# The probability of extraterrestrial life

Since, the discovery of exoplanets nearly 3 decades ago most astronomers, at least the public facing ones, seem to agree that it is just a matter of time before they find signs of life such as the presence of volatile gases in the atmosphere associated with life like methane or oxygen. I’m an agnostic on the existence of life outside of earth because we don’t have any clue as to how easy or hard it is for life to form. To me, it is equally possible that the visible universe is teeming with life or that we are alone. We simply do not know.

But what would happen if we find life on another planet. How would that change our expected probability for life in the universe? MIT astronomer Sara Seager once made an offhand remark in a podcast that finding another planet with life would make it very likely there were many more. But is this true? Does the existence of another planet with life mean a dramatic increase in the probability of life in the universe. We can find out by doing the calculation.

Suppose you believe that the probability of life on a planet is $f$ (i.e. fraction of planets with life) and this probability is uniform across the universe. Then if you search $n$ planets, the probability for the number of planets with life you will find is given by a Binomial distribution. The probability that there are $x$ planets is given by the expression $P(x | f) = C(x,n) f^x(1-f)^{n-x}$, where $C$ is a factor (the binomial coefficient) such that the sum of $x$ from one to $n$ is 1. By Bayes Theorem, the posterior probability for $f$ (yes, that would be the probability of a probability) is given by

$P(f | x) = \frac{ P(x | f) P(f)}{P(x)}$

where $P(x) = \int_0^1 P(x | f) P(f) df$. As expected, the posterior depends strongly on the prior. A convenient way to express the prior probability is to use a Beta distribution

$P(f |\alpha, \beta) = B(\alpha,\beta)^{-1} f^{\alpha-1} (1-f)^{\beta-1}$ (*)

where $B$ is again a normalization constant (the Beta function). The mean of a beta distribution is given by $E(f) = \alpha/(\alpha + \beta)$ and the variance, which is a measure of uncertainty, is given by $Var(f) = \alpha \beta /(\alpha + \beta)^2 (\alpha + \beta + 1)$. The posterior distribution for $f$ after observing $x$ planets with life out of $n$ will be

$P(f | x) = D f^{\alpha + x -1} (1-f)^{n+\beta - x -1}$

where $D$ is a normalization factor. This is again a Beta distribution. The Beta distribution is called the conjugate prior for the Binomial because it’s form is preserved in the posterior.

Applying Bayes theorem in equation (*), we see that the mean and variance of the posterior become $(\alpha+x)/(\alpha + \beta +n)$ and $(\alpha+x)( \beta+n-x) /(\alpha + \beta + n)^2 (\alpha + \beta + n + 1)$, respectively. Now let’s consider how our priors have updated. Suppose our prior was $\alpha = \beta = 1$, which gives a uniform distribution for $f$ on the range 0 to 1. It has a mean of 1/2 and a variance of 1/12. If we find one planet with life after checking 10,000 planets then our expected $f$ becomes 2/10002 with variance $2\times 10^{-8}$. The observation of a single planet has greatly reduced our uncertainty and we now expect about 1 in 5000 planets to have life. Now what happens if we find no planets. Then, our expected $f$ only drops to 1 in 10000 and the variance is about the same. So, the difference between finding a planet versus not finding a planet only halves our posterior if we had no prior bias. But suppose we are really skeptical and have a prior with $\alpha =0$ and $\beta = 1$ so our expected probability is zero with zero variance. The observation of a single planet increases our posterior to 1 in 10001 with about the same small variance. However, if we find a single planet out of much fewer observations like 100, then our expected probability for life would be even higher but with more uncertainty. In any case, Sara Seager’s intuition is correct – finding a planet would be a game breaker and not finding one shouldn’t really discourage us that much.

