The Plausible versus the Probable

This blog occasionally (always?) takes on what is the new trend in Skepticism. It has always been around a long time but currently it is making more noise than usual and it is no surprise that Loch Ness Monsters should come under their cannon fire.

Recently I have been defending the Spicers who claimed in 1933 to have seen Nessie cross the road (to get to the other side no doubt).

If one is a skeptic then it is bad enough to suggest large entities inhabit Loch Ness - but to also forage onto land offends logic in the extreme!

I thought I had laid to rest any notions of otters or deers crossing in front of the Spicers but Alexander Lovcanski put out an interesting piece that the Spicers saw a mirage enhanced otter that day. His analysis is here.

Okay, it deserves to be aired and analyzed. I put some questions to Alexander and then went away and thought about it.

I asked myself a seemingly simple question. What was the probability of the Spicers and this misidentified otter coming together in such a way to produce this effect? Or to put it more precisely - Nessie hit the news in April 1933 and the Spicers had their experience four months later in July 1933. What was the probability of otter, car and conditions confluencing in this miragical manner within the 81 days between the first public announcement of a sighting (the May 2nd edition of the Inverness Courier and the Spicers' encounter on July 22nd)?

I did some sums and came up with my own answers. The odds against it happening in that four months was about 2330 to 1 against. In other words, it was not at all likely to have happened. I have laid out the calculations at the end of this post for those who may want to suggest improvements in my assumptions.

I would add that changing the figures to lower the probabilities will present another problem to the skeptic. If one make the event more probable then over 77 years why have there not been more such misidentifications on land?

Now the retort may be that this is still more likely than a lumbering antediluvian crossing a road. But isn't that what the debate is all about? If you believe there is a large entity in Loch Ness then a land excursion moves from the impossible to the probable (depending on what you think it is). If you don't believe in such an entity, obviously no road crossing will ever occur.

But let us learn this lesson. Something may be plausible, but then ask yourself - is it probable?

CALCULATIONS

Calculate the probability of seeing an otter at the right position on the road
at the right distance in the right weather conditions between April and July 1933!

1. Otter Population around Loch Ness

Let us assume an even distribution of otters around Scotland's shores and a recent article estimated 7,000 otters live in Scotland.

Coastline of Scotland = 11800km - 16491km (depending how accurate you wish to be)
Coastline of Loch Ness = say 1% of Scottish coastline
7000 otters in Scotland - say 1% proportionately at Loch Ness = 70

The otter population suffered under hunting and pollution but has been on the increase in recent years so double for larger otter population in 1930s = 140

2. Number of times an otter crosses the road on Loch Ness during day = 0.5

This is not so easy to assume. Most otter activity is at dawn/dusk and near water courses so a 4pm crossing near dry ground is most unlikely. But for the sake of this study we will assume an even distribution of otter activity but a daytime crossing is still a rare event.

3. Road perimeter of Loch Ness = 85km = 85000m

Eliminate 55% off road which does not pass Loch side = 38250m
35% is Between Fort Augustus and Foyers 10% is around Drumnadrochit
Eliminate 10% which is too high above shore for otters to traverse
A lot of otters are never seen because the roads are not near the shore or the road is high above the water.

So drop the number of otters to account for the lack of road:
Correspondingly drop number of otters = 77

4. How much of the remaining road is conducive to the special mirage conditions of the article?

The requirement is a gently ascending road over 100-200m. I have driven around the Loch quite a few times and a lot of road is bends, long stretches. So not a lot of opportunity but we will be generous and say:
Number of "mirage points" on perimeter (i.e. a hump on an undulating road) = 1
per 4km = 10 overall

5. Where the otter lies is crucial.

If it is too far from the dip horizon on either side then the mirage will not happen. That is why the range is only 1m or +/- 0.5m either side:
Otter has to be laterally within 1 metres of the "mirage zone" to work or 10 * 1m
zones in total = 10m


