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Caravel Forum : Caravel Boards : Contests : Depicting the DROD Number (Our official contest for January.)
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eb0ny
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icon Re: Depicting the DROD Number (+2)  
For submission #1: DNoD.IP

This text was secreted, due to its size.
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[Last edited by eb0ny at 01-25-2008 05:46 AM]
01-13-2008 at 04:55 PM
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hartleyhair
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File: The Two Circles.doc (27.5 KB)
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icon Re: Depicting the DROD Number (+2)  
Meh, I'll have a go.

For Submission: The Two Circles

The Two Circles uses a more aesthetically pleasing form of Binary, with Circles and lines rather than ones and zeroes. Each of the two Circles is divided into four segments, making eight Radii. On the Radii are written (from outside inwards) circles and lines, representing 0s and 1s respectively. The number is written in much the same way as binary, but with the last digit first and working clockwise. Circles are placed in normal binary order.

Translation to ordinary numbers: As in binary.

For examples, please see attached file. Sorry to use a Word Document (I know not everyone has Word) but no other formats seemed to work...

EDIT: Ok, fixed the incorrect 29.5 quintillion example.

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[Last edited by hartleyhair at 01-14-2008 05:53 PM]
01-13-2008 at 06:37 PM
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Chalks
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icon Re: Depicting the DROD Number (0)  
quote:
hartleyhair wrote:
For examples, please see attached file. Sorry to use a Word Document (I know not everyone has Word) but no other formats seemed to work...

If you want a free program to open Word docs, try Open Office. I've been using it for about 2 months now, and I LOVE it.
01-13-2008 at 06:42 PM
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calamarain
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Regarding ease of decoding... if the tattoo/whatever has to be easy to decode without external computer software or extensive calculations...

...doesn't that just restrict us to some rewrite of a decminal number? I mean, binary is cool for example, but without a calculator or a computer there's no way we can easily convert numbers in the range of 10^18 to/from binary. Same for any other base other than decimal. I had a rather cool shorthand octal one that looked rather good, but you need to be able to calculate the decimal version of an octal number. Takes ages without a computer.

So, isn't our tattoo going to just have to output the decimal number in some way? Otherwise, it just isn't going to be decodeable without a computer.

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01-13-2008 at 11:22 PM
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Dex Stewart
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I don't think we should take decodability into account in any way. What if there are/will be any DROD players who were raised from childhood to use base 7 numbers? So I propose that no bad marks are given just because a base is used other than 10. Rather, you should be rewarded for proposing a system that is base-independent.

However, you still can't use base 18593 as in that case you'd have to design 18593 aesthetically pleasing, different characters for represantation.
01-13-2008 at 11:38 PM
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calamarain
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quote:
Dex Stewart wrote:Rather, you should be rewarded for proposing a system that is base-independent.

How is that possible? This is a genuine expression of interest - I can't think of how on earth you could represent number in some way that doesn't at least implicitly have a base. Can you give an example?

Also, the judging criterion specifically say that you get higher marks if you can code/decode it on the back of a napkin. And even higher marks if you don't need that :)

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[Last edited by calamarain at 01-13-2008 11:56 PM]
01-13-2008 at 11:45 PM
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ErikH2000
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File: 29.5Quintillion.jpg (24.1 KB)
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icon Re: Depicting the DROD Number (+2)  
Here is my own creation, which will not be considered for the contest. I wanted to show an early example of a numeral system that isn't based on the regular glyphs to give people some ideas. To save my self a little time, I'm not going to give a formal description of how it works. Basically, each line drawn represents a number between 0 and 255 which serves as a base 256 digit. The leftmost digits have higher values.

The line represents a series of base 2 "sub-digits". Right bumps are like ones and left bumps are like zeroes. The topmost bump (left or right) will always be a multiplier of ones, and then it goes down representing powers of two (2, 4, 8, 16...) with as many bumps as needed to represent the number.



The attached image shows what 29.5 quintillion looks like. To help you out, the digits go from left to right with the following values:

1 * 2^64 +
153 * 2^56 +
101 * 2^48 +
13 * 2^40 +
179 * 2^32 +
202 * 2^24 +
6 * 2^16 +
0 * 2^8 +
0 * 2^0 =
29.5 quintillion

If you wanted to depict the number one, it is the same as the leftmost digit in the depiction.

-Erik

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[Last edited by ErikH2000 at 01-14-2008 12:33 AM]
01-14-2008 at 12:33 AM
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ErikH2000
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quote:
hartleyhair wrote:
Meh, I'll have a go.

For Submission: The Two Circles


Ah, very cool! I just noticed this after making my example "unglyphy" post. I actually started on a system very close to yours before I backed off and made my simpler one. Mine also had the 8 spokes with each representing a base 256 value, but I needed 2^65 instead of 2^64. (I solved it by adding another symbol to represent the last bit.) When I saw yours, I wondered how you managed to get 29.5 quintillion encoded.

You actually encoded 27.5 quintillion. So I don't think you're quite done yet, Hartley.

-Erik


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01-14-2008 at 12:51 AM
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calamarain
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File: drodnumbers.PNG (12.2 KB)
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icon Re: Depicting the DROD Number (+2)  
For Submission: Shorthand Lines

An ancient system of representing high numbers, was found hidden in a dark corner of the DROD forum and has recently been brought to light by Internet Archaeologists, after going through several traps and a whole heaping load of forum games. After cleaning up the stone tablet that the system was found on, the archaeologists realised that the writing was too faded to read, even under oblique light...

...so they scrapped the project, lied and made up a bunch of crap at the last minute. But don't tell anyone!

Click here to view the secret text


The system of the shorthand lines is designed for efficiency but is reasonably calculable on the back of a napkin. The number in question is converted to octal (base 8) and each digit is replaced with the appropriate shorthand. The number is then written out in three lines, each with eight digits. If the number is insufficiently long to make three complete lines, any space at the end is filled in with the "blank" digit, until the end of a line is reached.

In order to decode the number, all one does is read off the digits of the tattoo, giving you the number in octal

Technically you have the number then... but if you want it in a more conventional form, you convert base-8 to base-10, giving you the original number.

Thus, you can scrawl the number of any DRODDER ever very quickly in your own blood.

Plus, you don't need to have it in the simple form of lines. They can be quite innocuous, and be encoded into other things. A few twisted wires left on the street. The lines in a painting. A readout on an electrocardiogram. Who knows, one could be written in your room right now?

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[Last edited by calamarain at 01-14-2008 01:17 AM]
01-14-2008 at 01:16 AM
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Dischorran
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For Submission: Abstract Linear

Somewhat similar to Calamarain's, unfortunately (honest, I made this before reading his post :)) - I would hope that he would be given some preference in voting for getting in before me.

The attached jpg (made in beautiful, beautiful Powerpoint) is pretty much essential for the description.

This is a standard positional base 10 system. 0=O, 1=|, 2=-, 3=/, 4=\, and 5-9 repeat 0-4 with a shorter line crossing it (or in the case of 5, a line spanning the width of the circle at any arbitrary angle). However, instead of position being read right to left starting at ones and going up, position is read by connectivity; the ones digit is marked by a filled-in triangle, the tens digit would "sprout" from it at any position, the hundreds digit would "sprout" from the tens digit, and so on. Repeated digits, aside from 0 and 5, would be separated by a dot for clarity, e.g. 22 = (triangle)-.- or -.-(triangle)

As seen in the representation of my own DROD number, this can yield many possible representations of a given number to suit the taste of the individual, although it is highly recommended to choose a simple, largely unidirectional representation for large numbers. The numbers are quite sensitive to the orientation of the overall figure relative to the viewer, but one would hope that in the case of a tattoo orientation would be implicit (if it is not, one would hope that the design would be recognizable to the next of kin).

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01-14-2008 at 01:54 AM
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eb0ny
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I have a question: in my post I asked about use of post-processing of the numering system to make it aesthetical. Is it permitted by the rules? Or does the number itself has to be aesthetical?

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01-14-2008 at 04:50 AM
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ErikH2000
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quote:
eb0ny wrote:
I have a question: in my post I asked about use of post-processing of the numering system to make it aesthetical. Is it permitted by the rules? Or does the number itself has to be aesthetical?

Well, that's a little iffy. The problem is that you weren't specific about how the aesthetic improvements would be applied, leaving it up to whoever was making a depiction. I think that if you want voters to credit you for the aesthetic value of the numeral system, then it could be added to your encoding system. As it stands, I think the aesthetic suggestions you've described are more like a comment which doesn't much affect the value of the numeral system.

I don't think I have to make a "ruling" here. I'm just describing my prediction of how voters may react. You can leave the entry as-is if you want, Eb0ny.

-Erik

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01-14-2008 at 05:46 AM
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hartleyhair
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quote:
You actually encoded 27.5 quintillion. So I don't think you're quite done yet, Hartley.


Gah!

Ok, I'll update in a bit. My excuse is that I was very, very tired.

EDIT: Before I embark on a wild correction hunt, am I correct in thinking that
1001100101100101000011011011001111001010000001100000000000000000
is 29.5 quintillion in Binary?

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[Last edited by hartleyhair at 01-14-2008 07:58 AM]
01-14-2008 at 07:42 AM
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Dex Stewart
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quote:
calamarain wrote:
Also, the judging criterion specifically say that you get higher marks if you can code/decode it on the back of a napkin. And even higher marks if you don't need that :)


I understand that. But while we, used to the decimal system can easily decode any system that uses the decimal system (a napkin is probably enough), aforementioned person who grew up with base seven will need hundreds or thousands of napkins to decode 'our' numbers, while one napkin will be enough for him to decode something from base seven. What the judging criterion say is that the 'morphing' from symbols to numbers should be as easy as possible. If a napkin is enough to morph the row of symbols you have to something which is representative of the real number - be it in base 7 or in base 10 - then you passed the test.
01-14-2008 at 08:04 AM
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techant
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quote:
Dischorran wrote:
For Submission: Abstract Linear

Somewhat similar to Calamarain's, unfortunately (honest, I made this before reading his post :)) - I would hope that he would be given some preference in voting for getting in before me.


Now I have to rework my idea itself because it was simular to both of these but base 10. :weep I am still considering smilie faces. :w00t

My issues with most of these so far is decoding and thereby encoding. I am not a math genius here, sorry. :fun So, if I met you in a public steam bath I might never figure out if we met before. :look

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01-14-2008 at 08:59 AM
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Maurog
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quote:
hartleyhair wrote:
Before I embark on a wild correction hunt, am I correct in thinking that
1001100101100101000011011011001111001010000001100000000000000000
is 29.5 quintillion in Binary?

Nope, it's
11001100101100101000011011011001111001010000001100000000000000000
You missed an initial 1 there.

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01-14-2008 at 09:03 AM
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techant
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quote:
Maurog wrote:
quote:
hartleyhair wrote:
Before I embark on a wild correction hunt, am I correct in thinking that
1001100101100101000011011011001111001010000001100000000000000000
is 29.5 quintillion in Binary?

Nope, it's
11001100101100101000011011011001111001010000001100000000000000000
You missed an initial 1 there.


Will I have to convert it to Binary when I see your tatoo??? :w00t

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01-14-2008 at 11:51 PM
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techant
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For Submission: My simple code

Use the chart below, but if you know your alphabet in English then you can probably do it in your head. Since the same number is used for either caps or lower case it keeps it simple. The capital letters help shorten the name when there are adjacent repeated numbers. The command to repeat always follows the letter to repeat. If a number has no repeating sequences then it is ended with a '*Z'. This tell us it is a member number and not some grossly misspelled word.

Also group the letters in sets of 4 starting from the left, do this unless one letter will be left alone, in that cas a single last group of 5 is fine. Also do not split caps count them as one letter this may result in a second to last group and a last group with less then 4 in their respective groups, that is allowed.

Table seen as separated sections:
Click here to view the secret text



My own very simple number 533 translates as:

ec*B
Which I happen to think looks quite sharp and I may tattoo it somewhere soon.

A longer number with repeating numbers like "249999999999999999999" would read as "bdiiiiiiiiiiiiiiiiiii" but when encode it is the easier to read "bdi* AI"

Then there is the poor fool who got the number '1' well that would look like 'a*Z'. And the poor fool who got the last number 29.5 quintillion (29500000000000000000)
well that ones not so bad. biez *AG
TESTED:

The Tattoo Test (Aesthetics)
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The Drawn In Blood Test (Elegance)
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The Cocktail Napkin Test (Encodability)
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The "Hey, I Know You!" Test (Decodability)
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Edited:
Fixed table error where J=10 was left instead of Z=0.
Fixed how does one look.
Fixed to obey this rule: * Each depiction for a number is repeatable, so that someone following your numeral system's rules will create a consistent depiction for any given number. As pointed out by Jutt


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[Last edited by techant at 01-16-2008 06:20 AM]
01-15-2008 at 04:06 AM
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Sillyman
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File: Drod Number.png (1.1 KB)
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icon Re: Depicting the DROD Number (+1)  
For Submission:

Sword System



On the left, 29.5 quintillion. On the right, 1.

Alright, here's how it works: It's a grid of several digit-ish elements, that I shall call "Smiters". Each smiter has a central element (With some method of distinguising direction) (Henceforth "Body") in the middle and lines of some sort(Henceforth "Swords") around it. The swords and body are valued as such:
923
814
765
Multiply the values of the swords and the body. There may be an arc between two swords, or a connection ("Hilt") between a sword and the body, if so, add them instead.
Now, this may not provide for many values, but you can have more than one smiter in the same number. Multiply all the smiters in the same collumn together, then add the collumns.

There are an infinite number of different representations of any one number. To encode a number, I suggest starting large and going smaller. This often provides a more effecient encoding.

I was inspired by DROD, as you may be able to tell. It does require knowing what direction the numeral was written, to fix that, I had the central dot require a small missing bit. Also, it was somewhat of a hassle to calculate a short transcription of such a large number as was required, so I just used a bunch of 100s and multiplied them together, then got the largest number I could easily make that was smaller than 295.

Tests coming up...

The Tattoo Test (Aesthetics)
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The Drawn In Blood Test (Elegance)

Click here to view the secret text


The Cocktail Napkin Test (Encodability)

Click here to view the secret text


The "Hey, I Know You!" Test (Decodability)

Click here to view the secret text


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FNORD

[Last edited by Sillyman at 01-15-2008 06:38 PM]
01-15-2008 at 07:53 AM
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Syntax
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quote:
eytanz wrote:
I think Syntax's point is that the rules allow for a numeral system that includes all (and only) the symbols that the forum allows to use when choosing user names. Thus, any string that is an acceptable user name is also an acceptable number, and it allows for a trivial mapping that he proposes.

In such a system, the number "3450987340" would be held by a user whose forum name is 3450987340. Such a user does not exist, but that's fine under the system. If you asked who is the username whose number is "eytanz", Syntax could calculate and determine that it is me.

Exactly. My point would be simply to map the username to a string which has the same characters as the username, in the same order.

I was under the impression that a DROD Number could contain letters as well as digits, so didn't have to be a number.
01-15-2008 at 08:30 AM
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Remlin
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icon Re: Depicting the DROD Number (+2)  
For submission: Drodlish

1 = ac
29.5 quintillion = eminabababababababab

This system translates two consecutive digits into two letters, a vowel and a consonent. (5 vowels and 20 consonents makes for 5*20 = 100 options - perfect! "y" is left out in the cold for not choosing a side and sticking with it.) This is essentially base 100 (which makes it easy to translate), but with the 100 'digits' chosen to guarantee you a pronounceable if not downright singable number.

To encode, first add a 0 at the beginning if needed to make an even number of digits total. Break the number into groups of two digits. For each group, divide by 20. The quotient, which will one of 0,1,2,3,4, corresponds to a,e,i,o,u. The remainder will be in the range 0 to 19 and correspond to the 20 consonents. (0 = b, 1 = c, 2 = d... 19 = z). Put all the letters together, and you're done.

For example, let's encode 9340782439083. Add a 0 and break into groups of 2, to get 09-34-07-82-43-90-83. Now 09 divided by 20 is 0 remainder 9, or a + m. Then 34 gives 1 remainder 14, or e + s. Continuing gets am + es + ak + ud + if + un + uf, or amesakudifunuf. Coincidentally, my childhood nickname.

To decode, reverse the process. Break your word into groups of two letters, which will each be vowel-consonant. Once again a,e,i,o,u represents 0,1,2,3,4, and the consonants are numbered in order, b = 0, c = 1.... For each letter group, multiply the vowel value by 20 and add the consonant value to get two digits of the final number. If you were trying to decode "ibod", from "ib" you'd get 2*20+0 = 20, from "od" you'd get 3*20+2 = 62, final result of 2062.

I like this system both because of the ease of translation from base 10 to base 100, and because the final result is much more fun and easy to remember than an actual number of the same length. Here's how I think this system does on the various tests:
Click here to view the secret text

01-15-2008 at 11:41 AM
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mrimer
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icon Re: Depicting the DROD Number (+1)  
For submission: Base 1000, triple compacted digits, or numeral dials

Design rationale:
We're highly used to the arabic numeral system and base 10, so it's easy for us to encode and decode such values. We're also used to grouping the digits in a large number into sets of three, or orders of one thousand. We have words to describe these orders of one thousand: thousand, million, billion, trillion, etc.

We're also used to reading values off dials such as clock faces, which have multiple hands, and power/volume dials, which count from 0 to 9 clockwise around a knob. When the numbers on a clock face are removed, we can still figure the time from the placement of the hands, and out of familiarity do this with relative ease.

Thirdly, we're familiar with the concept of locally offset symbols representing larger units of information. For example, a small icon could represent a single unit while an adjacent large icon represents a group of five, ten, fifty, etc. Consider how the stage number is represented in games like "Dig Dug" and "Galaga", or how a small square represents an energy tank of 100 energy units in the "Metroid" health interface).

Combining the intuitive features of these systems gives us a simple, compact, easy to read and write representation of numbers effectively in base-1000.

How to encode/decode:
Each order of one thousand occupies a place/position in the number, with each higher order of 1000 being placed to the left of the one previous (like our conventional system with positional orders of ten). At the center of each digit is the ones place, represented by an arabic numeral. A short, thin line represents the tens place and a dot the hundreds place. The line and dot are placed periperally around the ones digit, with positions from zero to nine in clockwise order. For example, "50" is represented by a line being drawn from the numeral "0" to the six o' clock position, or straight downward. For large numbers, it is often the case that tens and hundreds places are absent (zeroed). So, we may omit the line and dot in places where they are zero. This gives us large numbers in a compact notation. Dots overlapping a (much thinner) line are still easily visible.

Depiction of numbers:

1
29.5 quintillion (29 500 000 000 000 000 000)
111
1,234,567,890

Supplemental info:
Click here to view the secret text


____________________________
Gandalf? Yes... That's what they used to call me.
Gandalf the Grey. That was my name.
I am Gandalf the White.
And I come back to you now at the turn of the tide.

[Last edited by mrimer at 01-15-2008 07:24 PM]
01-15-2008 at 04:56 PM
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eb0ny
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icon Re: Depicting the DROD Number (0)  
Entry updated, probably the final version.

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01-15-2008 at 06:01 PM
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Jutt
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icon Re: Depicting the DROD Number (+1)  
For Submission: Contour Script

The Countour Script is basically a representation of decimal numbers, but in a way that is much more visually appealing and distinguishable. As it is designed for Drod numbers, it is standardized for 20 digit numbers, as these should be sufficient to hold any possible Drod number.
Although it is based on connection lines on a square grid, it should be easy enough to work without such grid. However, for the sake of explanation it will be used in this article.



Encoding and Decoding

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Samples

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The tests

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Holds: An Architects Audition, Artful Architecture, Salamander, Elusive Exhibitions, Leftover Levels, Six Times Six
Collaborative: Way Forward, Advanced Concepts 2
Styles/Mods: Basalt, Sandstone, Garden, Clock using game elements
01-15-2008 at 07:29 PM
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Sillyman
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File: EENHADINUMS.png (1.2 KB)
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icon Re: Depicting the DROD Number (+1)  
For Submission #2:

EENHADINUMS

Alright, anybody remember ENHADINUMS? Yeah. This extends them. There are 5 basic digits:
|- one
+- two
#- four
.- minus one
:- minus two

In addition, all the other tricks in the article are valid, though not necessary. Now this is the new part: By writing a line over a number, you multiply it by 1000. By writing a line under a number, you multiply it by 10. There are, again, an infinite number of ways of representing any one number. Direction should be unambiguous if at least one -1 is in the number, but if it is not, either indicate direction or choose a different representation.

