When AOE 3rd ED to be published?

[John Woodgate]

I read in sci.electronics.design that Tim Shoppa <shoppa@trailing-

Undoubtedly some people lump this into "new math" but I'm 99% sure that
my father (who learned arithmetic in a one-room schoolhouse in the
1930's) taught this method to me when I was in grade school.

Yes, many of these arithmetical methods are very old. In fact, does
anybody know of a 'new' one? Say, no earlier than 20th century.

 

[Keith R. Williams]

One neat trick is 9's complement to do subtractions. Do a
google search on "nine's complement". It's related to "casting out
9's".

....or 10's compliment.

You may laugh, but I've had to teach this to grad students in
introductory computer architecture/arithmetic classes.

Some time ago (~15 years) I taught an undergraduate (senior level)
microprocessor course. Most students had no clue what two's compliment
arithmetic was, and simply were blown away by the fact that a number
could be positive or negative, depending on the interpretation. After
a lecture of getting nowhere, I showed them 9's compliment and 10's
compliment arithmetic and then extrapolated that to 1's and 2's
compliment. They were skeptical of this "magic".

Undoubtedly some people lump this into "new math" but I'm 99% sure
that my father (who learned arithmetic in a one-room schoolhouse
in the 1930's) taught this method to me when I was in grade school.

I was in a "new math" curriculum in the fifth and sixth grades (early
60's). I can remember my father (a power engineer and EE Prof.) not
really understanding the "math", but knowing that it was important. We
were doing arithmetic in arbitrary bases (up to 32, IIRC) and
conversions between bases. It's a great way to get a good
understanding of number theory. Binary never scared me after having
done long division in base 29. ;-)

 

[Spehro Pefhany]

Terry Pinnell wrote...

Sheesh! We spent an entire summer on the it, and surely it's
far better than most other book indexes. It takes up 25 pages
of three-column fine print and has over 10,000 references with
about 4000 word entries. It even includes lots of words we
didn't write but thought someone else might use when seeking
the alternate word we did write.

I worry that we won't be able to do as well next time around.

But I have seen lots of complaints here. What can I say, does
this just illustrate the futility of creating a perfect index?

Well, you know what Kurt Vonnegut had to say about it, in _Cat's
Cradle_.

Best regards,
Spehro Pefhany

 

[Tom Del Rosso]

In John Woodgate typed:

I read in sci.electronics.design that Tom Del Rosso


Can you please tell us what it was?

Actually it didn't explain the method. It only said something like
"Subtract these numbers using disentopfritzenation", or something like
that.

 

[Terry Pinnell]

How about this for logic:

12 squared = 144
Therefore, reversing digits,
21 squared = 441

 

[Spehro Pefhany]

How about this for logic:

12 squared = 144
Therefore, reversing digits,
21 squared = 441

On an 8-digit calculator, 99999999 / 8.1 =
12345678

Best regards,
Spehro Pefhany

 

[Tom Del Rosso]

In John Woodgate typed:

Yes, many of these arithmetical methods are very old. In fact, does
anybody know of a 'new' one? Say, no earlier than 20th century.

The Laws of Form? I never got that method down. It's hard to
understand what the notation means conceptually. It was originally
logical arithmetic, but it is possible to use it for math.

Here is the 2+2=4 example from part 3 of an EE Times article series,
March 7, 1994:

11 2
<1> alternate notation for 2
<1><1> 2+2
<11> opposing brackets cancel
<<1>> substitute <1> for 11

The last line is supposed to represent 4.

It was hoped that parallel processors could operate on different parts
of a problem encoded in a large string.

The series ran on 2/14/94, 2/21/94, 3/7/94, 3/14/94.

 

[Paul Burridge]

I worry that we won't be able to do as well next time around.

But I have seen lots of complaints here. What can I say, does
this just illustrate the futility of creating a perfect index?

It should be a piece of cake nowadays. One assumes the new MS is on
digital storage media? Just do word searches for topics to be indexed
and note the page numbers. There are a bunch of freeware programs out
there on the Net that will take the slog out of it and practically
compile the index for you.

 

[Spehro Pefhany]

It should be a piece of cake nowadays. One assumes the new MS is on
digital storage media? Just do word searches for topics to be indexed
and note the page numbers. There are a bunch of freeware programs out
there on the Net that will take the slog out of it and practically
compile the index for you.

Oh, No NO NO *NO*. I'll allow that producing a crappy and virtually
useless index that sort-of looks like a real index is easier than
ever. That's why it's a good idea to actually try to use an index a
few times before buying a book, and set it aside gently (or throw it
with great force, as you prefer) if it fails the test.

Good indexers are amazing human beings, with intellectual wiring quite
different from a good writer's. Their craft has an entire philosophy
behind it, in many ways very close to math. I occasionally see posts
from their mailing list (forwarded from our staff indexer) and I'm
impressed with the complexity of their tasks and the level of thought
they bring to their jobs. (Indexers also bring a reader-centered view
to the use of the index, where a writer's indexing often follows the
organization of the book.)
-- Frank Willison, editor-in-chief, O'Reilly & Associates

Best regards,
Spehro Pefhany

 

[Richard Henry]

I was in a "new math" curriculum in the fifth and sixth grades (early
60's). I can remember my father (a power engineer and EE Prof.) not
really understanding the "math", but knowing that it was important. We
were doing arithmetic in arbitrary bases (up to 32, IIRC) and
conversions between bases. It's a great way to get a good
understanding of number theory. Binary never scared me after having
done long division in base 29. ;-)

The answer is 42.

