Page 1

P

Real nu

x²= -1

numbersystem

Thin Aung Ht


real

co su

) ^π + 1 = 0 q jewe

?

1 1+1+1+1+1+1+1 =

1

1

v

a ×1 =1 ×a = a 0 0

v

+ 0 = 0+

=


1 0 π π

^π + 1 = 0

Euler's formula e^ix = cos x + isin x

π =-1

π= 0

^ π = -1 + i × 0 ^ π = -1 ^π + 1 = 0

1

fundamental particle solution


1 100

1

) 100

0

0

)

1


q S = p ( 1 + r/ n )^nt 1 100

)1 1

1

=1

q S = p ( 1+ r/n ) ^n

S = 1 (1 + 1/1 )^ 1 =2

= S = 1( 1+ 1/2)^2 = 2.25 $

= S = 1( 1+ 1/4)^4 = 2.4414 !! = 1

=L

1

>>∞

1+ 1/

irrat polyno

^ transcend

q

1

0


base / ^

π π=C/ C= circumference , d = diameter = 2r C= π π

π

π

exponential function ^ ^1 = L

^

>>∞ 1+1/ ^ 1

e^ =L

>>∞ 1+ / ^

^ ^ = ∑ =0 >∞ ^ / ! =1 + x + x²/2! + x³/3! + x⁴ / ! +……

e^ix = 1+ ix + i²x²/2! + i³x³/3! + i⁴x⁴/ !+ ……

i² = - 1 , i⁴= 1, e^ix = 1+ ix - x²/2! - ix³/3! + x⁴/ ! +

=-

^ / ! + …………


e^ix = (1-x²/2!+x⁴/4! - … +

-ix³/3!+x^5/5!

+…… infinite

e^ix = cos x + i sin x v π= 0 ^ π = - 1+ 0 ^π + 1 = 0

π= - 1


wait!!

1

1 1

algeb

abxy

-

q

=

+

=

blan

x+

= =

q

blan

-၅= +

=၇ q

-

=

+=


-

=

= c

0

0

1

1

1+1+1

1 0

+ 0 + 1 + 1 + 1 +……+ 1 = __________________

0

a

1 + + 1 + 1 + 1 +…+ 1 = _______________

+

+

1


b + 1 + 1 + 1+ …+1 =

+

=

+

________________

1

1

a+(b+c)=(a+b)+c

natural 0 0+

+

+

+ ……+

=

___________________

ba= ab = 1

1

……

= ^

________________

b

^ = ^


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^1 = …………………… 0

1

algebra rational real 01

………

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=

v *

+

operation )

v a * b = identity =

q


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identity

+

0+

=

0 1

=

1

+ 0 a+b=0

a + (-a) = 0 inver

equation

a+b=c a + b + (-a) = c + (-a) b=c-a q

01

……… b = 5-8 = ???? -1- ……- - -1 0 1

……

=-


=

?? multiplicative v

=1

1

q

v

^-1

1/a

a× b× 1/a = c × 1/a b = c/a q

3/4 , 2/34

1/

^ =

^

^

= q irrational v

irratio

tran π

a^b = c then b=???

solution


b=l

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bas

natural logarithm

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Interlude Interlu

0

1


icon im

critical

critical thinking

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1


complex

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topo

function

fun diffe

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stand

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q l

C

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quantu

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v

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al

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l

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v

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v


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θ+ ²

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v


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C

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v

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v

electromagnetic force , v

v

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θ


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á …

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A--->AB , B---->A


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1 2 3 5 8 13 21 34 .........

