Innovation Through Combination: A Simple Approach

Business innovation is often about putting together old ideas in new ways. Instead of inventing something completely from scratch, companies take bits and pieces from what already exists and combine them to create something better. This article will look at how we can use a straightforward math concept called a “Presheaf” to explain this process.

#What Is Innovation?

Innovation is just a fancy word for doing something new or better. Think about how your phone allows you to take pictures, listen to music, and call your friends all in one device. Before, you might have needed a camera, a music player, and a phone. This combination of Features makes your phone innovative, even though those features existed separately before.

#Combining Existing Ideas

Since the time of Adam Smith, people have noticed that combining different elements leads to fresh ideas. For example, if you take the concept of a computer and add the ability to play music, you get a whole new product: a laptop that can also function as a music player.

Joseph Schumpeter, an economist, said that new Combinations of existing products or services lead to success in business. So, if a company can find clever ways to mix and match features, they have a better chance of beating the competition.

#The Challenge of Representing Innovation

While we talk about combining ideas, showing how these combinations happen is a bit tricky. Most of the time, we just describe things qualitatively, like saying, "This company is better because they do X and Y." But what if we wanted to be more precise about it?

Imagine trying to explain a recipe. You could say, "Mix one cup of flour with some sugar to make cookies." But what if you wanted to be more specific? By using a formula, you could explain exactly how much flour, sugar, and baking powder to use, along with cooking times and temperatures. That’s what a mathematical framework, like a presheaf, can help us do for business innovation.

#What Is a Presheaf?

Picture a presheaf as a collection of boxes. Each box contains different items, and the items can change depending on what you put into them. In our example, each box could represent a feature of a product.

Let’s say you have a box labeled "Camera Features." Inside, you could place items like “high resolution,” “night mode,” and “zoom function.” Depending on the camera you are talking about, some of these features might be present, while others might not.

The cool thing about presheaves is that they allow you to see which features can go together smoothly. For example, a high-resolution camera likely won’t have a terrible night mode, as they don't match well together. Our presheaf helps us understand how these features relate to one another.

#Business Strategies and Features

When companies create products, they have to think hard about the features they either want to include or leave out. A successful business strategy should have a well-thought-out combination of features.

Take a look at low-cost airlines. They combine features like fewer in-flight services, direct flights, and lower ticket prices to create a strategy that works. However, if they suddenly decided to offer five-star meals on their flights, it wouldn’t make sense, and they might go out of business.

So, how can we model these combinations effectively? This is where our presheaf comes into play again.

#The Role of Features in Product Design

Let’s take the wine industry as an example. When wineries decide what type of wine to produce, they think about many different features. These could include price, taste complexity, quality of aging, and the prestige of the vineyard.

A premium wine would usually be expensive, have a rich taste, and age well. On the other hand, a budget wine might combine lower values for all these features. By using a presheaf, we can represent these features and their relationships, making it easier to understand which combinations make a viable wine.

#Learning from Real-World Examples

Now, let’s look at a real-world example to see how this works. In 2001, Steve Jobs introduced the concept of the "digital hub," where he envisioned a world of devices revolving around a central computer.

Think about it: back in the day, your computer was the big deal. The idea was that all your devices, like cameras and music players, would connect back to your computer, making it the hub of your digital life. By examining this strategy through the lens of our presheaf, we can see how different device features combine to create a coherent system.

#Amalgamation: The Key to Innovation

Amalgamation is just a fancy word for combining different parts into one. In our case, we can merge the features of a computer and a camcorder to create a new product that offers both functionalities.

For instance, if a camcorder could connect to a computer easily, that’s a feature that benefits both devices. After all, who doesn’t want to edit their vacation videos right after capturing them?

When we think of amalgamation mathematically, we are talking about creating a new presheaf that combines the features of both original products. This allows us to extend the range of possible features and might lead to new sections or products that wouldn’t have been feasible if we kept the devices separate.

#The Importance of Compatibility

Let’s say we have three features: screen size, battery life, and editing capabilities. Understanding how these features interact is vital. If the screen size is small, it might constrain the editing capabilities because having a larger screen simply makes editing easier.

Our presheaf helps to highlight these compatibility issues. If we know that one feature is small, we can pretty much guess that others might be limited too. It’s just common sense, and our presheaf gives us a way to represent that logically.

#Connecting the Dots: Lessons from Wine and Digital Devices

To see how this concept plays out in different industries, let’s draw a parallel between the wine industry and the computer-camcorder connection.

For wine, producing a high-end bottle means balancing features. A low price might signal lower quality, while higher prices often indicate better taste and aging potential. By understanding these relationships, wineries can make informed decisions about which combinations of features to pursue.

Similarly, in the tech world, if a company is developing a new camera that connects to a computer, they will need to think about how features like resolution and editing capabilities will complement each other. If they make a high-res camera but it’s difficult to edit the footage, they’ll miss out on potential customers.

#Constraints and Innovative Thinking

As we discussed, more features bring along more constraints. While this might sound like a headache, it actually helps companies focus their efforts. When you know certain features won’t work together, it makes it easier to decide which combinations to pursue.

In other words, by narrowing down the options through our presheaf model, businesses can concentrate on what makes sense, fostering creativity in the process.

#The Digital Hub: A Prime Example

Let’s go back to Steve Jobs’ idea of the digital hub. By combining the features of different devices, he created a whole new way to think about technology.

Take the iMovie software, for instance. It made editing easier and allowed users to combine their videos with their computers seamlessly. The strong point is how this concept can apply to other areas, like music. iTunes served a similar purpose by bringing together music from different sources into one place.

#The Final Takeaway

We’ve walked through the process of understanding Innovations. Using presheaves allows us to see how features interact and make decisions about what combinations might work best.

By looking at familiar examples, like the wine industry and Steve Jobs’ digital hub, we can appreciate how innovation is often about blending existing ideas rather than inventing completely new things.

In a nutshell, the next time you enjoy a glass of wine or edit a video on your computer, remember that these innovations stem from the age-old principle of putting together what already exists in fresh and exciting ways!