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.

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.

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.

Contests Home

Previous Contests

**What Is “Fundamental”**

*October 28, 2017 to January 22, 2018*

*Sponsored by the Fetzer Franklin Fund and The Peter & Patricia Gruber Foundation*

read/discuss • winners

**Wandering Towards a Goal**

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

*December 2, 2016 to March 3, 2017*

Contest Partner: The Peter and Patricia Gruber Fund.

read/discuss • winners

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

*Contest Partners: Nanotronics Imaging, The Peter and Patricia Gruber Foundation, and The John Templeton Foundation*

Media Partner: Scientific American

read/discuss • winners

**How Should Humanity Steer the Future?**

*January 9, 2014 - August 31, 2014*

*Contest Partners: Jaan Tallinn, The Peter and Patricia Gruber Foundation, The John Templeton Foundation, and Scientific American*

read/discuss • winners

**It From Bit or Bit From It**

*March 25 - June 28, 2013*

*Contest Partners: The Gruber Foundation, J. Templeton Foundation, and Scientific American*

read/discuss • winners

**Questioning the Foundations**

Which of Our Basic Physical Assumptions Are Wrong?

*May 24 - August 31, 2012*

*Contest Partners: The Peter and Patricia Gruber Foundation, SubMeta, and Scientific American*

read/discuss • winners

**Is Reality Digital or Analog?**

*November 2010 - February 2011*

*Contest Partners: The Peter and Patricia Gruber Foundation and Scientific American*

read/discuss • winners

**What's Ultimately Possible in Physics?**

*May - October 2009*

*Contest Partners: Astrid and Bruce McWilliams*

read/discuss • winners

**The Nature of Time**

*August - December 2008*

read/discuss • winners

Previous Contests

read/discuss • winners

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

read/discuss • winners

read/discuss • winners

read/discuss • winners

Which of Our Basic Physical Assumptions Are Wrong?

read/discuss • winners

read/discuss • winners

read/discuss • winners

read/discuss • winners

Forum Home

Introduction

Terms of Use

RSS feed | RSS help

Introduction

Terms of Use

*Posts by the author are highlighted in orange; posts by FQXi Members are highlighted in blue.*

RSS feed | RSS help

RECENT POSTS IN THIS TOPIC

**Robert Paster**: *on* 3/5/11 at 22:44pm UTC, wrote I am pleased to see labeled as "sour grapes" the frequent rejection by...

**Ulla Mattfolk**: *on* 3/5/11 at 18:08pm UTC, wrote I think this is mainly a question of the formation of gates and borders...

**basudeba**: *on* 3/4/11 at 1:22am UTC, wrote Dear Sir, We do not understand why mathematics should be made...

**Robert Paster**: *on* 2/23/11 at 14:46pm UTC, wrote From a purely mathematical point of view, all mathematicians accept that...

**Robert Paster**: *on* 2/21/11 at 20:39pm UTC, wrote Thank you for your continuing commentary. Here are my thoughts: (1) I'm...

**Ulla Mattfolk**: *on* 2/20/11 at 16:53pm UTC, wrote http://www.youtube.com/watch?feature=player_embedded&v=aj4FozCSg8g A video...

**Anonymous**: *on* 2/17/11 at 19:31pm UTC, wrote Robert, I think it is too simplistic to say 'life is negentropic',that was...

**Robert Paster**: *on* 2/17/11 at 16:39pm UTC, wrote Thank you, Georgina, for your careful reading of my essay and for your...

RECENT FORUM POSTS

**Steve Dufourny**: "Hi Eckard,you seems persuaded by your Words and thoughts.I don t understand..."
*in* First Things First: The...

**Eckard Blumschein**: "In Darwinism/Weismannism there is no first cause, just a causal chain...."
*in* First Things First: The...

**Steve Agnew**: "There are some questions that do not seem to have answers in the classical..."
*in* Schrödinger’s Zombie:...

**Steve Agnew**: "Yes, there are two very different narratives. The classical narrative works..."
*in* Schrödinger’s Zombie:...

