Current Newsletter
Click Back to return
THE MATHWRIGHT LIBRARY NEWSLETTER, May 2004, VOL 5,
#10
A publication of Bluejay Lispware
James E. White, Editor
The official
publication of the New Mathwright Library and Café:
In this issue:
1)
Implicit
Surface Grapher
2)
How smart is your spreadsheet?
HiFi: Personal Household Finance Manager
1)
Implicit
Surface Grapher
What
does the surface in 3-space defined by the equation 
look like?
That's right, it's a doughnut,
or in mathematical terminology, a torus.
Equations
of the form F(x,y,z) = 0 often define interesting and exotic
surfaces in 3-space. And often, these surfaces cannot be represented as the
graph of a function, because it may not be possible to solve for one of the
variables in terms of the other two.
Then again, the equation may not define a surface at all. The condition (the
implicit function theorem) for it to define a surface is that it have nonvanishing
derivative (or gradient).
We
call the points where the derivative vanishes singular points, and
a great variety of interesting things can happen at such points. The red cone
pictured above has a single singular point at its vertex. The yellow surface
has no singular points. This tool can help you explore the singularities and
bifurcations of smooth functions of 3 variables. You can get very fine detail
if you draw in a small box, then fly into it.
Implicit
Surfaces is a utility that students may use to draw the solution of
an equation: F(x,y,z) = 0 . They define the function F(x,y,z)
by writing any expression in x,y and z. It is automatically set to 0 and the
surface is drawn.
Read
the information under the Instructions button for more detailed information
on how to use this tool. You will learn how to draw your surfaces, rotate
and translate them, draw them solid or wireframe, fly through them, and bring
them to life in other ways. If you have a picture you would like to keep,
take a snapshot (Workbook menu), and save it.
2)
How smart is your
spreadsheet ? HiFi:
Personal Household Finance Manager
Put
away your spreadsheets, and take a look at an entirely different way of doing
business! Spreadsheets are essentially calculators, and they do not generally
give advice. HiFi is a personal
consultant that you tune to your own finances: bills and their due dates,
income, and your desired budget for monthly expenditures. HiFi helps you plan
your monthly finances by setting a little money aside each period for bills
that will come due several months down the road, escrowing those future payments
in your savings account. It examines your budget each period and suggests
adjustments based on your real expenditures. And it notifies you when bills
are coming due so that you may pay them in a timely fashion.
At
the heart of the Mathscript language is an object-oriented LISP interpreter.
LISP is the language of choice for artificial intelligence design, and HiFi
is an Expert System
that can take much of the drudgery and guesswork out of managing your day-to-day
household finances.
This
16-page Microworld is personal consultant
that you can actually use to manage your finances, and that can demonstrate
some of the strategies of artificial intelligence programming.
HiFi
only gives advice, of course. You consult with it a couple of times a week,
and it generates this advice in its reports to you. It does this by visualizing
your checking and savings accounts as being composed of structured "objects."
Each bill is an object that knows when it will be due, and how much (roughly)
it will be. These objects collaborate with the HiFi manager, and sometimes
among themselves, so that if you should overspend, say, your "food"
budget, then "food" may "borrow" money for that period
from an underspent budget, such as "entertainment." If the transaction
is agreeable, then HiFi asks you whether you want to do it. If not, then it
simply expands the "food" budget and notifies you in the report
that it has done so.
The
important thing is that HiFi will not let you inadvertently overdraw your
checking account. If it sees that coming, with bills not yet due, that it
knows it must pay, then it will warn you. All in all, the system is an intercommunicating
system of autonomous objects that interacts with you through the manager.
Over the course of time, it will help you adjust your budget to the realistic
pattern of your expenditures, and generates reports that can keep you apprised
of the state of your finances every couple of weeks.
While
you may actually use HiFi to manage your finances, HiFi is mainly a demonstration
of Artificial Intelligence technology -- a teaching program -- so please read
the license agreement on installation. Mistakes happen, and you should always
compare HiFi's estimate of your accounts with what your banks think you have.
We cannot be responsible for either computer-generated (gasp!) errors or those
of the human kind.
The
simplest way to use HiFi is to pay your bills online when it asks you to.
All of this is explained in the 30 page manual that tells you step-by-step
how to set it up.
Since
it has to do with your finances, we chose to provide HiFi as an offline Microworld
that you run with Mathwright32 Reader, rather than in the browser. So when
you go to the title page, select Add to My Collection rather than Read
in my Browser to get the program. If you select Read in my Browser
you will see the 30-page manual, and this is available to all visitors, whether
or not they have Library memberships. Alternatively, you may download the
manual as a free PDF file and print it.