IAL 0: A Philosophical and Historical Introduction to Astronomy

Don't Panic


  1. Caveat Emptor
  2. Science in General
  3. Systems
  4. Physics
  5. Emergence: Some Subsections Are Reading Only
  6. Bayesian Analysis
  7. The Anthropic Principle: Reading Only
  8. The Branches of Physics: Reading Only
  9. The Hierarchy of Sciences: Reading Only
  10. Astronomy

  1. Caveat Emptor

  2. 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.

    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).

    In any case, it's traditional to begin the study of
    astronomy in Carl-Sagan mode.

  3. Science in General

  4. What is it?

    1. Definition of Science:

      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).

      So offering a single short
      definition of science is always inadequate.

      But how about: Science:

        The study of objective reality. OBJECTIVE meaning independent of the particular observers or general to all observers.

        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:

          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.

    2. The Scientific Method:

      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).

      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.

      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.

      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.

      Science is thus PROGRESSIVE-TO-A-SINGLE-OBJECTIVE-GAOL in that it approaches an objective goal---the exact knowledge of objective reality.

    3. Not All Things are Science:

      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).

  5. Systems

  6. 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.

    Context decides on which "system" is meant---as usual.

    1. System and Physical System:

      System and its special case physical system are explicated in the figure below (local link / general link: system_environment.html).

    2. Hierarchies of Systems:

      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.

      We discuss emergence in section Emergence below.

  7. Physics

  8. 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.


    Physics, in brief, is the science of matter and motion.

    For motion illustrated, see the figure below (local link / general link: muybridge_horse.html).

    We can expand a bit on

    1. Dividing Physics in Two:

      One way of dividing physics is into two broad fields: fundamental physics and applied physics:

      1. Fundamental 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.

          Note that the term "fundamental" is used in somewhat different ways in physics that context elucidates. We can give examples:

          1. "Fundamental" can mean very general laws or results. This definition seems most generally useful to yours truly. This meaning allows things to be more or less fundamental.
          2. "Fundamental" can mean the general laws of a particular paradigm (i.e., general theoretical framework). For example, within the paradigm of classical mechanics, Newton's laws of motion plus the classical force laws are fundamental.
          3. "Fundamental" can mean "just so" or "CANNOT be explained by anything else".
          4. "Fundamental" can be used to describe the most general theories we now have.
          5. "Fundamental" can be used in historical discussion to describe the most general theories we had once.
          6. "Fundamental" can be used to mean the absolutely true minimum set of physical laws that encompasses all the branches of physics and that we do NOT yet possess.

        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.

      2. Applied Physics:

        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).

      3. Fundamental and Applied Physics:

        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:

        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 facilities---this certainly true in astronomy as illustrated in the figure below (local link / general link: vlt_laser.html).

    2. The Theory of Everything:

      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).

      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.

      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).

    3. TOE-Plus Definintion:

      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.

    4. Do We Have TOE-Plus Now?

      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:

      1. General Relativity and Quantum Mechanics Inconsistent:

        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.

        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.

        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.

      2. Dark Matter and Dark Energy Unknown:

        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.

        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.

        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.

      And there are other reasons for why we know we don't yet 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.

  9. Emergence: Some Subsections Are Reading Only:

  10. 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).

    1. An Aphorism that Makes Emergence Intelligible:

      Before trying to define emergence, it useful to say that emergence makes intelligible a very well understood fact:

      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.

      So to a degree, everyone understands emergence even if they don't know the name.

    2. Defining Emergence:

      One narrow definition from Wikipedia:

        "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:

        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.

      Emerging from the broad definition, there are two kinds of emergent theories:

      1. Kind 1: Those that do NOT follow from a derivation from some underlying emergent theory and must discovered independently, usually by the scientific method. But they emerge from reality---meaning reality in a broad sense.
      2. Kind 2: Those that follow from a derivation from some underlying emergent theory mathematically or, at least, logically.

      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).

      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.

      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:

      1. If an emergent theory is of the Kind 1, you have all the fun of the scientific method: the cycle of theorizing and experimentation and/or detailed observation. In fact, you often rely on already known emergent theories to guide you. The discovery of the theory of relativity by Albert Einstein (1879--1955) was guided by Newtonian physics and classical electromagnetism, but the theory of relativity CANNOT be derived from them. So, in fact, you need both inductive reasoning (resulting probably in true conclusions based on data) and deductive reasoning (resulting in true conclusions based on true axioms).
      2. If an emergent theory is of the Kind 2, then one can grind it out by derivation from an underlying emergent theory. OK, maybe this isn't so fun.

      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.

      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.

    3. All of Mathematics: Reading Only:

      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.

    4. Chess: a Trivial Example of Emergence: Reading Only:

      A trivial, artificial example of an emergent theory is chess---illustrated in the figure below (local link / general link: chess_animation.html).

      The RULES and STRATEGY of
      chess are NOT dependent on physics or the physical bodies that manifest the game.

      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.

    5. The Scientific Method as an Emergent Theory: Reading Only:

      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.

    6. Psychology and Emergence: Reading Only:

      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).

      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).

      But in the opinion of many, we probably will someday, maybe even relatively soon.

      Why do we say an
      emergent theory governs psychology, NOT just physics, chemistry, etc.

      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.

    7. Evolution as an Emergent Theory:

      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.

      evolution is known to work in contexts other than life as we know it.

      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).

    8. The Theory of Everything (TOE) as an Emergent Theory: Reading Only:

      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:

      1. TOE (and NOT in our shorthand TOE-Plus) is NOT the base of all fundamental physics. It's really just the base of all fundamental particle physics.

        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.

      2. Many emergent theories applying to physical reality emerge from random events in natural history or human history and prehistory, and so CANNOT be derived just from TOE.

        Those emergent theories still exist as Platonic ideals even if their application our reality required random events.

      3. As mentioned above, there may be other realms of reality beyond the observable universe with different fundamental physics than ours. In which case, TOE would obviously be an emergent theory in realm of reality. However:

        1. It may be that TOE is the only fundamental particle physics, but we don't know that.
        2. It may be the TOE can be shown to be the only fundamental particle physics by logical necessity, but we don't know that.
        3. It may be that TOE is the only fundamental particle physics, that permits complex physical reality, but we don't know that.

      4. Even theories which can arguably be derived completely from TOE, like Newtonian physics (AKA classical mechanics), are:

        1. Discoverable without knowing TOE, and so are independent in that sense of TOE.
        2. Actually require accidents of natural history. Newtonian physics, for example requires a realm of reality big enough to have macroscopic parts.
        3. Still exist as Platonic ideals.

    9. The 2nd Law of Thermodynamics as an Emergent Theory:

      The 2nd law of thermodynamics is universally acknowledged law of physics:

      1. 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.

        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).

      2. The 2nd law of thermodynamics is mnemonicked by the aphorism:

      3. The 2nd law of thermodynamics 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 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).

      4. By the by, 1st law of thermodynamics is just the conservation of energy principle in the context of thermodynamics.

      5. Now 2nd law of thermodynamics is quantitatively formulated for the microscopic scale (i.e., the atoms and molecules and below)---but we won't go in to that. But note that we can track the emergence of 2nd law back to the interactions of particles.

        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).

      6. An example of the 2nd law of thermodynamics in action is in the free expansion of a gas as illustrated in the figure below (local link / general link: free_expansion.html).

      7. 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.

    10. Emergence is Everywhere:

      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.

    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.

  11. Bayesian Analysis

  12. Bayesian analysis is that probability theory dealing with the truth of theories and it has a big vogue these days.

    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.

    Why discuss Bayesian analysis?

    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.

    1. Bayes' Theorem, the Root of Bayesian Analysis (Reading only):

      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:

      1. P(A|B): the probabilty of event A given event B. In frequentist terms, P(A|B) = N_(AB)/N_(B): number of AB events divided by number of B events taken to the limit of infinite trials.

      2. P(B|A): the probabilty of event B given event A. In frequentist terms, P(B|A) = N_(AB)/N_(A): number of AB events divided by number of A events taken to the limit of infinite trials.

        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.

      So, for example, if you know P(B|A), P(A), and P(B), you know P(A|B).

    2. Truth of Theories:

      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).

      Leaving aside the complications of partially true
      theories, theories are true or NOT in an absolute sense.

      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.

    3. Bayesian Analysis and the Scientific Method:

      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.

    4. History of 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).

      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.

      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.

    5. Bayesian Analysis and Cosmology:

      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).

  13. The Anthropic Principle: Reading Only

  14. 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.

    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:

    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.

    1. The Basic Idea of the Anthropic principle:

      A conditional probability is

            P(A|B) = probability of A given B.

      Now say A exists and we have

            P(A|[not B]) = 0.

      Then B must exist.

