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ErikH2000
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icon Depicting the DROD Number (+3)  
I have concluded that the maximum number of DROD players that could ever exist on Earth between 1997 and forever is 29.5 quintillion. How did I arrive at this number? It was explained in the January Illumination newsletter. Our official contest for the month asks you to create a numeral system that will represent any possible "DROD Number". A DROD Number is a number between 1 and 29.5 quintillion which is assigned to a DROD Player to uniquely identify him.

We already have numeral systems that can do that. You're familiar with the Latin glyphs "0" through "9" and how they may be arranged using the Hindu/Arabic numeral system to represent whole numbers. (Yes, you are, even if you didn't recognize the names.) We could use that for representing the DROD Number, but it would do poorly for the first two of my four tests described below.

By the way, I have already came up with a functioning mechanism to assign DROD Numbers to anybody that wants one. In fact, your DROD Number has probably already been assigned. If you would like to know what it is, then, by all means, ask in this other topic.

The Tattoo Test (Aesthetics)

The Tattoo Test is a measure of how aesthetically pleasing the depiction is.

I expect that we will have many people wanting to tattoo themselves with a uniquely-identifying depiction of their personal DROD Number. So it should be something that looks good, right? Nobody wants to skin-carve "249999999999999999999" on himself, after all. But maybe if this DROD Number depiction were some wondrous collection of interconnected lines and arcs, then it would have good tattooability.

Judging aesthetic appeal is subjective, but at the low end of the scale you have something like a bar code. There are people with bar codes tattooed on them, but the ugliness of the depiction is usually part of some irony or overall statement. At the high end of the aesthetic scale you've got... I dunno... Prince's Love Symbol, the thing he was using to identify himself while he went nameless. But you can't reuse Prince's symbol, because he already assigned it to himself as a unique identifier. And I could be wrong, but I don't think he devised a system to similarly represent people beyond just himself.

The Drawn In Blood Test (Elegance)

The Drawn in Blood Test is a measure of how efficiently a depiction of a number conveys information.

Suppose you lost a knife fight and were laying slumped against a wall with minutes left to live. It would be natural to leave one last mark on the world before you passed on. So you want to draw your DROD Number on the wall, but without any pen or lipstick on-hand, it will have to be painted with your own blood. In this case, you would hope that the numeral system was very efficient in generating a depiction of your DROD number. You don't want something like the Babylonian system that makes you draw triangles when simple dashes should suffice. The preferred system would let you identify who you are with a minimum of strokes. You've only got so much blood, after all.

The Cocktail Napkin Test (Encodability)

The Cocktail Napkin Test is a measure of how easily a depiction of a number may be encoded.

If you know somebody's DROD Number, how long would it take you to work out the depiction of it on cocktail napkins? Cocktail napkins are those flimsy, paper napkins that rip if you push a pen into them too hard. Would you sit there for seventeen hours and work through a case of napkins? One day, you may be called upon to scribble up a number using your system. And it's more impressive if you can do it on the spot instead of retreating to your laboratory with all the big computers.

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

The "Hey, I Know You!" test is a measure of how easily a depiction of a number may be decoded.

So you're relaxing in a public steam bath, and you notice somebody next to you is sporting a sweet DROD Number tat. Hmmm, that DROD Number looks familiar. Is this person an old friend from back in the day, or maybe a bitter arch-rival? A good representation won't be hard to decode. Maybe you could work it out in a few minutes. And if you don't have to cart cocktail napkins into the steam bath, so much the better. We all know what a soggy mess that makes.

What are the Rules?

The numeral system that you devise and enter into the contest must meet the following submission criteria:
* The system uniquely depicts whole numbers from 1 to 29.5 quintillion.
* 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.
* The system's depictions must be two-dimensional and consist of marks visible to the human eye.
* The system is an original invention of your own, although borrowing ideas from existing systems is fine.

