- IFRS 17
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- IFRS 17
- News and Views
The Lighter Side
To celebrate the weekend, MBE digs up an interesting piece of finance trivia each Friday, looking at the lighter side of...
SIX APPEAL...when numbers are in their prime
19th January 2018
Can mathematics be sexy? In the sense that sex is Latin for six, then definitely!
Prime numbers have always held a mystique for mathematicians: they are the building blocks of all other numbers and hold great practical value in the fields of communications and computer science. Of particular interest (to those interested) are the patterns within prime numbers, with mathematicians throughout history hoping to unlock some kind of hidden formula.
Alphonse de Polignac proposed one such pattern in 1849: there are infinitely many cases of two consecutive prime numbers with difference n, where n is a positive even number. In other words, pick any even number and there will be an infinity of primes that you can add to it that will result in another prime but no other prime number will fall in between. Primes with a gap of 2 are called twins, those with a gap of 4 are cousins, while a prime gap of 6 makes for very sexy primes.
Sexy primes come in pairs, e.g. (5,11), (7,13), (11,17); triplets, e.g. (97,103,109), (101,107,113), (151,157,163) and quadruplets, e.g. (61,67,73,79), (251,257,263,269), (601,607,613,619).
In an arithmetic progression of five terms with common difference 6, one of the terms must be divisible by 5, because the two numbers are relatively prime. Thus, the only sexy prime quintuplet is (5,11,17,23,29); no longer sequence of sexy primes is possible.
So, numbers may not be the most glamorous entities in the world, but, if you catch them in their prime, they may just be sexy – in their own way.
Click a story below for more Lighter Side fun...
5th January 2018
What do you do when you have more money than you know what to do with? Try to monopolise a commodity apparently.
Silver Thursday was an event that occurred in the United States in the silver commodity markets on Thursday, 27 March 1980, following the Hunt brothers' attempt at cornering the silver market. A subsequent steep fall in silver prices led to panic on commodity and futures exchanges.
Nelson Bunker Hunt and William Herbert Hunt, the sons of Texas oil billionaire Haroldson Lafayette Hunt, Jr., were members of the fabulously wealthy family upon which the TV series Dallas was rumoured to have been based. For some time before Silver Thursday, the brothers had been attempting to corner the market in silver. In 1979, the price for silver jumped from $6.08 per troy ounce on 1 January 1979 to a record high of $49.45 per troy ounce on 18 January 1980: an increase of 713%. The brothers were estimated to hold one third of the entire world supply of silver (other than that held by governments). The situation for other prospective purchasers of silver was so dire that on 26 March 1980 the jeweller Tiffany's took out a full page advert in The New York Times, condemning the Hunt Brothers and stating "We think it is unconscionable for anyone to hoard several billion, yes billion, dollars' worth of silver and thus drive the price up so high that others must pay artificially high prices for articles made of silver".
But on 7 January 1980, in response to the Hunts' accumulation, the exchange rules regarding leverage were changed, when COMEX adopted "Silver Rule 7" placing heavy restrictions on the purchase of commodities on margin. The Hunt brothers had borrowed heavily to finance their purchases, and, as the price began to fall again, dropping over 50% in just four days, they were unable to meet their obligations, causing panic in the markets.
The Hunt brothers had invested heavily in futures contracts through several brokers, and when the price of silver dropped below their minimum margin requirement, they were issued a margin call for $100 million. The Hunts were unable to meet the margin call, and, with the brothers facing a potential $1.7 billion loss, the ensuing panic was felt in the financial markets in general, as well as commodities and futures. Many government officials feared that if the Hunts were unable to meet their debts, some large Wall Street brokerage firms and banks might collapse.
To save the situation, a consortium of US banks provided a $1.1 billion line of credit to the brothers which allowed them to pay the brokers, which, in turn, survived the ordeal.
In 1988, the brothers were found responsible for civil charges of conspiracy to corner the market in silver. They were ordered to pay $134 million in compensation to a Peruvian mineral company that had lost money as a result of their actions. This forced the brothers to declare bankruptcy, in one of the biggest such filings in Texas history.
Read more about this fascinating family here.
15th December 2017
Christmas time is here again and that means lots of time off work to spend with family and veg out in front of the TV. Need some playlist inspo? Why not put on some edutainment and watch some finance-related movies?
A wide range of websites, from imdb to the CFA Institute’s blog, have come up with their top picks for (mostly white collar crime-related) movies that every finance professional should watch. Here are Investopedia’s top 10:
10. The Big Short
9. Barbarians at the Gates
8. American Psycho
7. Glengarry Glen Ross
6. Rogue Trader
5. Trading Places
4. The Wolf of Wall Street
3. Boiler Room
2. Margin Call
1. Wall Street
8th December 2017
Every team is made up of different personality types, and some demand more time and attention from the leaders who manage them than others. Although there’s no hard and fast management strategy that fits every kind of employee, there is a rough framework managers can use to decide how to direct their energy toward getting the most out of all the personalities on their teams. Here’s a quick rundown of eight of the most common personality types and how to manage each one.
1. THE RISING STARS
2. THE DOMAIN MASTERS
3. THE SQUEAKY WHEELS
4. THE STEAMROLLERS
5. THE STOWAWAYS
6. THE JOYRIDERS
7. THE SQUARE PEGS
8. THE SLACKERS
Adapted from this article.
1st December 2017
While the Southern Hemisphere is enjoying the benefits of longer days and warmer temperatures, Northern Hemisphere dwellers are no doubt feeling the darkness creeping in more and more with each passing day. How does a 3pm sunset affect productivity levels at work?
Some research suggests that people are more productive during winter, due to the lack of more attractive options outdoors. Because workers have no interest in going outside, they focus more on their work, making them more productive. It was found that workers were more productive in the time it took to complete their tasks.
But if that’s the case, why do many of us feel less productive when the weather is miserable? And why do some researchers estimate that lack of productivity during the winter costs the economy billions of dollars each year?
When the sun is up, it signals to your body that you should be awake. When it’s dark out, your body thinks that it’s time for bed and automatically starts winding down.
The fact that you don’t get much sunlight in the winter actually tricks your body into thinking that it’s time for bed more, making you more tired, hence less productive.
Natural lighting renovations have been shown to result in happier workers, less absenteeism, and fewer illnesses, and, because better lighting encourages satisfaction among workers, it also results in increased productivity.
But in the winter months, when there is very little natural light to go around, not only are we deprived of its benefits (often resulting in SAD, or Seasonal Affective Disorder), but, we are also subjected to the productivity-zapping effects of artificial lighting.
If the lighting is too dim, it can cause eye strain and headaches because the eyes are forced to work much harder in order to see. Dim lighting can also result in drowsiness and lack of focus, which would obviously have a negative impact on employee motivation.
On the other hand, lighting that is too harsh, such as some florescent lighting, can also cause eye strain, and is cited as a trigger for migraine headaches. Harsh lighting also makes it more difficult for the eye to focus.
Of course, the best alternative to harsh lighting and dim lighting systems is natural light itself. But, in the meantime, while we eagerly await the other side of the solstice, perhaps sunlight-simulating lamps should become part of standard-issue office equipment…just to make us feel less SAD.
24th November 2017
Thanksgiving is a US holiday during which people consume huge quantities of turkey, stuffing, cranberry sauce and pie. From watching movies like The Addams Family Values we know a bit about the history of the holiday, but the food – especially the turkey – is an essential part of Thanksgiving.
One of the stranger things about this holiday, however, is that it seems to defy the most basic principle of economics: the price of turkey in the US actually goes down a few days before everyone starts cooking – which is when demand for the bird is at its highest.
Apparently, this happens every holiday season: The price falls just before Thanksgiving and stays low until Christmas. For example, in the average year, November’s price per pound for turkey is about 10 percent lower than the price in September.
In general, when there is a limited quantity of something to sell and demand for the product increases, so does its price. Hence exorbitantly expensive red roses on Valentine’s Day.
In more formal economic language, the demand curve for turkeys shifts outward at Thanksgiving, which means people at this time of year are interested in buying more of these birds regardless of the price. Even the most casual shopper in food stores this week can observe this increase or shift in demand as more people are buying turkeys to cook.
So why the discounts? Because for this time of year, not only does demand for turkeys increase, but the supply of turkey increases too. Even shops that don’t usually stock turkey may do for the holidays. This boost in supply drives prices downward.
This works for the sellers because they are interested in maximizing profits through volume – not in maximizing the revenue they get from selling each bird.
Turkeys are not very profitable items, even at full price. Sellers, however, know that people coming in to buy turkeys are likely to purchase other items, too, such as seasonings, disposable roasting pans and soda. The other items are where stores make their money, since the profit margins on these items are much higher than on frozen turkeys.
How does this dramatic increase in supply happen? Turkeys are slaughtered continuously throughout the year and then put into cold storage.
Turkey stocks slowly build up each year until they reach a peak in September. Between September and December, turkey stocks plummet as shops buy them up and put them on sale. Then farmers, processors and wholesalers slowly rebuild their stocks for the next year’s holiday season.
The 500 to 600 million pounds of turkey in cold storage by the end of each summer means there are almost two pounds of turkey for every non-vegetarian person in the US.
Wonder what the pilgrims would have to say about that…
17th November 2017
Just look at anyone trying to walk and text at the same time (especially when they are blocking your path) and you will know what researchers have been trying to tell us for a good few years now: productive multi-tasking is a myth!
It turns out that 98% of the population doesn’t multi-task very well. Only about 2% are good at multi-tasking and these “supertaskers” are true outliers. As for the rest of us, what we think of as multi-tasking is actually just shifting back and forth from one task to another, such as typing an email and then listening to that conference call conversation, then back to our email. Chances are, we miss out on the parts of the conversation that happen while you we type the email.
The problem with trying to multi-task is that we lose efficiency to the “switch cost” of shifting back and forth between tasks. Each time we do it, it takes our brain some time to refocus. So while it might seem efficient on the surface, it isn’t – studies show that multi-tasking can reduce productivity by as much as 40%.
To be fair, some of us have a harder time avoiding the multitasking menace than others. A University of Utah study identifies four types of people with a greater tendency to multitask:
So how can we start clawing back that 40%? How can frustrated leaders get people to focus during meetings when the thought of firing off a few emails or scrolling through Twitter at the same time is so tempting? How do we shift habits from multi-tasking to “single-tasking”?
Start with small steps. Implement a code of conduct during meetings. Be strict with yourself and dedicate time to new, complex tasks, leaving the multi-tasking to easier, familiar tasks.
