Solve if u r a genius

Solve if u r a genius - Less than 1% can do it!!!

I have some form when it comes to getting irritated by quasi-mathematical social media memes (see Facebook squares “puzzle” for example). Facebook, which I find myself using less and less frequently these days, has always been plagued by clickbait articles. Some of these can be rather unsavoury. One that does not have this particular issue, but which more than makes up for this in terms of general annoyance, is the many variants of:

Only a math[s] genius can solve [insert some dumb problem here] – can u?

Life is too short to complain about Facebook content, but this particular virus now seems to have infected LinkedIn (aka MicrosoftedIn) as well. Indeed as LinkedIn’s current “strategy” seems to be to ape what Facebook was doing a few years ago, perhaps this is not too surprising. Nevertheless, back in the day, LinkedIn used to be a reasonably serious site dedicated to networking and exchanging points of view with fellow professionals.

Those days appear to be fading fast, something I find sad. It seems that a number of people agree with me as – at the time of writing – over 9,000 people have viewed a LinkedIn article I briefly penned bemoaning this development. While some of the focus inevitably turned to general scorn being heaped on the new LinekdIn user experience (UX), it seemed that most people are of the same opinion as I am.

However, I suspect that there is little to be done and the folks at LinkedIn probably have their hands full trying to figure out how to address their UX catastrophe. Given this, I thought that if you can’t beat them, join them. So above appears my very own Mathematical meme, maybe it will catch on.

It should be noted that in this case “Less than 1% can do it!!!” is true, in the strictest sense. Unlike the original meme, so is the first piece of text!

Erratum: After 100s of views on my blog, 1,000s of views on LinkedIn and 10,000s of views on Twitter, it took Neil Raden (@NeilRaden) to point out that in the original image I had the sum running from n=0 as opposed to n=1. The former makes no sense whatsoever. I guess his company is called Hired Brains for a reason! This was meant to be a humorous post, but at least part of the joke is now on me.




Knowing what you do not Know

Measure twice cut once

As readers will have noticed, my wife and I have spent a lot of time talking to medical practitioners in recent months. The same readers will also know that my wife is a Structural Biologist, whose work I have featured before in Data Visualisation – A Scientific Treatment [1]. Some of our previous medical interactions had led to me thinking about the nexus between medical science and statistics [2]. More recently, my wife had a discussion with a doctor which brought to mind some of her own previous scientific work. Her observations about the connections between these two areas have formed the genesis of this article. While the origins of this piece are in science and medicine, I think that the learnings have broader applicability.

So the general context is a medical test, the result of which was my wife being told that all was well [3]. Given that humans are complicated systems (to say the very least), my wife was less than convinced that just because reading X was OK it meant that everything else was also necessarily OK. She contrasted the approach of the physician with something from her own experience and in particular one of the experiments that formed part of her PhD thesis. I’m going to try to share the central point she was making with you without going in to all of the scientific details [4]. However to do this I need to provide at least some high-level background.

Structural Biology is broadly the study of the structure of large biological molecules, which mostly means proteins and protein assemblies. What is important is not the chemical make up of these molecules (how many carbon, hydrogen, oxygen, nitrogen and other atoms they consist of), but how these atoms are arranged to create three dimensional structures. An example of this appears below:

The 3D structure of a bacterial Ribosome

This image is of a bacterial Ribosome. Ribosomes are miniature machines which assemble amino acids into proteins as part of the chain which converts information held in DNA into useful molecules [5]. Ribosomes are themselves made up of a number of different proteins as well as RNA.

In order to determine the structure of a given protein, it is necessary to first isolate it in sufficient quantity (i.e. to purify it) and then subject it to some form of analysis, for example X-ray crystallography, electron microscopy or a variety of other biophysical techniques. Depending on the analytical procedure adopted, further work may be required, such as growing crystals of the protein. Something that is generally very important in this process is to increase the stability of the protein that is being investigated [6]. The type of protein that my wife was studying [7] is particularly unstable as its natural home is as part of the wall of cells – removed from this supporting structure these types of proteins quickly degrade.

So one of my wife’s tasks was to better stabilise her target protein. This can be done in a number of ways [8] and I won’t get into the technicalities. After one such attempt, my wife looked to see whether her work had been successful. In her case the relative stability of her protein before and after modification is determined by a test called a Thermostability Assay.

Sigmoidal Dose Response Curve A
© University of Cambridge – reproduced under a Creative Commons 2.0 licence

In the image above, you can see the combined results of several such assays carried out on both the unmodified and modified protein. Results for the unmodified protein are shown as a green line [9] and those for the modified protein as a blue line [10]. The fact that the blue line (and more particularly the section which rapidly slopes down from the higher values to the lower ones) is to the right of the green one indicates that the modification has been successful in increasing thermostability.

So my wife had done a great job – right? Well things were not so simple as they might first seem. There are two different protocols relating to how to carry out this thermostability assay. These basically involve doing some of the required steps in a different order. So if the steps are A, B, C and D, then protocol #1 consists of A ↦ B ↦ C ↦ D and protocol #2 consists of A ↦ C ↦ B ↦ D. My wife was thorough enough to also use this second protocol with the results shown below:

Sigmoidal Dose Response Curve B
© University of Cambridge – reproduced under a Creative Commons 2.0 licence

Here we have the opposite finding, the same modification to the protein seems to have now decreased its stability. There are some good reasons why this type of discrepancy might have occurred [11], but overall my wife could not conclude that this attempt to increase stability had been successful. This sort of thing happens all the time and she moved on to the next idea. This is all part of the rather messy process of conducting science [12].

