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

**Fredric Litt**: *on* 3/10/11 at 3:57am UTC, wrote Thanks Russell, I haven't been getting many comments or ratings, either...

**Russell Jurgensen**: *on* 3/8/11 at 23:09pm UTC, wrote Dear Fredric, I wanted to say hello and let you know I enjoyed your essay...

**Dan Bruiger**: *on* 3/2/11 at 19:55pm UTC, wrote yeah, maybe Goedel has the last word... thanks again, Fred, and best...

**Fredric Litt**: *on* 3/1/11 at 23:40pm UTC, wrote Hi Dan, I guess we are using 'determinism' and 'causality' synonomously. ...

**Dan Bruiger**: *on* 2/28/11 at 23:56pm UTC, wrote Hi again, Fredric I guess the question remains, for me, whether there is...

**Alan Lowey**: *on* 2/21/11 at 11:55am UTC, wrote Yes Fredric, I think I see where you are coming from with this statement...

**Fredric Litt**: *on* 2/21/11 at 1:21am UTC, wrote Hello again Dan, It was an analogy to illustrate the difference between...

**Dan Bruiger**: *on* 2/20/11 at 18:13pm UTC, wrote Hi, Paul "Again using the computer's random numbers as an example, we KNOW...

RECENT FORUM POSTS

**Robert McEachern**: "They are proud, because they *have* solved some problems, which are..."
*in* Will A.I. Take Over...

**Joe Fisher**: "Today’s Closer To Truth Facebook page contained this peculiar piece of..."
*in* First Things First: The...

**Robert McEachern**: "Eckard, I do have an interest in the history, but not as much as I used..."
*in* First Things First: The...

**Georgina Woodward**: "The Schrodinger's cat thought experiment presents 3 causally linked state..."
*in* Schrödinger’s Zombie:...

**Roger Granet**: "Well put! Physics is hard, but biochemistry (my area), other sciences..."
*in* Will A.I. Take Over...

**Georgina Woodward**: "BTW The neck scarves are a promotional souvenir given out at non sports..."
*in* Schrödinger’s Zombie:...

**Steve Dufourny**: "lol Zeeya it is well thought this algorythm selective when names are put in..."
*in* Mass–Energy Equivalence...

**Steve Dufourny**: "is it just due to a problem when we utilise names of persons?"
*in* Mass–Energy Equivalence...

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 18, 2019

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

TOPIC: Experimental Mathematics and the Digital Nature of Reality by Fredric Alan Litt [refresh]

TOPIC: Experimental Mathematics and the Digital Nature of Reality by Fredric Alan Litt [refresh]

Quantum mechanics fails to explain the random or chaotic details of small numbers of events, such as those in atomic or molecular fluorescence or radioactive decay. An iteration algorithm is described that uses a scale parameter. As the value of the scale parameter changes, the function goes from equality with the continuous function, to smooth but disagreeing values, to oscillating, then chaotic values and finally to divergence. This algorithm simulates how reality might be indistinguishable from a continuous function at a large scale but diverge at smaller scale. In doing so, it reinforces the notion that time (and space) dimensions are discreet (digital) rather than continuous (analog).

Bachelor of Chemical Engineering, The Cooper Union, 1961 Doctor of Philosophy (Chemistry), The Johns Hopkins University, 1969 Thirty-seven years in industrial chemistry, retired 2004.

Hello Fredric, I liked your essay and agree with your example of the random number generator of a computer having accessibility. Fluorescence was also something that intersted me incidentally. I have some foundational insights into the visualisation of matter and particle/wave duality which may help you in your enquiries. Best of luck.

Alan

report post as inappropriate

Alan

report post as inappropriate

Thank you Alan,

The computer's "random number generator" is intended as a metaphor: We KNOW that there is an algorithm that the computer uses to generate a "random" series but, because we don't know the algorithm, the numbers can be accepted as random. We could, in principle, predict the numbers that follow if we were given the algorithm and a sufficient portion of the pseudorandom series. If so, the series would no longer be useful as "random" numbers. Fortunately, the algorithm is sufficiently complicated that we are not able to reverse engineer it.

