Sections
Everyone has their own take on things and their own nuances.
But on the other hand, the instructor doesn't think there is anything
unusual or eccentric---just
somewhat philosophical---like Omar Khayyam (1048--1123):
see see the figure below
(local link /
general link: omar_reading.html).
See
Carl Sagan (1934--1996)
the figure below
(local link /
general link: carl_sagan.html).
Whole books
are written about what science is:
e.g., A. F. Chalmers' (1939--)
What is this thing called Science? (1999).
And artworks often illustrate
science:
see the adjacent figure
(local link /
general link: vermeer_geographer.html).
But how about: Science:
The study aims at a complete understanding which includes
being able to predict the evolution of
systems of
the objects to the past and the
future
insofar as intrinsic randomness allows.
The understanding is in terms of
theories---whose statuses cover
a large range:
Because science studies objective things there is an
absolute gold standard---the objective things
themselves---against which theories in
science can tested.
This permits the
scientific method---which is
illustrated schematically
in the figure below
(local link /
general link: sci_method.html).
In particular, note that though the objective things are a GOLD STANDARD,
any particular
experimentation/observation
can LIE.
You should be as cautious about believing an
experimentation/observation
at the frontier of current understanding as about believing
a SPECULATIVE scientific theory.
In many cases,
experiments have to be confirmed, often many times, before
you can be sure people arn't just making errors.
Think of cold fusion
for example.
Some people thought they'd seen it for a little while before all the
errors in their experiments were elucidated.
But on the other hand,
"extraordinary claims require extraordinary evidence"
quoting Carl Sagan (1934--1996): but others
said similar things earlier: e.g.,
Marcello Truzzi (1935--2003)).
Science
is thus PROGRESSIVE-TO-A-SINGLE-OBJECTIVE-GAOL in that it approaches an objective goal---the exact
knowledge of objective reality.
Not all human endeavors are PROGRESSIVE-TO-A-SINGLE-OBJECTIVE-GAOL like
science---NOT in the same sense anyway.
For example---an important
example---art.
An artist may progress is realizing his/her vision.
Technique may progress: e.g., if you aim at painting with
photographic
realism, you can get closer.
But in general no: art
is NOT PROGRESSIVE-TO-A-SINGLE-OBJECTIVE-GAOL.
For further elucidation, consider the figure below
(local link /
general link: lascaux_horse.html).
Context
decides on which "system" is meant---as usual.
System
and its special case
physical system
are explicated in the figure below
(local link /
general link: system_environment.html).
Of course, there can be systems of
systems and whole
hierarchies of
systems.
In fact, everything is part of a hierarchy of
systems.
For a big example,
the Earth has
a place in a
hierarchy of
physical systems
as illustrated in the figure below
(local link /
general link: earth_hierarchy.html).
If the systems
in a hierarchy
of systems are
natural systems, then
usually they can analyzed using the concept of
emergence.
Physics,
in brief, is the science of
matter
and motion.
One way of dividing
physics is into two broad fields:
fundamental physics
and applied physics:
Fundamental physics
is the study of very general laws and very general results
(which are derived from those general laws).
The general laws and results can be more or less fundamental
(more or less general)
and are always (or almost always)
expressible as mathematical formulae and they
relate physical quantities: e.g.,
velocity,
mass,
energy,
etc.
Having mathematical formulae means exact relationships exist at least
as ideal limits that can be closely approached.
Applied physics
which is the science of applying the general laws and results
of physics
to solving particular (physical) systems.
The systems
may be natural (e.g., stars)
or artificial (e.g., lasers).
As an example of applied physics,
see the animation
of
Archimedes' screw
in the figure below
(local link /
general link: archimedes_screw.html).
The two fields---fundamental physics
and applied physics---actually
CANNOT be completely separated---there is NO hard line between them---for
example, a result may
straddle the line between being considered a very general result and just being
the solution of an important special-case problem.
There is no hard line among people either:
Those relatively few physicists who work mostly in
fundamental physics---they
are the great brains---also
often work in applied physics.
Often in astronomy,
fundamental physics
and applied physics are pursued with the
same facilities---this certainly true in
astronomy as illustrated in
the figure below
(local link /
general link: vlt_laser.html).
An important goal
of fundamental physics
ever since physics emerged from
general philosophy
in Classical Antiquity
is the search for the true, ultimate, really, really fundamental fundamental physical theory.
For a representative of
ancient Greek philosophy,
see Aristotle (384--322 BCE)
in the figure below
(local link /
general link: aristotle.html).
Nowadays people tend to call the fundamental fundmental physical theory the
Theory of Everything (TOE)---which is
NOT
a good name since the fundamental fundamental physical theory is NOT a theory of everything
in the opinion of the herd yours truly follows.
For toes, see
see the figure below
(local link /
general link: toe.html).
In fact, the usually-discussed TOE
excludes the
2nd law of thermodynamics,
and so is NOT even
a theory of all
physics.
The (usually-discussed) TOE
is just the fundamental
theory of
fundamental particle physics
(which includes
quantum field theory).
Now that's a lot, but it does NOT include
2nd law of thermodynamics
(and so in a sense does NOT include
thermodynamics).
So as shorthand,
we will usually just say
TOE-Plus
for the grand-total fundamental fundmental physics theory
which includes
TOE,
thermodynamics,
and anything else considered
physics.
But TOE-Plus is NOT
really a theory of everything---in the opinion of the
herd yours truly follows.
We discuss more on this point when we discuss
emergence below
in the section Emergence.
Does TOE-Plus actually exist?
In a sense, TOE-Plus must
exist since there must be some minimum set of
physical laws that describe
the part of reality marked off as
fundamental physics---but there
is no guarantee that
the TOE-Plus will
have only a few elegant axioms---but
physicists hope so.
Do we have the fundamental fundamental physical theory
(AKA TOE-Plus),
a minimum set of consistent physical laws, now?
Overwhelmingly, most physicists
would say NO for several reasons.