I’ll let my wife explain her perspective on these results in her own words:

In general you can’t explain everything about a complex biological system with one set of data or the results of one test. It will seldom be the whole picture. Protocol #1 for the thermostability assay was the gold standard in my lab before the results I obtained above. Now protocol #1 is used in combination with another type of assay whose efficacy I also explored. Together these give us an even better picture of stability. The gold standard shifted. However, not even this bipartite test tells you everything. In any complex system (be that Biological or a complicated dataset) there are always going to be unknowns. What I think is important is knowing what you can and can’t account for. In my experience in science, there is generally much much more that can’t be explained than can.

Belt and Braces [or suspenders if you are from the US, which has quite a different connotation in the UK!]

As ever translating all of this to a business context is instructive. Conscientious Data Scientists or business-focussed Statisticians who come across something interesting in a model or analysis will always try (where feasible) to corroborate this by other means; they will try to perform a second “experiment” to verify their initial findings. They will also realise that even two supporting results obtained in different ways will not in general be 100% conclusive. However the highest levels of conscientiousness may be more honoured in breach than observance [13]. Also there may not be an alternative “experiment” that can be easily run. Whatever the motivations or circumstances, it is not beyond the realm of possibility that some Data Science findings are true only in the same way that my wife thought she had successfully stabilised her protein before carrying out the second assay.

I would argue that business will often have much to learn from the levels of rigour customary in most scientific research [14]. It would be nice to think that the same rigour is always applied in commercial matters as academic ones. Unfortunately experience would tend to suggest the contrary is sometimes the case. However, it would also be beneficial if people working on statistical models in industry went out of their way to stress not only what phenomena these models can explain, but what they are unable to explain. Knowing what you don’t know is the first step towards further enlightenment.


Indeed this previous article had a sub-section titled Rigour and Scrutiny, echoing some of the themes in this piece.
See More Statistics and Medicine.
As in the earlier article, apologies for the circumlocution. I’m both looking to preserve some privacy and save the reader from boredom.
Anyone interested in more information is welcome to read her thesis which is in any case in the public domain. It is 188 pages long, which is reasonably lengthy even by my standards.
They carry out translation which refers to synthesising proteins based on information carried by messenger RNA, mRNA.
Some proteins are naturally stable, but many are not and will not survive purification or later steps in their native state.
G Protein-coupled Receptors or GPCRs.
Chopping off flexible sections, adding other small proteins which act as scaffolding, getting antibodies or other biological molecules to bind to the protein and so on.
Actually a sigmoidal dose-response curve.
For anyone with colour perception problems, the green line has markers which are diamonds and the blue line has markers which are triangles.
As my wife writes [with my annotations]:

A possible explanation for this effect was that while T4L [the protein she added to try to increase stability – T4 Lysozyme] stabilised the binding pocket, the other domains of the receptor were destabilised. Another possibility was that the introduction of T4L caused an increase in the flexibility of CL3, thus destabilising the receptor. A method for determining whether this was happening would be to introduce rigid linkers at the AT1R-T4L junction [AT1R was the protein she was studying, angiotensin II type 1 receptor], or other placements of T4L. Finally AT1R might exist as a dimer and the addition of T4L might inhibit the formation of dimers, which could also destabilise the receptor.

© University of Cambridge – reproduced under a Creative Commons 2.0 licence

See also Toast.
Though to be fair, the way that this phrase is normally used today is probably not what either Hamlet or Shakespeare intended by it back around 1600.
Of course there are sadly examples of specific scientists falling short of the ideals I have described here.



Bigger and Better (Data)?

Is bigger really better

I was browsing Data Science Central [1] recently and came across an article by Bill Vorhies, President & Chief Data Scientist of Data-Magnum. The piece was entitled 7 Cases Where Big Data Isn’t Better and is worth a read in full. Here I wanted to pick up on just a couple of Bill’s points.

In his preamble, he states:

Following the literature and the technology you would think there is universal agreement that more data means better models. […] However […] it’s always a good idea to step back and examine the premise. Is it universally true that our models will be more accurate if we use more data? As a data scientist you will want to question this assumption and not automatically reach for that brand new high-performance in-memory modeling array before examining some of these issues.

Bill goes on to make several pertinent points including: that if your data is bad, having more of it is not necessarily a solution; that attempting to create a gigantic and all-purpose model may well be inferior to multiple, more targeted models on smaller sub-sets of data; and that there exist specific instances where a smaller data sets yields greater accuracy [2]. However I wanted to pick up directly on Bill’s point 6 of 7, in which he also references Larry Greenemeier (@lggreenemeier) of Scientific American.

  Bill Vorhies   Larry Greenemeier  

6. Sometimes We Get Hypnotized By the Overwhelming Volume of the Data and Forget About Data Provenance and Good Project Design

A few months back I reviewed an article by Larry Greenemeier [3] about the failure of Google Flu Trend analysis to predict the timing and severity of flu outbreaks based on social media scraping. It was widely believed that this Big Data volume of data would accurately predict the incidence of flu but the study failed miserably missing timing and severity by a wide margin.

Says Greenemeier, “Big data hubris is the often the implicit assumption that big data are a substitute for, rather than a supplement to, traditional data collection and analysis. The mistake of many big data projects, the researchers note, is that they are not based on technology designed to produce valid and reliable data amenable for scientific analysis. The data comes from sources such as smartphones, search results and social networks rather than carefully vetted participants and scientific instruments”.

Perhaps more pertinent to a business environment, Greenemeier’s article also states:

Context is often lacking when info is pulled from disparate sources, leading to questionable conclusions.


Neither of these authors is saying that having greater volumes of data is a definitively bad thing; indeed Vorhies states:

In general would I still prefer to have more data than less? Yes, of course.

They are however both pointing out that, in some instances, more traditional statistical methods, applied to smaller data sets yield superior results. This is particularly the case where data are repurposed and the use to which they are put is different to the considerations when they were collected; something which is arguably more likely to be the case where general purpose Big Data sets are leveraged without reference to other information.

Also, when large data sets are collated from many places, the data from each place can have different characteristics. If this variation is not controlled for in models, it may well lead to erroneous findings.

Statistical Methods

Their final observation is that sound statistical methodology needs to be applied to big data sets just as much as more regular ones. The hope that design flaws will simply evaporate when data sets get large enough may be seducing, but it is also dangerously wrong.

Vorhies and Greenemeier are not suggesting that Big Data has no value. However they state that one of its most potent uses may well be as a supplement to existing methods, perhaps extending them, or bringing greater granularity to results. I view such introspection in Data Science circles as positive, likely to lead to improved methods and an indication of growing maturity in the field. It is however worth noting that, in some cases, leverage of Small-but-Well-Designed Data [4] is not only effective, but actually a superior approach. This is certainly something that Data Scientists should bear in mind.


I’d recommend taking a look at this site regularly. There is a high volume of articles and the quality is variable, but often there are some stand-out pieces.
See the original article for the details.
The article was in Scientific American and entitled Why Big Data Isn’t Necessarily Better Data.
I may have to copyright this term and of course the very elegant abridgement, SBWDD.



How to be Surprisingly Popular

Popular with the Crowd

This article is about the wisdom of the crowd [1], or more particularly its all too frequent foolishness. I am going to draw on a paper recently published in Nature by a cross-disciplinary team from the Massachusetts Institute of Technology and Princeton University. The authors are Dražen Prelec, H. Sebastian Seung and John McCoy. The paper’s title is A solution to the single-question crowd wisdom problem [2]. Rather than reinvent the wheel, here is a section from the abstract (with my emphasis):

Once considered provocative, the notion that the wisdom of the crowd is superior to any individual has become itself a piece of crowd wisdom, leading to speculation that online voting may soon put credentialed experts out of business. Recent applications include political and economic forecasting, evaluating nuclear safety, public policy, the quality of chemical probes, and possible responses to a restless volcano. Algorithms for extracting wisdom from the crowd are typically based on a democratic voting procedure. […] However, democratic methods have serious limitations. They are biased for shallow, lowest common denominator information, at the expense of novel or specialized knowledge that is not widely shared.

The Problems

The authors describe some compelling examples of where a crowd-based approach ignores the aforementioned specialised knowledge. I’ll cover a couple of these in a second, but let me first add my own.

How heavy is a proton?

Suppose we ask 1,000 people to come up with an estimate of the mass of a proton. One of these people happens to have won the Nobel Prize for Physics the previous year. Is the average of the estimates provided by the 1,000 people likely to be more accurate, or is the estimate of the one particularly qualified person going to be superior? There is an obvious answer to this question [3].

Lest it be thought that the above flaw in the wisdom of the crowd is confined to populations including a Nobel Laureate, I’ll reproduce a much more quotidian example from the Nature paper [4].

Philadelphia or Harrisburg?

[..] imagine that you have no knowledge of US geography and are confronted with questions such as: Philadelphia is the capital of Pennsylvania, yes or no? And, Columbia is the capital of South Carolina, yes or no? You pose them to many people, hoping that majority opinion will be correct. [in an actual exercise the team carried out] this works for the Columbia question, but most people endorse the incorrect answer (yes) for the Philadelphia question. Most respondents may only recall that Philadelphia is a large, historically significant city in Pennsylvania, and conclude that it is the capital. The minority who vote no probably possess an additional piece of evidence, that the capital is Harrisburg. A large panel will surely include such individuals. The failure of majority opinion cannot be blamed on an uninformed panel or flawed reasoning, but represents a defect in the voting method itself.

I’m both a good and bad example here. I know the capital of Pennsylvania is Harrisburg because I have specialist knowledge [5]. However my acquaintance with South Carolina is close to zero. I’d therefore get the first question right and have a 50 / 50 chance on the second (all other things being equal of course). My assumption is that Columbia is, in general, much more well-known than Harrisburg for some reason.

Confidence Levels

The authors go on to cover the technique that is often used to try to address this type of problem in surveys. Respondents are also asked how confident they are about their answer. Thus a tentative “yes” carries less weight than a definitive “yes”. However, as the authors point out, such an approach only works if correct responses are strongly correlated with respondent confidence. As is all too evident from real life, people are often both wrong and very confident about their opinion [6]. The authors extended their Philadelphia / Columbia study to apply confidence weightings, but with no discernible improvement.
A Surprisingly Popular Solution

As well as identifying the problem, the authors suggest a solution and later go on to demonstrate its efficacy. Again quoting from the paper’s abstract:

Here we propose the following alternative to a democratic vote: select the answer that is more popular than people predict. We show that this principle yields the best answer under reasonable assumptions about voter behaviour, while the standard ‘most popular’ or ‘most confident’ principles fail under exactly those same assumptions.

Let’s use the examples of capitals of states again here (as the authors do in the paper). As well as asking respondents, “Philadelphia is the capital of Pennsylvania, yes or no?” you also ask them “What percentage of people in this survey will answer ‘yes’ to this question?” The key is then to compare the actual survey answers with the predicted survey answers.

Columbia and Philadelphia [click to view a larger version in a new tab]

As shown in the above exhibit, in the authors’ study, when people were asked whether or not Columbia is the capital of South Carolina, those who replied “yes” felt that the majority of respondents would agree with them. Those who replied “no” symmetrically felt that the majority of people would also reply “no”. So no surprises there. Both groups felt that the crowd would agree with their response.

However, in the case of whether or not Philadelphia is the capital of Pennsylvania there is a difference. While those who replied “yes” also felt that the majority of people would agree with them, amongst those who replied “no”, there was a belief that the majority of people surveyed would reply “yes”. This is a surprise. People who make the correct response to this question feel that the wisdom of the crowd will be incorrect.

In the Columbia example, what people predict will be the percentage of people replying “yes” tracks with the actual response rate. In the Philadelphia example, what people predict will be the percentage of people replying “yes” is significantly less than the actual proportion of people making this response [7]. Thus a response of “no” to “Philadelphia is the capital of Pennsylvania, yes or no?” is surprisingly popular. The methodology that the authors advocate would then lead to the surprisingly popular answer (i.e. “no”) actually being correct; as indeed it is. Because there is no surprisingly popular answer in the Columbia example, then the result of a democratic vote stands; which is again correct.

To reiterate: a surprisingly popular response will overturn the democratic verdict, if there is no surprisingly popular response, the democratic verdict is unmodified.

Discriminating about Art

As well as confirming the superiority of the surprisingly popular approach (as opposed to either weighted or non-weighted democratic votes) with questions about state capitals, the authors went on to apply their new technique in a range of other areas [8].

  • Study 1 used 50 US state capitals questions, repeating the format [described above] with different populations [9].
  • Study 2 employed 80 general knowledge questions.
  • Study 3 asked professional dermatologists to diagnose 80 skin lesion images as benign or malignant.
  • Study 4 presented 90 20th century artworks [see the images above] to laypeople and art professionals, and asked them to predict the correct market price category.

Taking all responses across the four studies into account [10], the central findings were as follows [11]:

We first test pairwise accuracies of four algorithms: majority vote, surprisingly popular (SP), confidence-weighted vote, and max. confidence, which selects the answer endorsed with highest average confidence.

  • Across all items, the SP algorithm reduced errors by 21.3% relative to simple majority vote (P < 0.0005 by two-sided matched-pair sign test).
  • Across the items on which confidence was measured, the reduction was:
    • 35.8% relative to majority vote (P < 0.001),
    • 24.2% relative to confidence-weighted vote (P = 0.0107) and
    • 22.2% relative to max. confidence (P < 0.13).

The authors go on to further kick the tyres [12] on these results [13] without drawing any conclusions that deviate considerably from the ones they first present and which are reproduced above. The surprising finding is that the surprisingly popular algorithm significantly out-performs the algorithms normally used in wisdom of the crowd polling. This is a major result, in theory at least.
Some Thoughts

Tools and Toolbox

At the end of the abstract, the authors state that:

Like traditional voting, [the surprisingly popular algorithm] accepts unique problems, such as panel decisions about scientific or artistic merit, and legal or historical disputes. The potential application domain is thus broader than that covered by machine learning […].

Given the – justified – attention that has been given to machine learning in recent years, this is a particularly interesting claim. More broadly, SP seems to bring much needed nuance to the wisdom of the crowd. It recognises that the crowd may often be right, but also allows better informed minorities to override the crowd opinion in specific cases. It does this robustly in all of the studies that the authors conducted. It will be extremely interesting to see this novel algorithm deployed in anger, i.e. in a non-theoretical environment. If its undoubted promise is borne out – and the evidence to date suggests that it will be – then statisticians will have a new and powerful tool in their arsenal and a range of predictive activities will be improved.

The scope of applicability of the SP technique is as wide as that of any wisdom of the crowd approach and, to repeat the comments made by the authors in their abstract, has recently included:

[…] political and economic forecasting, evaluating nuclear safety, public policy, the quality of chemical probes, and possible responses to a restless volcano

If the author’s initial findings are repeated in “live” situations, then the refinement to the purely democratic approach that SP brings should elevate an already useful approach to being an indispensable one in many areas.

I will let the authors have a penultimate word [14]:

Although democratic methods of opinion aggregation have been influential and productive, they have underestimated collective intelligence in one respect. People are not limited to stating their actual beliefs; they can also reason about beliefs that would arise under hypothetical scenarios. Such knowledge can be exploited to recover truth even when traditional voting methods fail. If respondents have enough evidence to establish the correct answer, then the surprisingly popular principle will yield that answer; more generally, it will produce the best answer in light of available evidence. These claims are theoretical and do not guarantee success in practice, as actual respondents will fall short of ideal. However, it would be hard to trust a method [such as majority vote or confidence-weighted vote] if it fails with ideal respondents on simple problems like [the Philadelphia one]. To our knowledge, the method proposed here is the only one that passes this test.

US Presidential Election Polling [borrowed from Wikipedia]

The ultimate thought I will present in this article is an entirely speculative one. The authors posit that their method could be applied to “potentially controversial topics, such as political and environmental forecasts”, while cautioning that manipulation should be guarded against. Their suggestion leads me wonder what impact on the results of opinion polls a suitably formed surprisingly popular questionnaire would have had in the run up to both the recent UK European Union Referendum and the plebiscite for the US Presidency. Of course it is now impossible to tell, but maybe some polling organisations will begin to incorporate this new approach going forward. It can hardly make things worse.


According to Wikipedia, the phenomenon that:

A large group’s aggregated answers to questions involving quantity estimation, general world knowledge, and spatial reasoning has generally been found to be as good as, and often better than, the answer given by any of the individuals within the group.

The authors of the Nature paper question whether this is true in all circumstances.

Prelec, D., Seung, H.S., McCoy, J., (2017). A solution to the single-question crowd wisdom problem. Nature 541, 532–535.

You can view a full version of this paper care of Springer Nature SharedIt at the following link. ShareIt is Springer’s content sharing initiative.

Direct access to the article on Nature’s site (here) requires a subscription to the journal.

This example is perhaps an interesting rejoinder to the increasing lack of faith in experts in the general population, something I covered in Toast.

Of course the answer is approximately: 1.6726219 × 10-27 kg.

I have lightly edited this section but abjured the regular bracketed ellipses (more than one […] as opposed to conic sections as I note elsewhere). This is both for reasons of readability and also as I have not yet got to some points that the authors were making in this section. The original text is a click away.
My wife is from this state.
Indeed it sometimes seems that the more wrong the opinion, the more certain that people believe it to be right.

Here the reader is free to insert whatever political example fits best with their worldview.

