The Art of the Impossible

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Imagine a time machine exists, able to transport us (just us) to the future.

It can take us 1 year forward and we can register all that has changed, before returning to the present. We then know everything to come and with this knowledge possess unlimited opportunities for profit.

Sadly (as far as I know) this remains a frustrating Wellsian fantasy, so instead we are left to follow the wisdoms of experts; divining future paths, using their special powers of expertise.

But just to be thorough, to verify that confidence is merited in the predictive prowess of these experts. Let’s briefly review the outcomes of a study where 1,000 Investment Professionals answered the following question:

“Predict the number that is two thirds of the average number, that all those answering will select between 0 and 100?”

So, this is simply asking each of the 1,000 participants to work out what 66.66% of the average number picked by the 1,000 will be.


So, let’s go up the levels of analytical thought on this.

Level One – Firstly we can know that any answer above 67 cannot be right because 67 is the highest answer possible. This being the closest whole number to 66.66% of 100.

Level Two – Those answering 50 will simply be taking the average between 0-100 but requires the assumption that the average person will have answered 75 which is above 67 so can’t be right. Remember the aim is to identify the number which is two thirds of the average. 50 assumes the average responder has the mental acuity of Homer Simpson.

Level Three – Those that answered 32-34 have assumed that the average answer will be circa 50, two thirds of that being 33. This answer is more insightful but starts from the premise that the average person (at 50) will have been illogically incorrect in their selection.

Level 4 – Those that answered 22 are getting much closer as they have concluded that most people (the average) will stop analysing at level 3 so 67% of around 33 is 22.

However, there are other factors to weigh.

Level 5 – This is where the analysis requires some finesse, but it’s important to factor in that there will have been some very low answers which will bring the average down.

As examples of why there will be very low numbers selected:

Economists (a profession that excels at explaining tomorrow why they were wrong yesterday) may well (and did) answer 0 as the only answer which can’t be wrong.

66% of 0 is still 0.

Equally mathematicians may well use the Nash Equilibrium applicable to Game Theory which will give them an answer of 1 (and also did).

So, an estimate of the analytical prowess of those being asked needs to be factored in and if unknowable then an estimate of a percentage of answers that will be low, as this will reduce the overall average.


  1. The most popular answers were around 50, 34, 22, 1 and 0
  2. There were answers of 100!
  3. The actual average number selected was 26 (meaning the average respondent stopped their analysis between levels 3 and 4)
  4. So, the correct answer to the question is *17*
  5. Out of the 1000 participants 3 people chose 17
  6. In a separate question the 1,000 were asked whether they believed their abilities ranked them in the top 20% of their profession and just over 80% said they did
  7. If the acceptable correct answer is expanded to a band between 15 and 19 this would still mean less than 5% got it right


Many of you will have realised that even those who predicted 17 did not do so by working out a right answer because there is actually no right answer. They instead correctly guessed the interaction of the 999 variables and how on average they would make their decisions.

If the 1,000 respondents had all used every level of analysis above and concluded that the number was say between 15 and 19 (average 17) then the correct answer to the question would then not have been 17 but 12 (66.6% of the average). If they had all gone to this next level of analysis and answered 12 then the new correct answer would be 8 then 5 etc.

This is how it is logically possible to ultimately reach an answer of 0.

So, what’s the point of all this beyond the ability to mock those who selected 100?!

We think the fundamental insight this experiment gives is to help understand and therefore differentiate between those things that can be known in advance and those that practically can’t.

This is fundamental to the process of analysis in any scientific endeavour.

For a scientist to make a discovery of a new causal relationship.

“Doing X resulting in Y happening”

Results for the same exact inputs must consistently produce the same outcomes. If results are not knowable in advance, then no discovery has been made because the relationship between the causes and their effects are random.

So if we conclude that economic forecasting and the prediction of resultant moves in asset prices cannot be a science because they are unpredictable over periods such as a year, then why do so many continue to be so heavily influenced by it?

The next blog will attempt to answer this question but it seems apt to finish with a quote from Sherlock Holmes.

“Once you eliminate the impossible Watson, whatever remains, no matter how improbable, must be the truth”

Note: This is written in a personal capacity and reflects the view of the author. It does not necessarily reflect the view of LWM Consultants. The post has been checked and approved to ensure that it is both accurate and not misleading. However, this is a blog and the reader should accept that by its very nature many of the points are subjective and opinions of the author. Individuals wishing to buy any product or service as a result of this blog must seek advice or carry out their own research before making any decision, the author will not be held liable for decisions made as a result of this blog (particularly where no advice has been sought). Investors should also note that past performance is not a guide to future performance and investments can fall as well as rise.

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