We discuss two such reason here:
A longstanding reason is that our best theory of gravity is
Einstein's
general relativity
(see illustrative figure below:
local link /
general link: spacetime_curvature_earth.html), but
general relativity is
NOT consistent with
quantum mechanics
(the theory
of microscopic
particles)
which is arguably the best verified of all
physics
theories---your
cell phone and all modern
electronics would NOT work if
quantum mechanics
were NOT a highly accurate
theory.
Why don't we have an adequate theory of
quantum gravity.
The region where quantum gravity
is necessary to describe reality is very inaccessible
experimentally as discussed in the figure below
(local link /
general link: gravity_two_spheres_animation.html).
We hope one day to access adequately that realm in some way.
We do NOT know what two basic ingredients of
cosmology are.
We call these ingredients
dark matter
and dark energy---but those
are names for our ignorance.
We only know some of their effects on
cosmology,
the
large-scale structure of the universe,
and galaxies.
From those effects, we can calculate, probably pretty accurately, the
amounts of mass-energy of
dark matter
and dark energy.
Quantum field theorists
have their reasons for thinking there is
dark energy that is real
energy form.
We take up dark matter
and dark energy
in IAL 30: Cosmology.
Now the effects of
dark matter
and dark energy
are of fundamental importance, and thus so are
dark matter
and dark energy.
Since we don't know what
dark matter
and dark energy
are, we obviously do NOT have
TOE-Plus.
So the hunt for
TOE-Plus
continues---and hopefully when we find it, it will consist of
a few elegant axioms---which doesn't mean that it will be easy to understand---they
probably won't be easy to understand.
Form groups of 2 or 3---NOT more---and tackle
Homework 0
problems 2--10 on science
and physics.
Discuss each problem and come to a group answer.
Let's work for 5 or so minutes.
The winners
get chocolates.
See Solutions 0.
Before trying to define emergence,
it useful to say that
emergence makes
intelligible a very well understood fact:
So to a degree, everyone understands
emergence
even if they don't know the name.
One narrow definition
from Wikipedia:
Emergence
is the property of reality that
there are
important theories---important
sets of rules---that
are somewhat independent of other important
theories
and often hold in multiple contexts including imagined other realities.
These theories are exact in some ideal limit
which
in some cases can be reached trivially,
in some cases can approached arbitrarily closely at least
in principle,
in some cases can approached pretty closely,
and in some cases are only crudely reached in reality, but
still give useful order-of-magnitude results
or at least understanding.
A theory where NONE none of the above specified
conditions holds is NOT an important theory and is usually useless.
These theories can be called
emergent theories when you want to
emphasis emergence, but otherwise
just calling them important theories is best.
Emerging from the broad definition,
there are two kinds of emergent theories:
However, emergent theories
can switch from Kind 1 to Kind 2 in a logical
sense though they remain Kind 1 in a historical sense since they
were first discovered as Kind 1.
The switching process is actually pretty common in
physics.
An important example is Newtonian physics
which is historically Kind 1, but switched to
logically to Kind 2 when it was found to be derivable
from the theory of relativity:
it is the low-velocity, low-gravity limit of
the theory of relativity.
Another important example is
classical electromagnetism:
historically it is Kind 1, but it derivable from
quantum electrodynamics
which was discovered later in time.
Classical electromagnetism
is illustrated in the figure below
(local link /
general link: maxwell_equations.html).
It's NOT very useful as an axiom
since very little can be deduced from it alone.
The real work/fun is in obtaining important
emergent theories:
Despite its lack of obvious use in developing theories,
yours truly thinks yours truly's
broad definition is a useful perspective.
It's relatively merit-based about important
theories---it does NOT say
everything is really physics
or everything is really the
misnamed
TOE-Plus.
All of mathematics is sort of a grand
heap of an
emergent theory.
But to be general, yours truly likes to include it.
Of course, much of modern
mathematics has very little application
in understanding physical reality.
It's just part of conceptual
reality---concepts
are real things.
A trivial, artificial example of
an emergent theory
is chess---illustrated in
the figure below
(local link /
general link: chess_animation.html).
One can make chessmen
out of wood,
plastic, or nothing---you can just play
a game in your mind with some practice.
Chess does depend on
2-dimensional Euclidean geometry---and
so in that limited degree depends on an aspect of physical
reality---so it's NOT totally independent
of physics---just mostly so.
What does chess emerge from?
A combination of
random chance in
the history of games
and what human psychology thought of
as making an interesting
board game.
However, we can imagine chess
or something very like it
being developed by intelligent beings in other realms of existence.
Yours truly tends to agree
with Michel de Montaigne (1533--1592)
about chess.
One remarkable
emergent theory---which is
has arguably been proven empirically---is the
scientific method---see
figure below
(local link /
general link: sci_method.html).
It should work in any rational reality---or so
yours truly tends to believe.
Yours truly actually believes that the
scientific method is proven
theoretically
in a sense by Bayesian analysis.
However that is a long story which is we will NOT give though we discuss
Bayesian analysis a bit in
section Bayesian Analysis.
Note insofar as scientific method
is proven by Bayesian analysis,
it is NOT an independent theory, but
is based on the mathematical logic of
Bayesian analysis---so it emerges
from deduction NOT as in independent aspect of reality.
Psychology,
human and
in general,
is certainly governed by some
emergent theory.
This emergent theory is clearly
only partially understood---despite the efforts of
the scientists
and the sages---see figure below
(local link /
general link: confucius.html).
But in the opinion of many, we probably will someday, maybe even relatively soon.
After all our brains
are made of physical components obeying the laws of
physics
and chemistry, and
neuroscience
uses those laws to understand the
how the brain works.
But as we would now say, the brain
is the hardware
and the mind is the
software physically realized
in the hardware.
I think no one doubts there can be
minds
with quite different hardware:
i.e., artificial intelligence (AI)
and extraterrestrial intelligence.
And no one can rule out the possibility of
intelligences
in other realms of reality
where the physics is quite
different from our own.
Moreover, the particular laws of psychology
obeyed by a particular intelligence
would also depend
on the historical development of that intelligence
which is at least partially independent of
physics.
The upshot of this discussion is that the
laws of psychology
are independent to a large degree from
physics.
