Links to my other papers on the Web.

Links to my other papers on the web

So...        ...When I'm not writing for here, is appears that I am writing for somewhere else.  Well, I haven't been writing here, so that means I've been writing for somewhere else.  This post is to show you where I have been writing.

This first link is for my paper called "A Universe Invariant Numeral System".  You can find it here.  http://www.fqxi.org/community/forum/topic/847

The date of the posting is for 2/2/11, but the paper was originally released 1/17/10.  I sent it on that date to an Australian scientist to see if he would endorse it for the ArXiv.  The next day, 1/18/10 was MLK day (Martin Luther King) and most colleges and universities were closed in the U.S.  Now that info seems rather meaningless except for the event that happened to me on 1/19/10.  On 1/19/10 I went to the latest edition of Denver's "Café Scientifique" http://cafescicolorado.org/ , the speaker was Michell Shull, PhD, Professor of Astrophysical and Planetary Sciences, University of Colorado, Boulder.  The talk was interesting, but at the very end during the questioning, it got very interesting.  You see, some of the audience members aren't the general public you might think they are.  For Biology speakers, you will find people in the audience from all sorts of Biology related industries.  When a School of Mines professor spoke, all sorts of people in the minerals related industries showed up.  The same thing happened with our Astrophysical and Planetary sciences professor.  Some of those people can ask very specific field related questions.  So, these people were asking the pointed origins of the universe questions (I'm guessing they were Grad students), and the questioner keeps digging for a weakness.  The professor sort of relents and says something like 'we just don't know' and then he launches into a story (bad paraphrase).  Everyday he has access to "preprint" class of papers and that some of these papers are from very brilliant people and that today (1/19/10) he had seen a paper that had called into question some very basic notions.  Well, I knew that due to the MLK holiday(1/18/10), UC Boulder was closed for the day, so his first day back at work, after Sunday, 1/17/10, would have been Tuesday, 1/19/10 after MLK.  So, I don't know if this is my "inflated ego" or not, but his mentioning the "preprint" that he has access too and a paper that made him question his notions lead me to the conclusion that he was talking about my paper "A Universe Invariant Numeral System".  Now here is the part that is strange in my mind.  I sent the paper to a researcher in Australia, who had these qualifications; he had written a cogent paper on parallel universes and he could endorse for math.  I had sent the paper to him to endorse for math.  So, as far as I can tell, the Australian professor is in a completely different world(research wise) then the UC Boulder professor, but the Australian professor put my paper on that "preprint" server and for some reason a professor in a completely different field in UC Boulder read my paper on that server.  If those two worlds were indeed connected because of my paper, then my paper made some waves.

More waves.  About ten months later, I'm guessing October of 2010, I find that the "Institute for Advanced Study" (The U. S. school where Einstein was a professor), was celebrating it's 80th year of existence by a series of lectures that are posted online.  So, I'm reading the titles of the lectures when I run across this title "What if Current Foundations of Mathematics are Inconsistent?".  I watch the lecture.  It turns out that he argues, what if math is inconsistent all the way down to an elementary level, but we aren't smart enough to see it.  He bases his logic off a guy whose last name is Gentzen http://en.wikipedia.org/wiki/Gerhard_Gentzen who died shortly after WWII.  I suspect that what Gentzen actually said was, maybe a math could be created that was itself inconsistent, but still be used as a math, not that the whole of math was inconsistent.  The thing that got me was the repeated references to "even elementary math is inconsistent".  When you look at my paper, it is a very elementary paper.  I myself had a ninth grader read it, knowing that all you need to understand it is middle school algebra, and asked him if he understood it.  He said, Yes.  So, the references in the lecture to "elementary math", I believe are references to my paper.  More evidence of my "inflated ego".  The lecture appears to be an attempt to show that my paper is inconsistent by saying that all of math is inconsistent.  I call it the "Burning down the house solution to the might be dirty, babies bathwater".  Here is a link to that lecture.  http://video.ias.edu/voevodsky-80th

 Here is the link to my next paper on the web.  http://www.vixra.org/abs/1111.0052  This paper is the result of my finding what I think are UI (universe invariant) and US (universe specific) verses in the Bible.  You can judge for yourself if you think they are also UI or US verses.

