Re: [math-fun] Symbolic Calculation
In the early 70s there was an effort at HP to put a subset of Macsyma on a handheld device. This was crushed by their consultant W. Kahan, then a vocal and effective opponent of computer algebra. In a talk at Symsac 72 at IBM Yorktown, he claimed the only economically legitimate use for computers was beancounting, and likened Macsyma's symbolic integrator to "The Fisher Space Pen--the pen that writes underwater!" Joel Moses, then director of Macsyma, was completely cowed. TI bought Derive from Albert Rich to try to leverage sales of their handheld calculators with a scheme where Derive on an instructor's PC would download over a cable to a student's handheld. When this flopped, they pulled the plug on Derive development, which they were never really interested in. This is a shame--Derive had fans worldwide, and was improving rapidly. You can't have too much computer algebra. --rwg apg>Yes, but MuMath *actually* performs symbolic calculation (or that's the impression I got, anyway), whereas the Casio must perform an inverse lookup to convert from a decimal approximation to a symbolic expression. Sincerely, Adam P. Goucher
Your Casio is not the first "symbolic hand calculator"; MuMath was really the first:
http://en.wikipedia.org/wiki/MuMATH
At 09:46 AM 5/6/2011, Adam P. Goucher wrote:
Today I received a Casio fx-85GT calculator as a present from a couple of my friends. It gives expressions in exact forms as an alternative to the ordinary decimal output. For example, enter:
sqrt(8)
and it will output:
2*sqrt(2)
Of course, I believed that the calculator was performing symbolic manipulation -- very impressive for a handheld scientific calculator!
However, I then decided to test it:
ln(640320^3+744)/sqrt(163)
Instead of displaying the correct answer, 3.14159265..., a prominent image of the Greek letter pi was rendered!
Hmm...
I'm waiting for a version that prints "stop trying to test my symbolic calculation facilities with well-known near-miss identities!"
On this topic, there is this comic:
Sincerely,
Adam P. Goucher
I didn't realize (but might have guessed) that Kahan would do such a thing. The problem with TI's calculator division (unlike HP's calculator division, where they actually thought "outside the box" -- for a brief while in the late 1970s' you could purchase an 8" hard disk drive (5MBytes, I think) to hook up to your handheld HP calculator!!), TI was actually worried about the public school curricula. If the "math" wasn't covered in the approved math books, it simply didn't exist & would only distract the students. It's utterly amazing that junior high & high school students _still_ don't have access to Maxima (or equivalent) today. If long division & long square root extraction isn't worth student's time, then neither are most polynomial manipulations. The real problem is that if the current crop of H.S. "math" teachers didn't teach polynomial manipulations, they wouldn't have anything to teach at all & it scares the h*ll out of them. At 05:40 PM 5/6/2011, Bill Gosper wrote:
In the early 70s there was an effort at HP to put a subset of Macsyma on a handheld device. This was crushed by their consultant W. Kahan, then a vocal and effective opponent of computer algebra. In a talk at Symsac 72 at IBM Yorktown, he claimed the only economically legitimate use for computers was beancounting, and likened Macsyma's symbolic integrator to "The Fisher Space Pen--the pen that writes underwater!" Joel Moses, then director of Macsyma, was completely cowed.
TI bought Derive from Albert Rich to try to leverage sales of their handheld calculators with a scheme where Derive on an instructor's PC would download over a cable to a student's handheld. When this flopped, they pulled the plug on Derive development, which they were never really interested in. This is a shame--Derive had fans worldwide, and was improving rapidly. You can't have too much computer algebra. --rwg
apg>Yes, but MuMath *actually* performs symbolic calculation (or that's the impression I got, anyway), whereas the Casio must perform an inverse lookup to convert from a decimal approximation to a symbolic expression.
Sincerely,
Adam P. Goucher
Your Casio is not the first "symbolic hand calculator"; MuMath was really the first:
http://en.wikipedia.org/wiki/MuMATH
At 09:46 AM 5/6/2011, Adam P. Goucher wrote:
Today I received a Casio fx-85GT calculator as a present from a couple of my friends. It gives expressions in exact forms as an alternative to the ordinary decimal output. For example, enter:
sqrt(8)
and it will output:
2*sqrt(2)
Of course, I believed that the calculator was performing symbolic manipulation -- very impressive for a handheld scientific calculator!
However, I then decided to test it:
ln(640320^3+744)/sqrt(163)
Instead of displaying the correct answer, 3.14159265..., a prominent image of the Greek letter pi was rendered!
Hmm...
I'm waiting for a version that prints "stop trying to test my symbolic calculation facilities with well-known near-miss identities!"
On this topic, there is this comic:
Sincerely,
Adam P. Goucher
participants (2)
-
Bill Gosper -
Henry Baker