6. The otter has to be at beginning of "run" to have the desired effect

Or the sighting will be over in a flash. It is no use being half way or near the end at point of first sight:
Probability of otter about to cross the road = length of otter / length of road = 1.1/3.3 = 0.33

So combining all these "otter" factors together:
Probability that one of the 77 otters will cross one such area in one daylight
period = 77 * 0.5 * 0.33 * 10/38250 = 0.0033

7. What proportion of the daylight hours will be best for mirage conditions?

If it is nearing dawn/dusk then the temperature difference between the road surface and air above will not be high enough so for an average 12 hours of daylight deduct 6 hours:

Probability of good daylight mirage hours = 6/12 = 0.5

So otter crossing mirage area probability reduces to 0.5 * 0.0033 =
0.0017 in one day.

Now onto the other party - the car driver.

8. Assume car has to be at a dip approaching this hump for mirage to be effective.

Assume number of dips = number of humps = 10

9. Monster in sight for a "few seconds"

So at 9m/s zone = 9 * 3 = 27m
Car observer has to be within 27m of the dip zone for mirage to be effective or a total zone of 27 * 10 = 270m

That is the practical maximum but what was the actual range for an effective mirage? The small angle for an effective mirage suggest not much so let's third it: 9 * 10m = 90m

10. To see the whole mirage for a few seconds suggests the car has to be just entering the mirage zone

So probability that observer is at start of "mirage zone" = 1m/9m = 0.11

Probability that one car will be in this zone at any time = 90/38250 * 0.11 =
0.00027


11. Of course, it is the number of cars passing these optimal mirage points that counts so:

Number of cars on south side of road crossing these points in one day = one every ten minutes = 36 during the 6 hour mirage time window

This is based on my own observation in July 2010 between Dores and Whitefield
where a car passed every minute and the assumption that car ownership is 10 times more than what it was in 1933.

Probability that a car will be over one of these mirage dips over 6 hours at any

one time = 36 * 0.00027 = 0.0097

Probability that otter at hump zone and car at dip zone will coincide =

0.0097 * 0.0017 = 0.000016

12. Probability that weather will be hot, no clouds, no shade, no recent rain

= 1 in 3 = 0.33

Overall probability on one day = 0.0000053 or 189393/1 against

13. Sum up over entire period in question

81 days = 81 * 0.0000053 = 0.00043 or 2329/1 against

The Loch Ness Kelpie

Here is a great wee cartoon about the Loch Ness Kelpie. If you are wondering what a kelpie is (or was) this short film may help.

Now was Nessie a Kelpie, Water Horse or Water Bull? I never could quite tell ....

THE LOCH NESS KELPIE

Mirages and Nessie

Recently on one forum I frequent, the Spicer sighting has become somewhat of a touchstone on Nessie believers vs skeptics. Of course I could have picked other sightings to have defended Nessie upon because the Spicer sighting is to say the least unusual. But if you get good mileage on that then who knows what else will follow.

Having shrugged off the otter/deer explanations and saying you would have to be hallucinating to think deer or otter were a dragon like creature, lo and behold the next best thing to hallucinating comes up.

In the aptly named skeptic.org.uk website, Alexander T. Lovcanski suggests the Spicers saw an otter in special conditions which produced a mirage. His article is below.

link to article

My reply is below and Alexander may come up with plausible reasons why we should accept his assumptions and resulting hypothesis but I wonder why they don't just apply Occam's Razor more ruthlessly and say the Spicers lied - end of story. Let's face it, if you do not believe there is a large unclassified creature in Loch Ness then you are obliged to come up with some unusual explanations at times. I would guesstimate the odds of someone seeing a larger than usual otter under special mirage conditions crossing the road is thousands to one against. In July 1933, the Loch Ness Monster phenomenon was about three months old. So set the timer running from then and then ask what are the odds between April and July 1933 of someone seeing a larger than usual otter cross the road in front of them under special mirage conditons on the less frequented side of Loch Ness? And remember car ownership was far less in 1933 than today (George Spicer was a director of a Saville Row tailor which somewhat demonstrates the point).