The question is "What is 6 times 9?"

What base?

 

[Tom Del Rosso]

In Richard Henry typed:

The answer is 42.

The question is "What is 6 times 9?"

What base?

13

 

[Tom Del Rosso]

Oh, No NO NO *NO*. I'll allow that producing a crappy and virtually
useless index that sort-of looks like a real index is easier than
ever. That's why it's a good idea to actually try to use an index a
few times before buying a book, and set it aside gently (or throw it
with great force, as you prefer) if it fails the test.

In The C Programming Language, the index gives its own page number for
one word, but no others. (A program would not have thought of doing
that.)

 

[Bob Stephens]

Oh, No NO NO *NO*. I'll allow that producing a crappy and virtually
useless index that sort-of looks like a real index is easier than
ever. That's why it's a good idea to actually try to use an index a
few times before buying a book, and set it aside gently (or throw it
with great force, as you prefer) if it fails the test.

Good indexers are amazing human beings, with intellectual wiring quite
different from a good writer's. Their craft has an entire philosophy
behind it, in many ways very close to math. I occasionally see posts
from their mailing list (forwarded from our staff indexer) and I'm
impressed with the complexity of their tasks and the level of thought
they bring to their jobs. (Indexers also bring a reader-centered view
to the use of the index, where a writer's indexing often follows the
organization of the book.)
-- Frank Willison, editor-in-chief, O'Reilly & Associates

Best regards,
Spehro Pefhany

How do you feel about the "permutated index" so popular in the UNIX world?

 

[Spehro Pefhany]

How do you feel about the "permutated index" so popular in the UNIX world?

I think it's much better than nothing. Things are quite different in
the electronic realm, when you can brute-force search through 1,000
pages in a fraction of a second. You know a paper book's index has
failed when you are forced to go to the TOC, switch your thinking
around to the author's way of looking at things (with an almost
audible clank), and try to guess where s/he might have hidden that
darned information you need.

Best regards,
Spehro Pefhany

 

[Keith R. Williams]

The answer is 42.

The question is "What is 6 times 9?"

What base?

13

....but I thought the answer was 42. ;-)

 

[Costas Vlachos]

How about this for logic:

12 squared = 144
Therefore, reversing digits,
21 squared = 441

Nice one! Easy to find a counterexample though... In mathematics there are
cases where a counterexample can be very difficult to find, and this can
lead to false assumptions.

For example, if you try to find a positive integer solution to this
equation:

x^2 - 991*y^2 = 1

you may find it really hard to find any, and may think/assume that no
solution exists. But you'll be wrong... There are infinitely many... The
smallest one is the pair

x = 379,516,400,906,811,930,638,014,896,080
y = 12,055,735,790,331,359,447,442,538,767

Intuition can be a good thing as long as it is backed by rigorous proof. The
word "obvious" is a very dangerous one, especially in mathematics.

Costas

 

[John Woodgate]

I read in sci.electronics.design that Keith R. Williams

We
were doing arithmetic in arbitrary bases (up to 32, IIRC) and
conversions between bases. It's a great way to get a good understanding
of number theory.

It helps at the greengrocer's too, since you still use avoirdupois.

Binary never scared me after having done long division
in base 29. ;-)

That really does sound like masochism. The only system that uses base
29, AFAIK, is Harry Potter-type wizard currency.(;-)

 

[John Woodgate]

I read in sci.electronics.design that Richard Henry <[email protected]>

The answer is 42.

The question is "What is 6 times 9?"

What base?

4x + 2 = 54. Need I go on? ((c) L.C. Pascoe, who could teach even me a
bit of maths.)

For extra credit, I know you've been reading CLD instead of something
trivial.

 

[John Woodgate]

I read in sci.electronics.design that Tom Del Rosso

In John Woodgate typed:

Actually it didn't explain the method. It only said something like
"Subtract these numbers using disentopfritzenation", or something like
that.

We have recently had a TV mini-series where a group of year 11 students
were sent to a re-created 1950-style boarding school. They didn't like
it a bit! An initial maths test was failed dismally by all but one
(maybe two), and this test was for year 6 students in 1950.

However, I suspect that a group of year 11 students in 1950 might well
have been similarly disenchanted with the accommodation, discipline and
academic standards of a school of 1900. Especially the viva voce
translation from Latin and Greek.

 

[John Woodgate]

I read in sci.electronics.design that Spehro Pefhany <Spehro@Pefhany.?>

On an 8-digit calculator, 99999999 / 8.1 = 12345678

That could start a LONG thread! The arithmetical properties of 111...
(ad nauseam) and 123456789 can lead you into all sorts of interesting
by-ways.