In mathematics, an isomorphism is a structure-preserving mapping between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are isomorphic if an isomorphism exists between them. The word isomorphism is derived from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape".

In differential calculus and differential geometry, an inflection point, point of inflection, flex, or inflection (British English: inflexion) is a point on a smooth plane curve at which the curvature changes sign. In particular, in the case of the graph of a function, it is a point where the function changes from being concave (concave downward) to convex (concave upward), or vice versa.

When Arthur Patterson and Jim Swartz co-founded Accel, a core principle of their approach to investing was a thesis-based method called a “Prepared Mind”. Referencing the Louis Pasteur quote “chance only favours the prepared mind”, this method remains integral to how we approach, learn about and invest in new opportunities today. Prepared Minds involve our team honing in on specific categories and industries, being proactive, talking to our network, researching the trends shaping tomorrow’s world, finding the category leader - and then moving fast (for the right reasons!).

Returning to the example of fire, our intuitive knowledge of activation energy keeps us safe. Many chemical reactions have high activation energy requirements, so they do not proceed without an additional input. We all know that a book on a desk is flammable, but will not combust without heat application. At room temperature, we need not see the book as a fire hazard. If we light a candle on the desk, we know to move the book away. If chemical reactions did not have reliable activation energy requirements, we would live in a dangerous world.

Energy can have two dimensions. One is motivated, going somewhere, a goal somewhere, this moment is only a means and the goal is going to be the dimension of activity, goal oriented-then everything is a means, somehow it has to be done and you have to reach the goal, then you will relax. But for this type of energy, the goal never comes because this type of energy goes on changing every present moment into a means for something else, into the future. The goal always remains on the horizon. You go on running, but the distance remains the same. No, there is another dimension of energy: that dimension is unmotivated celebration. The goal is here, now; the goal is not somewhere else. In fact, you are the goal. In fact, there is no other fulfillment than that of this moment–consider the lilies. When you are the goal and when the goal is not in the future, when there is nothing to be achieved, rather you are just celebrating it, then you have already achieved it, it is there. This is relaxation, unmotivated energy

Second order thinkers ask themselves the question “And then what?” This means thinking about the consequences of repeatedly eating a chocolate bar when you are hungry and using that to inform your decision. If you do this you’re more likely to eat something healthy.