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RECENT POSTS IN THIS TOPIC

Luca Valeri: on 4/26/15 at 23:49pm UTC, wrote Hi Yafet, your reply on my comment also got lost before I had the chance...

Armin Nikkhah Shirazi: on 4/23/15 at 2:08am UTC, wrote Dear Yafet, It appears that my comment and your response disappeared...

Yafet Sanchez Sanchez: on 4/23/15 at 0:27am UTC, wrote Dear James, Your essay certainly is a wild ride. I think the effort you...

Yafet Sanchez Sanchez: on 4/22/15 at 23:48pm UTC, wrote Dear Luca, Thanks for your comment. Kant is one of my favorites. I agree...

Yafet Sanchez Sanchez: on 4/22/15 at 23:40pm UTC, wrote Dear Armin, I appreciate your interest in my essay. There might be many...

Yafet Sanchez Sanchez: on 4/22/15 at 23:37pm UTC, wrote Dear Akinbo, Thank you for your post. I like your example of the magician....

Luca Valeri: on 4/17/15 at 11:00am UTC, wrote Yafet, Really nice essay. I think it is important and most difficult to...

Armin Nikkhah Shirazi: on 4/14/15 at 22:39pm UTC, wrote Dear Yafet, Yours is a very subtle essay that gets to one of my favorite...


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FQXi FORUM
November 22, 2019

CATEGORY: Trick or Truth Essay Contest (2015) [back]
TOPIC: Is 1+1=2 an empirical proposition? by Yafet Erasmo Sanchez Sanchez [refresh]
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Author Yafet Erasmo Sanchez Sanchez wrote on Mar. 12, 2015 @ 15:35 GMT
Essay Abstract

The idea of meaning as use in language is explored in a mathematical and physical context. Two possible scenarios of further analysis are presented: Ordinal arithmetic and String theory

Author Bio

I am a PhD student from the University of Southampton studying how the incorporation of Quantum field theory change our notion of a singularity in General Relativity. I like Beethoven, Wittgenstein and Monet.

Download Essay PDF File

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Paul Merriam wrote on Mar. 16, 2015 @ 19:04 GMT
"Again, what gives life to the symbol game and eventually transforms it

into mathematics is the empirical regularity that must be associated with

the symbols."

That's cool.

What is the nature of the association?

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Author Yafet Erasmo Sanchez Sanchez replied on Mar. 25, 2015 @ 20:15 GMT
I am not sure I have a definite answer, but I think the association in many ways is similar in the way words (as string of symbols) acquire meaning as part of a language. The association of a string of letters to meaningful words relies on their use in a suitable context. This is related to our forms of life as humans.

In the specific case of mathematics we become aware of regularities in nature and as humans act roughly in the same way to the same mathematical contexts (to give further explanation a neurological, evolutionary and psychological analysis is needed).

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Christopher Adams Horton wrote on Mar. 20, 2015 @ 00:50 GMT
Yafet, you begin with a musing on 1 + 1 = 2, the very definition of unassailable established truth in popular language, and how you would explain it to a child.

For a very young child you would assume this 1 and that 1 refer to distinct but interchangeable objects, so that the 2 in 1 + 1 = 2 refers simply to the counting number with which you would name the result of grouping them. But...

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Author Yafet Erasmo Sanchez Sanchez replied on Mar. 25, 2015 @ 22:31 GMT
Christopher,

Consider the following question: Why Superman doesn't need a boss?

Because he has super vision.

I think mathematics is a language similar to English or any other natural language in many aspects. Now, if you allow me to extend the analogy as far as I like I think the problem your students are having is similar to the problem some students learning English have...

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James A Putnam wrote on Mar. 25, 2015 @ 04:15 GMT
Is 1+1=2 an empirical proposition?

My response is: Yes of course it is. With this qualification: There is no such thing as a number without a thing. The thing is what is to be counted. The plus sign either means that countable objects are being counted or it is ambiguous and no longer tolerable as a mathematical symbol. Perhaps the number 1 and the number 2 in the title 'equation' are being...

