[OC] Time vs. Size scaling relationship across 28 physical systems spanning 61 orders of magnitude (Planck scale to observable universe) Comparison

What This Visualization Shows

This data visualization displays "[OC] Time vs. Size scaling relationship across 28 physical systems spanning 61 orders of magnitude (Planck scale to observable universe)" and provides a clear visual representation of the underlying data patterns and trends. The visualization focuses on I spent the last few weeks analyzing the relationship between characteristic time intervals and system size across every scale of physics I could find data for.

So basically I looked at how long things take to happen (like how fast electrons orbit atoms, how long Earth takes to go around the Sun, how long galaxies rotate) and compared it to how big those things are. What I found is that bigger things take proportionally longer - if you double the size, you roughly double the time. This pattern holds from the tiniest quantum particles all the way up to the entire universe, which is wild because physics at different scales is supposed to work totally differently. The really interesting part is there's a "break" in the pattern at about the size of a star - below that, time stretches a bit more than expected, and above that (at galactic scales), time compresses and things happen faster than the pattern predicts. I couldn't find it documented before(it probably is), but I thought, the data looked interesting visually

**The Dataset:**

* 28 physical systems * Size range: 10^(-35) to 10^(26) meters (61 orders of magnitude!) * Time range: 10^(-44) to 10^(17) seconds (61 orders of magnitude!) * From Planck scale quantum phenomena to the age of the universe

**What I Found:** The relationship follows a remarkably clean power law: **T ∝ S\^1.00** with R² = 0.947

But here's where it gets interesting: when I tested for regime breaks using AIC/BIC model selection, the data strongly prefers a two-regime model with a transition at \~10^(9) meters (roughly the scale of a star):

* **Sub-stellar scales:** T ∝ S^(1.16) (slight temporal stretching) * **Supra-stellar scales:** T ∝ S^(0.46) (strong temporal compression)

The statistical preference for the two-regime model is very strong (ΔAIC > 15).

**Methodology:**

* Log-log regression analysis * Bootstrap confidence intervals (1000 iterations) * Leave-one-out sensitivity testing * AIC/BIC model comparison * Physics-only systems (no biological/human timescales to avoid category mixing)

**Tools:** Python (NumPy, SciPy, Matplotlib, scikit-learn)

**Data sources:** Published physics constants, astronomical observations, quantum mechanics measurements

The full analysis is published on Zenodo with all data and code: [https://zenodo.org/records/18243431](https://zenodo.org/records/18243431)

I'm genuinely curious if anyone has seen this pattern documented before, or if there's a known physical mechanism that would explain the regime transition at stellar scales.

**Chart Details:**

* Top row: Single power law fit vs. two-regime model * Middle row: Model comparison and residual analysis * Bottom row: Scale-specific exponents and dataset validation

All error bars are 95% confidence intervals from bootstrap analysis., which allows us to understand complex relationships and insights within the data through visual storytelling.

Deep Dive into the Topic

This data visualization represents a sophisticated analysis of complex information patterns that provide valuable insights into underlying trends and relationships. Data visualization serves as a bridge between raw numerical data and human understanding, transforming abstract statistics into comprehensible visual narratives.

The power of data visualization lies in its ability to reveal patterns, outliers, and correlations that might not be apparent in traditional tabular formats. Through careful selection of chart types, color schemes, and interactive elements, effective visualizations can communicate complex information quickly and accurately to diverse audiences.

Modern data visualization combines statistical analysis with design principles to create compelling visual stories. This interdisciplinary approach requires understanding both the underlying data and the cognitive processes involved in visual perception. The result is more effective communication of quantitative insights that can inform decision-making and drive positive change.

Data Analysis and Insights

The patterns revealed in this visualization demonstrate the importance of systematic data analysis in understanding complex phenomena. By examining different data segments, time periods, and categorical breakdowns, we can identify trends that inform strategic planning and decision-making processes.

Statistical analysis of this data reveals variations across different dimensions that provide insights into underlying drivers and relationships. These patterns help identify areas of opportunity, potential risks, and key performance indicators that can guide future actions and resource allocation.

The analytical approach used in this visualization enables comparison across different categories, time periods, or geographic regions, revealing insights that support evidence-based decision-making. This type of analysis is essential for organizations seeking to optimize performance and understand complex market dynamics.

Significance and Applications

This data visualization has important implications for understanding trends and patterns that affect decision-making across multiple sectors. The insights derived from this analysis can inform policy development, business strategy, resource allocation, and operational improvements.

For analysts, researchers, and decision-makers, this type of data visualization provides essential insights for strategic planning and performance optimization. Whether addressing operational challenges, market analysis, or policy development, understanding data patterns helps create more effective strategies and solutions.

The broader significance lies in how this information contributes to our understanding of complex systems and relationships. This knowledge helps predict future trends, identify potential challenges, and develop more informed approaches to problem-solving and opportunity identification.