In any case, I think this path, of proving the mathematical

underpinnings and/or pedigree and/or resume of the

computer programming languages had to be securely

established as a justification or litmus test for introducing

established as a justification or litmus test for introducing

them in mathematics classroom. I consider that whole

line of thinking somewhat bogus.

Robert was saying (paraphrase): just because algebra

books go: f(x, y) = x + y doesn't mean a computer

books go: f(x, y) = x + y doesn't mean a computer

language's def f(x, y): return x + y is relevant because

the former represents some high minded mathematical

entity while latter is "just a subroutine" and is really

about talking to the guts of a computer and so is not

about talking to the guts of a computer and so is not

appropriately "mathematics" at all.

I pointed out then and point out again that we long ago

accepted that "function keys" on a calculator are close

enough to what's in a math book to allow cos, sin,

tan, exp, log and many more without all these

justifications and caveats or proofs that calculators

had a right to advertise the "mathematical" nature of

I pointed out then and point out again that we long ago

accepted that "function keys" on a calculator are close

enough to what's in a math book to allow cos, sin,

tan, exp, log and many more without all these

justifications and caveats or proofs that calculators

had a right to advertise the "mathematical" nature of

these keys.[1]

As it happens, on a computer we might want to

compute (1 + 1/n) to the nth power to more

compute (1 + 1/n) to the nth power to more

significant digits than a Casio or Sharp or TI

allows, say to 300 decimal places or so, just for

the fun of it. Lets set our computation to 500

significant decimal digits. Is such innocent play

to be discouraged haughtily discouraged by

snooty "math purists" because (1 + 1/n) to the n

is only "math" if done on paper or if done with a

calculator, but is "not math" if done on some

bastard-child-of-mathematics "computer language"?

I think not.[2]

allows, say to 300 decimal places or so, just for

the fun of it. Lets set our computation to 500

significant decimal digits. Is such innocent play

to be discouraged haughtily discouraged by

snooty "math purists" because (1 + 1/n) to the n

is only "math" if done on paper or if done with a

calculator, but is "not math" if done on some

bastard-child-of-mathematics "computer language"?

I think not.[2]

On a computer, we might program a Taylor Expansion

of something, actually do some computations

with it out to 30 or so terms in a looping construct,

whereas on a calculator we would find this tedious

unless, drum roll, it were a *programmable* calculator.

Tiny screen, tiny language, but hey, we're really

computer programming now (a calculator with a

of something, actually do some computations

with it out to 30 or so terms in a looping construct,

whereas on a calculator we would find this tedious

unless, drum roll, it were a *programmable* calculator.

Tiny screen, tiny language, but hey, we're really

computer programming now (a calculator with a

programming language is just a special purpose

computer in my book).

computer in my book).

So why not allow (nay encourage) a bigger screen

and a more capable general purpose language?

Because the latter might not be "mathy" enough?

That just sounds like a completely lame excuse to

my ears and I see no need to justify introducing

a more capable-than-calculators technology on

the basis of BNF or lambda calculus or whatever.

I see no need for such abstruse and esoteric

a rationale, to defend the relevance of computing

technology to the math classroom. Computing

technologies go way back in mathematics, to

at least the abacus (3000 BC). I think it's a bit

at least the abacus (3000 BC). I think it's a bit

late in the game to be erecting artificial walls

against computer languages here in 2014, as

"not mathematical enough".

Which is why I never lent much credence to

these "history of computer science" arguments

as a justification for such a move. Robert turned

out to be supportive if we just finished Algebra first,

before turning to such texts as the Litvins

"Mathematics for the Digital Age" (which includes

dot notation).

these "history of computer science" arguments

as a justification for such a move. Robert turned

out to be supportive if we just finished Algebra first,

before turning to such texts as the Litvins

"Mathematics for the Digital Age" (which includes

dot notation).

So it was never really about "subroutines" not being

"mathematical" enough. That turned out to be a red

herring, and therefore so is much of this thread,

herring, and therefore so is much of this thread,

in terms of the argument it proposes to be

offering.

We don't really need a lot of esoteric "history of

computer science" justifications of this nature,

this late in the game. Common sense will do for

the most part, in this context.

offering.

We don't really need a lot of esoteric "history of

computer science" justifications of this nature,

this late in the game. Common sense will do for

the most part, in this context.