(*​​TakingDirac'slargenumbershypothesisandthecombinatorialhierarchyasastartingpoint,thisnotebookranksparticlesaccordingtohowwelltheiruseincalculatingthedimensionlessgravitationalcouplilngconstantfitsthefourthentryinthecombinatorialhierarchy.​​​​Thethirdentryofthecombinmatorialhierarchyis137,whichcorrespondstothedimensionlesscouplingconstantforelectromagnetism.Thefirstandsecondentriesareconjecturedtobelongtotheothertwofundamentalforces.*)​​​​CombinatorialHierarchy=Accumulate[NestList[Function[x,2^x-1],n,3]/.n->3]​​
Out[]=
{3,10,137,170141183460469231731687303715884105864}
In[]:=
CH4=N[Log10[Last[CombinatorialHierarchy]]]​​
Out[]=
38.2308
In[]:=
codata[canonicalName_]:=Around@@Entity["PhysicalConstant",canonicalName][{"Value","StandardUncertainty"}]​​DimensionlessGravitationalCouplingConstant[particle_]:={particle,(Log10[codata["PlanckConstant"]*codata["SpeedOfLight"]/(2Picodata["GravitationalConstant"]*ParticleData[particle,"Mass"]^2)]-CH4)^2}​​
In[]:=
SortBy[Map[DimensionlessGravitationalCouplingConstant,ParticleData[]],First@*Rest]
Power
:Infinite expression
1
0.×
-22
10
encountered.
Power
:Infinite expression
1
0.×
-22
10
encountered.
Power
:Infinite expression
1
0.
encountered.
General
:Further output of Power::infy will be suppressed during this calculation.
Out[]=

proton
,(4.47±0.04)×
-6
10
,
anti-proton
,(4.47±0.04)×
-6
10
,
neutron
,0.0000109
(
6±6
)
,
n
,0.0000109
(
6±6
)
,
′
η
(958)
,0.000399
(
5±4
)
,
*
K
0
(892)
,0.001438
(
5±7
)
,
*
K
0
(892)
,0.001438
(
5±7
)
,
f
0
(980)
,0.001592
(
7±8
)
,
*
K
-
(892)
,0.001776
(
2±8
)
,
*
K
+
(892)
,0.001776
(
2±8
)
,
a
0
-
(980)
,0.001941
(
7±9
)
,
a
0
0
(980)
,0.001941
(
7±9
)
,
a
0
+
(980)
,0.001941
(
7±9
)
,
ϕ(1020)
,0.00550
(
51±14
)
,
*
K
0
0
(800)
,0.00883
(
32±18
)
,
*
K
0
+
(800)
,0.00883
(
32±18
)
,
*
K
0
-
(800)
,0.00883
(
32±18
)
,
⋯968⋯
,
Z boson
,15.81914±0.00008,
top quark
,20.60754±0.00009,
top antiquark
,20.60754±0.00009,
down quark
,20.65342±0.00009,
down antiquark
,20.65342±0.00009,
up quark
,27.64339±0.00010,
up antiquark
,27.64339±0.00010,
electron
,42.58481±0.00013,
positron
,42.58481±0.00013,
electron neutrino
,∞,
electron antineutrino
,∞,
gluon
,∞,
muon neutrino
,∞,
muon antineutrino
,∞,
photon
,∞,
tau neutrino
,∞,
tau antineutrino
,∞
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