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RECENT POSTS IN THIS TOPIC

**Akinbo Ojo**: *on* 4/19/15 at 13:39pm UTC, wrote Hello Laurence, Well done on your interesting and easy to read essay. You...

**Marc Séguin**: *on* 4/18/15 at 1:23am UTC, wrote Dear Laurence, Thank you for the comments you left on my page. I basically...

**Laurence Hitterdale**: *on* 4/17/15 at 19:43pm UTC, wrote Dear Marc, Thanks for your clear and concise comments. I also appreciate...

**James Hoover**: *on* 4/16/15 at 20:35pm UTC, wrote Laurence, You are open to the MUH thesis and lack confidence that...

**Luca Valeri**: *on* 4/15/15 at 19:28pm UTC, wrote Hi Laurence, I think you wrote a great essay and I must agree with the...

**Alexey/Lev Burov**: *on* 4/14/15 at 4:39am UTC, wrote Dear Laurence, I consider your essay as one of the best in this contest...

**Joe Fisher**: *on* 4/11/15 at 18:53pm UTC, wrote Dear Professor Hitterdale, Thank you for leaving a comment about my essay....

**Laurence Hitterdale**: *on* 4/10/15 at 18:23pm UTC, wrote Dear Mr. Fisher, I appreciate your comments. As you ask, I have read your...

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Why do we remember the past and not the future? Untangling the connections between cause and effect, choice, and entropy.

Philosophers, physicists and neuroscientists discuss how our sense of time’s flow might arise through our interactions with external stimuli—despite suggestions from Einstein's relativity that our perception of the passage of time is an illusion.

A devilish new framework of thermodynamics that focuses on how we observe information could help illuminate our understanding of probability and rewrite quantum theory.

An unusual approach to unifying the laws of physics could solve Hawking's black-hole information paradox—and its predicted gravitational "memory effect" could be picked up by LIGO.

Objective reality, and the laws of physics themselves, emerge from our observations, according to a new framework that turns what we think of as fundamental on its head.

FQXi FORUM

October 15, 2019

CATEGORY:
Trick or Truth Essay Contest (2015)
[back]

TOPIC: Mathematical and Non-Mathematical Aspects of Existence by Laurence Hitterdale [refresh]

TOPIC: Mathematical and Non-Mathematical Aspects of Existence by Laurence Hitterdale [refresh]

Much of existence presents itself as mathematically ordered, but there are also aspects of existence that do not seem open to mathematical treatment in any obvious way. Max Tegmark’s Mathematical Universe Hypothesis (MUH) is a proposal that would, if correct, enable us to overcome this apparent heterogeneity. According to the Mathematical Universe Hypothesis, “Our external physical reality is a mathematical structure.” In this essay some ramifications of the hypothesis are explored, and a few difficulties are presented. The general argument for the MUH takes as its main premise the reality of the external world. This argument, as it stands, does not establish its conclusion. At a more detailed level, when we look at the contents of the world, conscious experience and temporal passage are two phenomena that are important challenges for the MUH. The MUH also has important cosmological consequences. One such consequence is a proposed answer to the question, “Why these particular equations, not others?” The answer inherent in the MUH is that there are no “other” unrealized equations, because, according to what Tegmark has called “mathematical democracy”, all mathematical structures are equally real. We explain how this answer is derived from the MUH. We also discuss two problems for this cosmological application of the MUH. One problem involves the treatment of non-mathematical possibilities, and the other problem concerns the definition of the relevant class of mathematical structures. From these various considerations, we reach two conclusions: at this time our best understanding of existence still retains the heterogeneity of mathematical and non-mathematical aspects; but nonetheless, even if further investigation does not substantiate the full generality of the MUH, such investigation will show that existence is more highly mathematical than we now believe.

Laurence Hitterdale holds a Ph.D. in philosophy from Johns Hopkins in Baltimore, Maryland. Having worked for both business firms and academic institutions, he is currently a professor of information systems at Glendale College in California. His philosophical work is focused on ontology, philosophy of cosmology, and philosophy of mind. In the 2014 FQXi essay contest his essay, “A Rope over an Abyss”, was awarded a special commendation (http://www.fqxi.org/community/essay/winners/2014.1). Additional essays are available at https://philosophicquestions.wordpress.com/.

