baring the abacus
212)
... I doubt that there has ever been a better way to learn the relationship between numbers - and even mathematics in general - than the slide-rule from days-gone-by, and the ability to plot functions using modern computer technology.
For the young people here who may not have ever used a slide rule, below is a link to a virtual slide rule:
virtual slide rule
I wish, and think it would be a great asset to Maplesoft to incorporate a "Virtual Slide-Rule" into their software. Not something as basic as the one shown at the link above, but rather one that could be zoomed in/out, display the results digitally, include new functionality such as that relating to integral and differential calculus as an example, and even plot the results. Myself, being 53 years of age and trying to pick up where I left off after dropping out of school in my youth somewhere between the 8th and 9th grade, can testify to the benefit of these two tools! I honestly believe, for example, that if Fourier (and likely many others) had a tool such as Maple, he would have come to his conclusions - and likely many more - more quickly.
The benefit of a virtual slide rule versus the old-style (I'll talk about my ideas for improving that style as well, further down), is speed and resolution. As those of you who have used a slide rule may know, the resolution isn't as easily obtainable as it is with software. The ability to zoom in and out on a virtual slide rule would eliminate that problem. By zooming in and out, the idea is not to just make the thing larger, but increasing the resolution of the numeric display so the final result of the calculation becomes the same as that of software performing a similar calculation. I've been using Maple only for a short while and have learned a great deal. I fairly recently purchased a very fine slide rule at an antique shop, the model shown at the link above coincidentally (many are available on ebay even), and am already able to get answers to problems much faster than a hand-held calculator or computer software.
So... Maplesoft developers, what do you think?
Jacques, if you are reading this, it would be my assumption, based on ideas that you've mentioned in this newsgroup, that this kind of idea may be appealing to you. Although the capability of computer software is a wonderful thing, there are still a few "bumps" when it comes to entering the data either by numerous mouse clicks, or of course the keyboard.
Concerning the idea of bringing back the old-style physical slide-rule, I think it would be great if it were to be redesigned in the same way as the caliper which has now also seen a new design within the last 15 years or so, by adding a digital display. I think both the software and hardware improvements to the slide rule would greatly benefit the student in the learning of mathematics.
In my opinion....
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Comments
Agreed
I guess it must be the fact that I still frequently turn to math books written over 100 years ago when I am interested in ``computational mathematics''. While I have integrated the use of the Internet (and computers) into my daily life in all sorts of scary ways, I am still not infatuated with everything that's new -- sometimes the old ideas really are better.
Slide rules are one of those old ideas that need to be re-examined by young minds. Not that we should use physical slide rules, but as you say, that the fundamental input/output paradigm embodied in slide rules could certainly be adapted to the computer age and provide for a very efficient means of interaction.
This is also why a lot of people still do their mathematics with pen and paper -- because it is generally way more efficient than using a computer to do the same thing. Maybe one day computers will have methods of interaction (and accompanying software) that make them just-as-efficient as pen and paper; lots of people have tried, but no one has yet succeeded. Here I mean to "write down" mathematics, by a trained mathematician/scientist/engineer/etc. If you are instead interested in "exploring" a mathematical idea, then Maple is frequently a better tool than pen and paper.
old ways - Jacques
Although I'm relatively new (or should I say "renewed") to mathematics, and even taking into consideration that I'm a programmer working with computers and computing software everday, I agree about the "old ways". The problem with many of the new ways of doing things, at least as related to learning or comprehension, is that there is just so much available, so fast, presented in such a way that the actual comprehension and retainability factor suffer. The answer to just about anything these days is usually nothing more than a "google search" away. I think kids, and even to some degree adults, blindly suffer from such convenience.
I must apologize, but you completely lose me when you refer to the pen and paper way of math being more efficient than computing - even with consideration of the ideas I've presented further up. You do mention "by a trained mathematician/scientist/engineer/etc" (I'm sure you know that I am not) which I guess carries a great deal of significance in this regard.
I should perhaps mention again, that I'm all for new technology. I couldn't have even begun to learn the math I've learned as quickly as I have without maple and the availability of the research resources now available, but also as mentioned, I think we need more of a combination of the old and new to improve comprehension and retainability.
New and old technologies
I am also all for new technologies (else what am I doing on this site?), but I am for new technologies that help me. I am just as happy using old tools if they are more efficient than the new ones. One the giant failures of the internet boom was the sheer number of technology-for-technology's sake ideas that were floated around, and even captured people's attention. This has not died down, but has mostly moved to the user-interface front rather than being about complete business plans.