The last link is to my latest essay for FQXi and their last contest that ended for entires on 8/31/12.  The essay got published on 7/10/12 and is titled "Gravity is a Dimension" http://www.fqxi.org/community/forum/topic/1324  By the way, the name of the FQXi contest is "Which of Our Basic Physical Assumptions Are Wrong?"

Jim Akerlund

My FQXi Essay "A Universe Invariant Numeral System"

Abstract

A proof is presented to show that there are parallel universes in math. It is then shown that these parallel universes have different values for the math constants. Math is then shown to be divided into universe invariant and universe specific groups. A universe invariant numeral system is presented. And finally we argue for the universe being digital, but as the paper shows, it's a bit more complicated then the digital we've been taught.

Parallel universes are a reality. Not only are they a reality, but they are also in math. We choose to show you this via a proof. This proof will show you that there are many different numeral systems other then the ones we use. The proof will use communitative Algebra to show you these many different numeral systems. The first two proofs are based from the book “A Survey Of Modern Algebra” by Garrett Birkoff and Saunders Mac Lane [1].

Here are the three basic laws of equality for any commutative ring R.

Reflexive law: a = a.

Symmetric law: If a = b, then b = a.

Transitive law: If a = b and b = c, then a = c, valid for all a, b, and c.

For all a in R, 1 * a = a.

Proof. For all a in R:

1) 1 * a = a * 1

2) a * 1 = a

3) 1 * a = a. ■

If u in R has the property that a * u = a for all a in R, then u = 1.

Proof. Since a * u = a holds for all a, it holds if a is 1.

1) 1 * u = 1

2) 1 = 1 * u

3) u = u * 1

4) u = 1. ■

With the above proofs we can now create a less simplified form of the three basic laws of equality for any commutative ring R for any single value of u.

Reflexive law: a * u = a * u.

Symmetric law: If a * u = b * u, then b * u = a * u.

Transitive law: If a * u = b * u and b * u = c * u, then a * u = c * u, valid for all a, b, and c.

We now propose the Meta-commutative ring R_u, where when u = 1 then it denotes the normal commutative ring R of this universe. For meta-commutative ring R_u, u ≠ 0.

Here are the three basic laws of equality of the meta-commutative ring R_u.

Reflexive law: a * u = a * u.

Symmetric law: If a * u = b * u, then b * u = a * u.

Transitive law: If a * u = b * u and b * u = c * u, then a * u = c * u, valid for all a, b, and c.

Each separate R_u defines a separate commutative ring.

Proof. If R₁ exists then R_m exists along with R_n. n ≠ m ≠ 1.

1) For all R_u, then a * u = a * u.

2) If R_n is not separate from R_m then (a * n = a * n) = (a * m = a * m).

3) But they are not equal therefore R_n is a separate Commutative Ring from R_m. ■

From the above proofs we can see that R_u ≠ R. But the above proofs only show that there could be other numeral systems, not that there are. We will now show you that these new numeral systems also allow different values of π. In math π is defined many different ways. We are referring to the value of the difference between a circles diameter and that same circles circumference on a “flat” surface. Of the many different ways π can be defined, these many different ways boil down to two separate routes; arithmetically or physically. For a physical discussion on changing the value of π in a parallel universe, I refer you to the authors 1997 paper, entitled “Foundations Of Parallel Universe Math” [2]. Here is an arithmetic equation for the value of π [3],

π/4 = 1/1 - 1/3 + 1/5 - 1/7 + 1/9 - ...

To have the same arithmetic equation calculate a different value of π, multiply both sides of the equation by u, where u is from R_u and you get this equation,

(π * u)/4 = u/1 - u/3 + u/5 - u/7 + u/9 - ...

