Saturday, 28 May 2016

Ersby’s Triangle: An Update

A few weeks ago, I decided to revisit my post about Ersby’s Triangle – a semi-serious look at the multiples of square numbers needed to create Pascal’s Triangle.


I wanted to see if there were any formulae to describe the numbers along a particular diagonal. At first, I tried my original method of pen and paper and simply messing around with sequences of different powers of numbers, but nothing seemed to work. I put it to one side and forgot about it.

Then today I discovered The On-Line Encyclopedia of Integer Sequences. So I typed in a few of the diagonals (from top left to bottom right) from Ersby’s Triangle.

I soon came up with some interesting results as the first two diagonals I looked at (after the diagonal with 1, 2, 3...) both linked to the largest number of pieces you could get from a shape with each cut. The first diagonal referred to two-dimensional shapes and the next one referred to three-dimensional shapes.

So I was excited to see if that continued, and if the next diagonal referred to four-dimensional shapes.

It didn’t. But, undeterred, I kept searching.

Then I noticed that a particular paper kept being cited in the search results I was getting. I followed the link to Catalan Triangle Numbers and Binomial Coefficients by Kyu-Hwan Lee and Se-Jin Oh from the University of Connecticut. And there, tucked away on page 14, was the closest I’ve ever come to being referenced in a mathematics paper.




Amazing. If only I knew what the paper actually meant.

References:

Lee, K.H., Oh, S.J., (2016) "Catalan Triangle Numbers and Binomial Coefficients," arXiv:1601.06685v

Tuesday, 25 August 2015

Fewer train reservations before disasters

In 1956, E.W. Cox wrote an article for the Journal of the American Society for Psychical Research in which he looked for evidence of precognition of fatal train crashes (10 fatalities or more) in the numbers of reservations bought for that particular train, with the hypothesis that any form of precognition would be visible in a drop in reservations for that train on that day.

I do not have a copy of the original paper by E.W.Cox, but I did find a page on the internet which had his data, as well as an examination of his methods. The page is currently (25th Aug '15) unavailable, but I have put a link at the bottom of this article.

He examined the data in two ways: one was to look at the data day by day. In this, he compared the reservations for the crash day with the previous seven days. The second way was to compare the crash day reservations with the same day on the previous four weeks.

His measure of success was if the number of reservations was the lowest of all the other days. This he called a hit, and its chances of success are calculated as 1 in 8 for the daily data and 1 in 5 for the weekly data.

He did this for 28 crashes.

For the monthly data, he found ten days when the lowest number of reservations fell on the day of the crash. In other words, ten hits out of twenty-eight trials, with a 1/5 chance of success. This is statistically significant at p=0.04, z=1.76 (one-tailed) or odds of 1 in 25.

For the daily data, there are nine hits for the twenty-eight days, with a 1/8 success rate. This gives use p=0.005, z=2.54 (one-tailed) or odds of 1 in 185.

The data are as follows:

(It's worth noting that Cox could not get all the data he needed, so when he had a gap, he inserted the average number for that set of data. I've highlighted those figures in brown.)



However, as the psuedo-scepticisme article points out, the data sample is too small to support a binomial distribution. Taking the rule of thumb that np=5 (n=number of trials, p=probability of success). In the case of the daily data that would be 28 * 0.125 = 3.5. Additionally, Cox allowed tied hits to stand, suggesting to me that the binomial method wasn't the right one to use.

I decided to take a look at the data myself, but this time I looked at whether the reservations for a particular day were significantly above or below the average for that set of weeks or days. I thought that this would be a more sensitive measure of success, especially given that some of the hits were by a margin of three or less reservations in difference.

I found that for the daily data, the day of the crash was significantly below the average (ie, fewer sales) seven times. This is the highest figure for this category, which supports the idea that precognition lead people to make fewer reservations on that day. However, there were also three occasions where the sales of reservations was significantly above the average. This makes it comparable to D-4 when there were five below average and one above.


On the weekly data, the day of the crash had seven occasions when it was significantly below average and four times above. This is actually worse than D-28 which also had seven below average but only two occasions when it was above. In fact, using Cox's original method, D-28 has ten hits out of twenty-eight, just like the day of the crash does.


I'm no statistician, so I encourage anyone to look at the spreadsheet I used, and perhaps suggest improvements. This can be downloaded here.

https://www.mediafire.com/?mwnxfrztogdt836

References:

Cox, W. E. (1956). "Precognition: An analysis. II. Subliminal precognition." Journal of the American Society for Psychical Research, 50, 99–109. as cited in the article “Pr├ęcognition subliminale lors d’accidents de train : relecture critique d’une recherche de W.E. Cox” http://www.pseudo-scepticisme.com/Precognition-subliminale-lors-d.html

Tuesday, 7 April 2015

Sunday, 29 March 2015

An older version of the Earth

Today I found this old world map dating from the early 1600s.


See the Wikipedia page for more details, and a far bigger version.

And I decided to see what it would look like mapped onto an actual globe. Since the free astronomy program Celestia allows you to do that quite easily. I spent a little time in photoshop to get the image to the right size and shape, and pasted it in. I was very pleased how well it turned out, even if some of the edges didn't quite match up. I felt like I was seeing the Earth as it would have been imagined by someone in the 1600s.

Europe and Africa...


The USA and Central America...


The Far East...


And India...



The ISS, heading towards the Nile Delta...


An old Earth at night...


Saturday, 7 March 2015

The Lawrence Livermore Remote Viewing session

One of the most famous successes of the US government-sponsored remote viewing program was the series of sessions where Joe McMoneagle described first the Lawrence Livermore Laboratory and then a wind farm, and finally a series of sketches resembling parts of a particle accelerator.