To submit your numeral system, please make a reply post to this topic following the format below:
quote:

- The text "For submission" at the beginning of the post. This indicates you are seriously submitting an entry and would like people to spend their time considering it.
- A depiction of the number one generated by your numeral system.
- A depiction of the number 29.5 quintillion generated by your numeral system.
- Optionally, you can include other sample depictions generated by your numeral system.
- Instructions on how to encode a number to a depiction. The instructions should work for the full range. The instructions should allow someone following them to arrive at an encoded depiction without using outside resources such as lookup tables, computer software, or other people.
- A description of how to decode a number from a depiction. The instructions should work for the full range. The instructions should allow someone following them to arrive at a decoded number without using outside resources such as lookup tables, computer software, or other people.
- Optionally, you can include other explanation text, observations, anecdotes, and whatnot.



The deadline for posting your submission is:
Local Time:02-18-2008 at 12:00 AM

If you have set your timezone under your forum profile, the above time will have been adjusted to an accurate local time.

You can make changes to your numeral system before the submission deadline. To do this, just edit your post to make the changes. An advantage to posting your numeral system early is that it may be discussed by the general forum population and give you ideas for improvement.

You may enter one, two, or three numeral systems. If you choose to submit multiple entries, please describe them in separate posts.

How Do I Win?

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. Forum members will be asked to rate the entry on a scale of 1 to 10 for how well it succeeds in the four tests (Tattoo, Drawn in Blood, Cocktail Napkin, and "Do I Know You?"). Each entry then receives a score which is the average of all the ratings from each test and each voter. Winners are then chosen based on this score, with three prizes awarded.

It's possible for one person to submit multiple entries, but only one of his entries can win a prize. The winner of the first prize will not be considered for the second or third prize. And the winner of the second prize will not be considered for the third prize.

What Do I Win?

The first prize winner will receive 100 rank points and any single item of his choosing from the Prize Pile. The second and third prize winners will receive 50 and 25 rank points, respectively. Someone who has never participated in a Caravel contest before will receive a 10 rank point "rookie bonus" for trying something new.

For anyone who is new to the forum, "rank points" are units of a little reputation system we use here. It's possible that if you have more rank points, people will respect you more, or something like that. The Prize Pile is a collection of several different prizes which are available to contest winners. Things like computer games, mousepads, t-shirts, and books. Many of the prizes are offered directly by other forum members out of the kindness of their hearts.

Thoughts on Strategy

A good starting point is to read a bit about numeral systems in some place like Wikipedia. Consider how well existing systems do against the four tests. You can maximize a numeral system to do well on one test, but it tends to come at the expense of doing poorly on the others. So finding the right trade-offs are necessary.

You may be bothered by the vagueness of definition for success in a test. Practically speaking, I can't give you an official definition. This is going to be decided imperfectly by public vote. You will be allowed to gather feedback prior to the vote, argue against other people's opinions, and change your entries. I understand the subjectivity can be dissatisfying, but I could not create a contest with objective rules without severely restraining the creative range of what people can enter.

I am hoping that we will see some interesting and insightful ways of depicting numbers.

-Erik

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[Last edited by ErikH2000 at 01-23-2008 01:40 AM]
01-12-2008 at 11:56 PM
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Chaco
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First of all, this is a fantastic idea for a contest - we have systems like scientific notation, of course, and many other ways to represent large numbers (such as Conway arrow notation) but we need something easy to use and yet precise to one number in 29.5 quintillion!

I will probably enter - I hope I can do reasonably well. :)

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01-13-2008 at 12:24 AM
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VodkaAndCoke
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This is a genius idea! I look forward to even start considering a solution.

However, I've not yet read that letters can't be used. This could be an oversight though... If letters could be used, the forum nick would be the most obvious solution. I'm assuming therefore that only digits must be used (possibly in a different formations).

Also, I presume any given nick should have one given "number" and vice-versa (ie 1 to 1 mapping).
01-13-2008 at 12:45 AM
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Syntax
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Erm... that was me. VodkaAndCoke came over for some DROD time but has since left :)
01-13-2008 at 12:46 AM
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ErikH2000
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quote:
Syntax (not VodkaAndCode) wrote:
However, I've not yet read that letters can't be used. This could be an oversight though... If letters could be used, the forum nick would be the most obvious solution. I'm assuming therefore that only digits must be used (possibly in a different formations).