10th November 2017
Decisions, decisions…pizza or burgers? Gym or sleep? To be or not to be? Founder of one of the world’s largest hedge funds, Ray Dalio, has some advice on how to approach the confusing and often irrational world of decision-making.
In our hunter-gatherer days it made sense for short-term impulses to take precedent: not reacting to impulses inspired by fear or anger could lead to death in the wild, but that’s no longer the case. In a modern society, short-term decisions are no longer always the most optimal.
As Dalio says:
Makes sense, but not always so easy to put into practice. One method that may help is the 10/10/10 method. Next time you feel a slight conflict about a decision or an action ask yourself three questions:
A little weekend motivation to keep your eyes on the prize!
3rd November 2017
AI, machine learning, robotics…so many buzz words and so little time! The future is here and it’s coming for the world of insurance.
Earlier this year, several life insurance companies started testing technology from a company called Lapetus Solutions, which uses facial analytics and other data to estimate life expectancy. Lapetus says its product, Chronos, would enable a customer to buy life insurance online in as little as 10 minutes by sending in a photo of themselves and without taking a life insurance medical exam.
A selfie reveals more than whether you’re having a good hair day. Facial lines and contours, tiny droops and dark spots could indicate how well you’re aging, and, when paired with other data, could someday help determine whether you qualify for life insurance.
Many life insurance companies are exploring how to use additional data, statistical models, artificial intelligence and other techniques to help make quick decisions to ease the policy buying process and boost sales. Consumers don’t like the wait on the typical application process, which can take weeks and often requires a medical exam.
You’d upload a selfie to the insurer online and answer health and other questions. The facial analytics technology would scan hundreds of points on your face and extract certain information, including your body-mass index, physiological age (how old you look) and whether you’re aging faster or slower than your actual age.
The insurer would combine the results with your application answers and, if it chooses, any other information it typically pulls. If approved for coverage, you could buy a policy immediately online.
Lapetus is also exploring how facial analytics may identify early signs of diseases such as diabetes, heart disease or dementia. And it’s developing a feature that it says will be able to tell whether someone ever smoked. Among the clues are early signs of crow’s feet around the eyes and under-eye bagging.
The technology revolution seems set to shake up over the insurance industry – but don’t worry, there’s still some time left to perfect your pout. Say cheese!
27th October 2017
Sometimes, the beauty of the finance world is in its creative ways of naming boring or unpleasant concepts. Salami slicing, also known as penny shaving, is the fraudulent practice of stealing money repeatedly in extremely small quantities, usually by taking advantage of rounding to the nearest cent in financial transactions. It would be done by always rounding down, and putting the fractions of a cent into another account. The idea is to make the change small enough that any single transaction will go undetected.
The con artist, for example, a bank employee, would transfer a few cents from hundreds of thousands bank accounts. Because the account owners won't notice the transaction or won't care about the missing money, the con artist tends to go undetected.
Variations on this theme include: the con artist taking percentages of cents that should just be rounded up or down, the con artist faking the transactions to 'test' accounts or, in non-financial situations, the con artist stealing a large object one piece at a time.
This scam seems to be a popular theme in the movies and TV series. Radar shipped a jeep home one part a time in M*A*S*H, a story line perhaps borrowed from the Johnny Cash song "One Piece At A Time”. The films Superman III, Office Space, Ghost In The Shell and Hackers all mention the swindle, stealing one penny at a time.
In real life, Micheal Largent of the US used this method to steal $50,000 over six months. He was caught because he opened accounts in the fictional names of characters from King of The Hill, a show created by Mike Judge, the director of Office Space.
In 1997, Willis Robinson reprogrammed the till at the Taco Bell he worked so that a taco which cost $2.99 was only charged at 1 cent on the internal computer. The customer pays full price, the till is still balance and Robinson got to keep the difference.
In 1998 four men were charged with fraud for allegedly installing chips in petrol pumps that cheated customers by overstating the amounts pumped by a small amount.
So keep a close eye on your pennies and your cured meats – every bit counts!
20th October 2017
It’s 3.15pm, you’ve hit the post-lunch slump, and you are rereading that IFRS17 paragraph for the twentieth time but may as well be the first.
The internet is bursting with advice on how to concentrate on a difficult or boring piece of work amidst a sea of distraction, but it may not all be realistic or palatable. Here are a few seemingly counter-intuitive ways – backed by science, apparently, and that don’t involve turning off your social media – to bring back your focus. It’s worth a shot, right?
So if it’s going to happen, then why not schedule it at a convenient time? Psychologists have distinguished between deliberate and accidental mind wandering, and say that only the accidental kind is bad for getting stuff done. People who slot in their daydreaming when they know that it won’t matter – when doing mindless admin, for example, suffer less than those whose minds skip off without their permission.
Make it harder
‘Load Theory’ is the idea is that there is a limit to how much information from the outside world our brains can process at any one time – once all of these processing ‘slots’ have been filled, the brain’s attention system kicks in to decide what to focus on.
Experiments suggest we might be better to work not in clean, tidy and silent surroundings, but in those that are messy and confusing. It works because once all the perceptual slots have been taken up, the brain has to pour all its energies into focusing on the most important task. Distractions simply get screened out.
Exercise, meditation and a good old dose of caffeine may all be good options.
Don’t try so hard
This, in fact, may be the most useful outcome of all the research into focus. The more we know about the brain, the clearer it is that stress is the enemy of concentration. So take the time to do whatever it takes to feel calmer and more in control, and, with luck, the work will take care of itself.
Adapted from this article.
6th October 2017
There’s no need to go on an expensive safari holiday to see some wildlife – you may be lucky, or unlucky, enough to spot a hippo next time you enter the boardroom!
In this context, HiPPO stands for the “Highest-Paid Person’s Opinion” and they bring with them all the destructive potential of the notoriously aggressive water-dwelling mammal. The term is used to describe the tendency of lower-paid employees to defer to higher-paid employees when a decision has to be made. It can also be used to describe an organisation’s reliance on human instinct rather than data in the decision-making process
Life is full of innovation-choking Hippos, in business, politics and social circles and some companies, like JC Penney, learnt about the danger they pose the hard way.
Hilda Burke, an integrative psychotherapist, says: “There is a belief that if you agree with the ‘leader of the pack’, in this case a Hippo, that you won’t be exposed, and that you are automatically protected by the weight his or her opinion carries. Using the jungle analogy, if you’re riding on a hippo’s back, the chances are that you’re pretty safe.”
It’s unhelpful, though. “Work is a habitat threatened and encroached upon by job and economic uncertainty. I imagine it can be mapped on to our evolutionary survival instincts,” she says. “But I wonder how far you can really go by just echoing a Hippo’s opinions and passing them off as your own, and indeed, what the price is within ourselves for being so adapted that we no longer can discern what our own thoughts, ideas and feelings are.”
So what to do if you’re a lower-paid junior with a bright idea in the meeting room? Try to conduct an experiment to test it out. Even hippos can’t argue with data.
29th September 2017
Actuaries learn many useful and widely-applicable nuggets of wisdom during their years of study. Not really. But it is always interesting to come across broader applications of very specific concepts, no matter how useless they appear to be.
One is example is the original story of the Markov Chain. A Markov Chain is a stochastic process for which one can make predictions for the future of the process based solely on its present state just as well as one could knowing the process's full history, hence independently from such history; i.e., conditional on the present state of the system, its future and past states are independent.
You probably knew that. But did you know that Markov founded this branch of probability theory by applying mathematics to poetry?
Suppose you are given a body of text and asked to guess whether the letter at a randomly selected position is a vowel or a constant. Since consonants occur more frequently than vowels, your best bet is to always guess consonant. Suppose you are told whether the letter preceding the one you chose is a vowel or consonant. Is there now a better strategy you can follow?
In 1913, A.A. Markov was trying to answer the above problem analysed twenty thousand letters from Pushkin's poem Eugene Origin. He found that 43% letters were vowels and 57%, consonants. So, in the first problem, one should always guess "consonant" and can hope to be correct 57% of the time. However, a vowel was followed by consonant 87% of the time. A consonant was followed by a vowel 66% of the time. Hence, guessing the opposite of the preceding letter would be a better strategy in the second case. Clearly, knowledge of the preceding letter is helpful. The real insight came when Markov took the analysis a step further.
Markov investigated whether knowledge about the preceding two letters confers any additional advantage. He found that there was no significant advantage to knowing the additional preceding letter. This leads to the central idea of a Markov chain - while the successive outcomes are not independent, only the most recent outcome is of use in making a prediction about the next outcome.
Now, how about introducing a course in Russian literature into the actuarial syllabus?
22nd September 2017
Last week we shared some tips on how to spot a fake “random” number. On the same theme, have you heard of Benford’s Law?
Benford’s law is a distribution that the first digits of many data sets conform to. It’s a non-uniform distribution, with smaller digits being more likely than larger digits and can be used as an indicator of fraudulent data, and can assist with auditing accounting data.
Accounts receivable, accounts payable, sales and expenses data are generally based on values from two types of variables being multiplied together i.e. prices and quantities. Alone, these variables are unlikely to conform to Benford’s law, but are likely to when multiplied together.
If some accounting data is expected to conform to Benford’s law but doesn’t, it might provide a good reason for further investigation.
The distribution table looks like this:
The distribution formula is as follows:
Benford's Law can most simply be explained with the following picture:
The underlying premise is that the subject population of quantities, expressed in the base 10 and more or less arbitrary units, will be fairly evenly distributed on a logarithmic scale. This is confirmed by the fact that the exponents on these constants are fairly uniformly distributed. As a result, the probability of the leading digit being "d" approaches:
For more explanations on why Benford’s Law works, click here.
15th September 2017
People make up “random” numbers for all kinds of reasons, ranging from the innocent (coming up with some dummy data to use in a maths example) to the less innocent (fake expenses for a tax return). Either way, they tend to fall into unconscious patterns when creating these numbers and there are a few tell-tale signs of how to spot them.
For instance, here is the invented amount of a bad cheque from a US embezzlement case: $87,602.93.
Just a few tricks to help you avoid being fooled by “randomness”!
8th September 2017
Ah, the technology age! It’s brought with it its own conventions, rules and language – and we aren’t talking about coding.
The tone of the humble work email is a language we are all well-versed in, although we may not always be conscious of it. Battles have been lost and won using passive aggressive phrasing.
Recently, writer Danielle René decided to ask her Twitter followers to share the best weapons in their verbal communication arsenal, tweeting: “What is your favourite phrase to use in a professional clap back? Mine is ‘per my last email…’.”