Hi Laurence,

It's good to see you back, and I think you have the makings of another winner here, in your understated style.

Like you, I accept the ERH as true [with the proviso that it is the*existence* of the external reality that is independent of us, not its local evolution.]

You discuss 'abstract entity' and 'mathematical structure'. Without repeating your...

view entire post

It's good to see you back, and I think you have the makings of another winner here, in your understated style.

Like you, I accept the ERH as true [with the proviso that it is the

You discuss 'abstract entity' and 'mathematical structure'. Without repeating your...

view entire post

report post as inappropriate

Dear Laurence,

An insightful essay and a pleasure to read. I think the answer is that Existence is infinite, therefore we cannot limit it by our own finite laws. Any infinite laws must content their own contradictions and deep paradoxes like what you wrote: " We began with the problem that existence, as it presents itself to us, appears to have both mathematical and non-mathematical aspects." Bravo.

Truly,

Leo KoGuan

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An insightful essay and a pleasure to read. I think the answer is that Existence is infinite, therefore we cannot limit it by our own finite laws. Any infinite laws must content their own contradictions and deep paradoxes like what you wrote: " We began with the problem that existence, as it presents itself to us, appears to have both mathematical and non-mathematical aspects." Bravo.

Truly,

Leo KoGuan

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Dear Laurence,

I found your essay very interesting. Reading it, a question came up to me.

In your essay, you defined a mathematical structure as a set of abstract entities with relations between them. Then you explain that entities are defined by their role in the network of relations. As you indicate, there is a difference between intrinsic irrelevance and no intrinsic properties of entities. If my understanding is right, in the first case, entities do not exist and in the second case, they exist but carry null information (outside the relation). Is my understanding right?

My question might be stupid but how can locality be achieved with only a set of relation?

Regards,

Christophe

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I found your essay very interesting. Reading it, a question came up to me.

In your essay, you defined a mathematical structure as a set of abstract entities with relations between them. Then you explain that entities are defined by their role in the network of relations. As you indicate, there is a difference between intrinsic irrelevance and no intrinsic properties of entities. If my understanding is right, in the first case, entities do not exist and in the second case, they exist but carry null information (outside the relation). Is my understanding right?

My question might be stupid but how can locality be achieved with only a set of relation?

Regards,

Christophe

report post as inappropriate

Dear Laurence,

While I agree on your basic considerations that the flow of time and consciousness are not mathematical, I think it is a pity that you focused most of your writings on the criticism of a specific view as if it was the mainstream and necessary point of reference with respect to which any other view would have to be defined. Indeed I think it only accidentally happened to be...

view entire post

While I agree on your basic considerations that the flow of time and consciousness are not mathematical, I think it is a pity that you focused most of your writings on the criticism of a specific view as if it was the mainstream and necessary point of reference with respect to which any other view would have to be defined. Indeed I think it only accidentally happened to be...

view entire post

report post as inappropriate

Hi Sylvain,

Thank you for your extended comments, in which you discuss a number of topics.

You are correct in pointing out that I do give considerable attention to a particular view on the main subject which I address. I wanted to focus on the ontology of the relationship between mathematical reality and physical reality. I did not want to focus on mathematics and physics as human activities, nor did I want to discuss questions primarily about the human understanding or experience in these two fields. Given my interest in objective reality, I thought that I could not present my own views without taking notice of a position on the very topic of interest to me, when that position has been worked out in some detail, and when that position has also been well-regarded and the subject of considerable interest and attention. I could have organized my writing differently, and I appreciate the fact that you argue that I should have done things differently. Nonetheless, because of the reason I have stated here, I took the approach that I did.

As you also state, I do not claim to have presented a conclusive solution to the problem of the relationship between the mathematical and non-mathematical aspects of reality. In this essay I try to argue for part of the answer. In particular, I contend that it is a mistake to hold that reality is wholly mathematical.

