The headline in the New York Post reads: 1 in 331 billion chance: Same New York lottery numbers drawn twice in one day. Sounds impressive – the problem is, it’s entirely wrong. What is true is that the same five numbers, 18, 21, 30, 35, and 36, were drawn in the New York Take Five lottery in both the midday and evening drawings for Thursday, October 27. The Post reports that “experts” (unnamed) told them the odds of this happening are 1 in 331 billion.

The Post called this a “lottery miracle” but in fact it is a classic example of what is called, with good reason, the “lottery fallacy”. The odds of winning the Take Five with one ticket on any particular game is 1 in 575,757. What the Post’s experts did was take a calculator and multiple those odds by itself, yielding 331,496,123,049. (So in their view an expert is anyone with a calculator.) But those are the odds of those five numbers coming up on two consecutive draws – not the odds of any five numbers repeating. The chance of any five numbers repeating is simply 1 in 575,757 – the odds of the evening numbers being the same as the midday’s (whatever those midday numbers were). This lottery happens every day, so in the last 10 years that would be 3,650 opportunities for this to happen. The odds of this coincidence happening each decade is closer to 1 in 157.

But the odds are even greater of such a coincidence happening for various reasons. First, there are about 180 lotteries in the world, 46 in the US alone. More subtly, we are determining the criteria for a lottery coincidence after the fact. What if the identical numbers came up twice in a row, just not twice in the same day (say an evening draw and the following morning draw). The Post would still falsely consider that a 1 in 331 billion miracle. That doubles the chance right there, for now both the morning and evening draw can match the one before (1 in 78 per decade).

People, however, consider it an amazing coincidence if the same numbers come up close together, even a few days apart. In 2009 the Bulgarian lottery turned out the same numbers in one week. This sparked the same reaction as the New York lottery results. This dramatically increases the probability of a hit, for now each sequence of numbers can be compared to every other sequence of numbers within several days. For one week of Lottery Five draws, that 14 sets of numbers, and 91 possible comparisons (using the formula k(k-1)/2).

There are other types of lottery coincidences also, such as the same person winning a lottery twice (even with different numbers). When this happens again many media outlets will commit the lottery fallacy and report the wrong odds. The odds of this specific person winning this specific lottery with two individual purchased tickets may be astronomical, but the odds of anyone winning any lottery twice having purchased multiple tickets is pretty good. Some kind of lottery coincidence should happen on a regular basis, and it does, at about the rate proper statistics predicts.

We can apply the lottery fallacy principle to things other than the lottery. We tend to notice patterns that stick out, such as any coincidental alignment of facts or occurrence. We are then impressed with the incredibly low odds of that particular alignment happening. But again, we should be considering the probability of any alignment happening. You dream of someone who haven’t seen in years, and they call the next day. Must be psychic – or just the predictable alignment of random events in your life. People tend to underestimate the possibility of an alignment, because they underestimate the number of variables at work.

Let’s say that 100 definable things happen to you in an average week (just to use a representative number – the actual number is likely far greater). That would be 4,950 opportunities for any two of those things to align in some way – every week. We also use loose criteria for what constitutes an alignment, usually deciding the criteria after the fact. This is true of all almost 8 billion people on the planet (7.98 – almost there).

The number of opportunities for an extremely unlikely alignment happening is equally massive. Apparently strange coincidences, in the aggregate, should happen all the time – so it should be no surprise that they do.

Often, contentious political and social questions have a scientific question in the middle of them. Resolving the scientific question will not always resolve the political ones, but at least it can properly inform the debate. The recent overturning of Roe v Wade has supercharged the debate about when human life begins. It may seem, then, that what  science has to say about this question is important to the debate. But it may be less useful than it at first appears.

For example, in a recent editorial Henry Olsen, who is pro-life, asserts – “The heart of the abortion debate: What is human life?” I actually disagree with this framing. That is often a subtle and effective way to manipulate a debate – you assume a certain framing of the question that is biased toward one side. In this case, if the question is – what is a human life – then the pro-life side only has to argue that a fetus is a human life. But this framing is wrong on multiple levels.

Olsen is trying to frame this as a scientific question, but really the abortion debate is much more of a philosophical question. First let’s address what science questions there are.

Is a fertilized human embryo “human life?” Sure. It’s a living organism, and it is certainly human. But that’s not the only question. One could also ask – when does a fertilized egg become a person? That is a more nuanced question. I think there is broad agreement that a baby is a person. At the other end of the process we have a single cell. That cell may have the potential to develop into a person, but the cell itself is not a person.