Because many people replying “no” felt that a majority would disagree with them.
Again I have lightly edited this text.
To provide a bit of detail, here the team created a questionnaire with 50 separate questions sets of the type:

  1. {Most populous city in a state} is the capital of {state}: yes or no?
  2. How confident are you in your answer (50- 100%)?
  3. What percentage of people surveyed will respond “yes” to this question? (1 – 100%)

This was completed by 83 people split between groups of undergraduate and graduate students at both MIT and Princeton. Again see the paper for further details.

And eliding some nuances such as some responses being binary (yes/no) and others a range (e.g. the dermatologists were asked to rate the chance of malignancy on a six point scale from “absolutely uncertain to absolutely certain”). Also respondents were asked to provide their confidence in some studies and not others.
Once more with some light editing.
This is a technical term employed in scientific circles an I apologise if my use of jargon confuses some readers.
Again please see the actual paper for details.
Modified very slightly by my last piece of editing.




Acrylamide [borrowed from Wikipedia]


This blog touches on a wide range of topics, including social media, cultural transformation, general technology and – last but not least – sporting analogies. However, its primary focus has always been on data and information-centric matters in a business context. Having said this, all but the more cursory of readers will have noted the prevalence of pieces with a Mathematical or Scientific bent. To some extent this is a simple reflection of the author’s interests and experience, but a stronger motivation is often to apply learnings from different fields to the business data arena. This article is probably more scientific in subject matter than most, but I will also look to highlight some points pertinent to commerce towards the end.

In Science We Trust?

The topic I want to turn my attention to in this article is public trust in science. This is a subject that has consumed many column inches in recent years. One particular area of focus has been climate science, which, for fairly obvious political reasons, has come in for even more attention than other scientific disciplines of late. It would be distracting to get into the arguments about climate change and humanity’s role in it here [1] and in a sense this is just the latest in a long line of controversies that have somehow become attached to science. An obvious second example here is the misinformation circling around both the efficacy and side effects of vaccinations [2]. In both of these cases, it seems that at least a sizeable minority of people are willing to query well-supported scientific findings. In some ways, this is perhaps linked to the general mistrust of “experts” and “elites” [3] that was explicitly to the fore in the UK’s European Union Referendum debate [4].

“People in this country have had enough of experts”

– Michael Gove [5], at this point UK Justice Secretary and one of the main proponents of the Leave campaign, speaking on Sky News, June 2016.

Mr Gove was talking about economists who held a different point of view to his own. However, his statement has wider resonance and cannot be simply dismissed as the misleading sound-bite of an experienced politician seeking to press his own case. It does indeed appear that in many places around the world experts are trusted much less than they used to be and that includes scientists.

“Many political upheavals of recent years, such as the rise of populist parties in Europe, Donald Trump’s nomination for the American presidency and Britain’s vote to leave the EU, have been attributed to a revolt against existing elites.”

The Buttonwood column, The Economist, September 2016.

Why has this come to be?
A Brief [6] History of the Public Perception of Science

Public Perception

Note: This section is focussed on historical developments in the public’s trust in science. If the reader would like to skip on to more toast-centric content, then please click here.

Answering questions about the erosion of trust in politicians and the media is beyond the scope of this humble blog. Wondering what has happened to trust in science is firmly in its crosshairs. One part of the answer is that – for some time – scientists were held in too much esteem and the pendulum was inevitably going to swing back the other way. For a while the pace of scientific progress and the miracles of technology which this unleashed placed science on a pedestal from which there was only one direction of travel. During this period in which science was – in general – uncritically held in great regard, the messy reality of actual science was never really highlighted. The very phrase “scientific facts” is actually something of an oxymoron. What we have is instead scientific theories. Useful theories are consistent with existing observations and predict new phenomena. However – as I explained in Patterns patterns everywhere – a theory is only as good as the latest set of evidence and some cherished scientific theories have been shown to be inaccurate; either in general, or in some specific circumstances [7]. However saying “we have a good model that helps us explain many aspects of a phenomenon and predict more, but it doesn’t cover everything and there are some uncertainties” is a little more of a mouthful than “we have discovered that…”.

There have been some obvious landmarks along the way to science’s current predicament. The unprecedented destruction unleashed by the team working on the Manhattan Project at first made the scientists involved appear God-like. It also seemed to suggest that the path to Great Power status was through growing or acquiring the best Physicists. However, as the prolonged misery caused in Japan by the twin nuclear strikes became more apparent and as the Cold War led to generations living under the threat of mutually assured destruction, the standing attached by the general public to Physicists began to wane; the God-like mantle began to slip. While much of our modern world and its technology was created off the back of now fairly old theories like Quantum Chromodynamics and – most famously – Special and General Relativity, the actual science involved became less and less accessible to the man or woman in the street. For all the (entirely justified) furore about the detection of the Higgs Boson, few people would be able to explain much about what it is and how it fits into the Standard Model of particle physics.

In the area of medicine and pharmacology, the Thalidomide tragedy, where a drug prescribed to help pregnant women suffering from morning sickness instead led to terrible birth defects in more than 10,000 babies, may have led to more stringent clinical trials, but also punctured the air of certainty that had surrounded the development of the latest miracle drug. While medical science and related disciplines have vastly improved the health of much of the globe, the glacial progress in areas such as oncology has served as a reminder of the fallibility of some scientific endeavours. In a small way, the technical achievements of that apogee of engineering, NASA, were undermined by loss of crafts and astronauts. Most notably the Challenger and Columbia fatalities served to further remove the glossy veneer that science had acquired in the 1940s to 1960s.

Lest it be thought at this point that I am decrying science, or even being anti-scientific, nothing could be further from the truth. I firmly believe that the ever growing body of scientific knowledge is one of humankind’s greatest achievements, if not its greatest. From our unpromising vantage point on an unremarkable little planet in our equally common-all-garden galaxy we have been able to grasp many of the essential truths about the whole Universe from the incomprehensibly gigantic to the most infinitesimal constituent of a sub-atomic particle. However, it seems that many people do not fully embrace the grandeur of our achievements, or indeed in many cases the unexpected beauty and harmony that they have revealed [8]. It is to the task of understanding this viewpoint that I am addressing my thoughts.

