MILAN JOSHI 4TH DIMENSION

7/29/2019 MILAN JOSHI 4TH DIMENSION

1/32

PUBLIC LECTURE

BY

DR MILAN A.JOSHI(Ph.D)


2/32


3/32

If there is anything that canbind the heavenly mind of man to

this dreary exile of our earthlyhome and can reconcile us withour fate so that one can enjoyliving-then it is verily theenjoyment of Mathematial

Science.


4/32

Arguing by analogy

Look at simpler circumstances to built insightand intuition.


5/32

SCIENCE FICTION , DRAMA , ART , PAINTING.


6/32


7/32

Degrees of spacial freedom


8/32

NUMBER OF PIECES OF INFORMATION REQUIRE

TO ISOLATE ANY PARTICULAR POINT IN SPACE

WITH CERTAIN REFERENCE..

0 DIMENSION: No information1 Dimension : 1 piece of information

it goes


9/32

Some believe it is

time.

Mathematicians andscientists focus on

the fact that it is a

direction different

from all direction innormal space.


10/32


11/32


12/32


13/32

SIMPLY A DOT


14/32

An object in the first

dimension consists

of only one of thefundamental units.

For example a line

only has length. A

line is onedimensional.


15/32

An object in the second

dimension consists of

two of the fundamental

units. For example, asquare has a length and

a width. Notice that is

you stack lines on top of

each other you create asquare, or an object in

two dimensions.


16/32

An object in the thirddimension consists ofthree of the

fundamental units. Forexample, a cube has alength, width andheight. Notice that isyou stack squares on

top of each other youcreate a cube, or anobject in threedimensions.


17/32

LOOK AT WORLD OF TWO DIMENSION


18/32

Flatlandis a book written in 1884that describes the phenomenonwe just looked at.

Flatland is a world of twodimensional creatures. The towns

consists of triangles, squares,pentagons etc The more sides aperson has the more importantthey are in society. A circle is themost important figure in theirsociety.

In flatland, all the creatures can

see are lines and points. Nothinghas a height.

Imagine being a caterpillar whocan only see straight forward.This is how this entire societylived until one day.

View from above.

View from flatland.


19/32


20/32


21/32


22/32


23/32


24/32

3 Cube :

8 vertices

12 edges 6 faces

4 cube

16 vertices

32 edges

24 faces


25/32

States a mathematicalrelationshipbetween thenumber of vertices,

edges and faces of apolyhedron.

In 3-dimensionalspace,

vertices-edges+faces=2

Or V-E+F=2

3-D Figure V E F V-E+F

Cube 8 12 6 2

Tetrahedron 4 6 4 2

Octahedron 6 12 8 2

Dodecahedro

n20 30 12 2

Icosahedron 12 30 20 2


26/32


27/32


28/32


29/32

Just by arguing by analogy what we see here is

powerful way of looking at not only our world

but the world that remains invisible and beauty

of this type of thinking is that we can takeideas issues and concept that seems so far so

removed literally invisible to us and we make

those things not into focus but we can began to

build intuition , what thinks look like , how arethey, how many vertices , how many faces, just

by arguing by analogy.


30/32

A cube in the forth dimension is really strange

to mention

So I took a math 180

The concept were weightyBut now I look at a cube in extension.


31/32

Power of arguing by analogy

And looking at simple things deeply.


32/32

THANK YOU

MILAN JOSHI 4TH DIMENSION

Documents

Transcript of MILAN JOSHI 4TH DIMENSION