You also raise important issues about the nature of consciousness and the relation of conscious subjects to external reality. Since this is not the general topic for the many essays in this contest, I will suggest that we leave the problems of consciousness for another time.

Laurence Hitterdale

Thank you for your extended comments, in which you discuss a number of topics.

You are correct in pointing out that I do give considerable attention to a particular view on the main subject which I address. I wanted to focus on the ontology of the relationship between mathematical reality and physical reality. I did not want to focus on mathematics and physics as human activities, nor did I want to discuss questions primarily about the human understanding or experience in these two fields. Given my interest in objective reality, I thought that I could not present my own views without taking notice of a position on the very topic of interest to me, when that position has been worked out in some detail, and when that position has also been well-regarded and the subject of considerable interest and attention. I could have organized my writing differently, and I appreciate the fact that you argue that I should have done things differently. Nonetheless, because of the reason I have stated here, I took the approach that I did.

As you also state, I do not claim to have presented a conclusive solution to the problem of the relationship between the mathematical and non-mathematical aspects of reality. In this essay I try to argue for part of the answer. In particular, I contend that it is a mistake to hold that reality is wholly mathematical.

You also raise important issues about the nature of consciousness and the relation of conscious subjects to external reality. Since this is not the general topic for the many essays in this contest, I will suggest that we leave the problems of consciousness for another time.

Laurence Hitterdale

Dear Dr. Hitterdale,

You wrote: “The apparently non-mathematical aspects of reality have received perhaps less attention.”

Perhaps you might care to read my non-mathematical assessment of how the real Universe is occurring.

This is my single unified theorem of how the real Universe is occurring: Newton was wrong about abstract gravity; Einstein was wrong about abstract...

view entire post

You wrote: “The apparently non-mathematical aspects of reality have received perhaps less attention.”

Perhaps you might care to read my non-mathematical assessment of how the real Universe is occurring.

This is my single unified theorem of how the real Universe is occurring: Newton was wrong about abstract gravity; Einstein was wrong about abstract...

view entire post

report post as inappropriate

Dear Laurence,

I agree with you that "our worldview would be greatly unified if we should come to understand that everything in existence can be fully described in mathematical terms." That's why in my essay I try to defend the possibility that all that exists is made of abstract (mathematical) structures. But I think that your argument about the (possibly) non-mathematical nature of the flow of time and consciousness is an important one. I like how you differentiate between "instrumental" abstractness as intrinsic irrelevance of what a structure is made of, and "absolute" abstractness as having no intrinsic properties whatsoever.

I agree with you when you say that "if both temporal passage and conscious experience are nothing but mathematical structures, they are peculiar structures which somehow are able to be something quite unlike the other members of the mathematical realm", but unlike you, I think that this is a real possibility.

Talking about the Mathematical Universe Hypothesis, you write: "Once the equal reality of all mathematical structures is asserted, the issue arises whether there is any reason not to admit also the reality of non-mathematical possibilities." I personally think that the MUH implies the reality of all structures (what I call the Maxiverse, a view that is close to David Lewis' modal realism), but I would say that ultimately, all structures are mathematical. But, as you rightly point out, what do we mean exactly when we say "mathematical structure"?

One thing is certain, I wholeheartedly agree with your conclusion: "The issue, though obviously difficult and unclear, is well worth further thought."

Strangely, your excellent essay has been a bit forgotten so far in the competition, and I hope bumping it higher will make it more noticeable. Good luck!

Marc

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I agree with you that "our worldview would be greatly unified if we should come to understand that everything in existence can be fully described in mathematical terms." That's why in my essay I try to defend the possibility that all that exists is made of abstract (mathematical) structures. But I think that your argument about the (possibly) non-mathematical nature of the flow of time and consciousness is an important one. I like how you differentiate between "instrumental" abstractness as intrinsic irrelevance of what a structure is made of, and "absolute" abstractness as having no intrinsic properties whatsoever.

