Mathematical Thinking in Physics

March 22, 2007

LogoVery nice set of articles and essays from the NASA Glenn Learning Technologies Project.


600-1: A Tomb of Jesus follow-up

March 4, 2007

I’ve just had an email. Prof Andrey Feuerverger has put up reasoning behind his 600-1 figure online. It helps make more sense of an odd claim and appears to confirm that this is an example of the Prosecutor’s fallacy. For example here are some of the assumptions:

  • We assume that ‘Marianemou e Mara’ is a singularly highly appropriate appellation for Mary Magdalene. Note that this important assumption is contentious and furthermore that statistically this assumption drives the outcome of the computations substantially.
  • We assume that Yose/Yosa is a highly appropriate appellation for the brother of Jesus who is referred to as Joses in Mark 6:3 of the NT.
  • We assume that the Latinized version Marya is a highly appropriate appellation for Mary of the NT.
  • It is assumed that Yose/Yosa is not the same person as the father Yosef who is referred to on the ossuary of Yeshua.
  • We assume that the presence of Matya does not invalidate the find but we assign no evidentiary value to it…

These assumptions are the very things we are testing for. It is claimed the statistics help prove that one of these ossuaries is of Mary Magdalene, but the statistics in fact are part of the claim that Mary Magdalene was buried with Jesus.
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Carnival of Mathematics

March 4, 2007

I’m late with this one. The 2nd Carnival of Mathematics is up at Good Math, Bad Math, which mentions the Roman Camp post here. I’m almost late enough to point to the next one, which will be up on Michi’s Blog.

Something else that doesn’t make sense: The Tomb of Jesus

March 4, 2007

Another test podcast recorded as I picked up a cold. The claims around the Tomb of Jesus are… Well by now everyone knows.

I’d be more impressed if it were the Tomb of Brian

February 28, 2007

[Cross-posted to HNN: Revise & Dissent]

I’ve been working through the statistical analysis of the Tomb of Jesus data provided by the Discovery Channel (PDF download). They argue that the chances of their tomb not being the tomb of Jesus are one in six hundred. I looked through it and found two major errors. One is simple to see if you’re a historian, and the other should be blindingly obvious to a statistician.

The odds were calculated by Prof Andrey Feuerverger, Professor of statistics and mathematics at the University of Toronto. He was given names found on four ossuaries, boxes for holding skeletal remains, from a tomb in Jerusalem. The names were in English translation Jesus son of Joseph, Mary, Jose, a dimuntive of Joseph and Mariamne. It’s argued that Mariamne is Mary Magdelene and Jose is a diminutive of Joseph, which makes hime Jesus’s brother. What Prof. Feuerverger did was look at how often these names turn up in this historical record and then calculate the probability that these would turn up in a tomb somewhere.

He started by saying:

son of Joseph
Jose Mary Mariamne Total
1/190 1/20 1/4 1/160 1/2,432,000

Then he divided by four to allow for historical bias. Why four is never explained. This gives a probabilty of finding the names in one tomb as 1/608,000. Obviously there was more than one tomb in Jerusalem in the first century CE. Prof Feuerverger uses a figure of 1000. This reduces the odds of finding a tomb which could be said to belong to Jesus to 1 in 608. Generally social scientists get interested around odds of 1 in 20, so this looks impressive.
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The Orientation of Roman Camps

February 17, 2007

I’m working on a problem which means I have to work out if a given set of astronomical alignments are significant. I have a possible solution, so now I’m testing it one someone else’s data. What I’m doing is treating the data as a Binomial Distribution. I have a few aims with this technique. First it has to give reliable results. Next I have to understand it. Thirdly and equally importantly I have to be able to describe it so that archaeologists and historians can follow the argument. If they can’t then it gets pointless writing. My analysis may not be correct, so I’m putting it up here and submitting that to Carnival of Mathematics and Tangled Bank to see if people think the maths is wrong. I’m also putting it up on Revise and Dissent where it will get submitted to the History Carnival and Four Stone Hearth to see if it’s intelligible and sounds reasonable to Historians and Archaeologists.

Roman Camps and their Orientations reconsidered.

There is currently a debate in the pages of the Oxford Journal of Archaeology on the orientations of Roman camps and forts. Richardson (2005:514-426) argues that the orientation of these camps is non-random and relied on some form of astronomical observation. He presents data which he argues supports his case. Recently Peterson (2007:103-108) has argued this relies on a flawed use of the Chi-squared test. I accept Peterson’s findings that Chi-squared is not a useful method. However examining the camps as a binomial distribution would be feasible and would make explicit the archaeological and astronomical assumptions made in the argument.

What is a Roman Camp?

The sites being examined are Roman camps and forts in England. One of the major advantages that the Roman army had over the native opposition when occupying new territory was their organisation. The Roman army was effectively a professional army taking on amateurs. Their camps reflect this organisation. Typically their early camps a ditch surrounded by a bank in a playing-card shape. They followed a set design. The rationale for this was if there were attacked by surprise equipment and people would be in the same place at each camp, minimising the effects of the surprise.

Wallsend fort
A Roman fort at Wallsend. Photo from Google Earth

The ancient sources give some detail on how to lay out a Roman camp. The main gate should face the enemy, or the line of advance (Vegetius 1.23, Hyginus 56). The rear gate should be on the higher ground to aid surveillance. Sites overlooked by hills were considered a bad idea, as were sites near woodlands which would allow the enemy to sneak up on the camp. The basic layout of the camp could be set up quickly by surveyors using gromae, surveying tools for laying out lines at right angles. Hyginus (chapter 12) states that you set up your groma at the junction at the centre of the camp and lay out your roads to the gates from there.

This would appear to be an efficient method of laying out a camp. Were observations to orientate the camp also part of the method? It doesn’t seem necessary, but Richardson (415,422-23) provides quotes from ancient sources which suggest this is plausible hypothesis in some circumstances.
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Vegetarians and Banks

December 20, 2006

The latest edition of the Tangled Bank is up at Salto Sobrius. It’s always worth a look. Had I been more on the ball I’d have submitted this story from Snail’s Tales: How come Cows are not smarter?

If you’ve read the BBC article on IQ and Vegetarianism, then you may find Aydin Östan’s take on it interesting. I’d assumed that the correlation was due to intelligent people being more likely to be health-conscious and the vegetarian diet is more healthy. At least compared to mine – I view vegetables as something food eats. So I didn’t pay it any more mind. If I had looked more closely I would have found a lot of the vegetarians ate meat, and what about the IQ of Vegans?