5: It's a Small World After All
The notion that it's a "small world" generally refers to the connections we have to other people, which often take us by surprise. The anecdote at the beginning of the chapter reflects this: a salesman calling on an executive notices some university logo in his office and, through a brief exchange, learns that his niece is a close friend of the man's daughter.
These sorts of connections "accelerate your trip up the pyramid." This hearkens to a very primitive notion of alliance that still holds true: the friend of my friend is a friend to me. This is largely because a person trusts the opinion of friends - and if their friend holds you in high regard, chances are that's a good recommendation. Word-of-mouth works in much the same way. It's quite common for a person to ask people whom they know and respect for recommendations - "do you know a good mechanic?" - and trust in those recommendations moreso than the recommendations of persons unknown.
(EN: the author doesn't mention the social motives - in many instances, individuals will change their opinions to match those of their friend. And so, if you dislike someone your friend likes, the difference of opinion is a threat to your relationship with that friend - so people will try to like the same things, and same people, as do those with whom they have a social connection.)
The author distinguishes "connecting" from "networking," in that the later is more broad and shallow - it's about getting your contact information into the hands of as many people as possible, or gathering the contact information of others, but it's just the basic facts - who you are, what you do, how to get in touch. Connecting is about developing a deeper connection with a smaller number of people.
That's not to say that networking is necessarily a bad thing, as it can be useful to have a large body of individuals to consider, but that networking alone is not enough: the people with whom you have connect know you - those with whom you have networked merely know of you.
Connect For Another Person
Introductions are an effective way to leverage the power of connections - asking someone you know to help you meet someone that they know, and whom you are having some difficulty getting to respond.
But in addition to leveraging connections for your own good, use your own connections to help others. If you have one acquaintance who's in need, and another who might help, then put them together. If they benefit from the connection (and generally, they will), then it will improve your relations with both parties - the person who needs help will be grateful, and the person who renders aid will appreciate your confidence in their ability to give help.
It may also be helpful to bring in others who are similar. An anecdote is presented about a salesman who was wooing a client who was a retired military officer and had little ability to "connect" with the man - but he was able to find an executive who had military experience to bring along as part of the team, mainly to connect with the prospect, and this sealed the deal.
There remain individuals with whom it is difficult to connect, and you hay have to hunt for someone who can help you with an introduction - but most people who have achieved some level of professional success are connected to many others you may know in the same industry. It just takes some digging, but chances are you will eventually find that someone you've connected with is connected to them: they have worked together, attended industry events, etc.
Connections as an Start
A final note on the topic of connections: while connections can give you a jump-start to forming a relationship, it is not a substitute for one. You cannot count on borrowed esteem for very long, and will need to establish a self-sustaining relationship after it gets you in the door.