By Harrison Hao Yang, Steve Chi-Yin Yuen, Harrison Hao Yang, Steve Chi-Yin Yuen
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Sample text
What we count is as important as how we count, and on this, quantitative reasoning is silent. We can measure grades, but are grades the measure of learning? We can measure economic growth, but is an increase in the circulation of money a measure of progress? We can easily mislead ourselves with statistics, as Huff (1993) shows, and in more esoteric realms, such as probability, our intuitions can be exactly wrong. We compensate for these weaknesses by recognizing that a single point of view is insufficient; we distribute what constitutes an ‘observation’ through a process of description and verification.
Through processes such as doubleblind experimentation, we additionally take care to ensure that our expectations do not influence the count. In statistical reasoning, we take care to ensure that we have a sufficiently random and representative sample, in order to ensure that we are measuring one phenomenon, and not a different, unexpected phenomenon. In both we employ what Carnap called the requirement of the total evidence: we peer at something from all angles, all viewpoints, and if everybody (or the preponderance of observers) conclude that it’s a duck, then it’s a duck.
If a signal has more than an even chance of being propagated from one entity in the network to the next, and if the network is fully connected, then the signal will eventually propagate to every entity in the network. The speed at which this process occurs is a property of the connectivity of the network. In (certain) random and scale free networks, including hierarchal networks, it takes very few connections to jump from one side of the network to the other. Cascade phenomena sweep through densely connected networks very rapidly.
