{"id":356313,"date":"2024-05-09T05:00:00","date_gmt":"2024-05-09T12:00:00","guid":{"rendered":"https:\/\/reasons.org\/?p=356313"},"modified":"2024-05-09T05:00:00","modified_gmt":"2024-05-09T12:00:00","slug":"bayes-babbage-and-belief-in-the-resurrection","status":"publish","type":"post","link":"https:\/\/reasons.org\/jesus\/death-resurrection\/bayes-babbage-and-belief-in-the-resurrection","title":{"rendered":"Bayes, Babbage, and Belief in the Resurrection"},"content":{"rendered":"\n

Bayesian statistics, first conceived by the Reverend Thomas Bayes in the 1740s, is at least partly responsible for several significant historical achievements. Bayesian statistics helped Alan Turing crack the Enigma cipher used by the Germans in World War II, aided researchers at Harvard in identifying the authors of the Federalist Papers, allowed the US Navy to locate Soviet submarines, and played a key role in the rise of artificial intelligence. Yet Bayes never envisioned the many applications of his idea. In fact, Bayes most likely came up with the theory named after him in order to disprove philosopher and skeptic David Hume\u2019s argument against the resurrection.<\/p>\n\n\n\n

This explanation seems likely because Bayes\u2019 work, which he never published, was discovered after his death by his fellow minister and mathematician friend and colleague Richard Price. Price used Bayes\u2019 theorem to argue that the existence of multiple independent witnesses to a miracle could overcome the improbability of the miracle happening and establish it as a fact. In this article we will take a brief tour of Bayes\u2019 theorem, explore how the inventor of the analytical engine (one of the first computers!) used Bayesian thinking to counter Hume\u2019s argument against the resurrection, and consider the role Bayesian statistics can play in Christian apologetics today.<\/p>\n\n\n\n

What Is Bayes\u2019 Theorem?<\/strong>
Bayesian statistics is often used to update prior beliefs after observing new data. How well do our existing beliefs explain the relevant data and do we need to update our beliefs? As an example, let\u2019s consider the likelihood that Thomas Bayes wrote his essay on probability to refute David Hume, given that Richard Price used Bayes\u2019 theorem for that very purpose. In this case, our \u201cprior\u201d belief is that Bayes wrote his essay to refute Hume, which we\u2019ll assign a probability of 60%. Why? If 60% seems a bit arbitrary, that\u2019s because it is<\/em> and this fact drives a school of statisticians called frequentists crazy\u2014but keep in mind that real life often requires making decisions in the face of uncertainty. Also, Bayes was known for engaging in intellectual debate and was devout in his faith.<\/p>\n\n\n\n

Now, our data in this case is that Price, a friend of Bayes, used Bayes\u2019 theorem to refute Hume. If Bayes himself had this purpose in mind, it is even more likely that Price, given their friendship, would do so. Thus, we\u2019ll assign the probability of our data about our belief to 80%. Now the tricky part. What is the likelihood that Price would use Bayes\u2019 theorem to refute Hume even if Bayes never intended it for that purpose? This is the probability of the data\u2014whether or not our belief is true\u2014and is necessary to calculate the probability of our belief given the data (see the equation below).<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

In this case, we\u2019ll say that the probability of Price using Bayes\u2019 theorem to refute Hume\u2014 regardless of Bayes\u2019 intent\u2014is reasonably high, since Price himself was eager to engage in such debates. We\u2019ll set the probability of the data regardless of our belief at 65%. We can then calculate, based on our assumptions, the probability of our belief that Bayes wrote his essay to refute Hume.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Now, if we change our assumption and decide that we have no idea how likely Price would be to use Bayes\u2019 theorem to refute Hume on his own, the probability Bayes wrote his essay to refute Hume jumps to 96% because the denominator in our equation changes from .65 to .5, giving us (0.8 * 0.6) \/ 0.5 = 96%. The point is that Bayes\u2019 equation can give different answers depending on how sure you are that a particular observation could have occurred without the effect you are checking. For example, it\u2019s not likely that a sunny day would give you a stomach ache, but sour milk definitely could. So, this is how you would calculate the probability of a stomach ache given a sunny day:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

I\u2019ll leave it to you to calculate this on your own. If you get stuck, just ask ChatGPT or Gemini and they can help you out. In real life there are cases where we can use historical data to know these probabilities more precisely, such as figuring out if a positive cancer test really means you have cancer, which is a very practical application of Bayesian statistics.<\/p>\n\n\n\n

Babbage\u2019s Refutation of Hume<\/strong>
Let us fast forward from Bayes in the 1740s to Charles Babbage, professor of mathematics at Cambridge and designer of a steam-powered programmable computer called the analytical engine, in the early 1800s. Babbage rephrased Hume\u2019s challenge to eyewitness testimony of miracles (such as the resurrection) as, \u201cThe falsehood of testimony of the miracle must be more improbable than the miracle,\u201d1<\/sup> or as an equation:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

In common vernacular, Hume would only believe claims of the miraculous if the probability that the witnesses were wrong was less than the probability of the miracle, which would be difficult if you assume miracles have a very low probability of occurring. If we assume mutually independent witnesses who are reliable 99% of the time, then the probability of N (number) such witnesses being wrong is given by the following equation:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

After crunching some numbers using Bayesian equations provided by Pierre-Simon Laplace (the scholar who came up with the mathematical equation for Bayes\u2019 theorem after rediscovering the same principle around 1774), Babbage came to the conclusion that as long as your witnesses speak truth more often than falsehood, there will always be a number of witnesses who can satisfy Hume\u2019s criteria (see Taylor\u2019s paper2<\/sup> for details). In other words, eyewitness testimony could mathematically provide reasonable evidence for a miraculous event, given certain assumptions about the eyewitnesses.<\/p>\n\n\n\n

So What?<\/strong>
Bayes\u2019 theorem does not offer \u201cproof\u201d of the miraculous, but it does help us understand how our assumptions impact our beliefs. Hume assumed the probability of the resurrection occurring was zero (weighting the scales just a tiny bit), whereas Babbage calculated it to be 5 * 10-12<\/sup>. By assigning the resurrection a nonzero probability, Babbage made it possible for eyewitness testimony (assuming certain properties of eyewitnesses) to function as reliable evidence for the resurrection (if it\u2019s zero then no amount of evidence would be sufficient). While neither of these numbers may be the \u201ccorrect\u201d number, they at least allow us to ask fun, meaningful questions, such as \u201cHow many eyewitnesses should be necessary for me to accept the resurrection as a historical event based only on the data available to me?\u201d<\/p>\n\n\n\n

Ultimately, Bayes\u2019 theorem helps us think about how prior assumptions influence our conclusions when we update our beliefs given a set of facts. Making our priors clear helps us have better apologetic conversations because we understand precisely where we are starting and, when engaging skeptics such as Hume, how to communicate in a way that may open doors for more meaningful dialogue.3<\/sup><\/p>\n\n\n\n

Endnotes <\/strong> <\/strong><\/p>\n\n\n\n

    \n
  1. Courtney K. Taylor, \u201cCharles Babbage and Mathematical Aspects of the Miraculous<\/a>,\u201d ACMS 22nd Biennial Conference Proceedings, Indiana Wesleyan University, 2019.<\/li>\n\n\n\n
  2. Taylor, \u201cBabbage and Mathematical Aspects.\u201d<\/li>\n\n\n\n
  3. For a scholarly book that considers the probability of God\u2019s existence, see Richard Swinburne, The Existence of God<\/a>, 2nd ed. (Oxford, UK: Oxford University Press, 2004).<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

    Bayesian statistics, first conceived by the Reverend Thomas Bayes in the 1740s, is at least partly responsible for several significant historical achievements. Bayesian statistics helped Alan Turing crack the Enigma cipher used by the Germans in World War II, aided researchers at Harvard in identifying the authors of the Federalist Papers, allowed the US Navy to locate Soviet submarines, and played a key role in the rise of artificial intelligence. Yet Bayes never envisioned the many applications of his idea. In fact, Bayes most likely came up with the theory named after him in order to disprove philosopher and skeptic […]<\/p>\n","protected":false},"author":588,"featured_media":356353,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_person_authors":[402419],"_kad_blocks_custom_css":"","_kad_blocks_head_custom_js":"","_kad_blocks_body_custom_js":"","_kad_blocks_footer_custom_js":"","footnotes":"","_classifai_error":"","_classifai_text_to_speech_error":"","_classifai_text_to_speech_scheduled":false},"categories":[64006,63966],"tags":[],"discipline":[],"reading-level":[64149],"class_list":["post-356313","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-death-resurrection","category-tools-tech","reading-level-advanced-deep-dive"],"acf":[],"yoast_head":"\nBayes, Babbage, and Belief in the Resurrection - Reasons to Believe<\/title>\n<meta name=\"description\" content=\"Bayesian statistics, first conceived by the Reverend Thomas Bayes in the 1740s, is at least partly responsible for several significant historical\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/reasons.org\/jesus\/death-resurrection\/bayes-babbage-and-belief-in-the-resurrection\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Bayes, Babbage, and Belief in the Resurrection\" \/>\n<meta property=\"og:description\" content=\"Bayesian statistics, first conceived by the Reverend Thomas Bayes in the 1740s, is at least partly responsible for several significant historical\" \/>\n<meta property=\"og:url\" content=\"https:\/\/reasons.org\/jesus\/death-resurrection\/bayes-babbage-and-belief-in-the-resurrection\" \/>\n<meta property=\"og:site_name\" content=\"Reasons to Believe\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/RTBOfficial\/\" \/>\n<meta property=\"article:published_time\" content=\"2024-05-09T12:00:00+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/reasons-prod.storage.googleapis.com\/wp-content\/uploads\/2024\/05\/Blog_Hero_Image-Bayes-Babbage-and-Belief-04252024.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1713\" \/>\n\t<meta property=\"og:image:height\" content=\"383\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Guest Writer\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@rtb_official\" \/>\n<meta name=\"twitter:site\" content=\"@rtb_official\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Guest Writer\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"7 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/reasons.org\\\/jesus\\\/death-resurrection\\\/bayes-babbage-and-belief-in-the-resurrection#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/reasons.org\\\/jesus\\\/death-resurrection\\\/bayes-babbage-and-belief-in-the-resurrection\"},\"author\":{\"name\":\"Guest Writer\",\"@id\":\"https:\\\/\\\/reasons.org\\\/#\\\/schema\\\/person\\\/bd0fdf7d6925b1c2bff03327f8913f94\"},\"headline\":\"Bayes, Babbage, and Belief in the Resurrection\",\"datePublished\":\"2024-05-09T12:00:00+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/reasons.org\\\/jesus\\\/death-resurrection\\\/bayes-babbage-and-belief-in-the-resurrection\"},\"wordCount\":1195,\"publisher\":{\"@id\":\"https:\\\/\\\/reasons.org\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/reasons.org\\\/jesus\\\/death-resurrection\\\/bayes-babbage-and-belief-in-the-resurrection#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/reasons-prod.storage.googleapis.com\\\/wp-content\\\/uploads\\\/2024\\\/05\\\/Blog_Hero_Image-Bayes-Babbage-and-Belief-04252024.jpg\",\"articleSection\":[\"Jesus's Death & Resurrection\",\"Human Tools and Technology\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/reasons.org\\\/jesus\\\/death-resurrection\\\/bayes-babbage-and-belief-in-the-resurrection\",\"url\":\"https:\\\/\\\/reasons.org\\\/jesus\\\/death-resurrection\\\/bayes-babbage-and-belief-in-the-resurrection\",\"name\":\"Bayes, Babbage, and Belief in the Resurrection - 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