In looking at the interval between natural events such as fluorescence or radioactive decay of single emitters, we certainly don't have such an algorithm. We can therefore assume the assume randomness and derive such (longer time period) properties such as half-life or fluorescence efficiency. My point is that using the series of emission events as a random series does NOT prove that the series is truly random; it shows only that we don't know the underlying algorithm (which might or might not exist).

When I read the subject of this essay contest literally only moments after reading an obituary of Benoit Mandelbrot, it occurred to me that the emission events need not be truly random; they might instead be chaotic and we might not be able to discern the difference using space and time as continuous functions.

I was therefore driven to find an example of a difference function that was IDENTICAL (not merely asymptotic) to the continuous function over part of its range but was also capable of giving chaotic behavior over another part.

report post as inappropriate

The computer's "random number generator" is intended as a metaphor: We KNOW that there is an algorithm that the computer uses to generate a "random" series but, because we don't know the algorithm, the numbers can be accepted as random. We could, in principle, predict the numbers that follow if we were given the algorithm and a sufficient portion of the pseudorandom series. If so, the series would no longer be useful as "random" numbers. Fortunately, the algorithm is sufficiently complicated that we are not able to reverse engineer it.

In looking at the interval between natural events such as fluorescence or radioactive decay of single emitters, we certainly don't have such an algorithm. We can therefore assume the assume randomness and derive such (longer time period) properties such as half-life or fluorescence efficiency. My point is that using the series of emission events as a random series does NOT prove that the series is truly random; it shows only that we don't know the underlying algorithm (which might or might not exist).

When I read the subject of this essay contest literally only moments after reading an obituary of Benoit Mandelbrot, it occurred to me that the emission events need not be truly random; they might instead be chaotic and we might not be able to discern the difference using space and time as continuous functions.

I was therefore driven to find an example of a difference function that was IDENTICAL (not merely asymptotic) to the continuous function over part of its range but was also capable of giving chaotic behavior over another part.

report post as inappropriate

Yes Fredric, I think I see where you are coming from with this statement "..after reading an obituary of Benoit Mandelbrot, it occurred to me that the emission events need not be truly random; they might instead be chaotic and we might not be able to discern the difference using space and time as continuous functions". It's a lack of understanding of the physical dynamical system which is paramount imo. Changing the subject slightly, I have a simple new idea in foundational physics which I would like your opinion on. It is the use of an Archimedes screw as a model for the graviton at the time of Newton. If he or one of his contemporaries had hit upon this simple idea then Einstein would never had thought of a spacetime continuum! We would have had an answer for dark energy as well! It's a lot to explain in one go and requires careful tactile consideration. It makes a lot of sense to have a mechanical particle as a force carrying entity imo. What do you think to this heretical idea?

report post as inappropriate

report post as inappropriate

Dear Fredric,

Your concept is very interesting—to consider functions that behave very differently in different domains, as an approach to the ‘analog’ and ‘digital’.

I cannot comment on your mathematical proposal, but my eye was caught by this passage:

‘True randomness requires that there be no relationship between one event and

the next event. Pseudorandomness, however, simply implies that we have not

(yet) been able to establish the cause-effect relationship of one event to the

next. For example, “random” numbers that are generated by computer

algorithms are actually pseudorandom rather than random.’

However, we are never in a position to establish absolutely that a pattern is ‘truly’ random. Secondly, we can only absolutely know that a pattern is pseudo-random if the generating algorithm is already known, which seems to beg the question.

If I understand correctly, your intent is to find the kind of function you describe, which gives a deterministic appearance in one range and a random appearance in another range, in order to find an ultimately deterministic basis for quantum (and/or other apparently chaotic) events? In other words, to show how quantum randomness is actually pseudo-random? I guess the important question is whether such an approach could actually match the results of the current quantum theory.

Best wishes and good luck,

Dan

report post as inappropriate

Your concept is very interesting—to consider functions that behave very differently in different domains, as an approach to the ‘analog’ and ‘digital’.

I cannot comment on your mathematical proposal, but my eye was caught by this passage:

‘True randomness requires that there be no relationship between one event and

the next event. Pseudorandomness, however, simply implies that we have not

(yet) been able to establish the cause-effect relationship of one event to the

next. For example, “random” numbers that are generated by computer

algorithms are actually pseudorandom rather than random.’

However, we are never in a position to establish absolutely that a pattern is ‘truly’ random. Secondly, we can only absolutely know that a pattern is pseudo-random if the generating algorithm is already known, which seems to beg the question.