What I tried to say about pen-and-paper is that there are some kinds of ``computations'' (mostly derivations, ie proofs) that I can do with pen-and-paper in seconds, while coercing Maple to do the same thing for me would take several minutes, at best. Frequently the problem has nothing to do with Maple -- most mathematics uses a 2D notation that is much much faster to write on paper than it is to type or click through or whatever. This is why people try again-and-again to come up with good pen-based computers! Hopefully, one day, they will.
Also, there are areas of mathematics in which Maple is still in a ``learning'' stage, so it can be easier to just "get the work done" the old fashioned way rather than fight with Maple [which for some of us means using Classic rather than Standard sometimes, not just pen vs technology].
got it
This explanation of the pen and paper idea makes perfect sense to me.
Thanks for your comments. I always enjoy reading your input within this newsgroup.
Slide Rule
The site here has a nice computerized version of a slide rule. The scroll wheel on my mouse zooms the display in and out. Not a Maple app, but just as interesting.
Regards,
Georgios Kokovidis
Dräger Medical
Georgios - slide rule
Below is a link to a pretty nice virtual Flash style slide rule from the University of Virginia. It shows spiraling logarithms, and can be used to do multiplication and find roots. As with the one you mentioned, it zooms - right-clicking mouse on flash app after first activating it with any mouse click, brings up a menu to zoom and other features. Once zoomed, clicking the left-mouse on it, allows it to be moved around so you can see the various areas of the slide rule.
link to slide rule
Below is a link to the mother site that has links to the slide rule as well as many other very nice flash apps (which can also be downloaded to mac or pc) including things such as integral and differential calculus.
another link
I think these are very good learning tools, and I will probably do another entry in my blog concerning such things.
slide rule, instrument for
slide rule, instrument for making numerical computations and readings, the results of which may be read easily and quickly after performing simple mechanical manipulations. Multiplication and division, finding of powers and roots, and other more complicated calculations may be performed with a slide rule. Based on John Napier's principle of the logarithm, it came into use after Edmund Gunter created a logarithmic scale in 1620. Gunter's rule consisted of a straight line on which numbers were spaced at intervals proportional to their common logarithms. Using this scale, William Oughtred and Edmund Wingate developed independently (c.1630) the first slide rules. Amédée Mannheim, a French army officer, in 1850 established the form that it maintained thereafter. This had three parts, the stock, the slide, and the cursor (indicator). The stock consisted of two fixed parallel rules, each with a scale on its inner edge. The slide was a single rule, moving between them. It had two scales on its outer edge, each scale corresponding to the fixed scale to which it was adjacent. The cursor, a transparent square with a hairline, could be moved the length of the rule to aid in reading it. In its many varieties it had additional scales for such calculation as logarithms, trigonometric functions, and square roots. By the late 1980s they had been supplanted by the electronic calculators, which were easier to use and more accurate.
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SlideRule Status
I figured I'd add some links to one of my slide rules that I made for a teacher of gifted 4th and 5th graders, as well as a link to a virtual ruler of the same. After deciding that the lines were kinda hard to keep track of for both his and my own somewhat tired eyes, I figured I'd add a glass cursor - like the slide rules of ancient times had. My cursor, is quite a bit bigger to accommodate that unusual shape of my slide rule.
2timv.com/KidsRule/MarkSlideFront.jpg
2timv.com/KidsRule/MarkSlideZoom.jpg
2timv.com/KidsRule/MarkSlideBack.jpg
2timv.com/KidsRule/MarkVirtualRule/
It looks rather large in the pictures, but it's only about 10". I set the main text on his to "Kidding Around!" at his request, but the usual is "Kid's Rule!" as I mentioned elsewhere in my blog.
Below is a link to the manual. It doesn't look as well as a pdf as the printed and bound copy, but it will at least give you an idea of what I give the kids to get them acquainted with the slide rule.
2timv.com/KidsRule/KidsRuleManual.pdf
virtual "Kid's Rule" update
I've updated my site for the slide rule I'm making for kids.
I've added an improved "virtual slide rule", as well as the same, except with some added
user-interraction capability. The links:
thekidsrule.com/VirtKidRule/
thekidsrule.com/VirtKidRule/Automated/
I realize that this is of interest to only a few members here, but I have received comments expressing interest in this from members of this group, so I figured I might as well continue this blog.
If you browse the pages there, you'll find one example showing how the slide rule can be moved to a particular position, and then without making any changes, all relationship between values of "candy bars" to "cost" can be determined. For example, and remember this is for kids:
If 5 candy bars cost $3, how much for 4 candy bars?
how many candy bars cost $1.20
how many candy bars cost $5.40
how many candy bars cost $3.60
for $1.50, how many can you buy?