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 the figure of
Carl Sagan (1934--1996) below.
Whole books
are written about what science is:
e.g., A. F. Chalmers' (1939--)
What is this thing called Science? (1999).
But how about: Science:
The study aims at a complete understanding which includes
being able to predict the evolution of the 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.
In particular, note that though the objective things are a GOLD STANDARD,
any particular
experimentation/observation
can LIE.
One 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
one 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"
(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.
Context
decides on which "system" is meant---as usual.
System
and its special case
physical system
are explicated in the figure below.
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.
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:
These laws/formulae relate physical quantities: e.g.,
velocity,
mass,
and
energy.
Having mathematical formulae means exact relationships exist at least
as approximations or as ideal limits.
Below is an animation
illustrating applied physics.
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.
Often in astronomy
fundamental physics
and applied physics are pursued with the
same astronomy as illustrated in the image below.
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.
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.
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
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 consider
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:
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.
We hope one day to access adequately that realm in some way.
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.
See the figure below for further discussion of
dark matter
and dark energy
and their abundance in the
observable universe.
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 Solution 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.
In view of the given definition,
all important theories are
emergent theories.
These theories can be called
emergent theories when you want to
emphasis emergence, but otherwise
just calling them important theories is best.
An example of an important
emergent theory
is shown in the figure below.
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:
This can be done whether an
emergent theory
accords with either of the narrow or broad
definitions.
A derivation from an
underlying system
may or may NOT be possible depending on the case in the later possibility.
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.
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.
It should work in any rational reality---or so
yours truly tends to believe.
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.
But in the opinion of many, we probably will, 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 algorithm method
and
the genetic programming 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.
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 dervived.
However:
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.
In which case,
TOE would
obviously be an emergent theory.
However:
Newtonian physics,
for example requires
a realm of reality
big enough to have
macroscopic parts.
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 a qualitative sense, it applies to your
living room.
In a quantitavie sense, it applies to the
free expansion of a
gas as the figure below illustrates.
We can track the
emergence of
2nd law
back to the interactions of particles.
We can also imagine the
2nd law
emerging in other realms of existence.
In fact, one has a hard time imagining a universe consisting of large numbers of entities
in which 2nd law
does NOT apply.
An important manifestation of the
2nd law is that
heat energy
always flows spontaneously from HOT to COLD (at least as long as there is NO
other flows: e.g., particles and
work
in the physics sense)
and that left to itself, as aforesaid in slightly different words,
a closed system
evolves to a state of
thermodynamic equilibrium
where everything is at one temperature
and there are no heat energy flows.
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.
Identifying
emergent principles
and
emergent theories
during the course of these lectures requires long discussions.
This lecture---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 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, pedagogically 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 doubt),
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 abbreviated just 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, see the figure below.
We can expand a bit on physics.
Note that the term "fundamental" is used in slightly different ways
in physics that context
elucidates.
We can give examples:
The 4th meaning is illustrated by the figure below showing ingredients in our
current most 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.
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 explanation is in the concept of
emergence.
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---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---yours truly
will offer a more general broad definition
of emergence:
Yours truly's
broad definition
of emergence just given
is so general as to be almost a trivial observation.
Yours truly tends to think of
emergent theories as
Platonic ideals---see the 2 figures below.
Despite its lack of obvious use in developing theories,
yours truly thinks yours truly's
broad definition is a useful perspective.
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 of chess are NOT
dependent on physics
or the physical bodies that manifest the
game.
In particular, we don't really understand
the emergence of our intrinsic sense of
consciousness
out of physical reality.
See the figure below.
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 upshot is that in opinion of yours truly
the theory of everything (TOE)
is an emergent theory
like all the other important theories.
Even if one of the "howevers" was true,
yours truly would still like 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.
The 2nd law of thermodynamics
states that a
closed system of particles subject to random processes
increases in entropy (i.e, in
disorder) as time passes
until it reaches the maximum possible entropy
for the closed system.
Entropy is precise measure of messiness in
physicsy sense---the most concise formula for
entropy is simple enough---see the figure below.
The 2nd law of thermodynamics
is mnemonicked by the
aphorism:
The
2nd Law of Thermodynamics
expresses the tendency of things left to themselves to go to heck.
The 2nd law
is independent of
the theory of everything (TOE)
and is clearly an emergent principle
by the narrow definition
of emergence---it arises in
sufficiently complex physical systems.
