# 6-inch bar

#### ssj5harsh

Here's a novel new way of storing information:
Give every symbol a code from 000 to 999. Write down the information in this form. Then the Key(Master) trick up our sleeve: Put a decimal point before it. Reduce the fraction to the simplest form. Then take a 6-inch platinum-iridium alloy bar and mark a line to split it into the fraction(using supercomputers, lasers, etc.). Store this Bar safely. Away from moisture, dust, etc.
In this way we can store any amount of information on a 6-inch bar, unlike CD's which have a limit. Or can we? Find the theoretical limitation of this method.

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#### BicycleTree

Dude! We don't need another brain teaser! Try "Procedure"!

#### mezarashi

Homework Helper
I'm sorry but I'm not getting the logic of your proposal. There is no free way of storing information. Are you simply proposing a storage method or a compressive algorithm? If you reserve a 0 to 999 for every character, you will need 1000 bits or 4 bytes per character. The current ASCII standards reserve 1 byte (255 possible characters). By making it a fraction, you are not introducing any compression at all. In fact, many fractions in computer programming are stored as integers. For example you want to describe a quarter pixel motion vector (1.25), the actual integer stored will be 5 or in binary as the computer sees it (101).

#### ssj5harsh

Sorry, bicycletree, I just wanted to type this down. I couldn't understand your problem on the first try. I'm going to go and try your problem right now

Mezarashi, I am suggesting a physical method of storing information. I say, make it into a fraction and mark the fraction on an unchanging bar. This way, there is no limitation on the capacity of the bar. With CD's we have a limit of 700 or so MB. It is higher for DVD's. The 000 to 999 is just a way to encode information. I put it in decimal system so that it is easy to understand.Here's an algorithm to read the bar:
1. Use supercomputers to measure the length of the bar on each side of the bar.
2. Divide the smaller by the bigger and convert it to denominator 10^x where x is some natural number.
3. Simply decode the information now by reading the numerator 3 digits at a time.

There you have it, All the information you can have in a single 6-inch bar. The question is to find the limitation of this method(it does indeed have one).This method is not a real theory, just a brain teaser.

Off to 'procedure' now!!!

#### mezarashi

Homework Helper
Well okay, I don't see any fundamental limit to this method other than the physical limit (i.e. when you get down to marking atoms) and most importantly the precision of our equipment. One little fault means that we lose just about all the information that we ever stored there. The string of numbers doesn't need to be converted to decimal. Simply divide the amount of digits read by a corresponding number of 9's, which will also be known to the decoder.

Here is how I understand it to work:

1. S = 111999000222 //series of 4 characters to be stored
2. 0.111999000222 //put the decimal infront of it
3. 0.111999000222 * 6.00000000 = F
4. Mark the bar at F inches

The problem apparent in this procedure is that the information must most definitely be buffered. Meaning, after you read the decimals half way through, and get 500 petabytes worth of integers, where are you going to put it. You can't perform the marking until the multiplication is completely done.

Even multiplying in parts:
(0.1*6) + (0.01*6) + (0.001*6) + (0.0009*6) + ....

This number becomes increasingly large if you add more data and you will need a large enough storage device on the super computer to store this data until you get the final result. Followingly you need to make sure your marking device is accurate enough to mark this and read it. In essense, you cannot store an infinite amount of data (unless you have an infinite buffer somewhere else) even if the physical limit doesn't come into play.

While writing that last paragraph, it did come to me that the marking device could be moved in increments, first by (0.1*6) then (0.01*6) such that there will be no need to store the information. Nonetheless during the decode process, you will indeed not be able to perform the reverse division without a buffer. My strongest point would still be the physical limit nonetheless.

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#### ssj5harsh

Well, you are right Mezarashi. That is just the answer I expected. Though you did talk a bit about the technical stuff (which wasn't really needed), the essence of this post is: YOU'VE CRACKED IT.

Hats off to you!

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