**Steve Dufourny**: "lol no indeed it is not a lot,like I said I liked your general ideas.I have..."
*in* The Demon in the Machine...

**Steve Agnew**: "There are three assumptions...is that a lot? The aether particle mass, the..."
*in* The Demon in the Machine...

RECENT ARTICLES

*click titles to read articles*

**First Things First: The Physics of Causality**

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

**Can Time Be Saved From Physics?**

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.

**Thermo-Demonics**

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

**Gravity's Residue**

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.

**Could Mind Forge the Universe?**

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.

RECENT FORUM POSTS

RECENT ARTICLES

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 14, 2019

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

TOPIC: Reality: Analog and Digital at the Same Time by Robert Paster [refresh]

TOPIC: Reality: Analog and Digital at the Same Time by Robert Paster [refresh]

Reality is always simultaneously analog and digital. This is best understood by using an established branch of mathematics, adelic mathematics, which requires any object or phenomenon to always be understood using both real mathematics (analog) and a specific form of discrete mathematics (digital mathematics) called p-adic mathematics. The author has reviewed theories of physics that use adelic mathematics and focuses on one, topological geometrodynamics, that creates a rich theory of particle physics, cosmology, biophysics, and cognition. This paper explains why a purely mathematical argument leads to the use of adelic mathematics, discusses this in the context of epistemology and cognitive science, then shows how topological geometrodynamics applies adelic mathematic to a reconfigured model of space and time.

Robert Paster is an independent science researcher who recently completed an extensive study, summarized in the book New Physics and the Mind, of theories of physics that reject mainstream approaches, including string theory. This book proposes criteria for selecting the best of these theories, which is one centered on adelic mathematics. Mr. Paster is currently developing this theory’s application to the mind, which will be published as a follow-up book, Digital Mind Math. Mr. Paster’s academic background includes degrees in mathematics from M.I.T. and education from Harvard.

Hello dear Robert Paster,

One of my favorites.

I like the rationalism like all rationalists of course.

The sorting seems on the road .

Program ....observation/experimentation.... observer experimentator....object...implying MODELS.

Method of reasoning and experimentation.........observation and description.

Comparative developments....determinism...

view entire post

One of my favorites.

I like the rationalism like all rationalists of course.

The sorting seems on the road .

Program ....observation/experimentation.... observer experimentator....object...implying MODELS.

Method of reasoning and experimentation.........observation and description.

Comparative developments....determinism...

view entire post

report post as inappropriate

What is the conclusion in your essay? There is no clear statement of problem from which you progress. There is only an assertion you place before the reader.

So, now what?

Its not clear to me why you were granted any degree of recognition as a 'winner' in this essay contest, aside from your rather scant references to technical proofs for you claim.

Aside from that, I am...

view entire post

So, now what?

Its not clear to me why you were granted any degree of recognition as a 'winner' in this essay contest, aside from your rather scant references to technical proofs for you claim.

Aside from that, I am...

view entire post

report post as inappropriate

Thank you for taking the time to read my essay and write down your response.

In terms of the conclusion in my essay, perhaps the very nature of the contest question results in a specific conclusion being a bit difficult to discern. I am claiming, in response to the contest question, that reality is both analog and digital, rather than just one or the other.

I hope you have the opportunity to read about adelic physics, either in my research summary New Physics and the Mind, or by reading Dr. Pitkanen's work directly (topological geometrodynamics).

My own personal interest lies in creating a Digital Mind Math that can be deployed for artifical intelligence and computer mathematics applications. This turns out to be quite a challenge, due in part to the complexity of the literature on p-adic mathematics. My current efforts involve original writing to create an accessible understanding of p-adic math at an elementary, intuitive level, which to my surprise has never been done.

In terms of the conclusion in my essay, perhaps the very nature of the contest question results in a specific conclusion being a bit difficult to discern. I am claiming, in response to the contest question, that reality is both analog and digital, rather than just one or the other.

I hope you have the opportunity to read about adelic physics, either in my research summary New Physics and the Mind, or by reading Dr. Pitkanen's work directly (topological geometrodynamics).

My own personal interest lies in creating a Digital Mind Math that can be deployed for artifical intelligence and computer mathematics applications. This turns out to be quite a challenge, due in part to the complexity of the literature on p-adic mathematics. My current efforts involve original writing to create an accessible understanding of p-adic math at an elementary, intuitive level, which to my surprise has never been done.

Hey

Could the p-adic shift be compared to a 'quantum jump' in your mind. That is something like an excitation and needs energy? Could this p-adicity be like the descreateness and on-shell characterof reactions and matter?

I have read Pitkänens works very much. They are the main inspirational texts for me, as I look mostly on biology. Bodily memory, emotions, magnetic body etc. are all characters of LIVING matter, directed by p-adicity?

In what way is ordinary matter and living matter different, according to your essay? I have an essay on living matter.

Ulla.

report post as inappropriate

Could the p-adic shift be compared to a 'quantum jump' in your mind. That is something like an excitation and needs energy? Could this p-adicity be like the descreateness and on-shell characterof reactions and matter?

I have read Pitkänens works very much. They are the main inspirational texts for me, as I look mostly on biology. Bodily memory, emotions, magnetic body etc. are all characters of LIVING matter, directed by p-adicity?

In what way is ordinary matter and living matter different, according to your essay? I have an essay on living matter.

Ulla.

report post as inappropriate

I'm always glad to hear from others who are studying Dr. Pitkanen's brilliant work on TGD topological geometrodynamics. Pitkanen writes quite a bit about "common rationals," meaning the rational numbers that are the common basis of the real representation and the p-adic representation. My own current applications of TGD are specifically about cognition, the mind, consciousness, and I'm currently working with a specific framework that may be a bit different than Pitkanen's much broader framework which applies not only to cognition but also to biophysics, particle physics, and cosmology.

Specifically, my current thinking is: Thinking is digital. Thoughts are analog.

By this I mean that the process of thinking takes place by a p-adic analysis, starting from the previous thought, of every possible next thought. Then, guided by the negentropy maximization principle, the selected next thought is momentarily experienced in a real (analog) way.

The amazing thing about p-adic mathematics is the extraordinarily large mathematical space in which it operates. This is because real nathematics achieves a mathematical space that is both complete and closed in such an easier way than p-adic mathematics does. In particular, Ostrowski says there are two ways (real and p-adic) to complete the rationals. Real numbers then form a closed number system quite quickly: with only a quadratic equation stated in real terms, we get the set of complex numbers, which is both complete and closed. On the other hand, it's an infinite-degree p-adic equation needed to create the closed set QbarP, which unfortunately is no longer complete. It is only the much larger set of numbers called omega that both completes and closes the p-adic numbers. It is p-adic numbers' operating within this extraordinarily large set of numbers that gives p-adic numbers the power to efficiently model the mind. (The other needed step is TGD's reconfiguration of spacetime to permit efficient p-adic modeling.)

I terms of ordinary matter vs. living matter, my own thinking is based on what seems to me to be a pretty convergent set of ideas: (1) TGD's negentropy maximization principle, (2) Piaget's equilibration, (3) the Chilean biologists' autopoiesis, (4) the concept of self-organizing systems. All these concepts have in common that what defines life is the tendency to fight thermodynamics' relentless increase in entropy.

Specifically, my current thinking is: Thinking is digital. Thoughts are analog.

By this I mean that the process of thinking takes place by a p-adic analysis, starting from the previous thought, of every possible next thought. Then, guided by the negentropy maximization principle, the selected next thought is momentarily experienced in a real (analog) way.

The amazing thing about p-adic mathematics is the extraordinarily large mathematical space in which it operates. This is because real nathematics achieves a mathematical space that is both complete and closed in such an easier way than p-adic mathematics does. In particular, Ostrowski says there are two ways (real and p-adic) to complete the rationals. Real numbers then form a closed number system quite quickly: with only a quadratic equation stated in real terms, we get the set of complex numbers, which is both complete and closed. On the other hand, it's an infinite-degree p-adic equation needed to create the closed set QbarP, which unfortunately is no longer complete. It is only the much larger set of numbers called omega that both completes and closes the p-adic numbers. It is p-adic numbers' operating within this extraordinarily large set of numbers that gives p-adic numbers the power to efficiently model the mind. (The other needed step is TGD's reconfiguration of spacetime to permit efficient p-adic modeling.)

