![]() He maintains that space itself can be thought of as a mesh that knits together a series of nodes in this fashion. Wolfram argues that extremely complex graphs resemble surfaces and volumes: add enough nodes and connect them with enough lines and you form a kind of mesh. In the same way that a collection of points and lines can approximate a solid cube, Wolfram argues that space itself may be a mesh that knits together a series of nodes. Keep applying the rule and, pretty soon, the network of friends forms a complex graph. Apply the rule again to every person (including the one you started with, namely: Betty). Apply the rule to Betty: now she has three friends. Next, add a simple rule: every person adds three friends. He does so via a branch of mathematics called graph theory, which studies groups of points or nodes connected by lines or edges. Wolfram is attempting to provide an alternative to string theory. This theory has been a work in progress for 50 years or so, and while it has achieved some success there is a growing dissatisfaction with it as an approach. The current best approach we have to quantum gravity is string theory. This has led to a quest for the holy grail of physics: a theory of quantum gravity, which would combine what we know from general relativity with what we know from quantum mechanics to produce an entirely new physical theory. General relativity “breaks down” when we try to extend it into the miniature realm where quantum mechanics rules. ![]() While we have an excellent theory of how gravity works for large objects, such as stars and planets and even people, we don’t understand gravity at extremely high energies or for extremely small things. These are general relativity – a theory of gravity and the large-scale structure of the universe – and quantum mechanics – a theory of the basic constituents of matter, sub-atomic particles, and their interactions. Why do we need such a theory? After all, we already have two extraordinarily successful physical theories. The guiding idea is that everything can be boiled down to the application of simple rules to fundamental building blocks. The new physics, he declares, is computational. ![]() Last week, Wolfram launched a new venture: the Wolfram Physics Project, an ambitious attempt to develop a new physics of our universe. System used by scientists the world over. He is also responsible for Mathematica, a computer He is the brains behind Wolfram Alpha, a website that tries to answer questions by using algorithms to sift through a massive database of information. So whether your studies are in algebra, calculus, or physics, Wolfram|Alpha can be your resource for learning about vectors.Stephen Wolfram is a cult figure in programming and mathematics. Wolfram|Alpha can even help you add and subtract two vectors using the tip-to-tail method. The radius gives you the magnitude of your vector, while the angles specify its direction. If you want to find both the magnitude and direction, you can represent the vector in polar or spherical coordinates. You can query Wolfram|Alpha for the vector’s length to find its magnitude:Īnd to find the direction, you can ask for the angles between the vector and the coordinate axes: Suppose you know only the point in R^n corresponding to your vector and you want to know its magnitude and direction. Wolfram|Alpha can now plot vectors with this arrow representation in 2D and 3D and return many other properties of the vector. The direction of the arrow matches the direction of the vector, while the length represents the magnitude of the vector. A vector is commonly defined as a quantity with both magnitude and direction and is often represented as an arrow. For example:Īnd in fact, Wolfram|Alpha can give lots of information on vectors. What do you get when you cross a mountain climber with a mosquito? Nothing-you can’t cross a scalar with a vector!īut what do you get when you cross two vectors? Wolfram|Alpha can tell you.
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