More recently, the austerity that has enveloped much of the developed world since the 2008 Financial Crisis has had two reinforcing impacts on science in many countries. First funding has often been cut, leading to pressure on research programmes and scientists increasingly having to make an economic case for their activities; a far cry from the 1950s. Second, income has been effectively stagnant for the vast majority of people, this means that scientific expenditure can seem something of a luxury and also fuels the anti-elite feelings cited by The Economist earlier in this article.

Anita Makri

Into this seeming morass steps Anita Makri, “editor/writer/producer and former research scientist”. In a recent Nature article she argues that the form of science communicated in popular media leaves the public vulnerable to false certainty. I reproduce some of her comments here:

“Much of the science that the public knows about and admires imparts a sense of wonder and fun about the world, or answers big existential questions. It’s in the popularization of physics through the television programmes of physicist Brian Cox and in articles about new fossils and quirky animal behaviour on the websites of newspapers. It is sellable and familiar science: rooted in hypothesis testing, experiments and discovery.

Although this science has its place, it leaves the public […] with a different, outdated view to that of scientists of what constitutes science. People expect science to offer authoritative conclusions that correspond to the deterministic model. When there’s incomplete information, imperfect knowledge or changing advice — all part and parcel of science — its authority seems to be undermined. […] A popular conclusion of that shifting scientific ground is that experts don’t know what they’re talking about.”

– Anita Makri, Give the public the tools to trust scientists, Nature, January 2017.

I’ll come back to Anita’s article again later.
Food Safety – The Dangers Lurking in Toast

Food Safety

After my speculations about the reasons why science is held in less esteem than once was the case, I’ll return to more prosaic matters; namely food and specifically that humble staple of many a breakfast table, toast. Food science has often fared no better than its brother disciplines. The scientific guidance issued to people wanting to eat healthily can sometimes seem to gyrate wildly. For many years fat was the source of all evil, more recently sugar has become public enemy number one. Red wine was meant to have beneficial effects on heart health, then it was meant to be injurious; I’m not quite sure what the current advice consists of. As Makri states above, when advice changes as dramatically as it can do in food science, people must begin to wonder whether the scientists really know anything at all.

So where does toast fit in? Well the governmental body charged with providing advice about food in the UK is called the Food Standards Agency. They describe their job as “using our expertise and influence so that people can trust that the food they buy and eat is safe and honest.” While the FSA do sterling work in areas such as publicly providing ratings of food hygiene for restaurants and the like, their most recent campaign is one which seems at best ill-advised and at worst another nail in the public perception of the reliability of scientific advice. Such things matter because they contribute to the way that people view science in general. If scientific advice about food is seen as unsound, surely there must be questions around scientific advice about climate change, or vaccinations.

Before I am accused of belittling the FSA’s efforts, let’s consider the campaign in question, which is called Go for Gold and encourages people to consume less acrylamide. Here is some of what the FSA has to say about the matter:

“Today, the Food Standards Agency (FSA) is launching a campaign to ‘Go for Gold’, helping people understand how to minimise exposure to a possible carcinogen called acrylamide when cooking at home.

Acrylamide is a chemical that is created when many foods, particularly starchy foods like potatoes and bread, are cooked for long periods at high temperatures, such as when baking, frying, grilling, toasting and roasting. The scientific consensus is that acrylamide has the potential to cause cancer in humans.


as a general rule of thumb, aim for a golden yellow colour or lighter when frying, baking, toasting or roasting starchy foods like potatoes, root vegetables and bread.”

– Food Standards Agency, Families urged to ‘Go for Gold’ to reduce acrylamide consumption, January 2017.

The Go for Gold campaign was picked up by various media outlets in the UK. For example the BBC posted an article on its web-site which opened by saying:

Dangerous Toast [borrowed from the BBC]

“Bread, chips and potatoes should be cooked to a golden yellow colour, rather than brown, to reduce our intake of a chemical which could cause cancer, government food scientists are warning.”

– BBC, Browned toast and potatoes are ‘potential cancer risk’, say food scientists, January 2017.

The BBC has been obsessed with neutrality on all subjects recently [9], but in this case they did insert the reasonable counterpoint that:

“However, Cancer Research UK [10] said the link was not proven in humans.”

Acrylamide is certainly a nasty chemical. Amongst other things, it is used in polyacrylamide gel electrophoresis, a technique used in biochemistry. If biochemists mix and pour their own gels, they have to monitor their exposure and there are time-based and lifetime limits as to how often they can do such procedures [11]. Acrylamide has also been shown to lead to cancer in mice. So what could be more reasonable that the FSA’s advice?
Food Safety – A Statistical / Risk Based Approach

David Spiegelhalter

Earlier I introduced Anita Makri, it is time to meet our second protagonist, David Spiegelhalter, Winton Professor for the Public Understanding of Risk in the Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge [12]. Professor Spiegelhalter has penned a response to the FSA’s Go for Gold campaign. I feel that this merits reading in entirety, but here are some highlights:

“Very high doses [of Acrylamide] have been shown to increase the risk of mice getting cancer. The IARC (International Agency for Research on Cancer) considers it a ‘probable human carcinogen’, putting it in the same category as many chemicals, red meat, being a hairdresser and shift-work.

However, there is no good evidence of harm from humans consuming acrylamide in their diet: Cancer Research UK say that ‘At the moment, there is no strong evidence linking acrylamide and cancer.’

