I listened to a recent interview (Part 2) with Matthew Ferguson on the Don Johnson show, which I found pretty impressive. Matthew Ferguson has a very interesting blog that I just found, and have been enjoying reading.

However, I did find several points in the informal debate that I thought could be handled better (from my armchair, of course!). Just to note that although I think that if I were there, I might have been able to deal with some of the questions better, I also think that nearly all of the debate was handled much better than I could have done. What struck me at one point, in Part 2, was Don’s zeal for the miracles collection by Craig Keener (review of Keener’s book here). He seemed to think that because there were hundreds of thousands of miracle reports, that that was evidence for their truth. He was, however, quick to dismiss any comparison with other pseudosciences. Ferguson admits on his blog that the "debate came off as a little ambushy" on this point, because he hadn’t read this book, and clearly couldn’t respond to all of them, but I think that misses the point. I think one can address the miracle claims without being entirely dismissive (and sounding closed minded) but putting them in their proper context.

Evaluating Miracle Claims – Some Lessons from UFOs

So in Keener’s book, there is a huge collection of claims of miracles. We could find an equally large collection of UFO sightings. Now, Don and other Christians would be quick to dismiss UFO sightings as irrelevant, but I would raise the questions:

• Given a set of claims, how do we determine whether they are true?
• Are any of them true?
• Do the number of claims contribute to their truth value?

I believe that the methods we use to determine the veracity of UFO claims can be used to investigate any claims, remarkable or not, including miracle claims. To start, we clearly we can’t personally investigate every single claim, and thus cannot comment on ones we haven’t investigated except to note where it seems similar to ones that we have. I have a friend who I managed (over several years) to break of his UFO enthusiasm – he was convinced by all of these television shows claiming evidence for alien spacecraft observations and visitations. He invited me over to his house periodically to watch these shows to get my reaction. This is the process that I would use:

1. I would write down each specific claim – what was actually being claimed, and what details were there? (names of places, time, who saw what, etc…)
2. I would note any initial inconsistencies (for example, there was once where, in the interview process, the different witnesses actually described different things! this seemed to go unnoticed by the reporter)
3. I would go home, and try to find out as much about the original details of the events. It would take me probably at least an hour for each case, and some I couldn’t track down. However, many of them I could. I would read the claims again, and the skeptical accounts, and the responses to the skeptics. I would try to see what the actual data was, how it was collected, when it was reported, etc…

What I found for every case that I personally investigated was the following:

1. Most of the actual, original claims were mundane. Lights in the sky, marks on the ground, etc…. No hard evidence of anything remarkable.
2. Misinterpretation of a known object, or objects, in the sky or on the ground.
3. The reporting of the claims grew more and more remarkable. A particularly good example was the Rendelsham Forest UFO case where the initial reports were just lights, and the later reports involved spacecraft, alien code-books, etc…
4. There were serious inconsistencies between reports, or anomalous non-reports (i.e. people who should have seen something but didn’t). A good example of this was a Chicago airport sighting where a small group of people, in a localized area of the airport, saw something yet the large number of other people in the nearby areas of the airport reported nothing.

I repeat – in every single case that I personally investigated, these points were in evidence. Then I look through something like the Condon report where they go through something like 30 years of data in the height of the UFO craze and don’t come up with even a single item that is not mundane in its nature. After that, new UFO claims I see with suspicion even if I don’t check them out. If something seems straightforward to check out, I might do it, but I don’t feel it is my job to investigate every claim. If there had been even a single case which pointed to something probably remarkable, I’d have a different attitude.

Lesson: if the claims made shrink and disappear at critical and skeptical investigation, the claim is not likely to be true.

Miracles

The Catholic Church has a division to investigate miracles, and has determined that some of them are genuine. However, the Catholic Church often has significant blinders, and definitely takes a long time to adjust to obvious mistakes (Galileo anyone?).

Take, for example, this site on top 10 miracles. I’ve personally researched about 3 or 4 of these, and it is quite clear that those are definitely frauds (#1, 2, 3, and 5 I’ve checked). Yet, do we get any retraction from the Catholic Church? Do we get any hint of skepticism? None at all.

