If you are aware of an interesting new academic paper (that has been published in a peer-reviewed journal or has appeared on the arXiv), a conference talk (at an official professional scientific meeting), an external blog post (by a professional scientist) or a news item (in the mainstream news media), which you think might make an interesting topic for an FQXi blog post, then please contact us at forums@fqxi.org with a link to the original source and a sentence about why you think that the work is worthy of discussion. Please note that we receive many such suggestions and while we endeavour to respond to them, we may not be able to reply to all suggestions.

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Please also note that we do not accept unsolicited posts and we cannot review, or open new threads for, unsolicited articles or papers. Requests to review or post such materials will not be answered. If you have your own novel physics theory or model, which you would like to post for further discussion among then FQXi community, then please add them directly to the "Alternative Models of Reality" thread, or to the "Alternative Models of Cosmology" thread. Thank you.

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How can mindless mathematical laws give rise to aims and intention?

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**Trick or Truth: The Mysterious Connection Between Physics and Mathematics**

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**How Should Humanity Steer the Future?**

*January 9, 2014 - August 31, 2014*

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Current Essay Contest

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Contest Partners: Fetzer Franklin Fund, and The Peter and Patricia Gruber Foundation

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How can mindless mathematical laws give rise to aims and intention?

Contest Partner: The Peter and Patricia Gruber Fund.

read/discuss • winners

Media Partner: Scientific American

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Which of Our Basic Physical Assumptions Are Wrong?

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RECENT POSTS IN THIS TOPIC

**Ray ASCHHEIM**: *on* 3/13/11 at 21:28pm UTC, wrote Dear Alex, Your essay may be a strong demonstration that Lorentz...

**Hector Zenil**: *on* 3/13/11 at 3:22am UTC, wrote Dear Alex, I'm glad to see you participating in the contest. Interesting...

**Paul Halpern**: *on* 3/11/11 at 15:52pm UTC, wrote Dear Alex, I very much enjoyed your essay, and your analysis of discrete...

**Alexander Lamb**: *on* 2/23/11 at 5:29am UTC, wrote Hi John, Thank you very much for following up on my ideas and writing...

**Alexander Lamb**: *on* 2/23/11 at 4:59am UTC, wrote Hi Honda, Delighted to hear your comment. I actually think that your...

**John Benavides**: *on* 2/21/11 at 11:42am UTC, wrote Dear Alex I read your extraordinary essay. The coincidences with what I am...

**Honda Shing**: *on* 2/21/11 at 7:42am UTC, wrote Dear Alex, Your essay gives me a lot to think about, especially the...

**Alexander Lamb**: *on* 2/14/11 at 16:47pm UTC, wrote **Essay Abstract** We propose that science should proceed under the...

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FQXi FORUM

September 18, 2021

CATEGORY:
Is Reality Digital or Analog? Essay Contest (2010-2011)
[back]

TOPIC: Let's Call the Whole Thing Off/On by Alexander Lamb [refresh]

TOPIC: Let's Call the Whole Thing Off/On by Alexander Lamb [refresh]

We propose that science should proceed under the assumption that Nature is discrete unless discrete models are proved untenable. We outline an argument that explains the reasoning for this position. We also describe examples of simple quantized mechanisms which give reason to believe that the discrete approach can capture all the observed symmetries of nature.

Alexander Lamb is a freelance researcher in computational physics, network science, machine learning, and population modeling. When not conducting research, he works in both business simulation technology and communication skills training for scientists. He teaches improv theater, writes science fiction novels, and speaks internationally on the use of behavioral science and improv for organizational change, innovation, and maximizing creativity in scientific collaboration. Alex obtained his Masters in Artificial Intelligence from Edinburgh, UK, and has ongoing research collaborations with UC Santa Cruz, UC Berkeley, and CNR-ISTI in Pisa, Italy.

Dear Alex,

Your essay gives me a lot to think about, especially the quantum mechanics (section 3.3) part. Simplicity is beauty -- I fully agree with your point about aiming for the simpliest model. Nevertheless, personally, I wish you had predicted a higher chance for continuous models, especially after my essay proposing such a hyper-continuity model. :-)

Honda

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Your essay gives me a lot to think about, especially the quantum mechanics (section 3.3) part. Simplicity is beauty -- I fully agree with your point about aiming for the simpliest model. Nevertheless, personally, I wish you had predicted a higher chance for continuous models, especially after my essay proposing such a hyper-continuity model. :-)

Honda

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Hi Honda,

Delighted to hear your comment. I actually think that your hyper-continuity approach may be an excellent continuum approximation to the kind of structures I'm proposing. I don't know how far you've gone with creating a mathematical formalism for the sort of structures you discuss, but I'd be very interested to see what such a formalism would look like.

Here's an example of the sort of question your approach made me think of, and which I'd love to be able to answer:

If we associate with each point in an infinite set some other points from that same set, what are the requirements that have to be satisfied for some consensus notion of manifoldness to emerge from that set, even if that notion is not shared by every point?

Delighted to hear your comment. I actually think that your hyper-continuity approach may be an excellent continuum approximation to the kind of structures I'm proposing. I don't know how far you've gone with creating a mathematical formalism for the sort of structures you discuss, but I'd be very interested to see what such a formalism would look like.