The question got everyone talking – and it seems that people are throwing out passive aggressive assaults left, right and centre.
Here are some of our favourites:
1st September 2017
Health warning to all the cubicle dwellers out there: they say sitting is the new smoking. While a brief period of sitting here and there is natural, long periods of sitting in front of spreadsheets day-in and day-out can seriously impact your health and lifespan: prolonged sitting increases the risk of heart disease, diabetes, obesity, and more.
25th August 2017
Worried that robots are on their way to taking over the world?
Professors Andrew McAfee and Erik Brynjolfsson from the MIT Sloan School of Management have recently undertaken research to consider where “humans fit in the new world of work.”
McAfee and Brynjolfsson’s research illuminates what has been dubbed a “Cambrian Explosion” in robotics. The original Cambrian Explosion in 500 million BCE saw the appearance of all major forms of life on earth and researchers feel we are now at a similar threshold for machines. The research focuses on “major developments in five parallel, interdependent and overlapping areas: data, algorithms, networks, the cloud and exponentially improving hardware”—or the handy acronym DANCE.
Data: The big data era is upon us with “signals from sensors in smartphones and industrial equipment, digital photos and videos, a nonstop global torrent of social media and many other sources.”
Algorithms: Big data “supports and accelerates the developments in artificial intelligence and machine learning, [whose] results get better as the amount of data they’re given increases.”
Networks: Improvements in wireless communication means “better and faster data accumulation.” It also means “robots and flying drones can coordinate their work and react together on the fly to quickly-changing circumstances.”
The cloud: The cloud makes an “unprecedented amount of computing power available to organizations and individuals,” accelerating the robotic Cambrian Explosion.
Exponential improvements in digital hardware: If Moore’s law—the steady doubling in integrated circuit capability every eighteen to twenty-four months—is any indication, it is likely we will “continue to enjoy simultaneously lower prices and higher performance from our digital gear processors, memory, sensors, storage, communications and so on for a long time to come.”
The question of when automation might replace humans entirely is still theoretical, according to McAfee and Brynjolfsson, but in the meantime, just DANCE!
18th August 2017
In the world of Artificial Intelligence (AI), why is it so challenging to replicate common sense, intuition, judgement…all those mystical human abilities that we know are there but can’t quite define?
What most definitions propose is that these skills relate to a human’s ability to reason beyond data and calculation – we regularly make decisions based on factors other than statistics and this skill isn’t congruent with the way we usually think about computers.
Mathematician Michael Polanyi studied the causes behind our ability to acquire knowledge that we can’t precisely explain. Try describing the colour blue to someone – we know it when we see it but it’s not that easy to put into words. Polanyi’s Paradox summarises the cognitive phenomenon that many times “we know more than we can tell”.
Polanyi’s Paradox has deep implications in the AI field: if we can’t explain our knowledge, how can we possibly train AI agents?
Thanks to Google, AI has evolved passed Polanyi’s Paradox. Take the game GO, for example. Many of the well accepted strategies in the ancient game are very hard to model as a series of rules and are typically more related with human’s intuition. But then, between 2016 and 2017, DeepMind’s AlphaGo program regularly defeated the world’s top GO players.
AlphaGo overcame the Polanyi Paradox using some clever AI techniques. Instead of relying on traditional symbolist’s algorithms such as inverse deduction to teach AlphaGo the rules of Go strategies, the DeepMind team used a combination of deep learning and reinforcement learning to train AlphaGo. Initially, AlphaGo studied millions of Go games to infer hidden patterns between a specific strategy and the outcome of the game. After that, researchers had AlphaGo play numerous games against itself to build new knowledge.
The AlphaGo example demonstrates that the way to build human-type judgment into AI systems is to design systems that learn on their own and include judgment-based decisions in the training data.
Makes one wonder about the implications for actuarial judgement…
4th August 2017
1 + 1 = 2
These mathematical equations are indisputable, right? Apparently not. In 1897, the legislators of Indiana tried to pass a bill that legally defined the value of pi as 3.2.
The story of the “Indiana pi bill” starts with Edward J. Goodwin, a physician who spent his free time dabbling in mathematics. Goodwin was obsessed with an old problem known as squaring the circle. Since ancient times, mathematicians had theorised that there must be some way to calculate the area of a circle using only a compass and a ruler. Mathematicians thought that with the help of these tools, they could construct a square that had the exact same area as the circle. Then all one would need to do to find the area of the circle was calculate the area of the square.
Unfortunately, it turns out that it’s impossible to calculate the area of a circle in this way. And at the time that Goodwin was toying with this problem, mathematicians already knew it was impossible: Ferdinand von Lindemann had proven it in 1882.
Did this deter Goodwin? No way. He persevered, and in 1894 he convinced the upstart journal American Mathematical Monthly to print the proof in which he “solved” the squaring-the-circle problem. One of the odd side effects was that the value of pi morphed into 3.2.
Goodwin then copyrighted his “proof”, planning to collect royalties from businesses and mathematicians who sought to exploit his method.
For the sake of students’ education though, he magnanimously offered to let the state use his masterpiece free of charge. But they could only avoid paying royalties if the legislature would accept and adopt this “new mathematical truth” as state law. Goodwin convinced Representative Taylor I. Record to introduce House Bill 246, which outlined both this bargain and the basics of his method.
Goodwin’s method and the accompanying bill never mention the word “pi,” but on the topic of circles, it clearly states, “[T]he ratio of the diameter and circumference is as five-fourths to four.” That ratio is 3.2. It goes further to bitterly condemn 3.14 as “wholly wanting and misleading in its practical applications.”
Stunningly, the Committee on Education sent the bill out for a vote, and it passed the House unanimously. Not a single one of Indiana’s 67 House members raised an eyebrow at a proof that effectively redefined pi as 3.2.
Luckily the state’s senators had a bit more numerical acumen. By this point, news of Indiana attempting to legislate a new value of pi and endorse an airtight solution to an unsolvable math problem had become national news, and papers all over the country were mocking the legislature’s questionable calculations.
28th July 2017
Although we have come a long way, women still form the minority of “traditionally male” professions. There are any number of reasons for this, but there may be one that has been overlooked…
According to a paper recently published in the Journal of Personality and Social Psychology, there could be a subtle gender bias in the way companies word job listings in such fields as engineering and programming. Although legislation effectively bans companies from explicitly requesting workers of a particular gender, the language in these listings may discourage many women from applying.
The paper found that job listings for positions in engineering and other male-dominated professions used more masculine words, such as "leader," "competitive" and "dominant." Listings for jobs in female-dominated professions – such as office administration and human resources – did not include such words.
A listing that seeks someone who can "analyse markets to determine appropriate selling prices" may attract more men than one that seeks someone who can "understand markets to establish appropriate selling prices." The difference may seem small, but according to the paper, it could be enough to tilt the balance. It was also found that the mere presence of "masculine words" in job listings made women less interested in applying – even if they thought they were qualified for the position.
Of course there are many other factors preventing women from entering and staying in these industries, but altering the way we use language could be one of the easiest places to start changing company culture from the outside in.
Companies in the technology world, for example, are paying more and more attention to gender diversity – and not just for altruistic reasons. Diverse teams are better problem solvers, and enabling cross-departmental communication is easier when engineering teams are more diverse.
So eliminate key man risk, reduce your man hours, forget about the everyman, and please don’t man up. Can we reach a non-gentlemen’s agreement on that?
21st July 2017
What’s more strange: the fact that Donald Duck starred in a movie about mathematics or that said movie was nominated for an Academy Award? Donald in Mathmagic Land is a 27-minute Donald Duck educational featurette released on June 26, 1959.
Some of the concepts explored in Donald’s journey include:
Pythagoras and music
Pentagram, golden section, and golden rectangle
Human body and nature
Infinity and the future
Donald discovers that pentagrams can be drawn inside each other indefinitely. Therefore, numbers provide an avenue to consider the infinite. Deep stuff!
By the end of the film, Donald understands and appreciates the value of mathematics. The film closes with a quote from Galileo: "Mathematics is the alphabet with which God has written the universe".
Watch the full film on YouTube here…think it could count towards CPD?
14th July 2017
Last week’s story revealed the dark side of Pythagoras…This week we stick with the theme of the Pythagorean Theorem. This theorem has been proved many times, but only once by a United States President. Five years before James A Garfield was elected president, he came up with a proof that involves a simple sheet of paper and some scissors.
Grab a piece of paper and cut two identical right triangles, trying to include one long side and one short side. Call the long side A, the short side, B, and the hypotenuse C. Place them, opposing points together, on a piece of paper so that they look like this:
Draw the third line in to make three triangles. The total area of a triangle can be calculated as one half the base times the height. Each of the original triangles has an area of ½ ab, and the third has an area of ½c^2.
A trapezoid has an area calculated by its height times one half the sum of its uneven sides. So the trapezoid has an area of ½ (a+b)(a +b).
Since these areas are the same, this leads us to an equation.
This simplifies to:
Multiply it all by 2, and you get:
And that’s how to solve a maths problem, presidential-style.
Adapted from this article.
7th July 2017
You may associate Pythagoras with right-angled triangles, but have you heard the rumour that he was also, you know, a megalomaniacal murderer?
Pythagoras was very passionate about numbers. So passionate that he founded a religion called Pythagoreanism in around 500 BCE. Pythagoras and his followers believed that numbers explained everything in life, from nature to music. Furthermore, they were sure that everything in the universe was expressible as the result of rational numbers.
Rational numbers are numbers that can be expressed as the ratio of two whole numbers – i.e., as a fraction. If it wasn't expressible as x/y, they didn't want to hear about it.
Legend has it that one of the Pythagoreans, Hippasus, noticed something about the pentagram: if it's divided up, there is a certain ratio between the carved up pieces. Hippasus found that the length of the red side divided by the green side is equal to the length of the green side divided by the blue side. And that's equal to the length of the blue side divided by the purple side. And none of these things are expressible as the ratio of two whole numbers. They form the golden ratio (approximately 1.61803).
The golden ratio appears in many works of art and architecture. It forms the background aesthetic of our lives to this day. Hippasus announced that he'd found a way to demolish Pythagoras' religion. Unfortunately, he made this announcement on a boat populated by only himself, Pythagoras, and some other Pythagoreans. The story goes that Pythagoras tipped him over the side, drowned him, and swore the rest of the group to secrecy.
It's doubtful this actually happened, especially since there's another rumour that Hippasus was killed not for coming up with the golden ratio, but with the square root of two - another irrational number. (He realised there was no rational way to express the diagonal of a square with sides one unit long.)