To be clear, you aren't limited to just using numeric digits. You could use letters, sure. You could invent something entirely different than traditional glyphs. And you might ask yourself if a glyph system is even the best thing.
quote:
Also, I presume any given nick should have one given "number" and vice-versa (ie 1 to 1 mapping).

That's true. A problem you have is that you need to give complete encoding and decoding instructions with your entry. At present, that would require publishing the mapping of usernames to IDs. It's not really possible for your instructions to be complete since you don't know the future mapping. You're relying on a private system to generate the mapping of 2 = ErikH2000, 11 = Schik, and so on.

I think your instructions really need to be self-contained and not rely on external systems, especially those that are private. The existing rules might already imply that now, but I'll go and clarify them.

-Erik

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01-13-2008 at 12:56 AM
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Syntax
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quote:
ErikH2000 wrote:
quote:
Syntax (not VodkaAndCode) wrote:
However, I've not yet read that letters can't be used. This could be an oversight though... If letters could be used, the forum nick would be the most obvious solution. I'm assuming therefore that only digits must be used (possibly in a different formations).

To be clear, you aren't limited to just using numeric digits. You could use letters, sure. You could invent something entirely different than traditional glyphs. And you might ask yourself if a glyph system is even the best thing.
-Erik

In that case then, the best mapping is nick -> nick as these are unique though, right?
01-13-2008 at 01:07 AM
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Chaco
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I'd like to point out a few things that I've thought about during this time. I will probably vote any system that considers the following higher.

The worst-case scenarios. Examples would be any number in the high quintillions with no consecutively repeating digits, or large numbers that are very similar but differ by a digit in the billions or wherever.

Scalability. I'd like to either be able to write my DROD number on a building wall or put it on the side of a DROD mug.

Monochromality. Ideally, I shouldn't need to have two different kinds of pen on me to write my DROD number. A single pen, pencil, or person's blood gives me two colors (the color, and the absence of that color) That should be sufficient.

These are the three things I'm attempting to cover with my system, and so far I think things are going well. I still need to try many numbers and see if the results are reasonable, though.

I agree with Erik's statement that doing research into number systems is helpful. :)

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01-13-2008 at 01:21 AM
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ErikH2000
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quote:
Syntax wrote:
In that case then, the best mapping is nick -> nick as these are unique though, right?

Usernames are unique, yes. But there must be some way of converting the username to a number, and you must have a capacity to represent every number between 1 and 29.5 quintillion.

To make this concrete, if I give you the number "3450987340", how will you arrive at the username that represents it? This would be an example of the encoding task.

-Erik

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01-13-2008 at 01:23 AM
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ErikH2000
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quote:
Nuntar wrote:
By the way, I'm assuming that you mean the American quintillion.

Yep, the American short form. 1 quintillion = 10 to the power of 18. Or as you say, "1,000,000,000,000,000,000".
quote:
But (I'm guessing from a cursory reading of the rules) it's OK to make a system that can go higher. If you want.

You bet!

-Erik

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01-13-2008 at 01:26 AM
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quote:
ErikH2000 wrote:
quote:
Syntax wrote:
In that case then, the best mapping is nick -> nick as these are unique though, right?

Usernames are unique, yes. But there must be some way of converting the username to a number, and you must have a capacity to represent every number between 1 and 29.5 quintillion.

To make this concrete, if I give you the number "3450987340", how will you arrive at the username that represents it? This would be an example of the encoding task.

-Erik


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.

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01-13-2008 at 01:30 AM
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Chalks
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Do we have to worry about decimal numbers, or only integers?
01-13-2008 at 01:39 AM
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Chaco
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quote:
Chalks wrote:
Do we have to worry about decimal numbers, or only integers?


So far, all DROD numbers that have been assigned to people have been integers. We also know that one DROD number is supposed to correspond to one person. Although it suggests it, this does not necessarily indicate that all DROD numbers are integers.