If I understand correctly, your intent is to find the kind of function you describe, which gives a deterministic appearance in one range and a random appearance in another range, in order to find an ultimately deterministic basis for quantum (and/or other apparently chaotic) events? In other words, to show how quantum randomness is actually pseudo-random? I guess the important question is whether such an approach could actually match the results of the current quantum theory.

Best wishes and good luck,

Dan

report post as inappropriate

Dear Dan,

Please also see my reply to Alan, above.

You comment, "However, we are never in a position to establish absolutely that a pattern is "truly" random." I fully agree. The point is that we can deduce larger-scale properties if we assume true randomness. Once we can predict the series however, these deductions are only approximately valid since our treatment of the data assumes randomness that really isn't there.

You comment further, "Secondly, we can only absolutely know that a pattern is pseudo-random if the generating algorithm is already known, which seems to beg the question." I don't agree that it begs any question. Again using the computer's random numbers as an example, we KNOW that they're pseudorandom because we know that an algorithm exists, even if we don't know what the algorithm is.

As I replied to Alan, we can reach certain larger-scale conclusions by treating the series as random, and we have done so through nearly the entire twentieth century. I'm suggesting that such series that we treated as random might instead be causal (one number deriving from the previous) if the relationship produced a mathematically chaotic output that we could not distinguish from random. This causality is present even in the chaotic portion of the range of the difference function, even where the equivalent continuous function still produces stable results.

I'm merely speculating whether solution of the differential equations of quantum physics as continuous functions hides the chaotic or pseudorandom behavior that might arrive from treating them instead as a discreet difference equation.

report post as inappropriate

Please also see my reply to Alan, above.

You comment, "However, we are never in a position to establish absolutely that a pattern is "truly" random." I fully agree. The point is that we can deduce larger-scale properties if we assume true randomness. Once we can predict the series however, these deductions are only approximately valid since our treatment of the data assumes randomness that really isn't there.

You comment further, "Secondly, we can only absolutely know that a pattern is pseudo-random if the generating algorithm is already known, which seems to beg the question." I don't agree that it begs any question. Again using the computer's random numbers as an example, we KNOW that they're pseudorandom because we know that an algorithm exists, even if we don't know what the algorithm is.

As I replied to Alan, we can reach certain larger-scale conclusions by treating the series as random, and we have done so through nearly the entire twentieth century. I'm suggesting that such series that we treated as random might instead be causal (one number deriving from the previous) if the relationship produced a mathematically chaotic output that we could not distinguish from random. This causality is present even in the chaotic portion of the range of the difference function, even where the equivalent continuous function still produces stable results.

I'm merely speculating whether solution of the differential equations of quantum physics as continuous functions hides the chaotic or pseudorandom behavior that might arrive from treating them instead as a discreet difference equation.

report post as inappropriate

(Sorry, that might have been a telling slip-up. Of course I meant a discrete function, not a discreet one. Nothing indiscreet about the alternative.)

report post as inappropriate

report post as inappropriate

Hi, Paul

"Again using the computer's random numbers as an example, we KNOW that they're pseudorandom because we know that an algorithm exists, even if we don't know what the algorithm is."

Yes, but my question is whether can we assume the analogy of this example applies in the case of the natural world?

Dan

report post as inappropriate

"Again using the computer's random numbers as an example, we KNOW that they're pseudorandom because we know that an algorithm exists, even if we don't know what the algorithm is."

Yes, but my question is whether can we assume the analogy of this example applies in the case of the natural world?

Dan

report post as inappropriate

Hello again Dan,

It was an analogy to illustrate the difference between random and pseudorandom numbers or intervals.

I didn't intend it to be a metaphor for real events. Whether it is or not is not the subject of the essay; the point is that the chaotic part of the series is completely causal, yet produces a series that is pseudorandom. The implication is that, confronted with a series of events that APPEARS random, you cannot assume that there is no causality underlying the series. The apparent random behavior does not mean that there is no such detailed explanation at a lower level. In other words, one CAN imagine the existence of a difference equation at a level below that of elementary particles, one that would predict the exact time intervals between such events. This potential ability compares with the lack of evident success using differential equations of continuous variables.