They do constitute an emergent theory as aforesaid.
Evolution
(by natural selection)
certainly happens to physical bodies.
We deduced
laws of evolution
(including the laws of heredity)
from observations of biota.
The actual origin of life
is still far from fully elucidated---but there's hope.
But the laws governing evolution
are independent of physics.
One can imagine evolution
applying to entities in other realms of reality
with different
fundamental physics.
Evolution
is an emergent theory.
We know it is true as a procedure because it works on the
computer.
The theory of evolution by natural selection
in computer calculations is used to find optimum solutions to
problems where one treats the solutions as breeding entities.
The techniques are called the
genetic programming method
and the
genetic algorithm method.
Both techniques have seen considerable development and may well become
even more important than they already are in scientific research, design,
and solving everyday problems.
In fact,
genetic programming
large language models (LLMs)
have combined to make a very powerful
solution finding technique
(see Jean-Baptiste Mouret, 2024,
Nature, "Large language models help computer programs to evolve";
Alhussein Fawzi & Bernardino Romera Paredes, 2023,
"FunSearch: Making new discoveries in mathematical sciences using Large Language Models).
Some would argue that
the theory of everything (TOE)
is the example
par excellence of
a NON-emergent theory---the
theory from which every other
theory
applying to physical reality
can be derived.
But yours truly like to think of
TOE as just another
emergent theory.
A good reason for thinking this way is that there may be regions outside of
the observable universe
where different "TOEs" apply.
But even if we found the truly "universal TOE" it would still just
be emerge from reality like other
emergent theories.
In any case,
yours truly would still likes to call
TOE
an emergent theory
(using the broad definition)
since yours truly
thinks of it as a Platonic ideal
and does NOT like singular exceptions to the rule that
all important theories are
emergent theories.
Some other semi-relevant considerations:
There is
an important fundamental
physical law
which everyone agrees is part of
physics---the
2nd law of thermodynamics
which we discuss in the next subsection---which everyone admits is independent
of TOE as usually discussed.
Those emergent theories
still exist as Platonic ideals
even if their application our reality required random events.
The
2nd law of thermodynamics
is universally acknowledged law of
physics:
The maximum entropy state is
thermodynamic equilibrium---which is
a timeless state at the
macroscopic scale---nothing is
changing---temperature,
pressure,
phase,
heat energy content, etc. are NOT
changing---and
temperature is
uniform---temperature is a measure of
thermodynamic equilibrium among other things.
At the microscopic level,
atoms
and
molecules are moving around, but that has
NO macroscopic effect.
In fact,
thermodynamic equilibrium
is a dead state.
Parts of
living organisms
are in thermodynamic equilibrium,
but overall they CANNOT be that and be
alive.
The 2nd law of thermodynamics
has been called
entropy arrow of time
since the
2nd law of thermodynamics
is one of the few time-asymmetric
physical laws
(see Wikipedia: Entropy as an arrow of time).
We can also imagine the
2nd law
emerging in
alternative realities with
alternative physics.
In fact, it is hard to think of a complex alternative
alternative reality
(one consisting of large numbers of entities) where it
does NOT hold.
Recall, I used the
nonce word
TOE-Plus
to include the totality of
physics including
the 2nd law of thermodynamics.
Also in fact, it is hard to think of a
living room where
2nd law does
NOT hold in a qualitative sense.
If you just let everything fall where it will in
your living room,
you would soon be living in a state of maximum
entropy: i.e.,
total squalor.
Achieving total squalor in Japanese
living room might take awhile.
See the figure below
(local link /
general link: living_room_japanese.html).
One aspect of the quantitative nature of
2nd law of thermodynamics
is that
entropy
(in an exact physics)
is precise measure of messiness in
physicsy sense---the most concise formula for
entropy is simple enough---see
tomb of
Boltzmann in
the figure below
(local link /
general link: ludwig_boltzmann.html).
You can make a reverse heat
energy flow (e.g., in refrigerators),
but that takes outside manipulation.
Stars
are providing a flow of
heat energy
in the form of
electromagnetic radiation
(i.e., photons) to
space.
In our current understanding of
cosmology,
the stars will NEVER succeed in
heating up the physical components of
space
(particles
and electromagnetic radiation (EMR))
to stellar temperatures
on average.
Emergence
and emergent principles
are, in fact, everywhere.
When you think about it, you always knew it.
So the
neither
theory of everything (TOE)
nor TOE-Plus
is a theory of everything.
Recall TOE is
really a theory of
particle physics
independent of all
natural history.
Now
TOE,
it is reasonable to say, sits at the bottom of
The Hierarchy of the Sciences
(see section The Hierarchy of Sciences below), but building up the rest of the
hierarchy needs a whole lot of emergence
involving all kinds of other laws
(e.g., 2nd law of thermodynamics
evolution by
natural selection)
which seem just as fundamental to the herd yours truly follows.
From the point of view of
emergence,
TOE is NOT
the only fundamental set of laws---there are lots of others.
We won't do that much in the lectures, but we should keep
emergence in mind.
To finish, I emphasize that the above discussion is somewhat
idiosyncratic to the instructor.
Others might put things differently or disagree, but I do NOT think
my view on emergence is eccentric.
I believe, I'm just following a herd.
In fact, in yours truly's opinion
Bayesian analysis
is the scientific method quantified
and the proof of the
scientific method.
See subsection
Bayesian Analysis and the Scientific Method
below.
It finds a lot of use in many
sciences: e.g.,
cosmology,
economics,
epidemiology,
medicine,
particle physics,
psychology,
sociology,
etc.
So it's an important science topic and
we do NOT discuss it elsewhere in
IAL---and this is the
philosophical-historical-tragic-comical-poetical introduction to
astronomy and
science in general---and
some students will encounter it sooner or later---and so we discuss it here.
In detail, it's hard to understand---but we won't do that---and hard to apply---but
there are computer packages.
Bayes' theorem is really simple:
it is easier to prove than to remember.
It is a relation between P(A|B) and P(B|A). To explicate:
So, for example, if you know P(B|A), P(A), and P(B), you know P(A|B).