Again, I follow the same steps as above. I do not take someone else’s word, necessarily, and I don’t discount them out of hand. The miracles of Fatima are a great example. First, we have "visions" from highly impressionable children, one of whom was known to have made up fanciful stories in the recent past. These children are the only ones who "see" it, until the last vision where hundreds claimed to see the "Miracle of the Sun". The problem? The initial stories did not agree, and we only get a semi-consistent story after the various witnesses spoke with each other and to a priest collecting the reports. Check out The Real Secrets of Fatima for the details. All of the elements spoken about above can be seen – initial mundane experiences, misinterpretation of known objects (i.e. the sun, and clouds), the exaggeration of stories in later recollection, serious inconsistencies in reports and notable non-reports.

The same goes for every faith-healer I’ve read about. A little digging, and a little skepticism, and the entire enterprise come crashing down. Many times it doesn’t take much digging!

If the truth is there, then it shouldn’t retreat under investigation.

This is not a matter of being too skeptical. It is a matter of not being credulous.

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Introduction

So I got pointed to the http://www.icr.org, which if you haven’t poked around on the site, you really should. It is quite interesting (not really in a good way). However, I want to look at a particular article on the young earth, arguing from population growth rates. The relevant sentences are:

Using census records from the last 400 years and a bit of algebra, and assuming a natural logarithmic growth, eight Flood survivors 4,500 years ago produce 7 billion people almost exactly. This is powerful evidence that biblical history is accurate, and man-made evolutionary history is not.

Then they footnote the following:

The formula for logarithmic human world population growth is $P = Po e^{rt}$, where P = the current population, Po = the initial population, e = the base of natural logarithms (2.718), r = the average annual population growth rate (0.456% or 0.00456 in the calculator), and t = the time interval from Po to P.

Finally, in the middle of the article, they are incredulous of the low net birth rate in pre-agricultural human populations:

Thus, the first human couple that supposedly evolved from ape-like ancestors would have had only 6 million descendants after 2.4 million years. This requires a population growth rate of about 0.000000009-essentially zero. Virtually no growth for 2.4 million years?

So, how do we respond to this sort of analysis? One could try to simply write it off as the rantings of a person blinded, by their religious bias, to a true understanding of science.  However I prefer an alternative approach. It may be tilting at windmills, but I prefer to take a claim at face value, and see why it fails, and to ask followup questions. Since the math here is so simple, it is easy to demonstrate any errors, assumptions, etc.. and get to the bottom of it. So, someone has made a claim, I don’t agree, how do I proceed?

Did they do their arithmetic right? Yes!

The first thing I like to do is, assuming they are right in all of their numbers, do they do the calculation correctly. This eliminates a pretty obvious error that could have caused the problem. I suspected they got it right, but I wanted to make sure. The math is

$P=P_o e^{rt}$

The code is:

r=0.00456
t=4500.0
Po=8.0

print Po*exp(r*t)/1e9,"billion"


Yielding

6.52849018681 billion


The other direction is, how long ago were there only 8 people?

$\begin{array}{rcl} P(t)&=&P_o \times e^{r\cdot t} \\ \log P(t) &=& \log(P_o) + r\cdot t\\ t&=& \frac{\log(P(t))-\log(P_o)}{r} \end{array}$

or


Po=6.5e9  # current population
r=0.00456
P=8       # target population

t=(log(P)-log(Po))/r print t, “years”

resulting in


-4499.04089302 years.


Is their growth rate correct?

Here I am using data from http://www.census.gov/population/international/data/worldpop/table_population.php. It is possible (in fact likely) that the original post used a slightly different data set, but they didn’t cite it so I can’t confirm that. The conclusions will not be qualitatively different, but that would be one of the questions I’d have for the author (see below).

It is instructive to look at the data set both on a normal scale and a log scale. The key thing here is that a constant growth rate translates to a straight line on the log scale. Let’s see if this is the case (see the lower of the two plots, especially):

Linear? Not so much.

I then chose a time-frame over which to calculate the average which gave (for my data set) as close to their growth rate above – this is essentially the growth rate consistent with the Biblical chronology. In my data set that average is from 1300 to 2010, or 700 years (theirs, they claim, it was 400 years so there is clearly a difference in data sets here – however, they don’t reference their actual data, and regardless, this same analysis would work in their case too).

You can see from here that this average yields the Biblical number of 4500 years ago, but that it is clearly not a good assumption to think that the growth rate, even over this time-frame, is constant. Because of this, depending on how far back you do the averaging, you get a different time of the Flood. For example, the following show cases for 1600-2010, and 1950-2010. The last one is the closest to a constant growth rate, but gives a ridiculous -1200 years back to 8 people!

(As an aside, Richard Dawkins does the same calculation with rats, and comes up with an astonishing 1900 or so for the beginning of the Earth.)