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Author Yafet Erasmo Sanchez Sanchez replied on Mar. 26, 2015 @ 11:52 GMT
Dear James A Putman,

Thank you for your comment. I agree number are used for counting, but how does the zero number fit with the idea of number if there is nothing to count?

Also, do you have any insights about ordinal arithmetic? There certainly we are talking about "counting" in some sense. However, it is infinite counting which I am not sure is easy to represent with physical...

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James A Putnam replied on Mar. 26, 2015 @ 20:39 GMT
Yafet Erasmo Sanchez Sanchez,

"...how does the zero number fit with the idea of number if there is nothing to count?"

I can't think of any case where zero is a number. If I am to make sense of zero it is not as a number but as a word indicating that I have not yet begun to count anything. If zero appears on a line with positive numbers to the right and negative numbers to the left,...

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James A Putnam replied on Apr. 8, 2015 @ 01:12 GMT
You are doing very well in this contest, but, you need 3 more ratings at the least. Hopefully, after receiving them, you will remain in the top 30. If not then you will need to work to get more ratings. I think that your essay can continue to rate high enough to enter into the finals.

James Putnam

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Joe Fisher wrote on Mar. 25, 2015 @ 19:19 GMT
Dear Potential Dr. Sanchez,

I have no wish to be disrespectful to you or to your essay, but I think abstract mathematics and abstract string theory have nothing to do with how the real Universe is occurring for the following real reason:

Do let me know what you think about this: This is my single unified theorem of how the real Universe is occurring: Newton was wrong about abstract...

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Author Yafet Erasmo Sanchez Sanchez replied on Mar. 26, 2015 @ 11:07 GMT
Dear Joe,

I am a little confused by your arguments. How are you defying abstract? Also, as much as I like or dislike your arguments the ultimate judge is empirical evidence. Following your reasoning are you able to model current empirical evidence and predict new empirical phenomena?

Kind Regards,

Yafet

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Author Yafet Erasmo Sanchez Sanchez replied on Mar. 26, 2015 @ 12:00 GMT
Dear Joe,

I made a typo I meant: How are you defining abstract?

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Joe Fisher wrote on Mar. 26, 2015 @ 15:07 GMT
Dear Yafet,

Thank you for not reporting to Fqxi.org that my comment was inappropriate and by doing so have the Administrator classify it as Obnoxious Spam and remove it.

1. When I type the word “abstract” definition into the Google Search Engine, It gives a listing of definitions starting with: “existing in thought or as an idea but not having a physical or concrete...

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Sujatha Jagannathan wrote on Apr. 1, 2015 @ 12:05 GMT
You have titled perfectly, also made some honorary effort of gatherings.

-With regards,

Miss. Sujatha Jagannathan

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Author Yafet Erasmo Sanchez Sanchez replied on Apr. 7, 2015 @ 16:25 GMT
Thank you Sujatha.

Yafet

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Michel Planat wrote on Apr. 3, 2015 @ 09:21 GMT
Dear Yafet,

Your short and well structured essay is interesting. I agree that the concept of meaning is very relevant in this discussion about the comparison of maths and physics. Let me know if I understand you well that meaning arises in a context. You can find in my essay, p.6, a Frege's quote "Never ask for the meaning of a word in isolation, but only in the context of a sentence". Contextuality is a very important concept in QM.

You talk about a multiplicity of meanings of string theory (ST), this often taken as a weakness of ST but it seems that your opinion is different. I wonder if it is not precisely the multiplicity of meanings of QM that makes this theory so rich. The philosopher Popper considers QM as non falsifiable may be as ST.

I hope you will have time to go through my 'moonshine' topic.

Best,

Michel

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Author Yafet Erasmo Sanchez Sanchez replied on Apr. 7, 2015 @ 18:44 GMT
Dear Michel,

I was not aware of Frege's quote. I liked it. I am not sure if I agree with Popper. Isn't the correct prediction of say the electromagnetic fine structure constant a sign of falsifiability. Or am I missing something?

Also I think it is a great philosophical exercise to think about QM and the context needed to make it a physical science.

