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\author{\href{http://arachnoid.com/administration}{Paul Lutus}\\
\href{http://arachnoid.com}{http://arachnoid.com}}
\title{No Theory, No Science}
\date{March 27, 2016 \linebreak \linebreak Most recent revision: \today}

\begin{document}

\maketitle

\begin{abstract}
\noindent\rule{.9\textwidth}{.1px}

The formal scientific standing of most technical fields isn't controversial -- biology is regarded as a science, astrology is regarded as a pseudoscience -- and scientific fields are defined by theories that have survived sincere efforts at falsification. But as to psychology, because of the field's ambiguous location on the spectrum of formal disciplines and because of recent controversies surrounding the linked issues of evidence and theory, there appears to be an attempt to, not move psychology toward science, but move science toward psychology. This article addresses these issues and, in an effort to clarify psychology's standing, presents and discusses a clear definition of science.

\noindent\rule{.9\textwidth}{.1px}
\end{abstract}

\tableofcontents
\listoffigures
\listoftables

\section{Definition of Science}

We start with a definition of science about which there is reasonable agreement. The question of what is and is not science is formally known as the \textit{demarcation problem}\endnote{\href{https://en.wikipedia.org/wiki/Demarcation_problem}{Demarcation problem} -- the problem of distinguishing science from non-science.}, and as time passes and more social issues come to rely on a scientific standing for credibility, the issue has become somewhat contentious.

\subsection{Required Properties}\label{required properties}

A search of online resources produces a brief but practical definition of science. A scientific theory must be:

\begin{enumerate}
\item empirical, meaning based on observations of nature\endnote{\href{https://en.wikipedia.org/wiki/Empirical_evidence}{Empirical evidence} -- evidence produced by observations of nature.}.
\item tentative, meaning always open to further investigation.
\item falsifiable, meaning capable of being proven false by contradicting observations of nature\endnote{\href{https://en.wikipedia.org/wiki/Falsifiability}{Falsifiability} -- the property of a scientific theory that it may be proven false by contradicting empirical evidence.}.
\item \label{null hyp}regarded as without merit until empirical evidence supports it (the \textit{null hypothesis}\endnote{\label{null hypothesis}\href{https://en.wikipedia.org/wiki/Null_hypothesis}{Null hypothesis} -- the default scientific position that there is no relationship between a cause and an effect until evidence supports it.}).
\end{enumerate}

Beyond the above points, an essential but less easily stated property of scientific theories is that they \textit{explain} one or more observations of nature, that is, they provide an intellectual framework for our observations, one able to predict observations not yet made. Here's an example -- if I say, ``the nighttime sky is filled with tiny points of light,'' I've offered a \textit{description}. But if I say, ``those points of light are actually distant thermonuclear furnaces like our sun,'' I have offered an \textit{explanation}, a \textit{theory}, one that can be tested and possibly falsified.

Another way to say this is that an observation \textit{quantifies}, but a theory \textit{synthesizes}, joins different observations in a unifying intellectual framework, a framework that may include the notion of first principles\endnote{\href{https://en.wikipedia.org/wiki/First_principle}{First principle} -- in science, an axiomatic paradigm that unites independent observations through a single proposition.}, which are axiomatic propositions that hold true across many seemingly unrelated observations.

\subsection{Sources}

The above points were to some extent derived from online resources, academic and legal. Here are some of them.

\subsubsection{Encyclopedia Britannica}

The online Encyclopedia Britannica entry for the term \textit{falsifiability}\endnote{\href{http://www.britannica.com/topic/criterion-of-falsifiability}{Criterion of falsifiability (Britannica)} -- a definition of falsifiability as it relates to science.} says that falsifiability is ``... a standard of evaluation of putatively scientific theories, according to which a theory is genuinely scientific only if it is possible in principle to establish that it is false.'' The article then offers counterexamples: ``According to [Karl] Popper[\endnote{\label{popper}\href{http://www.britannica.com/biography/Karl-Popper}{Karl Popper (Britannica)} -- philosopher of science.}], some disciplines that have claimed scientific validity — e.g., astrology, metaphysics, Marxism, and psychoanalysis —are not empirical sciences, because their subject matter cannot be falsified in this manner.''

\subsubsection{Wikipedia}

In its science article\endnote{\label{science}\href{https://en.wikipedia.org/wiki/Science}{Science (Wikipedia)} -- includes a concise definition of science.}, the online encyclopedia Wikipedia says, ``A scientific theory is empirical, and is always open to falsification if new evidence is presented.'' This description corresponds reasonably well with the science definition set out above.

\subsubsection{Legal Rulings}

As time passes, more social and legal issues cross paths with science, and legal rulings have become more reliant on scientific evidence, which requires that science have a clear definition. In an influential 1982 ruling\endnote{\href{http://en.wikipedia.org/wiki/McLean_v._Arkansas}{McLean v. Arkansas Board of Education} -- an influential legal ruling that relies on a definition of science.} whose purpose is to keep religious teachings out of public school science classes, a court defined science this way:

\begin{itemize}
\item It is guided by natural law;
\item It has to be explanatory by reference to natural law;
\item It is testable against the empirical world;
\item Its conclusions are tentative, i.e. are not necessarily the final word; and
\item It is falsifiable.
\end{itemize}

In my view the wording of the ruling could have been made less ambiguous. The last point -- falsifiability -- should have emphasized that this means falsifiable by means of contradicting empirical evidence. But as with the other definitions, this source shows essential agreement with the definition given at the top of this section.

A similar but more important ruling by the U.S. Supreme Court, now known as the \textit{Daubert} standard\textsuperscript{\ref{Daubert standard}}, changed the rules for scientific testimony in 1993. I cover this ruling in greater detail below, but \textit{Daubert} also defines science in a way consistent with the definition given above.

\subsubsection{Dictionaries}

For the benefit of students reading this article, I will explain why a dictionary is not a suitable resource for discovering the technical meaning of science, or for that matter, any technical term.

Contrary to common belief, a \textit{dictionary is not a list of word meanings}. A dictionary's purpose is not to define words correctly (i.e. \textit{prescribe}) but to report what people think words mean (i.e. \textit{describe}).