Bayes' theorem is simple.
Bayesian analysis is NOT.
So we won't expand on its mathematical detail here.
But it is used to judge the probability that theories
are true as aforesaid.
What the Devil you say.
Isn't a theory true or NOT?
For Himself,
see the figure below
(local link /
general link: dore_satan.html).
But Bayesian analysis
deals in truth to your knowledge.
If yours truly flips a coin and hide it under
a hand, is it heads or tails?
In an absolute sense, it's one or the other and yours truly even knows it
which it is.
But to your knowledge it's fifty-fifty.
Bayesian analysis
allows you to estimate---and in practical cases, it is almost always just an estimate---the
probabilities of theories.
But Bayesian analysis
is NOT just a one-off.
It is a way of updating the probabilities of theories using
Bayes' theorem.
In fact, there is nothing unusual about updating the probabilities of theories.
Qualitative
Bayesian analysis
is what every one has done forever---"This is probably true
based on everything we know now." etc.
But actual Bayesian analysis
has a lot more math
and computer number crunching to it.
The updating probabilities of theories by
Bayesian analysis
is, in fact, how
the scientific method is quantified
by Bayesian analysis.
The fact that in the ideal limit
Bayesian analysis should lead
to true theories is the
proof of the scientific method.
Yours truly explicates the updating procedure and the proof
of the scientific method in
An Educational Note
on Bayesian Analysis.
Bayes' theorem
was discovered in the
18th century
and many of the basic techniques of
Bayesian analysis
were worked out in the
1950s by
Sir Harold Jeffreys (1891--1989).
To explicate,
Bayesian analysis
is most useful when you have
theories A
that only make statistical predictions.
Then you accumulate large sets of
data B
(e.g., petabytes or
exabytes)
and calculate P(A|B).
The storing and calculating requires lots of
computer power.
The conditional probabilities
P(A|B) allows you to rank
the theories A
and hopefully eventually come to a conclusion which
theory A is true.
Using Bayes' theorem, you update
your probabilities as more data is accumulated.
As aforesaid,
Bayesian analysis
finds a lot of use in many
sciences: e.g.,
cosmology,
economics,
epidemiology,
medicine,
particle physics,
psychology,
sociology,
etc.
The need for
Bayesian analysis
was less in the old days
when there were easier things to discover
requiring simpler and fewer
theories
and much smaller data sets.
A further explication of
Bayesian analysis
is given in the aforementioned
An Educational Note
on Bayesian Analysis.
In cosmology,
we have a wealth of
accurate/precise
data
compared to what we had before circa 1992---we
call our time the
golden age of cosmology or the
age of precision cosmology.
But there are quasi-endless
cosmological models that
fit the data more-or-less well.
The data is mostly
statistics
and the cosmological models
predict a probability
of obtaining those
statistics.
How does one rank these
cosmological models in order
of likelihood?
Using Bayesian analysis.
It gives us P(A|BK): the
probability of
cosmological model A
given statistics B and
background knowledge K.
Alas, many uncertainties come into all
Bayesian analysis,
and so the ranking of
cosmological models
is NOT decisive so far.
But at least it
suggests which models are favored, and so are worth further development.
For some time, the
Λ-CDM model (AKA concordance model)
has been more-or-less
top dog, but
no one would be too surprised if it was outranked someday.
For a top dog,
see the figure below
(local link /
general link: wolf.html).
We discuss it in here in
IAL 0 because
it's a bit philosophical and does NOT fit anywhere else in
IAL.
The term
anthropic principle
was coined in 1973 though the
idea of such a thing goes back to 1904
(see
Wikipedia: Anthropic principle: Origin)
and perhaps earlier in a vague sense.
The anthropic principle has been controversial:
some argue that it is trivial or worthless as a scientific
principle.
Part of the problem is that there are different versions
of anthropic principle
(see Wikipedia: Anthropic principle: Variants).
However, it seems a basic
anthropic principle
has gained traction and is of some importance in modern
astronomy
and physics.
Put as an aphorism,
the anthropic principle states:
See Orson Welles (1915--1985)
observing in the figure below
(local link /
general link: orson_welles_chimes_at_midnight_a.html).
The essence of the anthropic principle is
"we exist" = A implying B must exist.
Put mathematically, we have A and we know P(A|[not B]) = 0,
and so B exists: i.e., P(B|A) = 1.
There is a bit more mathematical description and the
connection to
Bayes' theorem
in the A-principle file.
What's B? Any of a vast number of things that are necessary for us.
We'll give some examples below.
But "we exist" = A can be specified more precisely.
Possible A values roughly in order of increasing generality are:
Interestingly, there is historically a forerunner of
the anthropic principle
in Aristotelianism.
To explicate,
Aristotelianism considers
A to be
a final cause of B
since B exists, among other things, to make A possible.
This Aristotelian
teleological point of view
is useful in some contexts (e.g., things designed by
intelligence or
evolution),
but probably NOT many others.
An example
from evolution is that
animal flight (i.e., A)
is the final cause
of wings (i.e., B).
In the subsection below, we give an example of the
application of the
anthropic principle.
There were more examples once, but enough is enough.
Probably the most famous example of the use of
anthropic principle
was in the
discovery of the
triple-alpha process
in 1952.
Recall, the term
anthropic principle
was coined in 1973.
So only retrospectively has the term been applied to this
discovery.
The story in
point form:
In 1952,
the Big Bang theory
(then very rudimentary compared to today)
and the steady state universe
were considered the most---maybe the only---viable
cosmological models.
In other words, an
anthropic principle argument
argued for
the triple-alpha process---and,
as aforesaid,
this was before
the expression anthropic principle
was coined in 1973
(see Wikipedia: Anthropic principle: Origin).
The properties of the winners of a
lottery are quasi-unique
due to random peculiarities, but there
are always winners
of a lottery.
The foregoing in yours truly's
opinion shows that the
anthropic principle
is a useful scientific principle.
Given B (something
related to technologically advanced
human society as we know it),
we can explain in a sense the existence of A if P(B|not A) = 0 or P(B|not A) is close to 0.