I sure hope so, though.

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01-13-2008 at 01:41 AM
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techant
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Well this is a challenge! :w00t Maybe I will use smilies :D :rolleyes


Just kidding..fails the napkin test.

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01-13-2008 at 01:47 AM
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coppro
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Query: While it must be possible to map each number uniquely, is there any requirement about ease of encoding/decoding?
01-13-2008 at 01:50 AM
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Chalks
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quote:
coppro wrote:
Query: While it must be possible to map each number uniquely, is there any requirement about ease of encoding/decoding?

Yeah.
quote:
ErikH2000 wrote:
The "Hey, I Know You!" test is a measure of how easily a depiction of a number may be decoded.


[Last edited by Chalks at 01-13-2008 01:55 AM]
01-13-2008 at 01:55 AM
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Tim
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Let me try a very easy one to see what I am missing:

For submission: Trivial System

- A depiction of the number one generated by your numeral system.
DROD# one

- A depiction of the number 29.5 quintillion generated by your numeral system.
DROD# twenty-nine billiard, five hundred billion

- Instructions on how to encode a number to a depiction. The instructions should work for the full range. The instructions should allow someone following them to arrive at an encoded depiction without using outside resources such as lookup tables, computer software, or other people.
Translate the number using "(British) English". If there are difference between "American English" and "British English", a die will be rolled. The result of the die will not be used.
After this, the text "DROD# " will be added in front of the result.


- A description of how to decode a number from a depiction. The instructions should work for the full range. The instructions should allow someone following them to arrive at a decoded number without using outside resources such as lookup tables, computer software, or other people.
Remove the "DROD# " part. Write the number down in decimals using "British English". "American English" or "Simpuhl English" is not "British".

- Optionally, you can include other explanation text, observations, anecdotes, and whatnot.
For example, only "DROD# twenty-five" means 25. "DROD# eighteen plus seven" or "eytanz" does not represent 25.

Changes made using remarks from Chaco, Nuntar and Jutt. Thank you both.

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[Last edited by Tim at 01-16-2008 02:28 AM]
01-13-2008 at 01:58 AM
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ErikH2000
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quote:
eytanz wrote:
I think Syntax's point is that

Maybe it it is, (not sure) but in any case, I'll take evaluate your example...
quote:
the rules allow for a numeral system that includes all (and only) the symbols that the forum allows to use when choosing user names.

I agree so far.
quote:
Thus, any string that is an acceptable user name is also an acceptable number,

Agreed.
quote:
and it allows for a trivial mapping that he proposes.

I'm don't understand the mapping that is proposed, so I don't know if I agree or not.
quote:

In such a system, the number "3450987340" would be held by a user whose forum name is 3450987340.

Okay, you're saying that the DROD #3450987340 encodes to "3450987340", which means that in this case the depiction is simply the popular Arabic/Hindu with Latin glyphs. That's fine. I'll add that this method solves the encoding problem since it can be described how to encode any whole number between 1 and 29.5 quintillion this way.
quote:
Such a user does not exist, but that's fine under the system.

Agreed.
quote:
If you asked who is the username whose number is "eytanz", Syntax could calculate and determine that it is me.

You need to define what happens with "calculate and determine" before I can tell you if this works by the rules. So in your example, I am calling "eytanz" the depiction. How do you decode that depiction and arrive at the whole number between 1 and 29.5 quintillion assigned to you? (That number is "25", by the way.)

If the answer is just to look it up in an external table, whether that table is on the DROD forum server or kept some other place, then you haven't provided complete decoding instructions. Decoding instructions could include a lookup table in an effort to be complete. But then they would need to contain the complete mapping of existing and future DROD players, or a mapping for all 29.5 quintillion DROD Numbers. In theory, you could generate 29.5 quintillion arbitrary mappings in advance. But by the time you finish typing them all out to post in your entry, the contest will be over. And probably your computer crashed before that when you ran out of virtual memory on your hard disk. And also you died before you finished typing them all.

-Erik

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[Last edited by ErikH2000 at 01-13-2008 02:13 AM]
01-13-2008 at 02:09 AM
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Regarding Tim's Trivial System:

It seems like you've basically submitted the decimal system as your entry. I don't think it will do too well with some of the tests - you can do better than that. Allow me to offer some criticisms in the four areas:

Aesthetics - This is easily the most subjective test. In my opinion: well, it's a long string of numbers. Although I wouldn't outright call it ugly, I'm just not satisfied with low numbers such as 1 or 2, large numbers such as 9,000,000,000,000, or other long strings. I'd probably rate this a 3 or a 4.

Elegance - I wouldn't call this one very elegant - you have to write one numeral for each digit in your number, you also have to remember each digit of your number as a whole, and you need to be able to write them in order from left to right. It's mediocre at best, and I think our systems can do better in this department. I'd probably rate this a 2 or a 3.

Encoding is very easy, as there are no steps to decode or encode a number - the system is exactly the same as the decimal system used to represent the original DROD numbers. This one gets a 9 since there are no steps, but it takes some time, as you have to enumerate each digit of the DROD number, then write it in Arabic numerals. Not sure whether it is assumed that someone reading a DROD number knows Arabic numerals or whether that would count as a lookup table :)

Decoding, while equally straightforward, is somewhat difficult: how to easily tell the difference between a person with DROD number 2999999999999 and 29999999999999 without having to individually count the number of nines? How can one easily remember the DROD number 128576328693? I'd probably rate this one averagely - maybe a four.

Overall, that gives your system a total of about 18 out of 40 - meaning that, while this is a satisfactory system to use to represent DROD numbers as shown by the fact that Erik gave us the originals in this format, we can do better. Which is the entire point of this contest. :)

On the plus side, your system does pass my Monochromality and Scalability tests, although it does about average on my Distinguishability test.

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[Last edited by Chaco at 01-13-2008 02:15 AM]
01-13-2008 at 02:13 AM
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Tim
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Chaco, my Trivial encoding system is NOT the decimal system. It's "English"!

For example, "twenty-five" or "seventeen plus eight" represent the same person.

If it is wrong, then I think I need to change my post to show that.

Note to Nuntar: I will change the system as you proposed. Thank you.

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[Last edited by Tim at 01-19-2008 10:48 AM : added image for other entry]
01-13-2008 at 02:20 AM
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Ok, reading Erik's response to me tells me I misunderstood something, but it's 2:30 AM so I'm going to leave re-reading this thread to tomorrow morning.

By the way, I knew my number was 25 - as pointed out in the thread in the General forum, there's a pretty easy way to check, at least for some players.

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01-13-2008 at 02:31 AM
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Chaco
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quote:
Tim wrote:
For example, "twenty-five" or "seventeen plus eight" represent the same person.



Then your system fails the "repeatable depiction" criteria, since if I follow your instructions twice trying to depict the same number I can get two different depictions. I must only be able to get one string no matter how many times I follow the instructions on the DROD number 25, or any other number.

I think the system could be improved if you clarified what you mean by "English" since you've not really clarified how we're supposed to come up with the string representations of the numbers.

(Yes, I'm aware of exactly how your system works, but I'm not supposed to be. :) )

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01-13-2008 at 02:38 AM
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Tim
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quote:
Chaco wrote:
Then your system fails the "repeatable depiction" criteria, since if I follow your instructions twice trying to depict the same number I can get two different depictions. I must only be able to get one string no matter how many times I follow the instructions on the DROD number 25, or any other number.
Thanks! I will change that too.
quote:
I think the system could be improved if you clarified what you mean by "English" since you've not really clarified how we're supposed to come up with the string representations of the numbers.
I'm sorry, but I think I can only explain it to you using "English", or do you happen to know "Dutch"? ;)

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01-13-2008 at 02:46 AM
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Chaco
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icon Re: Depicting the DROD Number (+1)  
You've made a step in the right direction, but I think you still need to clarify "English" as used in your entry description.

I think you need to fully describe the decimal system in its entirety: for example, appending the word "twenty" before the three digit group name "billion" to make the string "twenty billion" representing 20,000,000,000 - since "twenty" represents 20 and "billion" represents 1,000,000,000, we are in effect saying "multiply one billion by twenty".

You have to describe exactly how to convert a series of digits into an English string, skipping no steps and making sure that all possible possibilities are covered. You must also define all strings that you use in your explanation as corresponding to some decimal number. After that, I think you should be set in using the decimal system as your entry. :)

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[Last edited by Chaco at 01-13-2008 03:11 AM]
01-13-2008 at 03:11 AM
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Tuttle
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icon Re: Depicting the DROD Number (+2)  
If I understand Tim's system correctly, I think the biggest problem is in the Elegance category. Assuming you formally document the decimal to English mapping, and settle on American English (since that's the definition of "quintillion" we're using), you still end up with some poor soul slumped against the wall trying to write "twenty-seven quintillion, one hundred and eighty-two quadrillion, eight hundred and eighteen trillion, two hundred and eighty-four billion, five hundred and ninety million, four hundred and fifty-two thousand, three hundred and fifty-three". It's efficient for some numbers (one, ten, fifty, one billion etc), but not for arbitrary ones that aren't nice round numbers.

[Last edited by Tuttle at 01-13-2008 03:30 AM]
01-13-2008 at 03:29 AM
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coppro
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For submission: Unoriginal System

Instructions: The number is given as 14 characters. The first 14 characters are always "DNoD", to uniquely identify this as a Deadly Number of Death.

The remaining digits form an eleven-digit base 59 number depicting the DNoD with the following values for symbols:

"0" : zero
Lowercase letters - their position in the English alphabet (a-z map to 1 - 26)
Uppercase letters - their position in the English alphabet, plus twenty-six (A-Z map to 27 - 52)
The remaining six numerals are symbols that map as follows:
+ : 53
- : 54
* : 55
/ : 56
! : 57
? : 58

Encoding and decoding are a simple matter of converting number bases.

Depiction of number 1 (admin's DNoD): "DNoD0000000000a"
Depiction of number 2 (Erik's DNoD): "DNoD0000000000b"
Depiction of number 2114 (my DNoD): "DNoD000000000iW"
Depiction of number 29.5 quintillion: "DNoD!Pqan!iiFN0"

This is a pretty unoriginal system.

If you think that this system is too hard to remember, do realize that it only really requires that you remember those six special characters, which I don't think is that hard. Plus, you are remembering an encoding scheme which packs almost 30 quintillion numbers into eleven characters. No one said it would be easy.
01-13-2008 at 04:09 AM
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Chalks
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icon Re: Depicting the DROD Number (+2)  
For Submission: Alphabet Based System

29,5000,000,000,000,000,000 = oYz8
1 = a
1175 (my number) = fS,
73,450,987,340 = dQYy.s,T

Values:
a = 1, A = 1
b = 2, B = 2
c = 3, C = 3
Etc.
Exception: Z = z = 00


Meanings:
Lowercase letter (e.g. 'a'): Double the value of the letter then subtract 1.
Uppercase letter (e.g. 'A'): Double the value of the letter.
Comma (','): Double result again, then subtract 1.
Period ('.'): Double the result again.
Any single number X (where X>1): Shows that the preceding set is repeated X times.



Instructions:
To encode a number, first divide it into subsets of 2 digits. 73,450,987,340 becomes 07,34,50,98,73,40. Then, perform the following steps.

1. If group (of two numbers) is even, goto 3.
2. If group (of two numbers) is odd, add 1, goto 3.
3. Divide by 2.
4. If result is greater than 26 and even, goto 7.
5. If result is greater than 26 and odd, add 1 and goto 7.
6. If result is less than 26, go to 8.
7. Divide by 2.
8. Take resulting number, and assign it a letter (a = 1, b = 2, c = 3, etc.)