I terms of ordinary matter vs. living matter, my own thinking is based on what seems to me to be a pretty convergent set of ideas: (1) TGD's negentropy maximization principle, (2) Piaget's equilibration, (3) the Chilean biologists' autopoiesis, (4) the concept of self-organizing systems. All these concepts have in common that what defines life is the tendency to fight thermodynamics' relentless increase in entropy.

Dear Robert,

I wanted to let you know that I have read your essay. As someone without a mathematical background I found a lot of the content to be discussing a subject of which I am largely ignorant.So bear that in mind when reading my comments. They are merely a reflection of my personal reaction and opinions.

It is a very different approach to the essay question from many others I have read. So you get some credit for originality. I do think that considering the mathematical processing of information by the mind is a worthwhile endeavor. I suspect that it is more complex and less precise than many mathematicians and physicists with mathematical viewpoint might care to admit.... The human organism is not a mere computer and does not merely process information input faithfully but also creates novel information and discards and amplifies information. As a computer or calculator would never do. There is filtering and thresholds of information flow that determine whether a particular input ever reaches the point of being processed into conscious awareness. I also said something similar to Julian Barbour.I do not know how much this is reflected in the mathematical models you are discussing.

I found there was insufficient information to assist the mathematically ignorant before casting them adrift in an alien world. The conclusion was similarly abrupt. Like suddenly and without warning hitting a rock in the ocean. You also appear to be considering reality to be only that which is experienced by the mind.Which does not take into account external reality. This may be due to a denial of external realism but you do not say as much.This means that your consideration of whether reality is analogue or digital is only a partial consideration of the subject.

I appreciate that an essay such as this is not written for the likes of me. I hope that you manage to find lots of like minded readers, who will appreciate what you are saying and the style of presentation, and can discuss the body of the work and its merit as I am unable to do. Good luck, Georgina.

report post as inappropriate

I wanted to let you know that I have read your essay. As someone without a mathematical background I found a lot of the content to be discussing a subject of which I am largely ignorant.So bear that in mind when reading my comments. They are merely a reflection of my personal reaction and opinions.

It is a very different approach to the essay question from many others I have read. So you get some credit for originality. I do think that considering the mathematical processing of information by the mind is a worthwhile endeavor. I suspect that it is more complex and less precise than many mathematicians and physicists with mathematical viewpoint might care to admit.... The human organism is not a mere computer and does not merely process information input faithfully but also creates novel information and discards and amplifies information. As a computer or calculator would never do. There is filtering and thresholds of information flow that determine whether a particular input ever reaches the point of being processed into conscious awareness. I also said something similar to Julian Barbour.I do not know how much this is reflected in the mathematical models you are discussing.

I found there was insufficient information to assist the mathematically ignorant before casting them adrift in an alien world. The conclusion was similarly abrupt. Like suddenly and without warning hitting a rock in the ocean. You also appear to be considering reality to be only that which is experienced by the mind.Which does not take into account external reality. This may be due to a denial of external realism but you do not say as much.This means that your consideration of whether reality is analogue or digital is only a partial consideration of the subject.

I appreciate that an essay such as this is not written for the likes of me. I hope that you manage to find lots of like minded readers, who will appreciate what you are saying and the style of presentation, and can discuss the body of the work and its merit as I am unable to do. Good luck, Georgina.

report post as inappropriate

Thank you, Georgina, for your careful reading of my essay and for your thoughtful comments.

The psychological theories that I am studying suggest p-adic mathematics as our first mathematics and our earliest technique for learning about the world. For this reason, I was surprised that I have not been able to find a satisfactory simplified, intuitive explanation of p-adic mathematics. Therefore, I am attempting to create this elementary explanation, which makes it both informative and disappointing that the essay I submitted did not accomplish this for you. What it tells me is that I need to present the concepts of p-adic mathematics even more slowly and simply, so thanks again for that feedback.

