"The world is my home, it's just that some rooms are
draftier than others"
Announcements
03/15/2008 - PAWS 2.03 release available, PAWS 1.5 still available as well.
05/20/2006 - What numbers are made of.
03/12/2006 - Proof of division by 0 and why it's useless
01/07/2006 - World Anvil initial beta now available!
Greetings!
Everybody's got to have a home page--This one's mine.
The lair is finally getting that comfy home feel. The carpet is down and
there are some tapestries hiding the bare dirt walls. :) The lair currently
contains:
1. SpellJammer and regular AD&D material.
2. A Text Adventure authoring system called PAWS. (Version
1.4 now available!)
3. The World Anvil OGC gaming tool. Forge your own reality!
(World Anvil Basic beta)
4. Proof of Mahavira's Conjecture. That's right, division
by 0 now has a working proof, alas, turns out it's fairly worthless.
5. Reverse Engineering Mathematics -- Why 0 is so
troublesome in math.
Current Projects
PAWS 2.0 Nearing Completion
I've dusted off PAWS after a 5 year hiatus, and released version 1.5. I've
also been working on PAWS 2.0, which from a user's perspective has a much
better interface. PAWS 2.0 will be released soon, possibly in time for
Valentine's day, 2008.
Reverse Engineering Mathematics
A non-Mathematician's Hunt for the Boojum
A new PDF, this one exploring what numbers are made of--literally.
Since Mahavira's conjecture is so monumentally useless (for all that it's true
for certain kinds of division) I set out to find out why. This PDF is suitable
for reading by non-mathematicians, it's in English, not Equation, and the
concepts involved are refreshingly simple.
Ever wondered what a number really is? It's a concept that has stumped
mathematicians and philosophers for millennia but I've made a darn good stab at
answering the question. I might even be right. :) And if I am the reason you
can't divide by 0 becomes blindingly obvious.
PDF Format (28
pages, 220k)
Mahavira's Conjecture Proven -- But It's Useless
Everyone knows you can't divide by 0--it's undefined. But in 830 A.D. the
Indian mathematician Mahavira said you could do it. The short version is a
÷ 0 = a. In other words, dividing by 0 is identical to dividing by 1--it
has no effect, just like adding or subtracting 0 has no effect. But there's a
problem. First, restated in English Mahavira's conjecture basically tells you
the amount remaining when no division takes place. Ferociously unhelpful, that. ☺
And that's the minor problem. The major problem is Mahavira's
conjecture breaks the link between multiplication and division, and so leaves
all higher mathematics a smoldering ruin. That's obviously not a
reasonable outcome.
So what's the bottom line? Well, yes Mahavira's conjecture works, but
only when only one unit of measure (quantity) is involved (it can't tell you
miles per hour, for instance, when there's 0 speed), and no it doesn't
solve anything except how much is left if you don't divide.
The word division means more than simply repeated subtraction, it's
the operation that lets you "undo" multiplication, and Mahavira's
conjecture doesn't address that, it only addresses repeated
subtraction.
For now, I'm going to leave the proof in place until I can rewrite the
document and change it's focus. Even though Mahavira's conjecture is a bust (it
does so much less than you would think) there's enough useful material before
the actual proofs that if you ignore page 16 and 17 it's still fairly useful. I
plan to completely rewrite the document, deleting Mahavira's conjecture and
pursue another goal, one that will, I hope, let other non-mathematicians get a
glimpse into the strangely interesting world of math.
I never believed I would ever look at math that way. This project flipped a
switch in my head. It's like there's this gyroscope starting to spin up in my
mind, and it won't stop accelerating.
Anyway, for what it's worth (surprisingly little) here's the proof in PDF
format:
PDF Format
(17 pages, 229KB)
I want to publicly thank the volunteers and moderators of a website called NRICH.Maths.org
for their infinite patience with a non-mathematician's feeble attempt at math.
Their input has been invaluable, they are the real deal and on top of
that they didn't just say "nope, wrong" and let it go at that, they
actually took the time to ask the right questions, they made me think, and work
through it, until I understood what was wrong with Mahavira's conjecture.
They know how to teach on that site! I think I got maybe one straight
answer (and that by accident) from them. Instead, they challenged me to defend
my proof (but oh so politely!), they never let me get away with intellectual
laziness, and I was always forced to think.
I program for a living, so problem solving is my bread and butter. But I have
never pushed so hard in my life. I was scrambling every single second, pushed to
my limits. The funny thing was, I loved it. It was like the quote from
the song Danger Zone.
She'll never say hello to you until you've got it on a red line overload
You'll never know what you can do until you get it up as high as you can go
Funny thing is, that's true. There's something about pushing one's limits
that's just, well, satisfying.
So to the members of NRICH, my heart-felt gratitude. Thank you for
showing me what teachers should be and so seldom are.
World Anvil
My current project is World Anvil, an ambitious one-stop shop for players and
DMs for our favorite fantasy role playing game from Wizards Of The Coast. When
completed World anvil will come in 3 "levels": Basic, Player, and
Designer.
The Basic level is free, and available from this website. It includes a dice
roller (one of the best around) and a table-generator similar in power to Table
Smith or Wintertree's old Table Master, including a simple scripting language.
World Anvil Basic is now in beta and you can download it from the World
Anvil page. The current beta contains the completed dice roller, but not the
table-generator, which is in development.
The Player and Designer levels are not free, not available yet
(they're under development), and not on this website. I plan to make them
available via RPGNow, a popular website that sells PDF gaming materials as well
as software for role-playing games.
Email Link
If you have any questions about either PAWS or World Anvil progress, or would like
to submit a feature wish list or have other feedback, feel free to email me!
This page was last updated on Friday May 23, 2008.