# The inherent conflict of liberalism

Liberalism, as a philosophy, arose during the European Enlightenment of the 17th century. It’s basic premise is that people should be free to choose how they live, have a government that is accountable to them, and be treated equally under the law. It was the founding principle of the American and French revolutions and the basic premise of western liberal democracies. However, liberalism is inherently conflicted because when I exercise my freedom to do something (e.g. not wear a mask), I infringe on your freedom from the consequence of that thing (e.g. not be infected) and there is no rational resolution to this conflict. This conflict led to the split of liberalism into left and right branches. In the United States, the term liberal is exclusively applied to the left branch, which mostly focuses on the ‘freedom from’ part of liberalism. Those in the right branch, who mostly emphasize the ‘freedom to’ part, refer to themselves as libertarian, classical liberal, or (sometimes and confusingly to me) conservative. (I put neo-liberalism, which is a fundamentalist belief in free markets, into the right camp although it has adherents on both the left and right.) Both of these viewpoints are offspring of the same liberal tradition and here I will use the term liberal in the general sense.

Liberalism has never operated in a vacuum. The conflicts between “freedom to” and “freedom from” have always been settled by prevailing social norms, which in the Western world was traditionally dominated by Christian values. However, neither liberalism nor social norms have ever been sufficient to prevent bad outcomes. Slavery existed and was promoted by liberal Christian states. Genocide of all types and scales have been perpetrated by liberal Christian states. The battle to overcome slavery and to give equal rights to all peoples was a long and hard fought battle over slowly changing social norms rather than laws per se. Thus, while liberalism is the underlying principle behind Western governments, it is only part of the fabric that holds society together. Even though we have just emerged from the Dark Years, Western Liberalism is on its shakiest footing since the Second World War. The end of the Cold War did not bring on a permanent era of liberal democracy but may have spelled it’s eventual demise. What will supplant liberalism is up to us.

It is often perceived that the American Democratic party is a disorganized mess of competing interests under a big tent while the Republicans are much more cohesive but in fact the opposite is true. While the Democrats are often in conflict they are in fact a fairly unified center-left liberal party that strives to advocate for the marginalized. Their conflicts are mostly to do with which groups should be considered marginalized and prioritized. The Republicans on the other hand are a coalition of libertarians and non-liberal conservatives united only by their desire to minimize the influence of the federal government. The libertarians long for unfettered individualism and unregulated capitalism while the conservatives, who do not subscribe to all the tenets of liberalism, wish to halt encroaching secularism and a government that no longer serves their interests.

The unlikely Republican coalition that has held together for four decades is now falling apart. It came together because the more natural association between religious conservatism and a large federal bureaucracy fractured after the Civil Rights movements in the 1960’s when the Democrats no longer prioritized the concerns of the (white) Christian Right. (I will discuss the racial aspects in a future post). The elite pro-business neo-liberal libertarians could coexist with the religious conservatives as long as their concerns did not directly conflict but this is no longer true. The conservative wing of the Republican party have discovered their new found power and that there is an untapped population of disaffected individuals who are inclined to be conservative and also want a larger and more intrusive government that favors them. Prominent conservatives like Adrian Vermeule of Harvard and Senator Josh Hawley are unabashedly anti-liberal.

This puts the neo-liberal elites in a real bind. The Democratic party since Bill Clinton had been moving right with a model of pro-market neo-liberalism but with a safety net. However they were punished time and time again by the neo-liberal right. Instead of partnering with Obama, who was highly favorable towards neoliberalism, they pursued a scorched earth policy against him. Hilary Clinton ran on a pretty moderate safety-net-neo-liberal platform and got vilified as an un-American socialist. Now, both the Republicans and Democrats are trending away from neo-liberalism. The neo-liberals made a strategic blunder. They could have hedged their bets but now have lost influence in both parties.

