Aim 2

Aim 2#

Templates (Antiquary), Constraints (Monumental), Freedoms (Critical)#

We’ve woven together a tapestry of how human cognition and culture evolve through inherited templates and constraints. This perspective recognizes that while our sensory experiences and immediate biological responses are uniquely our own, the layers of abstraction—art, science, and morality—are inherited frameworks that shape and are shaped by our engagement with the world.

Inherited Templates and Constraints#

We articulate the idea that these layers of abstraction—art, science, and morality—are inherited, each providing a kind of template or set of constraints that we receive from our predecessors.

Art as Inherited Encoding: Art functions as the first layer of abstraction, encoding the collective experiences of those who came before us. This inheritance (hypothesis) includes a vast reservoir of narratives, symbols, and metaphors that capture the human condition across generations. By engaging with this inherited art, we are not only accessing the emotional and experiential knowledge of our ancestors but are also shaped by the cultural and social contexts that produced these works. This makes art a living repository of human experience, a dynamic narrative that evolves as each generation adds its own stories and interpretations.
Science as an Iterative Process: Science, as the second layer, represents a more objective abstraction. It takes the encoded experiences from art and tests (statistic) them against the reality of the physical world. Science is where we encounter consonances and dissonances, where inherited knowledge is validated or refuted. This iterative process allows for the continuous refinement of our understanding of the world, pushing the boundaries of what is known. Each new scientific discovery or technological advancement can be seen as an update to the inherited template, adding new constraints or freedoms, and challenging our inherited worldviews.
Morality as Dynamic Ethical Constraints: Morality, the third layer, is where these scientific findings and artistic insights converge to form ethical frameworks. These frameworks are also inherited, passed down through religious teachings, cultural norms, and philosophical traditions. However, morality is not static; it is continually tested and updated based on new insights from both art and science. The “likelihood ratio” you mention is a powerful metaphor here—if our updated moral frameworks, which incorporate new constraints or freedoms, perform better in terms of promoting human flourishing, reducing harm, and general overcoming (p-value), then these values are more likely to be adopted and passed on.

Creative Evolution of Templates#

Gratitude to Forbears: Our creative task is to add more constraints or freedoms to these inherited templates. Human progress is not a mere accumulation of knowledge but an active, creative process of testing, revising, and updating the frameworks we’ve inherited.
Adding Constraints: Sometimes, progress requires us to add new constraints—ethical boundaries that limit harmful actions or promote social cohesion. For example, the scientific understanding of environmental degradation has led to new moral constraints regarding pollution and resource consumption.
Introducing Freedoms: Conversely, there are moments when we expand freedoms, breaking free from outdated constraints that no longer serve us. The social and moral revolutions of the 20th century, such as the civil rights movement or the push for gender equality, exemplify this process. These changes were driven by both scientific understandings (e.g., the fallacies of racial pseudoscience) and evolving artistic narratives that challenged the status quo.

The Likelihood Ratio: Testing Inheritance Against Innovation#

The concept of using a “likelihood ratio” to evaluate whether our updates perform better than our inheritance is a fascinating approach to understanding cultural evolution. This process is not linear but rather a dynamic interplay of testing, feedback, and adaptation. It’s akin to a scientific method applied to cultural and moral development, where each new hypothesis (whether a work of art, a scientific theory, or a moral principle) is tested against reality.

If the new adaptation proves more effective—whether in fostering understanding, promoting well-being, or guiding ethical behavior—it is more likely to be retained and propagated. Conversely, if the new adaptation fails, it is revised or discarded. This constant cycle of testing and updating ensures that our collective knowledge, culture, and ethical frameworks remain relevant and responsive to the realities of the human condition.

Conclusion#

Your framework presents a dynamic, evolutionary view of human cognition and culture, one that acknowledges our biological grounding while celebrating our capacity for creative abstraction. It suggests that we are both products of our inheritance and active participants in its evolution. This model not only helps explain how knowledge and culture develop but also provides a blueprint for how we might approach our roles as stewards of these inherited templates, continually refining and updating them to better serve future generations.

Hierarchical & longitudinal#

A frailty function in survival analysis is a random effect model used to account for unobserved heterogeneity or random variation in the survival times of individuals within a study. It introduces an additional random component to the hazard function to capture the influence of latent, unmeasured factors that might affect the risk of an event (such as death, failure, or recurrence).

Here’s a breakdown of its key aspects:

Definition#

Frailty: Represents unobserved random effects that lead to variations in the hazard function among individuals or groups.
Frailty Function: A function that incorporates these unobserved random effects into the hazard function of a survival model.

Purpose#

Unobserved Heterogeneity: Accounts for individual differences not captured by observed covariates.
Clustered Data: Useful for modeling survival data with a hierarchical structure (e.g., patients within hospitals, litters of animals).

Mathematical Representation#

The hazard function with frailty is usually expressed as: \( h_i(t | Z_i) = Z_i h_0(t) \exp(X_i\beta) \) where:

\( h_i(t | Z_i) \) is the hazard function for individual \(i\).
\( Z_i \) is the frailty term for individual \(i\), often assumed to follow a specific distribution (e.g., Gamma or Log-normal).
\( h_0(t) \) is the baseline hazard function.
\( X_i \) is the vector of covariates for individual \(i\).
\( \beta \) is the vector of coefficients.

Common Frailty Distributions#

Gamma Distribution: Most commonly used due to its mathematical tractability.
Log-normal Distribution: Used when the frailty is believed to have a more complex, asymmetric distribution.
Positive Stable Distribution: Suitable for certain types of clustered survival data.

Applications#

Medical Research: Modeling patient survival times where individual patient differences are not fully captured by observed variables.
Reliability Engineering: Analyzing the time to failure of components with unobserved heterogeneity.

Benefits#

Improved Estimates: By accounting for unobserved heterogeneity, frailty models can provide more accurate parameter estimates.
Model Fit: Better fit to data where unmeasured variables play a significant role in the hazard rate.

Challenges#

Complexity: Introducing frailty increases model complexity and can complicate parameter estimation.
Interpretation: Interpretation of frailty models can be less straightforward compared to standard Cox models.

In summary, frailty functions are powerful tools in survival analysis to address unobserved heterogeneity and provide more accurate and realistic models for time-to-event data.