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RECENT POSTS IN THIS TOPIC

Constantinos Ragazas: on 3/11/11 at 3:33am UTC, wrote Dear James, Energy quanta are a think of the past! We need “A World...

james akerlund: on 3/10/11 at 4:28am UTC, wrote Hi Paul, I read your author Bio for the paper you posted and I see you...

Paul Halpern: on 3/9/11 at 16:27pm UTC, wrote Dear Jim, Interesting to speculate about parallel realms with different...

Peter Jackson: on 3/5/11 at 16:31pm UTC, wrote Hi Jim Interestingly different paper, worth a higher place, though I'm not...

basudeba: on 2/5/11 at 2:36am UTC, wrote Dear Sir, Kindly excuse us if our post has hurt your feelings. That was...

james akerlund: on 2/4/11 at 4:20am UTC, wrote Dear Basudeba, I've done to you an injustice in the above post. I have...

james akerlund: on 2/4/11 at 3:33am UTC, wrote Dear Basudeba, I am easily confused and your post is confusing me in...

basudeba: on 2/4/11 at 1:33am UTC, wrote Dear Sir, We have gone through your excellent deductions. We have a few...


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FQXi FORUM
October 14, 2019

CATEGORY: Is Reality Digital or Analog? Essay Contest (2010-2011) [back]
TOPIC: A Universe Invariant Numeral System by James R. Akerlund [refresh]
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Author james r. akerlund wrote on Feb. 2, 2011 @ 09:43 GMT
Essay 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.

Author Bio

Jim Akerlund has been to several different colleges and universities, but has yet to receive a degree. He currently lives in Colorado where he works at jobs that have no homework and very little overtime, so that he can invest his time in the understanding of parallel unvierses. Current research interests are how math is communicated to the universes and how to communicate to other universes. If Erdös' "The Book" comes to mind then you know what he is pursuing.

Download Essay PDF File

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Anonymous wrote on Feb. 2, 2011 @ 20:09 GMT
So if we replace the symbol "1" with the symbol "u" we have a different numeral system. The symbols are arbitrary in the first place so I don't see how that changes anything.

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Author james r. akerlund replied on Feb. 3, 2011 @ 04:40 GMT
Whenever we use symbols, two things occur; one, the symbol is created, and two a definition is attached to that symbol. Many symbols have more then one definition. That is OK, because we usually resolve this by the context in which the symbol is used. If I had used "u" in a text message, then that would be defined as "you". In the paper, "1" is used in the way you would usually define as one. The definition of "u" is defined in the proof, and I state this several times in the paper when I say "as defined above". It is my belief that the definitions of "1" and "u" are different and therefore that is how things are changed.

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Anonymous replied on Feb. 3, 2011 @ 08:44 GMT
To me the proofs repetitively equate u with 1 and do not show any differentiation. I don't get how you believe the definitions are different when the proofs say they are equal.

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Author james r. akerlund replied on Feb. 4, 2011 @ 00:39 GMT
Hello Anonymous,

Here is a quote from the paper. It is after the first two proofs, but before the last one. "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." The "any single value or u" section of that sentence is telling you that u can have any value you can come up with and all of them not equal to 1.

Jim Akerlund

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basudeba wrote on Feb. 4, 2011 @ 01:33 GMT
Dear Sir,

We have gone through your excellent deductions. We have a few comments regarding the mathematical representation of physics.

In our essay, we have proved that physics is mathematical in specified ways only. All mathematical manipulations are not physics. The reason for this is simple. The validity of a mathematical statement rests on its logical consistency. The validity of a physical statement rests on its correspondence to reality. Thus, we have shown that all mathematical statements are not physical statements also and that all physical phenomena cannot be explained through mathematical equations. We quote some of your statements to prove the above view:

You say: 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.

There cannot be any dispute about the Reflexive law. But the Symmetric law and the Transitive law can be misleading. In the first place, if a is described not as a, but as b, then the statement a = b shows that a and b are not identical in all respects, but have similarities in some respects only. This creates a big difference between the mathematics involving a and b as shown below.

Number is a property of substances by which we differentiate between similars. If there is no other object similar to a given object, we call that as one. If there are similar objects, that gives rise to the number sequences based on the sequence of their perception. All physical phenomena is nothing but accumulation and reduction of numbers, thus, mathematical. However, fundamentally, mathematics is done only in two ways. Linear accumulation and reduction is called addition and subtraction. Nonlinear accumulation and reduction is called multiplication and division. Linear accumulation is possible only between similars, only between the a in your example. Nonlinear accumulation is possible only between partially similars, i.e., only between a and b in your example. The results of these two operations do not give identical result. 3a plus 2a is 5a, but 3a plus 2b is not 5a or 5b, when a = b. It is 3a+2b. Similarly, if 3a is multiplied by 2b, it is 6ab. This puts severe restrictions in the mathematics involving the Reflexive law and the other laws quoted by you. Often this difference is overlooked in theoretical formulations making the mathematical structures unphysical.

