SM Class 06 What is Space?

Starting from number A number, 7 A sequence of numbers, 1, 2, 3, 5, 8, 13, 21, … A collection of numbers.

From number to space Can this collection of numbers give you a sense of space?

From number to space Can this collection of numbers give you a sense of space?

From symbol to space Can this collection of dots give you a sense of space?

From symbol to space Can this collection of dots give you a sense of space?

Characteristics A collection of dots may not give you a sense of space. Their relationship among themselves about the togetherness can give you a sense of space.

The connection The use of lines more emphasizes the togetherness.

The connection If we label the dots, we can easily notice the configuration

The connection The connectivity information can be written down in symbol form like, (1,2,4,5,6), (3,7) Note that it is not a formal Mathematical notation.

Neighbour We can say that 1, 2, 4, 5, 6 are neighbours and 3, 7 are also neighbours. (1,2,4,5,6), (3,7)

Topology The connectivity and neighborhood give the concept of topology. Note that it is a very simplified description.

Möbius Strip

Escher

Klein Bottle

Characteristics Shape, size, orientation are not important in this context. The most important one is the connectivity.

Applications

London Tube Map

A Quiz

Space in real life Shape and size may be important in some applications.

Metric Space Need the concept of distance. That is, a function (d) which takes two points in the space and returns a real number. d (p1, p2) -> r

Distance The distance function (d) obeys the following, d (p1, p1) = 0 d (p1, p2) = d (p2, p1) d (p1, p2) + d (p2, p3) >= d (p1, p3)

Neighborhood By using the concept of distance, we can redefine the neighborhood. The neighborhood for a point p with a distance D are all the point x, such that d (p, x) <= D

Distance in 1D The distance function d = x - p in the real number line.

Distance in 2D The distance function d = Math.sqrt((qx-px)*(qx- px) + (qy-py)*(qy-py)) in the plane.

Neighbour in Digital We can say the neighborhood of 5 is the numbers 1, 2, 3, 4, 6, 7, 8,

Neighbour in Digital Or we can only include 2, 4, 6, 8 as the neighborhood of

What is the Creativity? Think of how the neighbours of 5 affect the value of 5 itself

Neighbour in Action Convolution Matrix

Scale :

Convolution Matrix Scale :

Convolution Matrix Scale :

Convolution Matrix Scale :

Game of Life By John Conway,

Game of Life - The Rules For a space that is 'populated': Each cell with one or no neighbors dies, as if by loneliness. Each cell with four or more neighbors dies, as if by overpopulation. Each cell with two or three neighbors survives. For a space that is 'empty' or 'unpopulated' Each cell with three neighbors becomes populated

Getting Virtual Cyberspace Virtual reality Virtual community

Cyberspace Exists in the computer network, the Internet. Can we apply the same spatial concept in this type of space?

Internet Connects computers together to form a network. Each computer (node) has an address (IP address). The lowest level of connectivity is real, e.g. Ethernet cable, etc.

IP Address Computers and other devices (like router, printer, webcam, etc.) have unique IP addresses, though some of them are private. The format of IP address is, aaa.bbb.ccc.ddd where each of the aaa, bbb, ccc, ddd is a number between 0 to 255, though some numbers are reserved and cannot be used.

IP Address Space Each IP address can be treated as a point in a space. Two IP addresses can be treated as neighbours if they are similar. For example, and It is very likely that they are in the same area and directly connected together.

Network Topology

PING ( ): 56 data bytes 64 bytes from : icmp_seq=0 ttl=252 time= ms 64 bytes from : icmp_seq=1 ttl=252 time= ms 64 bytes from : icmp_seq=2 ttl=252 time= ms 64 bytes from : icmp_seq=3 ttl=252 time= ms 64 bytes from : icmp_seq=4 ttl=252 time= ms 64 bytes from : icmp_seq=5 ttl=252 time= ms 64 bytes from : icmp_seq=6 ttl=252 time= ms 64 bytes from : icmp_seq=7 ttl=252 time= ms 64 bytes from : icmp_seq=8 ttl=252 time= ms 64 bytes from : icmp_seq=9 ttl=252 time= ms 64 bytes from : icmp_seq=10 ttl=252 time= ms Network Metrics Since IP address does not correspond to physical location, we have to use different ways to measure distance. Time (e.g. ping command)

Network Metrics Between 2 computers in the Internet, data needs to travel through a number of devices, like the routers. Distance can be measured in the number of Hops.

Virtual and Real Since IP address is registered with real world information like geographical details, it is possible to combine both the virtual and real world together.

Creativity Potential

Creative Applications A piece of text can be transformed into a space. Valence by Ben Fry. du/people/fry/valence/ applet/ du/people/fry/valence/ applet/

Creative Applications A word and its related topics can also be visualized in a space. Visual Thesaurus urus.com/ urus.com/

Creative Applications P2P network visualization Mini-tasking

Creative Applications Newsgroup discussion visualization WebSOM som/ som/

Creative Applications Every website Lisa Jevbratt ratt/1_to_1/index_ng.htm lhttp:// /~jevb ratt/1_to_1/index_ng.htm l

Creative Applications Babel By Simon Biggs iggs.easynet.co.uk/b abel/babel.htmhttp://hosted.simonb iggs.easynet.co.uk/b abel/babel.htm