The sense being that:
The anthropic principle
also sometimes allows you to infer the existence of A even if you didn't know that A existed before.
So it can be a discovery tool as famously shown by the
discovery of the
triple-alpha process
(see the above
section Anthropic Principle Example:
The Triple-Alpha Process).
If you extend the
anthropic principle with
Bayesian analysis, then
you may be able to estimate the
conditional probability P(A|B)
and decide whether A is likely to exist and be worth looking for if you do NOT
already know of it.
There are criticisms of the
anthropic principle
(Wikipedia: Anthropic principle: Criticisms),
but yours truly thinks those
are mostly directed toward more extravagant claims for it than those discussed here.
In IAL,
we occasionally refer to the
anthropic principle.
The branch theories
can be regarded as approximations to the exact fundamental
theory of physics,
theory of everything (TOE),
which is as yet unknown, PLUS important
some emergent principles
(e.g.,
2nd law of thermodynamics)---recall
yours truly calls this grand-total fundamental fundemental physics theory
TOE-Plus
faute de mieux.
But following the herd yours truly follows---which includes
one of yours truly's gurus,
Robert Laughlin (1950--)
(see Laughlin, 2005, p. 31)---the truer
perspective is to view the branch theories
as exactly true
emergent theories.
More than yours truly would like to give now.
But yours truly
could say that it seems to yours truly
the more fruitful perspective for yielding scientific progress in physics.
It also is the perspective that is more general in that
allows the branch theories
to fit into the general category of
emergent theories.
"More general" is often taken to be "truer" in science.
But you can often get very close to those limits and often very easily.
So close that often NO discrepancy between
experiment and branch theory can be detected.
The great exactness of the branch theories
is extremely valuable.
It is what has allowed how great progress in understanding the
universe and
in developing technology---despite NOT having
TOE-Plus.
In fact, we can repeat ourselves and say---going beyond physics----that
emergence allows us to understand much about
reality without having to know everything about reality.
The 2 figures below
(local link /
general link: physics_branches.html;
local link /
general link: physics_branches_related.html)
illustrate schematically the relationships of the
branches of physics.
There are many other ways of dividing physics
up into fields and sub-fields.
We are NOT going into all that.
Where does astronomy fit in to
physics.
Nowadays almost everyone agrees that
astronomy should be classified
as a field of physics.
Rather astronomy
makes uses of all
branch theories
discussed above plus
a lot of other physics
theories
of a less-grand sort---in fact, it uses
pretty much all the physics we know.
It applies these
theories
to the study the large objects of the
universe
and many of their smaller constituents too.
But astronomy is also
fundamental physics
since it includes
cosmology:
the science of the
universe as a whole on large scales.
Cosmology
is partially applied physics,
but it also fundamental physics
because it is, among other things, about the
reality
out of which all
physics arises.
In fact, it seems likely that
cosmology
and
TOE
are so deeply connected that one CANNOT be fully understood
without understanding the other.
We will NOT go into why at this moment.
The figure below
(local link /
general link: cosmos_history.html)
is a preview of
cosmology which
we take up in IAL 30: Cosmology.
Form groups of 2 or 3---NOT more---and tackle
Homework 0
problems 7--14 on
physics,
emergence, and
physical sciences.
Discuss each problem and come to a group answer.
Let's work for 5 or so minutes.
The winners
get chocolates.
See Solutions 0.
The point in doing so is to understand how the
sciences are related.
But to reiterate the theme of the section Emergence,
there are many important emergent theories
which emerge from reality
and are at least somewhat independent of each other, and so the bottom of the
hierarchy does NOT dictate everything else in it.
Yours truly orders, very undefintively,
the sciences in the
hierarchy:
Why this ordering?
However, as one goes up the hierarchy,
historically there were fewer
emergent principles
that were mathematical in formulation.
But there has been advances making
the originally non-mathematical
emergent principles
mathematical or at least more precise, and thus more like mathematical formulations.
Then
physics generally since the
branches of physics
follow directly from
TOE-Plus.
What changes going up the hierarchy above
physics?
Less dependence on physics and more on
emergent theories that are
NOT classified as
physics.
The transition from
physical sciences
to the life sciences
is a key point for "less dependence on physics"
at least in the judgment of tradition.
Nevertheless, the
life sciences do depend
on physics and there is even
a well defined field of physics
called biophysics.
Old-fashionedly, one would say there is really a lot
"less physics"
when you get to psychology.
For example, just try
deriving the Oedipus complex
from physics alone---a very uncomfortable
proposition.
For the Oedipus complex,
see the figure below:
local link /
general link: sigmund_freud.html).
However, in the modern age,
biophysics
is playing a role
in neuroscience, and
thus in psychology.
But these fields have their own
emergent theories
which are, however, often rather subjective---but there is a valiant attempt to
make history
a mathematical science---see
the figure below
(local link /
general link: historia.html).
Maybe one day,
history will be considered
a science without qualification---and
an art with a bit of qualification.
In the broadest sense, astronomy
is the study of all extraterrestrial phenomena and some terrestrial phenomena too.
Earth is a
planet, and so,
qua
planet, is a fit
subject for astronomy.
Astronomy
and mathematics
have always been closely allied since
astronomy
makes deep demands on
mathematics---predicting
eclipses, etc.---and
mathematics
often progressed in response to those demands.
In fact, up to just a bit later circa 1600
the leading
astronomers,
mathematicians,
and astrologers
were often the same people and the terms
astronomer
and mathematician
were often considered
synonyms
and also often considered
synonyms
for astrologer.
Why did astronomers
and mathematicians
and people believe in astrology?
It was so ancient and offered an explanation for all the crazy things people do.
And for
astronomers, it paid the bills.
But there were always people including many
astronomers who didn't
believe in astrology
or believed it was demonic.
Johannes Kepler (1571--1630),
a leading astronomer
and mathematician
of the
Scientific Revolution (c.1543--c.1687),
is a transitional case: he started out with a profound belief
in astrology
while admitting its practice was often fraudulent, but by the end of
his life seems have just seen it as a way to pay the bills.