This is not for want of trying. A massive report from the European Food Standards Agency (EFSA) lists 16 studies and 36 publications, but concludes

  ‘In the epidemiological studies available to date, AA intake was not associated with an increased risk of most common cancers, including those of the GI or respiratory tract, breast, prostate and bladder. A few studies suggested an increased risk for renal cell, and endometrial (in particular in never-smokers) and ovarian cancer, but the evidence is limited and inconsistent. Moreover, one study suggested a lower survival in non-smoking women with breast cancer with a high pre-diagnostic exposure to AA but more studies are necessary to confirm this result. (p185)’


[Based on the EFSA study] adults with the highest consumption of acrylamide could consume 160 times as much and still only be at a level that toxicologists think unlikely to cause increased tumours in mice.


This all seems rather reassuring, and may explain why it’s been so difficult to observe any effect of acrylamide in diet.”

– David Spiegelhalter, Opinion: How dangerous is burnt toast?, University of Cambridge, January 2017.

Indeed, Professor Spiegelhalter, an esteemed statistician, also points out that most studies will adopt the standard criteria for statistical significance. Given that such significance levels are often set at 5%, then this means that:

“[As] each study is testing an association with a long list of cancers […], we would expect 1 in 20 of these associations to be positive by chance alone.”

He closes his article by stating – not unreasonably – that the FSA’s time and attention might be better spent on areas where causality between an agent and morbidity is well-established, for example obesity. My assumption is that the FSA has a limited budget and has to pick and choose what food issues to weigh in on. Even if we accept for the moment that there is some slight chance of a causal link between the consumption of low levels of acrylamide and cancer, there are plenty of other areas in which causality is firmly established; obesity as mentioned by Professor Spiegelhalter, excessive use of alcohol, even basic kitchen hygiene. It is hard to understand why the FSA did not put more effort into these and instead focussed on an area where the balance of scientific judgement is that there is unlikely to be an issue.

Having a mathematical background perhaps biases me, but I tend to side with Professor Spiegelhalter’s point of view. I don’t want to lay the entire blame for the poor view that some people have of science at the FSA’s door, but I don’t think campaigns like Go for Gold help very much either. The apocryphal rational man or woman will probably deduce that there is not an epidemic of acrylamide poisoning in progress. This means that they may question what the experts at the FSA are going on about. In turn this reduces respect for other – perhaps more urgent – warnings about food and drink. Such a reaction is also likely to colour how the same rational person thinks about “expert” advice in general. All of this can contribute to further cracks appearing in the public edifice of science, an outcome I find very unfortunate.

So what is to be done?
A Call for a New and More Honest Approach to Science Communications

Honesty is the Best Policy

As promised I’ll return to Anita Makri’s thoughts in the same article referenced above:

“It’s more difficult to talk about science that’s inconclusive, ambivalent, incremental and even political — it requires a shift in thinking and it does carry risks. If not communicated carefully, the idea that scientists sometimes ‘don’t know’ can open the door to those who want to contest evidence.


Scientists can influence what’s being presented by articulating how this kind of science works when they talk to journalists, or when they advise on policy and communication projects. It’s difficult to do, because it challenges the position of science as a singular guide to decision making, and because it involves owning up to not having all of the answers all the time while still maintaining a sense of authority. But done carefully, transparency will help more than harm. It will aid the restoration of trust, and clarify the role of science as a guide.”

The scientific method is meant to be about honesty. You record what you see, not what you want to see. If the data don’t support your hypothesis, you discard or amend your hypothesis. The peer-review process is meant to hold scientists to the highest levels of integrity. What Makri seems to be suggesting is for scientists to turn their lenses on themselves and how they communicate their work. Being honest where there is doubt may be scary, but not as scary as being caught out pushing certainty where no certainty is currently to be had.


At the beginning of this article, I promised that I would bring things back to a business context. With lots of people with PhDs in numerate sciences now plying their trade as data scientists and the like, there is an attempt to make commerce more scientific [13]. Understandably, the average member of a company will have less of an appreciation of statistics and statistical methods than their data scientists do. This can lead to data science seeming like magic; the philosopher’s stone [14]. There are obvious parallels here with how Physicists were seen in the period immediately after the Second World War.

Earlier in the text, I mused about what factors may have led to a deterioration in how the public views science and scientists. I think that there is much to be learnt from the issues I have covered in this article. If data scientists begin to try to peddle absolute truth and perfect insight (both of which, it is fair to add, are often expected from them by non-experts), as opposed to ranges of outcomes and probabilities, then the same decline in reputation probably awaits them. Instead it would be better if data scientists heeded Anita Makri’s words and tried to always be honest about what they don’t know as well as what they do.


Save to note that there really is no argument in scientific circles.

As ever Randall Munroe makes the point pithily in his Earth Temperature Timeline –

For a primer on the area, you could do worse than watching The Royal Society‘s video:

For the record, my daughter has had every vaccine known to the UK and US health systems and I’ve had a bunch of them recently as well.
Most scientists I know would be astonished that they are considered part of the amorphous, ill-defined and obviously malevolent global “elite”. Then “elite” is just one more proxy for “the other” something which it is not popular to be in various places in the world at present.
Or what passed for debate in these post-truth times.
Mr Gove studied English at Lady Margaret Hall, Oxford, where he was also President of the Oxford Union. Clearly Oxford produces less experts than it used to in previous eras.
One that is also probably wildly inaccurate and certainly incomplete.
So Newton’s celebrated theory of gravitation is “wrong” but actually works perfectly well in most circumstances. The the Rutherford–Bohr model, where atoms are little Solar Systems, with the nucleus circled by electrons much as the planets circle the Sun is “wrong”, but actually does serve to explain a number of things; if sadly not the orbital angular momentum of electrons.
Someone should really write a book about that – watch this space!
Not least in the aforementioned EU Referendum where it felt the need to follow the views of the vast majority of economists with those of the tiny minority, implying that the same weight be attached to both points of view. For example, 99.9999% of people believe the world to be round, but in the interests of balance my mate Jim reckons it is flat.
According to their web-site: “the world’s leading charity dedicated to beating cancer through research”.
As attested to personally by the only proper scientist in our family.
Unlike Oxford (according to Mr Gove anyway), Cambridge clearly still aspires to creating experts.
By this I mean proper science and not pseudo-science like management theory and the like.
In the original, non-J.K. Rowling sense of the phrase.