The difference between random and pseudorandom is important only if you know the generating algorithm. With the chaotic part of the difference equation we do. But to an observer who is confronted only with the series, he can treat the events as random because he doesn't know the generating algorithm; if he did, his conclusions from his assumption of randomness would be only an approximation, although it might be a very good one.

Fredric Litt

report post as inappropriate

It was an analogy to illustrate the difference between random and pseudorandom numbers or intervals.

I didn't intend it to be a metaphor for real events. Whether it is or not is not the subject of the essay; the point is that the chaotic part of the series is completely causal, yet produces a series that is pseudorandom. The implication is that, confronted with a series of events that APPEARS random, you cannot assume that there is no causality underlying the series. The apparent random behavior does not mean that there is no such detailed explanation at a lower level. In other words, one CAN imagine the existence of a difference equation at a level below that of elementary particles, one that would predict the exact time intervals between such events. This potential ability compares with the lack of evident success using differential equations of continuous variables.

The difference between random and pseudorandom is important only if you know the generating algorithm. With the chaotic part of the difference equation we do. But to an observer who is confronted only with the series, he can treat the events as random because he doesn't know the generating algorithm; if he did, his conclusions from his assumption of randomness would be only an approximation, although it might be a very good one.

Fredric Litt

report post as inappropriate

Hi again, Fredric

I guess the question remains, for me, whether there is any such thing as a "truly random" event or process in nature. As you say, it may not be the issue you are addressing. I seem to believe that neither determinism nor indeterminism is a description applicable to the real world—only within mathematics, i.e. as decidability or computability. But I am open to arguments to the contrary...

Thanks,

Dan

report post as inappropriate

I guess the question remains, for me, whether there is any such thing as a "truly random" event or process in nature. As you say, it may not be the issue you are addressing. I seem to believe that neither determinism nor indeterminism is a description applicable to the real world—only within mathematics, i.e. as decidability or computability. But I am open to arguments to the contrary...

Thanks,

Dan

report post as inappropriate

Hi Dan, I guess we are using 'determinism' and 'causality' synonomously. In general, I believe that we can keep looking for causes at lower and lower levels until we are eventually stymied. At this point we need to explore a lower-level system -- molecules to atoms to atomic particles to quarks, etc. Philosophically this might go on indefinitely; maybe in fact, it MUST due to Godel's theorem implying that you can't prove a system by limiting yourself to properties within the system (one way Godel's theorem is explained to us mortals).

Similarly, in heat radiation theory, Planck succeeded where Boltzmann failed, by considering radiation incremental (ie: quanta) rather than continuous (waves). Photons became irreducible units of light just as atoms became irreducible units of chemical elements. These examples analogize discreetness of properties such as time and length. That's the background underlying my search for a function that would be identical to common (continuous) time and space, while still underlying a discrete or digital reality, that might predict a different behavior at really small units of time or space.

Fred

report post as inappropriate

Similarly, in heat radiation theory, Planck succeeded where Boltzmann failed, by considering radiation incremental (ie: quanta) rather than continuous (waves). Photons became irreducible units of light just as atoms became irreducible units of chemical elements. These examples analogize discreetness of properties such as time and length. That's the background underlying my search for a function that would be identical to common (continuous) time and space, while still underlying a discrete or digital reality, that might predict a different behavior at really small units of time or space.

Fred

report post as inappropriate

Dear Fredric,

I wanted to say hello and let you know I enjoyed your essay discussing the randomness of quantum events. I have been analyzing a model for continuous internal motion and have been thinking about randomness that would naturally arise. Even though you are suggesting discrete behavior, I like how you logically analyze the problem, and wanted to say thanks for an interesting and thought provoking essay.

Kind regards, Russell Jurgensen

report post as inappropriate

I wanted to say hello and let you know I enjoyed your essay discussing the randomness of quantum events. I have been analyzing a model for continuous internal motion and have been thinking about randomness that would naturally arise. Even though you are suggesting discrete behavior, I like how you logically analyze the problem, and wanted to say thanks for an interesting and thought provoking essay.

Kind regards, Russell Jurgensen

report post as inappropriate

Thanks Russell, I haven't been getting many comments or ratings, either favorable or unfavorable, and I appreciate your getting back to me.

Fred

report post as inappropriate

Fred

report post as inappropriate

Login or create account to post reply or comment.