Eva Brann discusses her book The Logos of Heraclitus (2011).
What is the world like, and how can we understand it? Heraclitus thinks that the answer to both questions is found in "the logos," which is a Greek word with multiple meanings: it can be an explanation, a word or linguistic meaning, science, rationality (the Latin word is "ratio"), the principle of exchange between things... So the world is logos, in that it behaves in a lawlike manner so that mathematics and science can describe it. His physics imagined a basic material (he calls it fire, but clearly doesn't mean the same thing as ordinary, visible fire) that transforms in lawlike ways (in definite ratios) into all the different parts of the world, and that it's these cycles of transformation, driven by the logos itself, that make the world the moving system it is.
The world's intelligibility--its singular logos--doesn't mean it's peaceful, though. The world is held together by tension; the logos is force. Confusingly to modern readers, Heraclitus believes that paradoxes really exist, that what in this discussion we call "stable ambivalences" hold, e.g. that relationships are made up of both love and strife, not in alternation but both, essentially, at the same time. Should this "logos" be thought of as God? Does it have a personality, a will? Is it immanent in the world or a transcendent force shaping the world? Heraclitus says that the logos "is unwilling and willing to be called by the name of Zeus." It's a stable ambivalence! Is your MIND BLOWN YET? Read more about the topic.
End song: "Trading Away" by New People, from Impossible Things (2011), written by Matt Ackerman. Why this song? Because fire is traded/transforms into everything else, and Heraclitus was a misanthrope.