Indiana Jones and The Anomalies of Data

One of an occasional series [1] highlighting the genius of Randall Munroe. Randall is a prominent member of the international data community and apparently also writes some sort of web-comic as a side line [2].

I didn't even realize you could HAVE a data set made up entirely of outliers.

Data and Indiana Jones, these are a few of my favourite things… [3] Indeed I must confess to having used a variant of the image below in each of my seminar deck and – on this site back in 2009 – a previous article, A more appropriate metaphor for Business Intelligence projects.

Raiders of the Lost Ark II would have been a much better title than Temple of Doom IMO

In both cases I was highlighting that data-centric work is sometimes more like archaeology than the frequently employed metaphor of construction. To paraphrase myself, you never know what you will find until you start digging. The image suggested the unfortunate results of not making this distinction when approaching data projects.

So, perhaps I am arguing for less Data Architects and more Data Archaeologists; the whip and fedora are optional of course!


Well not that occasional as, to date, the list extends to:

  1. Patterns patterns everywhere – The Sequel
  2. An Inconvenient Truth
  3. Analogies, the whole article is effectively an homage to
  4. A single version of the truth?
  5. Especially for all Business Analytics professionals out there
  6. New Adventures in Wi-Fi – Track 1: Blogging
  7. Business logic [My adaptation]
  8. New Adventures in Wi-Fi – Track 2: Twitter
  9. Using historical data to justify BI investments – Part III
[2] if you must ask.
Though in this case, my enjoyment would have been further enhanced by the use of “artefacts” instead.



More Statistics and Medicine

Weighing Medicine in the balance

I wrote last on the intersection of these two disciplines back in March 2011 (Medical Malpractice). What has prompted me to return to the subject is some medical tests that I was offered recently. If the reader will forgive me, I won’t go into the medical details – and indeed have also obfuscated some of the figures I was quoted – but neither are that relevant to the point that I wanted to make. This point relates to how statistics are sometimes presented in medical situations and – more pertinently – the disconnect between how these may be interpreted by the man or woman in the street, as opposed to what is actually going on.

Rather than tie myself in knots, let’s assume that the test is for a horrible disease called PJT Syndrome [1]. Let’s further assume that I am told that the test on offer has an accuracy of 80% [2]. This in and of itself is a potentially confusing figure. Does the test fail to detect the presence of PJT Syndrome 20% of the time, or does it instead erroneously detect PJT Syndrome, when the patient is actually perfectly healthy, 20% of the time? In this case, after an enquiry, I was told that a negative result was a negative result, but that a positive one did not always mean that the subject suffered from PJT Syndrome; so the issue is confined to false positives, not false negatives. This definition of 80% accuracy is at least a little clearer.

So what is a reasonable person to deduce from the 80% figure? Probably that if they test positive, that there is an 80% certainty that they have PJT Syndrome. I think that my visceral reaction would probably be along those lines. However, such a conclusion can be incorrect, particularly where the incidence of PJT Syndrome is low in a population. I’ll try to explain why.

If we know that PJT Syndrome occurs in 1 in every 100 people on average, what does this mean for the relevance of our test results? Let’s take a graphical look at a wholly representative population of exactly 100 people. The PJT Syndrome sufferer appears in red at the bottom right.

1 in 100

Now what is the result of the 80% accuracy of our test, remembering that this means that 20% of people taking it will be falsely diagnosed as having PJT Syndrome? Well 20% of 100 is – applying a complex algorithm – approximately 20 people. Let’s flag these up on our population schematic in grey.

20 in 100

So 20 people have the wrong diagnosis. One is correctly identified as having PJT Syndrome and 79 are correctly identified as not having PJT Syndrome; so a total of 80 have the right diagnosis.

What does this mean for those 21 people who have been unfortunate enough to test positive for PJT Syndrome (the one person coloured red and the 20 coloured grey)? Well only one of them actually has the malady. So, if I test positive, my chances of actually having PJT Syndrome are not 80% as we originally thought, but instead 1 in 21 or 4.76%. So my risk is still low having tested positive. It is higher than the risk in the general population, which is 1 in 100, or 1%, but not much more so.

The problem arises if having a condition is rare (here 1 in 100) and the accuracy of a test is low (here it is wrong for 20% of people taking it). If you consider that the condition that I was being offered a test for actually has an incidence of around 1 in 20,000 people, then with an 80% accurate test we would get the following:

  1. In a population of 20,000 one 1 person has the condition
  2. In the same population a test with our 80% accuracy means that 20% of people will test positive for it when they are perfectly healthy, this amounts to 4,000 people
  3. So in total, 4,001 people will test positive, 1 correctly, 4,000 erroneously
  4. Which means that a positive test tells me my odds of having the condition being tested for are 1 in 4,001, or 0.025%; still a pretty unlikely event

Low accuracy tests and rare conditions are a very bad combination. As well as causing people unnecessary distress, the real problem is where the diagnosis leads potential suffers to take actions (e.g. undergoing further diagnosis, which could be invasive, or even embarking on a course of treatment) which may themselves have the potential to cause injury to the patient.

I am not of course suggesting that people ignore medical advice, but Doctors are experts in medicine and not statistics. When deciding what course of action to take in a situation similar to one I recently experienced, taking the time to more accurately assess risks and benefits is extremely important. Humans are well known to overestimate some risks (and underestimate others), there are circumstances when crunching the numbers and seeing what they tell you is not only a good idea, it can help to safeguard your health.

For what it’s worth, I opted out of these particular tests.


A terrible condition which renders sufferers unable to express any thought in under 1,000 words.
Not the actual figure quoted, but close to it.