Thank you firstly for confirming my view that suggesting the Spicers merely saw an otter or deer is simplistic to say the least. Something delusional or illusional would be required to even begin to entertain such a theory.

Let me make a few points. Several things clearly have to be in place simultaneously:

1. A sufficiently hot day.
2. A larger than usual otter crossing the road.
3. Witnesses and otter in the proper positions for a mirage.
4. Suitable surface conditions.
5. Witnesses in an expectant mind to misinterpret mirage.

Now you say the temperature was 16 to 18 degrees centigrade on that day and it was already late afternoon at the time. I normally associate mirages with higher temperatures. I read that a temperature gradient has to be 4 to 5 degrees per metre for the mirage to be strong. Can you be sure these conditions were in place?

I understand a large otter is required to be stretched vertically to "monster" proportions by the mirage. One assumes then that a normal otter is insufficient? Also why the need to have the otter go from L to R, is the tail required on the right to produce the impression of a long neck? Can a mirage really fool someone into thinking the object is going in the opposite direction?

Also what about the horizontal? The witnesses say that the creature filled the road. I understand that road mirages work on the vertical best, how do you stretch an otter which has less that a metre visible across a road?

The road surface itself is important in this consideration. What was the composition of the Dores to Foyers road in 1933? We know road works were in progress on the A82 but what about the B852?

Were the witnesses in an expectant frame of mind? Perhaps they were to see something on the water - but on land?!

Also, why have we not heard of other such land sightings if these conditions are fulfilled? It seems nothing else has been heard of in the literature since! Either this is a very rare confluence of events or perhaps even such mirage conditions still do not fool people easily.

It would be an interesting exercise to work out the probability of such an event happening. I know if enough cars pass by that spot then it could happen eventually but despite the large increase in car ownership no further mirages of nessies across roads on hot days have been reported. I suspect your theory predicts more such sightings - or is this one of those one off special explanations?

Man, Monsters and Mysteries (Disney Film)

For your entertainment below, Walt Disney's documentary on the Loch Ness Monster made in the early 1970s. If you can put up with their ridiculous cartoon Nessie this documentary is a Who's Who of the Monster Hunt of the 1960s. I don't recognise everyone but with the YouTube time counter in parentheses you can spot the following Loch Ness Luminaries:



Not surprisingly, the video has now been removed. If you want it, you can buy it from amazon.com and hope your DVD player does region 1 as it is not available on amazon.co.uk. Happy hunting!

Some Deer Crossing Roads

Would you mistake these videos of deer running across a road for a big, grey, snail-like, prehistoric-like creature?





Thought not, nor did I. Feel free to suggest other clips!

England's Nessie

As reported by Sky News who have sonar equipment on the case:

article link

Search For England's Loch Ness Monster


Monster hunters have used sonar equipment for the first time to search for a mysterious creature reportedly living in England's largest lake. Skip related content

Sky News filmed out on Windermere with the team looking for proof that the beast exists.

In the last four years there have been seven reported sightings of a long humpbacked animal, now nicknamed Bow-Nessie.

Windermere hotel owner, Thomas Noblett, described his strange encounter in the water, saying: "All of a sudden I felt something brush past my legs like a giant fish.

"And then I was lifted up by a 3ft wave. I've no idea what it was."

During the sweep of the lake, the team spotted a strange 14 metre long disturbance in the water but were unable to detect anything on sonar.

Searching Windermere is a huge task as the lake is 220ft deep in parts and over ten miles long.

Hunt organiser, Dean Maynard, said: "We've had more creature sightings here than at Loch Ness in recent years so we think it's time that Bow-Nessie received more attention."

Last year, a local film crew spotted a 20 metre long object below the surface of the lake but sceptics believe the footage shows a wave from an unseen boat.

A Painting of the Loch Ness Monster?

I found this picture in a relatively old book on Nessie. It claims to be of a sighting of the monster but the source they claim for it (Mary Evans Picture Library) has no reference to it.

Has anyone else seen this before?