This is the letter I wrote to Professor David Hogg, the opponent of Fractal Cosmology.

Please see my posts 'Fractal Cosmology' and Letter to Fractal Cosmology Opponent Hogg, share this, and read my papers. Thank you.

Subject: Quaia catalogue corresponding with transitions in a physical inhomogeneous fractal model

Dear Professor Hogg,

Firstly, congratulations on your recent Quaia Quasar catalogue. I believe it, along with DESI, is one of the greatest achievements of all time.

My name is Blair Macdonald. Ordinarily, I would have no business with you as I am not a cosmologist; however, what I have found should interest you all. I have tried to make this as short and as simple as I can. Being it what it is, this is a complex. Bear with me, please.

In short: I have published a model that corresponds to your observations: it is the fractal. This is why this email is directed to Professor Hogg. I have taken fractals beyond the Italian fractal cosmologists. I have found, in terms of geometry, the universe behaves as a fractal, and this includes 'the quantum'.

Over the last 12 months, I have had two papers published in the International Journal of Quantum Foundations: speculations. (titles below if you do not want to open links) The first is on the fractal and the quantum, and the second—linked to the first, is a dynamic model of a growing fractal that pertains to cosmology and expected observations of the large-scale universe. Together I have attempted to describe two aspects of the same geometry.

The first deals with all the quantum and other problems of light and matter, including wave-particle duality behaviour of light, light speed, the measurement problem, entanglement and more. The isolated fractal does it all and is equally a very strange thing.

The second paper is an experiment pointing to cosmology and this one makes predictions, and this is why I am writing this to you (all).

Professor Hogg, you were once engaged in the discussion about whether the universe is fractal or not: the issue was left with you posing a challenge, setting a criterion of a 'physical' and 'inhomogeneous' fractal model. The following is from New Scientist Magazine.

'Hogg's team feel that until there's a theory to explain why the galaxy clustering is fractal, there's no point in taking it seriously.

"My view is that there's no reason to even contemplate a fractal structure for the universe until there is a physical fractal model," says Hogg. "Until there's an inhomogeneous fractal model to test, it's like tilting at windmills." '( NS Don't mention the F word 2007)

I have that physical inhomogeneous fractal model.

My fractal cosmological model is simple and unique: I inverted the fractal and measured its behaviour as it grew. It is a dynamic model that traces the growth of a fractal from its beginnings from the observational perspective of being within one. It shows what one would expect to see and it pertains directly to your quasar distribution and the quasar groups (LQGs) of your Quaia Quasar catalogue.

To help describe what we would expect to observe from my model I use the language taken from a real-life and familiar fractal, a tree. Of course, we are not living in a tree, but I will say it is as if the trunk ('of the tree') surrounds us, strangely. I have no other analogy for this oddity in our reality, so I use trees. Figure 1 is from my paper and is used here as an aid to my words.

In terms of cosmology, it is as if we are in 'the branches' (Figure 1 b, and c) of the tree (these are the small-scale clusters and superclusters) looking out and back to 'the truck' (the CMB). The massive 'boughs' of the tree (the LQGs) are further out before the smooth 'trunk', the > redshift z 2. This is the inhomogeneous smooth. It should be there. Take a look at — before the green leaves come — the biggest oak trees or similar you can find. Put yourself in the branches of one, and look down and out to the trunk, knowing the tree is growing and has a history. It is not a smooth path. We appear to be surrounded by this.

Tree Fractal with Map of Universe 2304.png

Figure 1

The fractal model demonstrates Hubble-Lematitre expansion (figure 2 is my Hubble fractal diagram), accelerated expansion and the changing distribution of galaxies from small to large scale. The branches in the fractal, the tree, accelerate apart from each other. Accelerated fractal growth, I have concluded, is the 'Dark Energy'.

Fractal Hubble-Lemaitre Diagram 2304.png

Figure 2

In support of my model, it has been found that real tree volumes indeed grow at accelerating rates with age (see below for title). And just like a tree, the universe may also have tropisms that alter the rates of growth; but the core principle, simplicity, holds.

Another key insight from this dynamic model is that the trunk (maybe the CMB) was once a seedling. On every tree, that seedling-sized branch (Figure 3 A-A), the twig (Figure 3 A-B), can be found. It is here where the tree grows, it is the one constant size (Figure 3 B) and if that is so, with respect to the growth of the universe: cosmic growth may have to do with light itself at the smallest 'quantum scales'. This links directly to my first paper.

Fractal Tree Growth from a Constant Leaf Size.png

Figure 3

A shows a seedling (A) and a twig from a grown tree (B). B shows a seedling with end twigs of the grown tree with its trunk.

Why am I writing to you?

As a consequence of my model, I have been watching out for large-scale surveys, DESI etc., as they have been coming in over recent years (even in the last few days! a new one from DESI). I am interested in the outer smoothness knowing that the LQGs are already there. Two weeks ago I saw in my feeds an article on your survey and so I when found your paper, I quickly looked through it hoping for a galaxy distribution diagram. If there was one, is there a 'long tail' smooth out to 'the edge'?

And there it was, in your Figure 11. (I must say that I did a little dance when I saw that.) The skewed bell shape with a tail is what should be expected, if fractal.

It was at this time, Professor Hogg, that I also saw your name as a co-author of the paper. Strange, but true. I knew then, given your history with fractal cosmology, I had to write this letter.

As a last note, I wrote in my papers that I do not think this fractal model takes away anything from what we have already established. GR, of course, holds; and the quantum (as I describe in the first) may be an inextricable part of this growth.

However, I will say, the cosmological principle may have to go. I am not alone in saying that these days. A tree is not homogenous, nor isotropic. The trunk holds a large proportion of the volume of the tree. Standing at a tree's base looking up (Figure 1 c), shows it is not the same distribution throughout; nor is it if observing from within the branches looking down (Figure 1 b). I think this is the same for the universe, and that is what the surveys are showing us.

These two papers and your observations, among others, should open what is a closed discussion on the topic of fractality. Take me out of it if you will, it is not about individuals, it is about geometry. I think, if we had this simple model one hundred years ago, we would have predicted and have been looking for the discoveries we have made since Hubble, including yours. The small-scale inhomogeneity and the outer large-scale smoothness are what you should see in a growing fractal. It is a geometry; just as eclipses are to planetary orbits.

I am careful not to speculate beyond what I have, but what I have should open the door to answering the greater questions. It is the best-fit tool; it has not failed me.

I hope this interests you all, and I hope to hear from you.

I would be open to suggestions and advice on what I should do, given my position.

Enjoy the solar eclipse today.

Yours Sincerely,

Blair Macdonald.

Paper titles:

International Journal of Quantum Foundations, Speculations. The Fractal Corresponds with Light and Foundational Quantum Problems https://ijqf.org/archives/6806). Experiment on Inverted Fractal Corresponds with Cosmological Observations and Conjectures
https://ijqf.org/archives/7011