I will read your 'moonshine' and comment when I finished it.

Kind Regards,

Yafet

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Nick Mann wrote on Apr. 5, 2015 @ 05:38 GMT
Yafet,

Are you familiar with the Wittgenstein-Turing colloquy at Cambridge in the late 30s re: building a bridge so it won't fall down? Cuts to the core of the whole mathematics vis-a-vis physics debate.

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Author Yafet Erasmo Sanchez Sanchez replied on Apr. 7, 2015 @ 16:31 GMT
I was not aware of that material. It seems very interesting. Thanks.

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Member Marc Séguin wrote on Apr. 6, 2015 @ 04:02 GMT
Dear Yafet,

Thank you for a short, to the point and well argued essay: I have read more than half the essays in this contest, and yours is one of my favorites. As a fan of Wittgenstein, I totally agree with you when you say:

"The main shift one would like to achieve is to move from the dichotomy of "true" and "false" propositions to the notions of 'sense' and 'nonsense'."

I quite liked your analysis of the question "What kind of endeavor is string theory?" in the closing paragraphs of your essay.

I find it strange that your essay has attracted so few votes so far. I hope that the rating I will give it will move it higher in the community rankings, and will give it a better chance to get noticed.

All the best,

Marc

P.S. My essay tackles the philosophical question of the ultimate relationship between "All of mathematics" and "All of physical existence": I hope it makes more "sense" than "nonsense"... ;)

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Author Yafet Erasmo Sanchez Sanchez replied on Apr. 7, 2015 @ 18:51 GMT
Dear Mark,

Thank you for your comment. Yes, Wittgenstein rocks.:) I like you enjoy my essay and even more if copying Wittgenstein: 'I was able to not spare you the trouble of thinking, but instead encourage you to have independent thoughts.'

I will read your essay and comment later.

Thank you for your support.

Yafet

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Jonathan Khanlian wrote on Apr. 7, 2015 @ 16:28 GMT
Hi Yafet,

I think understanding what mathematics really is all about will definitely inform physicists, so I thank you for you thought-provoking essay. Thoughts about Euclidean geometry come to mind as an area of Mathematics that you might have considered to be “hardened” at one point… that is, until Non-Euclidean geometry came along. Even the terms “point” and “line” can take on different meanings if one imagines different non-Euclidean spaces. Should physicists not be concerned about philosophical discussions around the meaning of symbols they write down, so long as most of their peers can extract the essence of what their formulas and definitions are suggesting?

Please check out my Digital Physics movie essay if you get the chance. There are some questions posed at the end of the essay that may interest you. Here is a couple that came to mind after reading your essay.

12) If I created a very simple formal system in which almost every statement was undecidable, and then I took advantage of this fact by choosing some of the most counterintuitive independent statements to add as axioms, is there any value in physicists studying this area of mathematics?

13) On the other hand, how can some statements in a formal system be considered more intuitive or self-evident than others if any string of symbols should be looked at as being devoid of meaning?

Thanks,

Jon

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Author Yafet Erasmo Sanchez Sanchez replied on Apr. 7, 2015 @ 18:34 GMT
Hi Jon,

I think the point you raised about geometry is very important; unfortunately I am afraid I have not a complete clear view of how to tackle the whole geometry in terms of use and meaning. Nevertheless, I would like to share some ideas I have about it.

I think I would still say that Euclidean geometry is completely harden.

The existence of other geometries didn't prove...

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Armin Nikkhah Shirazi wrote on Apr. 14, 2015 @ 22:39 GMT
Dear Yafet,

Yours is a very subtle essay that gets to one of my favorite philosophical themes: Meaning.

I have noticed that many times discussions fail to get to satisfactory conclusions because the participants do not seem to recognize that while they are using the same words, they attach different meanings to them, and a particular example comes up right in this contest: Your discussion of the meaning of the proposition 1+1=2 is exactly apropos to Edwin Klingman's (and his proponents) claim that he "debunked" Bell's theorem, which is at best (i.e. if correct) a more complicated version of your example of the two drops merging into one not being an applicable real-world example of the mathematics.

