I like starting with a question. So, let’s begin with: What does it mean to look at the world mathematically?
At its core, viewing the world mathematically means observing how things work, identifying patterns, and using logic to explain or predict outcomes. Mathematics isn’t just about numbers and equations; it’s a lens through which we can understand systems—natural or artificial—and their underlying principles.
A system can be thought of as a set of interconnected parts working together to produce a result. It's like a factory: different machines (components) work together to turn raw materials (inputs) into finished products (outputs).
Example:
- Input: A piece of wood
- Process: The saw cuts the wood, the machine sands it, and another machine adds a finish
- Output: A smooth, polished wooden table
This simple concept applies everywhere, from ecosystems to economies.
Let me eleborate on Process part. Process can be simply thought of as interaction between components in system. These components do specifc job on there own, In case of Table Making there are different components involved in system. They all have certain attribute and propery. We can call them variables in system. What will happen if we change the thickness of blade involved that cuts the wood or, what if we rotate that blade little slower. Things like thickness or sharpness of blade, Blade's rotations per minute these can be thought of as variables because they have value that can be changed.
These are systems created by nature. Think of weather patterns, ecosystems, or even our own bodies. For instance, the water cycle is a natural system that moves water through evaporation, condensation, and precipitation.
These are human-made. Cities, transportation networks, and computer algorithms are all artificial systems. Take traffic lights: they’re designed using logic and rules, often based on mathematics like probability and optimization.
By analyzing both natural and artificial systems mathematically, we can understand how they function and sometimes even predict their behavior.
Artificial systems are often easier to break down mathematically because they’re built on math.
Examples:
- Mechanical System: A car engine uses the principles of thermodynamics (how heat is converted to energy) and mechanical engineering (how parts move in relation to each other) to power the vehicle. The engine's efficiency depends on factors like fuel combustion, piston movement, and crankshaft rotation—all governed by physics.
- Computer systems uses algorithms and logic.
- Finance System: A stock market prediction model uses probability and statistics to forecast market trends. It analyzes historical data (price movements, trading volume) and applies statistical methods (like regression analysis) to predict the likelihood of future price changes.
Imagine a ballpoint pen.
If the ink flow (input) is inconsistent, the writing (output) will be uneven. Understanding this system helps engineers design pens that write smoothly and last longer.
I can list different reasons like math is a universal language, math develops your logic, and helps you think critically, but the most important part for me is Problem Solving. What we are discussing right now, Elon Musk calls it thinking from first principles. Thinking about a system mathematically forces us to break things down into smaller parts of a bigger system, then find the interactions, measure the properties to predict the impact of those interactions, and ultimately helps us with Problem Solving. It’s a buzzword these days, so it may sound cliché, but unlike others who use "Problem Solving" for whatever unrelated reason, I am akshually explaining what it means.
This is the part where many people hesitate. The truth is, you don’t need to be a genius. Even basic math can help you understand the world better. However, the deeper your knowledge, the more insights you’ll gain, and the easier it will be to see the patterns and logic around you.
Practice! Practice! Practice! The more you practice observing systems, the better you'll get at understanding them. Start with small systems and work your way up.
Observe Systems:
Break Down the System: Start by looking closely at any system. Break it down into its components. Try to understand how each part contributes to the whole.
Focus on Observations: Instead of rushing to a solution, focus on making as many observations as possible. Be thorough. Look for patterns, connections, and specific details, such as numbers or quantities.
Example: If you're observing the process of making a cup of tea, think about the temperature of the water, time it takes to steep, and how the ingredients interact. The more detailed your observations, the clearer the system becomes.
Ask Lots of Questions:
The key to learning in depth is asking questions. When you ask questions, you're digging deeper into the system's workings.
But remember, we'll discuss how to ask the right questions in another post.
Write Down Discoveries in Terms of Math:
Can you express your observations or discoveries mathematically? For example, if you eat more when you're not busy, how can we write that in a mathematical expression?
Example: Let’s say your value of Fan/Air Conditioner/Thermostate regulator changes throut the year. As a poor I only know of Fan Speed.
Fan Speed = Base Speed + (Temperature × C)
C is the sensitivity factor of the fan, i.e., how much the fan speed increases per degree of temperature.
Looking at the world mathematically isn’t about solving equations every day. It’s about developing a mindset that seeks to understand how things work, why they happen, and how they’re connected. Once you start thinking this way, you’ll see mathematics not just as a subject but as a way of understanding the beauty and complexity of the world around you.
So, what’s your next system to explore? 😊