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In philosophy, a '''model-dependent reality''' refers to a ''model'' or ''picture'' consisting of the combination of any set of observations accompanied by theoretical concepts that explain and connect those observations. There is no requirement that the theory be unique, or even that the data encompasses observations in every field. Data described equally well by different theories constitute different models, which all have equal claim to be valid. The universe of all observations possibly may be covered by a ''network'' of overlapping models and, where overlap occurs; multiple, equally valid, model-dependent realities exist.
{{Image|Signal envelopes.png|right|150px|Top and bottom envelope functions for a modulated sine wave.}}
 
In [[physics]] and [[engineering]] the '''envelope''' of a rapidly varying signal is a smooth curve outlining its extremes in amplitude.<ref name=Johnson/> The figure illustrates a sine wave varying between an upper and a lower envelope.
==Outline==
Recently the connection between theory and observations has been explored by physicists Stephen W. Hawking and Leonard Mlodinow in their book: ''The Grand Design'', where they propose the notion of a model-dependent reality.<ref name=hawkinggrand/>  They point out:
 
*that either an earth-centered (Ptolemaic) or a sun-centered (Copernican) picture of reality can be made consistent with the motion of celestial bodies;
*that goldfish physicists living in a curved bowl, though observing curved paths of motion of bodies that we observe as linear, could still formulate predictive laws governing motion as they see it;
*that we cannot know whether we live in a simulated world, a virtual reality, one that the simulators rendered self-consistent.
 
Each of those models of reality is not only data-dependent, but is picture- or theory-dependent.
 
In that regard, they each are an example of a ''model-dependent reality'':
 
<blockquote>
<p style="margin-left: 2.0%; margin-right: 6%; font-size: 85%; font-family: Gill Sans MT;">Instead we will adopt a view that we will call model-dependent realism: the idea that a physical theory or world picture is a model (generally of a mathematical nature) and a set of rules that connect the elements of the model to observations. This provides a framework with which to interpret modern science.<ref name=hawking/></p>
</blockquote>
 
<blockquote>
<p style="margin-left: 2.0%; margin-right: 6%; font-size: 85%; font-family: Gill Sans MT;">According to the idea of model-dependent realism...our brains interpret the input from our sensory organs by making a model of the outside world. We form mental concepts of our home, trees, other people, the electricity that flows from wall sockets, atoms, molecules, and other universes. These mental concepts are the only reality we can know. There is no model-independent test of reality. It follows that a well-constructed model creates a reality of its own.<ref name=hawking/></p>
</blockquote>
 
In adopting model-dependent realism, "it is pointless to ask whether a model is real, only whether it agrees with observation" (p. 46<ref name=hawkinggrand/>). If two different models agree with the observations, it does not make sense to consider one more true than the other, that one gives a truer picture of reality than the other, though one or the other may be more convenient to employ in a given situation, or otherwise more appealing.
 
Some find the ambiguity of reality introduced by alternative equivalent theories to be in itself an argument that such definitions of reality are inadequate.<ref name=Cao/>  That argument, however, has to be based upon criteria arrived at from ''outside'' model-dependent reality, and an example of such criteria is provided shortly.
 
It should be emphasized that there is no restriction in model-dependent realism to observable or measurable constructs. The alternatives:
<blockquote>
<p style="margin-left: 2.0%; margin-right: 6%; font-size: 85%; font-family: Gill Sans MT;">Do unobservable theoretical entities such as [[Quantum chromodynamics|quarks and gluons]] really exist in the physical world, as objective entities independent of human will, or exist merely as human constructions for their utility in organizing our experience and predicting future events?<ref name=Cao1/></p>
</blockquote>
are addressed by Hawking/Mlodinow in their model-dependent realism approach as follows:
 
