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Feature: A Modest Proposal
Posted by Nick on 5 May 2000, 01:24 GMT

Our next somewhat late (*g*) feature is written by Ben Kalafut. It talks about what TI should include in their next calculator (or calculator update :P). In my opinion, he makes some good points and some I don't quite agree with (or they aren't vital to the functionality of said calculator), but it's still worth a read and some frank discussion of opinions.

So let's do just that. Many (many) people have complained about TI's "actions," especially since after Hardware 2.00 and AMS v2.03 came out for the 68K calculators. Talk amongst yourselves - as usual, I'll try to offer any input I can.


I have owned three different TI calculators, and I have run into frustrating "brick walls" in the use and programming of each one.
I use my calculator for math and sciences; I have no real interest in gaming or getting my calculator to make sound or bit-mapped graphics. Yet sometimes, the calculators are just as useful as a Gameboy.
Even the "powerful" TI-89 and 92 don't contain what I would like to see in a graphics calculator/computer algebra system. Symbolic manipulation is a nice feature, certainly, but programming all but the most elementary routines becomes time-consuming or impossible. Texas Instruments should probably put out programs to perform Fourier, Laplace, and Z transforms, partial fraction decomposition, tensor mathematics, functional analysis, etc, but they do not do so, and apparently, no third parties are interested.
The problem, in my opinion, is that Texas Instruments considers the graphics calculator to be merely an educational tool. This is evident in the software applications which are written, and the nature of their press releases and advertisements. TI does not seem to recognize the (potential) utility of their calculators to researchers, college students, mathematicians, and professionals.
Some improvements which I would like to see on a hypothetical calculator which TI would put out to replace the 89 are:

1) True updates. I expected a boost in functionality between AMS 1 and 2.03, and all that seemed to occur was an improvement in memory allocation. Extending the function library from time to time would be nice.
2) A faster processor. The 68000 can certainly handle numerics well, but seems to bog down on all but the simplest symbolic operations.
3) Ability to define a function with multiple outputs. For example, a Gaussian elimination decomposition should return both the reduced matrix and the "O" matrix by which one may multiply the original to change it to the reduced form.
4) A true 3-D engine. It is nice to be able to enter functions of two variables, but one should be able to view three-dimensional plots obtained from numerical methods of problem solving, view three-dimensional data plots, or plot space curves parametrically.
5) Vector field plots, Poincar‚ return maps, improved slope and direction field applications.
6) LaPlace and inverse LaPlace transforms.
7) Partial fraction decomposition.
8) Improved ability to program new symbolic functions. The "part" function is a step in the correct direction but is neither sophisticated nor specific enough to be truly useful.
9) Ability to handle tensors.
10) Ability to enter strings, matrices, lists, etc as elements of lists or cell arrays
11) Ability to overload user-defined functions, so that they may return either symbolic or numeric answers, for example. Also, the ability to input fewer than the specified number of parameters to a function and not get errors.

These are just a few suggestions. I'm sure that those who are more advanced in mathematics than I have many more. I don't expect TI to come out with a calculator that does everything that Maple or Mathematica do, but by focusing too much on secondary education it is neglecting a potential market.
TI or a third party should also put out a compiled language for the calculators. I'm impressed with TI-GCC, but TI, having a team of professional programmers, could probably develop the standard libraries and even more powerful interaction with the calculator's built-in features. TI also has the muLisp language, and could possibly release a version for graphics calculators.
Another thing that has struck me is the poor quality of programs in the math and science archives.
A lot of the programs do things that the calculators already do! Additionally, many have poor documentation and terse interfaces. User-friendliness is not a major concern. Neither is standardization or development of syntaxes which make sense to anybody but the user. For the sake of consistency I have been writing my programs so that they either state, clearly, what should be input (rather than specifying a variable name), or in the case of those for the 89 which take inputs from the command line, do so in an order and syntax which follows that of TI's built- in libraries.
The graphics calculator has great potential as a mathematical tool in the classroom, the lab, and even in the professional world, but it will never realize that potential until Texas Instruments chooses not to focus strictly on the secondary education market and programmers (perhaps at the expense of gaming) develop better, more powerful, more consistent mathematics and science software.

 


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Re: Feature: A Modest Proposal
Akira_of_HLC  Account Info
(Web Page)

Please, all(or at least most) of those suggestions have almost no use in a calculator. Think about it. Why would you need a "true" 3D engine? Or a faster processor? I see no point. Calculators were not made for games. Sure they may be fun to program, but if you want to play games on a handheld system, buy a freaking gameboy, not a calculator. You referred to the gameboy as being an "advanced" peice of machinery, but true as that may be, there is not much aof a point to advancing a calculator just so some half-baked programmers can waste time with one.

Akira

     5 May 2000, 23:26 GMT

Re: Re: Feature: A Modest Proposal
Bennett Kalafut  Account Info

This comment is pretty funny, especially considering that I have no interest in gaming on the calculator, and that most of the suggestions made pertain to math (including the one about a true 3D engine!). Could Akira explain why a game programmer would want tensor mathematics, and more flexible functions and data types?