At what point does a clump of cells become an actual person (again – not just the future potential of one)? This is an unanswerable question, as there is no sharp dividing line. There is no definable moment. There are milestones we can use to make some reasonable judgement calls. For example, one might argue that a person has to have the capacity for self-awareness, some sense of self and of being. This requires at least a minimally functioning brain.

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Humans overall suck at logic. We have the capacity for logic, but it is only one of many algorithms running in our brains, and often gets lost in the noise. Further, we have many intuitions, biases, and cognitive flaws that degrade our ability to think logically. Fortunately, however, we also have the ability for metacognition, the ability to think about our own thinking. We can therefore learn logic and how to think more clearly, filtering out the biases and flaws. It is impossible to do this perfectly, so it is best to think of metacognition as a life-long project of incremental self-improvement. Further, our biases can be so powerful, that when we learn how to think about thinking we often just make our logical fallacies more and more subtle, rather than eliminating them entirely.

Some cognitive flaws are evolutionarily baked into our thinking, likely resulting from heuristics that are practical mental shortcuts but not strictly logically valid. There also appears to be some cognitive abilities that were not prioritized in our evolutionary history, and so our finite brain resources were simply not allocated to them. This is where most math and statistically related fallacies derive. We do not deal well with large numbers, and we have terrible intuitions regarding statistics and probability. We have developed elaborate formal systems for dealing with math and probability, essentially to replace or at least augment our intuitive thinking, and often these systems produce results that are counterintuitive.

Perhaps the most famous example of counter-intuitive statistics is the Monty Hall problem. You are given a choice of three doors, behind one is a prize. You can choose one door. The host of this game, who knows where the prize is, then opens one door without a prize (again – they know where the prize is and deliberately choose one of the unchosen doors without a prize), and then ask if you want to change your choice to the other unopened door. If you change your choice your odds of winning go up from 1/3 to 2/3. If you have not encountered this problem before, this may seem counterintuitive, but it is absolutely correct.

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Spanish company Nueva Pescanova is close to opening a commercial octopus farm in the Canary Islands. The purpose of this farm is to raise octopuses (and yes, that is an acceptable plural) for food, sparking another round in the debate over the ethics of raising animals for food. This also comes on the heels of the UK adding the octopus to the list of “sentient” animals, garnering for them certain legal protections.  This is a good opportunity to discuss what sentience means and ethics of eating animals.

Consciousness as a phenomenon of living things is a continuum, with things like bacteria, algae, and fungi at one end of the spectrum and humans at the other (humans are objectively the most encephalized or sapient species on Earth). Nowhere along this continuum are there any sharp demarcation lines. Therefore, as humans develop an ethical and moral philosophy for how we should treat each other, the obvious question becomes – to what extent should our ethical philosophy apply to other living things?

First we need to dispense with the extremist position that all life is equally deserving of dignity, respect, autonomy, and all the ethical considerations that flow from these principles. This is an unworkable position, and also does not stand up to close scrutiny. First, all living things exist to some extent in competition with each other. No living thing affords all other living things equal respect. If someone is infected with bacteria, those bacteria may very well kill them (after subjecting them to a horrible illness). Taking antibiotics is mass bacterial murder. Insects are definitely a step up from single-celled creatures, having a primitive neural algorithm that determines their behavior. And sometimes we need to control the population of insects as they try to eat our food, spread infections, destroy our homes, or otherwise be pests.

At the other end of the spectrum there are chimpanzees, our closest cousins, and the other great apes. They clearly have a highly sophisticated central nervous system. They can experience grief, have personalities, can plan ahead, and communicate. Because they are closely related to us, we have an easy time understanding that they are intelligent creatures who deserve to also be treated with dignity and respect. Still, this does not mean the same thing as for humans. Chimpanzees do not deserve the right to vote, or be held criminally accountable for their behavior or enter into a legal contract. While very close to humans, chimps have some obvious limits. There is a solid case to be made, however, that chimps should not be farmed for food or subjected to cruel experiments. They are intelligent sensitive creatures and should not be made to suffer at the hands of humans.

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If someone gets seriously ill from COVID, to the point that they need to be hospitalized and even placed in ICU, and they were unvaccinated, how much should we blame them for their illness? This question can have practical implications, if we base decisions on allocating limited resources and insurance coverage of vaccine status. I wrote about this dilemma recently on Science-Based Medicine (and then discussed it on the SGU), and it sparked a lively discussion. Some of the responses amounted to justification for blaming the victim, which is essentially the core of the issue, and an important concept for activist skeptics to handle.