<blockquote>
<p style="margin-left: 2.0%; margin-right: 6%; font-size: 85%; font-family: Gill Sans MT;">QCD <nowiki>[</nowiki>[[Quantum chromodynamics]]<nowiki>]</nowiki> also has a property called asymptotic freedom, which we referred to, without naming it, in Chapter 3. Asymptotic freedom means that the strong forces between quarks are small when the quarks are close together but increase if they are farther apart, rather as though they were joined by rubber bands. Asymptotic freedom explains why we don’t see isolated quarks in nature and have been unable to produce them in the laboratory. <i>Still, even though we cannot observe individual quarks, we accept the model because it works so well at explaining the behavior of protons, neutrons, and other particles of matter</i> [Emphasis added].
<ref name=hawkinggrand2/></p>
</blockquote>
 
In short, in the alternatives posed above by Cao,<ref name=Cao1/> model-dependent realism adopts the second view, accepts the unobservable constructs as aspects of reality, but rejects any posit of "objective" reality, which last is considered to be a chimera, like visions of oases in the desert.<ref name=gauge group=Note/>
 
==Background==
The "reality" of science, even when restricted to the interpretation of observations and measurements, has been much discussed. [[Pierre Duhem]] (1861-1916) held that while physical theory was no more than an aid to memory, summarizing and classifying facts by providing a symbolic representation of them, the facts of physical theory are to be distinguished from common sense and metaphysics. His views were further developed by [[W. V. O. Quine]] (1908-2000), who suggested "“our statements about the external world face the tribunal of sense experience not individually, but only as a corporate body”. It is impossible to test a scientific hypothesis in isolation, but only as part of a system. These two authors were much concerned with how a theory was coupled to concrete observation and measurement, and how it morphed with admission of new data.<ref name=Duhem/><ref name=Quine/>
 
The evolution of science forms part of this discussion. For example, Kuhn connected changes in scientists' views of reality to "revolutions" in science and changes in "paradigms".<ref name=Kuhn/> As an example, Kuhn suggested that the "Copernican revolution" replaced the views of Ptolemy not because of empirical failures, but because of a new "paradigm" that exerted control over what scientists felt to be the more fruitful way to pursue their goals. Such historical analysis goes beyond the objectives of model-dependent reality itself to involve model comparisons, a critique of models that are considered equal from the standpoint of model-dependent reality.
 
The matter is made more complicated by attempts to extend observations of scientific practice to wider realms, including religious systems, in an attempt to compare them. A key author in this arena was [[Ian G. Barbour|Barbour]] who proposed an approach called ''critical realism''.<ref name=Russell/> The word "critical" refers to reflection and analysis. This broad extension lies outside the realm of model-dependent realism itself, and falls into a much vaguer and more tendentious arena.
 
==Model assessment==
For many, probably including Hawking/Mlodinov, model-dependent reality may be seen as a technical term that is useful in broader discussions. For example, [[quantum mechanics]], which is a model-dependent reality describing (among other matters) atomic interactions, despite its experimental success, is widely found incomplete as it is "not accompanied by an interpretation that is widely convincing."<ref name=Fleming/> Steven Pinker discusses this question using several quotations, including one from [http://www.nobelprize.org/nobel_prizes/physics/laureates/1969/gell-mann-bio.html Murray Gell-Mann] that describes quantum theory as: "that mysterious, confusing discipline which none of us really understands but which we know how to use."<ref name=Pinker/> These reservations about quantum mechanics appear to seek what might be called ''physical intuition'', or something Feynman called ''visualization''.<ref name=Schweber group=Note/> The features of a "good" theory have been debated for centuries.<ref name=desiderata group=Note/> For example, Einstein felt that "elegance" was related to ''parsimony'': the fewer the postulates the better. Lorentz thought it was related to adaptability to new observations. [http://www.nobelprize.org/nobel_prizes/physics/laureates/1965/feynman-bio.html Feynman] and [[Freeman John Dyson|Dyson]] had contrasting views as well: Feynman wanted a picture the mind could grasp expressing the unity of nature, while Dyson wanted only a theory that would work within set limits. <ref name =Gratzer group=Note/>
 
Hawking/Mlodinov do not address the intuitive qualities of a model, but they do raise the question of what constitutes a good model. They suggest a "good model" has these characteristics:(p. 51<ref name=hawkinggrand/>)
#It is elegant
#Contains few arbitrary or adjustable elements
#Agrees with and explains all existing observations
#Makes detailed predictions about future observations that can disprove or falsify the model if they are not borne out.
 