While the threat of authoritarianism looms large, this is also an opportunity to accept the limits of liberalism and begin to think about what will take its place – something that still respects the basic freedoms afforded by liberalism but acknowledges that it is not sufficient. Conservative intellectuals like Leo Strauss have valid points. There is indeed a danger of liberalism lapsing into total moral relativism or nihilism. Guardrails against such outcomes must be explicitly installed. There is value in preserving (some) traditions, especially ancient ones that are the result of generations of human engagement. There will be no simple solution. No single rule or algorithm. We will need to explicitly delineate what we will accept and what we will not on a case by case basis.

# The machine learning president

For the past four years, I have been unable to post with any regularity. I have dozens of unfinished posts sitting in my drafts folder. I would start with a thought but then get stuck, which had previously been somewhat unusual for me. Now on this first hopeful day I have had for the past four trying years, I am hoping I will be able to post more regularly again.

Prior to what I will now call the Dark Years, I viewed all of history through an economic lens. I bought into the standard twentieth century leftist academic notion that wars, conflicts, social movements, and cultural changes all have economic underpinnings. But I now realize that this is incorrect or at least incomplete. Economics surely plays a role in history but what really motivates people are stories and stories are what led us to the Dark Years and perhaps to get us out.

Trump became president because he had a story. The insurrectionists who stormed the Capitol had a story. It was a bat shit crazy lunatic story but it was still a story. However, the tragic thing about the Trump story (or rather my story of the Trump story) is that it is an unintentional algorithmically generated story. Trump is the first (and probably not last) purely machine learning president (although he may not consciously know that). Everything he did was based on the feedback he got from his Twitter Tweets and Fox News. His objective function was attention and he would do anything to get more attention. Of the many lessons we will take from the Dark Years, one should be how machine learning and artificial intelligence can go so very wrong. Trump’s candidacy and presidency was based on a simple stochastic greedy algorithm for attention. He would Tweet randomly and follow up on the Tweets that got the most attention. However, the problem with a greedy algorithm (and yes that is a technical term that just happens to coincidentally be apropos) is that once you follow a path it is hard to make a correction. I actually believe that if some of Trump’s earliest Tweets from say 2009-2014 had gone another way, he could have been a different president. Unfortunately, one of his early Tweet themes that garnered a lot of attention was on the Obama birther conspiracy. This lit up both racist Twitter and a counter reaction from liberal Twitter, which led him further to the right and ultimately to the presidency. His innate prejudices biased him towards a darker path and he did go completely unhinged after he lost the election but he is unprincipled and immature enough to change course if he had enough incentive to do so.

Unlike standard machine learning for categorizing images or translating languages, the Trump machine learning algorithm changes the data. Every Tweet alters the audience and the reinforcing feedback between Trump’s Tweets and its reaction can manufacture discontent out of nothing. A person could just happen to follow Trump because they like The Apprentice reality show Trump starred in and be having a bad day because they missed the bus or didn’t get a promotion. Then they see a Trump Tweet, follow the link in it and suddenly they find a conspiracy theory that “explains” why they feel disenchanted. They retweet and this repeats. Trump sees what goes viral and Tweets more on the same topic. This positive feedback loop just generated something out of random noise. The conspiracy theorizing then starts it’s own reinforcing feedback loop and before you know it we have a crazed mob bashing down the Capitol doors with impunity.

Ironically Trump, who craved and idolized power, failed to understand the power he actually had and if he had a better algorithm (or just any strategy at all), he would have been reelected in a landslide. Even before he was elected, Trump had already won over the far right and he could have started moving in any direction he wished. He could have moderated on many issues. Even maintaining his absolute ignorance of how govening actually works, he could have had his wall by having it be part of actual infrastructure and immigration bills. He could have directly addressed the COVID-19 pandemic. He would not have lost much of his base and would have easily gained an extra 10 million votes. Maybe, just maybe if liberal Twitter simply ignored the early incendiary Tweets and only responded to the more productive ones, they could have moved him a bit too. Positive reinforcement is how they train animals after all.

Now that Trump has shown how machine learning can win a presidency, it is only a matter of time before someone harnesses it again and more effectively. I just hope that person is not another narcissistic sociopath.