1
00:00:03,889 --> 00:00:01,969
there are five exceptional lead groups

2
00:00:08,450 --> 00:00:03,899
associated with the octonials these are

3
00:00:10,190 --> 00:00:08,460
denoted G2 F4 E6 E7 and E8 with G2 being

4
00:00:11,930 --> 00:00:10,200
the smallest and E8 being the largest

5
00:00:13,490 --> 00:00:11,940
subgroups of these groups show

6
00:00:16,670 --> 00:00:13,500
remarkable overlaps with the group's

7
00:00:18,590 --> 00:00:16,680
su-3 su-2 and U1 which arise in particle

8
00:00:19,970 --> 00:00:18,600
physics as well as engaged theoretic

9
00:00:21,890 --> 00:00:19,980
approaches to general relativity

10
00:00:23,990 --> 00:00:21,900
octionic Maps can be used to generate

11
00:00:25,730 --> 00:00:24,000
Clifford algebras and Spinners made from

12
00:00:27,290 --> 00:00:25,740
these algebras so precisely the

13
00:00:28,970 --> 00:00:27,300
properties and symmetries observed in

14
00:00:31,490 --> 00:00:28,980
quarks and leptons of the standard model

15
00:00:33,229 --> 00:00:31,500
the octonians also label non-commutative

16
00:00:34,610 --> 00:00:33,239
manifolds which generalize the

17
00:00:36,650 --> 00:00:34,620
space-time manifold of the classical

18
00:00:38,870 --> 00:00:36,660
Universe this raises the possibility

19
00:00:40,910 --> 00:00:38,880
that a matrix valued classical Dynamic

20
00:00:43,010 --> 00:00:40,920
on the octoniotic geometry is the

21
00:00:45,290 --> 00:00:43,020
precursor of quantum theory and of

22
00:00:47,330 --> 00:00:45,300
space-time geometry as also a possible

23
00:00:48,590 --> 00:00:47,340
theory of unification there has also

24
00:00:50,510 --> 00:00:48,600
emerged a deep connection between

25
00:00:52,729 --> 00:00:50,520
autonions and twister theories negations

26
00:00:54,350 --> 00:00:52,739
of unification with autonions will be

27
00:00:57,350 --> 00:00:54,360
discussed in the forthcoming lecture