These desiderata of a "good model" allow critique of different models that are equal from the stance of model-dependent reality by itself. If these "principles of comparison" have indeed any justification outside of their general acceptance, these lie outside the tenets of model-dependent reality.<ref name=comparison group=Note/>
 
Unfortunately, even the most successful model of modern science, the [[Standard Model]] of particle physics, satisfies only the last criterion. As said by Hawking/Mlodinov (p. 52<ref name=hawkinggrand/>):
<blockquote>
<p style="margin-left: 2.0%; margin-right: 6%; font-size: 85%; font-family: Gill Sans MT;">
..many people view the "standard model" ...as inelegant. ...it contains dozens of adjustable parameters whose values must be fixed to match observations, rather than being determined by the theory itself.
</p>
</blockquote>The Standard Model fails the third criterion in not encompassing gravitation. Hawking/Mlodinov (p. 58<ref name=hawkinggrand/>) deal with the failure of a theory to encompass all observations using the notion of a ''network'' of overlapping theories, each describing some observations and agreeing with one another where the theories overlap. To quote:(p. 58<ref name=hawkinggrand/>):
<blockquote>
<p style="margin-left: 2.0%; margin-right: 6%; font-size: 85%; font-family: Gill Sans MT;">
No single theory within the network can describe every aspect of the universe... Though this situation does not fulfill the traditional physicists' dream of a single unified theory, it is acceptable within the framework of model-dependent realism.
</p>
</blockquote>
 
Presumably, each theory included in a network provides concepts for a "model-dependent reality", though that reality is restricted to the domain of data to which it applies. Where these model-dependent realities overlap, multiple interpretations of reality are available of equal value.
 
==Data collection==
{|align="right" cellpadding="10" style="background:lightgray; width:25%; border: 1px solid #aaa; margin:20px; font-size: 85%; font-family: Gill Sans MT;"
|...the measuring device has been constructed by the observer, and we have to remember that what we observe is not nature in itself but nature exposed to our method of questioning.
: &mdash;Werner Heisenberg, ''Physics and Philosophy''<ref name=Heisenberg/>
|}
The definition of model-dependent reality given by Hawking/Mlodinow is pretty straightforward if one has in mind a particular set of data to explain. Either the model explains the data or it doesn't, and if two models explain the data differently, any claim for the concepts employed by either as more true of "reality" must be based upon criteria lying outside the reach of model-dependent reality, such as the desiderata for a "good model" listed earlier.
 
The matter is less clear when one considers the selection of just what "data" must be explained. Our senses are limited, and we accept that we cannot see and hear everything that comprises reality. So we supplement the senses, for example, by using a telescope or a microscope. Historically the issue arose as to whether such instruments deceived us, and gradually they have been accepted as extensions of our natural capacities.<ref name=Hofstadter/><ref name=Schacht/>
 
The gathering of "data" supplementing our senses has gone far beyond the primitive telescope to its modern version (for example, the [[Hubble Space Telescope|Hubble telescope]]) and the microscope to its modern version (for example, the [[scanning tunneling microscope]]).<ref name =Hubble/><ref name=STM/> Today experiments may require expensive apparatus not available to all, involving observations not even interpretable by many. Examples are the colliders of high-energy physics,<ref name=collider/> and the sophisticated electronic image acquisition of modern astronomy, guided by elaborate computer processing and filtering.<ref name=CCD/> One might reasonably ask how well the acquisition of "data" is separated from the "theory" that explains how the acquisition process works, and that often suggests where to look for new "data".  The ''process'' by which data is allowed into the theory influences what is incorporated into "reality".
 
