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Part of project management requires the determination of the critical path. So what is that? We’ll take a simple example from the kitchen. This simple meal comprises grilled steak with vegetables and mash. The cook can only do one thing at a time, the meal needs to be ready as quickly as possible and all three components of the meal are to be ready for serving at the same time (no hot tray here!). The question is which is the sequence of the following processes which will determine the total time from start to finish.   The first thing we need…

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How, we often ask ourselves, can an attorney and advocate, defend someone whom they believe to be guilty? Do you remember those debating competitions of your school days? Each of two competitors was given opposing arguments in relation to a proposition. They then had to argue their side of the debate and the one who was most convincing would be the winner. Did the competitors have to agree with their own argument? No. What was being tested was not their beliefs, but their ability to debate an issue. When an advocate argues in favour of his client, he is doing…

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As you know, I am a bit of a Japanese abacus fanatic. This lead me to a fascinating method of multiplying using straight lines. Here’s how it works. We’ll take an example of 123 x 332 Draw parallel lines representing the number 123 Next draw a similar set of lines in the other direction representing 332 Now, all you have to do is separate the groups of numbers as I have done below Count the intersections in each group. This gives you 3 9 17 13 6 Carry the 10 of the 17 left to add it…

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Feng shui is an ancient Chinese science aimed at encouraging energy flow and balance within a given space.    Having lived in Hong Kong for two years, my lovely wife, Helen, tells me that it is pronounced fung shoi, so let’s go with that. There are all sorts of rules about how your house, for instance, should be placed in relation to its surroundings (particularly roads), which rooms should be used for what purpose (e.g. central, NE, SE, NE and SW), the layout of your furnishings and the materials that they are made of. Sure, you can engage a specialist…

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I was brought up to believe that and was never preceded by a comma. My daughter said it always is. Seems we were both wrong. Evidently, these are the rules – You can list A, B, and C as in Peter, Paul, and Mary had a party. or you can list A, B and C as in Peter, Paul and Mary had a party. The comma is optional However, if the list is only of two items, there’s no comma A, and B is wrong as in Peter, and Paul exchanged business cards. A and B is right as in…

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You hear about Bitcoin, then you must also hear the word blockchain. Ever wonder what the heck it is?   I like to think of it as a new Internet of events. The events are the blocks and the sequence is the chain. Hence blockchain. It was adapted by Satoshi Nakamoto, the unidentified person or group of people who enhanced it for Bitcoin. Let’s take a simple example – On 12 July 2008…

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I came across a mind blowing arithmetic pyramid and couldn’t resist the challenge of figuring out how it worked –  Here’s the magic pyramid that held me in awe (I can’t give credits, because I don’t know who discovered it) So why does it work? It turns out to rely on that magic little number 9, so let’s reverse engineer it – I found it easier to start with the big number so that I could figure out the logic. Notice how taking one of the starting numbers away shifts all of the numbers…

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We moved to apartment living in Rosebank in September and have, for the first time become aware of the beginnings of the devastation of the urban forest. On the upside, however, we also enjoy almost daily sightings of rose-ringed parakeets. I used to be a very keen birder, but nowadays, I simply enjoy hearing and seeing them and no longer go out of my way to tick new ones. So it’s years since I added another tick to the 700+ list that I had accumulated over time. Imagine my surprise then, when…

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Johannesburg has the world’s largest urban forest (the other claimant in Rio is outside the residential part of the city). But our forest is dying! Helen and I live in Rosebank in the heart of the so called “Parks” – Parkview, Parkhurst, Parktown, and we are watching the trees around us die. Sure, many of them fall to property developers – there seems to be an insatiable demand for residential apartments, so that Rosebank central (which is largely devoid of trees) is creeping outwards, but that’s not the problem that we see as we drive through our leafy neighbourhood. Next…

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Dear Cyril, There’s so much wrong with South Africa, you can’t possibly know where to start. There’s only one way out of your dilemma. You need to learn the technique of Dreaming Dreams. Here, I’ll teach you – But let’s just have a little chat first, to set the scene… If you try to prioritise your actions, you’ll find yourself trying to put out one fire while something else has to be left to burn. But so many of these fires are devastating and have to be tackled immediately. And how will you ever know whether…

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If A gets bigger whenever B gets bigger, did A cause B or did B cause A? This correlation is so often misinterpreted that it probably led to the expression “Lies, damned lies and statistics” Correlation can be positive (both things increase together) or negative (when one goes up, the other goes down) – Typical positive correlation would be an observation that the more laughter in a family, the better the kids do at school. Conclusion – laugh more with your family and that will improve your kids’ marks! An example of negative correlation would be finding that the more…

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We recently spent a week in Cape Town. The question was how to get from our apartment in Rosebank to O.R Tambo International. I was excited to see that the Gautrain bus passed right in front of our apartment. Wow! Life had suddenly become so much easier. So, a few days before our departure I set about planning how we would get to O.R Tambo International Airport by Gautrain. It ended up like this: Gautrain bus from our door to Rosebank Gautrain station Wait for…

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Why is Gallagher Combined School such a great school? Like Harbour and Associates, Gallagher School, of which I am co-owner, is driven by passion, love and innovation. We are passionate about giving the absolute best service to the clients of our practice and the learners at our school. In the practice we love working together and we love helping our clients. In the school we love our learners and they love us. In the practice, we are constantly re-inventing ourselves, never resting on our laurels, always looking for better ways to serve…

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When I learned that my grandson and his sister planned careers in robotics and the arts respectively, I realised that the arts was about the safest of the lot. I guess robotics and AI are pretty safe careers as it will presumably be some time before robots can design better robots, but surely some of the arts will never be displaced. I can’t, for example, imagine humans watching a play written or acted by robots, but which of the arts could they conceivably take over? Surely not dance, for the same reason as acting. How about replacing an orchestra? Why…

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There’s a mystery that I just cannot get my head around. What exactly is mathematics? Some would say it is a language. Yes, I would agree with that, but there’s more to it than that. My problem stems from my passion for quantum physics and the mysteries of the universe. You may or may not know that in Einstein’s time there were two principal branches of physics, the big picture that Einstein so eloquently described (it dealt with the sky at night, gravity, time, mass and energy) and the small picture, generally known as quantum physics (which deals with elementary…

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I had to go to the SARS Tax Practitioners’ Unit in Pretoria, then on to the Import Export Unit downtown Pretoria. The parking at Tax Practitioners is great, but downtown, it is positively dangerous and you can only find illegal parking “protected” by self appointed car guards. I’ve always had to take a chance, but when I mentioned it to Helen, she suggested I leave my car at Tax Practiitioners and Uber to Import Export, do my business, then Uber back to my car. Now why didn’t I think of that?…

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Is it my imagination or are the roads around Johannesburg getting fixed? I live in Fourways and work in Midrand. The first thing I noticed was that potholes were getting repaired, but it has gone beyond that, roads are being resurfaced all over the place and in many cases widened. I wonder whether Pretoria and Nelson Mandela Bay are getting the same treatment? Where is the money coming from? You don’t have to be a rocket scientist to figure out that the DA and other opposition parties are plugging the corruption leaks in the municipalities that they have taken over.

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Do you play cribbage? It is the best card game for two by far, or doesn’t anyone have time for card games any more? Here’s how we spiced the game up even more with jokers. Helen and I play about twice a week, usually when we’re taking something from the freezer that Helen cooked previously, or when I’ve brought in shushi from the local Japanese place. A game of cribbage has all of the elements essential to any good game – luck, skill and some really close finishes. We added an interesting variation, which worked out well. If you know…

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We all have times when there are just a stack of jobs to do and we have to decide which ones we’re going to tackle first. A knowledge of queueing theory can help us decide. Suppose you have 5 jobs in the queue and each one will take a different amount of time – Job 1 – 7 hours; Job 2 – 3 hours; Job 3 – 5 hours; Job 4 – 1 hour; Job 5 – 12 hours If you do the longest job first, then the next longest and so on, doing the shortest job last, then the…

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We needed to paint the garden wall and I had to break up the old trellis to separate it from the creepers which had intertwined with it. We were quoted about R15 000 for replacement trellisses and I figured I could do better. Here’s how – This is what I set out to achieve – D’you see the almost invisible trellis? First I pinned the wall 60cm apart horizontally and 40cm vertically Notice that this one is on a curved wall which solved another problem. Then, using 1.5mm braided stainless steel wire and electrical crimp unions I fitted the wire…

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