Galileo (1564--1642), on the
other hand, never believed in astrology---but
he was required to teach it since it was required for medical students.
Just ask yourself,
would you trust a doctor who couldn't prescribe for you
based on your horoscope.
After 1800, there was a bit
of a parting of the ways,
and only a fraction of
mathematicians
remained astronomers.
Certainly, after circa 1800,
leading mathematicians
stopped being leading
theoretical astronomers.
The mathematicians
abandoned us.
Examples of people who were both
leading astronomers
and leading
mathematicians are
Ptolemy (c.100--c.170 CE)
(the greatest theoretical astronomer
of Classical Antiquity:
see figure below:
local link /
general link: ptolemy_armillary.html),
Omar Khayyam (1048--1123),
Isaac Newton (1642/3--1727)
(see figure below:
local link /
general link: newton_principia.html),
Pierre-Simon Laplace (1749--1827),
and
Carl Friedrich Gauss (1777--1855).
Astronomy
is often cited as the oldest, empirical exact science---empirical meaning based on observation---exact
meaning using quantitative measurements.
This is all just point of view.
How old is astronomy as an exact science?
In a very elementary way, it may go back tens of thousands of years
in the Paleolithic.
For some explication,
see the figure below
(local link /
general link: sapien_neanderthal.html).
Many ancient cultures all over the world constructed such
astronomical monuments.
The most famous is
Stonehenge---see the figure below
(local link /
general link: sullivan_stonehenge_003_remains.html).
In
alignment astronomy,
you just record where objects rise
or set over the horizon as seen from some specific place: e.g.,
the center of Stonehenge.
Note the
Stonehengers (AKA Neolithic Britons)
were NOT literate, and so could NOT
record their sky lore
any other way, but in
astronomical monuments.
Stonehenge and other
astronomical monuments
from around the world were almost always NOT observatories.
They probably served multiple cultural functions and
recording sky lore was probably
a minor function in most cases.
For the
alignment astronomy
(probable and unlikely both) embodied in
Stonehenge,
see the Stonehenge map
in the figure below
(local link /
general link: stonehenge_map_refined.html).
On the other hand, the literate
ancient Mesopotamians---Sumerians
from sometime in the
3rd millennium BCE
and
Babylonians
from roughly the early
2nd millennium BCE
until circa the 2nd century CE---have left extensive astronomical
texts of observations and calculations.
The most advanced of the texts
come from
circa 400 BCE--circa 100 CE
(Neugebauer, 1969, p. 30).
The texts are on
clay tablets.
See the exmaple in the figure
(local link /
general link: sumerian_gods_tablet.html).
Such predictions are
presented in
ephemerides
(singular ephemeris) which are tables
of predictions.
What of Babylonian
physical/philosophical cosmology?
See the figure below
(local link /
general link: babylonian_cosmos.html).
The ancient Greeks
(circa 600 BCE--circa 400 CE)
also practiced
astronomy
and---as you might have guessed---invented various
philosophical and mathematical models of the
cosmos.
For
Ancient Hellas (AKA Ancient Greece) illustrated
by the Acropolis of Athens,
see the figure below
(local link /
general link: acropolis.html).
Of course, almost nobody else in the world had heard of
Aristotelian cosmology
until after circa 1800.
See the cartoon of
Aristotelian cosmology
in the figure below
(local link /
general link: aristotle_cosmos.html).
The eventual main competitor was the geocentric
Ptolemaic system
of Ptolemy (c.100--c.170 CE).
Ptolemaic system
was in many respects based on
Aristotelian cosmology, but
Ptolemy described the motions
of the astro-bodies
using
epicycle models
(which we will describe in
IAL 4: The History of Astronomy to Newton)
rather than with compounded celestial spheres,
but he still kept the celestial spheres
for other purposes at least in some fashion.
The Ptolemaic system
did give pretty accurate predictions of celestial motions for its day
(unlike Aristotelian cosmology
which was at best gave qualitative predictions)
and Ptolemy and his true disciples
believed that it was at least approximately a viable physical model of the
cosmos.
However, the
pure Aristotelians
argued that the
Ptolemaic system
was essentially a mathematical calculational device and NOT an actual physical model
of the cosmos---and they were largely
right about that---but they were
largely wrong in believing
Aristotelian cosmology had more
physical content.
For many centuries up to into the
17th century,
it seems that Aristotelian cosmology
and the
Ptolemaic system
managed to coexist even within individual minds albeit uneasily.
In the course of the
16th and
17th centuries---which is
the time of the
Scientific Revolution (c.1543--c.1687)---we
have the transformation
from Aristotelian cosmology
and the Ptolemaic system
to the
Copernican heliocentric solar system and then to
the quasi-infinite universe of
Newton---see the figure below
(local link /
general link: newton_apple.html).
Certainly, in Aristotelian cosmology
and the Ptolemaic system, the
physics
of
Earth
and
the Heavens are different.
We CANNOT do experiments on stars,
galaxies, etc.
But experiments on
Earth
do reveal aspects of the
physics
of outer space.
In fact, the unification of terrestrial and celestial
physics
is what has vastly increased the intelligibility
of the
universe.
Further astronomy history can be found in
IAL 4: The History of Astronomy to Newton
and, of course,
Wikipedia's
History of Astronomy.
Form groups of 2 or 3---NOT more---and tackle
Homework 0
problems 11--17 on emergence,
physical sciences,
and astronomy.
Discuss each problem and come to a group answer.
Let's work for 5 or so minutes.
The winners
get chocolates.
See Solutions 0.
This lecture---the philosophical-historical-tragic-comical-poetical introduction
to astronomy
(as illustrated by the everlasting figure above:
local link /
general link: moon_earthrise.html)---which
covers several fascinating topics relevant to
astronomy---is somewhat
idiosyncratic to the instructor
as almost any personal philosophical discussion must be.
In any case, it's traditional to begin the study of
astronomy
in
Carl-Sagan mode.
Question: Carl Sagan was:
Answer 3 is right.
What is it?
So offering a single short definition
of science is always inadequate.