The gathering of data is complicated by the limited access to these data-acquisition instruments, both in a required training that could be seen as indoctrination (not necessarily deliberate, but [http://legal-dictionary.thefreedictionary.com/de+facto ''de facto'']), and in limitations upon who, and what investigations, are worthy to use the instruments, as determined by various funding agencies and corporate laboratories. Although censorship is not the motivation directing government and corporate support, a preoccupation with popular and/or commercially attractive projects draws resources and talent away from less conspicuous goals potentially of more significance to a comprehensive "reality".<ref name=BellLabs/><ref name=Wilson/><ref name=Riordan/>  In effect, the expense and expertise of modern research result in blinkers.<ref name=DeSollaPrice/><ref name=Smolin/><ref name=Woit/>
 
The analysis as well as the gathering of data is becoming more complicated as our very notion of thinking, even of mathematical proof, is modified by technology, for example, by computers. Theoretical predictions are made by computer simulations that perform calculations beyond human capacity. The concepts entering a model-based reality may be only implicit in a computer programmable code, in open-ended algorithms, and may not be concepts the human mind is aware of directly.<ref name=Colburn/>
 
To a limited degree, the shaping of "reality" based upon modeling of selected data is a public enterprise, with all the foibles that implies. The public does not engage reality at a specialized deeply technical level, but at a metaphoric level:
 
<blockquote>
<p style="margin-left: 2.0%; margin-right: 6%; font-size: 85%; font-family: Gill Sans MT;">All theories have metaphorical dimensions...that give depth and meaning to scientific ideas, that add to their persuasiveness and color the way we see reality."<ref name=goodwin2001/></p>
</blockquote>
 
An explicitly metaphoric public participation is "eco-consciousness".<ref name=larson2011/> Metaphorical involvement also is evident in arenas such as [[gene]] research and [[Biotechnology#Subgroups_of_biotechnology|genetically altered organisms]], and investigations of [[Stem_cell#Ethical_considerations_regarding_embryonic_stem_cells|stem cell]]s, where the public is actively engaged.<ref name=Pence/> Another example is archaeology and the limitations exerted upon examination of burial sites.<ref name=Thomas/><ref name=Thomas1/> In some cases public participation leads to simple clamor, as in the case of [[global warming]].<ref name=Spencer/><ref name=Hoggan/> This broad public engagement, frequently informed by vested interests and oversimplifications, facilitates manipulation by groups with their own objectives, similar to the censorship found in the times of [[Vesalius]] and [[Galileo]] although lacking some of that institutional authority.<ref name=White/>
 
Although the above examples suggest an indictment of metaphor as a foible of public participation in shaping reality, public engagement in some form is necessary and desirable, and ultimately a goal of the entire enterprise.


