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TAPE counter units converted to TIME.

**Video Recorder or Audio
Tape Recorder counter units used for working out Time**

On a tape recorder or a videotape machine there used to be a "tape counter" which measured how far into the tape the playing/recording had progressed. However, although the counter units had some relationship to time, it was not a very good measurement as the tape counter moved slower at one end of the tape and faster at the other, even though the tape progressed at a constant rate of time. Whether it was a reel to reel player/recorder or a cassette, the mechanical tape counter was ubiquitous, and it was only later that these were replaced with digit counters which were replaced with truly time based units.

As I needed to know what time the recordings took, and I knew that the tape counter units had some relationship to time, I tried to devise a scientific function to calculate time from tape units and tape units from time. This proved very useful in videotape timing, and as far as I know it works generally for tape and cassette machines for audio and video.

By doing a few experiments of timing and measuring tape units it soon became clear that the relationship between tape counter units and time was a quadratic equation. Quadratic equations are reasonably easy to solve and there is a general purpose function for this.

At this point in the write-up I can't help thinking there are going to be some people saying "What's the formula for quadratic equations then?!" and there are going to be some who are going to be saying "What ARE quadratic equations?". If you would like to know about the algebra, here's an attempt at it: Quadratic Equations

Meanwhile, if you're not into the algebra, or you already know about all that kind of thing perfectly well, let's just carry on with the stuff about tape and time. The thing is that there's a mathematical relationship between the numbers on a tape recorder counter and the time elapsed, and it tends to be something like this:

ax^{2} + bx
+ c = n

...where n is the counter reading and x is the time elapsed. If you don't understand algebra, don't worry; It's just a formula that gives the answers. By this formula it's possible to work out time from tape counter units and vice-versa. Of course you have to find out what a and b and c are, but they are just numbers, and you can find them by experiments and some mathematical calculations. It's worth mentioning that they are different for different machines, and each cassette recorder or videotape player will have a different answers. But once calculated, the numbers remain constant, and can be used for working out time and tape for the lifetime of the machine.

There are some interesting things about all this, and it goes far beyond a convenient time-tape function!:

* Firstly, it's easy to see why mechanical tape counters became obsolete for most domestic applications, and were replaced by digital time clocks!

* It's interesting to note that you don't often see manufacturers putting a formula for the relationship in the backs of their manuals, so either they think it's too difficult for most people, or they haven't found out it's possible!

* It's notable to find a practical everyday application of quadratic equations! I have heard of people never using them after leaving school. (also see logarithms) And, even scientists who regularly use quadratic equations in their research work don't often find applications of quadratics at home.

* Another curious feature of the equation is that when you look at it, the "c" part of it gives a strange notion that there exists something along the conceptual lines as a "video tape Big Bang" at which the tape/time function would be going infinitely fast. That point for most VHS videorecorders is about 15 minutes before the start of the tape. Now obviously this raises some very odd ideas about the Universe. With the videocassette phenomenon it's easy to see how the formula has generated the effect, by the speculative notion that the hub of the tape reel could be considered to be entirely made of tape, which if it could be unwound would have a point at the very infinitesimal instant at the epicentre when tape units versus time would be going infinitely fast. For a VCR that's silly, and the hub of the reel is clearly not made of tape! But the equation is consistent with it being so made, and as I am a paranoid schizophrenic mad scientist I think it casts a suspicious shadow of doubt on the perfect assumption of the Big Bang theory. Or at least the "singularity" bit of it. (Don't get me wrong and write in about it all huffy and disgruntled. It's just an amusing notion. And besides, the Big Bang theory is well proven back thousands of millions of years. It's just the bit before 300,000 years when it might be the wheel hub ;-))

* Finally, to round off this odd review, I'll have to mention that tape recorders, video recorders, and other types of record/playback machines are available from places such as these electrical shops, and recording studio equipment is available from some of these music equipment shops. Most of the more recent equipment has a more linear digital time relationship. In fact, most equipment will by now be digital, so the tape/time thing may sound like I'm talking about how to wind up your gramophone to play your 78RPM gramophone records rather than playing your 300RPM compact discs or even your MP3 / Ogg Vorbis digital files, which have no RPM at all! See music shops, video/DVD etc.

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