North Texas Objectivist Society (NTOS) Message Board › Non-Mathematician Claims to Discover Hypercomplex Numbers, with Possible Imp

Non-Mathematician Claims to Discover Hypercomplex Numbers, with Possible Implications for Mathematics and the Philosophy of Science

Old Toad
OldToad
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Dallas, TX
Post #: 629
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For the mathematically inclined among us:

A Toronto, Ontario, writer and editor has arrived at a system of creating hypercomplex numbers -- numbers that extend the complex number system to more dimensions --using only high school algebra, as viewed through the lens of Ayn Rand's philosophy of Objectivism. He contends that this has implications for mathematics and the philosophy of science.

Rodney Rawlings calls his multidimensional numbers "RADN numbers" -- for "rotating any-dimensional numbers," ...

He says that he arrived at this result by asking himself what exactly numbers are, how they arise in the human mind, and what their relationship to reality is. But these questions were only so fruitful because he used a correct philosophy, he claims -- Ayn Rand's. ...

For the entire article, see: http://www.prleap.com...­

See Rawling's article at: http://www3.sympatico...­


Is there anything to it?
Old Toad
OldToad
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Dallas, TX
Post #: 630
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It was pointed out to me that Rawlings had previously posted about this subject on ObjectivismOnline.Net.

In looking up Rawlings on ObjectivismOnline.Net, including his posts and the replies and at some of the links in these posts, the only substantive criticism of Rawlings work was by "Eric" on August 13, 2006 at: http://forum.objectiv...­

Eric seems knowledgeable in this subject and says that Rawlings' work "doesn't really give an 'exact replica' of the complex number system in higher dimensions."

After Eric's criticism, on August 14, 2006, Rawlings posted an "Important Correction to Equations" on the "Rebirth of Reason" forum at:
http://rebirthofreaso...­

Rawlings continues to promote his work. Does Rawlings' correction (and subsequent corrections) answer Eric's criticism?
Old Toad
OldToad
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Dallas, TX
Post #: 631
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In looking at Eric's criticism of Rawlings' work a bit more, Eric had briefly explained to him that: "The problem is division: many of your "numbers" do not have multiplicative inverses." http://forum.objectiv...­

I now see this in Rawlings' current description of his work: "The 'RADN numbers' (known by science under another name) have a property of rotation like complex numbers, and are also commutative/distributive. (Division is deemed less crucial.)" See http://www.lulu.com/c...­

This indicates that Rawlings recognized the validity of Eric's criticism and dropped the original claim on Rawlings' thread that he had "found a method of creating n-dimensional spaces exactly analogous to the complex numbers? 2D space."

In this regard, how "crucial" is the property of "division"?

In another regard, the part of Rawlings' statement that: "The 'RADN numbers' (known by science under another name) ..." is also a bit puzzling to me. If previously known to science, what does Rawlings claim to have discovered?
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