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Quantum mechanics describes our relationship with reality, not reality itself
https://iai.tv/articles/quantum-mechanic..._auid=2020
INTRO: The physicist Antony Valentini recently argued in IAI News that quantum mechanics is a straightforward—though incomplete—description of material reality. Today, philosopher and former Director of Research at the renowned French National Center for Scientific Research, Michel Bitbol, makes the opposing case. Scientists, he argues, mistakenly assume that quantum mechanics must either be an incomplete description of a deterministic reality or a complete description of a genuinely random reality. A third option, too often ignored, is that the inevitability of probability at the core of physics is bound up with the agent's participation in its environment, and thus with our inseparability from the world. (MORE - details)
Topology takes a strange turn in 4 dimensions
https://www.yahoo.com/news/science/artic...00454.html
EXCERPT: In topology, mathematicians try to reduce objects to their essential properties. This allows them, for example, to make statements about an entire class of objects without having to examine each one individually. One famous example is that, topologically speaking, a doughnut and a cup of coffee with a simple ring handle are the same: they each have exactly one hole.
As long as you stay in one, two or three dimensions, everything is fine. But problems begin in four dimensions. The deformations you can make to transform two shapes into one another can become more complex. If you want to mold one smooth shape into another, sharp corners and edges can suddenly appear during the process. That's like saying that in order to transform a circle into an oval, you first need to reshape it like a star. This kind of change is unnecessary in one, two or three dimensions, but in four dimensions, it's sometimes unavoidable.
This phenomenon has led to the existence of two types of equality in topology: First, two objects are generally topologically equal if they can be deformed into each other—regardless of how the process occurs. There is also a stricter form of equality, however: two figures are what mathematicians call "diffeomorphic" if they can be deformed into each other smoothly, without ever creating corners or edges. Thus, in higher dimensions, there are objects that are topologically equal but not diffeomorphic—that is, they cannot be transformed into each other smoothly.
This is a general characteristic of higher dimensions. But four dimensions remain a special case. If you consider a space Rnspanned by n real numbers in each dimension (that is, something like an n-dimensional coordinate system), then this space is always unique for all dimensions n except four. In other words, all spaces that are topologically equivalent to the n-dimensional space Rn are also diffeomorphic to it. This means that one will not encounter vertices and edges when transforming one space into the other. In 1981 mathematician Michael Freedman discovered that the 4D space R4 is an exception. In fact, there are infinitely many 4D figures that can be transformed into the 4D R4 in different ways without being diffeomorphic: all of them exhibit a different kind of pattern of vertices and edges during the transformation.
This makes 4D space a very strange place. But it's not just 4D space itself that's strange—so are 4D figures... (MORE - missing details)
https://iai.tv/articles/quantum-mechanic..._auid=2020
INTRO: The physicist Antony Valentini recently argued in IAI News that quantum mechanics is a straightforward—though incomplete—description of material reality. Today, philosopher and former Director of Research at the renowned French National Center for Scientific Research, Michel Bitbol, makes the opposing case. Scientists, he argues, mistakenly assume that quantum mechanics must either be an incomplete description of a deterministic reality or a complete description of a genuinely random reality. A third option, too often ignored, is that the inevitability of probability at the core of physics is bound up with the agent's participation in its environment, and thus with our inseparability from the world. (MORE - details)
Topology takes a strange turn in 4 dimensions
https://www.yahoo.com/news/science/artic...00454.html
EXCERPT: In topology, mathematicians try to reduce objects to their essential properties. This allows them, for example, to make statements about an entire class of objects without having to examine each one individually. One famous example is that, topologically speaking, a doughnut and a cup of coffee with a simple ring handle are the same: they each have exactly one hole.
As long as you stay in one, two or three dimensions, everything is fine. But problems begin in four dimensions. The deformations you can make to transform two shapes into one another can become more complex. If you want to mold one smooth shape into another, sharp corners and edges can suddenly appear during the process. That's like saying that in order to transform a circle into an oval, you first need to reshape it like a star. This kind of change is unnecessary in one, two or three dimensions, but in four dimensions, it's sometimes unavoidable.
This phenomenon has led to the existence of two types of equality in topology: First, two objects are generally topologically equal if they can be deformed into each other—regardless of how the process occurs. There is also a stricter form of equality, however: two figures are what mathematicians call "diffeomorphic" if they can be deformed into each other smoothly, without ever creating corners or edges. Thus, in higher dimensions, there are objects that are topologically equal but not diffeomorphic—that is, they cannot be transformed into each other smoothly.
This is a general characteristic of higher dimensions. But four dimensions remain a special case. If you consider a space Rnspanned by n real numbers in each dimension (that is, something like an n-dimensional coordinate system), then this space is always unique for all dimensions n except four. In other words, all spaces that are topologically equivalent to the n-dimensional space Rn are also diffeomorphic to it. This means that one will not encounter vertices and edges when transforming one space into the other. In 1981 mathematician Michael Freedman discovered that the 4D space R4 is an exception. In fact, there are infinitely many 4D figures that can be transformed into the 4D R4 in different ways without being diffeomorphic: all of them exhibit a different kind of pattern of vertices and edges during the transformation.
This makes 4D space a very strange place. But it's not just 4D space itself that's strange—so are 4D figures... (MORE - missing details)