We do have quantitative formulations of
2nd law
in physics---but we won't go in to that.
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.
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.
We discuss it in here in IAL 0 because it's a bit philosophical and doesn't 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).
Yours truly will just offer yours truly's view.
The A-principle is just a nonce word for something that probably has a real name that yours truly is unaware of. We illustrate the A-principle and its generalization by a Bayesian analysis formula in the figure below.
The anthropic principle
is an important special case of the A-principle.
The A-principle is a way of partially explaining something and sometimes predicting that something exists.
To explain the A-principle:
Say B is necessary for the existence of A.
In terms of the probability theory, the last statement could be given as the conditional probability of B given A is 1: P(B|A) = 1.
Now say A exists, then P(B|A) = 1 implies B exists.
In one sense---but NOT all senses---the existence of A, explains the existence of B. From the other point of view A would NOT have the possibility of existence unless B existed.
This 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 is the final cause of wings.
The A-principle can be more useful than just giving one kind of explanation of B. You may NOT know B exists initially. Then the A-principle analysis of A tells you that B exists and you could go and discover it empirically.
So the A-principle is a discovery tool NOT just an explanatory tool.
Bayes' theorem is really simple in principle.
Say that P(AB) is the joint probability of events A and B. Then "obviously", we get Bayes' theorem
where P(A) and P(B) are the probabilities, respectively, of A and B, P(A|B) is the conditional probability of A given B, and P(B|A) is the conditional probability of B given A.
If Bayes' theorem still looks incredible, just imagine pulling all the B's out of statistical population, then all the A's out of the statistical sub-population of B's, then then clearly P(AB) = P(A|B)P(B) and, mutatis mutandis, P(AB) = P(B|A)P(A).
Bayes' theorem is often written in the form
Bayes' theorem is an exact general probability result and applies beyond Bayesian analysis which we discuss below.
However, Bayes' theorem is usually thought of in the context of Bayesian analysis.
The A-principle is actually just a special case Bayesian probability: the case where P(B|A) = 1.
To explicate, from Bayes' theorem, we find
If you know or can estimate all the probabilities on the left-hand side of the equation, then you can calculate a value for P(B|A), the conditional probability of B given A.
Say you didn't know that B existed, but P(B|A) > 0 and A existed. You then know that B has a probability of existing and if P(B|A) is sufficiently high, it it might be worthwhile to find it empirically.
If P(A|[not B]) = 0 in the Bayesian probability formula above, then P(B|A) =1 and you have recover the A-principle---which result we expected from the discussion in the second-to-last subsection.
Bayesian analysis (AKA Bayesian probability theory Bayesian statistics Bayesian inference) is really qualitatively perfectly well understood and has been used by everyone including biota since forever.
All of life's experience allows you to estimate qualitatively the probabilities of events in a new upcoming experience.
These are your priors (i.e., prior probabilities).
After the new experience, you update your probability estimates. These are your posteriors (i.e., posterior probabilities) which become your priors for your next experience.
All of life goes on like this: updating priors to posteriors---with usually fair-to-middling success.
This procedure can be called qualitative "Bayesian analysis".
Qualitative "Bayesian analysis" is, in fact, approximately the scientific method.
Bayesian analysis makes quantitative qualitative "Bayesian analysis".
Bayesian analysis is a probability theory about knowledge of the things.
Bayesian analysis began with the discovery of Bayes' theorem by Thomas Bayes' (1701?--1761) and was greatly extend by others including Harold Jeffreys (1891--1989) (see figure below).
Why is Bayesian analysis
so important since circa
the later 20th century
after being mostly ignored since
the 18th century?
Well it's main use is when you have vast quantities of data and many competing theories that are hard to rank qualitatively. This is actually, the situation nowadays in many sciences: e.g., cosmology, particle physics, medicine, epidemiology and economics. It didn't used to be the situation when there were easier things to discover requiring simpler and fewer theories and much smaller data sets.
Bayesian analysis gives you a tool for ranking theories to some accuracy/precision, and so determine which are most worthy of further study.
In fact, you need huge computing power to use Bayesian analysis in many applications---but nowadays, we have vast computing power.
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.
How does one rank these cosmological models in order of likelihood?
Using Bayesian analysis.
As weird as it may seem, it is possible given data D to calculate the conditional probability of model M---i.e., P(M|D)---using Bayesian analysis.
