As covered in a previous post, abductive thinking seeks to explain a series of facts we have observed. We are seeking  the hypothesis that best explains the facts at hand and can be used to predict either what will happen next for future events, or what additional evidence we should expect to find. It is the scientific method of thinking applied to real life, combining both System 1 (intuitive emotional) and System 2 (rational) thinking. 

At the core of abduction is Bayesian Thinking which is based on 2 assumptions. First, all beliefs can be expressed as probabilities, and second, beliefs should be updated when we receive new information. It is this iterative process that narrows the gap between what the brain perceives reality to be and what reality actually is. If we keep System 1 in check, we should be able to use System 2 to help us perceive the reality of the world around us. There is a lot to unpack there so here is a quick refresher on Bayes. Remember that E stands for Evidence and H stands for Hypothesis. The vertical bar means given that. 

P(H|E)= P(E|H) / P(E) * P(H)

This is written a little differently than before with the P(H) outside of the division bar to help illustrate a key point. P(H) is a hypothesis about something that exists in the real world. Evidence is evaluated according to its connection to the hypothesis P(E|H) vs it occurring naturally P(E). If the evidence is more likely to occur in accordance with the hypothesis, then the belief in the hypothesis will increase. If it is less likely to occur in accordance with the hypothesis, then the belief in the hypothesis will decrease. In either case, the initial belief in your hypothesis is critical. A base rate is needed for the hypothesis. If it is set too high or too low, then the evidence to support the hypothesis must be extraordinary. 

To see the process in action, let’s look at the Unidentified Anomalous Phenomena (UAP) formerly known as UFOs. I’m pretty sure most of us have seen things flying in the sky that we just can’t identify. A light in the sky at night that moves erratically, something that looks metallic high in a bright blue sky. There are things we just don’t know what it is so we devise theories to explain what we saw. Currently there are 4 main theories associated with UAPs. 

1. UAPS are extraterrestrial aliens visiting us from another planet, 
2. UAPs are advanced technology created here on Earth that we don’t know about, 
3. UAPs are simply ordinary technology such as drones and weather balloons we don’t recognize,
4. UAPS are naturally occurring phenomena (plasmas, atmospheric events, etc.) 

The first step is to set the base rate of P(H) for each of the theories. This will give us a general idea of where we believe each theory lies on the possibility scale. 

For theory 1, while it is likely there is some form of life on other planets, whether not there are space faring civilizations in an entirely different matter. Interstellar travel is virtually impossible with our physics (energy requirements, speed of light, etc). There simply is no hard evidence (more on this later) of extraterrestrials to date. So being skeptical in nature, I will set this rate at 5%. Since this is an extraordinary claim, I want to see extraordinary proof. 

Next up is theory 2, which is advanced technology owned by some government. Definitely more likely than aliens, but some of the physics displayed by UAPs is unlike anything seen before (tic-tac video is good at https://www.youtube.com/watch?v=zlrz84nEXtk ). So while this is more likely than aliens, its still a stretch so lets set this rate at 15%. 

Theory 3 postulates common technology such as drones and weather balloons remaining unidentified. In the New Jersey UAP craze in late 2024, its a safe bet to say industrial size drones were responsible for many of the sightings. Let’s call this 30%. The remaining 50% would then be classified as some sort of natural phenomena that we can’t identify which is theory 4. 

With our base rates settled, we are looking for evidence to either prove or disprove our theories. But not all evidence is created equal. We are looking for evidence with 2 distinct qualities; necessary and sufficient. Evidence that is necessary is mandatory for the phenomena to occur, but by itself cannot guarantee the outcome we are looking . Something else is required. For example oxygen is needed for fire, but cannot guarantee a fire. You need a spark. Evidence that is sufficient guarantees the outcome we are looking for is not unique. There could be other causes of the outcome. A match could cause a fire but so could lightening, or rubbing two sticks together. What kind of evidence are we looking for? The gold standard which is evidence that is both necessary and sufficient for the outcome we are looking for. 

We now have a goal as to what kind of evidence to look for and our base rates for the theories. Lets apply Bayesian logic to the aforementioned tic-tac video and see what happens to our theories. 

After intensive study and evaluation, and after ruling out theories 3 and 4, lets say we decide there is a 75% chance it is alien technology and 25% chance it is U.S military technology (I’m setting it high to make a point). Surely this evidence will change how I feel about extraterrestrial life. Using Bayes formula, we get 

(.75/.25)x.05=.15

In this example, even though the tic-tac video has a 75% chance of depicting extraterrestrial technology, the overall belief in theory 1 has only increased to 15%, which is now its new base rate. Had the initial base rate been 30%, the new base rate for theory 1 would be at 90%. The tic-tac video, as puzzling as it is, is neither necessary or sufficient to confirm the existence of otherworldly visitors. As a result, even though theory 1 has more evidence behind it, it still has a long way to go. Siting the late Carl Sagan: “Extraordinary claims require extraordinary evidence”. What kind of evidence could that be for UAPs? The ultimate evidence would be recovered alien artifacts including bodies. This is why the incidents in Roswell, New Mexico in April of 1947 are still of such great importance to UAP researchers. They believe the U.S government is in position of such evidence.

The UAP example gives us insight into what it means to be a Bayesian thinker even if you do not use the formulas, which itself is widely utilized in technology today (machine learning, spam filtering, medical diagnostics, risk assessment, legal and forensic analysis, etc.)

First, when thinking about some hypothesis, either yours or someone else’s, be careful with the base rate you start with. For critical issues, I start from a standpoint of skepticism. While not a cynic, I tend to be skeptical of most outrageous claims. The ability to think about your beliefs in percentages has the advantages of moving ourselves away from binary thinking and seeing the world in shades vs black and white. 

Second, Bayesian thinking is cumulative. If for example, hundreds and thousands of tic-tac videos are released, then each piece of evidence acts in sort of a compounding fashion. This is most evident in high profile criminal court cases. Often, these cases tend to be circumstantial, or death by a thousand cuts. While there is no so called smoking gun, the overall weight of the evidence is enough for a conviction. Each piece of evidence moves the needle towards a guilt verdict. 

Third, look for evidence that is necessary and sufficient, the gold standard. Something that is required for the outcome, guarantees it, and is. unique. Remember you are looking for the theory that best explains the facts at hand. If you are not finding such evidence, flip your around and adopt the opposite posture to see if it explains the world you are looking at any better. Flipping your beliefs around is also a good way to see another dimension of the world that is perhaps hidden to you. The other point here is that you can also do the reverse and look for evidence that eliminates hypotheses. Paraphrasing Sherlock Holmes, by eliminating the impossible, you wind up with the truth, no matter how improbable. 

Finally, use razors, rules of thumb, and heuristics to shave off anything that is unnecessary in an effort to simplify your thinking and eliminate unnecessary complexity. This provides a razor sharp focus on the things that matter, making you a more effective and direct thinker.