      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:

      1. Technologically advanced intelligent extraterrestrial life / Technologically advanced human society as we know it or in any possible formulation.
      2. intelligent extraterrestrial life / human life.
      3. life as we know it.
      4. life.
      5. liquid water.
      6. water.
      7. carbon.
      8. hydrogen.

      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).

    2. The Anthropic Principle Redux:

      In the subsection below, we give an example of the application of the anthropic principle.

      There were more examples once, but enough is enough.

    3. Anthropic Principle Example: The Triple-Alpha Process:

      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:

      1. Life as we know it requires carbon.

      2. Carbon is the only atom out of the whole periodic table (see figure below: local link / general link: periodic_table.html that permits complex molecules (i.e., organic molecules) needed for that complex structure life as we know it.

      3. Since carbon exists in the universe, there must be some way to make it in universe that began with the Big Bang---which did NOT make any carbon---or in the steady state universe which posited only a steady creation of hydrogen.

        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.

      4. But nuclear physics circa 1950 knew of NO process to make abundant carbon in stars where most elements were thought to be synthesized.

      5. Fred Hoyle (1915--2001) in 1952 hypothesized that a process with special properties, now called the triple-alpha process (see figure below: local link / general link: triple_alpha_process.html), had to exist since abundant carbon exists and we exist (see Wikipedia: Triple-alpha process: Discovery).

        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).

      6. The triple-alpha process was soon discovered soon thereafter experimentally.

      7. So the anthropic principle allowed us to discover something we didn't know existed before---the triple-alpha process.

      8. Note that we imply the existence of carbon, but carbon doesn't imply the existence of us.

      9. All kinds of life could exist in a universe with carbon.

      10. Many of our peculiarities are must be the result of chance.

        The properties of the winners of a lottery are quasi-unique due to random peculiarities, but there are always winners of a lottery.

      11. The anthropic principle can used to infer the causes or the probable causes of properties of us that are NOT just due to random chance.

    4. The Anthropic Principle: Is it a Useful Scientific Principle?

      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:

      1. You couldn't have B without having A.
      2. There may have been a lottery with many tickets and A had to turn up to allow some lucky winners who happen to include us (i.e., B).

      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.

  15. The Branches of Physics

  16. In modern physics, there are several important branches in which different branch theories hold.

    1. The Branches of Physics:

      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.

      Exact trueness only holds in ideal limits that in many (all?) cases can never be exactly reached.

      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.

    2. Astronomy: Both Applied and Fundamental Physics:

      Where does astronomy fit in to physics.

      Nowadays almost everyone agrees that astronomy should be classified as a field of physics.

        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.

      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.

      Astronomy is applied physics.

      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.

  17. The Hierarchy of Sciences: Reading Only

  18. 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).

    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?

    1. Why mathematics at the bottom? 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.

      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.

        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.

    2. Why what is above mathematics? Above mathematics, yours truly has put TOE-Plus, since the most fundamental laws of physics do control the physical stuff that makes up everything else that is physical and NOT just a Platonic ideal.

      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.

    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.

    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.

  19. Astronomy

  20. 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.

    1. What is Astronomy?

      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.

    2. Astronomers and Mathematicians:

      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.

      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.

      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 of the 17th century, 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.

      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.

      After 1800, there was a bit of a parting of the ways, and only a fraction of mathematicians remained astronomers.

      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).

      After circa 1800, leading mathematicians stopped often being leading theoretical astronomers. The mathematicians abandoned us.

    3. Astronomy: The Oldest Empirical Exact Science:

      Astronomy is often cited as the oldest, empirical exact science---empirical meaning based on observation---exact meaning using quantitative measurements.

      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.

    4. How Old is Astronomy as an Exact Science?

      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).

      Definite evidence of prehistoric
      astronomy is physically recorded/embodied in prehistoric astronomical monuments.

      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).

      The embodied
      astronomy is all pretty simple alignment astronomy, in fact.

      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).

    5. Literate Astronomy:

      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).

      The calculations were to make predictions of astronomical phenomena which is something
      astronomers are still tasked with doing.

      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).

    6. Ancient Greek Astronomy:

      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).

      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.

      See the cartoon of Aristotelian cosmology in the figure below (local link / general link: aristotle_cosmos.html).

      Aristotelian cosmology did have competitors in Classical Antiquity and later.

      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.

        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).

    7. Astronomy During the Scientific Revolution:

      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 below (local link / general link: newton_apple.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.

      The unification of terrestrial and celestial physics finally made astronomy somewhat experimental.

      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.