2 hours ago, joigus said:

What's your motivation, and why is exactly 1.58 the Hausdorff-Besicovitch dimension of time in your theory? When such values come about, it's normally because some kind of consistency condition forces it.

It's not a happy coincidence, I suppose, after trial an error with infinitely many possible values.

Thank you for the question — it’s a very important one.

The number 1.58 I use as the Hausdorff-Besicovitch dimension of time in my model is not random.

While it’s still more of an intuitive choice than a rigorously derived result (for now), it’s based on specific reasoning.

In this hypothesis, time is not represented as a one-dimensional line, but rather as a fractal hypercloud of possible trajectories.

The time we perceive is just a coherent path through this hypercloud.

The fractal dimension reflects the local complexity of branching — how diverse the nearby paths can be around each point.

Why 1.58 specifically?

Because it lies between 1 and 2:

1 represents a classical linear trajectory (no variation),

2 would be a full two-dimensional field of possibilities (no direction),

and 1.58 reflects a fractal structure, where direction exists, but branching is also present.

This value is very close to the golden ratio (φ ≈ 1.618), which often appears in self-similar and recursive structures — exactly the kind I associate with the nature of time.

I continue working toward a future derivation of this value, perhaps from a consistency principle — such as entropy flow, or quantum decoherence across alternative trajectories.

On 5/14/2025 at 3:14 PM, ZGeorg said:

Thank you for your question. At this stage, the fractal time model is still under development, and it does not yet provide quantitative predictions, such as specific signals for LIGO or parameters for CMB analysis. The topic is complex, and current efforts focus on refining the logic, identifying directions, and ensuring the coherence of the framework. Predictions remain qualitative, and i are working to explore paths toward greater specificity.

Moderator Note

You can come back to this when you’ve developed this to the point where it complies with our rules about testable predictions and having evidence to support it.