There are numerous in-built cognitive biases that make us bad at probabilistic reasoning in unfamiliar cases (Wikipedia’s growing list of cognitive biases includes dozens of examples of frequency or probability errors we are prone to).

There are even scientific studies of why professionals make the kinds of mistakes you are talking about (e.g. ignoring the effect of base rate on false negative and false positive rates in medical testing). Here is a summary.

The short answer is: our brain was not intelligently designed. It’s an ad hoc kluge. So it evolved a variety of disparate and contradictory heuristics that are “okay” for the use cases we evolved to tackle, but not mathematically precise, not even conceptually.

One of these errors is that we are impelled by our intuition to look for evidence supporting a belief, when in fact that is almost useless, we need to look for evidence refuting our belief, because our degree of belief should match the degree to which we tried and failed to refute it, not the degree to which we found evidence for it.

Another is that we overdetect agency. This includes seeing coincidences as agentive rather than just coincidences. Rare things can’t just “happen” is okay as a heuristic, but it has a failure rate, because the world is large, so rare things will just “happen,” just less often (see Everything You Need to Know about Coincidences).

Put these two together, and we intuitively try to make evidence fit a hypothesis, rather than test alternative hypotheses. This was the counter-intuitive finding that defined the discovery of the scientific method: comparing hypotheses is more important than “proving” them (and thus the fine tuning argument hides the prior probability question altogether by not comparing the priors for the alternatives, e.g. how lucky do we have to be to have gotten a god, much less a universe?), and falsification tests are thus essential to reliable knowledge acquisition. This is not how people inherently evolved to think. It’s a difficult skill that has to be learned, and even when learned, is hard to remember to apply to everything, because we keep falling back into our evolved heuristics instead (see The Argument from Reason).

Racism and sexism and other bigotries and stereotypes, even conspiracy theories, derive from the same errors.

Coming back to this post again after watching a video of yours and you made an excellent point about how what matters is the relative probability (i.e. how often an event occurs because of hypothesis 1 vs. hypothesis 2), not the absolute probability (how often the event occurs)

Do you have any idea or hypothesis behind why this seems so counter-intuitive at first? For example, I’ve noticed that a lot of people point to the improbability of fine tuning as an example to highlight that god may exist, but this is essentially focusing on 2.) not 1.), so this “mistake” seems to be widespread

So how would you then justify assigning a low probability to “aliens having visited earth at all in mankind’s history.” It seems obvious that it should be low, it how low?

You just contradicted yourself, take note. You question it having a “low probability” then admit it has a “low probability” and change the question to how low it is. These are not the same things. So you have to take care to correctly formulate your question. If the question is not why it’s low, but how low we should say it is, then ask that. As that was your reformulated question, I’ll assume that’s the one you actually meant to ask.

The raw observational expected rate of alien visitation is governed by Laplace’s Rule. Millions of days without the observation entails odds against of millions to one. And certainly it could be far lower depending on how you demarcate the measure. But dickering over whether it’s billions or millions to one against seems a fruitless enterprise, and one easily canceled by simply admitting we don’t know if it’s millions or billions only that it is no higher than millions, e.g. the frequency of our being right in similar circumstances is at least millions to one if we pick millions to one and perhaps only a thousand to one if we pick billions to one, so if we want greater certainty, millions to one is what we should choose to say.

This expected frequency then goes down when information accumulates that makes it even less likely than raw observational frequencies predict, e.g. interstellar distances, their motivations to produce what we observe rather than something more coherent and sensible, etc., all compound the probability by making the frequency of these things as determined from physics and observation within the raw frequency even lower than the raw frequency itself. So we can safely lower the millions to one to trillions to one (because the expected frequency of these other things is itself millions to one, and a million times a million is a trillion) and remain at the original high certainty we started with.