29.5 quintillion (29500000000000000000) on the left, 1 on the right:


Testing, one two three:

Tattoo Test: Not very artistic, but with a little thought, you can embellish it.

Drawn in Blood: Somewhat compact, and straight lines, which is easier to draw. But in a worst case scenario, it could be larger than decimal...

Cocktail Napkin: Again, a little mental math, but easier this time. If you don't want a complex depiction, you can simply build decimal out of the system and raise it to the necessary power.

Hey, I know you: Not that hard to distinguish. There is more than one representation of any one number, so it may take a little thought if you remember it differently. But the number can be reconstructed with ease.

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FNORD

[Last edited by Sillyman at 01-15-2008 09:22 PM]
01-15-2008 at 09:21 PM
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Jutt
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icon Re: Depicting the DROD Number (+3)  
Now that more submissions are coming in, I noticed that some may not be valid entries because they violate the submission criteria. I advise some contestants to improve their entries and avoid disqualification.

Tim's Trivial System:
I'd say that this doesn't meet the condition that the system must be an invention of your own, since you probably didn't invent the names for the English numerals.

Dischorrans Abstract Linear:
Violates the uniqueness/repeatability, as the text names many possible representations.

Techants My Simple Code:
Same problem, you state the shortening of repeating numbers is not required making it possible to encode some numbers in different ways. Also allowing the addition of filler letters has this problem.

Sillymans Sword System:
Also uniqueness/repeatability. You literally state there are infinitely many representations.

Sillymans Eenhadinums:
The system is besides the extension still quite similar to the one in the article you refered to. This may conflict with the rule that the system must be your own invention.
And again multiple representations.

Some of these are easily fixed, others will need more work.

____________________________
Holds: An Architects Audition, Artful Architecture, Salamander, Elusive Exhibitions, Leftover Levels, Six Times Six
Collaborative: Way Forward, Advanced Concepts 2
Styles/Mods: Basalt, Sandstone, Garden, Clock using game elements
01-15-2008 at 10:50 PM
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zex20913
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icon Re: Depicting the DROD Number (+1)  
For Submission: Number and Place

The key elements of any number in our base 10 system are digit and place. What my entry does is it represents the place value in a new and somewhat artistic manner.

Information Image: Attached in a Word document.

Encoding:

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Decoding:

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Tattoo Test:

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Drawn in Blood:
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Napkin Test:
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Hey, I know you!:
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Bonus statements:

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[Last edited by zex20913 at 01-15-2008 11:29 PM]
01-15-2008 at 11:21 PM
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techant
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icon Re: Depicting the DROD Number (0)  
quote:
Jutt wrote:
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Some of these are easily fixed, others will need more work.


Well I see what you mean and I am working on it. I did fix a typo in my table where I left "J=10" that was an error it was later changed to "Z=0", so I fixed that, but this is a bigger fix and will take awhile so I will be back. :lol

Thanks for catching it :thumbsup

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01-16-2008 at 12:48 AM
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calamarain
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icon Re: Depicting the DROD Number (0)  
quote:
Jutt wrote:
Now that more submissions are coming in, I noticed that some may not be valid entries because they violate the submission criteria. I advise some contestants to improve their entries and avoid disqualification.

*snip*
Is mine legal then?

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01-16-2008 at 01:56 AM
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Tim
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icon Re: Depicting the DROD Number (0)  
quote:
Jutt wrote:
Tim's Trivial System:
I'd say that this doesn't meet the condition that the system must be an invention of your own, since you probably didn't invent the names for the English numerals.
I've updated my entry to add something in front of the final result, and that part is invented by me. Obviously, the English representation of the numerals part is not my own invention, but are you saying that all the other entries that use Roman representation of the numerals are also unoriginal and should be disqualified?

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The best way to lose customers is to let little kids running loose on a forum with too many mod points.

[Last edited by Tim at 01-19-2008 10:46 AM : attached image for my other entry]
01-16-2008 at 02:34 AM
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