Evidence for a dictionary's true purpose can be shown by looking up the word ``literally'' -- a typical dictionary\endnote{\href{http://www.merriam-webster.com/dictionary/literally}{Literally (Merriam-Webster)} -- an example of an ambiguous word definition.} lists two meanings:

\begin{itemize}
\item ``in a literal sense or manner''
\item ``in effect,  virtually''
\end{itemize}

This dictionary definition means the word ``literally'' can be assumed to have its default meaning, and the opposite of that meaning as well. This makes a dictionary the wrong tool for finding a reliable definition of science or any other technical term.

\subsection{Skepticism and Authority}

Point (\ref{null hyp}) in the \nameref{required properties} list above summarizes an important property of scientific thinking, one that may be described as healthy skepticism toward ideas lacking empirical evidence. Formally described as the \textit{null hypothesis}\textsuperscript{\ref{null hypothesis}}, this precept is a litmus test for disciplined scientific thinking.

It is a corollary of the null hypothesis that evidence has the highest standing, and authority has no standing at all. This precept has deep roots in science, extending back in time at least to the founding days of the Royal Society\endnote{\href{https://en.wikipedia.org/wiki/Royal_Society}{Royal Society} -- the oldest scientific society still in existence.}, the oldest scientific society still in existence (dating to A.D. 1660), and whose motto is \textit{nullius in verba}\endnote{\label{nullius in verba}\href{https://en.wikipedia.org/wiki/Nullius_in_verba}{Nullius in verba} -- motto of the Royal Society.} or ``take no one's word for it.''

Science's skeptical posture toward authority poses a problem for the clinical practice of psychology, which requires a pseudo-medical authority to function, a topic to which we shall return.

\subsection{Science and Pseudoscience}

When people come to agreement on the meaning of science, the distinction between science and pseudoscience\endnote{\label{pseudoscience}\href{https://en.wikipedia.org/wiki/Pseudoscience}{Pseudoscience} -- a practice that superficially resembles science but that lacks one or more essential elements.} can be concisely expressed:

\subsubsection{Posture toward Evidence}

\begin{itemize}
\item A scientist assumes an idea has no merit until there is empirical evidence to support it\textsuperscript{\ref{null hypothesis}} and accepts personal responsibility for producing the evidence.
\item A pseudoscientist takes the opposite position -- he believes an idea is true until it's been proven false, accepts no responsibility for evidence, and requires others to produce the falsifying evidence.
\end{itemize}

The scientist's choices conform to the \nameref{required properties} of science put forth at the top of this section. The pseudoscientist's posture accurately reflects a number of modern practices that masquerade as science, and it often leads to a requirement for \textit{proof of a negative}, which in the general case is a logical error named \textit{argument from ignorance}\endnote{\href{https://en.wikipedia.org/wiki/Argument_from_ignorance}{Argument from ignorance} -- a logical error having to do with proof of a negative.}. An example may serve to reveal the error:

\begin{itemize}
\item To the claim ``Bigfoot exists,'' a scientist will assume the claim has no merit until empirical evidence supports it.
\item To the same claim, a pseudoscientist will assume the opposite -- that the claim is true until Bigfoot can be \textit{proven not to exist}.
\item But proving Bigfoot doesn't exist would require a search of the entire universe, an impossible burden of evidence, one aptly described in an analogy called Russell's Teapot\endnote{\href{https://en.wikipedia.org/wiki/Russell\%27s_teapot}{Russell's teapot} -- an analogy that reveals a logical error.}.
\end{itemize}

To summarize this point, to a scientist, Bigfoot's existence hinges solely on empirical evidence, while to a pseudoscientist, Bigfoot exists because it hasn't been proven not to exist. And because no one can possibly prove Bigfoot's nonexistence, the pseudoscientist is secure in his belief.

\subsubsection{Pseudodiseases}

If the pseudoscientist's outlook seems irrational, one that couldn't possibly be taken seriously, consider that psychologists accepted the existence of Asperger Syndrome\endnote{\href{https://en.wikipedia.org/wiki/Asperger_syndrome}{Asperger Syndrome} -- an autism spectrum condition, abandoned after its legitimacy was questioned.} without any evidence that it was real and distinct from other mental states, until the public cried foul and forced its abandonment\endnote{\href{http://www.nytimes.com/2009/11/03/health/03asperger.html?_r=0}{A Powerful Identity, a Vanishing Diagnosis} -- an account of the abandonment of Asperger Syndrome.}.

In an earlier episode, psychologists accepted the validity of Recovered Memory Therapy\endnote{\href{https://en.wikipedia.org/wiki/Recovered-memory_therapy}{Recovered Memory Therapy} -- a discredited therapy that claimed to be able to recover repressed memories of traumatic events, often of a sexual nature.} until the legal system, burdened with scores of nonsense sexual and other abuse claims, cried foul and changed the requirements for scientific testimony\footnote{But not for this reason alone -- the rules for scientific testimony were overdue for an upgrade.}.

\subsubsection{Scientific Testimony}

The practice of Recovered Memory Therapy, and the flood of bogus legal cases based on claims from this therapy, was one of the reasons the U.S. Supreme Court changed the rules for scientific testimony in 1993. In \textit{Daubert v. Merrell Dow Pharmaceuticals, Inc.}\endnote{\href{https://en.wikipedia.org/wiki/Daubert_v._Merrell_Dow_Pharmaceuticals,_Inc.}{Daubert v. Merrell Dow Pharmaceuticals, Inc.} -- an influential Supreme Court ruling that changes the standards for scientific testimony.}, the Court produced an influential ruling now known as the \textit{Daubert} standard\endnote{\label{Daubert standard}\href{https://en.wikipedia.org/wiki/Daubert_standard}{Daubert standard} -- a standard for scientific expert testimony.}. At risk of oversimplification, \textit{Daubert} says that scientific expert testimony must derive from scientific methodology, using a list of requirements that closely resembles the definition of science provided above, including the phrase ``Empirical testing: whether the theory or technique is falsifiable, refutable, and/or testable.''

The Court's ruling in \textit{Daubert} relies on, and quotes from, Karl Popper's\textsuperscript{\ref{popper}} book \textit{Conjectures and Refutations: The Growth of Scientific Knowledge}\endnote{Conjectures and Refutations: The Growth of Scientific Knowledge, Popper, (5th ed. 1989)}: ``the criterion of the scientific status of a theory is its falsifiability, or refutability, or testability.'' In an online excerpt\endnote{\href{http://worthylab.tamu.edu/Courses_files/Popper_ConjecturesandRefutations.pdf}{Science: Conjectures and Refutations
} -- an online excerpt from Karl Popper's book with a similar title.} from \textit{Conjectures}, Popper says about Marxism, psychoanalysis, and individual psychology, that they ``had in fact more in common with primitive myths than with science; that they resembled astrology rather than astronomy.''