Bottom Line

The biggest problem with this calculation is assuming a constant growth rate. Once it isn’t constant, then the time-frame over which you calculate the average makes a big difference. Only one possible time-frame will result in something consistent with the Biblical account, so one would have to justify:

1. Why you can possibly assume constant growth rate in the distant past knowing it wasn’t constant in the time-frame we know about.
2. Even given a solid justification (which I don’t believe actually exists…but I’m open to suggestions), you have to further justify why the particular time average you take, that is consistent with the Biblical account, is the one you should take.

You can’t use as a reason “because it’s consistent with the Biblical account”, because the entire point is to justify the Biblical account, or to demonstrate that the data is consistent with it. It’s not, if you have to postulate that the Biblical account is correct, and choose the specifics of the calculations to meet that.

Questions for Brian Thomas, M.S. at the ICR.

Here are the questions I’d like answered. I’m not expecting any, but I’d be thrilled to get one!

1. What data set did you use? I’m sure it won’t make any difference, but it is good to make sure that we all agree on the numbers.  I’d be happy to run my analysis through any data set that you provide.
2. Using your data set, and your analysis, do you confirm my observation that your result is sensitive to the time-frame (i.e. the 400 years in your case, 700 years in mine) over which you are obtaining your “average” growth rate?
3. If it is, do you have a justification for using that, and only that, time-frame?
4. Do you have a justification for using an average growth rate model in the face of data that clearly shows that the growth rate is not constant?

Comment about Growth Rates before Agriculture

The original article was astounded that the growth rate, prior to agriculture, could be so low.  Essentially, they seem to believe that exponential growth should have started once you had people, and gone at a constant rate the entire time.  However, before agriculture, there would have been a fairly low carrying capacity, and human population would follow logistic growth, not exponential.  Near the carrying capacity, the growth rate is essentially zero, exactly as observed.  A little bit of reading on how populations actually change might be helpful to these people.

Posted in Religion, Science | 3 Comments

Design, the Origin of Life, and Creationism

I just listened to a recent Unbelievable podcast, an episode about the origin of life.  The creationist made the claim that all of the scientific attempts at a naturalistic, non-design method for creating the initial life on the planet have met with dead ends.  He further added that this should make one start considering supernatural, design methods for creating the initial life.

Aside from not understanding science, a question stuck in my head, and I think the answer really shows the hand of these so-called intelligence design “scientists” as religionists in disguise.  The question is the following:

Once you rule out all of the naturalistic, non-design explanations [which we haven't, by the way], and if design is so evident in the biological molecules, then the next step should be to consider and rule out naturalistic design explanations…i.e. alien life designed life on this planet.

Why is this explanation never raised by ID proponents?  They claim that the “designer” is not, necessarily, God yet I never see them rule out alien minds as the designers.  They jump from naturalistic, non-design right over to supernatural “explanations”.  I think, when pressed, they would have to deal with alien design, and their true nature.

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Consciousness in infants

I’ve always been interested in the origin of consciousness, and am intrigued by attempts to quantify it and to detect it.  A recent article in Science seems to address part of the origin of consciousness in infants.  It makes you wonder what infant experience is like, and perhaps the semi-conscious experience of dogs, cats, octopi, and dolphins.  The abstract is:

Infants have a sophisticated behavioral and cognitive repertoire suggestive of a capacity for conscious reflection. Yet, demonstrating conscious access in infants remains challenging, mainly because they cannot report their thoughts. Here, to circumvent this problem, we studied whether an electrophysiological signature of consciousness found in adults, corresponding to a late nonlinear cortical response [~300 milliseconds (ms)] to brief pictures, already exists in infants. We recorded event-related potentials while 5-, 12-, and 15-month-old infants (N = 80) viewed masked faces at various levels of visibility. In all age groups, we found a late slow wave showing a nonlinear profile at the expected perceptual thresholds. However, this late component shifted from a weak and delayed response in 5-month-olds (starting around 900 ms) to a more sustained and faster response in older infants (around 750 ms). These results reveal that the brain mechanisms underlying the threshold for conscious perception are already present in infancy but undergo a slow acceleration during development.

Some recent presentations

For any that are interested, I’ve given or been part of a number of presentations recently. Two of particular interest were done today for Research and Engagement Day (REDay) at Bryant University.  The first on science and faith, and the other on the mathematics of the zombie apocalypse [with a handout].  Enjoy!

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10 signs of intellectual honesty

by Judith Curry

When it comes to just about any topic, it seems as if the public discourse on the internet is dominated by rhetoric and propaganda. People are either selling products or ideology. In fact, just because someone may come across as calm and knowledgeable does not mean you should let your guard down and trust what they say. What you need to look for is a track record of intellectual honesty.

This post, and others like it, are things I try to communicate to my students. Recognizing, and publicly acknowledging ones shortcomings, is a big one in my book.

Introduction

This weekend I got hooked on a funny little probability puzzle, and have finally found some closure. It started with an off-hand comment by a student, which led me to think more deeply about the problem once I actually worked it out. The problem was simple enough:

You draw two cards from a deck, and ask what is the probability that the first is a black card, and the second is a jack. In math notation, we want:

$P(B1,J2)$

I compared with replacement to without replacement, and got the same answer, much to my surprise. After satisfying my surprise with a numerical simulation, I thought, “there are clearly cases where it does make a difference between replacement and no replacement (drawing two jacks, for example), so where does it matter?”

Another case

So I did another case:

You draw two cards from a deck, and ask what is the probability that the first is a face card, and the second is a jack. In math notation, we want:

$P(F1,J2)$

With replacement:

$\begin{array}{rcl} P(F1,J2|{\rm replace}) &=& P(F1) \times P(J2) \\ &=&\frac{12}{52} \times \frac{4}{52} = \frac{48}{2704}=0.0178 \end{array}$

Without replacement

$\begin{array}{rcl} P(F1,J2|{\rm no-replace}) &=& P(F1) \times P(J2|F1) \\ &=&\frac{12}{52} \times \left(P(J2|F1,J1)P(J1|F1)+P(J2|F1,\overline{J1})P(\overline{J1}|F1)\right)\\ &=&\frac{12}{52} \times \left(\frac{3}{51} \cdot \frac{4}{12}+\frac{4}{51} \cdot \frac{8}{12} \right)\\ &=&\frac{44}{2652}\\ &=&0.0166 \end{array}$

The General Case

It appeared to me that there was a pattern – some relationship between the number of jacks, the number of cards, and the number of the sub-population (color, face, etc…) such that the replacement and the no-replacement cases would come out the same, because most cases don’t. So I looked at it in general, where I define:

$\begin{array}{rcl} N_C &=& \mbox{number of cards} \\ N_J &=& \mbox{number of jacks} \\ N_F &=& \mbox{number of the sub-population (faces, color, etc...)}\\ N_{JF} &=& \mbox{number of jacks in the sub-population} \end{array}$

With replacement:

$\begin{array}{rcl} P(F1,J2|{\rm replace}) &=& \frac{N_F}{N_C} \cdot \frac{N_J}{N_C} \end{array}$

Without replacement

$\begin{array}{rcl} P(F1,J2|{\rm no-replace}) &=& P(F1) \times P(J2|F1) \\ &=&\frac{N_F}{N_C} \times \left(P(J2|F1,J1)P(J1|F1)+P(J2|F1,\overline{J1})P(\overline{J1}|F1)\right)\\ &=&\frac{N_F}{N_C} \times \left( \frac{N_J-1}{N_C-1}\cdot \frac{N_{JF}}{N_F} + \frac{N_J}{N_C-1}\cdot \frac{N_F-N_{JF}}{N_F} \right) \end{array}$

Solving

When these two expressions are the same, we have:

$\begin{array}{rcl} \frac{N_F}{N_C} \cdot \frac{N_J}{N_C}&=&\frac{N_F}{N_C} \times \left( \frac{N_J-1}{N_C-1}\cdot \frac{N_{JF}}{N_F} + \frac{N_J}{N_C-1}\cdot \frac{N_F-N_{JF}}{N_F} \right) \end{array}$

which, believe it or not, simplifies to

$\begin{array}{rcl} N_F/N_C &=& N_{JF}/N_J \end{array}$

or, in other words, for the replacement and non-replacement probabilities to be the same in this simple game, the fraction of the subpopulation to the deck has to be the same fraction as the jacks in that subpopulation to the number of jacks. In the case of color, 1/2 the deck is black and 1/2 the jacks are black. However, 3/13 of the deck are face cards and 4/4 of the jacks are face cards. An interesting symmetry.

Essentially, when there exists this symmetry, knowledge of the first draw gives you no information about the second. I imagine there is some fancy math theorem to this effect, but it is still pretty cool.

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