8/10 What's the difference between P(A,B), P(A,B=true), P(A=true,B=true) and
P(A|B)? I'm trying to follow the ID thread below. Thx.
\_ P(A,B) is a table, with an entry for each possible value combinations
of A and B. The numbers in the table have to sum up to 1. Each
entry in the table corresponds to the probability of A and B
attaining the indexing values. P(A=true,B=true) is a number, the
probability that both events happened. P(A,B=true) is a table
where each corresponds to some value of A, and means 'probability
that A takes on that value and B is true.' P(A|B) = P(A,B)/P(B)
where you divide consistent entries. P(A|B) is a table with an
entry for each possible combination of values of A and B, where the
entry means 'the probability A attains the given indexing value
given that the given indexing value of B was observed.'
For now you can ignore what happens if A or B range over
reals (or take some measure theory). -- ilyas
\_ P(A,B) is a table, with an entry for each possible value
combinations of A and B. The numbers in the table have to sum up
to 1. Each entry in the table corresponds to the probability of
A and B attaining the indexing values. P(A=true,B=true) is a
number, the probability that both events happened. P(A,B=true)
is a table where each corresponds to some value of A, and means
'probability that A takes on that value and B is true.' P(A|B) =
P(A,B)/P(B) where you divide consistent entries. P(A|B) is a
table with an entry for each possible combination of values of A
and B, where the entry means 'the probability A attains the given
indexing value given that the given indexing value of B was
observed.' For now you can ignore what happens if A or B range
over reals (or take some measure theory). -- ilyas
[ reformatted - 80x24 formatd ]
\_ I was disappointed that the thread got stuck on the argument
over observational bias, but never questioned the underlying
assumption that an alteration in the universal constants
would have precluded life. Life is a powerful phenominon,
and there are (at least) two independent instances of it on
Earth alone. (e.g. The oxygen based life covering most of
the earth and oceans, plus the ferric/ferrous based life
found in the heat vents around Seven Mile Trench and
lots of mines and a river in Spain) -mel
\_ I was assuming life cannot arise without powerful energy
sources like stars which an alteration of constants would
likely not produce. Why did I assume this? Because
life is a 'low entropy' process, and such a process needs
a lot of energy coming down to maintain itself.
These 'two independent instances'
aren't really independent (they arose from a common
ancestor) they just use a different metabolic mechanism.
Many other metabolism types were used at various points
in Earth's life. -- ilyas
These 'two independent instances' aren't really
independent (they arose from a common ancestor) they
just use a different metabolic mechanism. Many other
metabolism types were used at various points in Earth's
life. -- ilyas
\_ My mistake in calling the ferrooxindans independent.
Obviously since they have DNA and a biological cell,
there is a common ancestor involved. A better point I
should have made regarding them is that most people
would have trouble imagining life existing without
oxygen, but these bacteria do that just fine. I
doubt that life in a more generic sense has all
that strict a set of requirements on what environmental
conditions under which SOMETHING will evolve. -mel
\_ Origins are a problem. -- ilyas
\_ URL?
\_ google "ferrooxidans" -mel
\- hello, it is true that is if you tweak certain numbers
you cannot have even matter [like without CP violation
you cannot explain why we dont have a lot of anti-
matter hanging around], while tweaking yet other
numbers would not allow nuclei to form, this would
would live in a soup of only elementary particles
(although possibly some rarely seen ones like the
OMEGA- made from SSS). However, there are some
free parameters which if tweaked slightly IN ISOLATION
we still could get a pretty similar universe in terms
of large structure. However it is possible something
like the water molecule would not exist. Water is not
important to cosmology but it is obviously important
to LIFE. If something like the FERMI CONSTANT were
different it would change the energy of the fundemantal
reactions in the stars which would in turn change their
geometry and power spectrum ... so again large con-
sequences for "life" and our solar system, but at
the large scale and with a "non-antropic eye" the
universe may not be too different [there is actually
more to the Fermi value, but that is beyond the scope
of this discussion]. One may also wish to explore
what is the fundamental cause of the PAULI EXCLUSION
PRINCIPLE of FERMIONS which allows for elements and
chemistry to exist via the AUFBAU PROCESS (I am not
very familar with this area of summersymmetry but if
the world were made out of the integral spin ss
cousins of the electron, photon etc, i believe the
universe would turn into one GIANT ATOM/BOSE CONDENSATE).
i believe speculating in terms of these free parameters
is about the only reasonably way to look at this.
you cant arbitrarily ask "what if there was no
conservation of mass-energy" ... you have to replace
it with something you can plug into equations. You
may wish to learn about the CKM MATRIX. ok tnx.
universe would turn into one GIANT ATOM/BOSE
CONDENSATE). i believe speculating in terms of these
free parameters is about the only reasonably way to
look at this. you cant arbitrarily ask "what if there
was no conservation of mass-energy" ... you have to
replace it with something you can plug into
equations. You may wish to learn about the CKM
MATRIX. ok tnx.
[ reformatted - 80x24 formatd ]
\_ Water is very important to life on Earth, but
in a universe where water didn't exist, there
is little reason to believe that no other
compound would supply a similar role as a
convenient solvent. Removing basic rules like
Pauli Exclusion or Conservation of Energy is
outside the scope of what interests me. As
for learning about the CKM Matrix, I still
recall the sequence up, down, strange, charm,
beauty and truth even a decade or two out of
my last Physics class. The interestng question
to me is what the minimal set of requirements
are to generate an evolutionary system. -mel
\_ Did I say "up down" or "top bottom"? Sigh.
This isn't my day for accuracy. Time to go
to sleep -mel
\- 1. top and bottom have won out over truth and
beauty.
2. second, those 6 quarks dont form a sequence
... there are 3 (+2/3,-1/3) charge
pairs falling into 3 mass generations.
their masses are 1/3 of the free parameters
in the std model.
3. speculations based on minor tweaks like
if the earth were 10 percent larger or
10% closer to the sun or had a greater
tilt or weaker van allen belt etc may be
perfectly interesting but those are not
really cases of "the laws of physics being
different" or "the nature of the universe
being different" ... those are accidental
details in a way things like the CKM matrix
coefficients are not. when you are talking
about something like the standard model,
"emergent phenomena" is things like stars
and elements and chemical phenomena ... it's
still a long way from DNA.
4. "life" may have been able to overcome the
consequnces of certain fundamental changes
[like changing some masses would cause
the list of stable isotopes to change, so
"life" would have to pick some different
chemical pathways, since the relative abun-
dances would greatly shift], but there are
other changes which are so massive, life
obviously could not have evolved ... like
if it were not possible to form stable
nuclei -> no atoms -> no chemistry.
5. my point was without some knowledge of
"the standard model" you cant tell which
"tweaks" are "surivivable" and which lead
to a "boring universe" and which are some
where in between.
chemistry to exist via the AUFBAU PROCESS. ok tnx. |
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