The study of objective reality.
OBJECTIVE meaning independent of the particular observers or
general to all observers.
completely wrong,
discarded (but maybe NOT forever),
highly speculative,
something to them (but maybe NOT a lot),
trivial,
useful, very useful, educationally useful,
heuristic,
completely adequate to explain the things they address,
challenging alternative (i.e., devil's advocate),
astonishing if they were right,
astonishing if they were wrong,
right without a doubt (except for an ineradicable
philosophical skepticism),
right by mathematical proof,
right by definition.
Note that the
scientific method
in practice is history
(specifically science history) and is full of messy
contingencies.
"Contingencies" or "chancy, it-depends kind of events"
are part of the modern historian's
everyday jargon.
Cold Fusion
qua
cold fusion was a mistake, but
low-energy nuclear reactions (LENRs)
may be real as yours truly has belatedly learnt
(see It's
Not Cold Fusion... But It's Something, 2016dec07, Steven B. Krivit, Michael J. Ravnitzky).
Maybe some apologies are in order for past scorn---NOT for the first time
in science.
On every sweep through the CYCLE of
the scientific method,
the theory and
experimentation/observation
become more exact and/or more general and/or more far-reaching---at least that
is the hope.
Before going on, we should introduce a bit of
science
jargon:
system
and its special case
physical system---which is
usually just abbreviated to system.
Astronomy is a field of
physics
(as we discuss below in section Astronomy) and uses
a lot of physics, and so
physics needs a bit of discussion.
Light is usually NOT considered
matter, but is considered
in physics.
But to be brief we can include light under
the heading of
matter as
a shorthand.
One could say "stuff and motion", but that sounds weird and pedantic.
For motion illustrated,
see the figure below
(local link /
general link: muybridge_horse.html).
We can expand a bit on physics.
Note that the term "fundamental" is used in somewhat different ways
in physics that context
elucidates.
We can give examples:
The meanings of fundamental
are illustrated in the figure below
(local link /
general link: particle.html)
showing ingredients in our
current most fundamental physics---a preview
of things we mostly will NOT go on to view in
IAL.
Most physicists work mostly in
applied physics, but
again there is NO hard line between that work and
fundamental physics.
Astronomy
itself includes both
fundamental physics
and applied physics
as discussed below in
subsection
Astronomy: Both Applied and Fundamental Physics.
The fundamental fundamental physical theory is the minimum consistent set of laws or
axioms from which
the rest of
fundamental physics
can be derived---it would be the most general physics theory.
And there are other reasons for why we know we don't
yet have TOE-Plus.
Since reality and therefore physics
should be self-consistent, it is believed that
there must be a theory of
quantum gravity
that has general relativity
(or some better replacement) as its macroscopic limit.
In physics jargon,
"macroscopic"
means anything much larger than atomic scale (∼ 10**(-10) m)
and "microscopic"
means anything atomic scale or smaller.
The terms are used loosely.
The fact that we have no adequate theory of
quantum gravity
yet means we do NOT
yet have TOE-Plus.
In fact, the simplest form of dark energy
is NOT really an energy form at all.
It is the
cosmological constant Λ (pronounced Lambda)
(discussed in
IAL 30: Cosmology) which
is a modification of gravity
in general relativity.
It is the simplest of all modifications
to general relativity
to get the effect of
acceleration of the universe,
and so is favored
by Occam's razor over
other modifications.
In fact, astronomers often
just say
Lambda as
synonym
for dark energy.
See the figure below
(local link /
general link: pie_chart_cosmic_energy.html)
for further discussion of
dark matter
and dark energy
and their abundance in the
observable universe.
Group Activity:
Why did yours truly
say above in section Physics that
TOE-Plus
is NOT really a theory of everything---at least in the opinion of the
herd
yours truly follows---the
herd itself is shown
the figure below
(local link /
general link: sheep_herd.html).
The explanation is in the concept of
emergence---as illustrated
in the figure below
(local link /
general link: whale_breaching.html).
Identifying
emergent principles
and
emergent theories
during the course of these lectures requires long discussions.
You don't have to know everything about reality
in order to know something about it.
For an example
of the aphorism in action,
you don't have to know any of the formalism of
classical physics
in order to drive a
car---see
figure below
(local link /
general link: stanley_steamer.html)---even though
cars certainly obey
all the laws of classical physics.
Just an aphorisms, but
aphorisms are often clearer than
formal definitions.
"In philosophy,
systems theory,
science, and
art,
emergence is a
process whereby larger entities, patterns, and regularities arise through
interactions among smaller or simpler entities that themselves do
NOT exhibit such properties."
At the risk of being
idiosyncratic---like
Job is thought to be by his
friends as seen in the figure above
(local link /
general link: book_of_job.html)---yours truly
will offer a more general broad definition
of emergence:
In view of the given definition,
all important theories are
emergent theories.
Yours truly tends to think of
emergent theories as
Platonic ideals---see
the 2 figures below
(local link /
general link: platonic_solids.html;
local link /
general link: pegasus.html).
Yours truly's
broad definition
of emergence just given
is so general as to be almost a trivial observation.
The point that many important theories
are NOT derivable from
physics
and/or
fundamental physics
is emphasized in the following subsections
Rather than try continue in a general analysis of
emergence---which quickly becomes
abstract ...
... tedious, unmemorable, and
a shaggy dog story--- ...
... we'll just consider
examples of
emergence in the following subsections
which illustrate
its features and importance as a concept.
The RULES and STRATEGY
of chess are NOT
dependent on physics
or the physical bodies that manifest the
game.
In particular, we do NOT really understand
the emergence of our intrinsic sense of
consciousness
out of physical reality.
See the figure below
(local link /
general link: neural_consciousness.html).
Why do we say an emergent theory
governs psychology, NOT
just physics,
chemistry, etc.
Actually, evolution
is known to work in contexts other than
life as we know it.
The
2nd law of thermodynamics
expresses the tendency of things left to themselves to go to heck.
Question: The spontaneous increase in
entropy in
a closed system
is very important in astronomy because
the observable universe
(apparently a closed system):
Answer 1 is right.
