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zex20913
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icon Re: Depicting the DROD Number (+1)  
One question--4, really.

How are you going to rotate a wubba? A tar/mud/gel mother?

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01-23-2008 at 11:43 AM
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Chaco
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quote:
zex20913 wrote:
One question--4, really.

How are you going to rotate a wubba? A tar/mud/gel mother?


Easy - give it a sword :)

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01-23-2008 at 12:20 PM
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captainzakku
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quote:
zex20913 wrote:
One question--4, really.

How are you going to rotate a wubba? A tar/mud/gel mother?


If you look at #99, with Halph, the H is rotated as well. So for the Wubba you would rotate the W as well. All of the letters should be included in the designs, and in the rotations. I believe all of the symbols should still look unique, even when rotated, as long as you include the letters.

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[Last edited by captainzakku at 01-23-2008 01:15 PM]
01-23-2008 at 01:14 PM
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calamarain
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quote:
captainzakku wrote:
quote:
zex20913 wrote:
One question--4, really.

How are you going to rotate a wubba? A tar/mud/gel mother?


If you look at #99, with Halph, the H is rotated as well. So for the Wubba you would rotate the W as well. All of the letters should be included in the designs, and in the rotations. I believe all of the symbols should still look unique, even when rotated, as long as you include the letters.
Erm... if you rotate a H 180 degrees, it will look the same.

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01-23-2008 at 02:02 PM
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File: DROD Rings.png (46 KB)
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icon Re: Depicting the DROD Number (+1)  
For submission: (Five) Rings

Samples
See the attachment.

Summary
The basic diagram consists of concentric circles with ten intersecting radii. Digits are represented as marks on those intersections, four digits to a circle.

Encoding
1) Pad the number with leading zeroes so that its length is a multiple of four. For example, 62 becomes 0062.
2) Draw a diagram with concentric circles, one for each group of four digits. Draw ten evenly-spaced (at 36°) lines from the centre to the outermost circle. (Yes, that's five diameters, but they should be treated as ten lines.)
3) Make a short thick mark from the centre of the circle outwards a short way along one of the lines. This line now represents zero. The other lines represent one through nine, moving clockwise.
4) Look at the first digit of the number. Start at the point where the outermost circle meets that numbered line, and make a short thick mark along the line away from the centre.
5) Look at the second digit of the number. Start at the point where the outermost circle meets that numbered line, and make a short thick mark clockwise along the circle.
6) Look at the third digit of the number. Start at the point where the outermost circle meets that numbered line, and make a short thick mark along the line towards the centre.
7) Look at the fourth digit of the number. Start at the point where the outermost circle meets that numbered line, and make a short thick mark anticlockwise along the circle.
8) Repeat steps 4 through 7 for the next four digits and the next circle in. Keep repeating this process until the last four digits have been marked on the innermost circle.

For the sake of repeatability and creating a single correct representation for a given number, the following style guidelines exist. However, in the spirit of robustness, diagrams should still be decodable even if these guidelines are only loosely adhered to.
1) Where the diagram is drawn on a surface which has an obvious orientation, the zero line should point upwards.
2) The circles should be evenly spaced. If the innermost circle has radius r, the next circle should have radius 2r, the third circle radius 3r and so on.
3) Marks should be 0.3r in length. This avoids any potential overlaps.
4) Marks should be 2.5 times as thick as the other lines in the diagram.
5) The radius of the innermost circle should be 50 times the width of the normal lines (20 times the width of a mark).

Overall scale is deliberately left undefined, as this will depend on the surface and available tools. A tattoo in a private area will necessarily be smaller and more precisely drawn than a near-death finger painting.

Decoding
Note that digits are written from left to right (you're dealing with the most significant digit first).
1) Look at the mark in the centre of the diagram to identify the zero line, and hence the other line numbers.
2) Look at the outermost circle for the mark pointing outwards. Write down its number.
3) Look at the outermost circle for the mark pointing clockwise. Write down its number.
4) Look at the outermost circle for the mark pointing inwards. Write down its number.
5) Look at the outermost circle for the mark pointing anticlockwise. Write down its number.
6) Repeat steps 2 through 5 for the next circle in and the next four digits. Keep repeating the process until the innermost circle has been read.