It should be apparent that the \textit{Daubert} legal standard provides a basis for excluding psychological testimony on the ground that psychology fails \textit{Daubert}'s requirements for scientific substance.

\subsubsection{Pseudopatients}

Because the mind cannot be a source of empirical evidence, psychologists are forced into reliance on the self-reports of their clients. In the now-famous Rosenhan experiment\endnote{\href{https://en.wikipedia.org/wiki/Rosenhan_experiment}{Rosenhan experiment} -- a now-famous study in which researchers acquired psychological diagnoses without actually having the diagnosed conditions.}, researchers gained admission to a mental hospital by feigning symptoms of mental illness. Of eight pseudopatients including Rosenhan, all were promptly diagnosed with serious mental ailments and admitted to the facility for treatment. Then, on cue, the pseudopatients announced they were feeling much better and asked to be released. But as a condition of their release, all were forced to admit to having been mentally ill, and were required to take antipsychotic medications.

After publication of the results and subsequent controversy, an unplanned second phase of the study began -- an offended mental hospital administration challenged Rosenhan to send more pseudopatients to the facility to try to gain admission by faking symptoms. In the following weeks 193 new patients arrived at the hospital, and of that number, 41 were identified as faking their symptoms and refused admission. But in fact, Rosenhan had not sent any more pseudopatients to the mental hospital -- the rejected patients sincerely believed they were suffering from a mental illness.

The self-reporting problem reveals the difference between the mind and the brain. Imagine an actor, skilled in the dramatic arts and familiar with the symptoms of, say, Asperger Syndrome\textsuperscript{\ref{asperger syndrome}} or Post-Traumatic Stress Disorder\endnote{\href{https://en.wikipedia.org/wiki/Posttraumatic_stress_disorder}{Posttraumatic stress disorder} -- a mental disorder said to result from stressful life experiences.} -- can such an actor fake the symptoms of a \textit{mind} dysfunction and acquire a phony psychological diagnosis? Well, yes -- indeed it's been shown repeatedly, in many experiments like the above, and in police reports\endnote{\href{http://www.bbc.com/news/magazine-23063124}{Ian Brady: How easy is it to fake mental illness?} -- a notorious case in which a multiple murderer faked mental illness to avoid prison.}, that a person sufficiently motivated can play the system and acquire a mental diagnosis for research or personal gain.

Now let's compare the practice of psychology to the practice of medicine. Can the same actor fake the symptoms of a \textit{brain} dysfunction and acquire a phony medical diagnosis? Well, no, he can't, because physicians have objective laboratory criteria to detect brain dysfunctions -- empirical evidence that rises above opinion.

Let's summarize. A psychology pseudopatient can gain admission to a \textit{mental} hospital and receive pseudotherapy for a nonexistent \textit{mind} pseudodisease, but a medical patient cannot gain admission to a \textit{medical} hospital and receive therapy for a nonexistent \textit{brain} disease.  The reason is that psychological evidence is neither empirical nor objective -- it relies on statements made by people who may have any number of reasons for deceiving themselves, or others, or both. What conclusions can we draw from this? One, that \textit{the mind is not the brain} -- the mind is an idea, not an organ. And two, that psychologists and psychiatrists accept pseudopatients and dispense pseudodiagnoses because psychology is a pseudoscience\textsuperscript{\ref{pseudoscience}}.

The point of this section is not to say that all mental illnesses are phony -- it is to say that we have no objective way to find out. It's also not to claim that psychologists and psychiatrists don't help people. Many of these people are very skilled and helpful, but this results from their individual abilities, not because of psychology's standing as a science.

\subsubsection{Psychology Defined}

The online encyclopedia Wikipedia\endnote{\href{https://en.wikipedia.org}{Wikipedia} -- online encyclopedia} has a psychology section that sees frequent edits as social events unfold. At one time psychology was defined as ``the study of the mind and behavior,'' until someone pointed out that this made psychology seem less scientific than neuroscience\endnote{\label{neuroscience}\href{https://en.wikipedia.org/wiki/Neuroscience}{Neuroscience} -- the scientific study of the nervous system.}, defined as ``the scientific study of the nervous system.'' So, Wikipedia editing being a relatively open process, someone simply added the word ``scientific.'': ``The \textit{scientific} study of the mind and behavior.'' Much better.

But eventually someone, possessed of more than average insight, realized the new definition included a contradiction in terms -- how can study of the mind be scientific? The mind isn't accessible to empirical study, even for something so trivial as producing an empirically testable, falsifiable claim that the mind exists. How then can study of the mind be described as scientific?

It seems this outlook won over its critics, and the current Wikipedia definition of psychology\endnote{\href{https://en.wikipedia.org/wiki/Psychology}{Psychology} --  the study of behavior and mind.} has been changed to read, ``the study of behavior and mind.'' The definition goes on to say psychology ``... is an academic discipline and an applied science ...''.

I won't try to imagine the struggle over this definition that must have taken place behind the scenes, because applied science\endnote{\href{https://en.wikipedia.org/wiki/Applied_science}{Applied science} -- a discipline that applies scientific knowledge to practical problems.} isn't science\textsuperscript{\ref{science}}, it is the application of results acquired from a science, by people who don't necessarily understand the science they're applying.

The new definition of psychology as ``applied science'' represents an incremental step toward the truth, but as Louis Pasteur\endnote{\href{https://en.wikipedia.org/wiki/Louis_Pasteur}{Louis Pasteur} -- French chemist and microbiologist.} said, ``There are no such things as applied sciences, only applications of science.''\endnote{\href{https://en.wikiquote.org/wiki/Louis_Pasteur}{Wikiquote : Louis Pasteur} -- ``There are no such things as applied sciences, only applications of science.''} Pasteur took this position to object to things being defined as science solely on the ground that scientific methods are applied. Were this practice to be accepted, such fields as Astrology would become science on the ground that a person could use scientific methods to create unscientific results.