==Notes==
==Notes==
{{reflist|group=Note|refs=
{{reflist|group=Note|refs=
<ref name=gauge group=Note>
One might ask how arbitrary concepts enter this view of reality. For example, in [[electromagnetism|electromagnetic theory]] one can introduce a [[vector]] and a [[scalar]] [[potential]], neither of which is unique, and is free to choose an admixture of the two called a "gauge". Apparently then, one could view each different gauge as a feature of reality in one of a family of overlapping realities, all of which describe the same observations. A contrasting view is found in: {{cite book |title=Science at century's end: philosophical questions on the progress and limits |author=Gorden N Fleming |editor=Martin Carrier, Gerald J. Massey, Laura Ruetsche, eds |url=http://books.google.com/books?id=o-f--xkHos4C&pg=PA244 |pages=p. 244 |isbn=0822958201 |publisher=Pittsburgh University Press |year= 2004 |quote=But the gauge-independent formalism would delineate the aspects of the the theory one could safely take seriously, the aspects one could tentatively invest with ontological content.}}
</ref>
<ref name=Schweber group=Note>
Quoting Feynman about his creative process: "It is impossible to differentiate the symbols from the thing; but it is very visual. It is hard to believe it, but I see these things not as mathematical expressions but a mixture of a mathematical expression wrapped into and around, in a vague way, around the object. So I see all the time visual things associated with what I am trying to do." {{cite book |title=QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga |author=Silvan S. Schweber |url=http://books.google.com/books?id=61n5dE7FJQgC&pg=PA465 |pages=p. 465 |isbn= 0691033277 |year=1994 |publisher=Princeton University Press}} A more technical description is provided by {{cite book |title=The Genesis of Feynman Diagrams |author=Adrian Wüthrich |url=http://books.google.com/books?id=-y7hxVHO7xMC&pg=PA9 |pages=p.9 |publisher=Springer |year=2010 |isbn=9048192277}}
</ref>
<ref name=real group=Note>
As humans, after all, we may have an intuition or even a need for something we call "reality", and model-dependent realism may seem insufficiently visceral to fill that need.
Whatever concepts we adopt in our personal reality, the history of change in the sciences shows unequivocally that today's reality will be replaced by a more satisfactory one waiting in the wings. We know that there is always more to come that we do not know now.
</ref>
<ref name=desiderata group=Note>
For example, Einstein and Heisenberg had an extensive exchange over whether a good theory could contain unobservable quantities. Einstein said it was unavoidable, while Heisenberg's aesthetic was to have every item in the theory directly observable. See: {{cite book |title=Quantum: Einstein, Bohr, and the Great Debate about the Nature of Reality |url=http://books.google.com/books?id=vNv-MekPHSkC&pg=PA226 |pages=pp. 226 ''ff'' |author=Manjit Kumar |isbn=0393339882 |publisher=W W Norton & Company |year=2011}}
John Slater took the view that theory was experiment's handmaid: "Questions about a theory which do not affect its ability to predict experimental results correctly seem to me quibbles about words, ..." See {{cite book |title=Genius: The Life and Science of Richard Feynman |author=James Gleick |url=http://books.google.com/books?id=j42RD66g72oC&pg=PT315 |page=p. 54 |isbn=0679747044 |publisher=Vintage |year=1993}}.
</ref>
<ref name =Gratzer group=Note>A description of the encounter between Feynman and Dyson during a four-day drive to Albuquerque is found in: {{cite book |title=Eurekas and euphorias: the Oxford book of scientific anecdotes |author=Walter Gratzer |url=http://books.google.com/books?id=yDBep9y0SVsC&pg=PA104 |pages=p. 104 |isbn=019860940X |year=2004 |publisher=Oxford University Press |quote=Feynman distrusted Dyson's mathematics, and Dyson suspected Feynman's intuition.}}
</ref>
<ref name=comparison group=Note>
For further discussion of the appraisal of theories see, for example, {{cite book |title=The Rationality of Science |author=W. Newton-Smith |url=http://books.google.com/books?id=c0RbL0vs8rAC&pg=PA112 |pages=pp. 112 ''ff'' |chapter=TS Kuhn: from revolutionary to social democrat; §3: The five ways|isbn=0415058775 |year=1981 |publisher=Psychology Press |quote=The fact that science is progressing in the sense of generating theories of greater verisimilitude provides reason for thinking that the methods employed (the principles of comparison) are in fact legitimate evidential principles.}} The four desiderata of a good model by Hawking/Mlodinov are expressed differently as "the five ways", a partial list of principles of comparison attributed to [[Thomas Samuel Kuhn|Kuhn]], author of a well known book (called one of the most influential books since WW II by ''The Times Literary Supplement'') {{cite book |title=The structure of scientific revolutions |url=http://books.google.com/books?id=xnjS401VuFMC&printsec=frontcover |author=Thomas S Kuhn |year=1966 |isbn=0226458083 |edition=3rd ed |publisher=University of Chicago Press}}.
</ref>
}}
}}
==References==  
==References==  
{{reflist3 test|refs=
{{reflist|refs=
 
<ref name=BellLabs>
 
For example, even in the very liberal environment of [[Bell Laboratories]] engaged in "fundamental research", experiments following discovery of the [[cosmic background radiation]] by [http://nobelprize.org/nobel_prizes/physics/laureates/1978/penzias.html Arno Penzias] and [http://nobelprize.org/nobel_prizes/physics/laureates/1978/wilson.html Robert Woodrow Wilson] were frowned upon. So was much of the research underlying the modern [[integrated circuit]], research that had to be conducted in the wee hours of the morning, so as not to interfere with "important" corporate research.


<ref name=Johnson>
{{cite book |title=Software Receiver Design: Build Your Own Digital Communication System in Five Easy Steps |url=http://books.google.com/books?id=LNea1qui1KcC&pg=PA417 |pages=p. 417 |chapter=Figure C.1: The envelope of a function outlines its extremes in a smooth manner |author=C. Richard Johnson, Jr, William A. Sethares, Andrew G. Klein |isbn=0521189446 |year=2011 |publisher=Cambridge University Press}}
</ref>
</ref>


<ref name=Cao>
This argument is attributed to [[Thomas Kuhn]]  in {{cite book |title=From Current Algebra to Quantum Chromodynamics: A Case for Structural Realism |author=Tian Yu Cao  |pages=p. 4 |url=http://books.google.com/books?id=lPaq8-dZ_L8C&pg=PA4 |isbn= 0521889332 |year=2010 |publisher=Cambridge University Press}}
</ref>
<ref name=Cao1>
This question is a close paraphrase of a statement in {{cite book |title=From Current Algebra to Quantum Chromodynamics: A Case for Structural Realism |author=Tian Yu Cao  |pages=pp. 2-3 |url=http://books.google.com/books?id=lPaq8-dZ_L8C&pg=PA3 |isbn= 0521889332 |year=2010 |publisher=Cambridge University Press}}
</ref>
<ref name=CCD>
Most telescopic images are collected today using the [[charge-coupled device]] or CCD, and computer processed. See, for example, {{cite book |title=Handbook of CCD astronomy |author=Steve B. Howell |isbn=0521617626 |edition=Volume 5 of Cambridge observing handbooks for research astronomers; 2nd ed |publisher=Cambridge University Press |year=2006 |url=http://books.google.com/books?id=ZZCTqanpsZUC&printsec=frontcover}} In addition, the telescope itself is aimed and adjusted using computer programs.
</ref>
<ref name=Colburn>
{{cite book |title=Philosophy and computer science |author=Timothy R. Colburn |url=http://books.google.com/books?id=luF4ElMxqg4C&pg=PA68 |pages=pp. 68 ''ff'' |chapter=Chapter 6: Models of the mind |publisher=ME Sharpe, Inc. |year=2000 |isbn=156324991X }}
</ref>
<ref name=collider>
{{cite web |url=http://public.web.cern.ch/public/en/LHC/LHC-en.html |title=The large hadron collider |publisher=CERN |accessdate=2011-07-26}}
</ref>
<ref name=DeSollaPrice>
{{cite book |title=Little Science, Big Science and beyond |author=Derek J.De Solla Price |url=http://books.google.com/books?id=i16EQgAACAAJ |year=1986 |isbn=0231049560 |publisher=Columbia University Press |isbn=0231049560}}
</ref>
<ref name=Duhem>
{{cite web |url=http://plato.stanford.edu/entries/duhem/#Sci  |title=Pierre Duhem |year=2011 |author=Roger Ariew |work=The Standard Encyclopedia of Philosophy (Spring 2011 edition) |editor=Edward N. Zalta ed. |accessdate =2011-08-26}}
