Why good ideas are oft-born as twins

"We often praise ideas for their originality and criticise other ideas for being insufficiently novel. So, what do we make of the fact that most important breakthroughs in sci-tech history—the telegraph, telescope, and transistor; the laws of calculus and gravity—were 'simultaneously invented' by independent people around the same time? (Alexander Graham Bell and Elisha Gray notoriously filed for a telephone patent on the same day.)
    "Which is to say: Some of the most important ideas in the world weren't 'new' when the inventor we credit came up with them.
    "It's even more uncanny than that. Charles Darwin and Alfred Russel Wallace didn't just independently come up with the basics of evolution. They both cited the exact same essay—Malthus's infamous 'Principle of Population'—as inspiration for thinking about species evolution as a competitive game where unforgiving environments shape genetic survival. As @DavidEpstein writes in today's essay, adapted from his ... new book Inside the Box, the frequency of idea twins in history suggests that once a problem is framed by a generation of thinkers with sufficient clarity and precision, the answer almost 'wants' to be found."

~ @Derek Thompson summarising David Epstein's essay 'Why Your Best Ideas Aren’t Original'

"All abstract knowledge depends, for its meaning and validity, on other knowledge that sets the context for it. For example, algebra depends on addition, and calculus depends on algebra. The more complex the knowledge, the more extensive the knowledge that must precede it.
    "One major aspect of the fact that knowledge depends on other knowledge—the aspect most relevant to and most violated in education—is that more abstract knowledge depends on less abstract knowledge. This is the principle of the hierarchy of knowledge."

~ Lisa Van Damme from her article 'The Hierarchy of Knowledge: The Most Neglected Issue in Education'

"Valid concepts [once discovered] function as a 'green light' to induction, permitting [further] generalisations from observed particulars, while invalid concepts block or distort the process."

~ summary of the inductive process given in David Harriman's 2011 book The Logical Leap: Induction in Physics & Philosophy

"[I]nherent in this is that concepts are future-looking. A concept is like a policy or a commitment. It’s like forming a file. ... A file, if you have a filing system, does not only organise and condense data that one already has, it does so on the premise of keeping up with this method of organisation. ... 
    "[T]o form a concept [then] is to institute a policy of applying what one knows from the study of each instance to the study of each other instance, to regard the instances as interchangeable, at least within a certain context, within a certain, you know, varying in degree. And this policy applies to information yet to be discovered, as well as to the information one already has ..."

~ Gregory Salmieri from his 2006 essay 'Objectivist Epistemology in Outline'