-Ben Kalafut

     6 May 2000, 00:55 GMT

Re: Re: Feature: A Modest Proposal
BLAlien  Account Info

Well, that's not entirely true. See, my principal banned all electronic gaming (Game Boys, Virtual pets, etc...) since she has some weird grudge against harmless fun. Except, let me say that again, EXCEPT, graphing calculators. We need them for math class, and it would be illegal for them to delete all the games on all of our calcs. So they just let us play them during lunch hour and stuff. Sure, Sqrxz may be no substitute for Super Mario Bros DX, but if it's the best I can get, then I'm satisfied.

     6 May 2000, 01:58 GMT


Re: Re: Re: Feature: A Modest Proposal
JaggedFlame

It's ILLEGAL to delete your students' programs? Wow! I never knew that! Is there some official law that says that?

My math teacher will certainly be surprised to hear this when he goes on his next game-deleting spree... :-)

     6 May 2000, 04:47 GMT

Re: Re: Re: Re: Feature: A Modest Proposal
Akira_of_HLC  Account Info
(Web Page)

Well, I suppose, THORETICALLY, since you own the calculator, and you put the games on it on your own free time, the school system has no right to invade your privacy. I don't think that there is a law in the books that says that no person that doesn't own the machinery can delete items off it without given permission, but I'd check the computer crimes statutes in your state's written law journal(it costs around $70 for the book, $30 for the CD).

The crimes are in the New Mexico State Statutes are written in Chapter 30, Article 45.

They may be in other places in a diferent state staute book.

Akira

     6 May 2000, 20:07 GMT


Re: Re: Re: Re: Re: Feature: A Modest Proposal
Jeff Meister  Account Info

But you'd be suspended before you could do this :).

Actually, I read on another comment board somewhere that the teachers can delete your games. But, if you see the teacher coming, throw your calculator into your backpack. Now he/she can't get it without a search warrant. Hmm... nah you'd get suspended for this too.

Welcome to the public school system. The minute you step through the door, all your civil rights (and some other not-so-civil ones) go bye-bye :/.

- Jeff

     6 May 2000, 20:36 GMT


Re: Re: Re: Re: Re: Re: Feature: A Modest Proposal
vod

I dont know about the teacher, but the principal could search your bookbag (and you if they want) (you really dont have many rights on school grounds) and then you could be written up for "talking back" or something to a teacher.

     7 May 2000, 00:54 GMT


Re: Re: Re: Re: Feature: A Modest Proposal
Jim Haskell  Account Info
(Web Page)

See, that's why I use a magical program to hide my games (as well as my, erm, "study aids" coughcoughcheatprogschoughcough...) =)

     6 May 2000, 22:42 GMT


Re: Re: Feature: A Modest Proposal
Daniel Bishop  Account Info

> Why would you need a faster processor? Try these:

1. Graph Y=fnInt(sqrt(e^(-x²)/(2pi)),X,0,X)+.5
2. Find a t confidence interval on the 83.
3. Do a residual plot on 100-element lists.
4. Calculate 2000! (Download a program for this.)

Makes you realize the disadvantage of a 6 MHz processor, doesn't it? Speed is almost as important for math as it is for games.

     6 May 2000, 02:25 GMT

Re: Re: Re: Feature: A Modest Proposal
David Strauss  Account Info
(Web Page)

Hardly anyone actually does that, especially finding 2000!. Also, it's a 10-12 MHz processor, not a six.

     6 May 2000, 03:22 GMT

Re: Re: Re: Re: Feature: A Modest Proposal
Sebastian Reichelt  Account Info

Isn't it only running on 6 MHz? Please tell me if I'm wrong.

     6 May 2000, 03:26 GMT


Re: Re: Re: Re: Re: Feature: A Modest Proposal
JaggedFlame

Well, he means the TI-89/92+ run on 10-12mHz processors. Maybe the six was some other calculator...

     6 May 2000, 04:48 GMT


Re: Re: Re: Re: Re: Re: Feature: A Modest Proposal
CircaX  Account Info
(Web Page)

The 83 has a 6Mhz (geez, I THINK....I cnat remember now)

     6 May 2000, 15:21 GMT


Re: Re: Re: Re: Re: Re: Re: Feature: A Modest Proposal
compman32386  Account Info
(Web Page)

A TI-83 runs at 6mhz.

     6 May 2000, 19:18 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Feature: A Modest Proposal
Akira_of_HLC  Account Info
(Web Page)

The 81 ran at (I think) 2MHz
The 85 runs at 5MHz
The 86 runs at 4.8MHz(yes, the 85 is faster)
The 89 runs at 12MHz
The 92 runs at 10MHz
The 92+ runs at 12 MHz

Hope this helps

     6 May 2000, 19:54 GMT

Re: Re: Re: Re: Re: Re: Re: Re: Re: Feature: A Modest Proposal
Mike Ptyza  Account Info
(Web Page)

Hardware version 1 89's only run at 10MHz, while the hardware version 2 89's run at 12MHz.

     8 May 2000, 03:49 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Feature: A Modest Proposal
Sebastian Reichelt  Account Info

Ooohhh, that was it. I guess I just heard about the 10/12 MHz difference, and got the wrong number into my head. Thanks.