\section{Scientific Theories}

\subsection{Dictionary Definition}

A large chasm separates the public's understand of science, and science itself. The public view of science can be gauged by examining a dictionary's definition of science\footnote{For reasons given earlier, a dictionary records what people think words mean, not technically accurate definitions.}. The Merriam-Webster\endnote{\href{http://www.merriam-webster.com/}{Merriam-Webster} -- online dictionary.} online dictionary defines science this way\endnote{\href{http://www.merriam-webster.com/dictionary/science}{Merriam-Webster : Science} -- a dictionary definition of science.}:

\begin{itemize}
\item  knowledge about or study of the natural world based on facts learned through experiments and observation
\item a particular area of scientific study (such as biology, physics, or chemistry) : a particular branch of science
\item a subject that is formally studied in a college, university, etc.
\end{itemize}

At small risk of oversimplification, this defines science as knowledge, as facts. But science is not a \textit{product}, it is a \textit{process}, a discipline for arriving at testable theories about nature, and the most important part of the process is a sincere effort to prove theories false.

The end product of scientific activity is, not theories that have won a popularity contest, but theories that have survived repeated efforts at falsification and that remain open to similar efforts in the future.

\subsection{Mathematical Theories}

(Readers not interested in a technical description of science may prefer to skip forward to this section's \nameref{Science Summary} on page \pageref{Science Summary}.)

The highest quality science resides in theories expressed mathematically, for the reason that mathematics expresses theories, and suggests comparisons with nature, in a clear and unambiguous way. When comparing mathematical and other kinds of theories, the former's clarity of expression means:

\begin{enumerate}
\item Mathematical theories are more easily falsified by comparison with nature.
\item Because of point (1) above, mathematical theories are regarded as more reliable.
\item It's much easier to see connections and associations between mathematical theories than for theories lacking this property. Over time this may reveal connections between theories, and sometimes between fields, that either strengthens or falsifies the theories\footnote{Both outcomes are regarded as beneficial to science.}.
\end{enumerate}

Here's an example of point (3), showing connections between mathematically expressed theories:

\subsubsection{Kepler's Laws}

In 1609, Johannes Kepler\endnote{\href{https://en.wikipedia.org/wiki/Johannes_Kepler}{Johannes Kepler} -- early astronomer, responsible for eponymous laws of planetary motion.} published his laws of planetary motion\endnote{\href{https://en.wikipedia.org/wiki/Kepler\%27s_laws_of_planetary_motion}{Kepler's laws of planetary motion} -- an early mathematical description of planetary motion.}, which say that:

\begin{enumerate}
\item The orbit of a planet is an ellipse with the Sun at one of the two foci.
\item \label{equal areas}A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
\item The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.
\end{enumerate}

\subsubsection{Newton's Theory of Gravity}\label{newton gravity}

In 1687, Isaac Newton\endnote{\href{https://en.wikipedia.org/wiki/Isaac_Newton}{Isaac Newton} -- scientist and polymath.} created a theory of gravitation consistent with Kepler's Laws. At first Newton relied on Kepler's Laws for intuition about what form a gravitational theory might take, then, as his theory developed, he was able to test whether the result agreed both with Kepler's Laws and with what astronomers observed.

\subsubsection{Conservation of Energy}\label{conservation of energy}

In 1676, Gottfried Wilhelm Leibniz\endnote{\href{https://en.wikipedia.org/wiki/Gottfried_Wilhelm_Leibniz}{Gottfried Wilhelm Leibniz} -- scientist, mathematician, a contemporary of Isaac Newton.} created an early expression of the idea of conservation of energy\endnote{\label{conservation}\href{https://en.wikipedia.org/wiki/Conservation_of_energy}{Conservation of energy} -- the theory that energy is neither created nor destroyed, only changed in form.}, the idea that energy is neither created nor destroyed, only changed in form.

\subsubsection{Kinetic Energy}\label{kinetic energy}

First articulated by Liebniz and Johann Bernoulli\endnote{\href{https://en.wikipedia.org/wiki/Johann_Bernoulli}{Johann Bernoulli} -- scientist, mathematician, contemporary of Liebniz.}, kinetic energy\endnote{\label{kinetic endnote}\href{https://en.wikipedia.org/wiki/Kinetic_energy}{Kinetic energy} -- energy of motion.} is the energy a body possesses resulting from its motion. It is proportional to a body's mass times the square of its velocity. 

\subsubsection{Gravitational Potential Energy}\label{gravitational potential energy}

Gravitational potential energy\endnote{\label{potential energy}\href{https://en.wikipedia.org/wiki/Potential_energy\#General_formula}{Gravitational potential energy} -- the energy arising from position within a gravitational field.} is energy arising from an object's position in a gravitational field, and includes the idea that ascending within a gravitational field requires an expenditure of energy.

\subsubsection{Synthesis}

Above we list five apparently independent scientific theories, each expressed mathematically, each empirically falsifiable by comparison with nature. As it turns out, because of the clarity of expression granted by mathematics, the five theories can be tested \textit{and potentially falsified} at once by observing the motion of a body in an elliptical orbit:

% from /netbackup/data/python_projects/gravitation_elliptical_orbit_equal_area_computation/kepler_equal_area_orbit_generator.py

\begin{figure}[H]
\centering
\includegraphics[width=.4\textwidth]{graphics/elliptical_orbit_example.png}
\caption{Computer-modeled elliptical orbit}
\label{fig:Orbit}
\end{figure}


By observing the motion of orbiting bodies, astronomers subject mathematical theories about nature to a rigorous empirical test that could overthrow all of them. In an elliptical orbit (see Figure \ref{fig:Orbit}), the principle at work is that, as the orbiting body moves closer to the parent body, it loses gravitational potential energy (decreased distance) but gains kinetic energy (increased velocity). In order for the orbit to confirm \nameref{conservation of energy} (\ref{conservation of energy}), the two kinds of energy, potential and kinetic, \textit{must sum to a constant} everywhere in the orbit. As it happens, in computer models of elliptical orbits as well as in observations of nature, the results agree with theory to ten or more decimal places:

\begin{itemize}
\item Observed and modeled orbits agree with Kepler's Second (equal-area) law\textsuperscript{\ref{kepler second law}} to a high degree of precision (the shaded sections A-D in Figure \ref{fig:Orbit} all have equal areas).
\item The motion of bodies in elliptical orbits agree with \nameref{newton gravity} (\ref{newton gravity}, also see equation 
\ref{equation:NewtonianGravitation} in this article's appendices).
\item Bodies in elliptical orbits show energies consistent with theories of \nameref{kinetic energy} (\ref{kinetic energy}) and \nameref{gravitational potential energy} (\ref{gravitational potential energy}) at each point in their orbits.
\item The total energy of an orbiting body, the combination of kinetic and potential energies, sums to a constant, confirming \nameref{conservation of energy} (\ref{conservation of energy}). 
\end{itemize}

See the \nameref{app:Energy Conservation} appendix on page \pageref{app:Energy Conservation} for a more technical treatment of this subject.

\subsection{Summary}\label{Science Summary}

The above analysis shows how science is created. As in all worthwhile scientific analyses, it's entirely dependent on observations of nature, it's expressed mathematically, and it's falsifiable. If any part of the analysis fails, the entire analysis fails. If the analysis fails, the theory fails.

To emphasize this point, let me compare science to psychology.

In science:
\begin{addmargin}[2em]{0em}
\begin{itemize}
\item The process begins with observations of nature,
\item moves to the shaping of theory,
\item compares the theory to nature in new contexts to see if it remains valid,
\item and may end with the theory's application to practical problems.
\end{itemize}
\end{addmargin}

At each step in this process, the null hypothesis\textsuperscript{\ref{null hypothesis}} rules -- without supporting empirical evidence, a theory is assumed to have no merit.

In psychology, the order of events is reversed:

\begin{addmargin}[2em]{0em}
\begin{itemize}
\item Psychologists begin by applying an idea\footnote{We can't call them theories, that would be misleading.} to patients in clinical settings,
\item then compare the idea to other ideas,
\item then sample public and legal opinions,
\item then abandon the idea\footnote{Yes -- over time, all psychological ideas are abandoned (\ref{app:Psychological Pseudoscience}).}.
\end{itemize}
\end{addmargin}


At each step in this process, the null hypothesis is \textit{ignored} -- ideas are assumed to be valid to the degree that no one has yet proven them false. A historical list of psychological ideas, provided in the \nameref{app:Psychological Pseudoscience} appendix, shows this process clearly.

The irony of modern psychology is that psychologists insist that their activities pass muster as science, and their clients believe them.

\section{Recent Controversies in Psychology}

\subsection{Replicability}

It's been recognized for some time that the rate of successful \textit{replications}\endnote{\href{https://en.wikipedia.org/wiki/Reproducibility}{Reproducibility} -- the property of a scientific study that it can be repeated with the same outcome.} (efforts to reproduce a prior result) in psychology is very low, primarily because replications are rarely undertaken. There are many reasons for this -- psychology journals favor original work over re-examinations of prior work\endnote{\label{publication bias}\href{https://en.wikipedia.org/wiki/Publication_bias}{Publication bias} -- a bias in scientific publishing that favors original work over reexamination of prior results.}, psychologists expect more professional advancement from original work compared to reviews and reassessments of work performed by others\endnote{\href{https://en.wikipedia.org/wiki/Replication_crisis\#A_disciplinary_social_dilemma}{A Disciplinary Social Dilemma} -- a list of reasons why psychologists are reluctant to replicate the work of others.}, and psychologists have a generally negative view of replication efforts\endnote{\href{http://calteches.library.caltech.edu/51/2/CargoCult.htm}{Cargo Cult Science} -- a now-famous speech about pseudoscience given by Richard P. Feynman in 1974.}.

\subsubsection{Failed Replications}

About the replication issue, some psychologists move beyond indifference to hostility. In an article entitled ``On the evidentiary emptiness of failed replications''\endnote{\href{http://jasonmitchell.fas.harvard.edu/Papers/Mitchell_failed_science_2014.pdf}{On the evidentiary emptiness of failed replications} -- an article by Harvard psychology professor Jason P. Mitchell.}, Harvard psychology professor Jason P. Mitchell\endnote{\href{http://psychology.fas.harvard.edu/people/jason-p-mitchell}{Jason P. Mitchell} -- Harvard psychology professor.} says, ``Recent hand-wringing over failed replications in social psychology is largely pointless, because unsuccessful experiments have no meaningful scientific value ... the likeliest explanation for any failed replication will always be that the replicator bungled something along the way.'' It seems not to have occurred to Professor Mitchell that the original finding might also have resulted from someone bungling something along the way, and the scientific purpose of replication is to evaluate this possibility.

Professor Mitchell goes on to say, ``The field of social psychology can be improved, but not by the publication of
negative findings ... authors and editors of failed replications are publicly impugning the scientific integrity of their colleagues.'' But one purpose of science is to transcend feelings on a journey toward facts, and how we feel about the outcome must never be allowed to undermine the process.

It's my hope that the above represents a minority outlook. Among properly trained scientists it's recognized and accepted that successful study replications are essential to the scientific standing of a theory or a field\endnote{\href{https://en.wikipedia.org/wiki/Scientific\_method}{Scientific method} -- a summary of the process of science.}. This is the basis for the replication crisis\endnote{\href{https://en.wikipedia.org/wiki/Replication_crisis}{Replication crisis} -- a crisis of credibility surrounding study replications, either because they aren't conducted or the replication fails.} in psychology.

\subsubsection{Reproducibility Project}

In response to pressure to address the replication crisis, Brian Nosek and associates in the Reproducibility Project\endnote{\href{https://osf.io/ezcuj/}{Reproducibility Project: Psychology} -- a project meant to address psychology's low study replication rate.} carried out a large-scale study meant to test the replicability of 100 high-profile psychology studies published in three psychology journals.

In August 2015, the project published its conclusions\endnote{\label{reproducibility}\href{http://www.nature.com/news/over-half-of-psychology-studies-fail-reproducibility-test-1.18248}{Over half of psychology studies fail reproducibility test} -- a summary of the Replication Project's activities.}. The study found that, of the 100 studies, only 39\% could be replicated, and of the successful replications, the average effect size was half that of the original study.

In some ways the result of the study caused more controversy than the original observation (that psychological studies are rarely subjected to replication efforts), and some researchers have objected to the study's design and conclusions\endnote{\href{http://news.harvard.edu/gazette/story/2016/03/study-that-undercut-psych-research-got-it-wrong/}{Study that undercut psych research got it wrong} -- critics respond to the replication study.}, but without going so far as to suggest or perform their own replications.

\subsection{Ego Depletion Effect}

In a related controversy, a psychological effect called ``ego depletion''\endnote{\href{https://en.wikipedia.org/wiki/Ego_depletion}{Ego depletion} -- a popular psychological idea that appears to have been debunked.}, for some time a mainstay of much psychological research, publication and thinking, appears to have no reliable statistical basis. The authors of a debunking meta-analysis\endnote{\label{ego depletion}\href{http://www.psy.miami.edu/faculty/mmccullough/Papers/Carter_McCullough_EgoDepl_PubBias_Frontiers.pdf}{Publication bias and the limited strength model of
self-control} -- an apparent refutation of psychology's ``ego depletion'' idea.} summarize their conclusion by saying, ``... we found very strong signals of publication bias\textsuperscript{\ref{publication bias}}, along
with an indication that the depletion effect is actually no different from zero.''

\subsection{The Role of Theory}

It is the thesis of this article that low study replication rates, and widely held beliefs that have no reliable basis, result from a critical structural deficit in modern psychology -- an absence of defining, empirical theories. Instead of comparing experimental results to established theories, because there are no such theories available psychologists are reduced to comparing one experimental result to another experimental result, a task not unlike herding cats.

Psychology, in contrast to fields like physics, biology and others, has no empirical, testable, falsifiable theories to define the field, guide research efforts, and incrementally build on prior theoretical falsifications and confirmations. To put this another way, psychology doesn't \textit{explain} the human mind, it \textit{describes} it. It should be apparent that a field only able to describe, that cannot explain (i.e. propose falsifiable theories), doesn't meet science's definition\endnote{\href{https://en.wikipedia.org/wiki/Descriptive_science}{Descriptive science} -- a science in name only, one that can only describe and offers no falsifiable explanations.}.

In recent discussions with psychologists, I've been told that it's not so, that psychology does have theories, for example the Placebo Effect\endnote{\href{https://en.wikipedia.org/wiki/Placebo}{Placebo Effect} -- a phenomenon in which an agent with no known biological effect produces unexplained benefit.} and In-group Bias\endnote{\href{https://en.wikipedia.org/wiki/In-group_favoritism}{In-group favoritism} -- a bias in favor of the interests of one's own group.}, to name just two. But those ideas originated in fields other than psychology, they're observations, not theories (they have no explanations able to rise above the status of anecdote), and because they don't presume to explain observations, they're unfalsifiable.

The Placebo Effect is a perfect example of something that appears to be a theory but that fails one or more of a theory's requirements. There's universal agreement that the effect is real, but it's equally true that no one knows how or why the effect exists. Until the effect can be explained, and the explanation tested in a way that could lead to a falsification, \textit{and} a testable prediction made about an as-yet unobserved corollary, it's not a scientific theory. Also, the characterization of the effect originated in, and is most reliably confirmed through changes in, biology, not psychology.

\subsection{Summary}

These findings warrant much greater skepticism toward psychology's claims than exists at present. Based on the outcome of the reproducibility study\textsuperscript{\ref{reproducibility}}, the ego depletion meta-analysis\textsuperscript{\ref{ego depletion}} and related findings, those who read the professional psychological literature are cautioned that, statistically speaking, the probability is \textit{greater than even} that a given article's claims don't correspond to reality, and for the minority of articles having some connection with reality, the significance of the result is much less than claimed.

\section{Moving the Goal Posts}

\subsection{Postmodernism}

In my conversations with psychologists I frequently hear that science doesn't have a clear definition, that anything even superficially related to science qualifies as science, and/or that science is like art -- it's all in the eyes of the beholder. Not only are these claims not true, but they can lead to real social harm.

Apart from the social and political consequences of a slippery definition of science, to argue that something as basic as science cannot have a clear definition is to embrace \textit{deconstructive postmodernism}\endnote{\href{https://en.wikipedia.org/wiki/Deconstruction}{Deconstruction} -- the core of deconstructive postmodernism, the idea that there are no shared, objective truths, that everything is opinion.}, essentially the outlook that there are no shared, objective truths, that everything is a matter of opinion. With a little insight one can see the logical error implicit in the postmodernist position: it denies the existence of shared, objective truths, then tries to start a dialogue requiring what's just been denied.

Recent events have undermined the above debate. A number of legal precedents, including the U.S. Supreme Court ruling in \textit{Daubert}\textsuperscript{\ref{Daubert standard}} discussed above, define science in a way that's compelling on institutions and individuals who must pay attention to issues of law -- that is to say, all of us. According to these sources, psychology doesn't meet science's definition.

\subsection{Authority in Psychology}

For some time I've been hearing from psychologists that authority plays an important part in psychology. This obviously undermines the field's claims to a scientific standing (because science rejects authority\textsuperscript{\ref{nullius in verba}}), but it also reveals a practical problem for clinicians -- without some kind of authority, how can a psychologist meet the expectations of typical modern clients of psychological practice, many of whom simply want to be told what to do?

A medical doctor's diagnoses and proposed treatments have a persuasiveness resulting from the fact that modern medicine is based on science -- the doctor can appeal to reason instead of authority. But psychology isn't a medical field and isn't based on scientific results, which means a psychologist can only argue from a position of authority -- the old-fashioned, arbitrary kind of authority that lacks a rational basis. But as public understanding of science and evidence-based practice\endnote{\label{evidence-based practice}\href{https://en.wikipedia.org/wiki/Evidence-based_practice}{Evidence-based practice} -- a gradual shift toward clinical practice based on scientific results.} improves, psychology's authority is being gradually undermined.

One solution to this dilemma is for a student to acquire a medical degree and its scientific connections, then acquire a psychology degree and a knowledge base that psychology's clients actually care about. This successful strategy produces an individual called a \textit{psychiatrist}\endnote{\href{https://en.wikipedia.org/wiki/Psychiatrist}{Psychiatrist} -- a psychologist with a medical degree.}, a profession invented to lend scientific substance (medicine) to an unscientific enterprise (psychology). (Another advantage is that psychiatrists can write drug prescriptions, a lucrative practice that often becomes the primary activity.) Second only to the invention of Asperger Syndrome\textsuperscript{\ref{asperger syndrome}}, psychology's invention of the psychiatrist has been the most successful strategy yet to acquire unearned public approval.

\subsection{Neuroscience}

But there's a basis for optimism, for change. The biggest future threat to the imagined authority of psychology is neuroscience\textsuperscript{\ref{neuroscience}}. Neuroscience will eventually mature to the point where it can offer real diagnoses -- and some treatments -- for what psychologists claim to be mental illnesses. During that process, today's ``mental illness'' category will narrow, and eventually disappear entirely, along with mind studies as a serious pursuit.

Because of the existence and rapid growth of neuroscience, because of an increased respect for the scientific method and evidence-based practice\textsuperscript{\ref{evidence-based practice}}, because of a gradual awakening to the fact that ``mental'' illnesses are either fantasies or physical illnesses with mental symptoms, the end of the historical trend described here will be an \textit{abandonment of mind studies}.

In the closing remarks of a recent ``NOVA Science Now'' episode entitled ``How Does the Brain Work''\endnote{\href{http://www.youtube.com/watch?v=qnwyEDiiNpc&t=51m07s}{NOVA Science Now : ``How does the Brain Work?'', Neil DeGrasse Tyson (51:07 to 51:45)}}, astrophysicist and science popularizer Neil DeGrasse Tyson compared psychology to alchemy, saying, ``Our best hope today lies with the neuroscientists. What are thoughts but electrical impulses among brain cells? What are ideas but novel firings of those cells? What are mental problems if not impulses that have misfired? In the way that chemistry arose from the ashes of alchemy, neuroscience, a field still in its infancy, may one day subsume psychology, laying bare our inner universe, which has remained hidden for so long.''

\subsection{Gender Shift}

In 1970, women acquired 20\% of psychology degrees, but in 2005, women acquired 72\% of those degrees\endnote{\href{http://www.apa.org/monitor/jun07/changing.aspx}{The changing gender composition of psychology} -- over time, more women are entering the profession.}. During the same period, income from, and employment opportunities in, psychology declined compared to other fields, as a result of which psychology degree holders now have the highest unemployment rate of any degreed profession\endnote{\href{http://www.cbsnews.com/news/25-college-majors-with-the-highest-unemployment-rates/}{25 college majors with the highest unemployment rates} -- clinical psychologists top the list at 19.5\% unemployment.} -- in fact, in recent years the unemployment rate among clinical psychologists has been more than twice that of the population as a whole.

I have a prediction about psychology -- we're already seeing employment opportunities disappear at an astonishing rate, but this is just the beginning. Today, psychology employment is evaporating. Tomorrow, \textit{psychology will evaporate}\footnote{But psychology won't disappear. Instead it will have the status of astrology -- a harmless diversion for weak-minded people.}. It will be replaced by neuroscience.

But I have a higher purpose than alerting students to the fact that they're entering the wrong field (true, but never mind). When I examine the historical gender-shift statistics quoted above, I despair the flight of women from STEM\footnote{Science, Technology, Engineering, and Mathematics.} professions\endnote{\href{https://en.wikipedia.org/wiki/Science,_Technology,_Engineering,_and_Mathematics}{Science, Technology, Engineering, and Mathematics (STEM)} -- professions with high present and future potential.}, where they belong and where humanity's future lies.

In furtherance of the goal of getting more women out of the dead-end field of psychology and into STEM professions, I offer this advice:

\begin{itemize}
\item When you hear people identify psychology as a profession women are designed for, ask yourself whether you're the kind of woman designed to swallow that kind of argument.
\item When you hear someone tell you, face to face, that a field of study is too difficult for you, ask yourself if that same advice would be offered to a man in the same circumstances.
\item Learning science/technology/engineering/mathematics may be hard, but throwing your life away is harder.
\item Someday in the next 50 years, a brave soul is going to step out of a spacecraft onto the surface of Mars and start preparing that planet for human habitation\endnote{\href{http://arachnoid.com/restoring_mars}{Restoring Mars} -- a strategy to prepare Mars for human habitation.}. Would you like to play a large or small part in getting her there, or would you prefer to be an unemployed psychologist?
\end{itemize}

\section{Appendices}

\subsection{Psychological Pseudoscience}
\label{app:Psychological Pseudoscience}

Because psychologists cannot shape and test unifying empirical theories about the mind, this allows them to invent imaginary diseases and offer imaginary cures. Here are a few examples psychologists have dreamt up over the years, based on popular sentiment, prejudice, and social fads.

\vspace{\baselineskip}
\input{/netbackup/data/latex_related/pseudoscience_list/pseudoscience_list.tex}
\vspace{\baselineskip}

Some notes for the above list:

\begin{itemize}
\item It's hardly comprehensive -- it only shows a few highlights in the history of modern psychology.
\item As with all psychological ideas, each of them has been abandoned.
\item On reviewing the list, with a little insight one can see it represents an evolutionary process, of learning by experience, and each new imaginary ailment shows more sophistication in appealing to public taste and prejudice.
\item To date, by far the most successful imaginary ailment has been Asperger Syndrome, for these reasons:
\vspace{\baselineskip}
\begin{itemize}
\item It exploits a superficial association with an objectively real organic ailment with genetic roots (Autism\endnote{\href{http://en.wikipedia.org/wiki/Autism}{Autism} -- an organic condition with genetic roots that psychology has attempted to treat.}), that, because of its biological origins, lies outside psychology's purview.
\item Its diagnostic indicators are close enough to the normal behavior of intelligent people that the latter are assured of receiving the diagnosis if they want it (in a practice called ``pathologizing normal behavior'').
\item In a stroke of public relations genius, psychologists ``diagnosed'' a number of famous people, living and dead, with Asperger's, including Isaac Newton, Thomas Jefferson, Albert Einstein and Bill Gates. This has had the effect of making a mental illness diagnosis seem appealing, desirable, even a status symbol, for the first time.
\end{itemize}
\end{itemize}


Asperger's was as wildly successful as Recovered Memory Therapy was wildly unsuccessful, but Asperger's finally became a victim of its own success. So many people clamored to be allowed into the exclusive Aspie\footnote{Aspie: one who has acquired an Asperger's diagnosis.} club that even psychologists realized they had given birth to a monster. So to prevent further damage to psychology, they removed Asperger's from the DSM\endnote{\href{http://en.wikipedia.org/wiki/Diagnostic_and_Statistical_Manual_of_Mental_Disorders}{Diagnostic and Statistical Manual of Mental Disorders} -- a key volume sometimes called psychology's bible.}, psychology's ``bible'', only to discover that, like an undead zombie, Asperger's has taken on a life of its own.

In a perhaps unintended irony, those responsible for removing Asperger's from the diagnostic guide explained their decision by saying, ``It's not an evidence-based term\textsuperscript{\ref{vanishing diagnosis}},'' overlooking the fact that none of the DSM diagnoses are evidence-based (all rely on lists of symptoms, none rely on a knowledge of causes, i.e. science).

