Following on from the optical illusions that I featured earlier in the week, here is another picture with something subtly (or perhaps not so subtly) wrong with it. Can you spot what?
Author: Peter James Thomas
The triangle paradox
This seems to be turning into Mathematics week at peterjamesthomas.com. The “paradox” shown in the latter part of this article was presented to the author and some of his work colleagues at a recent seminar. It kept company with some well-know trompe l’œil such as:
and
and
However the final item presented was rather more worrying as it seemed to be less related to the human eye’s (or perhaps more accurately the human brain’s) ability to discern shape from minimal cues and more to do with mathematical fallacy. The person presenting these images (actually they were slightly different ones, I have simplified the problem) claimed that they themselves had no idea about the solution.
Consider the following two triangles:
The upper one has been decomposed into two smaller triangles – one red, one green – a blue rectangle and a series of purple squares.
These shapes have then been rearranged to form the lower triangle. But something is going wrong here. Where has the additional white square come from?
Without even making recourse to Gödel, surely this result stabs at the heart of Mathematics. What is going on?
After a bit of thought and going down at least one blind alley, I managed to work this one out (and thereby save Mathematics single-handedly). I’ll publish the solution in a later article. Until then, any suggestions are welcome.
For those who don’t want to think about this too much, the solution has now been posted here.
Half full, or half empty?
Someone being described as a “glass half-full” or “glass half-empty” sort of person is something that one hears increasingly frequently. I was recently discussing this with a friend and we both agreed that the analogy was unhelpful. First it supports a drastically simplistic and binary view of people having fixed attitudes and behaviours in all circumstances. Day-to-day observation suggests on the contrary that a person my be an avid optimist one day about one thing and a manic pessimist the next day about another thing. This rather shallow type of characterisation rather reminds me of some of the subjects I touched on in The Big Picture and Pigeonholing – A tragedy some time ago.
However, there is a more fundamental consideration; wilful inaccuracy. A glass that is half empty is also half full; that’s the definition of a half. Either description is 100% valid and therefore logically can tell you nothing about the person’s mindset.
Instead what might be more apposite is to adopt a different way to divide sheep from goats. This is still rather too binary for my taste, but at least it has the merit of a greater degree of rigour. I propose dividing people according to how they view a glass that is three quarters empty:
- I still have some left: optimist
- There isn’t very much left: pessimist
I think that all of our lives would be much the better for adopting this simple principle.
Accordingly, I am going to submit this recommendation to the International Standards Organisation for their urgent consideration. I’ll make sure that I keep readers up-to-date with how my submission progresses.
An informed decision
A friend and fellow information professional is currently responsible for both building a new data warehouse and supporting its predecessor, which is based on a different technology platform. In these times of ever-increasing focus on costs, she had been asked to port the old warehouse to the new platform, thereby avoiding some licensing payments. She asked me what I thought about this idea and we chatted for a while. For some reason, our conversation went off at a bit of a tangent and I started to tell her the story of an acquaintance of mine and his recent sad experiences.
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My acquaintance, let’s call him Jim to avoid causing any embarassment, had always been interested in cars; driving them, maintaining them, souping them up, endlessly reading car magazines and so on. His dream had always been to build his own car and his eye had always been on a Caterham kit. I suppose for him the pleasure of making a car was at least as great, if not more, as the pleasure of driving one.
Jim saved his pennies and eventually got together enough cash to embark on his dream project. Having invested his money, he started to also invest his time and effort. However, after a few weeks of toil, he hit a snag. It was nothing to do with his slowly emerging Caterham, but to do with the more quotidian car he used for his daily commute to work. Its engine had developed a couple of niggles that had been resistant to his own attempts to fix them and he had reluctantly decided that it was in need of some new parts and quite expensive ones at that. Jim had already spent quite a bit of cash on the Caterham and more on some new tools that he needed to assemble it. The last thing he wanted to do now was to have a major outlay on his old car; particularly because, once the Caterham was finished, he had planned to trade it for its scrap-metal worth.
