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And indeed particularly in chemistry and engineering it’s often been in the background, justifying all the computations routinely done using entropy. There was also a sense that regardless of its foundations, the Second Law was successfully used in practice.
So did that mean we were “finished” with calculus? Somewhere along the way we built out discrete calculus , asymptotic expansions and integral transforms. And in Version 14 there are significant advances around calculus. Another advance has to do with expanding the range of “pre-packaged” calculus operations.
Since the standard Wolfram Language evaluator evaluates arguments first (“leftmost-innermost evaluation”), it therefore won’t terminate in this case—even though there are branches in the multiway evaluation (corresponding to “outermost evaluation”) that do terminate. As the Version 1.0
The fall of 2021 involved really leaning into the new multicomputational paradigm , among other things giving a long list of where it might apply : metamathematics, chemistry, molecular biology, evolutionary biology, neuroscience, immunology, linguistics, economics, machine learning, distributed computing. Let’s talk first about chemistry.
Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. Chemistry / Molecular Biology. In standard chemistry, one typically characterizes the state of a chemical system at a particular time in terms of the concentrations of different chemical species.
Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. Chemistry / Molecular Biology. In standard chemistry, one typically characterizes the state of a chemical system at a particular time in terms of the concentrations of different chemical species.
Sometimes textbooks will gloss over everything; sometimes they’ll give some kind of “common-sense-but-outside-of-physics argument”. Once one has the idea of “equilibrium”, one can then start to think of its properties as purely being functions of certain parameters—and this opens up all sorts of calculus-based mathematical opportunities.
It didn’t help that his knowledge of physics was at best spotty (and, for example, I don’t think he ever really learned calculus). In 2015 Ed told me a nice story about his time at Caltech: In 1952–53, I was a student in Linus Pauling’s class where he lectured Freshman Chemistry at Caltech. It’s just my nature.
You can give Threaded as an argument to any listable function, not just Plus and Times : ✕. we’re adding SymmetricDifference : find elements that (in the 2-argument case) are in one list or the other, but not both. Now we can use the path function to make a “spiralling” tour video: College Calculus. In Version 13.1
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