Regards.

Basudeba.

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Author james r. akerlund replied on Feb. 4, 2011 @ 03:33 GMT
Dear Basudeba,

I am easily confused and your post is confusing me in spades. So, in order to begin to ease this confusion I am going to take one of your sentences and ask you some questions about it. Here we go.

This is the sentence I wish to ask you questions about

"Number is a property of substances by which we differentiate between similars."

A) How many "t"'s are in the sentence? Answer 5

B) How many letters are in the sentence? Answer 66

C) How many letters and punctuation marks are in the sentence? Answer 67

D) How many spaces, letters, and punctuation marks are in the sentence? Answer 78

As far as I can tell, your sentence, I quote, is a definition of number. If that is the case, then some of the answers to A, B, C, and D aren't valid numbers according to your definition. According to your definition, only A is the valid answer. B isn't valid because letters aren't similar to "t"'s they are different from them. As for C and D they are just more examples of non-similar things that according to your definition aren't a number. Can you see my confusion?

Jim Akerlund

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Author james r. akerlund replied on Feb. 4, 2011 @ 04:20 GMT
Dear Basudeba,

I've done to you an injustice in the above post. I have faked ignorance on my part when I asked you questions about your definition of number. I know that, in math, the question of the definition of number is not a light subject and can not be answered in one sentence. Some of the best minds in math have been asking what a number is throughout it's history. As far as I know, that answer still hasn't been resolved. Here is a website that gives one 19th centuries mathematicans attempts to resolve the issue of what a number is. http://plato.stanford.edu/entries/frege-logic/ I suggest you read the article, it may alter your future research directions. I apologize if the above post insulted you.

Jim Akerlund

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basudeba replied on Feb. 5, 2011 @ 02:36 GMT
Dear Sir,

Kindly excuse us if our post has hurt your feelings. That was not our intention. Since it is the forum of Foundational Questions Institute, we wanted to point out the conceptual aspects.

Regarding your first post, we may realize that you are only proving our point. How did you count the numbers 5, 66, 67 and 78. One by one only. How did you count the different characters? By differentiating between similars only. What is our statement? It is the markings on your computer screen that is a substance. How did you "know"? Because you perceived it, which is nothing but the result of your measurement, which in turn is nothing but comparison with similars.

Regarding your second post, we thank you for your information. We have written a complete book on this subject and analyzed the different aspects of numbers including number sequence, negative numbers, zero, infinity, etc. elaborately in this book. In case you want to read, kindly forward your mailing address to mbasudeba@gmail.com

Thanks and regards,

basudeba

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Peter Jackson wrote on Mar. 5, 2011 @ 16:31 GMT
Hi Jim

Interestingly different paper, worth a higher place, though I'm not a mathematician. I've derived a unification model that leads to a logical proof of multiple universes you may be interested in. Do read my essay; http://fqxi.org/community/forum/topic/803 but the logical conclusions on universes is at; http://vixra.org/abs/1102.0016

Best of luck

Peter

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Paul Halpern wrote on Mar. 9, 2011 @ 16:27 GMT
Dear Jim,

Interesting to speculate about parallel realms with different mathematical systems. Fascinating to imagine that the mathematical laws could be different elsewhere.

Best regards,

Paul

Paul Halpern, The Discreet Charm of the Discrete

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Author james r. akerlund replied on Mar. 10, 2011 @ 04:28 GMT
Hi Paul,

I read your author Bio for the paper you posted and I see you have studied general relativity. Well, in order to study general relativity you have to understand tensor calculus. I do not know of a program that teaches you tensor calculus without studying and writing mathematical proofs. I suspect that you are so famaliar with proofs that you could recite from memory Euclid's proof that there are an infinite number of primes. Are you saying, from your post, that Euclid was only speculating that there are infinite primes? I have seen some strange things in math lately, I'm just wondering if this is a new trend I need to start reading up on.

Jim Akerlund

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Constantinos Ragazas wrote on Mar. 11, 2011 @ 03:33 GMT
Dear James,

Energy quanta are a think of the past! We need “A World Without Quanta”! And you can make that critical difference to help bring it about. Cast your approval for a world that makes sense and bring this essay out of the cusp of 'being or not being'! The results are deeply significant and totally iconoclastic. But we need to bring this essay to the 'church' on time! You among others will be better for it!

All the best,

Constantinos

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