Blaming the victim can occur in many contexts. Within skeptical circles the most common manifestation is to blame people for being gullible (which is essentially the opposite of being skeptical). If someone, for example, falls for an obvious con it is easy to feel contempt or even anger toward that person for their gullibility. Sometimes gullibility is combined with scientific illiteracy. There are numerous pseudoscientific products on the market that require someone to have essentially no idea how the world works in order to believe the claims (or alternatively to compartmentalize any thoughts of mechanism of action). There are products that claim to improve the taste of wine simply by waving a plastic card over the glass, or to improve your athletic performance because you wear a small piece of rubber on your wrist – imbued with “frequencies” that harmonize with your body’s natural rhythms. There are fuel additives or devices that claim to dramatically improve the fuel efficiency of your car without any downside. And of course there are endless free energy devices that “they” don’t want you do know about.

It’s easy to write all this off as “caveat emptor” – if people pay a small price for their gullibility and scientific illiteracy, that is perhaps how it should be. We can then congratulate ourselves on being less gullible and more knowledgeable. Or we may moralize about individual responsibility, touting the fact that we invested the time to learn how to protect ourselves in a world full of con artists and scams. Blaming the victims of scams gives us the illusion of control (we can protect ourselves) and serves our sense of justice (people largely deserve what they get). But is this sort of blaming the victim morally or intellectually justified?

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What do economics, biological evolution, and democracy have in common? They are all complex adaptive systems. This realization reflects one of the core strengths of a diverse intellectual background – there are meaningful commonalities underlying different systems and areas of knowledge. In fact, science and academia themselves are complex adaptive systems that benefit from diversity of knowledge and perspective. All such systems benefit from diversity, and suffer when that diversity is narrowed, possibly even fatally.

A recent collection of studies focuses on American democracy as a complex adaptive system, and explores the mathematical underpinnings of how democracies behave and change over time in response to specific variables. Some of the insights are not surprising, but the research adds mathematical rigor to these phenomena. For example, you will likely not be surprised to learn that social media echochambers (what they call “epistemic bubbles”) lead to increased polarization of political views. But how, exactly, does this happen?

What various researchers found is that when we obtain our political news from a network of like-minded people several things happen. First, the group tends to narrow over time in terms of political diversity. This happens because those who are considered “not pure enough” are ejected from the network, or leave because they feel less welcome. Further, people within the network tend to get access to less and less political news total, and the news they are exposed to is increasingly polarized. This doesn’t happen when such networks do not routinely share political news to begin with.

The core problem, therefore, seems to be the diversity of sources of information. Similar networks of people, in fact, can have a moderating effect on individual members, if the group maintains a diversity of sources of information reflecting a diversity of political opinions. Further, a healthy moderating effect is supported by individual members exploring outside the group for sources of information.

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It is not uncommon, if you do not like any particular finding of scientific research, to attack the institutions of science or even the very notion of science itself. These kinds of attacks are now common in the anti-vaccine pushback against common sense public health measures, and often from a religious or ideological perspective. It’s not surprising that the false claim that science is just philosophy has reared its head in such writings. The attack on science also tends to have at least two components. The first is a straw man about how scientists are pretending that science is a monolithic perfect and objective entity. This is then followed by the claim that, rather, science is just opinion, another form of subjective philosophy. This position is entirely wrong on both counts.

Here is one example, embedded in a long article loaded with misinformation about vaccines and the COVID pandemic. There is way too much misdirection in this article to tackle in one response, and I only want to focus on the philosophical claims. These are now common within certain religious circles, mostly innovated, at least recently, in the fight against the teaching of evolution. They have already lost this fight, philosophically, scientifically, and (perhaps most importantly) legally, but of course that does not mean they will abandon a bad argument just because its wrong.

First the straw man:

The second consequence of “following science” is that it reinforces one of modernity’s most enduring myths: that “science” is a consistent, compact, institutionally-guaranteed body of knowledge without interest or agenda. What this myth conceals is the actual operation of the sciences—multiple, messy, contingent, and tentative as they necessarily are.

The myth is itself a myth. It exists almost nowhere except in the minds of science deniers and those with an anti-science agenda. Elsewhere the author admits:

As a lay person, unqualified to judge the technical issues, I have concluded only that there might be a legitimate question here, and one that must, necessarily, remain open until time and experience can settle it.