When reviewing psychology's history and the connection between wealth, power and what society chooses to describe as mental illness, it becomes clear that to predict the outcome of a mental health controversy one need only ask, ``Who pays the psychologists?''

\subsection{Energy Conservation}
\label{app:Energy Conservation}

The principle of energy conservation\textsuperscript{\ref{conservation}} states that energy cannot be created or destroyed, only changed in form. As it happens, with respect to an orbiting body four independent physical theories, each expressed mathematically, support a fifth theory (energy conservation), and in principle could falsify it.

\vspace{\baselineskip}

The first theory to be tested is known as Kepler's Second Law\endnote{\label{kepler second law}\href{https://en.wikipedia.org/wiki/Kepler\%27s_laws_of_planetary_motion\#Second_law}{Kepler's Second Law} -- ``A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.''}: ``A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.''

The second theory is that of gravity, which (at relatively low velocities) has this mathematical expression\endnote{\href{http://en.wikipedia.org/wiki/Gravitation\#Newton.27s_theory_of_gravitation}{Newton's theory of gravitation} -- a pre-relativistic gravitational theory.}:

\begin{equation}
\label{equation:NewtonianGravitation}
f = \frac{G m_1 m_2}{r^2}
\end{equation}

\vspace{\baselineskip}
\begin{tabular}{ll}
$f$ & Force, Newtons. \\
$G$ & The universal gravitational constant\endnote{\href{http://en.wikipedia.org/wiki/Gravitational_constant}{Gravitational constant} -- a fundamental parameter in modern physics.}, colloquially known as ``Big G''. \\
$m_1$ & Mass of body 1, kilograms. \\
$m_2$ & Mass of body 2, kilograms. \\
$r$ & Distance between $m_1$ and $m_2$, meters.
\end{tabular}
\vspace{\baselineskip}

When expressed as a time-dependent differential equation\endnote{\href{http://en.wikipedia.org/wiki/Differential_equation}{Differential equation} -- an equation that includes Calculus derivative terms.}, the physics behind equation \ref{equation:NewtonianGravitation} causes an orbiting body to describe an elliptical orbit (Figure \ref{fig:Orbit} on page \pageref{fig:Orbit}), one easily confirmed by empirical observation.

With respect to such an elliptical orbit and barring frictional losses, the principle of energy conservation requires that two kinds of energy, gravitational potential energy (theory three) and kinetic energy (theory four), should sum to a constant.

\vspace{\baselineskip}

The third theory, gravitational potential energy $E_p$, has this expression:

\begin{equation}
E_p = \frac{-G m_1 m_2}{r}
\end{equation}

With this additional term:

\vspace{\baselineskip}
\begin{tabular}{ll}
$E_p$ & Gravitational potential energy, Joules. \\
\end{tabular}
\vspace{\baselineskip}

The fourth theory, kinetic energy $E_k$, has this expression:

\begin{equation}
E_k = \frac{1}{2} m v^2
\end{equation}

Where:

\vspace{\baselineskip}
\begin{tabular}{ll}
$E_k$ & Kinetic energy, Joules. \\
$m$ & Mass of moving body, kilograms. \\
$v$ & Velocity of moving body, meters per second. \\
\end{tabular}
\vspace{\baselineskip}

The combined equation for total orbital energy $E_t$ is:

\begin{equation}
\label{CombinedEnergy}
E_t = E_k + E_p = \frac{1}{2} m v^2 + \frac{-G m_1 m_2}{r}
\end{equation}

The meaning of equation \ref{CombinedEnergy} for the present topic is that Kepler's Second Law, gravity, gravitational potential energy ($E_p$) and kinetic energy ($E_k$) represent four independent theories with excellent observational evidence, but when they're evaluated together, they confirm a fifth theory, conservation of energy ($E_t$). The reasoning that leads to this theoretical unification is only possible because the theories are expressed mathematically.

\subsubsection{Computer Model}

A computer-based orbital model was created to draw Figure \ref{fig:Orbit} on page \pageref{fig:Orbit} and to provide the numerical results shown in Table \ref{table:Kinetic and Potential Orbital Energies}. The model's results agree with theory within the accuracy limitations of computer floating-point processing.

% from /netbackup/data/python_projects/kepler_orbit_equal_area_computation/kepler_equal_area_orbit_generator.py

\begin{table}[ht]
\centering
\begin{tabular}{ |c|c|c|c|c| }
\hline
\rowcolor{LightGray}
Orbital Segment & Kinetic energy ($E_k$) & Potential energy ($E_p$) & Total energy ($E_t$) & Area m$^2$ \\ \hline
A & \num{2.186810407e+08} & \num{-9.143857387e+08} & \num{-6.957046980e+08} & \num{1.340966475e+21} \\ \hline
B & \num{4.778249536e+08} & \num{-1.173529652e+09} & \num{-6.957046980e+08} & \num{1.340966475e+21} \\ \hline
C & \num{1.721929414e+09} & \num{-2.417634112e+09} & \num{-6.957046980e+08} & \num{1.340966475e+21} \\ \hline
D & \num{2.144985881e+09} & \num{-2.840690579e+09} & \num{-6.957046980e+08} & \num{1.340966475e+21} \\ \hline
\end{tabular}
\caption{Kinetic and Potential Orbital Energies}
\label{table:Kinetic and Potential Orbital Energies}
\end{table}

The fourth column in Table \ref{table:Kinetic and Potential Orbital Energies}, labeled ``Area m$^2$'', confirms Kepler's empirical ``equal-area'' law. The third column, labeled ``Total energy ($E_t$)'', is the sum of potential and kinetic energies and confirms the modern energy conservation theory.

\ParDivider

This example demonstrates the power of mathematics to show a relationship between apparently unrelated scientific theories. As explained above, Kepler's Second Law, the theories of gravity, potential energy, kinetic energy, and conservation of energy can all be stated separately, but because of their mathematical expression, as shown in Table \ref{table:Kinetic and Potential Orbital Energies} the first four theories validate the fifth in a clear and objective way.

This is a model for science. The five theoretical claims are expressed using mathematical equations, easily compared to nature, quantitative, predictive, falsifiable, and mutually supporting. Only perfect theoretical consistency, and perpetual agreement with observation, allows the structure to remain standing. To a scientist, this counts as a strength.

\theendnotes
\end{document}