Most recent email: December 24, 2017
Dear Prof. Freeman Dyson:
Over five years ago, you sent me a response to my email (Editor’s note: Just below Dyson’s response) regarding our rather unusual project of our high school geometry classes. At that time, we were searching for scholars like you to help us figure out what was wrong with our simple logic and the simple logic inherent within our mathematics. Nobody had truly challenged that mathematical logic; you were the first. I treasured that response. Perfectly exquisite. Most helpful, but at that time, I did not know how to respond to you. Today, I think maybe I do. So, let me take my three questions and your answers one-by-one.
1. If the Planck Length is a dimensionful number representing a singularity or a point, can we multiply it by 2 and assume two points? …multiply it again and assume 4, then 8, 16, 32 and on up to 1024 by the 10th doubling? You replied, “Since space has three dimensions, the number of points goes up by a factor eight, not two, when you double the scale. Since space has three dimensions, the number of points goes up by a factor eight, not two, when you double the scale.” That was our introduction to dimensional analysis and scaling laws. It is a huge study and we were grateful for the suggestion. The vertex count, accelerates so much more quickly multiplying by 8 (as opposed to 2). Still, we kept the doubling number thinking it might have some future applicability.
2. Can we assume nested geometries throughout? Your answer: “The universe we live in is not nested at all. On the contrary, larger levels of structure are quite different from smaller levels. Larger levels bring qualitatively new structures. For example, a galaxy does not look like a big star, and a star does not look like a big planet, and a planet does not look like a big elephant, and an elephant does not look like a big bacterium, and a bacterium does not look like a big atom.”
I’ll readily admit that I was disappointed with this answer. It seemed to me that the hexagonal structures in chemistry were the first bellwether that geometries were somehow pervasive throughout the universe, seen or unseen. My first thought was to the various carbon structures, then up to the symmetry structures of cells and then down to the symmetry structures in physics and Wigner’s classifications. If there are large scale and small scale symmetries, why can’t we explore possible ways to link them up? Of course, I am thinking that symmetry groups become increasingly rich, embedded, nested, and combinatorial as we start to go smaller than particle physics, i.e. below Notation 67. I would hypostatize that everything below Notation 67 is increasingly an expression of basic geometries and that these geometries continue within each notation. We see the expressions that manifest within the visible part of the doubling, but do not see all the inherent geometries that are the deep infrastructure, including all the spheres from the first notations creating an intense fabric that envelopes the universe! It is a rather different view of Michaelson-Morely’s ether.
3. Is there any particular recent work to which you would want us to take note? I want to re-open the entire history of renormalization of which you had a most significant role. If Newton’s absolute space-and-time is wrong, and our nascent model is closer to the truth, I would love your counsel to see how such a configuration might effect the decisions to renormalize.
I hope your health is good and your spirits are high.
Freeman Dyson's response is shared here with his permission.
From: Freeman Dyson
Date: Mon, Oct 22, 2012 at 11:12 AM
Subject: Re: 34 years later… Might it be useful to see the universe as 202.34 notations
that are necessarily related through simple geometries all nested within each other?
To: Bruce Camber
Dear Bruce Camber,
Thank you for the invitation to comment. Without seeing your scheme, it is hard to judge whether it would make sense. If I take your three questions literally, the answer is No to all three.
1. Since space has three dimensions, the number of points goes up by a factor eight,* not two, when you double the scale.
2. The universe we live in is not nested at all. On the contrary, larger levels of structure are quite different from smaller levels. Larger levels bring qualitatively new structures. For example, a galaxy does not look like a big star, and a star does not look like a big planet, and a planet does not look like a big elephant, and an elephant does not look like a big bacterium, and a bacterium does not look like a big atom.
3. I don’t know any recent work that would be important for your project. There are plenty of new pictures for you to choose from, both in the large and in the small, from galaxies to viruses.
Sorry I do not have any more useful ideas. I will be interested to see what comes out of your project.
* Editor’s note and reference: http://www.av8n.com/physics/scaling.htm We can extend this idea into three dimensions. The volume goes up by a factor of eight because the cube is twice as wide…
Here is the letter to which Prof. Dr. Freeman Dyson was responding:
First email: Fri, 19 Oct 2012, Bruce Camber wrote:
> Dear Prof. Dr. Dyson:
> Just over 34 years ago I contacted you regarding a special project at MIT called,
> “An architecture for integrative systems.” It was a display project in the main rotunda
> just off Massachusetts Avenue. It borrowed Erwin Schrodinger’s title from his much
> earlier work, a book entitled, “What is life?” Seventy-seven leading, living scholars
> participated and you were one of them. We are taking that old product and re-purposing
> it online within a very similar framework — Small Scale, Human Scale, Large Scale —
> however, we are using base-2 exponential notation from the Planck Length to the
> edges of the observable universe which gives us 202.34 ordered steps in which to context
> information. By assuming nested geometries at each doubling, it seems that we
> will have an inherent structure for analogous or metaphorical connection-making.
> But before we go too far, I would like to re-engage you and ask for your advice:
> 1. If the Planck Length is a dimensionful number representing a singularity
> or a point, can we multiply it by 2 and assume two points? …multiply it again
> and assume 4, then 8, 16, 32 and on up to 1024 by the 10th doubling?
> 2. Can we assume nested geometries throughout?
> 3. We will use the same infrastructure as used by Wikipedia to build it out, so
> owner’s of information can readily edit and update content. Is there any particular
> recent work to which you would want us to take note?
> Thank you.