π * u is your new value of π. You can do this same procedure to all arithmetic equations of π. But this would seem to imply that all we have done is derived non-euclidean values of π. This is not the case, because we can also get different values of e. Here is an arithmetic equation to calculate the value of e [4],

e = 1/0! + 1/1! + 1/2! + 1/3! + 1/4! + ...

To have the same arithmetic equation calculate a different value of e, multiply both sides of the equation by u, where u is from R_u and you get this equation,

(e * u) = u/0! + u/1! + u/2! + u/3! + u/4! + ...

e * u is your new value of e. You can do this same procedure to all arithmetic equations of e, and we also say that all arithmetic equations of any mathematical constant can also be changed in like manner to arrive at other universes values of those mathematical constants; this includes i, φ and others. No where in non-euclidean geometry does it mention that different values of e or other mathematical constants can be found.

The above paragraph splits math into two different groups. These two groups are universe specific (US) math and universe invariant (UI) math. We will define universe specific as; events, ideas, memes, rules, and laws that are specific to exactly one universe. We will define universe invariant as; events, ideas, memes, rules, and laws that are the same in all parallel universes. The definitions for US and UI are not limited to math concepts alone, but this paper will only be concerned with math concepts. The above paragraph shows us that the mathematical constants are US, but the equations calculating them are UI. The number line R and the value of 1 are also US, as shown in the above proof. The proof itself is UI. The value of 0 is UI. Here is a general rule for determining whether a math statement is UI or US. A UI statement will not change its meaning when a known US statement is applied to it A US statement will change its meaning. This mixture of US and UI, in math, is limiting our understanding of math, because math is not complete without application to all parallel universes. What we need, to begin a parallel universe understanding of math, is a UI numeral system; because, as was shown above, our current numeral system is US. To that end is the reason for this paper. The author believes he has found a UI numeral system that is currently not being taught or investigated.

Here is that UI numeral system. The numeral system is binary, but it doesn't use 1 and 0, but instead uses u and 0, where u is the same as defined above. All the rules of binary math apply to this numeral system, unless it is revealed that any one or more of these rules are US. If a rule is found to be US that rule can not be applied to get a UI result. Depending on where that US rule is, and it's importance with respect to the other binary rules of math, it may or may not invalidate other binary rules of math, to maintain a UI numeral system. Here are the numbers 1 – 10 as represented in our UI numeral system when u = 1,

1 = u

2 = u0

3 = uu

4 = u00

5 = u0u

6 = uu0

7 = uuu

8 = u000

9 = u00u

10 = u0u0.

The above numeral system assumes that the place value concept is UI. As our computers currently operate, they already operate on a binary numeral system, what's it to say, we take the results of our computer and say that it is a UI result? Until we understand more completely our US and UI mixture in math, all we can say is that somewhere in the computer calculation a US aspect has been entered into the calculation and that makes the whole calculation US. It is the authors belief that the actual value of u in the UI numeral system is all possible values of u, when performing an equation. When you assign “one” value to u you then make the result US, and that “one” value will always be relative to this universe.

It is the authors belief that u is a new number unlike any we have encountered before.

So, we go onto the question of "Is reality digital or analog?" We believe the above paper shows the digital aspects of this universe and the parallel universes, but the above paper also shows that the digital in this universe isn't the same as the digital in any of the parallel universes.

References

1. Birkhoff, Garrett, and MacLane, Saunders. “A Survey Of Modern Algebra”. (1997). A. K. Peters, Wellesley, Massachusetts.
2. Akerlund, Jim. “Foundations Of Parallel Universe Math”. (August, 1997). Newsgroup: Alt.sci.physics.new-theories. http://groups.google.com/group/alt.sci.physics.new-theories/msg/2bcd2fade2f7cf50
3. Blatner, David., "The Joy Of p". (1997). Walker Publishing.
4. Wikipedia. “e (mathematical constant)”. (December, 2009). http://en.wikipedia.org/wiki/E_(mathematical_constant) .