The result will always be fuzzy because our knowledge is fuzzy and therefore the math will reflect and measure that very fuzziness. So we can say “trillions to one against” with a high confidence (there being a high frequency of that inference model being right) and we can say “quadrillions to one against” with a lower confidence (because the frequency, of stretching our certainty that far on existing data going wrong for us, is going to be higher).

I mistakenly thought the app was broken, but it isn’t. What I need to know again is rather, what Odds are you entering, not percentages. The calculator doesn’t use percentages. It uses odds.

For example, you can do it all by hand. Odds Form is easiest, rather than percentages, which is why the calculator is built that way. Basic formula is Final Odds (on Historicity) = Prior Odds x Likelihood Ratio. Prior Odds for you on the low end will be 1/10; high end, 99/1. For “Brother of the Lord” you then have to ask: how much more or less likely is that piece of evidence on historicity than on non-historicity, and enter the resulting odds.

For instance, in OHJ I put odds on this on the low end of 1/2, meaning this evidence is twice as likely on nonhistoricity than on historicity (given the peculiarities I note that are usually overlooked); but on the high end I put 2/1, meaning this evidence is twice as likely if Jesus existed than if he didn’t (and is therefore evidence for historicity), again for the reasons I articulate in the text.

So when you say the probability of the Brothers of the Lord data is 95-99%, what do you mean? If that’s the probability of that data on historicity? Or on nonhistoricity? The odds will be the ratio. So if you think that evidence is more likely on historicity (and thus is evidence for historicity), you might enter 99/95, but that would mean it is extremely weak evidence, making almost no difference to the question. More likely you want to say something like 3/1 or 2/1 or 10/1 or something (though whatever you choose, you have to be able to defend why you think that and not something else). On the high end. And on the low end maybe 1/1 or 2/1 or even 1/2 or 1/5 or whatever (ditto).

The calculator will give you results as percentages rather than final odds (it does the conversion for you). But if you do it by hand, you will get odds (converting that then to percentages is a task). So if you set the low end at 1/10 prior and 1/2 Brothers, your final odds will be 1/20, or 20 to 1 odds against historicity. Or if you set the low end at 1/10 prior and 2/1 Brothers, your final odds will be 2/10 = 1/5, or 5 to 1 odds against historicity. And if you set the high end at 99/1 prior and the high end for Brothers at 2/1, your final odds will be 198/1, or almost 200 to 1 odds in favor of Jesus existing.

Etc.

First, the Bayesian Calculator in CHRESTUS is Odds Form, so I’m not sure you are inputting correctly. When you say here “10%” as the prior for historicity, do you mean you entered odds of historicity of “1 in 10”? And when you say “99%,” that you entered “99 to 1”?

Second, when you say “Evidence 1: Brother of the Lord” etc. do you mean on historicity or on non-historicity? You have to enter two sets of values, one set of “best” and “worst” for each. I now just looked in the app, and its missing a whole section (the second one, i.e. the best and worst odds on non-historicity section, necessary for the calculator to work). So something is broken. I’ll get the tech on it ASAP. We’ll need to find the problem, fix the problem, then run updates on both platforms; all that can take a few weeks, alas.

Wait, no, ignore that second point. The app is working fine. It just requires Odds Form entries. See my comment on your second query.

Another round, this time really trying to make the strongest case, leaving out things like the silence of Paul/epistles:

Priors: worst 50% best 99%

Brother of the Lord
worst 95% best 99%

Mission:
worst 95% best 99%

Tacitus:
worst 80% best 95%

Overall – worst 26% best 48%

Wow, it’s really hard to get over 50%!

Can anyone who understands Bayesian reasoning explain why this happens?

Am I correctly using the Bayesian calculator on CHRESTUS?

Here’s my inputs; what I think are the strongest bits of evidence FOR Jesus.

Prior probabilities that Jesus existed:
worst case 10% best case 99%

Evidence 1: Brother of the Lord.
Worst case 95% best case 99%

(I wasn’t sure how to integrate my two assumptions here. I think it’s about 95% likely that Paul meant a fraternal brother, but also 5% likely that the Gal 2 passage is an interpolation.)