The view expressed in the essay is definitely that reality is both analog and digital, not just that this is how the mind analyzes reality. This is because all reality is adelic. All mathematics is adelic. Rational numbers are incomplete, and there are two and only two ways to complete the rational numbers (real mathematics and p-adic mathematics). No one can claim that reality's existence is only in the realm of rational numbers. This would be unsatisfactory and incomplete. Reality needs a complete realm, and there are two and only two complete realms, analog and digital, real and p-adic. This is a point about external reality, not just about how the mind understands reality.

I'm a bit surprised by some of the skills you say a computer or calculator would never do, such as discarding, amplifying, filtering based on threshholds of information flow. These skills are all routinely performed by any of today's mechanisms of artificial intelligence, and my thesis is that p-adic mathematics (applied to TGD's reconfigured spacetime) does this better than today's real-mathematics-based A.I. does this. Did you watch Watson compete against humans in Jeopardy? For every answer, the screen displayed the results of Watson's filtering and discarding, showing a probabilistic threshhold analysis that told Watson whether to ring in or not. Watson's top three answers were displayed, with a defined threshhold against which each answer was probabilisticaly measured.

The psychological theories that I am studying suggest p-adic mathematics as our first mathematics and our earliest technique for learning about the world. For this reason, I was surprised that I have not been able to find a satisfactory simplified, intuitive explanation of p-adic mathematics. Therefore, I am attempting to create this elementary explanation, which makes it both informative and disappointing that the essay I submitted did not accomplish this for you. What it tells me is that I need to present the concepts of p-adic mathematics even more slowly and simply, so thanks again for that feedback.

The view expressed in the essay is definitely that reality is both analog and digital, not just that this is how the mind analyzes reality. This is because all reality is adelic. All mathematics is adelic. Rational numbers are incomplete, and there are two and only two ways to complete the rational numbers (real mathematics and p-adic mathematics). No one can claim that reality's existence is only in the realm of rational numbers. This would be unsatisfactory and incomplete. Reality needs a complete realm, and there are two and only two complete realms, analog and digital, real and p-adic. This is a point about external reality, not just about how the mind understands reality.

I'm a bit surprised by some of the skills you say a computer or calculator would never do, such as discarding, amplifying, filtering based on threshholds of information flow. These skills are all routinely performed by any of today's mechanisms of artificial intelligence, and my thesis is that p-adic mathematics (applied to TGD's reconfigured spacetime) does this better than today's real-mathematics-based A.I. does this. Did you watch Watson compete against humans in Jeopardy? For every answer, the screen displayed the results of Watson's filtering and discarding, showing a probabilistic threshhold analysis that told Watson whether to ring in or not. Watson's top three answers were displayed, with a defined threshhold against which each answer was probabilisticaly measured.

From a purely mathematical point of view, all mathematicians accept that rational numbers do not form a satisfactory number system because they (1) are not complete, and (2) are not closed.

There are two and only two ways to complete the rational numbers: real numbers and p-adic numbers.

This is what motivates adelic mathematics, the mathematics that insists we always look at physical phenomena, at reality, as both analog (real) and digital (p-adic). This is why purely mathematical reasoning leads to the conclusion that reality is always simultaneously analog and digital. This is a point about reality (not a point only about cognition or the mind).

Once you close both sets of numbers, you see how appealing it is for the mind to be p-adic-based. Closing the real numbers (as complex numbers) is very straightforward. But closing p-adic numbers (as omega) creates a great numerical space in which each p-adic number in omega represents an enormous amount of information. This is why the mind has adapted to use p-adic mathematics as the mathematics of cognition, best understood by applying p-adic mathematics to topological geometrodynamics' reconfiguration of spacetime.

But the underlying reality is adelic, that is, always simultaneously analog and digital.

There are two and only two ways to complete the rational numbers: real numbers and p-adic numbers.

This is what motivates adelic mathematics, the mathematics that insists we always look at physical phenomena, at reality, as both analog (real) and digital (p-adic). This is why purely mathematical reasoning leads to the conclusion that reality is always simultaneously analog and digital. This is a point about reality (not a point only about cognition or the mind).