So P(M|D) is implicitly a conditional probability given the everything we know about reality.
In fact, Bayesian analysis is what everyone has done forever qualitatively---"This will probably happen based on everything we know now." etc.
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.
When you're top dog, the underdogs are always nipping at your heels.
The anthropic principle seems to be of increasing importance in astronomy and physics.
Put as an aphorism, the anthropic principle states:
Possible A values roughly in order of increasing generality are:
The anthropic principle can be called an emergent principle since it should emerge in any imaginable inhabitable universe, I think.
Rather than give a general explication of the anthropic principle, we'll just consider some interesting examples of its use in the following subsections.
The existence of hydrogen (A of the A-principle) implies the strong nuclear force can't be much stronger than it is (B of the A-principle)).
The figure below explains why not.
More generally, it seems likely that
the fundamental physical constants
and the cosmological parameters of
Big Bang cosmology
are fine-tuned for life as we know it
(see Wikipedia: Fine-tuned universe).
The anthropic principle
explains this by saying, they have to be that way for us to be here to observe them.
But this is NOT a satisfying or complete explanation.
Three possible further explanations occur to folks:
That we exist is is just
coincidence of that absolute logic.
But this
explanation invites the question
"What is the explanation for the
intelligent creator?"
The multiverse
is usually thought of as eternal and infinite.
The physics
and cosmology of each
pocket universe
is set randomly by some truly fundamental fundamental
physics.
The observable universe
is embedded in a particular
pocket universe
which is "JUST RIGHT" for life as we know it.
The multiverse is, in fact,
a lottery and
in a lottery
there are always
lucky
winners---see
the figure below.
So many features of life,
humankind,
and human society just as it is
were determined randomly.
The winners may have thought it was all their own prowess.
The
dinosaurs
probably thought they were tough hombres---until that
asteroid did them in
(see Cretaceous-Tertiary (K-T) extinction event).
The
discovery of the
triple-alpha process
(see figure below)
shows the
anthropic principle is useful
as a discovery tool.
The story in
point form:
In other words, an
anthropic principle argument
argued for
the triple-alpha process---and
this was before the
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 lottery.
The great coincidence
is that the
angular diameters
Sun
and Moon
on the sky
are very nearly equal.
The two figures below expand on the
great coincidence
and briefly discuss
anthropic principle argument why it
might NOT be just a coincidence.
The foregoing in yours truly's
opinion shows that the
anthropic principle
is a useful scientific principle.
Given A being something
related to technologically advanced human society as we know it,
we can explain in a sense B if P(B|A) = 1 or P(B|A) close to 1.
The sense being that:
The anthropic principle
also sometimes allows you to infer the existence of B even if you didn't know that B existed before.
If you extend the
anthropic principle with
Bayesian analysis, then
you may be able to estimate the
conditional probability P(B|A)
and decide whether B is likely to exist and be worth looking for if you don't already know.
There are criticisms of the
anthropic principle
(Wikipedia: Anthropic principle: Criticisms),
but yours truly thinks those
are directed toward more extravagant claims for that than those discussed here.
Yours truly thinks
in terms of the multiverse,
but all the explanations are highly speculative and probably NOT
mutually exclusive.
Of course, inside the
observable universe taken
as a given and on Earth
itself, there were other
lotteries.
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 two figures below illustrative 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 following diagram is a bit of a preview of
cosmology which
we take up in IAL 30: Cosmology.
"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.
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 Solution 0.
The point in doing so is to understand how the
sciences are related.
Yours truly likes to organize them
as emerging in steps from the lowest level of
physics: i.e.,
from
theory of everything (TOE),
the most fundamental theory of
particle physics---which
we don't yet know.
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 everything is NOT
TOE.
Yours truly orders, very loosely speaking,
the sciences in the
hierarchy:
As one goes up yours truly's ordering, there is
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 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
"less physics"
when you get to psychology.
For example, just try
deriving the Oedipus complex
from physics alone---a very uncomfortable
proposition.
However, in the modern age,
biophysics
is playing a role
in neuroscience, and
thus in psychology.
Yours truly, as aforesaid, likes to think of
mathematics
as a big heap of emergent theories
which in fact underlies all the other
sciences---so
yours truly has put it at the bottom
of yours truly's
hierarchy.
One must add that like art,
mathematics
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.
As one goes up the hierarchy as given by yours truly,
historically there were fewer
emergent principles
that are mathematical in formulation.
