1. Mathematical Exercise for Time
The reason for exploring this Fibonacci model of time is that the model should
logically lead to the physical expansion of our 3-dimensional space (universe) as a
function of time t.
It seems the concept of time could also be described as a directional motion of
the (Fibonacci number) 3 dimensions of space progressing through the (Fibonacci
number) 5 dimensions of space. The physical units would need to be transformed,
but physical results would be exactly the same in this model and could be
transformed back into the variable t anytime as desired.
This Fibonacci model of time could be further explored by postulating that 5
spatial dimensions would then mathematically require an alternate value
of:
e = lim
𝑛→∞
(1 +
1
𝑛
) 𝑛
because the corresponding statement:
∫
1
𝑥
𝑒
1
𝑑𝑥 = 1
suggests that the number 1 in 3-dimensions should be different from the number
1 in 5-dimensions and should no longer represent a 2-dimensional area but
perhaps would represent a 3-dimensional volume instead.
If we continue the mathematical exercise for time t, we would need to assume
that, if 3-dimensions were mathematically traversing through 5-dimensions, then
5-dimensions would need to be similarly traversing through 8-dimensions, and so
on into Fibonacci infinity.

2. In the infinite Fibonacci limit, then (as shown below) the logarithmic base should
be continually increasing at the rate:
(1/𝛾)^(1/𝛾) = 12.42
and to continue the mathematical model, then the number 1 would appear to be
increasing throughout higher Fibonacci dimensions by the factor:
(
1
12.42
)F(n+1)/F(n)
= (0.08)F(n+1)/F(n)
or about (8%) x [(F(n+1)/ F(n)] or 8% (Fn+1 / Fn) for each successive higher
dimension from the dimension Fn ( e.g. F3+1 / F3 =
5
3
)
where, regarding each adjacent dimension to Fn
𝛾 = lim
𝑛→∞
𝐹 𝑛−2
𝐹 𝑛
= 0.382
and, e.g.
F2 / F4 =
2
5
adjacent to F3 (where Dn = 3)
F3 / F5 =
3
8
adjacent to F4 (where Dn = 5)
and so on.
Then the figurative 5-dimensional number 1 should look more like the number
1.08 as mathematically perceived in 3-dimensions, and we would determine:

3. e1 = 0
e2 = e0
e3 = e1
e5 = e3
(5/2)
e8 = e5
(8/3)
e13 = e8
(13/5)
and the sequence of dimensional logarithmic base:
{LD} = {0, 1, e, e5/2
, e5
8/3
, e8
13/5
, … }
where the rate of dimensional increase for the logarithmic base:
RLOG = lim
𝑛→∞
𝑅 𝐷(𝑛)
{RD} = { (1/1)1/1, (1/1)5/2, (5/2)8/3, (8/3)13/5, ... }
RLOG = (1/𝛾)^(1/𝛾) = 12.42
The reason for exploring this Fibonacci model of time is that the model should
logically lead to the physical expansion of our 3-dimensional space (universe) as a
function of time t.
To be a worthwhile mathematical exercise, there would need to be a correlation
between the mathematical growth rate of the logarithmic base and the observed
physical expansion of 3-dimensional space as perceived through telescopes, and
the like, while we attempt to measure the Hubble value H0.
<Fibonacci_Hubble.pdf>