Still, it makes you think twice about contradicting your manager, doesn’t it?
30th June 2017
Today’s story is hot off the press – just for the techies!
Artificial Intelligence and Machine Learning usually work best with a lot of computing power behind them to process data, compute possibilities and instantly come up with better solutions.
Most AI systems rely on local sensors to gather input, while more powerful hardware in the cloud manages the output. It's how Apple's Siri, Amazon’s Alexa and IBM’s Watson work. It is, though, a limiting approach when it comes to applying intelligence when there isn't Internet connectivity.
Now, Microsoft researchers have figured out how to compress neural networks down from 32 bits to, sometimes, a single bit and run them on a $10 Raspberry Pi, a low-powered, credit-card-sized computer with a handful of ports and no screen. It's really just an open-source motherboard that can be deployed anywhere. The company announced the research in a blog post yesterday.
Microsoft's work is part of a growing trend of moving Machine Learning closer to devices and end users.
Despite the differences between an iPhone and a Raspberry Pi, the trend is clear. These companies are moving intelligence closer to the local hardware and, where possible, relying less on constant access to massive data and intelligence stores in the cloud.
Often, places with no internet connectivity are where AI is needed most. It's an approach that will make sense for smaller, sensor-based tasks that can learn by location, intention, recent action and the device data.
Adapted from this article.
23rd June 2017
Anyone living in the UK might have noticed the balmy weather we’ve been having… Tropical temperatures may be paradise to some and the opposite to others, but love it or hate it, there’s an actuarial angle here. Does exposure to extreme temperatures have an effect on life expectancy?
The results of a Google search on this topic are conflicting and very US-centric. Here are some of the more interesting findings gleaned from various studies:
One study found that the immediate effects of spikes of heat and of cold lead to increases in the death rate. The main difference is that the spikes in extreme heat tend to drop off rapidly, while the death rates associated with extreme cold tend to have longer lasting effects. The number of annual deaths attributable to cold temperature was estimated at 1.3% of total deaths in the US.
To back up these findings, a study at Stanford University found that a warmer climate would reduce deaths markedly in the United States (a similar study in the UK found the same). The study considered whether temperature or increases in the amount of sunlight reduced mortality but found that warm temperatures had a more significant effect than long summer days.
On the other hand, researchers from the University of Michigan, in a study published in the journal Cell, reported that worms exposed to cold temperatures demonstrate a genetic response that triggers longer life spans. The researchers went on to speculate that the phenomenon may translate to humans since similar genetic pathways are present in human beings.
Also, scientists at the Scripps Research Institute in California found that reducing the core body temperature in mice extends their lifespans by up to 20 percent.
But then, another study showed that lab worms exposed to repeated heat shocks lived 10-20% longer. In response to the treatments the worms generated a surge of a protective hormone dubbed heat shock protein, and that heat shock protein also increases life span. This result is as an example of hormesis, the paradoxical adaptation that makes animals live longer when they are exposed to challenges and hardships. Starvation, various toxins in low doses, infections, heat and cold can all lead to a longer life.
So, what is the answer and, more importantly, will average temperature make it as a risk factor in the standard life insurance underwriting procedure any time soon? Something to ponder as you soak up (cower from) those summer rays.
16th June 2017
Wars have been waged for it, countries have been built on it and it’s been known to make grown men drool…yes, we may be talking about the allure of beautiful women, but in this context, we are talking about gold.
Humankind's attitude to gold is bizarre. Chemically, it is uninteresting - it barely reacts with any other element. Yet, of all the 118 elements in the periodic table, gold is the one we humans have always tended to choose to use as currency. Why? Why not osmium or chromium, or helium, say - or maybe seaborgium?
Well, let’s go through a process of elimination:
We can immediately eliminate the right-hand side of the table – noble gases and halogens wouldn’t be very practical to use as currency.
The two liquid elements - mercury and bromine - are poisonous - not a good quality in something you plan to use as money. Similarly, we can cross out arsenic and several others.
On the left-hand side of the table, the alkaline metals and earths are just too reactive (remember the fizzy chaos of dropping sodium or potassium into a dish of water in high school?). A similar argument applies to another whole class of elements, the radioactive ones: you don't want your cash to give you cancer. Out go thorium, uranium and plutonium, along with a whole bestiary of synthetically-created elements - rutherfordium, seaborgium, ununpentium, einsteinium - which only ever exist momentarily as part of a lab experiment, before radioactively decomposing.
Then there's the group called "rare earths", most of which are actually less rare than gold. Unfortunately, they are chemically hard to distinguish from each other, so you would never know what you had in your pocket.
This leaves us with the middle area of the periodic table, the "transition" and "post-transition" metals. We've got some very tough and durable elements - titanium and zirconium, for example, but they are very hard to smelt. The specialist equipment required wasn't available to ancient civilisations. Aluminium is also hard to extract, and it's just too flimsy for coinage. Most of the others in the group aren't stable - they corrode if exposed to water or oxidise in the air.
So, what's left?
Of the 118 elements we are now down to just eight: platinum, palladium, rhodium, iridium, osmium and ruthenium, along with gold and silver. These are known as the “noble” metals because they stand apart, barely reacting with the other elements. They are also all rare, another important criterion for a currency.
But all the noble metals except silver and gold are so rare that you would have to cast some very tiny coins, which you might easily lose. They are also hard to extract.
That leaves silver and gold.
Both are scarce but not impossibly rare. Both also have a relatively low melting point, and are therefore easy to turn into coins or jewellery.
Silver tarnishes - it reacts with minute amounts of sulphur in the air. That's why we place particular value on gold.
It turns out then, that the reason gold is precious is precisely that it is so chemically uninteresting. Gold's relative inertness means it doesn’t lose its looks, even after thousands of years.
So what does this process of elemental elimination tell us about what makes a good currency?
Firstly, it doesn't have to have any intrinsic value. A currency only has value because we, as a society, decide that it does. It also needs to be stable, portable and non-toxic. And it needs to be fairly rare - you might be surprised just how little gold there is in the world (it's guesstimated that all the gold in the world would form one 20 metre cube).
But gold has one other quality that makes it the stand-out contender for currency in the periodic table. Gold is... golden. All the other metals in the periodic table are silvery-coloured except for copper - but copper corrodes, turning green when exposed to moist air. That makes gold very distinctive.
And, of course, gold is beautiful, which is perhaps the most powerful driver of all.
The piece above has been adapted from this BBC article.
9th June 2017
If you are a fan of 80s teen movies (and, let’s face it, who isn’t?) you will remember the scene in Ferris Bueller’s Day Off where the gang visits what looks like, based on the hand movements and bad suits, some kind of psychotic corporate rave.
What is actually being depicted is the Chicago Mercantile Exchange (CME), whose trading floor operates (to a lesser extent now than then) using the “open outcry” method of communication. It involves shouting and the use of hand signals to transfer information primarily about buy and sell orders. The part of the trading floor where this takes place is called a pit.
Since the development of the stock exchange in the 17th century in Amsterdam, open outcry was the main method used to communicate between traders. However, this started changing in the latter half of the 20th century, first through the use of telephone trading and then, starting in the 1980s, with electronic trading systems.
What we see in Ferris Bueller, specifically, is hand signaling, also known as arb or arbing (short for arbitrage). As well as at the CME, the system is also used at the American Stock Exchange (AMEX).
Generally, numbers one to five are gestured on one hand with the fingers pointing directly upwards. To indicate six to ten, the hand is held sideways, parallel to the ground. Numbers gestured from the forehead are blocks of ten, blocks of hundreds and thousands can be indicated by repeatedly touching the forehead with a closed fist. The signals can otherwise be used to indicate months, specific trade option combinations or additional market information.
Be careful - hands move pretty fast...if you don't stop and look around once in a while, you could miss them!
For a tutorial on hand signalling, watch this handy video.
2nd June 2017
Hard day at work? Ever feel like just taking it easy and letting the government take care of you? Some governments are willing to do so more than others…France, for instance, has introduced a law that gives workers the right to ignore email after 6 PM. And Sweden continues to experiment with a six-hour workday. Here are some more examples of countries with generous social benefits…
19th May 2017
Yesterday the IASB issued the finalised IFRS 17 Insurance Contracts. In honour of this international accounting event, here are some fun facts about our well-balanced colleagues…
1. The developer of modern accounting was Luca Pacioli
Italian mathematician Luca Pacioli published the first book about double-entry bookkeeping in 1494. It described keeping accounts for assets, liabilities, capital, income, and expenses, much like the systems used today in balance sheets and income statements.
2. The world's first accountants originated in Ancient Mesopotamia
3. Many accounting terms have Latin roots
4. Mick Jagger, Janet Jackson, Eddie Izzard and John Grisham studied accountancy
John Grisham, author of The Firm, has a degree in accounting from Mississippi State University.
5. Oscar winning films featuring accountants
6. The Romans were obsessed with accounting
7. The founder of pottery company Wedgwood was the first cost accountant
During a slump in business in 1772, Josiah began to make a concentrated effort to establish the profit or loss realised each time a particular product was sold from his factory. He recognised the sense in recording not just the cost of materials and labour but calculations for coal, storage and transport.
8. Bubble gum was invented by an accountant
9. There is a patron saint of accountants
12th May 2017
It’s likely that if you’re reading this, you’ve done a lot of reading over the years, whether it’s university course notes, Act Ed files or pop-finance works like “Rich Dad Poor Dad”. But novels and other works of fiction also have many lessons to teach about business, leadership, economics, and career development. Below are five suggestions to get you started…
1. The Grapes of Wrath by John Steinbeck
2. Don Quixote by Miguel de Cervantes
3. The Trial by Franz Kafka
4. Something Happened by Joseph Heller
5. The Way We Live Now by Anthony Trollope
So next time you feel guilty about reading a novel instead of doing actual work on the train, just think of it as part of your “personal development plan”.
5th May 2017
We are familiar with the dot-com and US housing bubbles of recent memory, but in the early 1700s (1716 – 1720) two of the largest economic bubbles in history arose and burst at more or less the same time in different parts of Europe…
The South Sea Bubble was a speculative stock bubble in Britain, which was centred on the shares of the South Sea Company, an international trading company that was granted special trading rights in the South Seas (now called South America) by the British government. South Sea Company executives spread rumors that greatly embellished upon the commercial value of the company’s trading rights, which caused its shares and the shares of similar companies to soar. Shortly after the stock speculation mania swept throughout Britain, with scientist Isaac Newton and author Thomas Swift (who wrote Gulliver’s Travels) among the investors, the South Sea Bubble popped and caused a very severe economic crisis. When Newton lost a fortune in the crash, he famously remarked, “I can calculate the movement of the stars, but not the madness of men.”