But there is a tremendous effort to make
the non-mathematical
emergent principles
more precise, and thus more like mathematical formulations.
Another somewhat related way specifying the
hierarchy of the
sciences is illustrated
in the figure below.
In this figure,
the hierarchy
the length scales of the
universe
are mapped to
the hierarchy.
Again, one should take the word hierarchy loosely.
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.
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.
This is all just point of view.
In fact, historically,
the terms
astronomer
and mathematician
(and astrologer too)
were often regarded as near synonyms.
Advanced mathematics---advanced for
the time that is---found little use outside of astronomy---unlike
nowadays when advanced mathematics is used for
many things---and pure mathematicians---those
poor devils---have no need to apply their science at all.
It's particularly important to note that until
19th century, leading
mathematicians were also often
leading theoretical astronomers:
e.g., Ptolemy (c.100--c.170 CE),
(the greatest theoretical astronomers
of classical antiquity),
Omar Khayyam (1048--1123),
Isaac Newton (1642/3--1727),
Pierre-Simon Laplace (1749--1827),
and
Carl Friedrich Gauss (1777--1855).
See example leading
mathematicians
cum
leading theoretical astronomers
in the figures below.
It's only after circa 1800
that leading mathematicians
stopped often being leading
theoretical astronomers too.
The mathematicians
abandoned us.
How old is astronomy as an exact science?
Well there are moon-shaped cut marks on bone
tally sticks
in groupings of order 30 from as long ago as 36,000 BCE
(which is in the Paleolithic)
that seem to be counts of days during a
lunar month
(No-xxiv).
In many societies, the start of the
lunar month is the actual
observation of the first crescent even though that is obviously dependent on weather.
In ancient times, astronomy and
meteorology were NOT clearly
separated---both are about sky phenomena.
The Moon is
much farther away than clouds, but that is NOT obvious to naked-eye observation.
Certain evidence of prehistoric astronomy
is physically recorded/embodied in
prehistoric monuments.
Many ancient cultures all over the world constructed such astronomical
monuments.
The most famous is
Stonehenge.
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.
See the crude Stonehenge map and
Stonehenge videos below.
Note the
Stonehengers (AKA Neolithic Britons)
were NOT literate, and so couldn't
record their sky lore
any other way, but in monuments.
Stonehenge and other
monuments
from around the world were almost always NOT observatories.
They probably served multiple cultural functions and
recording sky lore was probably
a mnor function in most cases.
On the other hand, the
ancient Mesopotamians---Sumerians in
3rd millennium BCE
roughly speaking and
Babylonians
from roughly the early
2nd millennium BCE
until circa the 2nd century CE)---were
literate---"they wrote on clay"
(Edward Chiera (1885--1933))---and
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).
Buried in dry earth like that in
Tigris-Euphrates River area,
baked clay tablets last for thousands of years---a very
non-volatile memory medium.
But we don't really know how the
Sumerians and
Babylonians
conceived of the
universe outside of purely
mythological conceptions.
Maybe they thought the sky was a big dome over
Tigris-Euphrates River area
which was traversed daily by the
astronomical objects.
What the Sumerians thought
of the physical universe
is totally lost and
even the later Babylonians
didn't leave us much explication of
their Babylonian physical cosmology
(see Wikipedia:
Babylonian astronomy: Babylonian cosmology).
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.
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.
Below is very simplified diagram of the
Aristotelian cosmos
as understood in Renaissance Europe.
In the course of the
16th and
17th centuries---which is
the time of the Scientific Revolution---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 and
Newton videos below.
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 Solution 0.
There are several vague ways of organizing the
sciences in
a hierarchy.
mathematics,
TOE-Plus Definintion,
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,
pyschology).
Why
mathematics at the bottom?
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 brief historical introduction to
astronomy.
A more detailed historical account is given in
IAL 4: The History of Astronomy to Newton.
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.
The high mathematical demands of astronomy---predicting
eclipses, etc.---made it convenient in the olden days for
astronomers
and mathematicians
to be the same people.
The mean lunar month is 29.53059 days
(Cox-16).
Thus a lunar month counted from first crescent to
crescent could be 29 or 30 days or shorter or longer if
bad weather prevents one from seeing the actual first crescent.
So plausibly exact astronomy---in a very modest sense---goes
back tens of thousands of years.
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).
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.
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: