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 <[email protected]> wrote: > [email protected] 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 --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---
