Linked
In Linked by Barabasi, he discusses the idea that everything is interconnected and there are networks in so many things that we experience in our daily lives. He discusses graphs and networks along with the inherent constraints that they bring. I agree with his interpretation of these systems. It makes sense that the way that a graph or network is constructed will directly affect how they are used. Topology is an amazing field of mathematics. It has so many applications and wondrous ideas that allow many people to realize the elegance in everyday systems. One complex example of how topology can lead to great discoveries is evident when dealing with string theory. Barabasi had briefly mentioned "superstrings" when discussing the reductionist point of view. These are tiny vibrating "strings" of energy that are present at the plank level and are the fundamental building blocks of matter. String theory is not yet proven, yet the mathematics that it takes advantage of involves complicated topology that is utilized in an 11 dimensional space. Physicists and mathematicians have come up with a representation of space called a Calabi-Yau manifold. The topology of these multidimensional spaces allows for many of them to exist, yet only one is what physicists expect to accurately describe our universe. Another example of an interesting topology theory involves maps. If someone were to make any number of shapes on a map, such as countries or states, they would only need a maximum of 4 colors to differentiate between the different shapes. Another more familiar topology application is a Möbius strip. All of these applications of topology require a strict set of rules and regulations or else they would be completely different.
Barabasi also discusses "random graph theory" and "random network theory." He talks about how at a party, or any other event, each person can represent a node. These nodes can be connected indirectly to any other node by a series of other nodes. This idea is the basis for the game 6 degrees of separation. The theory that all of these nodes can be connected after such a short number of node interactions is a powerful idea. One example that comes to mind that demonstrates this well is the social network website Facebook. On Facebook, people add friends to their list of friends. When they see that those friends have friends that they know, they often add them to their list as well. After only a little while, there is a giant web of people who are added that all know each other either directly or indirectly. It is this idea of "random network theory" that gives an incite as to how information is spread so rapidly. The longer a network is able to develop, such as the network of Facebook friends, the more nodes are added through other nodes, at what appears to be an exponential rate.
Barabasi also discusses "random graph theory" and "random network theory." He talks about how at a party, or any other event, each person can represent a node. These nodes can be connected indirectly to any other node by a series of other nodes. This idea is the basis for the game 6 degrees of separation. The theory that all of these nodes can be connected after such a short number of node interactions is a powerful idea. One example that comes to mind that demonstrates this well is the social network website Facebook. On Facebook, people add friends to their list of friends. When they see that those friends have friends that they know, they often add them to their list as well. After only a little while, there is a giant web of people who are added that all know each other either directly or indirectly. It is this idea of "random network theory" that gives an incite as to how information is spread so rapidly. The longer a network is able to develop, such as the network of Facebook friends, the more nodes are added through other nodes, at what appears to be an exponential rate.
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