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]−

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classical counterpart

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v


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vel

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theta = tan^-1 v^ /


v= q

Ro


centripetal force v á …


v

=

v

v 0

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v v


=

=v

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v^ /

Theory of thought


? conclusion ----->

--->

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output

Propo

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Theory v

v

False

/ 1

1/0 0


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0

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proposition da /

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v


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algebra

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+

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v 1

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v v v i L

L

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USS cyclops


US board on geographic name

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v

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v

direction

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v

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Quadratic

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v=

/ v acceleration

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quadratic q

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)

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v


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=

v conserv

v


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vv

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v


á ‡

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number

functiona

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v

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v equation classical mechanic

= v

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v

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q q

q


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v


q

q

v

q q

q v

old f

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symplectic v

v

Classical mechan

q

v

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v

v

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]=

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/

commuta

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1

q/

0

q

/

q/

{ q ,H } = dq//dt= dH/dp

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j j

{q

j}= j

1

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0

mat

1


=

v C

)

Galileo relativity

inertia = prime =

= +

x,y,

t= t'


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rotation

rotatio

x' = Rx

v

v

x' = x+vt v= /

=v

v


x' =x+c y' =y+c z'= z+c |x'| |x| |y'|= R |y| |z'| |z| x'= x+vt y'=y+vt z'= z+vt t'=t

=

L

relativity

L

(fra


structure

v

á ‡

!!

v

=

S

v

S'

v+


c v+

v -

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v

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-


= /

Lore

gamma factor

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x'= r(x-vt) t'=r(t-v/c^2*x) x-v


T=rT'

L=L'/r causali

L

Minkowski space special rel

v


imaginary number i

dimension

special relat v

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i v

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v


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limi

q v

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soc

soci conceptual


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gas molecules

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j

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v

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v

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probability

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gas


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Entropy

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Macrostate W =1/ =1/


gas Gas one

10^ W ^10^

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HHHHHHHHHT HTHHHHHHHH ....... =10 W


a varies b

v

1/ =

v

=

const

=

L

^ =

=

a^x=b =

10

= 10 = ^


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W(1+2) = W(1)*W(2) S(1+2)= k log W(1)+k log W(2)

regeneration

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statistical

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dE = dQ + dW

Second Law of thermodynamics

100


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disc


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touch screen

s

intensity

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Intensity

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q

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q


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basic conceptual

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v^

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Consciousne

)

(partic graviton

Thomas

electr


)

L=nh' L L L= v

�

h' = h/2

=1

v=

/

discrete va

L

h'


/ L= )

d=h/mv

v= =

/ / v

r = n h/mv C= nd C

C


standing

v

v

Buccal cavit

v

v +

=

) )

=

= v

v


---------

1

funct P12 1

1 1

v

1

v

1

v v

=0 v

P12=P1+P2

1


-------

h

classical

I=h^2

1

v

1

I1 =|h1|^2 1

curve

=0

^ + ^

^

v I1

I12=|h1+h2|^2

=


(a+b ^ = ^ + ^ +

2ab

I12 = |h1+h2|^2 = |h1|^2 + |h2|^2 + 2|h1| |h2|cos delta = I1 + I2 + 2 sqr I1 I2 cos delta 1

1 1

-----------classical mechanic

"

v 1 1=

1|^2

=

2|^2

1

1

v


1 =

1+

2|^2

!!

1 " !!

v

Double split ex


?


v

state sta state

state

= p


uncertainty principle delta x * delta p> h'/2

/ /

v

v

W v

q

q

d^2 y/dx^2 = 1/v^2 * d^2 y/dt^2 1/v^ y v

y= y0 e^i(kx -wt)


0

y

v q

=

0 e^i/h'(Px-

=

=

= /

)

E=h'w So w= E/h' ----------------------= /

=

/

= /

= / =

) =

)

k=p/h' ) --------------------------------------= 0 ^

=

-

0 ^/

-


v

q

E= KE+PE = 1/2 mv^2 + V(x) = p^2/2m +V(x)

=

^ /

+

------------------------------------= = d/dt

( E=h'w) 0 e^i/h'(Px-Et) = -/ properties -/

)

/ / /

= =

- /


------------------------------------

= /

0 ^/

-

= / =-

/

p^2 = - ^

^ /

^

-------------------------------

= /

=

/

^ /

+

=

- ^ /

- ^ /

^ /

=

^ /

^ +

^ +


------------------

---------------------

----------------------


j

/

=

v

=

0 e^i/h' (Px-Et) classical


probability amplitude =

|^2

=a+bi complex num

-0

0 0

200%

00

0% 0

1

1 100

0

0 1

0 0

1

complex number

j = a+bi j *= a-bi imagina

^ =

*=(a+bi)(a-bi)

