This is partially correct and partially misleading. The part that is misleading is to think of a n-sphere as necessarily being embedded in some other space. I think that is where UberQwerty gets confused.
A topological space is a set of points with the notion of a neighborhood of each point. If every point in the space has a neighborhood that looks like (homeomorphic) familiar 3-space then it is a 3-manifold. Similarly for n-manifolds. (Example: the ordinary hollow sphere is a 2 manifold because little sections of it look like a plane.)
Our ordinary experience (excluding relativity, string theory, etc.) says we live in a universe that is a 3-manifold.
Poincare says that a 3-manifold that is simply connected (e.g., able to draw a curve between any two points without going out of the space) and closed (any sequence of points that tend to a limit have that limit in the manifold) is actually topologically eqivalent to the set of points in 4-space equidistant from a given point.
So thinking of the apparent 3-dimensional universe, it doesn't have "holes" or weird twists like you can do in 2 dimensions on a Mobius band.
This really has great medical potential, but I can imagine similar developments of the future used for other purposes. Being able to monitor bodily chemicals could be extremely valuable, but also subject to unexpected uses.
As condition of your employment, you agree to a permanent tattoo that indicates drug use. Or, The court orders you to get a drug-monitoring tattoo and scan it by your home internet-connected device every 6 hours.
I can't be certain that this patent app is the one from JVC/Hudson, but the description is pretty detailed about the method and sounds a lot like what is described in the article. So if you want to dig into what is current in the US Patent office, look at this.
http://appft1.uspto.gov/netacgi/nph-Parser?TERM1=2 0020080960&Sect1=PTO1&Sect2=HITOFF&d=PG01&p=1&u=%2 Fnetahtml%2FPTO%2Fsrchnum.html&r=0&f=S&l=5 0
Sorry if I messed up the link, but you can just search at uspto.org in the patent applications for number 20020080960
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This is partially correct and partially misleading. The part that is misleading is to think of a n-sphere as necessarily being embedded in some other space. I think that is where UberQwerty gets confused.
A topological space is a set of points with the notion of a neighborhood of each point. If every point in the space has a neighborhood that looks like (homeomorphic) familiar 3-space then it is a 3-manifold. Similarly for n-manifolds. (Example: the ordinary hollow sphere is a 2 manifold because little sections of it look like a plane.)
Our ordinary experience (excluding relativity, string theory, etc.) says we live in a universe that is a 3-manifold.
Poincare says that a 3-manifold that is simply connected (e.g., able to draw a curve between any two points without going out of the space) and closed (any sequence of points that tend to a limit have that limit in the manifold) is actually topologically eqivalent to the set of points in 4-space equidistant from a given point.
So thinking of the apparent 3-dimensional universe, it doesn't have "holes" or weird twists like you can do in 2 dimensions on a Mobius band.
This really has great medical potential, but I can imagine similar developments of the future used for other purposes. Being able to monitor bodily chemicals could be extremely valuable, but also subject to unexpected uses.
As condition of your employment, you agree to a permanent tattoo that indicates drug use.
Or,
The court orders you to get a drug-monitoring tattoo and scan it by your home internet-connected device every 6 hours.
I can't be certain that this patent app is the one from JVC/Hudson, but the description is pretty detailed about the method and sounds a lot like what is described in the article.2 0020080960&Sect1=PTO1&Sect2=HITOFF&d=PG01&p=1&u=%2 Fnetahtml%2FPTO%2Fsrchnum.html&r=0&f=S&l=5 0
So if you want to dig into what is current in the US Patent office, look at this.
http://appft1.uspto.gov/netacgi/nph-Parser?TERM1=
Sorry if I messed up the link, but you can just search at uspto.org in the patent applications for number 20020080960