But now things got worse, Jim’s current car failed its MOT (vehicle safety inspection for any non-UK readers) because the faulty engine did not meet emission standards. However, one of his friends came up with a potential solution. He said, “As you have already assembled the Caterham engine, why not put this into your current car and use this instead? You can then swap it out into the Caterham chassis and body when you have built this.”
This sounded like a great idea to Jim, but there were some issues with it. His Cateham was supplied with a Cosworth-developed 2.3-litre Ford Duratec engine. This four-cylinder twin cam unit was the wrong size and shape to fit into the cavity left by removing the worn-out engine from his commuting car. Well as I had mentioned at the start, Jim was a pretty competent amateur mechanic and he thought that he had a good chance of rising to the challenge. He was motivated by the thought of not having to shell out extra cash and in any case he loved tinkering with cars.
So he put in some new brackets to hold the Caterham engine. He then had to grind-down a couple of protruding pieces of the Duratec block to gain the extra 5 mm necessary to squeeze it in. The fuel feeds were in the wrong place, but a bit of plumbing and that was also sorted. Perhaps this might cause an issue with efficiency of the engine burn cycle, but Jim figured that it would probably be OK. Next the vibration dampers were not really up to the job of dealing with the more powerful engine and neither was the exhaust system. No worries, thought Jim, a tap of a hammer here, a bend of a pipe here and he could also add in a couple of components that had been sitting at the back of his garage rusting for years as well. Eventually everything seemed fine.
Jim ventured out of his garage in his old car, with its new engine. He was initially a bit trepidatious, but his work seemed to be hanging together. Sure the car was making a bit of a noise, shaking a bit and the oil temperature seems a bit high, but Jim felt that these were only minor problems. He told himself that all his handiwork had to do was to hang together for a few more months until he finished the rest of the Caterham.
With these nice thoughts in mind, Jim approached a bend. The car flew off the road at a tangent as he realised – too late – that he had been travelling at Caterham speeds into the corner and didn’t have a Caterham chassis, a Caterham suspension, or Caterham brakes. His old car was not up to dealing with the forces created in the turn. His tyres failed to grip and, after what seemed like an eternity of slow-motion spinning and screeching and panic, he find himself in a ditch; healthy, but with a wheel sheared off and smoke coming out of the front of the car. A later inspection confirmed that his commuting car was a write-off, and his insurance policy didn’t fully cover the cost of a new vehicle.
Jim ended up having to buy another day-to-day car, which delayed him from spending the additional money necessary to get the Caterham on the road for quite some time. However, after scrimping and saving for a while, he eventually got back to his dream project, only to find that combination of the modifications he had to make to the Duratec engine, plus the after effects of the crash meant that it was now useless and he needed to purchase a replacement.
So because Jim didn’t want to run to the expense of maintaining his old car while he built his new one, he would instead have to buy a new temporary car plus a new engine for the Caterham. Jim was just as far off from finishing the Caterham as when he had started, despite wasting a lot of time and money along the way. A very sad story.
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Suddenly I realised that I had been wittering on about a wholly unrelated subject to my friend’s data warehousing problem. I apologised and turned the conversation back to this. To my astonishment, she told me that she had already made up her mind. I suppose she had taken advantage of the length of time I had spent telling Jim’s story to more profitably weigh the pros and cons of different approaches in her mind and thereby had reached her decision. Anyway, she thanked me for my help, I protested that I hadn’t really offered her any and we each went our separate ways.
I found out later she had decided to pay the maintenance costs on the old data warehouse.
I would like to apologise in advance if anyone at Caterham, Cosworth, Ford, or indeed Peugeot, takes offence to any of the content of the above story or its illustrations. I’m sure that you make very fine products and this article isn’t really about any of them.
I will be presenting at the IRM European Data Governance Conference
This IRM UK event will be taking place in central London from the 21st to 23rd March 2011. It is co-located with another related IRM conferences on Master Data Management.
My presentation will be entitled Making Business Intelligence an Integral part of your Data Quality Programme. Full details may be obtained from the IRM conference web-site here.
Medical malpractice
I was listening to a discussion with two medical practitioners on the radio today while driving home from work. I’ll remove the context of the diseases they were debating as the point I want to make is not specifically to do with this aspect and dropping it removes a degree of emotion from the conversation. The bone of contention between the two antagonists was the mortality rate from a certain set of diseases in the UK and whether this was to do with the competency of general practitioners (GPs, or “family doctors” for any US readers) and the diagnostic procedures they use, or to do with some other factor.
In defending her colleagues from the accusations of the first interviewee, the general practitioner said that the rate of mortality for sufferers of these diseases in other European countries (she specifically cited Belgium and France) was greater than in the UK. I should probably pause at this point to note that this comment seemed the complete opposite of every other European health survey I have read in recent years, but we will let that pass and instead focus on the second part of her argument. This was that that better diagnoses would be made if the UK hired more doctors (like her), thereby allowing them to spend more time with each patient. She backed up this assertion by then saying that France has many more doctors per 1,000 people than the UK (the figures I found were 3.7 per 1,000 for France and 2.2 per 1,000 for the UK; these were totally different to the figures she quoted, but again I’ll let that pass as she did seem to at least have the relation between the figures in each country the right way round this time).
What the GP seemed to be saying is summarised in the following chart:
I have no background in medicine, but to me the lady in question made the opposite point to the one she seemed to want to. If there are fewer doctors per capita in the UK than in France, but UK mortality rates are better, it might be more plausible to argue that less doctors implies better survival rates; this is what the above chart suggests. Of course this assertion is open to challenge and – as with most statistical phenomena – there are undoubtedly many other factors. There is also of course the old chestnut of correlation not implying causality (not that the above chart even establishes correlation). However, at the very least, the “facts” as presented did not seem to be a prima facie case for hiring more UK doctors.
Sadly for both the GP in question and for inhabitants of the UK, I think that the actual graph is more like:
This exhibit could perhaps suggest that the second doctor had a potential point, but such simplistic observations, much as we may love to make them, do not always stand up to rigorous statistical analysis. Statistical findings can be as counter-intuitive as many other mathematical results.
Speaking of statistics, when challenged on whether she had the relative mortality rates for France and the UK the right way round, the same GP said, “well you can prove anything with statistics.” We hear this phrase so often that I guess many of us come to believe it. In fact it might be more accurate to say, “selection bias is all pervasive”, or perhaps even “innumeracy will generally lead to erroneous conclusions being drawn.”
When physicians are happy to appear on national radio and exhibit what is at best a tenuous grasp of figures, one can but wonder about the risk of numerically-based medical decisions sometimes going awry. With doctors also increasingly involved in public affairs (either as expert advisers or – in the UK at least – often as members of parliament), perhaps these worries should also be extended into areas of policy making.
Even more fundamentally (but then as an ex-Mathematician I would say this), perhaps the UK needs to reassess how it teaches mathematics. Also maybe UK medical schools need to examine numeric proficiency again just before students graduate as well as many years earlier when candidates apply; just in case something in the process of producing new doctors has squeezed their previous mathematical ability out of them.
Before I begin to be seen as an opponent of the medical profession, I should close by asking a couple of questions that are perhaps closer to home for some readers. How many of the business decisions that are taken using information lovingly crafted by information professionals such as you and me are marred by an incomplete understanding of numbers on the part of [hopefully] a small subsection of users? As IT professionals, what should we be doing to minimise the likelihood of such an occurrence in our organisations?
Projects
At the risk of over-extending the business metaphor offered by rock climbing (and the even greater risk of boring readers who don’t have the slightest interest in my climbing rehabilitation), here is a brief update on my injury situation; closing with the normal technology-focussed twist. I suppose that part of my motivation in composing this piece lies in the fact that some of my recent climbing-related writing has been on the negative side; albeit focusing on business lessons that can be gleaned from my past rock climbing mistakes. Instead this article adopts a more positive tone looking for ways in which signs of progress in a sport can set you up for professional success.
I have previously explained how I managed to injure my hand climbing a while back. Given the horrendous popping noise my left ring finger made when I hurt it, it is a reasonable assumption that I have a partial pulley tear. Having already not climbed at any serious level for some time, this injury kept me away from both rock and wall for several months. On the odd occasion that I did climb, it was a rather tentative and worried affair. Part of me felt that I would not ever be able to climb even adequately again; part of me didn’t want to get a hand surgeon’s opinion, lest it confirmed my worst fears. This was not a great mental attitude to adopt obviously and I rather felt that a chunk of my life was missing, or at least going badly.
However, having recently relocated to Cambridge (England not Massachusetts), my partner and I discovered the Kelsey Kerridge Sports Centre and learnt that their indoor climbing wall was in the process of being extended and upgraded. Just before Christmas we went along, to be honest without any great expectations; either of the wall or the standard of my climbing. However we were pleasantly surprised by a relatively extensive and modern facility and some very well-set and interesting problems (for an explanation of why climbs in bouldering are called problems and indeed a definition of bouldering, see Perseverance). Another plus is that many of these used plastic holds (manufactured by Sheffield’s Core Climbing) that were quite friendly to injured fingers; or at least at the lowly grades that I was initially climbing at.
Since first going we have become regulars and even interspersed a couple of trips to our old London climbing haunt of The Arch. I have been taking the (probably psychological) precaution of using climbing finger tape to bind up the damaged area. I learnt my lesson and started on easy ground with little potential to aggravate my finger. The build up to harder climbing (for me) was measured, despite a growing desire to push myself. So far, despite a couple of twinges, it has been going OK.
The quality of setting at Kelsey Kerridge has been such that, though not much has changed at the wall since mid-December, as my climbing has steadily improved, I have been able to find more interesting problems at the next level. Indeed I seem to have found a number of projects (again see Perseverance for a definition), at an increasing level of difficulty and which have taken between two and five sessions to finally crack.
Two sessions ago, I finally got up my first indoor V4 in literally years. This was something of a landmark not only because it means that I am getting back to the vicinity of where I was pre-injuries, but more specifically as the problem requires a big, dynamic move onto a small edge for my damaged left hand. It even began to feel quite comfortable making this move after a while.
This video is of me on a V3 problem at Kelsey Kerridge
Even now, I am still taking to heart the learnings that I pointed out in earlier articles and am not trying to push things too quickly. However, I am have now completed several climbs that I could not even pull onto a few weeks back and have some harder projects on which I am making significant and somewhat surprising progress.
It feels good to be back climbing at any level and even better that my hand is – [undamaged] fingers-crossed – holding up so far. A positive learning here is that when you feel at a low ebb – as inevitably happens to the most enthusiastic of project managers, running the most dynamic and important of projects – maybe the physical act of doing something is the best antidote. Even if what you do does not work out immediately, it may provide you with other ideas that might be more successful.
Contemporaneous to this climbing progress, I am taking on new challenges in my work life. At least for me, success on climbing projects gives me a great fillip when thinking about the longer term projects I face in a work context. Success in one area of life can be contagious. Making slow, but steady progress at the wall makes me feel that many things are possible in my professional arena. It is nice to be back in what I hope will continue to be a virtuous circle.
For anyone interested in other analogies I have drawn between climbing and business and technology issues, here is a list in chronological order:
- Perseverance
- A bad workman blames his [Business Intelligence] tools
- Running before you can walk
- Feasibility studies continued…
- Incremental Progress and Rock Climbing
How to use your BI Tool to Highlight Deficiencies in Data
My interview with Microsoft’s Bruno Aziza (@brunoaziza), which I trailed in Another social media-inspired meeting, was published today on his interesting and entertaining bizintelligence.tv site.
You can take a look at the canonical version here and the YouTube version appears below:
The interview touches on themes that I have discussed in:
Thanks to Jim Harris’ OCDQ Blog
I would like to start 2011 by thanking Jim Harris for selecting one of my articles – Who should be accountable for data quality? – as a Best Data Quality Blog Post Of 2010 on his Obsessive Compulsive Data Quality blog.
I would recommend Jim’s excellent site as a great repository for current thinking and best practise in this crucial area.
Some thoughts on the IRM(UK) DW/BI conference
As previously advertised, I presented at the recent IRM(UK) DW/BI seminar in London. As a speaker I was entitled to attend the full three days, but as is typically the case, other work commitments meant that I only went along on the day of my session, 4th November. A mixture of running into business acquaintances, making sure that audio/visual facilities work and last minute run-throughs of my slides all conspired to ensure that I was able to listen to fewer talks that I would have liked. In comparing notes with other speakers, it is generally the same for them. Maybe I should consider attending a seminar as a delegate sometime!