When I was a naive boy
physicist,
I thought physics
was really everything---everything could be reduced to
physics---I was
reductionist.
But then I saw the
light and believed in
emergence.
Bayesian analysis
is that probability theory
dealing with the truth of
theories
and it has a big vogue these days.
Question: Have you ever heard of
Bayesian analysis
or Bayesian-something or
Bayes' theorem?
Why discuss Bayesian analysis?
Answer 2 is right since you just have.
Now
P(AB) = N_(AB)/N = [N_(AB)/N_(B)]*[N_(B)/N] = P(A|B)P(B) ,
where N is all events.
But clearly
P(AB) = N_(AB)/N = [N_(AB)/N_(A)]*[N_(A)/N] = P(B|A)P(A) .
Thus Bayes' theorem
P(AB) = P(A|B)P(B) = P(B|A)P(A)
or asymmetrically
P(A|B) = P(B|A)P(A)/P(B) or P(B|A) = P(A|B)P(B)/P(A) .
And that's all there is to it.
Leaving aside the complications of partially true
theories,
theories are true or NOT
in an absolute sense.
However, Bayesian analysis
seems to have come into widespread use only since circa
1990.
The reason for this is only since then has sufficiently abundant
computer power and
data storage have become available.
The anthropic principle
is a peculiar example
of an emergent principle---an
example that is when
using the general broad definition
of emergence
yours truly adopts.
Things have to be the way they are or we wouldn't be here to observe them.
The anthropic principle
can be called an
emergent principle
since it should emerge in any imaginable inhabitable universe or so
yours truly thinks.
We will NOT give a thorough explication
of the anthropic principle,
but we will give some explication,
its connection to
Bayesian analysis
(which is a hot topic),
and some interesting
examples of its use.
P(A|B) = probability of A given B.
Now say A exists and we have
P(A|[not B]) = 0.
Then B must exist.
In modern physics,
there are several important
branches
in which different branch theories hold.
"Truer perspective" is an expression that takes some argument.
Exact trueness only holds in ideal limits that in many (all?) cases can never be exactly reached.
Historically, it is true that
they were sometimes regarded as distinct
sciences and this distinction vestigially
lingers in the factoids
that university Physics Departments
are often called Physics & Astronomy Departments
and astronomy sometimes has
its own separate university department.
However astronomy is NOT a
branch of physics
in the sense used above.
There is NOT a branch theory
of astronomy.
Group Activity:
There are several vague ways of organizing the
sciences in
a hierarchy---which are only symbolized by the
totem pole
in the figure adjacent
(local link /
general link: hierarchy_totem_pole.html).
mathematics,
TOE-Plus,
theory of everything (TOE),
physics generally,
the physical sciences
(e.g., chemistry,
geology,
meteorology,
climatology),
the life sciences
(e.g., biology,
zoology,
botany,
neurology,
neuroscience),
the social sciences
(e.g., economics,
human geography,
political science,
psychology).
One must add that
mathematics,
like art,
evolves by an expansion into different realms of experience and creation---it
has a myriad of goals many of which can be unrelated to the other
sciences.
Another somewhat related way specifying the
hierarchy of the
sciences is illustrated
in the figure below
(local link /
general link: science_hierarchy.html).
In this figure,
the length scales of the
universe
are PARTIALLY mapped to
the hierarchy---undefinitively mapped.
Fields of study NOT traditionally considered sciences
do NOT easily fit into the hierarchy of
the sciences:
philosophy,
history,
ethics,
the arts,
etc.
In this section, we give a short semi-historical introduction
to astronomy.
More on the history of astronomy
is given in
IAL 4: The History of Astronomy to Newton.
Astrology
via the zodiac is illustrated
in the figure below
(local link /
general link: zodiac_woodcut.html).
After circa 1600,
there was a
definitive parting of the ways
and astronomers
and mathematicians
have nothing to do with
astrology anymore---we don't talk to
the astrologers.
However, if leading astronomers
and leading
mathematicians
gave up being also
leading astrologers
after circa 1600,
they continued to often be the same people up to
1800,
and the terms
astronomer
and mathematician
continued to then to be often used as near
synonyms.
One can say that astronomy
predates
physics---of which
astronomy is now a part---and then was absorbed by
physics.
Or one could argue that astronomy
was the original physics.
One can quibble, but there really is NO other plausible candidate than
astronomy for
oldest emprical exact science if one regards
mathematics
as an abstract science that is only applied in the physical world.
Definite evidence of prehistoric astronomy
is physically recorded/embodied in
prehistoric
astronomical monuments.
The embodied astronomy
is all pretty simple
alignment astronomy,
in fact.
The calculations were to make predictions of astronomical phenomena
which is something astronomers are still tasked with doing.
The model of the cosmos that eventually
became dominant was that of
Aristotle (384--322 BCE)---the
"supreme authority": see the figure below
(local link /
general link: aristotle_supreme.html).
In fact, it became a sort of philosophical dogma in
ancient Greek astronomy,
Medieval Islamic astronomy,
Medieval European astronomy,
and early modern astronomy
up to the 17th century.
Aristotelian cosmology
was geocentric and imagined the astro-bodies
as being carried around on compounded
celestial spheres
that were invisible and were moved by gods which in later
monotheistic times
were replaced by angels.
Aristotelian cosmology
did have competitors in Classical Antiquity
and later.
Coexist in minds in western
Eurasia that is---no one else in
the world had ever heard of them until after circa
1600.
A very simplified diagram of the
Aristotelian cosmos
as understood in Renaissance Europe
is shown in the figure below
(local link /
general link: aristotle_cosmos_system_renaissance.html).
See also the
Newton videos below
(local link /
general link: newton_videos.html)
An important part of
Newton's
achievement was showing that the same physical laws that apply on
Earth
apply in space.
Question: This demonstration of same physics
on Earth and in
space is:
The unification of terrestrial and celestial
physics
finally made
astronomy
somewhat experimental.
Answer 2 is right in my opinion anyway---and in the opinion of
history.
Group Activity: