ages of the universe

t
P
In[]:=
8.1×
60
10
Out[]=
Solve[Ξκ^(σ/Sqrt[Ξ]),Ξ]
In[]:=
Solve
:Inverse functions are being used by Solve​, so some solutions may not be found; use Reduce for complete solution information.
Ξ
2
σ
2
Log[κ]
4
2
ProductLog-
1
2
2
σ
1
2
σ
2
Log[κ]
2
Log[κ]

,Ξ
2
σ
2
Log[κ]
4
2
ProductLog
1
2
2
σ
1
2
σ
2
Log[κ]
2
Log[κ]


Out[]=
Ξ/.Last[%]
In[]:=
2
σ
2
Log[κ]
4
2
ProductLog
1
2
2
σ
1
2
σ
2
Log[κ]
2
Log[κ]

Out[]=
FullSimplify[%,{κ>1,σ>0}]
In[]:=
2W
1
2
σlog(κ)

Out[]=
Asymptotic[ProductLog[x],{x,Infinity,2}]
In[]:=
Out[]=
Expand[%]
In[]:=
Out[]=
Exp[2(Log[x/2]-Log[Log[x/2]])]
In[]:=
2Log
x
2
-LogLog
x
2


Out[]=
FullSimplify[%,x>0]
In[]:=
2
x
4
2
Log
x
2

Out[]=
Exp[2(Log[x/2])]
In[]:=
2
x
4
Out[]=
Asymptotic[Exp[2ProductLog[x/2]],{x,Infinity,1}]
In[]:=
Out[]=
2ProductLog[x/2]
In[]:=
2ProductLog
x
2

Out[]=
FullSimplify[%,x>0]
In[]:=
2ProductLog
x
2

Out[]=
2
x
4
2
Log
x
2

/.xσLog[κ]
In[]:=
2
σ
2
Log[κ]
4
2
Log
1
2
σLog[κ]
//TraditionalForm
In[]:=
2
σ
2
log
(κ)
4
2
log

1
2
σlog(κ)
Out[]//TraditionalForm=
2W
1
2
σlog(κ)

Exp2ProductLog12
ages of the universe

t
P
Log[κ],
2
σ
2
Log[κ]
4
2
Log
1
2
σLog[κ]
/.σ->
ages of the universe

t
P

In[]:=

2ProductLog[4.032340124650201475155`2.5340906449161738*^60Log[κ]]

,
1.625976688086400237032351`2.2330606492521925*^121
2
Log[κ]
2
Log[4.032340124650201475155`2.5340906449161738*^60Log[κ]]
,1.625976688086400237032351`2.2330606492521925*^121
2
Log[κ]

In[]:=

2ProductLog4.0×
60
10
Log[κ]

,
1.63×
121
10
2
Log[κ]
2
Log[4.0×
60
10
Log[κ]]
,1.63×
121
10
2
Log[κ]

Out[]=
LogPlot[%,{κ,1,3}]
In[]:=
Out[]=
LogPlot[
2ProductLog[4.032340124650201475155`2.5340906449161738*^60Log[κ]]

,{κ,1,3},FrameTrue]
In[]:=
Out[]=
Series[Exp[2ProductLog[1/2σLog[κ]]],{κ,1,2}]
In[]:=
1+σ(κ-1)-
1
2
σ
2
(κ-1)
+
3
O[κ-1]
Out[]=
fff[κ_]:=Exp2ProductLog12
ages of the universe

t
P
Log[κ]
In[]:=
fff[1.01]
In[]:=
9.5154×
112
10
Out[]=
fff[2]
In[]:=
4.3×
116
10
Out[]=
fff[10]
In[]:=
4.7×
117
10
Out[]=
fff[1.1]
In[]:=
8.43691×
114
10
Out[]=
ages of the universe
UnitConvert
t
P
Sqrt[xi]/.xi10^116
In[]:=
8.1×
118
10
Out[]=
GridMapText[NumberForm[#,1]]&,"elementary length (​
L
​)",UnitConvert
l
P
Sqrt[xi],"elementary time (​
T
​)",UnitConvert
t
P
Sqrt[xi],"elementary energy (​
E
​)",UnitConvert
E
P
Sqrt[xi],"ElectronVolt","elementary lengths across current universe",2
radii of the visible universe

l
P
Sqrt[xi],"elements in spatial graph",
radii of the visible universe
UnitConvert
l
P
Sqrt[xi]^3,{"elements in branchial graph",xi},"overall updates of universe so far",UnitConvert
ages of the universe

t
P
Sqrt[xi],"individual updating events in universe so far",UnitConvert
radii of the visible universe
UnitConvert
l
P
Sqrt[xi]^3*
ages of the universe

t
P
Sqrt[xi]/.xi10^116.,{2},FrameAll,FrameStyleLightGray,AlignmentLeft
In[]:=
Out[]=
UnitConvert
ages of the universe

In[]:=
4.3×
17
10
s
Out[]=
Log[2,10^116]//N
In[]:=
385.344
Out[]=
UnitConvert

In[]:=
1.9561×
9
10
kg
2
m
/
2
s
Out[]=
10^35810^-30
In[]:=
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Out[]=
N[%]
In[]:=
1.000000000000000×
328
10
Out[]=
UnitConvert

Sqrt[xi],"ElectronVolt"
In[]:=
UnitConvert
xi

4.1855×
-23
10
/
2
c
,ElectronVolt
Out[]=
GridMapText[NumberForm[#,1]]&,"number of elements in an electron",
^2
Sqrt[xi],"radius of an electron",UnitConvert
Sqrt[xi]*
^2
Sqrt[xi]^(1/3),"number of elementary lengths across an electron",
^2
Sqrt[xi]^(1/3)/.xi10^116.,{2},FrameAll,FrameStyleLightGray,AlignmentLeft
In[]:=
number of elements in an electron
4.×
35
10
radius of an electron
1.×
-81
10
m
number of elementary lengths across an electron
7.×
11
10
Out[]=
10^9010^35
In[]:=
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Out[]=
N[%]
In[]:=
1.×
125
10
Out[]=
10^358/%
In[]:=
1.×
233
10
Out[]=

Max version

k^(th/
Number of spatial nodes: (tH/T)^3 = (tH/tP)^3 Xi^(3/2)
Xi ~ κ ^ (( (tH/tP)^3 Xi^(3/2)) * (Sqrt[Xi] tH/tP))
Xi = κ ^ ((tH/tP)^4 Xi^2)