[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

This page is part of the web mail archives of SRFI 77 from before July 7th, 2015. The new archives for SRFI 77 are here. Eventually, the entire history will be moved there, including any new messages.

*To*: Per Bothner <per@xxxxxxxxxxx>*Subject*: Re: meta-comment on typing*From*: bear <bear@xxxxxxxxx>*Date*: Tue, 18 Oct 2005 11:27:03 -0700 (PDT)*Cc*: "Marcin 'Qrczak' Kowalczyk" <qrczak@xxxxxxxxxx>, srfi-77@xxxxxxxxxxxxxxxxx*Delivered-to*: srfi-77@xxxxxxxxxxxxxxxxx*In-reply-to*: <4352B55D.6010901@xxxxxxxxxxx>*References*: <43440EDA.1020900@xxxxxxxxxxx> <20051005220034.GH6680@NYCMJCOWA2> <43445027.1010408@xxxxxxxxxxx> <20051006045500.GA2668@NYCMJCOWA2> <4344B83B.50705@xxxxxxxxxxx> <878xx75dt4.fsf@xxxxxxxxxxxxx> <4344D02F.5030704@xxxxxxxxxxx> <Pine.LNX.4.58.0510161238590.13563@xxxxxxxxxxxxxx> <4352B55D.6010901@xxxxxxxxxxx>

On Sun, 16 Oct 2005, Per Bothner wrote: >Your argument hinges on the term "addition", which you don't define, >so it's meaningless. Well, I thought most of us learned what addition was in kindergarten, got negative numbers somewhere in second or third grade, and then got complex numbers somewhere in junior high. Seriously, I mean plain, ordinary, linear addition, the same as anyone who uses the term unqualified outside of computer science. Addition, as per the generally accepted definition, is not a modular operation. It is transitive, commutative, and reversible. Modular addition is transitive and commutative, but it is not reversible; every modular addition loses information. > What it really boils down to: > * Is it wise/useful/desirable to overload operations so > that different (but in-some-way-related) operations are named > by the same operation name? I believe that it is not. > * Is it wise/useful/desirable overload the operation names for > standard arithmetic to objects that don't obey all the rules > of complex number arithmetic? I believe that it is not. > * A slightly different question: what is a number? Is a quantity > with a dimension a number? Is a 32-bit unsigned machine integer > a number? Is a complex a number? Both of the first two cases are examples of numbers plus additional information. A number with a dimension (such as "42 sunburned pigs") is a number plus additional information. A 32-bit machine word is a bit field which may be interpreted as a particular way of representing a member of a particular subset of numbers, but it is not itself a number. In this case the additional information is the width including leading zero bits, which is implied by the size of the representable subset, not by the number represented. A complex number is more debatable; I think I am willing to call it a number, but doing so often weirds math in the same way that verbing nouns weirds language. > I have no problem with you saying that you don't think my idea > is a good idea. (I'm not sure it is myself - probably not for R6RS.) > But I don't think you have basis for calling t "dead wrong". Well, I think that any operation that can take two positive arguments and produce a negative result is not addition. It fails to follow at least one of the basic properties of addition, reversibility. For example, if I know that I added something to 27 and got -32, reversibility means I should be able to uniquely determine what was added to 27; under the rules of linear addition, it would have to be -59, not any positive number. But with modular addition, it could be either of two numbers, -59 and ($MODULUS - 59), so modular addition isn't reversible like linear additon. There are several other properties of linear addition that fail for modular addition, too, but I won't go into them just now, because any one of them is actually enough for me to consider something to be a different operation. I think that calling a nonreversible operation "addition" without further qualifiers, is, in fact, dead wrong. Sorry, but I truly believe that's just a statement of the mathematical facts. And yes, there are similar objections to overloading multiplication, etc, with modular analogues. Bear

**Follow-Ups**:**Re: meta-comment on typing***From:*Alan Watson

**References**:**meta-comment on typing***From:*Per Bothner

**Re: meta-comment on typing***From:*John.Cowan

**Re: meta-comment on typing***From:*Per Bothner

**Re: meta-comment on typing***From:*John.Cowan

**Re: meta-comment on typing***From:*Per Bothner

**Re: meta-comment on typing***From:*Marcin 'Qrczak' Kowalczyk

**Re: meta-comment on typing***From:*Per Bothner

**Re: meta-comment on typing***From:*bear

**Re: meta-comment on typing***From:*Per Bothner

- Prev by Date:
**Re: Arithmetic issues - feedback** - Next by Date:
**Re: Arithmetic issues** - Previous by thread:
**Re: meta-comment on typing** - Next by thread:
**Re: meta-comment on typing** - Index(es):