MILAN JOSHI 4TH DIMENSION
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Transcript of MILAN JOSHI 4TH DIMENSION
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PUBLIC LECTURE
BY
DR MILAN A.JOSHI(Ph.D)
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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.
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Arguing by analogy
Look at simpler circumstances to built insightand intuition.
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SCIENCE FICTION , DRAMA , ART , PAINTING.
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Degrees of spacial freedom
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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
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Some believe it is
time.
Mathematicians andscientists focus on
the fact that it is a
direction different
from all direction innormal space.
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SIMPLY A DOT
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An object in the first
dimension consists
of only one of thefundamental units.
For example a line
only has length. A
line is onedimensional.
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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.
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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.
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LOOK AT WORLD OF TWO DIMENSION
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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.
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3 Cube :
8 vertices
12 edges 6 faces
4 cube
16 vertices
32 edges
24 faces
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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
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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.
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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.
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Power of arguing by analogy
And looking at simple things deeply.
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THANK YOU