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I am now offering my essay "Understanding Imaginaries Through Hidden Numbers" for free on Scribd for a while. Many will recall that mathematics was a topic that interested Ayn Rand throughout her life. In fact, in her last years she was studying the subject. She believed that there was an intimate connection between mathematics and concept formation. In particular, she was interested by the fact that "mathematics has something to do with the essential pattern of concept formation-- ... it serves as an ideal" (page 202 of ITOE). Also, she noted that "Man's mathematical and conceptual abilities develop simultaneously." My essay sheds a bit of light on these ideas, in that it explains the connection and the reason for the timing. In addition: A definition for the concept "number" is offered on the above basis. A new way of looking at mathematical operations and complex numbers is explained. This new way of looking at complex numbers is shown to directly lead to hypercomplex numbers (numbers that are in more than two dimensions). In fact, I had not known that such numbers existed until I discovered them on my own in the process of thinking about these questions. Above all, my viewpoint ties numbers to reality in accordance with Ayn Rand's epistemology and carries her ideas further. The differences of my viewpoint from those of previous Objectivist writers on the subject in THE INTELLECTUAL ACTIVIST are laid out. The URL for the essay is: http://www.scribd.co...-Hidden-Numbers

Computer-created music for a song, with lyric: You’re Always in My Thoughts Hope some like the tune, at least.

FREE FOR A LIMITED TIME! Download now! Playable by high school or college band. Level 3. Includes 46-page score and all parts (.pdf). Available here: http://www.lulu.com/content/499103 Based on series of original tunes ending with majestic theme carried by unison trombones. Premiered at Upper Canada College, Toronto, and well received! This free offer is being made as a final check that the newly computer-created score is error-free, and it would be appreciated if those who avail themselves of this score would kindly inform the author if any glitches are found. Anthem (for Concert Band)

I am offering an essay that brings Objectivist epistemology to bear on mathematics in a novel way, leading to new conclusions. Its title is "Understanding Imaginaries Through Hidden Numbers." It is available here: http://www.lulu.com/content/750696 The article’s title refers, among other things, to the imaginary unit i used in complex numbers, but all the more basic ideas of math are covered as well. Most importantly for Objectivists: • How do we arrive at concepts of numbers? • Why do we learn mathematical ideas at roughly the same time as the rest of our early concepts? • How would one define "number"? • What is the meaning in physical reality of the so-called imaginary/complex numbers? The 38-page essay is dense with ideas, many of them different from those of other Objectivist thinkers on the topic. I present my reasoning step by step in a manner that encourages introspection, and lay out the fundamental aspects of human life that give rise to mathematical concepts. I believe readers will find the presentation persuasive, and perhaps begin to see mathematics in a new way. There is another factor that might commend my ideas to those who accept Ayn Rand’s epistemology: in the course of pondering the deepest meaning of numbers, to my great surprise I discovered a new and immensely useful kind of number that I had never known existed--multidimensional numbers analogous to the (two-dimensional) complex numbers, with no restriction on the number of dimensions. The essay presents the main intellectual steps by which this result was achieved. For a while after this discovery, I thought I might have arrived at an entirely new mathematical idea; but protracted Internet research on my part gradually established that the numbers I had invented were already known to higher mathematicians as a certain class of what are called hypercomplex numbers. However, I also found out that some mathematicians consider this particular form of the numbers that I had reinvented to be especially important--a conclusion that I saw would follow from the reasoning that had brought me to that point. Which, of course, should be highly interesting to Objectivists, since it goes to prove Ayn Rand’s hotly disputed contention that philosophy can indeed serve as a guide to science. Understanding Imaginaries Through Hidden Numbers

If you mean rationalistically deducing from a priori axioms, no science works that way, including philosophy. What you do is observe reality first, then integrate your knowledge into concepts and continually update your concepts and definitions as you discover new connections and causes. (Perhaps you know this, and it was merely an unfortunate wording on your part. If so, sorry!)

What a coincidence! Yesterday I posted these messages on Objectivist newsgroups:

My knowledge of music suggests that, happily, this is false.

Well, I must say, that's a wonderful speech, and I am almost fully convinced. I need one more question answered: How does the story end? Are Gecko's ideas and actions shown to lead to good results, without any drawbacks? In other words, what's the movie's bottom line on this issue? What point of view gets the last, all-pervasive word?

Well, now I am swayed so I may see it when I get a chance. Thanks!

Ah, that's better, and that would sway me a bit. Perhaps Stone, or one of the script writers, was ambivalent.

By the way, outside its use poetically (as Rand sometimes used it in the context of sexual hunger), the word "greed" is always pejorative.

But if he's presented as evil generally, a "lizard"--and by Oliver Stone, no less--and the word "greed" is used without any elaboration, I have to question whether the takeover is being presented as good. If you can convince me otherwise, I'll try to see the movie. But I need a lot more convincing than this!

Scattered comments: I haven't seen the movie, but Gekko's slogan "Greed is good" is clearly meant to be self-evidently evil. Anyone who had an unalloyed positive reaction to it strikes me as a bit clueless! A gecko is a lizard. "Roark" has no "e" in it.

I think the theory in this link becomes more and more silly as it goes up. A dimension is merely some necessary, measurable aspect of a thing that can vary independently of the other aspects. (See the article referenced in my signature for more on this!) Mathematics will only tell you the logical results of certain fundamental numerical processes. There is no substitute for actually finding out the nature of the aspects in question and the relations, if any, between them. Time, for example, is not merely an aspect of existence of the same order or type as length etc. There is not necessarily analogous "traffic" between all "dimensions."

Thanks. I'll keep it in mind. However, I was never much concerned with sound quality--just good melodies and good songs as such!

You might try the download option. Can't see how it would make any difference, but computers are funny ...

Sorry, the link was wrong. I've fixed it.

Some people like my tunes, so here's a page with five of them: http://www.acidplanet.com/artist.asp?songs=587414&T=6059

Exact replicas of complex number system in n dimensions using basic algebra Not knowing hypercomplex numbers, and using only basic algebra, I found a method of creating n-dimensional spaces exactly analogous to the complex numbers’ 2D space. These number systems exhibit the feature of multiple imaginary units, multiplication by which causes a visit to each of the axes in turn, once on the plus side and once on the minus. This is exactly analogous to the behavior of i in the complex number system. The method is described here: http://rebirthofreason.com/Forum/GeneralForum/0935.shtml R. Rawlings

No, I'm saying there is no nit--and your thinking so makes you wrong. She is not saying "The word existence means the same thing as the word identity"--nor is she implying it. She is saying that the meaning of existence is always and only the existence of some specific thing with specific properties.

I don't have much time for online discussion, but I'll jump in to say this. Of course the two words don't mean the same thing, but AR's point is that if something is, it has a specific nature. She is looking beyond the language and into the facts. This is a basic error that critics of Rand's thought continually make. They are language-plus-logic-focused, whereas Rand is concepts-based-on-observation-plus-logic-focused. She wants to make new identifications, not tease out old connections. In a sense, she strives to rewire the human brain--if you can grasp what I am referring to. Until you understand what is meant by "Existence is identity," and the thinking method behind that statement, I think you are not ready to have any other questions answered. It would only lead to a blizzard of further questions based on language plus logic only. Keep thinking! I mean this in a friendly way.

Here's a person who would be perfect for Ragnar (he's a musician, but he also acts) (and his hero has always been Superman):