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The principal value Arg of the blue point at 1 + i is π/4. This means that things like the way reasoning is performed, the mathematical notation, inference rules and which assumptions and models are used when doing math can be changed, but the phenomenons of reality described through the math are unaffected.
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Users might only have certain parts of those abilities.Figure 3. Abstract manipulation of mathematics: The ability to manipulate mathematics in its abstract form.Probability Manipulation: As the probability for something to happen is usually expressed as mathematical value, a user might be capable of influencing probability by changing that value.Manipulation of form: The user might be capable of changing the form, volume, area and similar of things, as those are also mathematical properties of objects.Spatial Manipulation: Since concepts like distance and properties of space are in abstract form part of the mathematical studies changing the mathematics describing those could also have effect on the real properties of space.For example by creating a mathematical contradiction and through the principle of " ex falso sequitur quodlibet" the validity and usefulness of logic could be undermined. Logic Manipulation: Since mathematics builds upon, includes and extends logic, changing mathematics can have an effect on the underlying logical concepts.One possible application would for example changing 5 dimensional things to 3 dimensional and vice versa. With Manipulate, you can design programs that allow. Dimensional Manipulation: Since dimensions are a mathematical concept, a user of this ability might be capable of changing the attributes of dimensions and the concept of them in itself. One of the more interesting developments in recent releases of Mathematica is the Manipulate function.Another application of this is to forcefully apply mathematical operations to reality, for example building the sum of two things making them fuse together. For example by changing the laws so that 1+1=3, it could be made so that if one apple is taken and another one put to it, the resulting amount of apples is three apples. Operation Manipulation: By changing the way mathematical operations work real phenomena described through them may have different results.By manipulating the subject itself the results of measuring the quantity of something can be changed, effectively making it so that there is more of something or less.
MATHEMATICA MANIPULATE CODE
A Wolfram employee created a fully functional, interactive graphical user interface with just a few lines of code in about 2. I’ll never forget the first time I saw a Mathematica Manipulate it was at the 2006 International Mathematica Symposium in Avignon when version 6 was still in beta. Integrate videos and other web content directly into your Mathematica notebooks. Use Manipulate, 3D graphics and other interactive functions directly in your browser.