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RECENT POSTS IN THIS TOPIC

Eckard Blumschein: on 11/4/12 at 16:21pm UTC, wrote Roger, You didn't yet comment on my views[/link). What about the...

Sergey Fedosin: on 10/4/12 at 7:13am UTC, wrote If you do not understand why your rating dropped down. As I found ratings...

Benjamin Dribus: on 9/28/12 at 18:00pm UTC, wrote Dear Roger, Thanks for the kind remarks... I also posted a similar reply...

Roger: on 9/27/12 at 3:57am UTC, wrote Ben, Thank you for the nice comments! You should be careful, though,...

Benjamin Dribus: on 9/26/12 at 22:42pm UTC, wrote Dear Roger, I think you are pretty much right on target (and I'm a...

Roger: on 9/20/12 at 3:16am UTC, wrote Hi. Thanks for the comments. I scanned over your essay, and while I'm not...

Hoang Hai: on 9/19/12 at 14:36pm UTC, wrote Dear Very interesting to see your essay. Perhaps all of us are convinced...

Yuri Danoyan: on 9/10/12 at 17:54pm UTC, wrote Roger have you read my essay? http://fqxi.org/community/forum/topic/1413


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FQXi FORUM
July 19, 2019

CATEGORY: Questioning the Foundations Essay Contest (2012) [back]
TOPIC: Thought Experiments in the Abstract Field of the Mathematics of Infinities Produce Experimental Artifacts Suggesting That Their Use in the Real-World Science of Physics Should Be Reexamined by Roger Granet [refresh]
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Author Roger Granet wrote on Aug. 10, 2012 @ 12:47 GMT
Essay Abstract

Here, I question the assumption in set theory that the size of an infinite set is the same as the size of an infinite subset derived from it as well as the validity of using this result in physics. Consider a thought experiment in which one wants to study the properties of the single set of the positive integers within the framework of that single set system, and one wants to compare the total number of positive integers in the set to the total number of even integers. The traditional experimental processing method extracts the even integers, puts them into a separate subset and pairs off the subset's and set's members one-to-one with a function. After finding no elements left over, the original set and the subset extracted from it are said to be of the same size. However, this method dramatically alters the original single set system and ignores the inherent relationships of that system in which every even integer is always accompanied by an adjacent odd integer. When one takes this relationship into account, one finds that there are twice as many positive integers as even integers within the single set system. The traditional processing method produces an experimental artifact. This should be unacceptable in a well done experiment. While this may be acceptable in the abstract field of mathematics, one cannot simply study a subset of a real, physical system in isolation without considering the inherent relationships between the subset and the rest of the system. And yet, the mathematics of infinities is based on doing just that and is used extensively in physics. I suggest that physics should require the use of  proper experimental technique, especially in its logical foundations.

Author Bio

I have Masters degrees in biochemistry and business and work in Columbus, OH (USA) as a biochemist. I have a lifelong interest in thinking about the question "Why is there something rather than nothing?". Set theory, including topics related to null and infinite sets, are related to this topic, and this essay sprang from thinking in those areas and from my background in biochemistry. Other essays on this question and infinite sets are at: sites.google.com/site/ralphthewebsite

Download Essay PDF File

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Eckard Blumschein wrote on Sep. 1, 2012 @ 13:27 GMT
Dear Roger Granet,

Having thoroughly dealt with Cantor's naive set theory, I feel confirmed by Ebbinghaus in that Cantor was simply wrong. Since you are also questioning set theory, I would appreciate if you were ready to comment on my views. Did you get aware of other allies here?

Regards,

Eckard

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Roger replied on Sep. 5, 2012 @ 04:58 GMT
Eckard,

Hi. I just returned today from a several-day long vacation so that's why I haven't responded sooner. I don't remember seeing any essays this year that have really done much with set theory as it relates to physics, and in terms of allies, you're the only that's posted any kind of a reply to my essay at all. Even among "crackpots", I seem to be a crackpot! :-) But, I have seen several essays that have questioned the seeming supremacy among physicists of mathematical rather than physical/mechanical thought. That seems to be kind of a general theme among many of the essays. To me, I'm a little disappointed in the reasoning ability of physicists (at least the ones I can understand) and mathematicians in that they:

o Make a lot of unfounded assumptions.

o Many seem to claim that mathematical constructs or physical laws exist "out there" somewhere and can serve as the first cause of the creation of the universe. Logically, this is no different than assuming a "god" created the universe. It's possible, but they need some evidence other than their say so.

o They use mathematics as the basis of physics and yet use very poor experimental technique (in my essay) in their mathematical thought experiments.

In trying to make some progress in basic questions, I think we should try to avoid all, or as many as possible, assumptions and start our reasoning from basic logic. While I may not achieve it, that's the approach I've tried to take with my thinking.

What was the name of your essay? I'll go back and read it more carefully. I had scanned them all up through about 4-5 days ago, but hadn't read too many thoroughly due to work and family time constraints.

Thanks!

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Eckard Blumschein replied on Nov. 4, 2012 @ 16:21 GMT
Roger,

You didn't yet comment on my views[/link).

What about the property of an infinite quantity to be not larger than an also infinite part of it, you will perhaps agree on oo + 1 = oo. Incidentally, Georg Cantor was not the first one who used the self-contradictory expression "infinite number". Even Weierstrass used it.