Notes
This system has a number of pleasant side effects:
1) More dedicated DROD players (lower DROD numbers) get simpler diagrams. In fact, every currently allocated DROD player only needs one circle.
2) The sequence of marks (outwards, clockwise, inwards, anticlockwise) bears a striking resemblance to the North, East, South, West sequence known from serpent behaviour. This serves as a useful memory aid.
3) Careful selection of duel venues (for example in a pub near the dart board) can simplify dying gasp drawings -- the circle and lines already exist (ignoring every second line), and a number can then be written in as few as five marks.
4) If Erik underestimated his market, the system expands far beyond 29.5 American quintillion -- nothing prevents sixth and subsequent circles from being added.

The Tests
Aesthetics: It's simple, it's clean, and it can be as subtle or as bold as you like.
Elegance: Single short strokes rather than complex shapes make drawing simple. For lower numbers, a basic framework may already be available -- objects such as dart boards, CDs or speed limit signs can be used for pre-drawn circles in an emergency.
Encodability: It's pretty simple -- draw some circles, draw some diameters, make some marks. The sequence of marks is easily memorable from serpent movement; no heavy mental work is required.
Decodability: Also very simple -- read the marks off in order. The simple system of marks means that even a sloppily drawn diagram should still be readable.

01-23-2008 at 03:09 PM
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captainzakku
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.
Erm... if you rotate a H 180 degrees, it will look the same.


This is true, but Halphs head and arms will be inverted, so while the H might look right side up, Halph's body won't. I believe I've thought through every possible rotation on each symbol, but I appreciate others double checking my work.

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01-23-2008 at 03:38 PM
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mrimer
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icon Re: Depicting the DROD Number (0)  
quote:
Chaco wrote:
quote:
zex20913 wrote:
One question--4, really.

How are you going to rotate a wubba? A tar/mud/gel mother?


Easy - give it a sword :)
Heh. In the "RPG" puzzler being developed, it is technically possible to make a wubba with a sword. However, I haven't endeavoured to actually construct such an abomination. :P

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01-23-2008 at 04:49 PM
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calamarain
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quote:
mrimer wrote:
Easy - give it a sword :)
Heh. In the "RPG" puzzler being developed, it is technically possible to make a wubba with a sword. However, I haven't endeavoured to actually construct such an abomination. :P

Hello. My name is Wubba Montoya. You killed my father. Prepare to die.
Hello. My name is Wubba Montoya. You killed my father. Prepare to die.
Hello. My name is Wubba Montoya. You killed my father. Prepare to die.

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01-23-2008 at 04:54 PM
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eb0ny
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captainzakku wrote:
...but I appreciate others double checking my work.
Err... isn't this your responsibility?

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01-23-2008 at 06:57 PM
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Tuttle
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quote:
eb0ny wrote:
quote:
captainzakku wrote:
...but I appreciate others double checking my work.
Err... isn't this your responsibility?
Of course it is. It's also almost impossible to do properly, which is why constructive comments and questions are always appreciated. :) I suspect anyone who's ever written anything major (essays, speeches, computer programs etc) will tell you that no matter how much they check their own work, other people can still find mistakes. As the author you tend to see what you were thinking rather than what you actually wrote, so you can gloss over things without realising it. A fresh mind tends to spot those inconsistencies much more easily.

[Last edited by Tuttle at 01-23-2008 10:21 PM]
01-23-2008 at 10:20 PM
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coppro
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Wubba Montoya evolved into Wubblade Montoya.
01-24-2008 at 12:14 AM
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kyevan
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icon Re: Depicting the DROD Number (0)  
quote:
mrimer wrote:
Our arabic numerals have a one-to-one representation and they work just fine.


Actualy, that's not true.

1
01
1.000000
0.9(with a bar over it.)

Those are all the same number. and yes, point-nine-repeating is equal to one. It's freaky, but it works out.
01-24-2008 at 01:10 AM
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ErikH2000
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How is .9999999999999999999999999999 (and then some) equal to 1?

Isn't it just an infinitesimal amount smaller than 1?

-Erik

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01-24-2008 at 01:42 AM
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Chaco
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icon Re: Depicting the DROD Number (+1)  
This question is asked a lot.

Let's define our .99999999... (and then some) as a geometric sequence:

.9 + .09 + .009 + .0009 + ...

We have here an infinite geometric sequence with first term equal to .9 and common ratio equal to .1. The sum formula for infinite geometric sequences is:

(first term) / (1 - ratio)

So, that gives us:

.9 / (1 - .1)

which after some simple math evaluates to exactly one.

Remember, when you get infinitesimally closer over an infinitely long period of time, you eventually reach the finite number - provided you add up all infinity terms :)

(This is the first time I've tried to answer this question myself, so let me know if I messed up something)

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[Last edited by Chaco at 01-24-2008 01:52 AM]
01-24-2008 at 01:52 AM
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Tuttle
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icon Re: Depicting the DROD Number (0)  
There are a handful of proofs at http://en.wikipedia.org/wiki/0.999... .

Personally, I like getting people to work out the average. Start with showing that if the average of a and b is b, then a=b, and then use long division to show that the average of 1 and 0.999... is 0.999.... Most people I've tried to explain it to can get that one.

[Last edited by Tuttle at 01-24-2008 01:59 AM : Fixed link]
01-24-2008 at 01:58 AM
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Sillyman
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So? The others still hold true. Thank you for pointing out this flaw in Mr. Imer's statement, kyevan. Now, will you revise the rules for flawless consistancy?

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01-24-2008 at 03:00 AM
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Syntax
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Erm... 0.999 recurring is not equal to 1.

It may tend to 1 but I tend to like DROD yet am not DROD.
01-24-2008 at 03:04 AM
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Jatopian
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So um, can we split threads (and delete this post afterwards) before we get irrevocably off-topic?

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01-24-2008 at 03:07 AM
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Sillyman
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... I hate it when people can't see proof.

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01-24-2008 at 03:08 AM
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kyevan
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quote:
Sillyman wrote:
So? The others still hold true. Thank you for pointing out this flaw in Mr. Imer's statement, kyevan. Now, will you revise the rules for flawless consistancy?


I think it should work if you define a single canonical form. If other forms can be DECODED to the same value, but there is an unabiguous set of ENCODING rules, it should work out pretty clearly, I think.
01-24-2008 at 03:18 AM
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ErikH2000
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Jatopian wrote:
So um, can we split threads (and delete this post afterwards) before we get irrevocably off-topic?

Yeah, I'm sorry to drag this off-topic. Please, if there is more talk about .9999999999999999999999999 = 1, let's have it in a new topic.

-Erik

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01-24-2008 at 03:41 AM
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coppro
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quote:
ErikH2000 wrote:
Yeah, I'm sorry to drag this off-topic. Please, if there is more talk about .9999999999999999999999999 = 1, let's have it in a new topic.

-Erik
Oh dear. You've created a monster.

Oh, and to steer back on topic, I just wanted to add that I still haven't added images. This weekend is wide open after tommorrow's Physics exam, so I'll get them up sometime.
01-24-2008 at 03:52 AM
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techant
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quote:
After the submission deadline has passed, some entries may be disqualified if they don't meet the submission criteria. The remainder of the entries will be rated by the forum community.


I can tell that some of you are greater 'numbers' people then me.
Click here to view the secret text
The great .999.. = 1 debate is one such evidence. I really don't want to be disqualified because I missed some point in the submission criteria, I am sure that is true for everyone.

I would be thankful to anyone who reviews my entry and notices if I :blush have missed something. Jutt caught one thing which I fixed but with mine so many entries back it is by now out of site out of mind. That is until the final evaluation, and then it is too late I fear. So, any warning would be very helpful.

I am considering a second entry but I would want to repeat any mistakes I may have made in my first entry. :fun

And, yes I do know it is my responsibility but what are friend for if they can't help you out now and then. :w00t



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[Last edited by techant at 01-24-2008 09:16 AM]
01-24-2008 at 09:12 AM
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captainzakku
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quote:
techant wrote:
I would be thankful to anyone who reviews my entry and notices if I :blush have missed something. Jutt caught one thing which I fixed but with mine so many entries back it is by now out of site out of mind. That is until the final evaluation, and then it is too late I fear. So, any warning would be very helpful.


In looking through I could not find any mistakes. I think the major strength, and part I liked the best, was the simplicity of encoding/decoding. My comment would be that your system is best for people with repeating numbers, and unfortunately the vast majority of people would have few, if any repeating numbers.

