John Link

I'm pleased to announce the release of my new CD, 24 Preludes of Frédéric Chopin, by the John Link Project. This CD documents the 2007 world premiere of my arrangements for five singers, guitar, bass, drums, and violin of Frédéric Chopin's 24 Preludes, Opus 28, published for solo piano in 1839. I was the guitarist for all 24 preludes and a vocalist for one of them (No. 6), as well as the mixing engineer for all the audio. I also designed the artwork for the packaging. I guarantee that you have never heard Chopin's Preludes played the way we played them, with the melody, harmony, and rhythm so clear. I find that pianists typically play many of the Preludes (Nos. 1, 3, 5, 11, 14, 16, 18, 22, and 23) much too fast and without any sort of groove. Just wait until you hear our renditions at appropriate tempos. They really swing! Go to http://www.cdbaby.com/johnlinkproject to hear samples from the CD. There are two ways to purchase the CD: 1) ) Order through cdbaby by going to http://www.cdbaby.com/johnlinkproject and clicking on the BUY NOW button. 2) Go to http://www.isadoraduncan.org/emporium.html and order the CD along with the DVD The EveryWoman Series: The Red Thread by Lori Belilove & The Isadora Duncan Dance Company. (The CD and the DVD were recorded in June of 2007 at the Ailey Citigroup Theater in New York City where the performances by the John Link Project of Chopin's 24 Preludes served as accompaniment for Lori Belilove's original choreography.) By the way, Lori Belilove is my wife. I'm very proud of this new CD and DVD and hope that you will enjoy them and be inspired by them. John Link

Why are you sad about something that is good? I think "excommunication" is more probably appropriate than "schism". John Link

What great news! What great irony! http://www.nytimes.com/2010/01/20/us/polit...l?th&emc=th John Link

Do you really mean to imply that Bloomberg intends to increase the risk of heart disease? John Link

This is the first I've heard of the World Calendar. I found these: http://www.theworldcalendar.org http://en.wikipedia.org/wiki/World_Calendar John Link P.S. It looks quite interesting, but I don't like that my birthday would always be on a Monday!

I recently bought the new version of We the Living and will watch it for the first time tomorrow evening (on our big screen!) with some friends. John Link

Earlier today I wrote the following statement in another online discussion group: Math Guy, is that the sort of statement supported by your work? John Link

Isn't that just a link to the first post in this very thread? Or did you intend to link to something else? John Link

Agreed. And it seems that there are at least a few posting in this thread who would accept as valid only the positive integers and positive rational numbers. How poor we would be in such a case! John Link

That's quite reasonable, but if I remember correctly at least one poster in this thread expressed concern about the validity of negative integers, so the assumption that the real numbers are understood is not going to be satisfied by at least some in this thread. John Link

I think that part of the difficulty in this thread comes from the fact that the mathematical knowledge of the participants varies greatly, and what some consider to be mathematical concepts unrelated to reality others would be explained by others as lack of understanding of the mathematical concepts. John Link P.S. By the way, I'm enjoying this thread and the other math thread on .999... tremendously, being reminded of how much I love mathematics. I'm even considering offering my services as a tutor. P.P.S. I think I must have come across exp(pi*i) + 1 = 0 during graduate school, but I don't remember the proof and maybe I ought to review it. That is really cool!

Wikipedia has an article about .999... http://en.wikipedia.org/wiki/0.999... John Link

Not so. The equal sign "=" is used in mathematics to indicate identity. See http://en.wikipedia.org/wiki/Equal_sign To anticipate objections to what I have written, consider the following true equation: 3+2 = 13-8 The expressions on the two sides of the equal sign (i.e., "3+2" and "13-8") are not the same, but the numbers on the two side of the equal sign (i.e., 3+2 and 13-8) are the same. John Link

If you're going to be dealing with limits of infinite series and expect to be taken seriously I suggest you do not use the radical sign to indicate long division. The radical sign has a well-established meaning, and that meaning is not long division! All you needed to write was "1/3 =" and say that you were expressing that ratio by considering the long division of 3 into 1. Also, any sum with an infinite number of terms is defined as the limit of the partial sums, so the expression to which you object is perfectly fine. John Link

Agreed. John Link

Do you accept that 1/3 = .333... ? (If not, then we've really got to start at the beginning.) Do you accept that .333... + .333... + .333... = .999... ? (If not, what do you say the value of .333... + .333... + .333... is?) I'm sure you accept that 1/3 + 1/3 + 1/3 = 1 Assuming you answered YES to my two questions we have the following: 1 = 1/3 + 1/3 + 1/3 = 333... + .333... + .333... = .999... So 1 = .999...

Your point is clear, but it does not support a conclusion that negative numbers are somehow invalid. I suggest you read what has been written in this thread about the validity of negative numbers and understand why they are not only perfectly valid but also absolutely necessary. What you have written above seems to suggest that only the counting numbers (i.e., 1, 2, 3, 4, 5, ...) are valid. Maybe you would also accept rational numbers formed from the counting numbers? If we (humankind) were to accept only counting numbers and rational numbers formed from the counting numbers we would set science and technology backwards many centuries! John Link

But of course there is! If my liabilities exceed my assets by one dollar then my net worth is -$1. John Link

Both links are incorrect.

Can you give a citation for the rumors? John Link

No, "..." does not mean infinite, it means infinitely repeating. John Link

Given the apparent difficulties of understanding that 0.999...=1.0, much of which seems to be related to difficulty with the concept of infinity, I wonder what sort of discussion might ensue if I started a thread about the various orders of magnitude of the infinities? How about this: There are infinitely many integers, infinitely many rational numbers, and infinitely many real numbers. The infinity of the integers is equal to the infinity of the rational numbers, while the infinity of the real numbers is greater than the infinity of the integers and rational numbers. Just trying to cause trouble! John Link

Do you mean that you were afraid that you would deserve to be excommunicated? John Link

That's one interpretation of the meaning of his impossibility theorem, but I believe that that interpretation is not correct. John Link

Yes, please! And the quotes ought to be of what Kant wrote, rather than what someone else wrote what Kant meant by what he wrote. John Link