The joys of upgrades...the blogger site keeps unpublishing my blog! A small price to pay for all the nifty new features. Actually, I don't appear to be paying any price at all for the privilege of using the service.

I've been trying to force myself to finally start on the core of the descriptive mathematics site, but I am lost in a crisis of faith.

My version of math history is that the transcendental idealists set forth on the rather silly quest of trying to create a completely perfect mathematics, logic, language and philosophy. This quest for absolute perfection of logic and language has diverted our attention from the real wealth of mathematics...that is math gives us the ability to communicate about extremely complex topics like physics, the economy, etc..

The true wealth of mathematics is that it allows for a large number of diverse logical models. There is often similarities between subjects. Pursuing and discussing such similarities provides a great deal of insight, but we do not really need to unify all math and logic under a single banner.

The core of the descmath is to be a presentation on the Calculus. The problem is that the very aims of the model are diametrically opposed to just about all of the articles of faith professed by the transcendal idealists that control the subject.

To me, mathematics is like literature. It does not matter that the Lord of the Rings is not consistent with Star Wars. Different models provide different insights.

Anyway, I need to force myself to just finish the project. I really shouldn't care if the project is of absolutely no use to anyone accept as a fun little claim of intellectual independence.

Anyway, I need to publish this entry so my blog works again.

I popped up a review for The Golden Ratio by Mario Livio. Considering that Livio spent a great deal of effort in his work debunking the mysticism associated with the study of the golden ratio, the introduction of Platonic mysticism in the last chapter really stood out. Of course, Platonic mysticism tends to jump out of science in the same fashion. At its most severe, Platonism elevates mathematics itself to a religion. For that matter, one can find a great deal of Platonic notions in Christianity the many religions that preceded Plato.

In the last chapter, Livio introduces Benford's Law as an example of a secret hidden, unintuitive law that is behind mathematics. Benford's Law really is the observation that in a random selection of integers, more numbers begin with the digit "1" than with the digit "9." Personally, I don't see why this is counterintuitive...it seems to me that it is a direct result of way natural numbers work. Any way, I tossed up a a quick article on Benford's Law.

Many believe that U.S. society, which has always placed a premium on breakthroughs by individual achievement, must redefine its notion of success to include incremental advancements, often produced by committee in relative anonymity.

Reforms, not rhetoric, needed to keep jobs on U.S. soil; By Ed Frauenheim and Mike Yamamoto

I think this article has it wrong. The breakthroughs in science, computer science, etc.. are still made by individuals. We just never learn about the individuals. We have simply separated reward from effort. Rewards go to "innovators" not "inventers." The rewards and acclaim for a new discovery will go to the CEO or Venture Capital firm. The only rewards for wage employees is an insincere memo about how the company considers its employees its most important asset.

Perhaps our problem is that we have spent so much effort defending capitalism against communism that we have inadvertantly lost the value that the United States used to place on all people...not just the owners of capital. The current structure does not lend itself to allowing anyone beyond the board room the ability to really achieve their potential.

Hooray!!!! I got my very first PayPal payment. All of my pathetic attempts to music online, selling philosophical ponderings, and all the other weird auctions and ecommerce attempts never actually resulted in sales.

My first PayPal Payment came from an affiliate program for AirlineCareers.com which offers a school for airline attendants. I ran their ad for a year and got $27.00. Paypal took a $1.11 to complete the transaction. I guess they have transformed from the bait mode to switch mode.


Unfortunately, my attempts at promoting worthy causes has been as flat as my crass commercial interludes. The Gandhi Alliance for Peace and UNAU are having a Canines Against Landmines event on Saturday at Jordan Park in Salt Lake. The clicker on this site shows the site getting 8 hits a day for the week. The logs show all but two of the hits in the last three days were either from Googlebot or myself.

The Ghandi Alliance for Peace will be having a Canine Against Landmines event on Saturday May 8th, 2004 in Jordan Park (Salt Lake City). My vain hope is to use the web to encourage people in the area to attend. Unfortunately, it is next to impossible to target such an audience with the web.

In the web publishing arena, I just uploaded Which Dialectics is Which. My mother put this article together in the 70s. The purpose of the article was to show how the term "dialectics" has been used at different times. I mentioned the time of writing as she spends more time on Moa Tse Tung than current thinkers might. We did not include the references to make it difficult for people to turn in this work as a homework assignment.

