41–50 of 124 posts
Is it glass wool hanging down from his underfloor ceiling in insane qualities? I was raised to believe it's extremely dangerous to health, people crawling there scare me. Of course it's easier with forklift.
Real life Gyro Gearloose!!! In the next video he talks about how a Klein bottle is made, and how, contrary to a bottle, it has no edge. I'm not sure I understand why a bottle "has to" have an edge? Surely it's possible to make a bottle with no edge? For example, if one takes a sphere and progressively turns it into a bowl (by punching into it), and then makes the bowl deeper, it still has just one surface and no edge…
I could paint the inside of your surface red and the outside blue (where by "inside" I mean the part you've trapped air in). That's not the case with Cliff's bottles.
The abstract object doesn't, the 3d manifestation of it does.
Real life Gyro Gearloose!!! In the next video he talks about how a Klein bottle is made, and how, contrary to a bottle, it has no edge. I'm not sure I understand why a bottle "has to" have an edge? Surely it's possible to make a bottle with no edge? For example, if one takes a sphere and progressively turns it into a bowl (by punching into it), and then makes the bowl deeper, it still has just one surface and no edge…
The rim of your bowl is the edge: it's a point where the curvature changes suddenly. But that's not the important thing: the important thing is that not only is there only no edge, but only one surface. Let's talk topology for a bit. A manifold can be thought of as essentially a flat and infinitely thin sheet. If you have a spherical manifold (and your bowl would be a spherical manifold), it has two surfaces: one on…
So in fact, what I understand so far is:
- a (hollow) sphere has two surfaces, one inside and one outside, and you can't connect one to the other (you can't walk from one to the other)
- a potato, or a bowl also have the same properties: two distinct surfaces
- a bottle is not a special kind of bowl, it's more of a broken sphere (an egg the top of which has been removed) so that both surfaces (in and out) are accessible (but disjoint)
- to make a true bottle out of a bowl one needs to somehow "collapse" the inner and outer surfaces (therefore creating an edge)
- if you make a bottle that has a hollow space between the inside and the outside (think Thermos), then you actually have three surfaces
Is this correct?
Wow, synchronicity -- I just received a klein bottle order in the mail from him YESTERDAY.
I love my KB. :D
Is it glass wool hanging down from his underfloor ceiling in insane qualities? I was raised to believe it's extremely dangerous to health, people crawling there scare me. Of course it's easier with forklift.
That was asbestos, glass wool is reasonably safe to be around.
Earlier quoted context omitted.
The rim of your bowl is the edge: it's a point where the curvature changes suddenly. But that's not the important thing: the important thing is that not only is there only no edge, but only one surface. Let's talk topology for a bit. A manifold can be thought of as essentially a flat and infinitely thin sheet. If you have a spherical manifold (and your bowl would be a spherical manifold), it has two surfaces: one on…
But with an ordinary bottle, the edge is the point (if I may), because if a bottle had no edge, couldn't it be said that has just one ordinary surface? So in fact, what I understand so far is: - a (hollow) sphere has two surfaces, one inside and one outside, and you can't connect one to the other (you can't walk from one to the other) - a potato, or a bowl also have the same properties: two distinct surfaces - a bott…
In topology, you deal with manifolds. Manifolds have no thickness, but they do have area.
In topology, there's no such thing as a 'filled' sphere: a sphere in topology has no edges and an inside surface and an outside surface, much like a football.
There are two ways you can make a 'bottle': you can deform a sphere, which gives you a 'bottle' much like a vaccuum flask; or you can deform a planar manifold (which is like a sheet of paper). The former will have two surfaces and no edge, whereas the latter will have two surfaces and one edge, that being the rim.
A broken sphere would be a planar manifold.
A vaccuum flask is simply a deformed sphere in topological terms, and thus only has two surfaces, the inside and the outside.
Earlier quoted context omitted.
I could paint the inside of your surface red and the outside blue (where by "inside" I mean the part you've trapped air in). That's not the case with Cliff's bottles.
If you stick a cork in the bottom, his bottles have an inside and an outside. The abstract object doesn't, the 3d manifestation of it does.
It's just sealing the local minimum. (Maximum? I don't really know what the sign should be for this. Probably maximum, for enclosed volume, since I'm not sure if it's reasonable to talk about the topology having a minimum in this context...)
Earlier quoted context omitted.
That was asbestos, glass wool is reasonably safe to be around.
jup, just don't handling it sucks (it gets everywhere and itches if it penetrates your skin. construction workers often don't seem to give much of a * though...)
Cliff Stoll in case people were wondering: https://en.wikipedia.org/wiki/Clifford_Stoll I have his original book my shelf, it was fascinating when it came out. His Klein Bottle company is here: http://www.kleinbottle.com/
The Copy on Kleinbottle.com is marvelous, its like pouring hot cocoa spiced with love: From http://www.kleinbottle.com/drinking_mug_klein_bottle.htm : "The 7 mm air space separates the inside from the outside, so ice water won't cause condensation. This extends the life of hot or cold drinks, saves energy, and helps stave off the dreaded local thermodynamic equilibrium." But seriously just read the whole page, this i…