Theory at Five Levels

  1. Child: A theory is like a story that scientists tell to explain how something in the world works. For example, why do things fall down instead of up? There’s a theory for that called gravity. A theory isn’t just a guess; it’s a story that has been tested many times and seems to explain what we see really well.

  2. Teenager: A theory is an explanation or a model developed by scientists to describe a particular phenomenon or set of observations. It’s more than just a guess or a hypothesis; it’s backed up by a large body of evidence. For example, the theory of evolution explains how different species change over time and how new species come to exist.

  3. Undergrad majoring in the same subject: In the scientific context, a theory is a well-substantiated explanation of some aspect of the natural world that has been confirmed through repeated experimentation and observation. It’s an overarching explanation that can incorporate various facts, laws, and hypotheses to describe a phenomenon. Theories also provide the framework for making predictions about future observations. An example is the theory of general relativity, which has been repeatedly confirmed and is fundamental in physics.

  4. Grad student: A theory, in a scientific context, represents the pinnacle of scientific understanding for a particular domain or phenomena. It integrates a body of empirical evidence, tested hypotheses, and well-grounded propositions capable of explaining and predicting aspects of the world. Theories are robust and dynamic, continually being refined and expanded upon in response to new evidence or reinterpretation of existing evidence. A significant feature of a scientific theory is its falsifiability, that is, it can be proven wrong with new observations or experiments.

  5. Colleague (Fellow Researcher/Engineer): As we both know, a scientific theory represents the consolidation of well-tested and generally accepted hypotheses, laws, and facts into a comprehensive framework capable of explaining and predicting observable phenomena. The development, refinement, or even replacement of a theory is a fundamental aspect of the scientific method and drives our progress in understanding the natural world. Its strength lies in its empirical grounding and its potential for falsifiability and predictive power, offering us not just description, but a mechanism for the advancement of knowledge.

Richard Feynman Explanation

Alright, let’s think about it this way. Let’s say you and I are playing a game of catch. You throw the ball to me, and I catch it. Now, we do this a couple of times, and you start noticing something. Every time you throw the ball, it moves in this nice arc before landing in my hands. You can predict where the ball is going to land based on how you throw it.

Now, let’s say you take this observation and generalize it. You say, “Whenever anyone throws a ball, it will move in an arc.” That’s a theory! It’s a way for you to make sense of the world around you based on what you’ve observed.

In science, theories are explanations of certain phenomena. They are grounded in empirical evidence, meaning they’re based on observations and experiments. But unlike in our game of catch, scientific theories have to stand up to rigorous testing and scrutiny.

Theories are not just guesses. They are sophisticated explanations that can make predictions about the future. They also give us the ability to see patterns that we might not otherwise notice. And that’s pretty incredible!

So whether you’re figuring out the path of a thrown ball, understanding how computers work, or unraveling the mysteries of the universe, theories are your best friends. They provide a framework that helps make sense of the world in a consistent, reliable way.

Expressing Theory in Code

Theories can often be expressed in code, especially theories related to math, physics, statistics, computer science, and certain fields of social sciences. When we translate a theory into code, we are creating a computational model of that theory.

For example:

  • Mathematical theories are regularly translated into code for computation. One can code the Pythagorean theorem to calculate the length of a side of a right triangle, or code the algorithm for quick sort based on the theory of divide and conquer.

  • Physics theories can also be translated into code. For example, the laws of motion can be coded to simulate physical systems in video games or in simulations used in scientific research.

  • In machine learning and artificial intelligence, many algorithms are based on statistical theory, such as regression, clustering, and neural networks. These algorithms are coded and used to make predictions, classify data, and learn from data.

  • Theories from social sciences, like economics, can also be modeled with code. An example is agent-based modeling, where individual agents and their decision-making processes are coded to simulate complex social systems.

So, coding a theory is essentially creating an algorithm or a program that operates according to the rules, principles, or equations that the theory provides. However, not all theories can be coded - especially those from areas like philosophy or abstract thinking, which might be too qualitative or lack the precise, quantifiable rules needed for coding.

Let’s take a very simple theory - the theory of Pythagorean Theorem. This theory states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as:

a² + b² = c²

We can express this theory in Python code to calculate the length of the hypotenuse given the lengths of the other two sides. Here’s a simple Python function to do this:

import math

def calculate_hypotenuse(a, b):
    return math.sqrt(a**2 + b**2)

# Test the function
print(calculate_hypotenuse(3, 4))  # This should print 5.0

In this code, the calculate_hypotenuse function takes in the lengths of the two sides of a right-angled triangle (a and b) and returns the length of the hypotenuse. It calculates this using the formula from the Pythagorean theorem, which is implemented here with the Python math.sqrt function (to calculate the square root) and the ** operator (to square the lengths of the sides).