Eckard

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Armin Nikkhah Shirazi wrote on Sep. 6, 2012 @ 10:41 GMT
Hi Roger,

I just read your essay, and while I am not a mathematician (I do study physics) your argument totally makes sense to me.

Have you considered discussing this with some mathematicians? If you have but your argument was dismissed without a solid reason (e.g. proof) for why it has no merit, I would go to another mathematician.

Unfortunately my knowledge in this area is...

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Author Roger Granet replied on Sep. 9, 2012 @ 03:48 GMT
Armin,

Hi. Thank you for the feedback! I've tried many times to get mathematicians, physicists and philosophers to listen to this and other ideas with almost no success. I think very few even read or seriously think about the points raised and just object because I'm an amateur and the idea goes against accepted thought. Most of the few comments I have received reflect very poor...

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Yuri Danoyan wrote on Sep. 10, 2012 @ 17:54 GMT
Roger

have you read my essay?

http://fqxi.org/community/forum/topic/1413

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Hoang cao Hai wrote on Sep. 19, 2012 @ 14:36 GMT
Dear

Very interesting to see your essay.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the focus of interest of the human science: it is a matter of mass and grain Higg boson of the standard model.

Knowledge and belief reasoning of you will to express an opinion on this matter:

You have think that: the Mass is the expression of the impact force to material - so no impact force, we do not feel the Higg boson - similar to the case of no weight outside the Earth's atmosphere.

Does there need to be a particle with mass for everything have volume? If so, then why the mass of everything change when moving from the Earth to the Moon? Higg boson is lighter by the Moon's gravity is weaker than of Earth?

The LHC particle accelerator used to "Smashed" until "Ejected" Higg boson, but why only when the "Smashed" can see it,and when off then not see it ?

Can be "locked" Higg particles? so when "released" if we do not force to it by any the Force, how to know that it is "out" or not?

You are should be boldly to give a definition of weight that you think is right for us to enjoy, or oppose my opinion.

Because in the process of research, the value of "failure" or "success" is the similar with science. The purpose of a correct theory be must is without any a wrong point ?

Glad to see from you comments soon,because still have too many of the same problems.

Regard !

Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY

August 23, 2012 - 11:51 GMT on this essay contest.

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Roger replied on Sep. 20, 2012 @ 03:16 GMT
Hi. Thanks for the comments. I scanned over your essay, and while I'm not sure I understood it because of language issues, certain quotes like the following:

"It would be more reasonable if we develop an essay contest to contest this determination on the basic theory with specific questions, eg: a specific definition and detail...

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Member Benjamin F. Dribus wrote on Sep. 26, 2012 @ 22:42 GMT
Dear Roger,

I think you are pretty much right on target (and I'm a mathematician!). The great British physicist and mathematician Roger Penrose has asked a lot of similar questions and raised a lot of similar points, although I haven't read most of his work on these subjects first-hand. In particular, there are a lot of different ways of measuring the size of sets, and people often focus only on the "cardinality," which is in some ways the coarsest way of measuring and tells you the least information. In terms of cardinality, it's true that the even numbers are the same size as the integers, but as you point out, the whole point of identifying this set as "even integers" specifies the set of integers itself as the "parent set," as you put it, which means you are really referring to two sets rather than one. I would have to agree that it's rather idiotic to then proceed to ignore the relationship of the set to its parent set when talking about size.

My own attempts at fundamental physics involve mostly countable sets (sometimes finite) and issues like these arise all the time. In particular, I often have to think about one "partially ordered set" as a subset of another. Often these sets have the same cardinality, but are definitely not the "same size." If you're interested, you might look at my essay On the Foundational Assumptions of Modern Physics. What I try to do is build up fundamental physics from simple principles like cause and effect. This leads to some rather thorny mathematics, but my view is that the physical principles ought to be simple and well-motivated, and the math ought to be whatever it has to be to get the job done.

Anyway, I enjoyed reading it! Take care,

Ben Dribus

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Roger replied on Sep. 27, 2012 @ 03:57 GMT
Ben,

Thank you for the nice comments! You should be careful, though, saying nice things about a "crackpot"! They might not let you finish the PhD! :-)

I think your way of thinking shown by your saying "What I try to do is build up fundamental physics from simple principles like cause and effect. This leads to some rather thorny mathematics, but my view is that the...

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Member Benjamin F. Dribus replied on Sep. 28, 2012 @ 18:00 GMT
Dear Roger,

Thanks for the kind remarks... I also posted a similar reply to your comments over on my thread, but thought it would be easier if they were here as well. I took a look at your website, but unfortunately only the top of the page would load; I don't know if this is a site issue or a browser issue.

I think your point about considering the "physical" relationships between...

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Sergey G Fedosin wrote on Oct. 4, 2012 @ 07:13 GMT
If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is
and
was the quantity of people which gave you ratings. Then you have
of points. After it anyone give you
of points so you have
of points and
is the common quantity of the people which gave you ratings. At the same time you will have
of points. From here, if you want to be R2 > R1 there must be:
or
or
In other words if you want to increase rating of anyone you must give him more points
then the participant`s rating
was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

Sergey Fedosin

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