The Mississippi Bubble was a speculative stock bubble in France that occurred at the same time as Britain’s South Sea Bubble. The seeds of the bubble were sown in 1715, when France was nearly insolvent from war and sought the help of Scottish economic theorist John Law. Law decided to create a national bank that would accept deposits of gold and silver currency and issue “paper” money or bank notes in return. Very soon, Law’s national bank began to issue much more paper currency than it received in gold and silver currency deposits, which created an inflationary economic “bubble boom”.
One of Law’s international trading companies, the Compagnie des Indes, became one of the prime beneficiaries of the inflationary boom as its shares skyrocketed and created many millionaires (this is how the French word millionaire came about), based on the supposedly immense bounty of resources in the Mississippi Territory, including gold and silver. For a time, it seemed as if France’s financial problems were over, until the Mississippi Bubble burst (when it turned out that France’s North American colonies along the Mississippi River were not as rich in resources as previous thought) and Law’s trading company shares and paper bank notes plunged in value and threw France into an even greater economic crisis than it had before the bubble.
Law himself was an interesting character: a financier, gambler and playboy who escaped to continental Europe to avoid imprisonment after shooting a man in a duel, he found himself on the run again after the bubble burst. He escaped France, disguised as a woman for his own safety, and spent the rest of his life as an impoverished gambler in various parts of Europe.
Although traditionally considered a bubble, if we’re going to be technical about it, the Mississippi Bubble wasn’t actually a bubble. A bubble is primarily caused by widespread mania and speculation, followed by a brutal collapse in asset values. In contrast, the Mississippi Bubble was the result of failed monetary policies that caused excessive money supply growth and inflation.
Still not something you’d want exploding in your face though.
28th April 2017
“There are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns – the ones we don't know we don't know.”
Uncertainty is a continuum that ranges from that which we are certain of at one end through to that which we are completely ignorant of at the other. This continuum may be divided into three broad categories: aleatory, epistemic and ontological uncertainty.
All this uncertainty – a risky business indeed!
Adapted from this article by Matthew Squair
21st April 2017
In a normal free market economy, a customer will pay for a product or service and implicitly trust that the legal, ethical, and economic forces at play will ensure she gets it. But, we know that airlines operate in a slightly different reality from everyone else. In a world where people will crawl over broken glass for that slightly cheaper seat on a budget flight, it’s no wonder that overbooking is a thing and, for the most part, no one gets hurt.
In view of the recent scandal of United Airlines, overbooking on airlines has again come into an unsavoury limelight, but, infuriatingly, we can’t deny that the stats behind this practice do add up in favour of the airline…
This TED-Ed video explains the maths behind overbooking, which takes a few factors into account: the number of seats on the plane, the (larger) number of tickets sold, the percentage of ticketholders that will probably show up, the likelihood of each one of those percentages, and the cost of hotels and other necessary costs if all the planning goes wrong and too many people do show up.
The most frustrating part is that the data and maths could be used to ensure that the maximum number of tickets is sold with a near zero percent chance of too many people showing up. Instead, the most profitable solutions often involve a not insignificant chance that a few passengers will be inconvenienced (or worse), because the extra ticket sales outweigh having to put someone up in a hotel now and then.
Even a simplified binomially distributed example is complicated, with the real-life maths approaching flight price modelling complexity (yikes!). So instead of trying to understand the system, we could either try to beat it (by hoping you get bumped and claiming maximum compensation), or just try our best to show up on time, check in early, and hoping that someone else is running late.
7th April 2017
Ever since Scottish inventor John Shepherd-Barron dreamed up the concept of an ATM in his bathtub in 1967 (true story!), these magical machines have been doling out the cash like loving parents at a theme park. The ATM was one of the first inventions to electronically automate an everyday task (and spare us the agony of dealing with actual people and restrictive banking hours), but now, with the ubiquitous popularity of card payments and online banking, what does the future hold for the humble ATM?
You may be thinking, “Wait, the ATM has a future?” It does. For all our contactless cards and talk of mobile payments, cash is still king, and may be for some time. Cash today is used for half of all purchases under $50 in the USA and 18-to-24-year-olds are the age group most likely to prefer cash as a form of payment.
It’s not just evolving consumer behaviour driving these changes. Branches can account for half of a bank’s total operating costs, and when profits are down those buildings and the people who work there can become untenable. ATMs cost less, and they can already do about 60% of transactions done at the teller window.
Another game changer for the industry, once it becomes more affordable, is likely to be robotics. One company has built a hexagonal ATM-turned-bank branch that houses a whirling robotic arm, seemingly combining an ATM, bank teller services, safe-deposit box, vending machine and insurance office in one place.
It looks like ATMs, robotic or otherwise, have not outlived their Eureka moment just yet.
31st March 2017
Banana republic is a political science term used originally for politically unstable countries in Latin America whose economies are largely dependent on exporting a limited-resource product, e.g. bananas. The history of the first banana republic begins with the introduction of the banana to the US in 1870, by Lorenzo Dow Baker, captain of the schooner Telegraph. He initially bought bananas in Jamaica and sold them in Boston at a 1,000 percent profit.
24th March 2017
In the Raconteur Business Transformation report, you can read all about the journey of Netflix to the entertainment giant it is today. For example, did you know that Blockbuster passed up the opportunity to buy Netflix in 2000 in what has been awarded the dubious honour of one of the biggest corporate misjudgements of all time?
Another former tech giant that has made some forehead-slapping misjudgements over the years is Yahoo…
Back in 1998, two unknown individuals, Larry Page and Sergei Brin, offered to sell their little startup to Yahoo for $1 million so they can resume their studies at Stanford. The company that Page and Brin were looking to sell was the soon-to-be patented PageRank system and represents the core of Google's existence. Yahoo turned down the offer as it wanted its users to spend more time on its own platform, contrasting PageRank, which sends a user to the most relevant web site.
Yahoo had another opportunity to acquire Google. In 2002, Yahoo's CEO at the time, Terry Semel, engaged in negotiations to acquire Google, which lasted several months. The outcome of the negotiation was Semel balking at Google's price tag of $5 billion. Today, Google and its parent company Alphabet boast a market capitalization of more than $500 billion.
Yahoo's failed attempt at acquiring Facebook added insult to injury.
As the story goes, Yahoo was nearly able to acquire the popular social network in 2006 for $1bn, but due to a faltering stock price, Yahoo lowered its offer to $850m, allowing Facebook CEO Mark Zuckerberg to walk away from the deal.
Yahoo has made plenty of bad moves in acquiring (or not acquiring) other companies, but its crowning failure was its handling of its own potential sale.
In 2008, Microsoft, eager to compete with Google, was willing to pay $44bn for Yahoo, but thanks to what many considered gross incompetence, Yahoo's board rejected the offer.
In 2016 Yahoo announced that it would sell its core business to Verizon for about $4.8 billion. Following this news, a number of commentators were quick to bring up that Yahoo was once the darling of the new millennium's tech future, with its market cap maxing out at over $125 billion. Now, the company would go for about 4% of that.
17th March 2017
The tech world was abuzz this week with news of the acquisition by Intel of Mobileye, the assisted driving software company, for $15.3 billion – the largest ever acquisition of an Israeli company. This news correlates with the current wave of self-driving car enthusiasm, but we thought we would look at some of the quirkier start-up ideas out there…
Bird Control Group
So just because you aren’t going to be the founder of the next Mobileye, do not despair! Even the craziest idea can make it big, so reach for the stars (hopefully not in ash form though).
SYMBOLISM...the rise and rise of @
10th March 2017
Called the “snail” by Italians and the “monkey tail” by the Dutch, it’s hard to remember (thanks to email addresses and Twitter handles) a time when the @ sign was just an obscure symbol on our keyboards. @ has even been inducted into the permanent collection of the Museum of Modern Art, which cited its modern use as an example of “elegance, economy, intellectual transparency, and a sense of the possible future directions that are embedded in the arts of our time.”
The origin of the symbol itself is something of a mystery. One theory is that medieval monks, looking for shortcuts while copying manuscripts, converted the Latin word for “toward”—ad—to “a” with the back part of the “d” as a tail. Or it came from the French word for “at”—à—and scribes, striving for efficiency, swept the nib of the pen around the top and side. Or the symbol evolved from an abbreviation of “each at”—the “a” being encased by an “e.” The first documented use was in 1536, in a letter by Francesco Lapi, a Florentine merchant, who used @ to denote units of wine called amphorae.
The symbol later took on a historic role in commerce. Merchants have long used it to signify “at the rate of”—as in “12 widgets @ $1.” The machine age, however, was not so kind to @. The first typewriters, built in the mid-1800s, didn’t include @. Likewise, @ was not among the symbolic array of the earliest punch-card tabulating systems (first used in collecting and processing the 1890 U.S. census), which were precursors to computer programming.
The symbol’s modern obscurity ended in 1971, when a computer scientist named Ray Tomlinson, while developing Arpanet (a forerunner of the Internet) was facing a vexing problem: how to connect people who programmed computers with one another.
Tomlinson’s challenge was how to address a message created by one person and sent through Arpanet to someone at a different computer. The address needed an individual’s name, as well as the name of the computer, which might service many users. And the symbol separating those two address elements could not already be widely used in programs and operating systems, lest computers be confused.
He doesn’t remember what he wrote in that first email – perhaps the first hash tag?
3rd March 2017
The following piece has been adapted from 5 digital transformation mistakes to avoid, which appeared in Raconteur’s Business Transformation Report 2017.
Digital transformation is high on the corporate agenda, but for many businesses it remains a challenge. The IDC FutureScape: Worldwide Digital Transformation 2016 Predictions report has surmised that 70 per cent of digital transformation initiatives will ultimately fail because of insufficient collaboration, integration, sourcing or project management. For many businesses, the initial hurdle is to define what digital transformation means for their organisation.
This lack of a clear definition underpins five main pitfalls of digital transformation:
1. Scope creep
2. Latest tech
24th February 2017
Ever had trouble claiming for a broken mirror or stolen laptop? Don’t feel bad – insurance companies have had to deal with a lot worse! Here are some of the most expensive insurance claims of all time…
The world banking crisis 2008
Icelandic ash clouds
The single largest personal insurance claim
17th February 2017
Once at an Amazon offsite retreat, managers suggested that employees should increase communication with each other. To their surprise, founder and CEO Jeff Bezos stood up and announced, “No, communication is terrible!”