     8 May 2000, 22:27 GMT

Re: Re: Re: Re: Re: Re: Re: Re: Re: Feature: A Modest Proposal
compman32386  Account Info
(Web Page)

Actually, the 85 & 86 have a 6mhz processor in them, but the reason the 86 only runs at 4.8 mhz is because TI reduced the 86's non-user available memory by 50% so the 86 could have 16k more user-available memory. That is why the 85 is 1.2mhz faster han the 86.

     9 May 2000, 01:06 GMT

Re: Feature: A Modest Proposal
Rgb9000  Account Info

I always thought the 81 ran @ 1 Mhz.
But who cares anyway!?

2400 bytes ram, bah.

A true 'dinosaur' in todays modern calc era.

     12 May 2000, 00:12 GMT


Re: Feature: A Modest Proposal
Rgb9000  Account Info

I always thought the 81 ran @ 1 Mhz.
But who cares anyway!?

2400 bytes ram, bah.

A true 'dinosaur' in todays modern calc era.

     12 May 2000, 00:13 GMT

Re: Re: Re: Re: Feature: A Modest Proposal
Daniel Bishop  Account Info

Look at the 83's specs. It's only six MHz.

How often have I needed to do these four things?
1. Once
2. Nearly every day (I'm in AP stats)
3. Several times (same reason as #2)
4. Never

You have a good point, but remember that there actually are people who need to do this.

My point was that faster processors are needed for reasons other than games. I would appreciate comments from calculus and statistics students who agree with me.

     6 May 2000, 21:21 GMT

Re: Re: Re: Re: Feature: A Modest Proposal
Ryan Abbott  Account Info

If you wanted to compute 2000! it would be easier to use the formula n!=sqrt(2pi)*(n)^(n+1/2)*exp(-n) which gives very good approximations for large n.

     7 May 2000, 09:42 GMT


Re: Re: Re: Re: Re: Feature: A Modest Proposal
Paul Schippnick  Account Info
(Web Page)

Your equation (n!=sqrt(2pi)*(n)^(n+1/2)*exp(-n)) is not quite correct and is missing a term.

n! ~ sqrt(2*pi*n)*n^n*exp(-n + 1/(12*n))

And if you don't want an overflow it has to be done in logarithms.

(ln(sqrt(2*pi*n)) + n*ln(n) - n + (1/(12*n)))/ln(10)

And for better accuracy start with the smallest term first on the calculator 1/(12*n)

     10 May 2000, 12:43 GMT


Big n
Ryan Abbott  Account Info

"x==y" let x be y
n! ~ sqrt(2pi*n)*n^n*exp((1-12n^2)/(12n)) == j

ln(j) = (n+1/2)*ln(n)+1/(12n)+ln(2pi)/2-n == k
So clearly e^k = j~n!

To express j as power of 10:
j = 10^(k*ln(e)/ln(10)) = 10^(k/ln(10))

To express j in scientific notation:
k/ln(10) == L
floor(L) == p
10^(L-p) == c
So j = 10^L = c*10^p

Some examples of this method on my TI-92:
2,000! ~ 3.31628*10^5735
2,000,000! ~ 3.77683*10^(1.17335*10^7)
2,000,000,000! ~ 3.72392*10^(1.77335*10^10)
I don't know how accurate the last one is.

P.S. I had some trouble posting. If this shows up more than once, I am sorry.

     13 May 2000, 09:02 GMT

Re: Re: Re: Re: Feature: A Modest Proposal
Ryan Abbott  Account Info

Of course with that formula you just get inf istead of 2000! spit back at you, so it's not much help on TI-89/92+

     7 May 2000, 09:47 GMT


Re: Re: Re: Re: Feature: A Modest Proposal
Ryan Abbott  Account Info

Of course with that formula you just get inf istead of 2000! spit back at you, so it's not much help on TI-89/92+

     7 May 2000, 09:47 GMT

Re: Re: Re: Feature: A Modest Proposal
Akira_of_HLC  Account Info
(Web Page)

O.K..now, tell me why I should ever want to do this?

     6 May 2000, 19:55 GMT


Re: Re: Re: Re: Feature: A Modest Proposal
Daniel Bishop  Account Info

How many calculus and statistics courses have you taken? There is a real need to do these things. (except that you'll probably never need to know that 2000!=3.316275090e5735) Just because YOU never need to graph integrals or use stats functions doesn't mean that NO ONE does.

     6 May 2000, 21:10 GMT

Re: Re: Re: Feature: A Modest Proposal
Reno  Account Info

coding could be a problem with the speed of these calculations as well...

     8 May 2000, 21:16 GMT


Re: Re: Re: Feature: A Modest Proposal
Ryan Abbott  Account Info

Sometimes a little thinking can be a substitute for a faster processor. Unless you want to know 2000! exactly, there are methods (see below) for calculating this with little effort computationally. In fact you can determine 2,000,000,000!(not exatly though)fairly quickly if you know how and you take the necessary precautions to avoid internal operational error.

     13 May 2000, 09:42 GMT

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