Thank you for your interest..
As you know, I did send the paper you requested, and you acknowledged on your own essay thread. I hope my Gravity Research Foundation essay is of some value.
Regards,
Jonathan
Thank you for your interest..
As you know, I did send the paper you requested, and you acknowledged on your own essay thread. I hope my Gravity Research Foundation essay is of some value.
Regards,
Jonathan
Jonathan Dickau,
I enjoyed your essay because it is open to the idea that math itself contains the seeds of consciousness. I am an agnostic when it comes to the existence of consciousness or volition before it emerges in physical form but do agree with you that these must be based on a mathematical structure.
Fractal structures are ubiquitous in nature; causal lattices find a home in various mappings from the most fundamental particle interactions through the most complex structures in the universe, neural nets.
Also, I think that to dismiss imaginary and complex numbers as nonphysical is shortsighted as the equations that contain them fit with physical observation in a way that classical equations (those with just real numbers) do not. You put it well when you say: "... Nor does it make sense to assert that the real world is content to function within the space of real numbers."
Hawking's question: "what puts the fire in the equations?" becomes relevant here. It has long been the contention of philosophers that abstract objects are causally inert; and here again I am an agnostic. There is the old saw in physics, which may well be operant, that whatever is not forbidden is mandatory; so given a start, any start, to physical existence, even a probabilistic one, it opens the door for a physical emergence of consciousness.
Another of your observations, beautifully put: "... non-zero ordinary or simple numbers are the end of the process chain."
I am being speculative here, but it seems the complex interference patterns of the eigenstates of physical being held in superposition takes place in a complex space. And, as George Ellis puts it, collapse of the wavefunction is contextual. The inner product of that interference pattern is discarded by observation (probabilistically, by decoherence or by a conscious intervention) and what remains is the real number part.
The rules of non-commutative and non-associative math make it a tougher slog to an understanding. In none of my science classes was this presented as a path forward. At the point where the math becomes that much more challenging, for those of us who possess more scientific curiosity than mathematical ability, it becomes very discouraging indeed to be confronted with this much homework; it becomes a barrier to entry. When the phenomenon we see in nature do not yield to the simple formulations about the mathematics we know well, and then again to the intermediate formulations and then again to the more difficult formulations, it then finally occurs to us that, yes indeed, it can be this difficult. It goes against the grain of the human tendency to look for the keys under the lamp post, where the looking is easier.
Also, I really like the idea that, on its smallest levels, the structure (quantized discrete structures?!) of space goes (go) back to being 2-D and you go on to suggest that dimensionalities should be viewed as a spectrum, and further they are not limited to integer values and change over time, which opens the idea even more. Well done, sir! That opens the problem up nicely. I don't believe we will ever be able to go back to conceiving of physical reality limited to a simple Euclidean form.
I don't think of nature or math as an orchestrator of relationships; nature does not have to resort to trying these combinations out in sequence. Mathematics holds all of the eigenstates of physical being in superposition and can solve them by the interference patterns they produce; they shimmer into existence by virtue of their holographic fruitfulness.
Some of the underlying structures are more fruitful than others, so one would intuit that evolution would occur over a spacio-temporal spectrum of emergence. As you say: "we will see that math requires it."
Best regards,
Jim Stanfield
Thank you very much Jim!
As I recall; I am preaching to the choir for you, because your essay strongly espoused a view that the universe is mathematical at its roots. But your detailed comments indicate that you read the essay top to bottom, which means I kept your attention throughout. Some of the complication introduced by hyper-complex terms that arise in Physics were there to start with, only not acknowledged on their own terms (pun intended). The fact remains that nature is often more complex than we imagined, so it is not such a stretch that hyper-complex numbers are required to model its evolving grace of form.
For what it's worth; Paul Kainen endorses the way I used his work in my essay, and was flattered to be mentioned in connection with statements by Connes. Those were his comments to me in correspondence after seeing the essay. But a lot of people stop short of the answers that are right in front of them, because their knowledge of the Maths that would let them take the next step is lacking. So they imagine no answers exist, because a lot of the experts (save Connes and a few radical figures) are failing to see the potential or the need for non-commutative and non-associative geometry and algebra, for Physics at all.
It appears that you grasp some parts of my essay that others would have missed, so I am leaving the full comment visible for now. A good friend of mine uses the words "if they only did the Math right" frequently, when referring to the fact that most Physics folks take the easy way out, while other folks are not afraid to follow the arc of analytic continuation out to its completion - taking the next step until there are none. My friend is rather smart, though. Another contest participant, Andy Beckwith, is a 999 (99.9th percentile) and he just returned from Rencontres de Moriond, but we both agree he is much smarter.
However we all agree some of this stuff should be basic training for serious Physics folks, that most will only learn if they go for a second or third doctoral degree. This is no priority for American scholars, unfortunately, so there are a lot of folks with an incomplete education in the Mathematics which would allow them to invent next-generation Physics. People like Ed Witten (whom I have met) have a big enough mathematical toolbox and a broad enough perspective to explore many paths and be less attached to something like String Theory (though he is its guru). But not all are accorded the freedom to look where the answers actually are.
More later,
Jonathan
One needs to acknowledge..