This is in line with his two-pizza team rule: teams shouldn’t be larger than what two pizzas can feed. When it comes to communication, this rule focuses on quality rather than quantity. Compare the interactions at a small dinner party with a larger gathering like a wedding. As group size grows, it becomes impossible to have meaningful conversations with every person, which is why people start clumping off into smaller clusters to chat.
For Bezos, small teams make it easier to communicate more effectively rather than more, to stay decentralised and moving fast, and encourage high autonomy and innovation.
The issue with larger teams isn’t quite the team size itself; it’s the number of links between people that is the problem, which may be expressed as: n(n-1)/2 (where n = number of people).
What is the magic number? Bezos’s two-pizza rule works out to at most 6 or 7 non-ravenous people. So, start thinking of splitting into subgroups when you approach double digits.
10th February 2017
Currencies around the world have some interesting nicknames - the dollar is a greenback (initially only the back of the note was printed in green) and a pound coin originally weighed one troy pound of sterling silver, giving the currency the name "pound sterling". The New Zealand dollar is called the kiwi (for obvious reasons), and the new South African Rand notes, bearing the likeness of Nelson Mandela are affectionately dubbed “Randelas”.
The Canadians in particular have had some fun with their currency - they trade in loonies and toonies!
The Canadian one dollar coin, commonly called the loonie, is a gold-coloured one-dollar coin introduced in 1987. It bears images of a common loon, a well known bird in Canada.
The coin has become the symbol of the Canadian dollar: media often discuss the rate at which the loonie is trading against other currencies. The nickname loonie (huard in French) became so widely recognised that in 2006 the Royal Canadian Mint secured the rights to it. When the Canadian two-dollar coin was introduced in 1996, it was in turn nicknamed the "toonie" (a portmanteau of "two" and "loonie").
There is also the relatively recent tradition of the “lucky loonie”, which entails Canadian ice hockey team players or supporters hiding a loonie in the ice in the hope that it will bring victory to their team.
So before you make any disparaging “Looney Tunes” remarks, first look at the size of the ice hockey players who take their lucky loonies very seriously!
3rd February 2017
New technology launches always come with the obligatory hype. Remember the introduction of the iPad? We went from not knowing we needed them to not being able to live without them and now, for many people, they seem to have outlived their usefulness.
The American IT research and advisory firm, Gartner has actually branded that process as a graphical presentation and dubbed it the “hype cycle”, which represents the maturity, adoption and social application of specific technologies, and how they are potentially relevant to solving business problems and exploiting new opportunities.
An example of a hype cycle is found in Amara's law, coined by Roy Amara, and which states that:
Each Hype Cycle drills down into the five key phases of a technology's life cycle:
Technology Trigger: A potential technology breakthrough kicks things off. Early proof-of-concept stories and media interest trigger significant publicity. Often no usable products exist and commercial viability is unproven.
Peak of Inflated Expectations: Early publicity produces a number of success stories — often accompanied by scores of failures. Some companies take action; many do not.
Trough of Disillusionment: Interest wanes as experiments and implementations fail to deliver. Producers of the technology shake out or fail. Investments continue only if the surviving providers improve their products to the satisfaction of early adopters.
Slope of Enlightenment: More instances of how the technology can benefit the enterprise start to crystallise and become more widely understood. Second- and third-generation products appear from technology providers. More enterprises fund pilots; conservative companies remain cautious.
Plateau of Productivity: Mainstream adoption starts to take off. Criteria for assessing provider viability are more clearly defined. The technology's broad market applicability and relevance are clearly paying off.
Interesting…but this sounds a bit like another cycle we’ve been going through with technology for years: the Five Stages of Grief!
27th January 2017
Nothing – apart from the Queen, Big Ben and tikka masala, perhaps – is more quintessentially London-y than the quirks and foibles that survive as remnants of a history reaching back centuries. Obscure and head-scratching traditions may be observed by the unsuspecting visitor throughout England (see gurning, straw bear and cheese rolling), but nothing quite matches the pomp and ceremony of the City of London itself.
20th January 2017
As if we don’t have enough foes to deal with, the latest character to be vilified in the court of public opinion is none other than…the humble office cake!
Office cake culture, which has blossomed into a firmly entrenched, almost daily way of life in many companies, has come under fire for its hazardous affect on our physical health, proving, once and for all, that nothing in this world is sacred.
Ignoring the benefits of our daily (short)bread to our mental wellbeing, the Faculty of Dental Surgery at the Royal College of Surgeons (RCS) has warned that the growing trend in large offices to celebrate birthdays, holidays, exam passes and “just because” is contributing to poor oral health and the obesity epidemic.
Tam Fry, from the National Obesity Forum, said of the biscuits, chocolates and cakes that perk up otherwise drab workdays that: “Such food is neither a treat nor a reward.
“You may not know who in the office is secretly dieting in which case they won’t appreciate your gesture: if you do know, you’re plainly malicious.
“If you want to give them anything, give them a smile, a hug or both!”
Other suggestions to combat the villainous Viennoiserie and diabolical donuts include:
Celebratory celery stick, anyone?
13th January 2017
“Mathematical beauty” – the notion that some mathematicians may derive aesthetic pleasure from their work, and from mathematics in general – may seem like a bit of a stretch as a concept. But if “Beauty is truth, truth beauty”, then it makes sense that mathematics, which is the is one of the only areas of knowledge that can objectively be described as "true" (because its theorems are derived from pure logic), should be the epitome of beauty.
And if a bevy of the world’s most desirable theorems held a beauty pageant, who would be the fairest of them all?
Euler’s identity, apparently, as decided in a poll conducted by The Mathematical Intelligencer in 1990.
Euler’s identity looks like this:
In case it’s not obvious, the equation is considered beautiful because three of the basic arithmetic operations occur exactly once each: addition, multiplication, and exponentiation. The identity also links five fundamental mathematical constants:
The number 0, the additive identity.
Furthermore, the equation is given in the form of an expression set equal to zero, which is common practice in several areas of mathematics.
A study of the brains of sixteen mathematicians found that the "emotional brain" (specifically, the medial orbitofrontal cortex, which lights up for beautiful music, poetry, pictures, etc.) lit up more consistently for Euler's identity than for any other formula.
Stanford University mathematics professor Keith Devlin has said, "like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence". It seems like beauty is more than skin deep after all!
6th January 2017
It’s 2017, the future is here and we have computers to do tasks that we are too slow, unreliable or lazy to do ourselves. Over the last few months there seems to have been an increase in concerns around automation and what it means for our future job security. But while these fears may be unfounded in some sectors and valid in others, a phenomenon known as the paradox of automation, where workers are denied the chance to practise their skills because computers do it all for them, has helped build a case against animation; advocating the use of our brains instead.
Driving on “autopilot”, for example, has made us lazy and dangerous drivers. A small group of traffic planners around the world has been pushing against the usual strategy of giving drivers the clearest possible guidance as to what they should do and where they should go: traffic lights, bus lanes, cycle lanes, left- and right-filtering traffic signals, railings to confine pedestrians, and of course signs attached to every available surface, forbidding or permitting different manoeuvres.
Laweiplein in the Dutch town of Drachten was a typically “automated” junction, and accidents were common. Frustrated by waiting in jams, drivers would sometimes try to beat the traffic lights by speeding across the junction – or they would be impatiently watching the lights, rather than watching for other road users. With a shopping centre on one side of the junction and a theatre on the other, pedestrians often got in the way.
The late Dutch traffic engineer, Hans Monderman, the most famous of the group, decided to create the “squareabout”. Instead of explicit efforts at control, he built a square with fountains, a small grassy roundabout in one corner, pinch points where cyclists and pedestrians might try to cross the flow of traffic, and very little signposting of any kind. It looks much like a pedestrianisation scheme – except that the square has as many cars crossing it as ever, approaching from all directions. Pedestrians and cyclists must cross the traffic as before, but now they have no traffic lights to protect them. Locals think it is dangerous – but that’s the idea.
It is precisely because the squareabout feels so hazardous that it is safer. Traffic glides through slowly but rarely stops moving for long. The number of cars passing through the junction has risen, yet congestion has fallen. And the squareabout is safer than the traffic-light crossroads that preceded it, with half as many accidents as before. Drivers never quite know what will happen next, and as a result they drive slowly and on high alert. And at the gentle speeds that have become the norm, drivers, cyclists and pedestrians have time to make eye contact and to read one another as human beings, rather than as threats or obstacles. When showing visiting journalists the squareabout, Monderman’s would close his eyes and walk backwards into the traffic. The cars would just flow around him without so much as a hoot.
In this squareabout, drivers are never given the opportunity to glaze over and switch to the automatic driving mode that can be so familiar. The chaos of the square forces them to pay attention, work things out for themselves and look out for each other – a lesson we should remember whenever computers threaten makes us feel inferior or obsolete.
23rd December 2016
Christmas time is here again and that means that good old St Nick will have his work cut out for him. But let’s just be realistic for a minute. How many children would Father Christmas need to get to on Christmas Eve and would this be possible?
Philip Bump decided to quantify Father Christmas’ task, setting out assumptions, methodology and caveats to determine how many (Christian) children he would have to get to, racing west across the face of the globe to stay ahead of the sun.
He needed to figure out how many Christian children live in each country of the world. The region being important because it would impact the feasibility of reaching them. So, he would need the population broken down by age, religion and time zone in each country.
Thanks to the CIA, he could readily determine populations by age and religion, and, by combining the two measures, roughly approximate the number of Christians for any given age group. (For the purposes of the experiment, Bump assumed people 14-and-under receive presents from Santa). Time zones were easily obtained via Wikipedia.
The equation was therefore: compare population of young people with density of Christianity and plot it on the globe. From that, you've got total populations and the times at which Father Christmas should hit them. Ignoring the mechanics of distance between houses, it seemed that the maths should have been easy. It wasn’t. All the complexities and oddities Bump encountered are described in his article; but for those who prefer a bit of instant gratification, here’s the end result of his experiment:
At the time of calculation, there were just over 526,000,000 Christian kids under the age of 14 in the world who celebrate Christmas on 25 December. In other words, Father Christmas had to deliver presents to almost 22 million children an hour, every hour, on the night before Christmas. That's about 365,000 a minute; 6,100 a second. Doable? Well, that depends on the population distribution and his longitudinal starting point, nevermind dealing with countries with multiple time zones and different number of dark hours available in the different hemispheres...
You could read all about Bump’s experiment here…or you could stop being an actuary (just for a day), and enjoy your presents – however they were delivered.