I am surprised by the low response rate to your essay. If I may speculate, perhaps the title of your essay turned off some people because to most people the answer to the question it poses seemed so obvious that they didn't bother to see your argument that it really isn't if one is completely divested from the world we live in (again your merging-drops world is a great example). The subtlety of your argument may have escaped some, or perhaps your subtle criticism of ordinal arithmetic and string theory at the end might have antagonized others.

Be that as it may, I found your essay a very thoughtful exploration of meaning in relation to mathematics and physics.

Best wishes,

Armin

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Author Yafet Erasmo Sanchez Sanchez replied on Apr. 22, 2015 @ 23:40 GMT
Dear Armin,

I appreciate your interest in my essay. There might be many reason why I have such a low response. Anyhow, I enjoyed thinking about this topics while doing the essay and I certainly will continue.

Kind Regards,

Yafet

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Luca Valeri wrote on Apr. 17, 2015 @ 11:00 GMT
Yafet,

Really nice essay. I think it is important and most difficult to understand the relation of physics and mathematics by simple examples. I basically agree with all your are saying in your excellent essay.

One thing you left out in your analysis is the Kantian question: “What did we already accept in order to think that mathematics or physics is possible?”

You say that: “The truth of a mathematical propositions is independent of any physical phenomena.” I would say, that in order to be able to do mathematics some physical conditions have to be met: constancy of certain phenomena. Maybe also the structure of time.

In physics the situation similar, when we say, that physics is an empirical science. The structure of time seems to be a precondition of experience.

Maybe also the conservation of energy (Time translation invariance): Once Heisenberg heard about an experiment that showed, that the energy was not conserved. He reacted instantaneously: “Impossible!” How could he know that? How comes that some physical (empirical) statements although empirical seem always to hold true in our experience? The Kantian response to that is: because they are preconditions of objective experience to be possible.

Again I think you wrote a great essay and I would love you could read mine and comment on it.

Best regards,

Luca

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Author Yafet Erasmo Sanchez Sanchez replied on Apr. 22, 2015 @ 23:48 GMT
Dear Luca,

Thanks for your comment. Kant is one of my favorites. I agree with you that to do mathematics we need a background or context and that is provided by the regularity of nature and our psychology. Although the true of such statements is not. But notice, that without the background, the true become irrelevant or nonsensical.

I think Heisenberg, didn´t know. He believed so. But remember, how many things we consider impossible until they actually happened. Nevertheless, I believe you are asking the deeper question, how can we actually come to realise such regularities. I am afraid I don´t have an answer for that.

I will read your essay and comment on it. Meanwhile enjoy this video from the birthday boy.

https://www.youtube.com/watch?v=rzpL_5CI0WQ

Kind Regards,

Yafet

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Author Yafet Erasmo Sanchez Sanchez wrote on Apr. 23, 2015 @ 00:27 GMT
Dear James,

Your essay certainly is a wild ride. I think the effort you put to understand mathematics and nature from another point of view is remarkable.



If I understood correctly you want to make physics concepts as empirical as possible and you claim that:" The general theory of relativity presents space-time to us as a real property.

There is no empirical...

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Armin Nikkhah Shirazi wrote on Apr. 23, 2015 @ 02:08 GMT
Dear Yafet,

It appears that my comment and your response disappeared before I had a chance to see what your response was (except for the beginning, which can be seen in the side bar). I wonder whether the moderator can reinstate them?

Armin

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Luca Valeri wrote on Apr. 26, 2015 @ 23:49 GMT
Hi Yafet,

your reply on my comment also got lost before I had the chance to watch the video you posted. Maybe you could repost it.

You are right, Heisenberg believed only that energy conservation holds. But it is as right as we cannot have absolute certainity of anything. But also we cannot doubt everything. So if we believe physics is possible, we might believe that the laws of physics are time translation invariant and from that energy will be conserved.

However you might like the film "The Oxford Murders". A film about a serial killing involving a Wittgenstein expert. Where the induction problem plays an eminent role.

Best

Luca

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