Here's an example of the sort of question your approach made me think of, and which I'd love to be able to answer:

If we associate with each point in an infinite set some other points from that same set, what are the requirements that have to be satisfied for some consensus notion of manifoldness to emerge from that set, even if that notion is not shared by every point?

Dear Alex

I read your extraordinary essay. The coincidences with what I am trying to propose are so shocking that my legs are trembling. I try to explained why, I think you have the information I am missing. The discrete models that you are proposing are just a partial description of the order I am trying to find, that it explains why we see the properties of the classical world we see. Particularly, the fact of no locality in my approach is expressed by the fact that when we collapse to a classical world we are taking a generic ultrafilter on the order topology which is a global fact. The way you relate the nodes of the graph is just the structure of the order, for example, the Continuum Hypothesis example shows that if the order is not choosen right, we don't get the result in the classical world, this is what it is happening in your models. When you say how we should iterate your models what are you doing is describing how the order topology should behave locally, i.e. you are choosing the ultrafilter.

Finally your concern about the logic we should use it is missing something. We already use classical logic to describe and model quantum reality, it is what the classical approach does, but we can't understand very well quantum reality. What you do is construct your model by try and error and you try to explain why some iterating model gives the result you are looking for and others not. Why I am trying to say is that, if we introduce non classical logics, in my case a intuitionist one, we can explain these phenomena perfectly.

I would like to hear your opinions again.

J.Benavides

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I read your extraordinary essay. The coincidences with what I am trying to propose are so shocking that my legs are trembling. I try to explained why, I think you have the information I am missing. The discrete models that you are proposing are just a partial description of the order I am trying to find, that it explains why we see the properties of the classical world we see. Particularly, the fact of no locality in my approach is expressed by the fact that when we collapse to a classical world we are taking a generic ultrafilter on the order topology which is a global fact. The way you relate the nodes of the graph is just the structure of the order, for example, the Continuum Hypothesis example shows that if the order is not choosen right, we don't get the result in the classical world, this is what it is happening in your models. When you say how we should iterate your models what are you doing is describing how the order topology should behave locally, i.e. you are choosing the ultrafilter.

Finally your concern about the logic we should use it is missing something. We already use classical logic to describe and model quantum reality, it is what the classical approach does, but we can't understand very well quantum reality. What you do is construct your model by try and error and you try to explain why some iterating model gives the result you are looking for and others not. Why I am trying to say is that, if we introduce non classical logics, in my case a intuitionist one, we can explain these phenomena perfectly.

I would like to hear your opinions again.

J.Benavides

report post as inappropriate

Hi John,

Thank you very much for following up on my ideas and writing back. I'm very glad that you find merit in them. Certainly you're right that the kind of models I propose don't make ideal predictions. Each experimental particle only produces a single outcome. I'm also delighted that you're thinking about these topics from the continuum direction, as what my work lacks is a continuum approximation and I'm still struggling to generate one. (Regardless of whether we expect the universe to be continuous or discrete, it still appears continuous at familiar scales and a working physics theory needs to be able to reconcile with that fact in order to be useful!)

One researcher whose work you may be interested in is Andrei Khrennikov. I saw him talk at DICE 2010 and he was very persuasive. He has a working model of QM that is continuous but not dependent on complex numbers. It seems tantalizingly close to the wave expansion model that I employ. I'd be keen to hear your opinion of his approach and wonder if it may be of use to you.

Alex

Thank you very much for following up on my ideas and writing back. I'm very glad that you find merit in them. Certainly you're right that the kind of models I propose don't make ideal predictions. Each experimental particle only produces a single outcome. I'm also delighted that you're thinking about these topics from the continuum direction, as what my work lacks is a continuum approximation and I'm still struggling to generate one. (Regardless of whether we expect the universe to be continuous or discrete, it still appears continuous at familiar scales and a working physics theory needs to be able to reconcile with that fact in order to be useful!)

One researcher whose work you may be interested in is Andrei Khrennikov. I saw him talk at DICE 2010 and he was very persuasive. He has a working model of QM that is continuous but not dependent on complex numbers. It seems tantalizingly close to the wave expansion model that I employ. I'd be keen to hear your opinion of his approach and wonder if it may be of use to you.

Alex

Dear Alex,

I very much enjoyed your essay, and your analysis of discrete models and symmetry groups. Your "Principle of Minimal Complexity" seems useful. A fascinating and thorough approach!

Best wishes,

Paul

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I very much enjoyed your essay, and your analysis of discrete models and symmetry groups. Your "Principle of Minimal Complexity" seems useful. A fascinating and thorough approach!

Best wishes,

Paul

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Dear Alex,

I'm glad to see you participating in the contest. Interesting essay.

Best.

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I'm glad to see you participating in the contest. Interesting essay.

Best.

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Dear Alex,

Your essay may be a strong demonstration that Lorentz invariance is possible in a discrete approach. On some posts, some people just says that lack of Lorentz invariance simply falsify all discrete models. Your work deserve more impact. I hope that here, it will convince our FQXI community that Lorentz invariance is not incompatible with discrete models. We just have to see your youtube videos.

All the best

Ray

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Your essay may be a strong demonstration that Lorentz invariance is possible in a discrete approach. On some posts, some people just says that lack of Lorentz invariance simply falsify all discrete models. Your work deserve more impact. I hope that here, it will convince our FQXI community that Lorentz invariance is not incompatible with discrete models. We just have to see your youtube videos.

All the best

Ray

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