# Re: Information entropy of physical fundamental constants

```
Brent> all physical measurements will be rational numbers```
```
Well, it is quite a statement ;o) so you may write down an exact
Planck constant (h), please illustrate that...
If you experience difficulty to do that for ( h ) please try write
down an exact gravitational constant ( G )...

Ref: Planck constant:  h = 4.135 667 33(10) × 10−15 eV s
(10) The two digits between the parentheses denote the standard
uncertainty in the last two digits of the value.

SB> there is no way to write down an exact arbitrary irrational number
Brent> There is no problem writing down irrational numbers:
Brent> sqrt(2), pi,... See nothing to it.  ;-)

You miss the key word "arbitrary", it is simple to show that the
number of irrational numbers which can be expressed/encoded with ZERO
entropy equals to number of rational numbers (sqrt(2) is one of such
examples).

--sb

On Jul 23, 4:30 pm, Brent Meeker <meeke...@dslextreme.com> wrote:
> stefanba...@yahoo.com wrote:
> > SBJ: Information entropy of physical fundamental constants
>
> > The fundamental constant can be measured increasingly accurate, it
> > does not seem (for me) that the  repetitive pattern of rational
> > numbers after some number of digits may take place;
>
> Physical measurements are always relative, i.e. one quantify is measured in
> units of another quantity.  It is generally thought that there is a smallest
> possible unit, the Planck scale, so all physical measurements will be rational
> numbers (integers in Planck units).
>
> >if it is the case
> > then there is not enough "room" in the universe / multiverse to
> > accommodate such information as exact representation of fundamental
> > constant - just in principle, there is no way to have it exact as
> > there is no way to write down an exact arbitrary irrational number and
> > it is not a technical limitation it is a fundamental limitation unless
> > it may be represented as a rational number ;o).
>
> There is no problem writing down irrational numbers: sqrt(2), pi,... See
> nothing
> to it.  ;-)
>
> Of course from an information standpoint you want to know their bits.  But it
> also easy to write down a quite short program that will compute whatever bit
> you
> want to know for those irrational numbers.  But you are right that for almost
> all real numbers is impossible to give them a finite representation.  But why
> believe in those numbers anyway, they are convenient fictions.
>
> >Information Entropy
> > can be measured as an average number of bits per symbol/digit encoded
> > by rank-0 context model + entropy encoder (let say arithmetic
> > encoder). Therefore, there are two distinct possibilities: entropy
> > equals zero or Log2(10) (for decimal representation) or simply: ZERO
> > or NON-ZERO. I have my ideas how NON-ZERO case may workout but I'm
> > interested to listen others opinions.
>
> Most cosmogonies assume the (microscopic) entropy of the universe is zero.  It
> started at the Planck scale, where there is room for at most one bit and since
> QM insists on unitary evolution the entropy cannot change (as measured at the
> Planck scale).  The increase in entropy we see is due to our coarse graining,
> or
> as Bruno would say, "above our substitution level".  It is impossible to
> however
> to use the negative information to get back to local zero because the
> expansion
> of the universe has carried the correlations beyond the relativistic horizon.
> At least that's the common theory.
>
> Brent
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