Once you close both sets of numbers, you see how appealing it is for the mind to be p-adic-based. Closing the real numbers (as complex numbers) is very straightforward. But closing p-adic numbers (as omega) creates a great numerical space in which each p-adic number in omega represents an enormous amount of information. This is why the mind has adapted to use p-adic mathematics as the mathematics of cognition, best understood by applying p-adic mathematics to topological geometrodynamics' reconfiguration of spacetime.

But the underlying reality is adelic, that is, always simultaneously analog and digital.

http://www.youtube.com/watch?feature=player_embedded&v=aj4Fo

zCSg8g

A video with l-adic primes and partionic number tree.

report post as inappropriate

zCSg8g

A video with l-adic primes and partionic number tree.

report post as inappropriate

Dear Sir,

We do not understand why mathematics should be made incomprehensible in stead of being scientific and rational.

Numbers are a property of all substances by which we distinguish between similars. Distinguishing between similars is a matter of perception at “here-now”. When there is the perception of an object without similars, it is one. Depending upon the repetition of...

view entire post

We do not understand why mathematics should be made incomprehensible in stead of being scientific and rational.

Numbers are a property of all substances by which we distinguish between similars. Distinguishing between similars is a matter of perception at “here-now”. When there is the perception of an object without similars, it is one. Depending upon the repetition of...

view entire post

report post as inappropriate

I think this is mainly a question of the formation of gates and borders that creates forms that creates structures.

report post as inappropriate

report post as inappropriate

I am pleased to see labeled as "sour grapes" the frequent rejection by academic physicists of any role for the mind in physics. Unfortunately, I find that physics and the mind is seen by many physicists as a rogue inquiry. I have, however, uncovered a couple hundred physicists' theories of the mind and summarized them in my book New Physics and the Mind.

My primary interest is "digital mind math," a mathematical model of how we think, using a specific form of discrete mathematics, not binary, but p-adic. Ulla Marianne Mattfolk's comment regarding "the formation of gates and borders that create structures" is a nice description of how p-adic mathematics works. It is ultrametric (non-Archimedean) mathematics, and many statements about p-adic mathematics would be absurd if they were made about real mathematics. For example, the meaning of the digits in a p-adic number is quite different than the meaning of the digits in a real number. Also, the size of a p-adic number does not depend on what the specific digits are, but instead is determined by the count of the number of digits to the right of the decimal point for a particular value of p.

And don't forget the purely mathematical argument: there are two and only two ways to complete the rational numbers, real and p-adic. This gives great intuitive weight to the concept that we should be looking to p-adic mathematics as a critical analytic technique.

A good starting point is to consider how much artificial intelligence has achievbed using binary mathematics. Arbitrary assignments of binary labels to objects and relationships allows computers to interact with us in very complex ways. The theory of "digital mind math" is that, if we advance the computer mathematics from binary to p-adic, we will achieve the full level of human thinking.

My primary interest is "digital mind math," a mathematical model of how we think, using a specific form of discrete mathematics, not binary, but p-adic. Ulla Marianne Mattfolk's comment regarding "the formation of gates and borders that create structures" is a nice description of how p-adic mathematics works. It is ultrametric (non-Archimedean) mathematics, and many statements about p-adic mathematics would be absurd if they were made about real mathematics. For example, the meaning of the digits in a p-adic number is quite different than the meaning of the digits in a real number. Also, the size of a p-adic number does not depend on what the specific digits are, but instead is determined by the count of the number of digits to the right of the decimal point for a particular value of p.

And don't forget the purely mathematical argument: there are two and only two ways to complete the rational numbers, real and p-adic. This gives great intuitive weight to the concept that we should be looking to p-adic mathematics as a critical analytic technique.

A good starting point is to consider how much artificial intelligence has achievbed using binary mathematics. Arbitrary assignments of binary labels to objects and relationships allows computers to interact with us in very complex ways. The theory of "digital mind math" is that, if we advance the computer mathematics from binary to p-adic, we will achieve the full level of human thinking.

Login or create account to post reply or comment.