The remarkable similarities between the sketches and the locations of the target person has been frequently reproduced in parapsychological books and websites. It can be found on Joe McMoneagle’s site (here, here and here), on Russel Targ’s site (here and here) and on Dr Edwin May’s site (here and here).

This fairly typical summary of this remote viewing session comes from the book “The ESP Enigma” by Diane Hennacy Powell, M.D.

“His most amazingly accurate results include the time he drew the locations of a CIA team while the agents were hiding in the San Francisco area. First the agents hid in Lawrence Livermore Laboratory, which is a hundred miles away from SRI. McMoneagle drew many of the laboratory buildings and structures as visible from Lawrence Livermore’s West Gate side, including a T-shaped, six-story building that was covered with glass and adjacent to a line of trees. The team traveled to the Livermore Valley Foothills Windmill Farm as their next target, and McMoneagle drew the windmill structure with almost 100 percent accuracy.”

The report on Dr May’s site is the most detailed, and he has written about it in his book “Anomalous Cognition: Remote Viewing Research and Theory.” As such, his version of events is the one I shall be comparing to the original report, An Application Oriented Remote Viewing Experiment, written by Dr May in 1988.

This remote viewing experiment consisted of four sessions over the course of one day, 7th May. All of these sessions were to be focused on one location, as specified by the presence of a “beacon”

The description from the 1988 report reads:

"Viewer 372 [ie, Joe McMoneagle] and a viewing monitor were aware that the target material was of [redacted] significance and was located within the greater San Francisco Bay area. They were told that an individual [redacted] described by name and Social Security number was in the target area during the viewing sessions, and that two members of the SRI staff (known to V372 and the monitor) would serve as a “beacon” and would be at the specific target of interest between 2200 hours on May 7 and 0800 hours on May 8, 1987."


It is worth noting at this point that McMoneagle and the interviewer were not completely blind to the nature of the target, as described in some versions of these events. Additionally, at the start of the first session, McMoneagle is told by the interviewer that the beacon is a physicist, which is another piece of information that could influence his remote viewing session.

Dr May's website includes a section listing the times and circumstances of each of the four sessions. Dr May quotes the 1988 report almost verbatim, except for a couple of sentences that he has omitted from the website. Below is a quote from Dr May’s site. The sections in bold are those which are in the original 1988 report, but are missing from the version online.

"0800 Hours — Receiver 372 was asked to describe the geographical area and the gestalt of the area of interest. He was also asked to provide as much detail as possible in real-time (i.e., at 0835) and was targeted upon the sponsor's on-site representative. At this time, the representative was sleeping (approximately 2 miles from [redacted: the target location]) after having been awake the entire previous night.

1010 Hours — The receiver was asked to describe the details and activity at the site designated by the sponsor's on-site representative as of 0000 hours 7 May (i.e., the previous night).

1600 Hours — The receiver was asked to describe, in real-time, the details and activity at the site designated by the sponsor's on-site representative. At this time, this individual was eating dinner (approximately 2 miles from [the target location])

2400 Hours — The receiver was asked to describe, in real-time the details and activity at the site designated by two SRI personnel."



These omissions, which pinpoint the target person’s location, become pivotal when trying to properly assess the results of this experiment. Dr May writes “During the 0800h session, the target person was located in building A at LLNL,” although the 1988 report tells us something quite different. The target location, the Advanced Technology Accelerator, is 15km (9 miles) from the Lawrence Livermore Labs and so the two versions of events do not match up.

Similarly, the claim “at 1600h he was driving through the windmill electric power farm at the Altamont pass” does not agree with the original report for two reason. Firstly, as seen above, the target was eating dinner, not driving his car. Secondly, the drawing and description of the wind farm came from the 0800h session, not from the afternoon 1600h session.


Since reading the original report makes it clear that neither the target person nor the other two beacons were ever at the Altamont Wind Farm nor the Lawrence Livermore Labs, where has this reputation for being incredible successes come from?

In the 1988 report, the inclusion of these two locations as targets alongside the inital (primary) target is explained thus:

“We have also identified targets of lesser interest in the [redacted] environment. We have designated a wind-power electric generator farm at Altamont Pass but adjacent to [redacted] as a secondary target, and the [redacted] main complex, which is farther away geographically but is functionally associated with [redacted] as a tertiary target.”


I have emailed Dr May to ask if he recalled exactly when during the experiment the secondary and tertiary targets were defined but have received no reply.

The paper “Anomalous Cognition Technical Trials: Inspiration for the Target Entropy Concept” by May and Lantz (included in the book Anomalous Cognition) tells us

“Three separate targets within this trial were identified depending upon where the beacon person was at the time of the session.”

This does not accord with the original report. Is it possible that the wind farm and the laboratory were added to the session as “targets” after the sessions were complete?

As for the successful viewing of the particle accelerator, this took place on the third and fourth sessions and it is difficult to tell how blind to the target the interviewer is, since he sometimes prompts Joe McMoneagle with technical names for things he is describing.

But one thing is clear, claims that Joe McMoneagle remote viewed to an uncanny accuracy the location of a distant individual is not supported by the original report. The details as to why the secondary and tertiary targets were chosen are very sketchy and the constant inaccuracies in the retelling of this experiment means this cannot be taken seriously as an example of anomalous cognition.

The original 1988 report can be downloaded from here.



References:

Diane Hennacy Powell, M.D., “The ESP Enigma: The Scientific Case for Psychic Phenomena,” (2009) Walker & Company

Edwin May & Nevin Lantz, “Anomalous Cognition Technical Trials: Inspiration for the Target Entropy Concept” in “Anomalous Cognition: Remote Viewing Research and Theory,”edited by Edwin May & Sonali Bhatt Marwaha, (2014) McFarland

Edwin May, “An Application Oriented Remote Viewing Experiment,” (1988) SRI International