=a^2-abi +abi-b^2i^2 =a^2+b^2


0

1

a^2 + b^2 =1 normaliza

0 1

0

infinite

1 1+

1


v

Wavelik v

A + superposition principle =

+

B

=1 + 0 = 0.1 + 0.9 =..... + ....... = 0.5 + 0.5 = .....+....... = 0.9 + 0.1 =0+1 =1 1

)

w v v

B


v

=

+

=

B|^2

^ +

B|^ +

B|cos t +

+

state,wave function,probability v

vec v Hilbert

ih' d/dt

=

v


v

Classical

v v

/ /

=

=

|^2

)


particle

potent

atomic model

so

solar

v

q

spin

radial distance c qu

q

1 =1


orbital quantum

q v

L^

=

+1 v

^ q +1 =0 1

1

-1

0 01 01

C =0

s

=1

p

=

d

= L 3 dimens

z


m=-l,-l+1,...,0,...,l

1

m=-1,0,1 m=-2,-1,0,1,2 +1 =

m

orientation

=

1/ num

-

spin quantum

q

Componen

1/

-1/

z

1/

orb energy

v ^

112 248 3 9 18 4 16 32 magic number 2,8,18,32

1

elem


+ v q


Symmetry Symmetr Reflect

v symmetry

law o

v

v

charge

sy

La

v


v

diff

Quantum

U1

Electrowea

SU(

Quantu

U g

U

special u

Group the

modular re

v

1

relatively prime

1

1 (1,5)=1

၇ ၇

1

1 0 1 mod5

1

mod n

=1 =0 =1 1

0


relatively p (a,p)=1 ^ -1 = 1 á …

v

^ = 1 =1

n

1 1 k

v

(k,n)=1

(1,5)=1 (2,5)=1 (3,5)=1 =1

v

-1


=

(n)= number of k { k=1,2,..,n-1 | (k,n)=1}

1,2,3,4,5,6,7 1 1,3,5,7 =

v ^

=1 v

^ =1 =1

=1 C =

=

v

1 1,2,3,4


C x mod 5 | 1 | 2 | 3 | 4 ______________________ 1|1|2|3|4 _______________________ 2 |2 | 4 | 1 | 3 ________________________ 3|3|1|4|2 ________________________ 4|4|3|2|1 1

1 1

Symmetry 2 (n) el

multiply mod n closure

closure


theory of q

quadratic

q General solution

q

variable x

^

C

^ ^

Quintic

^ q

q

quinti q

q

infinitely

q x=-b +/- sqr b^2-4ac/ 2a +/-

+

-

cubic

j ၅

j

quintic ၅

set

၅ ၅

j

! !=

1=


shuffle Gene j j j j

cl

1

object != 1

1

1

1

1

1

1

1

1

1

231

(12) (13) 1

1 1

1

1

1

1

1


e , (12) , (13) , (23) , (123) , (132)

S={ e,(12),(13),(23),(123),(132)}

1

1

213

(23)

(1

1

123 1

1

1

(132)

=1

se

set

operati identity element e

1

1 v

operate =

v

[(12)(23)] (13)= (12) [(23)(13)]


defining property

á …

á …

polynomial

Symmetry 3 group theory operation operati

ge=eg=g v

^-1

gg^-1=e=g^-1g v (g1 g2)g3 =g1 (g2 g3) operati

operation


ge j shape

j

j

Symme

j

0

)

r1 r2 1 u1 u2 u3

j


)

!=

1=

se 1 object

D3={ r0,r1,r2 1

1

}

j symmetry(3)

operation *

1

u1r1=u3 ta 1 1

q Elect

U

Quantum chromodyna C

SU(1) U U

q

j U

gluon


U

U

special unitary group

v Special relativit

Poicare group

j q

v


Gauge theory

v

General

coo background v

Quantum field t

Quantum electrodynamics

Quantum chromodynamics gauge

U1

U

U group

gauge ?


geometry

shape

၅ one

၅ j

v ၅ ၅

၅/ ၅

mental image ၅


á …

fancy n

^ + ^ =1

Cartesian


= F=- grad V F= - grad mgh F= - d(mgh)/dh F=-mg v q

one dimensional

=-

0

0

=v

gauge transformatio

cl

gauge


v

v

gr j Symmetry group

j

U1 classical electromagnetism q


v q

zero-sum

decis q

game

q

zero sum Equalibrum q

player


g

prisoner's dilemma

1

) á … ?

v

evolution society


social

á ‡ civilization

Dynamic of Civilization

archaeology,Culture,


Age of Empero

v -

upgrade

v

civil

? civilization

v

Babylonian

civil

mesoamer

Fall ofC v

v civil Malthus growth

mod

1 00 v population


let's take a little maths population

/

dp/dt varies with p v

p immigra

k= sq dp/dt = (s-u)p exponential p= p° e^(s-u)t

A

constant of pr


resource

s= rA

=s = (rA - cp)

dp/dt = (rA - cp ) p - up

civilizatio =

-

/

civil v population p v =

v /

/


A° = 2k ( p/A-

resource

colon

q

limiting factor

limit

r driving forc democra v v

spread of cu v culture


cultural re educa

v

) cycle trading

logic ,

= a²=ab a²+a²=a²+ab 2a²=a²+ab ²− ²−

= ²+

=1 ²−


²− 2=1 !!

Proof

reasoning

l logical

r

v v

conc

: spec

v

)

=


²−

arit p

i

v

v

induction natural 01

၅ 0

+1

)

0 ၅

၅ 0 "

0+1+2+.....+n=n(n+1)/2 k +1 0=0(0+1)/2=0


+1 1+2+......+k+k+1= k(k+1)/2 +k+1 =k²+k+2k+2/2 =k²+3k+2/2 =(k+1)(K+2)/2 +1

+1 ၅ 0

deduction/induction Deduction /induc

elem

A=B,C=B then A=C) ²= ²+ ²= ²+

)

²= ²


a+b=0 a + b-b=0-b a =-b ၅ ၅

၅ ၅

(

-

spherical geomet


deduction/inductio / de

/ pr Proof

compl Incompleteness th first order logic

C formalL

(

)


/ Nat rational Number,intege

) str struc a*a=2

complex number

Not X

C )C

/ = number (Q)

/

C v

U

rational


"

/

v

/

Peano arithmetic /

halting

/

/ / L

/ /


v O

/ / / /

/

/

/

v

v²=2GM/R v

R=2GM/v²


Rs= 2GM/c²

v

s

)

v v v k


non decreasing property

dA/dt >/= 0

²


²

²

plank Length ²

²

Zeroth law

v First Law

=

+

μ

= / π

+Ω + surface grav Q

Ω / π


Second Law

dA/dt > or = 0 generalized second law

L

Total entropy= S+ A/4

Third Law

v

0

= / π =1/ =

/ π

1/


-


Entanglement tow

) quantum teleportation Quantum teleportat

entanglement

v


Wave functio

EPR

q

axiom

v

1

0


>= 1/

0> + 1> |>

0

1

1/ 1/

1

0

superposition > = a |0> + b|1> Superposit

Tensor pro 1

✪ ₁>

₂>

>=

₁> ✪

₂>

> = a₁ |0>+b₁|1> ✪ a₂|0>+b₂|1> > =a₁a₂|00>+a₁b₂|01>+b₁a₂|10>+b₁b₂|11>

> = 1/

01> + 10> 01>

1

1/

0 0

-1/2

₁ ₂

1

10>


q

1

0

၅ ၅

၅ /၅

counterfactual definitene

counterfactual C v

loca


v

reality local hidde v v inequali = Violation of q

v

L


ER=EPR


C

j hypothe

j

=

á …

q

EinsteinRosen b

-


back to t -

v special

v

teleport quantum teleportatio

classical -

v


ER=EPR


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