To look at it another way, if there were 99 people with numbers 1-99, only 9 of them would have repeating numbers (11, 22, 33 etc). 1-999, again only 9 would have 3 repeating numbers (111, 222, etc), and I believe 171 would have two repeating numbers.

Proof:
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The remaining 819 would have no repeating numbers. I saw that as the biggest weakness of your system, that it does not necessarily make depicting those numbers any easier.

If you were to design another system, that would be the one area I would focus on fixing.

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[Last edited by captainzakku at 01-24-2008 01:56 PM]
01-24-2008 at 01:27 PM
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mrimer
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quote:
kyevan wrote:
quote:
mrimer wrote:
Our arabic numerals have a one-to-one representation and they work just fine.


Actualy, that's not true.

1
01
1.000000
0.9(with a bar over it.)

Those are all the same number. and yes, point-nine-repeating is equal to one. It's freaky, but it works out.
Sure, sure. Possibly none of the systems posted here actually forbid representing your number with an extra zero in front, or adding decimal places, or placing a bar over the last decimal digits. In fact, I expressly considered these mathematical possibilities when designing my system. I don't think allowing the possiblity of augmenting our systems with existing mathematical constructs goes outside the bounds of the rules.

For example, any of our madeup systems could express the number "2" as its respective representation of "1", with a plus sign, and then another representation of "1". But that doesn't mean we need to include a bunch of fine-print legalese saying this isn't allowed in our entries in order to satisfy the 1:1 rule. This is quite different in intent than generating a new, unique set of rules for many-to-one encoding/decoding processes expressly for use in our numbering scheme designed for this contest.

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[Last edited by mrimer at 01-24-2008 07:22 PM]
01-24-2008 at 07:16 PM
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Jatopian
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Am I the only one who understands this contest perfectly and yet is completely lost?

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01-24-2008 at 11:03 PM
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techant
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quote:
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Click here to view the secret text


Yes, I see your point and that will be my focus next, once I get my filings done for Jan and can concentrate. :w00t Thanks for checking it out :thumbsup

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01-25-2008 at 04:32 AM
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RuAdam
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icon Re: Depicting the DROD Number (0)  
I have to say I really like this contest, and I'll try to come up with something.

But there is one thing I don't quite understand. I don't quite get the "Hey, I Know You!" test. At first I thought this is something about how easy it is to remember a number and indentify it. But it turns out that it's about how easy it is to decode the number, and I think this doesen't make much sense.

We already have an encodability test. And decoding is usally about the same difficulty of encoding if we know the coding process. I mean this isn't a code to crack, so basicly it's just "follow the encoding instructions bacwards". And as I seen in most submited entrys it really is just that what they say regarding this test.

Also I can't understand why would I want to decode a DROD number into a decimal number. Why whould that be easier to remember. For example let's say that we take the method Syntax submitted at the beggining. The problem was how do we convert a number into a nick. Let's say that we have a time machine. and we go to the future, and gather all the nicks to all the DROD numbers, and devise an insanely difficult method in witch encoding would take at least 10 years, but the result would be, that everybody's DROD number would be the persons nick.
How would this system go with this test? Well it fails terribly. We need super-computers to decode, and even than it takes 10 years. But actually, if the number would be the persons nick, that system would make it the easiest to tell if you know that person or not.
01-25-2008 at 07:56 PM
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Tuttle
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Wrt the need for a decodability test, here's a system which is easy to encode but a pain to decode:

Not An Entry: Stacks On

Encoding: Write the most significant digit of the number so it fills an imaginary box 1cm x 1cm. Write the next digit the same way, but in an imaginary box positioned 1mm lower and 1mm to the right. Repeat the shift and write for the rest of the digits.

Decoding: Read the uppermost digit and write it down. Read the next uppermost digit and write it to the right of the previous one. Repeat for the rest of the digits.

I can encode a 20-digit number in a few seconds. Good luck reading it. :)

[Last edited by Tuttle at 01-26-2008 05:30 AM : left/right/whatever]
01-26-2008 at 03:27 AM
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kyevan
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On the other hand, it'll be not too hard to distinguish two completely different DNODs in that system, as an abstract symbol.

My not-a-submission: Write it out in D'ni :P
01-26-2008 at 04:14 AM
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