Quotes About Topology

People simply can't accept that patterns carry their own intelligence, quite apart from the semantic content that clings to their surfaces; if you manipulate the topology correctly, that content just comes along for the ride.

Analyzing Topology Using CDP and LLDP The first two major sections of this chapter showed two features—Syslog and NTP—that work the same way on both routers and switches. This final section shows yet another feature common to both routers and switches, with two similar protocols: the Cisco Discovery Protocol (CDP) and the Link Layer Discovery Protocol (LLDP). This section focuses on CDP, followed by LLDP.

There was a long history of speculation that in quantum gravity, unlike Einstein's classical theory, it might be possible for the topology of spacetime to change.

Minus one/plus enjoyment—this is the necessarily distorted structural topology where the subject of the unconscious dwells. This subject is never neuter; it is sexed, since sex(uality) is nothing but a configuring of the signifying minus and of the surplus-enjoyment: a configuring which cannot escape contradiction, the latter being the logical consequence of the one (the Other) that is not there.

Arithmetic and number theory study patterns of number and counting. Geometry studies patterns of shape. Calculus allows us to handle patterns of motion. Logic studies patterns of reasoning. Probability theory deals with patterns of chance. Topology studies patterns of closeness ans position.

Map coloring problem. Find the smallest number m such that the faces of every planar graph can be colored with m or fewer colors in such a way that faces sharing a border have different colors.

Topology] is a purely qualitative subject where quantity is banned. In it two figures are always equivalent if it is possible to pass from one to the other by a continuous deformation, whose mathematical law can be of any sort whatsoever as long as continuity is respected.

A topologist enters a coffee shop, orders coffee and a doughnut, and is served. Preoccupied with topological theorems, he takes a bite out of his coffee cup and has to finish his thoughts in a nearby emergency ward. His mistake is somewhat understandable as a doughnut and coffee cup are topologically equivalent

In battle, topography is fate.

Topology is the science of fundamental pattern and structural relationships of event constellations.

There were topologists who could build architectural structures in their imaginations, then turn them over, then flip them inside out, then spin them around, then open them up and go inside them.

If by following Pannenberg we believe that the eschaton, as "now" and "future," has already appeared proleptically in the events of Easter while yet remaining still to come, we might expect that the universe already has a more complex topology than that of ordinary spacetime in which simple worldlines trace out the history of particles. We might even expect to find hints of this more complex topology prefigured within the theories of physics and cosmology.

I thought of computers as very low class. I thought of myself as a pure mathematician and was interested in partial differential equations and topology and things like that.

Intersections of lines, for example, remain intersections, and the hole in a torus (doughnut) cannot be transformed away. Thus a doughnut may be transformed topologically into a coffee cup (the hole turning into a handle) but never into a pancake. Topology, then, is really a mathematics of relationships, of unchangeable, or "invariant," patterns.

Indeed, it is a proven mathematical theorem that a doughnut is topologically distinct from a sphere.

Ludwig Schlafi (1814-1895) proved that there are six regular four-dimensional polytopes (generalisations of polyhedra): the 5-cell made of tetrahedra, the 8-cell or tesseract made of cubes, the 16-cell made of tetrahedra, the 24-cell made of octahedra, the 120-cell made of dodecahedra, and the 600-cell made of tetrahedra.

Lisa: Well, where's my Dad? Professor Frink: Well, that should be obvious to even the most dimwitted individual who holds an advanced degree in hyperbolic topology that Homer Simpson has stumbled into...the third dimension.

A geometry implies the heterogeneity of locus, namely that there is a locus of the Other. Regarding this locus of the Other, of one sex as Other, as absolute Other, what does the most recent development in topology allow us to posit?

The topography of L.A. is fascinating.

Topologically, a P and a q are equivalent, as are a coffee mug and a doughnut.

With their cell phone, they have access to all people; with GPS, to all places; with the Internet, to all knowledge. They inhabit a topological space of neighborhoods, whereas we lived in a metric space, coordinated by distances.

Hausdorff dimension

Space is a spin network whose nodes represent its elementary grains, and whose links describe their proximity relations. Spacetime

There's so many mysteries related to how flies are able to make their way through the world. I'd certainly like to know a lot more about how their brain works. I'd certainly like to know a lot more about just how they're put together. I mean, these animals are basically, topologically, spheres. They don't have bones as we do, of course.