Here are the possible steps taken:
1, 3, 4, 7, 8 = A.
1, 3, 5, 7, 8 = a.
1, 3, 6, 8 = A

2, 3, 4, 7, 8 = a,
2, 3, 5, 7, 8 = A,
2, 3, 6, 8 = a


Decoding is much simpler. For example, the number "AE.OY,z4s.3" becomes 02,20,30,99,00,00,00,00,74,74,74 becomes 220,309,900,000,000,747,474.
A = 1 * 2
E. = 5 * 2 * 2
O = 15*2
Y, = 25 * 2 * 2 - 1
z4 = 00,00,00,00
s. = (19 * 2 - 1) * 2 = 74, s.3 = 74,74,74



:D

Edit: 2 rules for this system. Z is not allowed to represent anything, use lowercase z at all times. Also, "a." is improper, use "A" instead (both would equal 2).

Edit 2: Make that 3 rules: "A." is also improper. Use "B" instead (both equal 4). In general, if there are two possible ways to represent a number (I think that only happens with 2 and 4), use the representation that has the least number of characters.

[Last edited by Chalks at 01-13-2008 03:35 PM]
01-13-2008 at 05:06 AM
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golfrman
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icon Re: Depicting the DROD Number (+1)  
quote:
Chalks wrote:
Decoding is much simpler. For example, the number "AE.OY,z4s.3" becomes 02,20,30,99,00,00,00,00,74,74,74 becomes 220,309,900,000,000,747,474.
A = 1 * 2
E. = 5 * 2 * 2
O = 15*2
Y, = 25 * 2 * 2 - 1
z4 = 00,00,00,00
s. = (19 * 2 - 1) * 2 = 74, s.3 = 74,74,74



This is one of the most confusing things I've ever read.

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01-13-2008 at 05:14 AM
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Chalks
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icon Re: Depicting the DROD Number (0)  
quote:
golfrman wrote:
quote:
Chalks wrote:
Decoding is much simpler. For example, the number "AE.OY,z4s.3" becomes 02,20,30,99,00,00,00,00,74,74,74 becomes 220,309,900,000,000,747,474.
A = 1 * 2
E. = 5 * 2 * 2
O = 15*2
Y, = 25 * 2 * 2 - 1
z4 = 00,00,00,00
s. = (19 * 2 - 1) * 2 = 74, s.3 = 74,74,74



This is one of the most confusing things I've ever read.

heh, I was afraid of that. Basically, there are two operations you can perform: multiply by 2 then subtract 1, or just multiply by 2. 'A' and '.' means the latter, 'a' and ',' means the former. Reading left to right, you simply perform those operations (where a or A = 1, b or B = 2, etc).

Edit: Each letter begins a new set of 2 digits in the decoded number.

[Last edited by Chalks at 01-13-2008 05:20 AM]
01-13-2008 at 05:19 AM
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Maurog
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icon Re: Depicting the DROD Number (+2)  
Yay! A whole three slots, this means I can waste one just for fun! Here we go...

Gaming the System System
Let N be your DROD number, 1 <= N <= 29.5*10^18.
To depict your number:
Draw a circle, put a dot as its center, and draw a small arrow upwards from the topmost circle point perpendicular to the circle.

Now, let angle A be A = N / (29.5*10^18) *360 degrees. Draw a straight line from the circle center to the circle edge at angle A from the hypothetical (center to topmost point) line. All done.

This system passes the first 2 tests perfectly, although I admit it might not score so well on the other two. Oh well, 50% at the very least is not a bad result at all...

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01-13-2008 at 10:08 AM
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Mikko
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icon Re: Depicting the DROD Number (0)  
quote:
coppro wrote:

Encoding and decoding are a simple matter of converting number bases.

Depiction of number 1 (admin's DNoD): "DNoD0000000000a"
Depiction of number 2 (Erik's DNoD): "DNoD0000000000b"
Depiction of number 2114 (my DNoD): "DNoD000000000iW"
Depiction of number 29.5 quintillion: "DNoD!Pqan!iiFN0"



IMO, converting to 59-base is not a simple matter. It's quite challenging to calculate something like 17*59^10 even if you have several napkins to do it on.
01-13-2008 at 12:23 PM
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