The repeating nines situation is a great example of where two things might have the same value, but still be different. This type of stuff happens all the time in real life.

For example: I might own a business and render you a service. The service costs a thousand dollars. I prefer cash on the barrel head, but you hand me a credit card. I take the credit card, run the charge and consider that good. Paying me with cash or credit has the same effect. It balances the account between us.

A month later, I get some pathetic late night call from you. Being a nice guy, I rush down to the courthouse and bail out that deadbeat brother of yours. I write a thousand dollar check. You come to my place of business an hour later and hand me your credit card to pay your bill.

This time, however, I am livid. A credit card balanced the account in the past. This time I am yelling at you. What is wrong with me? Didn't I say cash and credit were equivalent? $1000 = $1000.

Our could it be that there is a difference between the two figures? The two numbers might have the same value but still be different. As you probably know, merchants have to pay a service fee to run credit card charges. Business people eat the fee as a cost of doing business, but in a straight cash transfer, there is no margin. Equal values aren't always the same.

I believe that the mystery of calculus is better understood in the old Aristotelian sense of potential infinity. The summation of summation of 9/10 + 9/100 + 9/1000 ... is something different than one...although they have the same value. For that matter, it is probably this having the same value while being different that makes calculus work.

There, that project is done. Well mostly done. I finally finished the first draft of A Tale of Two Paradoxes. I suppose that I will have to someday look at it again and correct all the spelling and grammar mistakes. I wish I could afford an editor. I find I can do a passable editing job if I leave and article alone for a few months, then revisit it.

Anyway, this is the latest effort to address the paradoxes of transfinite theory. It has a few modest improvements over the previous efforts. It strongly emphasize that the diagonal method is simply a form of the liar's paradox. The two paradoxes are Galileo's paradox and the liar's paradox. Transfinite theory uses Galileo's paradox to assert that the set of rationals is the same "size" as the integers, then uses the liar's paradox to say that the real numbers are a different size. This is the denumerable/nondenumerable dichotomy. Mathematics is supposed to somehow arise from the opposition of these two terms.

The purpose of this set of articles is to address the use of paradoxes as the foundations of mathematics. It is not about the conclusions of theory, but about the foundations. So I added a few words on the difference between discrete and continuous mathematics. Discrete mathematics works only with terms of finite length. Continuous math uses terms of infinite length. The differences between these branches arise from definitions, not paradoxes.

We can create only a finite number of unique strings from a finite number of characters. Expressing a totality, like the set of real numbers, requires an infinite number things: Discrete mathematics is content to work with finite entities. Continuous mathematics must allow for the use of infinite terms. The difference between the subjects does not arise from a fundamental dichotomy created by paradoxes.

The article does not deny the existence of paradoxes. It simply says that they sould be treated as a side dish. For example, we should not use Galileo's paradox as the definition of the infinite!!!!! Anyway, I hate this work on transfinite theory. I will not let the site fester for a few months and work on things I enjoy.

I can't believe twenty days past this quickly. I am finally getting around to doing the hour or so program writing and debugging needed to finish the comment program. I think it was the dread of javascript that made me put writing off. Once I finish the comments, I will add more stuff.

BTW, I just added myself to Blogarama.com.

The comment section is still in test mode. That is why you see a test on all of the blog entries on this page. I didn't get a chance to finish the code. Of course, having an unfinished project in production has inspired me to work on other things.

I finally figured out what to do with the site map problem. The site map for the Salt Lake City community directory had close to 300 links. Google suggests limiting the page to 100 links. So, I made a buffer that lets me select which pages I block from the site map. I also now display it in alphabetical order.

Kids are coming over. That means I will not be able to finish the comments for another day. You can try the program. It is in a half-assed state.

In the time honored spirit of cowboy programming. I will be doing some testing in production.

I decided to write a program so people could leave comments. I want to see what Blogger passes to my web host...so I added a test button which does absolutely nothing of interest except show the unique ID of each post on this page. In a couple of hours, I will probably turn the "test" link into a comment link. If you are interested in programming. You could read my intro to PHP.