Evidence 2: Tacitus – which makes it into Dawkins’s new book as the best evidence FOR.

Worst case 20% best case 80%

(Considering possible interpolation vs Christians who knew the truth telling Tacitus that Jesus was historical)

Evidence 3: Silence of Paul/Epistles/Church fathers

Worst case 5% best case 50%

Why so low on both sides?
It’s not just Paul who seems to know little to nothing about Earthly Jesus. Even Irenaeus reports hearing Polycarp talking about seeing the Lord in an oddly detached manner:
“I can speak even of the place in which the blessed Polycarp sat and disputed, how he came in and went out, the character of his life, the appearance of his body, the discourses which he made to people, how he reported his intercourse with John and with the others who had seen the Lord, how he remembered their words, and what were the things concerning the Lord which he had heard from them, and about their miracles, and about their teaching, and how Polycarp had received them from the eyewitnesses of the word of life, and reported all things in agreement with the Scriptures.”

‘Seen the Lord’ is followed by stories only of THEIR miracles and THEIR teaching, but nothing about the miracles and teachings of Jesus. Odd!

The next 2 pieces are included because I asked the Prof of the History of Christianity at Oxford what he thought was the best evidence FOR historicity.

Evidence 4: The Christian Mission

Would there have been a Christian mission without a physical Jesus?

Worst case 33% Best case 95%

The worst case is based on the fact that if Jesus was a celestial being that makes THREE religions founded by angels, so Christianity would have a 1/3 chance of being one. (is this circular? It feels like maybe…)

I’m not sure what I’m doing with the best case number. I guess that reflects that angel-inspired missions don’t seem to be much barrier to a religion.

Evidence 4: Paul disagrees with Jesus about divorce.

My professor friend reckons Paul’s disagreement corroborates the teaching re divorce (NONE!) that is related in Matthew, which is nowhere in Scriptures, so would be new and therefore most likely from a real person.

Worst case 80% Best case 99%

I tried to make this one heavily in favour.

According to the calculator on CHRESTUS:

Overall: Worst case 0% Best case 27%

That’s still pretty low…I was surprised.

Could you please let me know if I have done something wrong?

Thanks!

It isn’t relevant. They can either accept the conclusions here argued and thus renounce what they previously argued, or reject them and be a Doofus.

So if you want to know which now it is, and for some reason still want to know, you should ask them.

Their Doofus statements I lift as examples—but don’t credit to them, since I am making a generic and not a personal argument—appeared on Facebook principally and are scattered and buried in complex threads in numerous places. It isn’t even worth your bother digging through all that. It’s easier to just ask them point blank: what do they think of the positions here argued and why. Then you’ll know straightaway whether they are still a Doofus or not.

In short, this is advice on how to detect a Doofus is for you, the reader. Not for them. They had their chance to learn all this already. I cannot tell you whether they learned that lesson by now.

I noticed a couple of comments in this article that mention Loftus and Miller, but unfortunately they don’t supply very much context and I wasn’t around during the time of the disagreement(s), so I can’t seem to figure out what they might have said. (E.g. I can’t find any quotes or links to their statements/articles. The one quote of the word “conceding” is again in reference to the “Not Be a Doofus” article, but I couldn’t find “conceding” at that article either.)

So, I’m just wondering if you could clarify or reference what the context of Loftus’ (and Miller’s I suppose 🙂 ) statements/arguments/articles/whatevers were? Maybe a quote, link, or even just an article title and/or date?

Oh, and in case reference to them was accidentally polished out of the “Doofus” article, I thought you might want to know about that.

It’s curious. A while back (several years now) I recall Loftus starting to take probability seriously, so I was kinda surprised to read that he seems to have thrown Bayes overboard. Would be interesting for me to get some perspective on how/where he went off track.

Cheers!