My talk from about a month ago at MIT has been posted online and is available for all the watch. The audio quality is very good, but the video isn’t as great, so I really hope you like my voice! The Q&A is also captured, and it had many good questions for an audience sized I was happy with.
If you enjoyed that talk, don’t forget I have a book on the subject 😉
When someone mentions Galileo, one of the first things to come to mind is his fight with the Catholic Church about the motions of the Earth and the centrality of the Sun. The Galileo Affair has been one of the keystones on those arguing that science and religion tend to (or naturally) come into conflict. Many historians have rightly contextualized the events, pointing out the political and personal levels that brought the great Italian scientist before the Inquisition and placed under house arrest for promoting the theories of Copernicus. Also a big part of the contextualization has been to show how Galileo was a devout man, a Catholic, and had no wish to fight religion but if anything better understand it and the Bible.
However, a recent biography by historian David Wootton, Galileo: Watcher of the Skies, has an intriguing argument to change this stance that has been a consensus position for centuries. Wootton notes that plenty of less than pious figures in this time would display affirmations of belief and the necessary genuflections, but privately they could be skeptical of various dogmas. There were obvious social repercussions to publicly speaking against the Mother Church or the Christian faith more broadly. The example of Giordano Bruno is an obvious case of what happens when one publicly denies the divinity of Christ. So there is some degree that Wootton has to make his position an argument from silence: a lack of piety or mention of religious matters in the voluminous surviving writings of Galileo. On its own, that may be curious but hardly compelling.
However, Wootton has a particular avenue for arguing his new position. Continue reading
The holidays are approaching fast, and the first snows are coming over the United States. The ever-expanding day of Christmas will truly be here soon. And all around the world, both preachers and even some scientists will be talking about a perennial subject: the Star of Bethlehem and what it could have been. Since the 1930s, planetaria the globe over have had presentations of what planet or exploding star could have been the famed light that brought wise men from the East to a lowly crib in a tiny town in Judea.
But can science really explain this celebrated celestial event? Is it something actually miraculous or a literary artifice? How can someone tell? Moreover, why is this a subject that draws both astronomers and theologians to ask these sorts of questions?
All that and more is considered in The Star of Bethlehem: A Skeptical View. Not only covering all of the major and minor hypotheses to explain the meaning and motions of the Star, including the extraterrestrial, it investigates what was possibly on the mind of the ancient author of the Gospel story and what is in mind for many others that continue to pursue this subject. The Star of Bethlehem was also the subject of a major conference at the University of Groningen, and the major conclusions of SoB: ASV find support by experts in many fields.
So this holiday, learn about fascinating astronomical science, history, religion, cultures from the Romans to the Persians to the ancient Jews, and also understand a bit more about how science and religion interact through history and today.
Author: Dr. Aaron Adair is a professor of physics at Merrimack College, where he both teaches and conducts education research, along with continuing investigations of ancient religions and the heavens. He received his PhD from Ohio State University and worked as a planetarium show presenter at Michigan State University. He has previously published on the subject of the Star in Zygon and was an invited speaker to the University of Groningen’s conference on the Star.
Praise for SoB: ASV:
“Well researched, scientifically reasoned, elegantly concise, this book will long be required reading on the ‘Star of Bethlehem’. Full of fascinating historical facts, and better informed and more careful than any other book on the subject, this should be on the shelf of everyone interested in that legendary celestial event.” Richard Carrier, Ph.D., author of Proving History: Bayes’s Theorem and the Quest for the Historical Jesus.
“A fascinating and readable feat of hardcore historical legwork and keen scientific analysis.” David Fitzgerald, author of The Complete Heretic’s Guide to Western Religion: The Mormons.
“…tightly-argued, well-reasoned…. Adair masterfully demonstrates why every effort to rationalize the Star thus far has failed…. A concise and rigorous must-read for anyone interested in religion, history, and modern efforts to understand the past.” Jason Colavito, author of The Cult of Alien Gods.