Happy holidays from all at MBE – see you in 2017!
16th December 2016
Contrary to what insurance pricing legislation suggests, women do, in fact, live longer than men – a phenomenon that has been true for centuries and doesn’t seem to be changing. But as male and female lifestyles converge (the backbreaking male labour of the past making way for the same sedentary jobs that women have), what other factors are at play to explain the stubbornness of the gender mortality gap?
The survival advantage of women is seen in every country, in every year, for which reliable records exist. The difference in lifespan has even remained stable even throughout monumental shifts in society. In 1800 in Sweden, for example, life expectancy was 33 years for women and 31 for men; today it is 83.5 years and 79.5 years, respectively. In both cases, women live about 5% longer than men.
Factors such as smoking, drinking, and overeating may partly explain why the size of the gender gap varies so widely between countries. In Russia, for example, men are likely to die 13 years earlier than women, partly because they drink and smoke more heavily. But then female chimpanzees, gorillas, orangutans, and gibbons also consistently outlive the males of the group – a fact that can’t be ascribed to poor lifestyle choices.
Instead, it would seem like the answer lies in our evolution; and there are many plausible theories which could help explain this biological difference, from the benefits of having two X chromosomes to the “jogging female heart” hypothesis, to the simple fact that taller people (which men generally are), with more cells in their bodies, are more likely to develop harmful mutations and suffer worse wear and tear.
But perhaps the true reason lies in testosterone – the hormone that drives most other male characteristics. A study of 19th century Korean court life shows that eunuchs lived for around 70 years – compared to an average of just 50 years among the other men in the court. Even the kings – who were the most pampered people in the palace – did not come close.
Although not all studies of other types of eunuch have shown such pronounced differences, overall it seems that people (and animals) without testicles do live longer. Sorry, guys.
Not only do women escape the risks of testosterone – they may also benefit from their own “elixir of youth” that helps heal some of the ravages of time due to the presence of the antioxidant hormone, oestrogen.
The reason for this may be a kind of evolutionary pay-off that gave both men and women the best chances of passing on their genes. During mating, women would be more likely to go for alpha males, pumped up on testosterone. But once the children are born, the men are more disposable; it matters more for the children that the mother’s body should be in good shape, rather than the father’s.
Now there’s some, um, ballsy water-cooler chat for you! Read more here.
9th December 2016
In an age where the form and function of the traditional office model is being questioned and reshaped, a number of fads, have come and gone, relegated to the “it seemed like a good idea at the time” archives.
2. Treadmill desks
3. Hot desking
4. Internal grass
5. Exercise balls
So, perhaps these (and other) fads, haven’t quite taken off…we’d still like to try the slide though.
2nd December 2016
The last few weeks have seen us travel back to Roman and medieval times to find out more about pension provision in the olde worlde. Today’s instalment explores how feudal economies looked after their old…
In land-based feudal economies, monasteries were able to offer what was in effect an index-linked annuity, called a “corrody”. This entitled beneficiaries to food (and, apparently just as important, ale) together with lodging over their remaining lifetimes in return for a lump sum at the outset. Corrodies could offer basic rations or a more generous lifestyle.
In 1313 Gunvor Olavsdatter bought the luxury version from the bishop of Stavanger in Norway. It provided not just her accommodation, but also the best-quality food and 2.7 litres of beer every day (and more at festivities). Her ‘premium’ for these benefits was the bestowal of land “to a value of 120–130 cows” upon the cathedral.
In 1316 William de Schokerwych paid £60 for a corrody granted by the priory of Worcester in England, which included stabling for a horse, and meat and fish when they were served to the monks. Although prices often fell as well as rising, the protection against inflation was particularly valuable since prices could spike up when harvests were poor, rising for example by a third in southern England in 1272 and 1291.
Wherever possible, older people continued to work until they became unfit or disabled. Artisans and merchants were generally better placed to do this than laborers. This approach has echoes in modern times as well. The obvious solution to ever rising life expectancy is to extend working lives, the more so since work is now so much less physically burdensome than in earlier times.
New annuity product idea: monthly pay cheque and daily beer…I think we have a winner!
25th November 2016
The second instalment in our examination of historical retirement provision looks at the middle ages – even Chaucer needed actuarial services!
One of the first predecessors to the gold tables that actuaries of today know and love was the Roman jurist Ulpian’s life table, constructed in the early third century CE, which estimated life expectancies from birth to over 60.
This table was not used for annuity functions, but rather to offer guidance on the fair division of tax burdens for heirs, legatees and tax collectors: the Roman tax authorities preferred to tax annual amounts rather than lump sums, which was apparently a less onerous procedure.
A thousand years in western Europe medieval societies were forging new forms of pension provision, despite the lack of formal pension schemes (there has been a widespread “pensions culture” in Britain since about 1300).
One not so ordinary pensioner was the poet Geoffrey Chaucer, who lived between around 1343 and 1400 and was granted several pensions including a daily pitcher of wine (commuted into cash after a few years).
Medieval pensions were funded by the church, which meant that clergymen naturally benefited, especially by the later middle ages. In the diocese of Exeter, four pensions are recorded for parish priests between 1300 and 1420 but the number then increases sharply to 11 in the 1420s, 33 in the 1430s and then 16 in the 1440s. In a classic non-separation of church and state, the state could also call upon the church’s resources. Already by the 14th century the King’s clerks – the civil servants of the day – were retiring to provincial “benefices,” a term for an ecclesiastical income.
Perhaps if people of the middle ages had taken Chaucer’s observation in The Canterbury Tales that “death is the end of every worldly pain” seriously, we would have no need for these pension provisions at all!
18th November 2016
How were pensioners looked after in the olden days? Over the next few weeks on The Lighter Side we’ll look at how people retired at various points in history…
In the Roman empire, life expectancy was around 25 – but this was largely due to high infant and child mortality rate…so there were still quite a few people making it to normal retirement age (around 7% of the population in the first and second centuries were over 60).
Fast forward a thousand years, and this proportion was still more or less the same in medieval populations. So these earlier civilizations also had to work out arrangements for looking after the old. In ancient times, instead of current workers subsidising the retired (as in modern pensions arrangements), support was provided within families. Familial obligation was taken so seriously that in Athens, in the fifth and fourth centuries BCE, children risked losing their citizenship if they did not support their parents.
This wasn’t the case in ancient Rome, but two millennia ago its first emperor, Augustus, pioneered the first state pension scheme financed by taxes. Retiring legionaries who had served for 25 years received a generous lump sum worth 13 times their annual salary. The scheme was financed through a new inheritance tax set at 5% of the value of an estate and a 1% auction tax. Despite the (begrudgingly acquired) tax income, this scheme came close to bankrupting the state.
Does this sound a bit like defined benefit pension schemes from the not too distant past? Well, Augustus' motivation was similar…employers offering pensions to long-serving workers in exchange for their loyalty. He also launched this scheme to ensure that soldiers were loyal to Rome and not to their commanders (who had provided for their retirement until then).
Although the insurance industry, like Rome, wasn’t built in a day, it does seem (to use another cliché) that the more things change, the more they stay the same.
11th November 2016
If your mind and soul (and bank balance) are wrapped up in the internet, then your online passwords can be seen as the keys to your heart. These days ‘password’ and ‘qwerty’ just won’t cut it to access your online accounts. Unique and strong password creation and memorisation is a bona fide art and there are all kinds of tips and tricks to help you keep track of them.
Not too long ago, the conventional wisdom was never to write down passwords — but that was when most of us only had a few to remember. Some experts have since changed their minds. Says one: 'The probability of someone breaking into your house and stealing your written-down passwords is considerably more remote than the 1-in-3 to 1-in-4 probability that your computer will fall to a criminal’s malware'.
Password cracking software generally uses a huge dictionary of possibilities, which it tries one after another, so the key precaution is not to use an actual word as your password, which is why many sites require the use of numbers and capitals.
However, this method may be counterproductive, as, for these sites, would-be hackers could immediately eliminate all the words that are all lower case, those that contain no numbers, and those that contain fewer than the minimum number of characters; effectively making their job earlier. The merit of these rules, though, is that they do force you to use a password which cannot be found simply by trawling through a standard dictionary.
Read some tips on how to create a password to remember here and remember the wise words of Clifford Stoll: “Treat your password like your toothbrush. Don't let anybody else use it, and get a new one every six months.”
4th November 2016
Carrots and peas, Romeo and Juliet, actuaries and puzzles…matches made in heaven! Actuaries (well, mathematicians, but close enough) have been associated with puzzles for centuries – something about our competitive and dogged streak when it comes to problem-solving (or our cryptic nature in general) will not allow us to overlook the challenge of a juicy cryptic crossword clue…in fact, anyone who has studied history (or Keira Knightley films) will know that in the Second World War many of British military intelligence’s heroes, the mathematicians of Bletchley Park who broke the apparently unbreakable Enigma machine code, were crossword fanatics.
Cryptic crossword creation is both a science and an art. There are guidelines around creating clues, for example, a good clue should contain:
There are also well known tools and devices crossword fanatics use to crack clues, such as common abbreviations, indicators of anagrams and use of punctuation.
Some of the more ingenious clues we’ve come across include:
•Opposed to previous duck course (9)
•Bank deposits say, key currency (5,6)
•Risk acne eruption without this? (8)
Need some more procrastination? Why not try your hand at an actuarial cryptic crossword (yes, they do exist!)?
Send in your correct answers to email@example.com and the next coffee is on us! Or, if the answers are proving elusive, email us anyway and we’ll provide some hints (don't worry, we won’t tell anyone!).
Actuarial Cryptic Crossword
(Created by Benjamin van Heerden (FASSA))
28th October 2016
The birthday paradox, also known as the birthday problem, states that in a random group of 23 people, there is about a 50 percent chance that two people have the same birthday.
This seems like a paradox to us – with only 22 other people in the room, finding for a 1 in 365 day (excluding 29 February birthdays) does not seem more likely than not to be possible. But let’s dust off our Stats 101 brains and look at some probability theory…
Remember that in the scenario, there will be 23 people, each making comparisons with the 22 other people. The total number of unique comparisons (or combinations) is thus 22 + 21 + 20 + … + 1 = 253. So each group of 23 people involves 253 comparisons, or 253 chances for matching birthdays.
However, we are not looking at just one, but at 253 comparisons. Every one of the 253 combinations has the same odds, 99.726027 percent, of not being a match. If you multiply 99.726027 percent by itself 253 times, or calculate (364/365)253, you'll find there's a 49.952 percent chance that all 253 comparisons contain no matches. Consequently, the odds that there is a birthday match in those 253 comparisons is 1 – 49.952 percent = 50.048 percent, or just over half!