I agree with you when you say that "if both temporal passage and conscious experience are nothing but mathematical structures, they are peculiar structures which somehow are able to be something quite unlike the other members of the mathematical realm", but unlike you, I think that this is a real possibility.

Talking about the Mathematical Universe Hypothesis, you write: "Once the equal reality of all mathematical structures is asserted, the issue arises whether there is any reason not to admit also the reality of non-mathematical possibilities." I personally think that the MUH implies the reality of all structures (what I call the Maxiverse, a view that is close to David Lewis' modal realism), but I would say that ultimately, all structures are mathematical. But, as you rightly point out, what do we mean exactly when we say "mathematical structure"?

One thing is certain, I wholeheartedly agree with your conclusion: "The issue, though obviously difficult and unclear, is well worth further thought."

Strangely, your excellent essay has been a bit forgotten so far in the competition, and I hope bumping it higher will make it more noticeable. Good luck!

Marc

report post as inappropriate

Dear Marc,

Thanks for your clear and concise comments. I also appreciate your kind words. After reading your essay and reviewing some of the exchanges on your forum page, I find that my additional reflections fit better as comments on your essay than as responses to your comments here. Accordingly, I have added some remarks to the discussion on your forum page.

Best wishes,

Laurence Hitterdale

Thanks for your clear and concise comments. I also appreciate your kind words. After reading your essay and reviewing some of the exchanges on your forum page, I find that my additional reflections fit better as comments on your essay than as responses to your comments here. Accordingly, I have added some remarks to the discussion on your forum page.

Best wishes,

Laurence Hitterdale

Dear Laurence,

Thank you for the comments you left on my page. I basically agree with everything you mentioned. We obviously have been thinking a lot of the same thoughts about the implications of mathematical existence!

All the best,

Marc

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Thank you for the comments you left on my page. I basically agree with everything you mentioned. We obviously have been thinking a lot of the same thoughts about the implications of mathematical existence!

All the best,

Marc

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Dear Laurence,

Thank you for your interesting and inspiring essay where you touch very important issues connected to MUH. In the conclusion you claim: “I have argued that we cannot yet regard the hypothesis as successful. We should not, however, suppose that we have reached the end of the story” … I fully agree. And in another place: “It is not clear how the concept of mathematical...

view entire post

Thank you for your interesting and inspiring essay where you touch very important issues connected to MUH. In the conclusion you claim: “I have argued that we cannot yet regard the hypothesis as successful. We should not, however, suppose that we have reached the end of the story” … I fully agree. And in another place: “It is not clear how the concept of mathematical...

view entire post

report post as inappropriate

Dear Dr. Hitterdale,

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

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I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

report post as inappropriate

Dear Laurence,

I liked your essay, and I found it very well written, well documented, containing interesting insights. It takes a lucid look at the MUH, with its goods and possible shortcomings, especially in connection with consciousness and passage of time.

Best wishes,

Cristi Stoica

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I liked your essay, and I found it very well written, well documented, containing interesting insights. It takes a lucid look at the MUH, with its goods and possible shortcomings, especially in connection with consciousness and passage of time.

Best wishes,

Cristi Stoica

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Dear Professor Hitterdale,

Thank you for leaving a comment about my essay.

Corporate Communism has corrupted all aspects of American life. Reality is free and accessible for everybody. Scientific projects are extremely expensive and obtainable by the fortunate few. Providing mathematicians continue to provide seeming logical hints for the existence of the big bang creation of the universe that allows the physicists to borrow billions of dollars to seek alien life and attempt to build time travelling machines, the relationship between mathematics and physics will be very close and comfortable.

Joe Fisher

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Thank you for leaving a comment about my essay.

Corporate Communism has corrupted all aspects of American life. Reality is free and accessible for everybody. Scientific projects are extremely expensive and obtainable by the fortunate few. Providing mathematicians continue to provide seeming logical hints for the existence of the big bang creation of the universe that allows the physicists to borrow billions of dollars to seek alien life and attempt to build time travelling machines, the relationship between mathematics and physics will be very close and comfortable.