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In 2017 astronomers spotted a very unusual object approaching Earth. What was most unusual about it was that it was on a trajectory that would take it out of the solar system. Given its path it could only have come from outside the solar system – our first ever discovered extrasolar visitor, named Oumuamua. For an extrasolar object, it came improbably close to the Earth and the Sun, which gave us a great opportunity to take a close look at it. And then, as it passed by the sun and headed out of the solar system it became even more unusual. First, we could see that it was an very long and flat object, not typical for a comet or asteroid. Second it accelerated as it moved away from the sun, like a comet would from sublimation of ice into gas acting like a rocket. But we could not see a comet-like tail, and the albedo was off. Curiouser and curiouser.

This lead some to speculate wildly that Oumuamua may be an alien artifact, most famously Avi Loeb, a Harvard scientist who has now even published a book – Extraterrestrial: The First Signs of Intelligent Life Beyond Earth. This is a clear case of the “aliens of the gap” fallacy – any astronomical phenomenon we do not currently fully understand must be evidence of alien technology. Of course, all natural explanation must first be excluded. But even then, we don’t have aliens, we have an unknown phenomenon that needs further exploration.

Oumuamua is now yet another great case in point. Two Arizona State University astrophysicists, Steven Desch and Alan Jackson, have come up with a plausible explanation for Oumuamua’s funky properties. Perhaps, they hypothesized, our attempts so far to explain the object’s behavior and properties failed because we were making false assumptions about what kind of ice it might contain. We assumed it would have a profile of ice similar to the comets we know. But what if the ice is made of something else, because Oumuamua is not a typical comet. When they looked at the properties of nitrogen gas – bingo. This would nicely fit the data, including the combination of the rate of acceleration from ice sublimation near the sun and the low albedo – not as much reflective ice would have been necessary to cause the acceleration.

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I interviewed philosopher Philip Goff for the SGU (the show will air tomorrow with an edited version, and the full 1 hour discussion will be available for SGU members) about the multiverse and the fine-tuning problem. I was hoping by the end of the discussion one of us would have been convinced the other was correct (and I don’t care which, I just want to be confident that I understand this problem). In the end, we did not resolve our difference, but we did really clarify the issues well. This is a good exercise in logic, and also demonstrates how difficult it can be to deal with some statistical issues. I still admit I could be wrong here, I just don’t understand why. But here is the follow up.

First – here is Philip writing about our conversation and why he thinks he is still correct. In this post I will summarize where I think the discussion is and why I am still not convinced.

Here are the points of common ground (approved by Philip):

1 – The probability of our universe existing is unaffected by the presence or absence of other universes. To think otherwise is the inverse gambler’s fallacy.

2 – The probability that some universe capable of evolving complex life exists (assuming the premises of the fine-tuning problem) is higher if there are multiple universes than if there is only one universe.

3 – The key to the question of inferring a multiverse from the observation of our universe (again, assuming the fine-tuning problem and that there is no other solution) is therefore asking the right question – do we consider the probability of our universe existing or of some universe existing?

4 – There is a selection effect in that only a universe capable of evolving sentience would be observed (assuming no external observer).

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A couple weeks ago I wrote about the logical implications of the multiverse as a potential solution to the so-called fine-tuning problem. I was responding to a paper discussed by a philosopher  (Goff) claiming that the multiverse hypothesis is not a valid argument but rather based on a logical fallacy, the inverse gambler’s fallacy. I won’t repeat the entire discussion here, just read the original article. I am writing this follow up because the original article garnered a great deal of discussion. I also presented the issue on the SGU, triggering a flood of e-mail responses. Clearly I need to take another bite at this apple.

I do think the discussions have clarified my thinking, although they have not changed my position. I am still willing to change – statistics can be very counterintuitive and can hinge on seemingly unimportant details. The Monty Hall problem is a classic example, which some call a “statistical illusion”. One where I was tripped up previously deals with gambling, this time the regular gambler’s fallacy. A number of sources will claim that casinos win largely because players go bust, and end their betting as a loser, but the house never busts. So there is an “absorption wall” at one end, but not the other. Players can keep playing if they win, long enough to lose again in some cases, but have to stop if they lose too much. While this seems to make sense, it is wrong. The house wins entirely because the odds are in their favor, and the loser absorption wall has no effect on this outcome. This is because players are just as likely to win or lose after they go bust, so going bust does not prevent them from winning more than it prevents them from losing even more.

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