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FreeThinker

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A weird experience a few years ago...

My son remarked that he was doing logarithms at school. I said that I would have thought calculators had done away with the need for logarithms. He said "No, why would they?". It turned out that to him a logarithm was simply the power of ten that yielded the number in question. He didn't know about anti-logarithsm, had never seen a book of log-tables and was unaware that you could multiply numbers using logs.

Logarithms were still in his syllabus... but in a stamp-collecting role

It's surprising but there are still times when all the computers and calculators I have around me are still outdone by pencil, paper and a set of log tables. Not often but every once in a while I find myself turning to the old ways in desperation when my latest calculation has sent whatever machine I am using into terminal lock down due to a memory leak.

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Normal calculators don't do large numbers well. Without some idea of how to handle them, something we learned in math classes without modern appliances, if you needed an answer, you'd be lost. It still helps to have an understanding of mathematical functioning. Students today to a man in 4th and 5th grade ask why they need to learn this stuff when they have other ways of getting the answers.

C

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I'm with Nigel and Cole on that.

I find it amusing to say "That's a yield of about 8%" and watch the stunned expressions of people to whom mental arithmetic is alien.

I came across "Favela Maths" a few years ago. Apparently in the slums of Brazil kids are incredibly adept at mental arithmetic... its the difference between eating and not, when working out prices. Say an item is 19c each... to buy 20 is easy... 380c, but what if there are only 18 left? 18x19 is a much more difficult sum... no it isn,t ! the way the kids do it is 20x19 is 380, subtract 2x19 (38) is 342 (perhaps like them I checked that answer in my head by dividing by 2 then 3 and then again by 3, the increasingly complex operation getting easier as the numbers get smaller. That is their trick, convert the difficult sum into a series of easier ones. I found the idea fascinating... thank goodness for PBS radio on long journeys.

Intelligence is more important for survival in a slum than it is in the suburbs.

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But I mention this because in college I was tempted to take the fledgling computer science class, until I read through the textbook. Here was a melding of math and a foreign language. This was back in the days of punch cards and everyone had to learn the language to make that work. This is why I laud Bill Gates and what he has done to make computer technology available to the masses.

I think I could be good at math if I applied myself -- I do an awful lot of very fast calculating in my head -- but I have almost zero interest in mathematics. I'm more an English guy; I exempted two years of college English when I was a senior in high school.

Many years later, I got interested in databases and started building (from scratch) an enormous database of information about all the charted American hits from the early rock era to the present. About halfway through the project, where I had to learn scripting and some low-level programming language techniques, I realized to my shock: "oh, crap! This is math!"

It's frightening to consider how much of everyday life boils down to a database. The ATM, your credit cards, your mail, the gas pump, your paycheck, your taxes... it's all being compiled in a database. God help you when that database gets screwed up.

I like the idea of putting knowledge in a database so that you can access it in many different ways, but I quickly learned that a lot depends on how the information is entered into the database. Type it in wrong... nobody will ever be able to find it. I see a lot of problems like this on the web. Google has done an amazing job at interpreting what you meant to search for vs. what you actually typed.

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Normal calculators don't do large numbers well. Without some idea of how to handle them, something we learned in math classes without modern appliances, if you needed an answer, you'd be lost. It still helps to have an understanding of mathematical functioning. Students today to a man in 4th and 5th grade ask why they need to learn this stuff when they have other ways of getting the answers.

When I was in high school I had a TI graphing calculator that I used in my Algebra 2/Trig class. Yeah, a laptop would be better, but we couldn't use a computer in the class and we could use a graphing calculator. I still have it, a TI-89 Titanium. I haven't used it since the 10th grade.

Colin :icon_geek:

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When I went to school, calculators were just becoming affordable. I remember going to exams with a calculator, spare battery (it ate them), a slide rule and taking the loaned log tables too.

But a trick I and a couple of friends learnt was that we could beat the early calculators in doing reciprocals by learning what 1 to 10s reciprocal was, and interpolating the rest. We'd have a good enough answer while the calculator owner was still pushing buttons.

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When Vassar college took delivery of their first computer, IBM as a demo programmed it to calculate a series of approximations converging on pi by calculating the circumference of a polygon inscribed in a circle and then doubling the number of sides and calculating again. Of course it didn't work because when the length of a side of the polygon was too small to be held in the same register as the sum of all the sides the series of calculations stopped converging on pi. There were many red faces because at the time they had no idea what had gone wrong.

I believe there are many mistakes being made by spreadsheets and other calculations which make no allowance for the limitations of 'IBM double precision arithmetic'; in fact the only computer language I know that explicitly allows for this is J (which is an improvement on APL).

Love,

Anthony

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When Vassar college took delivery of their first computer, IBM as a demo programmed it to calculate a series of approximations converging on pi by calculating the circumference of a polygon inscribed in a circle and then doubling the number of sides and calculating again. Of course it didn't work because when the length of a side of the polygon was too small to be held in the same register as the sum of all the sides the series of calculations stopped converging on pi. There were many red faces because at the time they had no idea what had gone wrong.

I believe there are many mistakes being made by spreadsheets and other calculations which make no allowance for the limitations of 'IBM double precision arithmetic'; in fact the only computer language I know that explicitly allows for this is J (which is an improvement on APL).

Love,

Anthony

I did my Masters dissertation on the use of C++ for Safety Critical Programming, during my research I had to look at a number of safety incidents which involved computers, more than half were caused by the fact that the programmer had not understood the mathematics of what he was trying to do and did not realize that the capacity of the maths processor was not sufficient for the mathematical operation being attempted.

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I did my Masters dissertation on the use of C++ for Safety Critical Programming, during my research I had to look at a number of safety incidents which involved computers, more than half were caused by the fact that the programmer had not understood the mathematics of what he was trying to do and did not realize that the capacity of the maths processor was not sufficient for the mathematical operation being attempted.

Half of my real-world job is coming up with workarounds for badly-designed computer software used for sound recording and picture editing. Usually at that point, I mutter, "OK, now we have to get out the hammer," and I pound the computer into submission until it does what I want.

You can blame the hardware, the software, or the programmer, but I like to think there's Cosmic Interference from Evil Elves.

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Half of my real-world job is coming up with workarounds for badly-designed computer software used for sound recording and picture editing. Usually at that point, I mutter, "OK, now we have to get out the hammer," and I pound the computer into submission until it does what I want.

You can blame the hardware, the software, or the programmer, but I like to think there's Cosmic Interference from Evil Elves.

The first programming job I had was in an office that had a 10lb lump hammer in a glass fronted box on the wall. Underneath was the notation "Ultimate Debugging Tool, for Emergency Use Only". There have been many times since then when I wished other organizations had one available on their wall, especially international banks.

By the way there is no Cosmic Interference from Evil Elves, there is only malignant computer intelligence. Only an intelligent system could possibly work out how to crash in the most embarrassing way at the most inconvenient time. First law of computers, the size and effect of any computer crash is directly proportional to the importance of the observer who is available to observe the impact of the crash. You have the office junior watching and the program will run perfectly, have the Head of Finance who is paying for it and there will be problems, have the CEO of the client and you might as well not switch the system on.

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