Joe Fisher

report post as inappropriate

Dear Laurence,

I consider your essay as one of the best in this contest and give you my highest rating. I like your analysis of Tegmark's MUH implications and problems, and essentially agree with you in everything except one important point. Namely, you write

"Less clear are the prospects for a suitably defined totality of logical possibilities (i.e., the Level IV multiverse or something similar). If such an all-encompassing totality is genuinely real, then it might in some sense provide an ultimate explanation for existence."

I do not share your 'if'. In our essay we are refuting the possibility of that sort of multiverse. We are doing this on the grounds of the logical simplicity, large scale and high precision of the already discovered laws of nature.

Best regards and good luck!

Alexey Burov.

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I consider your essay as one of the best in this contest and give you my highest rating. I like your analysis of Tegmark's MUH implications and problems, and essentially agree with you in everything except one important point. Namely, you write

"Less clear are the prospects for a suitably defined totality of logical possibilities (i.e., the Level IV multiverse or something similar). If such an all-encompassing totality is genuinely real, then it might in some sense provide an ultimate explanation for existence."

I do not share your 'if'. In our essay we are refuting the possibility of that sort of multiverse. We are doing this on the grounds of the logical simplicity, large scale and high precision of the already discovered laws of nature.

Best regards and good luck!

Alexey Burov.

report post as inappropriate

Hi Laurence,

I think you wrote a great essay and I must agree with the comment of Sylvain Poirier that it is a petty that you focused so much in discussion of Tegmarks MUH and did not share more of your own view on how and why mathematics is so effective in physics.

However you have done your criticism so well, that it was a joy to read. The argumentation was very coherent and careful. You dived into the swamp of ontology without going under. Congrats.

In my essay I tried to avoid to enter in a ontological debate and focused on what we can know.

Best regards,

Luca

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I think you wrote a great essay and I must agree with the comment of Sylvain Poirier that it is a petty that you focused so much in discussion of Tegmarks MUH and did not share more of your own view on how and why mathematics is so effective in physics.

However you have done your criticism so well, that it was a joy to read. The argumentation was very coherent and careful. You dived into the swamp of ontology without going under. Congrats.

In my essay I tried to avoid to enter in a ontological debate and focused on what we can know.

Best regards,

Luca

report post as inappropriate

Laurence,

You are open to the MUH thesis and lack confidence that progressive discoveries will realize a thoroughly mathematical nature.

I am not an advocate of MUH but I appreciate your incisive discussion. I realize that arguments against math's unreasonable effectiveness, which I suppose tend to support MUH, cite failures of math models to predict weather unfairly. So many things that math models depend on our understanding of complex forces and our ability to model unseen or multitudinous variables.

My essay concentrates on the pedestrian, the connections of mind, math, and physics in achieving stellar things: quantum biology epiphanies, DNA mapping, and BB simulations: http://fqxi.org/community/forum/topic/2345.

Thanks for sharing your ideas.

Jim

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You are open to the MUH thesis and lack confidence that progressive discoveries will realize a thoroughly mathematical nature.

I am not an advocate of MUH but I appreciate your incisive discussion. I realize that arguments against math's unreasonable effectiveness, which I suppose tend to support MUH, cite failures of math models to predict weather unfairly. So many things that math models depend on our understanding of complex forces and our ability to model unseen or multitudinous variables.

My essay concentrates on the pedestrian, the connections of mind, math, and physics in achieving stellar things: quantum biology epiphanies, DNA mapping, and BB simulations: http://fqxi.org/community/forum/topic/2345.

Thanks for sharing your ideas.

Jim

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Hello Laurence,

Well done on your interesting and easy to read essay. You are correct when you say,*"Existence perplexes us in various ways."* . I have just one question to ask you: **Can what exists perish, or is it eternally existing?**

After contemplating an answer, if you still have time before the competition ends, you may read my essay, where I give my perspective.

Best regards,

Akinbo

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Well done on your interesting and easy to read essay. You are correct when you say,

After contemplating an answer, if you still have time before the competition ends, you may read my essay, where I give my perspective.

Best regards,

Akinbo

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