Dr. Aaron Adair, Star of Bethlehem Press Kit
I am about to fly off for my talk and conference about the Star of Bethlehem, but before that I have received a review copy of a new book on something quite biblical as well. Those that have been following what is often labeled “New Atheism” know it’s biggest names: Dawkins, Harris, & Hitchens. Dan Dennett is often included to create the Four Horsemen of the Atheist Apocalypse, but that analogy is weak given the untimely passing of Hitchens.
Nonetheless, other names in the growing atheism movement have tried to carry on the mantle, especially those with greater specialization in areas that these authors may not be well-versed in. Be that professional moral philosophy, theological history, political policy and religious influence, and so on. Dawkins is often criticized about his lack of philosophical prowess in his The God Delusion, and similar things could be said, among other things, about Harris and Hitchens. But when those with expertise come in, the case that these authors have made becomes overwhelmingly rational.
Several months ago I was asked to participate on a conference about the Star of Bethlehem at the University of Groningen. But before I get there, I will be stopping in Cologne (Köln) in Germany to give a lecture for the Skeptics in the Pub group there. My lecture will be in English, if for no other reason than my German is nothing to listen to (one can say ein Bier, bitte only so many times). Besides the links above see the Post by The Star of Bethlehem: A Skeptical View book page.
Connecting to my previous post on the need to be well-read-up in order to do critical thinking, I am going to be doing a series of book reviews.
Here I want to discuss a few books published recently and which I have read in the last few months that are focused on math. They are not books on how to do math (i.e., textbooks), but instead they discuss mathematical concepts and their relations to ways of thinking about the world. Sometimes they touch on theological issues, sometimes a lot. But all three are good reads.
Dot, Dot, Dot: Infinity Plus God Equals Folly 
Infinity is a really, really weird concept. It takes any intuitions we have and makes us say apparently silly things. But there are rigorous ways of dealing with infinity, but there are also limitations, even for the most brilliant mathematicians.
One of the points is that you never really reach infinity. No matter where you start on a number line or how long you count forward, you never even get closer to infinity. This means that it is not possible to use something finite to create an infinite set. That is, you cannot construct infinity from finite sets and operations. Hence we get lazy when writing a set that is supposed to go on forever with … (hence the title of the book). And yet we can talk about infinite sets. In fact, we can talk about different sized infinities. If that didn’t make sense to you, then you are getting the point about how weird infinity is.
In this book, mathematician James Lindsay shows many important points about how infinity is used and understood by mathematicians and how the terminology is poorly used in other contexts, especially when applied to God. In many ways the book is focused on problems with the infinite god concept, but what I found as one of the more interesting threads running through the book is the problem with mathematical Platonism. What Lindsay shows very well is how much math is a human project. We chose the various axioms and definitions, and those different choices can lead to all sorts of amazing conclusions. But showing how much math is a human invention, it shows that there isn’t really a “true form” of the set of all rational numbers and the like. We chose the rules. Historically, there have been arguments about whether negative numbers are really numbers, or if i is a number or not. Or even if zero is a number! Why do most people consider these objects numbers in the end? Because of what we can do with them. They are practical, even imaginary numbers (I couldn’t do the physics I learned in grad school without them).
Seeing the human side of math (rather than the human side of certain mathematicians) was excellent, especially when it comes to the sorts of concepts that bugger human comprehension. I value the volume for doing more than just showing what makes an infinite God incoherent, but it shows how much math is truly a human adventure and not simply that boring stuff forces on you in school.
The Drunkard’s Walk: How Randomness Rules our Lives 
Infinity blows our intuitions away because of how far it is beyond our experience, but we live in a world where apparently random things happen. Nonetheless, we get confused and confounded by probabilities all the time. Here physicist Leonard Mlodinow shows many aspects of the historical threads that touch on how we developed and understand probability. There is plenty of talk about gambling with games of chance, but that’s largely because a lot of probability theory was first developed to understand just that. Sometimes we joke that lotteries are a tax on those that are bad at math, but really understanding math (especially statistics) belies that argument (a really good anecdote for that is talked about in the next book below).
When it comes to thinking about things in the political arena, this book is great because of the focus it provides on judicial cases. There are plenty of ways that probabilities can be abused, where meager evidence is made to look extraordinary by making sins of probability calculation. In particular, not all probabilities are independent. Consider the following numbers that I have made up: 1/3 of men have a mustache, 1/3 of men have a beard. What is the probability of a man having a mustache and a beard? If you multiple those two fractions together, you get 1/9. However, these are hardly independent probabilities; if you have a mustache, you are more likely than average to have a beard as well. Heck, with current fashion trends as I have noticed it may be more rare to have a mustache without a beard–perhaps it makes people think porn-stache. Why would this sort of consideration be important? Well, suppose you have an eyewitness say a suspect has a mustache and beard. If you nab a person fitting that description he won’t be nearly as likely a suspect as you think; it is not 1 in 9. Moreover, considering that in a given city there could be a million people, then the chances of nabbing the right suspect by using these criteria are really bad. And yet a case like this (with some additional details) was used at first to convict a couple of a significant crime.
It’s number games like this that make it in fact difficult to know what are the real numbers if you are on a jury. You can be told that a DNA sample matching a random person is less than one in a million, and so you think a positive match in a court case means that person’s blood being at the scene of the crime is really high (more than 99.9999%). But a more relevant probability is the lab making a mistake, like mixing up which sample to test. That is much more probable. Still not likely (less than 1 in a 100), but not as super-solid as you think.
So if you are deciding a person’s life, an idea of what constitutes good evidence and what reasonable doubt would mean should be well-shaped. Even if you don’t have numbers, thinking about things in terms of less than, more than, equal, much less than, etc., is very important to making such decisions. And for a lot of other things. We live in a world that is governed by the unpredictable and probabilistic, and not just at the quantum level. Books likes this from Mlodinow help tune our probability intuitions. Also, Mlodinow is a great and humorous writer.
How Not to Be Wrong: The Power of Mathematical Thinking 
The title is ambitious, no? But there is truth in how powerful thinking mathematically can be. A refrain of this book is that math is the extension of common sense. Instead of thinking of math as a bunch of algorithms to memorize and steps to get to the “right” answer, what math is supposed to do is model ones thinking. And if you model your thinking clearly and consistently, then you can more confidently achieve accurate results.
More importantly, though, it to see if you project your reasoning does it lead to nonsense? In the first section of this book by mathematician Jordan Ellenberg there is a lot of emphasis on how not all curves are lines. By that, he means that not all trends are so straight-forward as have more, get more. For example, there is the concept of the Laffer Curve. This is about what should the tax rate be if the government wants to maximize its income. Obviously if the tax rate is zero, then the government will take in nothing. If you raise the tax rate, then you can bring in more money. But does that mean a higher rate rate always brings in more? If you made the tax rate 100%, then no one would have an incentive to work since all of their money is taken from them. Might as well not work at all, or find ways of hiding it. So again, the government will take in no income. Thus, the optimum tax rate for government income must be between 0 and 100%. Where that is is an empirical question (and if that is a worthy goal is another question), but clearly increases the tax rate is not going to necessarily mean more income. And of course, if you absurdly make the tax rate greater than 100% then no way will anyone work since you will owe more than you have no matter how much you work. In other arenas, it is clear that following a linear model of the relationship between things is not reasonable and even ridiculous.
Now, there is some overlap between this book at the previous two above, but Ellenberg’s volume covers a lot of areas in math and its relation to arguments and concepts in the real world, sometimes with surprising results. Would you guess that using a finite geometry you can figure out what are the best lottery tickets to pick are, given certain lottery rules for winning? A group buying up tickets in Massachusetts did, and they pulled in some serious dough.
One of the sections of the book I found most interesting is how our measure of public opinion can give contradictory results. Suppose on third of voters want to not cut spending, one third want to cut spending and cut it from defense, and one third want to cut spending and cut it from entitlements. If a politician doesn’t cut spending, 2/3rds will be unhappy; if a politician cuts spending in defense, 2/3rds will be unhappy; and if a polotician cuts spending on entitlements, 2/3rds will be happy. In other words, no course of action is the “right” one, as no matter what a majority will be against you. Now, you could instead rank priorities. For example, the first person may say their first choice is to no cut spending at all, but if spending had to be cut it should first come from defense before coming from entitlements. Another person can also rank their choices as they see fit. If you say the first choice is given 2 points, the second choice 1 point, and the third choice 0, then you can add up the choices of everyone and find where the ranked preferences lead. This method, called the Borda count, is similar to how your GPA is calculated (A = 4, E/F = 0), and it is used in some elections around the world. With it, you can get a different result than you would with the majority vote system. You could imagine how it would have affected the 2000 US Presidential elections; almost all of the votes for Ralph Nader would have gone to Gore and then Gore would have wold Florida (and thus the presidency), so a Borda count could have changes the history of the first decade of the 20th century (how much, I don’t know). But there exist other ways of potentially running a voting system, and they all have points to consider. If you consider all the options, you realize that it is possible to get different results with different polling/voting methods. So it’s almost like there isn’t really public consensus on issues, unless there is a significant majority.
I won’t get into everything Ellenberg goes into, and I want to leave his stories of the various mathematicians and statisticians as he tells them. But the key point is that you can see how you can build your own mathematical models of what you think is correct or fair and reasonable and see that it implies. Don’t consider math just stuff with calculators but a way of thinking. It won’t guarantee you are right, but it’s a far more useful and enlightening way to figure out the world. The real world, not just that of abstractions.
I am in the process of finishing up my PhD thesis in physics education (hoping to defend it this August), but I have been continuing to search the literature for insights or contrary results to what I had come to expect. That makes for plenty of work, but it is rewarding, adding information to the mind as well as analyzing it into a better understanding that was there before.
So in the process of reading blogs I discovered a new book that touched upon some of the very things I had researched and put into my masters thesis paper, but perhaps not as I understood it. That book was Seven Myths about Education (UKamz) by Daisy Christodoulou, which only came out a couple of weeks ago (as an eBook). Christodoulou is a teacher from England who was in the classroom for three years before becoming a researcher into educational pedagogy. Her book, along with the non-profit she is involved with on how to teach, are the product of that research. Focusing on cognitive research, her own experiences, and the methods expounded upon by other education researchers in both the United States and the United Kingdom, she has argued that there are these seven (in particular) ideas that are inter-connected yet detrimental to how to teach effectively.
The structure of the book is to lay out what she considers a myth, its theoretical or historical backing, its use in modern (usually English) teaching, and why it is a myth. Her list of seven is:
1 – Facts prevent understanding
2 – Teacher-led instruction is passive
3 – The 21st century fundamentally changes everything
4 – You can always just look it up
5 – We should teach transferable skills
6 – Projects and activities are the best way to learn
7 – Teaching knowledge is indoctrination
The titles for each chapter come from these myths, so let’s unpack them. “Facts prevent understanding” is a rather condensed way of saying that the method of presenting information for students to memorize is not effective, and instead we need to teach how to learn. “Teacher-led instruction is passive” is about how if a teacher says it, then it must be the case that students are just sitting there; students need to lead the instruction. “21st century education” is about how the knowledge that worked in the old days is not terribly relevant today and we can Google information when needed, which leads into “you can always just look it up.” Teach transferable skills” is about focusing on making students have skills that can work in unique, not-before-seen contexts, apparently without the content knowledge. “Project and activities are the best way to learn” is about inquiry-based activities and crafts that are, again, primarily student-run with minimal guidance from the teacher. Lastly, “teaching knowledge is indoctrination” is about post-modern critiques of knowledge and social order via the indoctrination of facts.
In each chapter, Christodoulou is able to point to good psychological or cognitive science that illustrates what the problems each of these myths have. In particular, Christodoulou brings up the issue of working memory vs. long-term memory. The primary issue is that when you need or interpret something, you already need to have a lot of content knowledge to work with. If too many things are unknown, your working memory is overwhelmed (you can’t consciously think about too many things at once) and it’s nearly impossible to understand or analyze. One poignant example presented concerned reading: when looking at students who are given various reading strategies for dealing with an unknown document or piece of text, pupils who had a wide knowledge base (and not necessarily very knowledgeable about anything in particular) did better even if they did not have such reading strategies. That is, a good knowledge base was more important than reading skills.
Christodoulou also brings up the work of E. D. Hirsh and his work on core knowledge and cultural literacy, as well as the method of direct instruction by Siegfried Engelmann; most of the focus is on Hirsh, perhaps largely because his work was in English and reading, and Christodoulou also seems to have this as her background. Key though are the results that showed that the methods described by Hirsh and Engelmann were effective, and more-so that the minimal-guidance methods that teachers were use (Myths 2, 6 esp.)
So far, the book has gotten some considerable praise by one education researcher in the HuffPo, and Harvard cognitive scientist Steven Pinker also seems to approve of it (at least he tweeted the HuffPo piece). In other avenues there has been a negative response, sometimes even mean-spirited, so everyone is not glowing because of the book. However, there is a good case made here about how not to teach, but there are issues that make it difficult to give a full endorsement. There is some need for supplementation and contextualization to provide a fuller picture and a better way to think about teaching pedagogy. This is needed in part because the book attacks ways of teaching that, though not uncommon, are also an extreme interpretation of educational theory, which itself often supports itself by attacking extreme forms of “Victorian” or “Prussian” education; with the extremes fighting, you end up getting a cycle of what is “in” for teaching, and that cycle seems to be about 40 years long. Progress can be made, but the full spectrum must be before us. And I pretty much have to think that because I find my research and work to be somewhere in the middle of things. Continue reading
I have been getting deep into the writing hole now with a goodly number of projects. I have begun going through the outline and intro of my PhD thesis with my adviser which we hope to have done by the summer. With a little luck, I’ll be a doctor of something before the next academic year starts. I am also working on a book chapter in another project. I am also having the fun of getting to go through the manuscript of my Star of Bethlehem book with my editor. Worst part of that: seeing all the mistakes you make even though you went through it 100 times before sending it.
Yeah, writing can be one of the most humbling activities you can do. But there is the reward of finally getting something out there in print. I am glad that I’m not self-publishing, not having another mind make sure I’m not fooling myself in thinking what I said makes sense. Self-publishing definitely has its place, but at least for me, I would be afraid of publicizing my inability to use the English language before it’s too late. Heck, I’m surprised that blogging hasn’t already done that, but from what I can tell there is leniency on the Internet for typos… except when it comes to your enemies.
Well, back to work. Haven’t perfected a computer code that will write for me yet.
In the publishing world, the news is out that Fox News pundit Bill O’Reilly is coming out with a new book. With the previous sales figures from his books about killing Abraham Lincoln and John F. Kennedy, up next is a book, written with Martin Dugard, is Killing Jesus. At this rate, by the end of the decade there will not be any famous historical figures that O’Reilly has not killed.
Besides the humor of how the layout suggests that Bill has been a time-traveling psychopath, I am getting a kick out of this because of the results from his previous books. For example, the book Killing Lincoln was so full of errors that most Lincoln-related places were unwilling to sell it, including Ford’s Theater where the president was killed. There have also been issues noted with Killing Kennedy, though I haven’t seen the backlash of fact-checkers as severely as in the first case.
So now that O’Reilly and Dugard are about to publish on Jesus, we may expect things to be problematic. For one thing, I really doubt that these two are going to be taking a critical look at the sources involved. There were lots of errors in the Lincoln book because they relied on poor secondary sources, but with the Gospels there are only poor secondary sources. I would be at least curious what sorts of modern research they will rely on. Will they be using the lunar eclipse of 33 CE in their work (which I showed to be flawed), for example? Will there be references to Raymond Brown, John Dominic Crossan, Rudolf Bultmann, and other critical voices, or is this going to be treating all the Gospels as, well, gospel truth?
Looks like we’ll see in September, which is also about the time by book on the Star of Bethlehem will come out. Perhaps O’Reilly will debate me then as he did Jon Stewart? One can only hope.
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Fleeing Nergal, Seeking Stars 