Applying the negation of the axiom of choice
Quantum mechanics
household names
Philosophy of logic
|
|
comments (3)
|
Philosophy of logic
A logic theory may result in household words
I proved with a logic theory that any universe collappses (Big Crunch).
So, there was another universe previously to ours and there will be
another universe after the Big Crunch of ours.
The universes start with a Big Bang.
The Big Crunches happen after an infinite time with time becoming
a Dedekind cardinal number.
See :
"About space and time in quantum mechanics" Adib Ben Jebara
Bulletin of Symbolic Logic September 2008 , pp. 410-411.
In the future, urelements and Dedekind Cardinals may become household
words, after ten years or so.
Set theory with urelements applied to elementary particles is a
strange theory which challenges.
The progress may work in such a way.
Besides, the beauty of the theory may be discovered.
The beauty comes from the theory being in the middle of other theories
and comes from several theories interacting in it.
The theories are set theory, cosmology, quantum mechanics and
philosophy of science.
Besides, it is surprising that an axiom (axiom of choice) introduced
in 1904 did not surrender its truth until now.
The explanation could be that most rresearchers have only a narrow
area of interest.
That something in pure mathematics could be argued in physics is
something new.
That is why, among other things, I have difficulties spreading my
idea.
Researchers being narrowly specialized will not last forever,
according to me.
Also, according to me, pure mathematics will be applied in the
far future.
But the main point is may be the unity of science in the future.
Adib Ben Jebara
Apt F3 Residence Badr Manar 1 Tunis 2092 Tunisia
About the very numerous
|
|
comments (0)
|
Mr Andreas Blass was kind to clarify the following about alephs:
The alephs are a proper class.
The alephs are indexed by ordinals such as omega, omega+1,...
2 omega,...
Alephs are cardinalities of well orderable sets.
Let us consider the ordinal corresponding to the cardinality of
the set of real numbers, with the notation c.
Let us consider the aleph indexed by c, the alephs smaller than
that one would be as numerous as the real numbers.
One should start to feel some dizziness from the very numerous.
Let us consider the ordinal corresponding to the cardinality of
the set of subsets of the set of real numbers, with the notation
s.
Let us consider the aleph indexed by s, the alephs smaller than
that one would be more numerous than the real numbers.
Aleph indexed by s is itself big beyond imagination. It is
difficult to get an intuition of it.
Such an aleph appears almost never in mathematical texts.
Physical space could not have the dimension of such an aleph (I
explained in "Physical space is infinite", in ASL Winter Meeting
2006 2007, why physical space is infinite).
So, for what could be used a very big aleph ?
May be the number of Big Bangs, each associated with a previous
Big Crunch, is infinite and a very big aleph, as it probably never
ends (although it takes an infinite time for a Big Crunch to happen).
Indeed, it is in the fields of cosmology and cosmogony that we can
hope to find use for the very big alephs.
I think there was no beginning for the cosmos, it was always there
and that is why very big cardinals should be used to study the cosmos.
Adib Ben Jebara
About urelements and astronomical black holes
|
|
comments (0)
|
In "About space and time in quantum mechanics" of ASL Winter Meeting 2007 2008, it is not clear at what time will happen the Big Crunch. It is, since the Big Bang, at time p, p being the Dedekind cardinal cardinality of U set of urelements.
ZFU, set theory with urelements can be applied to space and time which are U1xU2.
Let us assume that there are no urelements where matter is, in the astronomical black holes. It means that space and time are not well defined there. It enables us to avoid an infinite density and paradoxes for time.
The assumption is of some importance as black holes may be the missing mass to explain gravitational forces in a galaxy. Mr Andreas Blass commented that if the missing mass is known to be rather far from the centers of the galaxies, may be there are black holes there, more difficult to detect.
Adib Ben Jebara.
About research in mathematics and philosophy of mathematics
|
|
comments (0)
|
Mathematics are giving shape to the physical world. To reduce mathematics to logic is like reducing physics to mathematics.
Mathematics are a way to contemplate Good which is a way to contemplate God.
The evolution of the philosophy of mathematics is slow, for instance platonism is always here.
Either set theory will be increasingly used in physics and other sciences or it will remain just a part of mathematics.
What will happen is probably something in the middle with isolated researchers finding out how to apply it.
There will be more set theory taught and less logic as set theory will show even more its usefulness in the remaining parts of mathematics.
Platonism will be more spread because less dogmatic about what exists.
Nowadays, research in mathematics and in philosophy of mathematics make complicated things even more so. This occurs as a lack of creativity.
Some are fatalist about it, thinking that the great theories are already made.
The future will contradict them as new theories will appear.
The new theories are not always accepted at once.
Adib Ben Jebara.
This is your Blog!
|
|
comments (0)
|
This is your blog! A place to talk about what you're doing and thinking and have your friends and visitors comment. You can insert photos and links and 
here too.
