RE: Jesus as Lord - why is this appealing to so many?
February 14, 2018 at 9:07 pm
(This post was last modified: February 14, 2018 at 9:26 pm by polymath257.)
First quote:
"First, the Standard Model of particles and forces is one of the best tested and most successful theories in all the history of physics. So are the theories of relativity and quantum mechanics. All these theories imply or assume that, using Cantor’s technical sense of actual infinity, there are infinitely many infinitesimal instants in any non-zero duration, and there are infinitely many point places along any spatial path. So, time is a continuum, and space is a continuum.
The second challenge to Hilbert’s position is that quantum theory, in agreement with relativity theory, implies that for any possible kinetic energy of a free electron there is half that energy−insofar as an electron can be said to have a value of energy independent of being measured to have it. Although the energy of an electron bound within an atom is quantized, the energy of an unbound or free electron is not. If it accelerates in its reference frame from zero to nearly the speed of light, its energy changes and takes on all intermediate real-numbered values from its rest energy to its total energy. But mass is just a form of energy, as Einstein showed in his famous equation E = mc2, so in this sense mass is a continuum as well as energy."
Second quote:
"Disagreeing, the theoretical physicist Roger Penrose speaks about both loop quantum gravity and string theory and says:
...in the early days of quantum mechanics, there was a great hope, not realized by future developments, that quantum theory was leading physics to a picture of the world in which there is actually discreteness at the tiniest levels. In the successful theories of our present day, as things have turned out, we take spacetime as a continuum even when quantum concepts are involved, and ideas that involve small-scale spacetime discreteness must be regarded as ‘unconventional.’ The continuum still features in an essential way even in those theories which attempt to apply the ideas of quantum mechanics to the very structure of space and time.... Thus it appears, for the time being at least, that we need to take the use of the infinite seriously, particular in its role in the mathematical description of the physical continuum. (Penrose 2005, 363)"
Yes, a defined set that has an infinite number of elements. For example, the set of integers.
What it adds to the discussion is precision. Whether something 'ends' or 'is complete' is, at best, ambiguous. But putting things in correspondence with natural numbers (Cantorian equivalence of size) is precisely defined.
So, does the collection of integers end? not in the sense that for every integer there is a larger and a smaller integer. Is it complete? yes. It is *one* collection of things. It isn't a process. It is one thing: the collection of integers.
And, there are differing sizes of infinity (in the Cantorian sense). These are actual sets (like the set of real numbers).
And this shows the concept if NOT logically contradictory.
"First, the Standard Model of particles and forces is one of the best tested and most successful theories in all the history of physics. So are the theories of relativity and quantum mechanics. All these theories imply or assume that, using Cantor’s technical sense of actual infinity, there are infinitely many infinitesimal instants in any non-zero duration, and there are infinitely many point places along any spatial path. So, time is a continuum, and space is a continuum.
The second challenge to Hilbert’s position is that quantum theory, in agreement with relativity theory, implies that for any possible kinetic energy of a free electron there is half that energy−insofar as an electron can be said to have a value of energy independent of being measured to have it. Although the energy of an electron bound within an atom is quantized, the energy of an unbound or free electron is not. If it accelerates in its reference frame from zero to nearly the speed of light, its energy changes and takes on all intermediate real-numbered values from its rest energy to its total energy. But mass is just a form of energy, as Einstein showed in his famous equation E = mc2, so in this sense mass is a continuum as well as energy."
Second quote:
"Disagreeing, the theoretical physicist Roger Penrose speaks about both loop quantum gravity and string theory and says:
...in the early days of quantum mechanics, there was a great hope, not realized by future developments, that quantum theory was leading physics to a picture of the world in which there is actually discreteness at the tiniest levels. In the successful theories of our present day, as things have turned out, we take spacetime as a continuum even when quantum concepts are involved, and ideas that involve small-scale spacetime discreteness must be regarded as ‘unconventional.’ The continuum still features in an essential way even in those theories which attempt to apply the ideas of quantum mechanics to the very structure of space and time.... Thus it appears, for the time being at least, that we need to take the use of the infinite seriously, particular in its role in the mathematical description of the physical continuum. (Penrose 2005, 363)"
(February 14, 2018 at 3:18 pm)RoadRunner79 Wrote:(February 14, 2018 at 1:28 pm)polymath257 Wrote: Well, to be complete means that we can tell exactly when something is in the list or not. For example, the number 1273749
is in the list 1,2,3,.... but the number 1.34 is not.
It is complete in the real world if everything in the list actually exists and we can tell exactly when something is in the list and when it is not.
I do believe that I was acting more on the second definition prevously. The first definition to me seems like you are saying a defined set, which seems pretty useless to me. If you cannot tell what is or is not in the set, then what good is it? In the end, I don't see that the involvement of sets (completed or otherwise) is really adding anything to the conversation. You can correct me if I'm wrong.
So to clarify what I am disputing is an actual infinite. Which would be completed or ended, on something which is unending. This is contradictory. You can not have an infinite. Even really in the abstract, you don't have an infinite number of things. You have a concept, which you think gives you an infinite number of things. But it's a never ending process (here there be dragons) which can never actualize infinity.
Yes, a defined set that has an infinite number of elements. For example, the set of integers.
What it adds to the discussion is precision. Whether something 'ends' or 'is complete' is, at best, ambiguous. But putting things in correspondence with natural numbers (Cantorian equivalence of size) is precisely defined.
So, does the collection of integers end? not in the sense that for every integer there is a larger and a smaller integer. Is it complete? yes. It is *one* collection of things. It isn't a process. It is one thing: the collection of integers.
And, there are differing sizes of infinity (in the Cantorian sense). These are actual sets (like the set of real numbers).
And this shows the concept if NOT logically contradictory.