The science of optical perspective is encoded in Projective Geometry, a branch of Mathematics which oddly turns out to be connected with the octonions. 'Why should this be?' I wonder, but know it is true. So there are ways the everyday and higher Maths are intertwined. However; sometimes fundamental realities really are as simple as we imagine them to be, as with your 'beautiful universe' theory. So do not lose sight of the fact you can be on to something, even if that is not the full picture or a commanding view.
My main point is that Math evolves, as you appear to agree, only I think Math moves forward under its own power.
All the Best,
Jonathan
How nice that optical perspective/ projective geometry are related to octonians! As a primarily visual person I fully understand the former, but the algebraic form confuses me. I have invented a mechanical device the Perspector to draw perspectives of 3D objects and in one of my fqxi essays used the example of perspective to show how an observer's point-of-view can 'distort' an object while the object is actually unchanged (to contrast Einsten's observer-based Special Relativity from one embedded in an absolute universe).
Dear Jonathan,
With great interest I read your essay, which of course is worthy of high rating.
I share your aspiration to seek the truth
«But scientists now think space itself must have a microscopic and quantum mechanical structure, like a fabric with an amazing weave that knits space and time together.»
I agree with you
«I assert that nature puts the looming realities of higher Math to work automatically, because they help set nature in motion, and keep it on course toward ideal or optimal goals.»
«So it is easy to forget that every object is the product of a process by which it came to be, and that ongoing processes maintain its form - giving it specific properties.»
«geometry enters the calculation in an organic way.»
«I see the most recent void discovery as further evidence that the universe is fractal at all scales.»
I wish you success in the contest.
Kind regards,
Dear Jonathan.
We meet again :) If you Think of the elephants, how do they communicate? How is the room defined?
Maybe this has been forgotten in QG frame?
Sheers
Ulla.
Dear Jonathan,
Good to see you again here. I thought I had written earlier on your essay, but I now see why I didn't. Our views are almost orthogonal, so it makes little sense for me to critique your essay. But it is good you present the Platonic view of math, as I try to present the Realist view of physics. Thus those who are undecided get a chance to ponder both views of reality.
There are some excellent essays (as usual) and I count yours as one of them. I particularly like the following:
"I'm sure nature is perfectly happy with processes taking more or fewer stages to complete, but the math itself dictates that certain patterns are more stable than others."
I think that works from both of our perspectives.
Best wishes to you, and as our mutual friend Ray Munroe used to say:
Have fun,
Edwin Eugene Klingman
Thanks greatly Ulla!
The elephants dance! And they talk over great distances in a low hum. The room is the entire universe. And people don't realize that primordial gravity waves are the deep low hum of the elephants. I'm glad you could come by.
I loved your essay.
All the Best,
Jonathan
Thanks so much Ed!
I will indeed have fun. And I feel well-qualified to critique your essay, so I have done so. I could do quite a credible job of presenting the realist view, I'll have you know, but I'm much happier reading what you have to say on that view of things. I never want to be accused of being a hard nosed realist.
All the Best,
Jonathan
Wow Thank You Vladimir,
I appreciate your good words and high regard. I don't think I've read your essay yet, so I'll wait to comment here until I do.
I wish you luck as well.
Regards,
Jonathan
Thanks to everyone who has come here..
I appreciate your interest in my ideas, and I am pleased that you have chosen to give me a high standing in this esteemed company. With so many distinguished professional scientists in this year's essay entrants, and with so many wonderful essays by amateurs and retired pros, I am privileged to be among you.
I will quietly read and grade a few more essays tonight, leaving brief or no comments, but I want to continue to show my support by giving my time to review your work.
Good luck to all.
Warm Regards,
Jonathan
Hi Jonathan,
A draft of my second paper on quantum correlations has been posted at sites.google.com/site/quantcorr. There is also a file with C functions for calculating correlations based on the "geometric probability" of crossing a threshold.
Cross posted on my blog under your thread.
Best wishes,
Colin
Thanks Colin..
I'll check that out.
JJD
Jonathan,
I did start to read your essay during the contest, but I did not comment or rate your essay (I never rate without comment). Your paper seems to be all about mathematic's relationship with the universe and not about existence of life or intelligence. I felt it was off-topic. As an essay, it is well written and clear. You try to present your ideas to a general science readership and do not require reference to other papers to understand your essay. I would have given it a "6". Readable counts for a lot with me.
All the best,
Jeff
Thanks Jeff,
I also value readability highly, in FQXi contests. Some folks seem to feel that only correct assertions or reasonable conclusions are worthy of credit, but I found quite a few essays I thought were wrong-headed or off-topic, and yet were sufficiently well-written to make me think - and thus require some acknowledgement by according them points in the rating. I didn't give out any ones this time, and I even gave Joe Fisher a 5 - though I don't agree with much he says - because his writing has continued to improve.
I will go back and read your essay, even though it won't count toward your score or my popularity, because I value your opinion.
All the Best,
Jonathan
Jonathan,
I don't know if I would give Joe Fisher a "5", but he does add something to the contest. He has a throw all the concepts in science into a blender and make it into art style of writing like Jackson Pulluk (sp?) did for painting.
I did see many math as a bases for the Universe essays, so maybe I was off-topic.
Jeff