Brent>> all physical measurements will be rational numbers
SB> Well, it is quite a statement ;o) so you may write down an exact
SB> Planck constant (h), please illustrate that...
SB> If you experience difficulty to do that for ( h ) please try
SB> down an exact gravitational constant ( G )...
Brent>No, problem. Like most physicists I write h=1, G=1, c=1.
Apparently no problem ;o)
On Jul 24, 9:29 pm, Brent Meeker <meeke...@dslextreme.com> wrote:
> stefanba...@yahoo.com wrote:
> > 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 )...
> No, problem. Like most physicists I write h=1, G=1, c=1.
> > 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.
> The uncertainty is in the conversion to eVs. It arises because different
> got different numbers when measuring, but each measurement was a rational
> > 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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