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Research shows that excessive homework leads to increased stress, physical health problems and a lack of balance in students' lives. Another common argument is that homework helps students develop skills related to problem-solving, time-management and self-direction. Yet, this is the workload most schools place on high school students.
For this week’s EdSurge Podcast, we talked with Khan to hear more about his vision of AI tutors and the arguments from his recent book. What would you say to that argument? I mean, he took calculus in seventh grade. The book is called “ Brave New Words: How AI Will Revolutionize Education (and Why That's a Good Thing). ”
And it’s all based on ideas from our Physics Project —and on a fundamental correspondence between what’s happening at the lowest level in all physical processes and in expression evaluation. And this is where we can start making an analogy with physics. And now there’s a deep analogy to physics.
1 Mathematics and Physics Have the Same Foundations. 2 The Underlying Structure of Mathematics and Physics. 23 The Physicalized Laws of Mathematics. 29 Counting the Emes of Mathematics and Physics. 1 | Mathematics and Physics Have the Same Foundations. 3 The Metamodeling of Axiomatic Mathematics. Graphical Key.
One might have thought it was already exciting enough for our Physics Project to be showing a path to a fundamental theory of physics and a fundamental description of how our physical universe works. Despite this, however, fundamental physics always seemed to resist its advance. The Path to a New Paradigm.
But by the end of the 1800s, with the existence of molecules increasingly firmly established, the Second Law began to often be treated as an almost-mathematically-proven necessary law of physics. The theory of heat will hereafter form one of the most important branches of general physics.
It’s yet another surprising construct that’s arisen from our Physics Project. In the language of our Physics Project, it’s the ultimate limit of all rulial multiway systems. And here is a rulial multiway system made from hypergraph rewriting of the kind used in our Physics Project , using all rules with signature : ✕.
I had begun my career in the 1970s as a teenager studying the frontiers of existing physics. And at first I couldn’t see how computational rules could connect to what is known in physics. But I didn’t stop thinking “one day I need to get back to my physics project”. But now with the Physics Project I was doing this.
Line, Surface and Contour Integration “Find the integral of the function ” is a typical core thing one wants to do in calculus. But particularly in applications of calculus, it’s common to want to ask slightly more elaborate questions, like “What’s the integral of over the region ?”, or “What’s the integral of along the line ?”
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.
The Second Law of thermodynamics is considered one of the great general principles of physical science. Sometimes textbooks will gloss over everything; sometimes they’ll give some kind of “common-sense-but-outside-of-physicsargument”. But our Physics Project has changed that picture. Why does the Second Law work?
Beginning about five years ago—particularly energized by our Physics Project —I started looking at harvesting seeds I’d sown in A New Kind of Science and before. Our modern Wolfram Language tools—as well as ideas from our Physics Project—provided some new directions to explore. But I still thought I pretty much knew what we’d find.
One might have thought it was already exciting enough for our Physics Project to be showing a path to a fundamental theory of physics and a fundamental description of how our physical universe works. Despite this, however, fundamental physics always seemed to resist its advance. The Path to a New Paradigm.
Indeed, so confident was he of his programming prowess that he became convinced that he should in effect be able to write a program for the universe—and make all of physics into a programming problem. 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).
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. If we define a month “physically”, it corresponds to a certain fractional number of days: ✕.
An instantaneous moment (or perhaps a single elementary time from our Physics Project )? In physics textbooks, it’s traditional to carefully distinguish absolute temperatures, measured in kelvins, from temperature scales, like degrees Celsius or Fahrenheit. Calculus & Its Generalizations. A month (whatever that means)?
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