To find more about why this concept seems so unintuitive, read Understanding the Birthday Paradox.
21st October 2016
Have you ever been taken by surprise by the result of, say, a national referendum, because everyone you were exposed to on social media was planning to vote the other way? You might have been trapped in a filter bubble.
A filter bubble is a result of a personalised search (most famously, Google’s Personalised Search results and Facebook’s news stream) in which a website algorithm selectively guesses what information a user would like to see based on information about them (such as location, past click behavior and search history). As a result, users become separated from information that disagrees with their viewpoints, effectively isolating them in their own cultural or ideological bubbles.
The term was coined by internet activist Eli Pariser who believes that these algorithms cause users to get less exposure to conflicting viewpoints and are isolated intellectually in their own informational bubble. Pariser related an example in which one user searched Google for "BP" and got investment news about British Petroleum while another searcher got information about the Deepwater Horizon oil spill.
A potential downside to filtered searching is that it "closes us off to new ideas, subjects, and important information" and "creates the impression that our narrow self-interest is all that exists", warns Pariser. It is potentially harmful to both individuals and society, in his view. He says that "invisible algorithmic editing of the web" may limit our exposure to new information and narrow our outlook. According to Pariser, the detrimental effects of filter bubbles include harm to the general society in the sense that it has the possibility of "undermining civic discourse" and making people more vulnerable to "propaganda and manipulation".
A filter bubble has been described as exacerbating a phenomenon that has been called splinternet or cyberbalkanisation, which happens when the Internet becomes divided up into sub-groups of like-minded people who become insulated within their own online community and fail to get exposure.
On the other hand, some reports are sceptical about the extent to which personalised filtering is happening and whether such activity is beneficial or harmful. In fact, some studies show that consumers use the filter to expand their taste, not limit it.
With apologies to the Bard: bubble, bubble, toil and trouble, indeed!
14th October 2016
October is the month for all things creepy and there are few things creepier than crop circles…but did you know that many of them display complex mathematical characteristics?
7th October 2016
Traditionally, the image associated with “actuary” is one of a maths genius with less than perfect social skills. But that is changing, especially as computers only become more powerful in their ability to do technical actuarial work – good communication is key to our profession (from exam stage to communicating to clients and board members, to winning new business). Luckily for us, emotionally intelligent beings are made, not born, and mastering the following “soft skills” can go a long way to ensure that we look at other people’s shoes, instead of our own, when we speak to them:
And, when in doubt, throw in a corny actuarial joke to break awkward silences...like this one:
The source of this article was a piece written for The Actuary magazine, available here.
30th September 2016
What number can you count to using your hands? Most of us would probably say ten (for our ten fingers)…and that is how the decimal system came about. But ancient Babylonians would argue that 60 was the logical counting base. And not because they had 60 fingers…
The way the ancient Babylonians counted to 60 on their hands (and thus ended up using a sexagesimal system) was as follows: count three bones of each finger on one hand using the thumb on the same hand (start at the top of your little finger and count down the bones 1... 2... 3, then move on to the next finger 4... 5... 6... and so on). Having got to 12 you count this off as one '12' on the other hand and go back to the beginning. You can do this five times, with twelve bones per time and thus count to 60 on two hands without having to write anything down.
This Babylonian numbering system is the reason behind 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day. Also 12 inches in a foot, 12 months in a year, 360 degrees in a circle and any number of other imperial measurements. Babylonian advances in mathematics were probably facilitated by the fact that 60 has many divisors (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60 - in fact, 60 is the smallest integer divisible by all integers from 1 to 6), Also, numbers which are multiples of 12 (such as 24, 60, and 144) are all also divisible by 2, 3, 4, and 6, whereas 10 is only divisible by 2 and 5 - so it's easier to count halves, quarters and thirds in a base 12 system.
Due to artefacts of their writing system surviving thousands of years, archaeologists have even found what appear to be school exercises in arithmetic and geometric problems - we can’t help but feel for the children who had to learn their times tables to the power 60!
23rd September 2016
Feeling blue at work lately? The solution to happiness may just come down two science – four chemicals which give us feelings of satisfaction in different ways:
It has been argued that these chemicals have wired us to be driven, organised, relationally-motivated creatures. We succeed because we understand the benefits of co-operation and teamwork. Feeling better now?
16th September 2016
Computers have slowly started to encroach on activities we previously believed only the human brain could handle. IBM’s Deep Blue supercomputer beat Grand Master Garry Kasparov at chess in 1997, and in 2011 IBM’s Watson beat former human winners at the quiz game Jeopardy. But the ancient board game Go has long been one of the major goals of artificial intelligence research. It’s understood to be one of the most difficult games for computers to handle due to the sheer number of possible moves a player can make at any given point. But earlier this year, DeepMind an artificial intelligence system created by Google beat a professional Go player at the game.
Why is this a big deal? While computers “solved” games like draughts years ago (i.e. each possible outcome of the game has been recorded), chess has not yet been solved. And Go is much more complex than chess – the game possesses more possibilities than the total number of atoms in the universe! There are over five times the number of spaces on a Go board than on a chess board—361 vs. 64. The number of possible Go moves is around 150–250 per turn (in chess, the average number of moves is 37). Because an exhaustive computer program for Go must calculate and compare every possible legal move in each player turn, its ability to calculate the best plays is sharply reduced when there are a large number of possible moves. Most computer game algorithms, such as those for chess, compute several moves in advance. Given an average of 200 available moves through most of the game, for a computer to calculate its next move by exhaustively anticipating the next four moves of each possible play (two of its own and two of its opponent's), it would have to consider more than 320 billion (3.2×1011) possible combinations. To exhaustively calculate the next eight moves, would require computing 512 quintillion (5.12×1020) possible combinations. The most powerful supercomputer in the world would require 4 hours to assess all possible combinations of the next eight moves in order to make a single play.
So how did Google’s AI system come out on top? Instead of relying on “brute force”, DeepMind used a system modelled on the human brain – building two neural networks to enable the programme to choose moves that “felt right”. Seems like the next level of Artificial Intelligence has just been given the Go-ahead!
Read more about DeepMind here.
9th September 2016
London recently commemorated the 350th anniversary of the Great Fire of London, which started in a baker’s shop in Pudding Lane, quickly spread, and blazed for five days, causing untold damage to the city. But, what rose like a phoenix from the ashes of the Great Fire was the world’s first insurance company!
2nd September 2016
These days we take for granted the familiar open-plan office layout in which we spend the better part of our waking hours. But modern office design is the result of an evolution: what started out, in the early 20th century, as a design exercise in extracting maximum efficiency from an organisation and its staff has now become a much more cultured process – and the latest trend (to which many companies have not yet caught on) is to incorporate natural elements in office design.
26th August 2016
“IS Helpdesk? Hi, my computer isn’t working.”
So if you are planning a PICNIC this weekend, don't be an ID-10T and forget to bring the (POB)CAKe.
19th August 2016
They say life moves pretty fast…if you don’t stop and look around once in a while, you could miss it. And that’s more true than ever. In 2016, everything is faster than before: computers, cars, and even people.
Usain Bolt's gold medal sprint in 2012 came in at 9.63 seconds, beating his own time to make him faster than every Olympic medallist since 1896. His best dash, at 9.58 seconds, is the World Record - making him the fastest person ever timed. All eyes were on his performance in the Rio Olympic Games, where he made history as the three-time gold medal holder.
But are Olympic runners getting faster with time, or is Usain Bolt just a superhuman determined to beat record upon record?
Looking at trends in men’s and women’s sprinting times, athletes do seem to be generally faster now.
There are a number of possible reasons for this: athletes have enjoyed a century of improvements in nutrition, fitness, equipment, footwear and track surfaces. Natural influences of how and where the athlete is born have also proven to be important. Technology has also allowed athletes to train more effectively, and helped their trainers obtain more data on their personal biology and genetics.
This has allowed them to trim fractions of seconds from their times, helping to drive averages and world records further down.
"Consider that Usain Bolt started by propelling himself out of blocks down a specially fabricated carpet designed to allow him to travel as fast as humanly possible. Jesse Owens, on the other hand, ran on cinders, the ash from burnt wood, and that soft surface stole far more energy from his legs as he ran."
"Rather than blocks, Jesse Owens had a gardening trowel that he had to use to dig holes in the cinders to start from. Biomechanical analysis of the speed of Owens’ joints shows that had been running on the same surface as Bolt, he wouldn’t have been 14 feet behind, he would have been within one stride."
A trend is not a trend until it has a graph; and the one below shows the number of seconds it took the gold medal winner to run 100 metres at each year the Olympic Games have been held; i.e. the race against time:
12th August 2016
Stats 101 taught us that the normal distribution can be used to approximate the binomial distribution. You too can investigate this hypothesis with the use of a simple piece of apparatus called the Galton board (named after the English scientist Sir Francis Galton), also known as a quincunx or bean machine.
5th August 2016
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Read more on the story here.
20th May 2016
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6th May 2016
Bookmakers are now looking at paying out a total of £25m, with the biggest winnings reported to be a whopping £100,000. The pay-outs break the record for the biggest loss in British sporting history, and equate to nearly half of what Leicester’s entire squad this season cost the club – a reasonable £54.4m compared to the hundreds of millions spent by the likes of Manchester United, Chelsea, Manchester City and Arsenal. So what should we bet on next? We may be a risk averse bunch, but, as Tom Hanks discovered, high risks can win you high returns!
29th April 2016
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19th February 2016
That’s right, the Qwerty keyboard, which has been hardwired in the brain of every typist and computer-user for almost 150 years, won its place in history by its ability to slow typists down.
The first attempt of Qwerty keyboard inventor, Christopher Sholes, was alphabetical, but the typebars clashed due to the key arrangements. So Sholes arranged them in a way to make the machine work. Frequency and combinations of letters had to be considered to prevent key clashes.
12th February 2016
Using a ratio of neocortical volume to total brain volume and mean group size, he came up with a number: 150. Anything beyond that would be too complicated to handle at optimal processing levels.
29th January 2016
22nd January 2016
The problem with this type of mnemonic is how to represent the digit zero (which occurs in pi at the thirty second place). Several people have come up with ingenious methods of overcoming this, most commonly using a ten letter word to represent zero. In other cases a certain piece of punctuation indicates a naught.
15th January 2016
So even though 2016 promises to bring a lot of exciting technological developments, it seems that robots taking over the world isn’t one we have to worry about just yet!