Nevertheless, I did get along to some presentations and also managed to finally meet Dylan Jones of dataqualitypro.com (@DataQualityPro) in person after running into each other virtually for years. Unfortunatlely, I also managed to fail to connect with a number of tweeps of my acquaintance including: Loretta Mahon Smith (@silverdata) – who even attended my talk without us bumping into each other – and Scott Davis (@scottatlyzasoft); I guess that is just how it goes with seminars sometimes.
Story-telling and Information Quality
At face value these may seem odd bed-fellows. However, Lori Silverman of Partners for Progress managed to intertwine the two effectively. This was despite being handicapped by an attack of laryngitis that meant that her, already somewhat nasal tones, from time to time morphed into a shriek. Sitting as I was directly beside a loudspeaker, I felt some initial discomfort and even considered departing for a less auricularly challenged part of the conference centre. However I was glad that I decided to tough it out because Lori turned out to be a very entertaining, engaging and insightful speaker. I won’t steal her thunder by revealing her main thesis and instead suggest that you try to catch her speaking at some future point, she is well worth listening to in my opinion.
Open Source BI makes headway in the Irish Government sector
I next attended a presentation by leading open source BI company Jaspersoft. This was kicked-off by their CEO Brian Gentile who then introduced a case study about an Irish Government department rolling-out the company’s products. The implementer, was System Dynamics, Ireland’s largest indigenous IT business solutions company*.
System Dynamics CEO Tony McGuire and BI Team Lead Emmet Burke both spoke about this recent project, which covered 500+ users. Open source has traditionally had something of a challenge establishing a foothold in the public sector. The assertion made in this session was that the current fiscal challenges faced by the Irish Republic meant that it was becoming an option they were giving greater credence to. I guess, as with many areas of open source applications, it is probably a case of waiting to see whether a trend establishes itself.
John Taylor of Information Builders was speaking in the room that would next host my session and so I was able to catch the last 15 minutes of his presentation on Information Management, which seemed to have been well-attended and well-received.
Measuring the benefits of BI
My presentation occupied the graveyard slot of 4:30pm and I led by saying that I fully realised that all that stood between delegates and the drinks reception was my talk. Given the lateness of the hour, I had been a little concerned about attendance, but I guess that there were at least 50 or so people present. All of them stuck it out to the bitter end, which was gratifying.
There is always the moment of frisson in public speaking when, at the end of the talk, you ask whether are any questions with an image of tumbleweed spinning across the prairie in your mind (something that happened to me on one previous occasion a long time ago). Thankfully the audience asked a number of interesting and insightful questions, which I answered to the best of my ability. Indeed I was locked in discussions with a couple of delegates long after the meeting had officially broken up.
In my introduction, I began by issuing my customary caveat about the danger of too blindly following any recipe for success. I then provided some background about my first major achievement in data warehousing and went on to present the general framework for success in BI/DW programmes that I developed as a result of this. In concluding the first part of the speech, I attempted to delineate the main benefits of BI and also touched on some of its limitations.
Having laid these hopefully substantial foundations, the meat of the presentation expanded on ideas I briefly touched on in my earlier article Measuring the Benefits of Business Intelligence. This included highlighting some of the reasons why measuring the impact of BI on, say, profitability can be a challenge, but stressing that this was still often an objective that it was possible to achieve. I also spent some time examining in detail different techniques for quantifying the different tangible and intangible impacts of BI (most of which are covered in the above referenced article).
My closing thought was that, in situations where it is difficult to precisely assess the monetary impact of BI, the wholehearted endorsement of your business customers can be a the best indirect measurement of the success (or otherwise) of your work. I would recommend that fellow BI professionals pay close attention to this important indicator at all stages of their projects.
You can view some of the tweets about IRM(UK) DW/BI here, or here.
Disclosure: At the time of writing, System Dynamics is a business partner, but not in the field of business intelligence.
Peter James Thomas 