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Topic: [HM] Dedekind's objection to the Newtonian concept of number.
Replies: 23   Last Post: Aug 2, 2006 12:39 AM

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Romulo Lins

Posts: 32
Registered: 12/3/04
Re: [HM] Geometric Representation of Complex Numbers
Posted: Aug 2, 2006 12:39 AM
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Dear all,

just to add to that conversation.

The title of Wessel's paper directly refers to the 'analytical
representation of direction'. That is, he, as a surveyor, was not
interested in some 'foundational' issue, but rather with how to make
complex numbers work for his profession.

Even a superficial examination of his text clearly indicates that he
develops a discorse 'about lines' through which he can represent *the
lines and the calculus he developed for them* using complex numbers, not
the other way round.

By the time he read his memoir (1797), hardly any mathematician (with the
exception of the exceptional ones) was interested in 'foundations'. Why
would a surveyor be?

For many years I have been puzzled by the recurring insistence on saying
that Wessel was the first one to present a work on the geometrical
foundations/representation of complex numbers. He even mentions series!

The truest pearl I found in his memoir is in (his) 'paragraph' 3, where he
states (for no further use!) something quite close to the 'linear
independence' of length, width and depth (sorry if the words are not
accordingly to the English translation; I hope the sense is still
available).

all the best,
Romulo


> There was no connection between Wessel and Argand that anyone knows about.



Date Subject Author
5/26/05
Read [HM] Dedekind's objection to the Newtonian concept of number.
Robert (Bob) Eldon Taylor
5/3/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Robert (Bob) Eldon Taylor
5/8/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Heinz Lueneburg
5/16/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Robert (Bob) Eldon Taylor
5/17/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Heinz Lueneburg
5/19/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Robert (Bob) Eldon Taylor
5/23/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Heinz Lueneburg
5/27/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Robert (Bob) Eldon Taylor
5/28/06
Read [HM] Periodicity
Samuel S. Kutler
5/29/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Samuel S. Kutler
6/26/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Robert (Bob) Eldon Taylor
5/29/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Heinz Lueneburg
6/21/06
Read [HM] An Arbitrary Quadrilateral
Samuel S. Kutler
6/22/06
Read Re: [HM] An Arbitrary Quadrilateral
Joseph Malkevitch
6/22/06
Read Re: [HM] An Arbitrary Quadrilateral
Emmanuel Cardona
6/25/06
Read [HM] Geometric Representation of Complex Numbers
Samuel S. Kutler
6/26/06
Read Re: [HM] Geometric Representation of Complex Numbers
Luis Puig
6/26/06
Read Re: [HM] Geometric Representation of Complex Numbers
Ken.Pledger@vuw.ac.nz
6/27/06
Read Re: [HM] Geometric Representation of Complex Numbers
Sanford L. Segal
8/2/06
Read Re: [HM] Geometric Representation of Complex Numbers
Romulo Lins
6/26/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Robert (Bob) Eldon Taylor
7/19/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Heinz Lueneburg
7/22/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Robert (Bob) Eldon Taylor
7/11/06
Read Re: [HM] Dedekind's objection to the Newtonian concept of number.
Robert (Bob) Eldon Taylor

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