 Apr. 2018, www.britannica.com/science/DNA-fingerprinting#ref153186. Dror, Itiel E., and Greg Hampikian. “Subjectivity and Bias in Forensic DNA Mixture Interpretation.” Science & Justice, vol. 51, no. 4, 2011, pp. 204–208., doi:10.1016/j.scijus.2011.08.004. Jobling, Mark A., and Peter Gill. “Encoded Evidence: DNA in Forensic Analysis.” Nature Reviews: Genetics, vol. 5, no. 10, Oct. 2004, pp. 739–751., doi:10.1038/nrg1455. Thompson, William C, et al. “How the Probability of a False Positive Affects the Value of DNA Evidence.” Journal of Forensic Sciences, vol. 48, no. 1, Jan. 2003, pp. 1–8., doi:10.1520/jfs2001171.