Mathematics Tips


Thank goodness the Arabic peoples invented something called base ten numerology (with Arabic numbers too); which in itself was very handy since they also had eight fingers and two thumbs handy. If you did not catch that handy pun, it is way past your bed time and you need your sleep... go away.

In grade school we were taught most ancient Arabs had sheep and got tired of counting sheep (with a mark in the dirt or on a tree) with one mark representing each lamb, ewe, or ram. Therefore, we were taught, Arabs started substituting odd marks for each set of ten sheep and had more time for other things.

My class mates and I decided there were fallacies in these lessons. Upon researching, we found that most Arabs did not tend sheep, that most folks would not tend sheep because of what sheep do, that this is the very reason shepherds were invented, and that shepherds were more than likely not responsible for devising the base ten system.

Regardless of its origin, the base ten system swept the world like a Mongolian horde. It was/is so popular that even we were taught it at a young age several thousands of years later. Too bad it does not work as well with computers as with sheep. This is simply because the first computer geeks had no fingers; they were all thumbs. So, unless you understand algorithms, binary language, or other such core system languages; forget what you know about math for a few minutes (most folks find comfort in doing that).

Tip One: Re-think your numerology. Count by two (four, eight, etc.); since they are magic numbers in virtual realities. The binary mathematical system only has two numbers; zero and one. Since zero means nothing and one means the first full unit of something, it becomes apparent that there are two relationships involved in the binary system; nothing and something respectively. Before you think of this as rambling or a Monty Python thing, I must point out that many of you have one or more off/on switches on your system which read 0/1.

O110100 in binary language is eight bits of information which comprise a byte and reads off, on, on, off, on, off, off (how's that for twosies Jethro Bowdene!?) Most computers were using eight bit technology back in the sixties, seventies, eighties, and nineties. Remember the number eight is a magic number. Our 386 PCs came stock from the factory with eight bit capabilities in the early nineties. Some 486 PCs had the first 16bit functions and, dern, if Bill Gates didn't come up with a 32 bit operating system introduced with Windows 3.1, ...no 3.11, ...no 32s, ...OK, OK, with Windows 95 and NT.

The point here is that one must count twos by sets of eight, sixteen, thirty two, etc. My reason for illustrating this and pointing it out is to prepare you for the following tips.

Tip Two: Standards of measurement with memory include several words from the ancients; which include prefixes (kilo) for a number and a suffix for a byte (byte). Although kilo means 1,000 with most things (kilograms, kilometers, etc.) this can not be with computers as it is not divisible evenly by eight. So, kilo means 1,024 when applied to the computer since 2 x 4 x 8 x 16=1,024. You may also note that 128 is devisable by eight and so is 64; but we're talking today stuff (not Commodore 64).

Please keep in mind that some acronyms exist for our standards. Byte (b), kilobyte (kb), megabyte (mb), and gigabyte (gb), are pretty common.

Now the crash on it all. 1kb=1,024 bytes, 1mb=1,024kb, and 1gb=1,024mb. These standards are pretty common in today's market quotes on memory. My system has a 64bit soundcard with 256kb of flash memory on it, my modem has a transfer rate of 28.8kb/s (kilobytes per second) baud rate, my 128bit video card has 16mb of SDRAM, and my motherboard has 64mb of EDO SIMMS RAM and can be upgraded to 128mb of mixed Fast Page or EDO SIMMS RAM, or 64mb of tandem DIMMS RAM.

Tip Three: This eight thing applies to formatting hard drives with most operating systems. Formatting your hard drive is limited to counting megabytes of memory in partitions (allotments) by eight. I have a 2.1gb hard drive which has a real capacity of 2,111.8gb. However, I can only access and partition 2,047mb of space. OK, if I were to settle for using UNIX as an operating system, I could get most of the 2.1gb; but then Lara Croft would have to raid tombs somewhere else!

Tip Three: With large partitions, many kilobytes of hard drive space can be lost. This is again because of the magic numbers, your file's sizes, and how they are stored in "clusters". If you have a hard drive formatted to 127mb, it has clusters which are 2kb in size. If, in a directory there are five files which are 5kb, 6kb, 13kb, 15kb, and 2kb in size (totaling 41kb) they actually take up 44kb of clustered space (loosing 3kb of hard drive space). This is because the 5kb, 13kb, and 15kb files use up 6kb, 14kb, and 16kb of space respectively. In other words, only one file will be using any part of a cluster. Hey, a 3byte file uses the whole 2kb cluster!

Real problem is, if your partition is larger than 127mb, your clusters are too. It goes this way with cluster sizes: 127mb partition=2kb clusters, 128mb-255mb partitions=4kb clusters, 256mb-511mb partitions=8kb clusters, 512mb-1,023mb partitions=16kb clusters, 1024mb-2047mb partitions=32kb clusters, 2048mb-4095mb partitions=64kb clusters. I don't have one of the new 40gb hard drives, but speculate they also have larger clusters.

So, you have a 4gb hard drive which only has one partition of 4094mb of space? Wow, the scenario in the first paragraph of this tip uses 320kb of space! Now do you see why some folks format their hard drives and form smaller partitions (see my Storage Tip on formatting)? This is also one reason why better programs are made up of a few large files instead of a lot of small files. Oh my, look at how many files Windows 95 has! NT doesn't have so many.


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