</ref>
<ref name=Fleming>
{{cite book |title=Science at century's end: philosophical questions on the progress and limits of science |chapter=Limits and the future of quantum theory |author=Gordon N Fleming |editor=Martin Carrier, Gerald J. Massey, Laura Ruetsche, eds |isbn=0822958201 |year=2004 |publisher=University of Pittsburgh Press |url=http://books.google.com/books?id=o-f--xkHos4C&pg=PA237&dq=%22an+interpretation+that+is+widely+convincing%22&hl=en&ei=R8q6TrehIvTXiAKihJyZDA&sa=X&oi=book_result&ct=result&resnum=1&ved=0CC4Q6AEwAA#v=onepage&q=%22an%20interpretation%20that%20is%20widely%20convincing%22&f=false |pages=pp. 237 ''ff''}}
</ref>
<ref name=goodwin2001>
{{cite book |author=Brian Goodwin |edition=Reprint with a new preface of 1994 ed |year=2001 |title=How the Leopard Changed Its Spots: The Evolution of Complexity |chapter=The myth behind the metaphors |pages=p. 33  |publisher= Princeton University Press |url=http://books.google.com/books?id=3BLQntp8ifIC&pg=PA33 |isbn=0691088098 }} Title links to Google Books preview.
</ref>
<ref name=hawking>
{{cite book |author=Hawking SW, Mlodinow L. |title=cited work|isbn=0553805371 |url= http://www.amazon.com/Grand-Design-Stephen-Hawking/dp/0553805371#reader_0553805371 |pages=pp. 42-43 |chapter=Chapter 3: What is reality?}}
</ref>
<ref name=hawkinggrand>
{{cite book |author=Hawking SW, Mlodinow L.|year=2010 |title=The Grand Design|location= New York|publisher=Bantam Books|isbn=978-0-553-90707-0 |edition=Kindle edition|url= http://books.google.com/books?id=RoO9jkV-yzIC&dq=the+grand+design&q=model+dependent#v=snippet&q=model%20dependent&f=false}}
</ref>
<ref name=hawkinggrand2>
See above reference: {{cite book |author =Hawking SW, Mlodinow L.|year=2010 |title=The Grand Design |url= http://www.amazon.com/Grand-Design-Stephen-Hawking/dp/0553805371#reader_0553805371 |pages=p. 110 |chapter=Chapter 5: The theory of everything|isbn=978-0-553-90707-0 }}
</ref>
<ref name=Kuhn>
{{cite book |title=The structure of scientific revolutions |url=http://books.google.com/books?id=xnjS401VuFMC&printsec=frontcover |author=Thomas S Kuhn |year=1966 |isbn=0226458083 |edition=3rd ed |publisher=University of Chicago Press}}
</ref>
<ref name=Heisenberg>
{{cite book |author=Werner Heisenberg |title=Physics and Philosophy: The Revolution in Modern Science |location=New York |publisher=Harper Perennial Modern Classics  |year=2007 |edition=Reprint of Harper & Row 1962 ed |pages=p. 58 |url=http://www.amazon.com/gp/reader/0061209198/ref=sib_dp_pt#reader-link |isbn=0061209198 |chapter=Chapter III: The Copenhagen interpretation of quantum theory}}
</ref>
<ref name=Hofstadter>
Initially, many refused to believe the results of the telescope. Kepler wrote to Galileo that such persons were "stuck in a world of paper" , blind not by force of circumstance but of their own foolish will. {{cite book |author=Dan Hofstadter |title=The Earth Moves: Galileo and the Roman Inquisition |chapter=Chapter 2: The telescope; or seeing |pages=pp. 53 ''ff'' |publisher=W W Norton & Co |year=2009 |isbn=978-0-393-06650-0|url=http://books.google.com/books?id=Ybu81FJA3jgC&printsec=frontcover}}
</ref>
<ref name=Hoggan>
{{cite book |title=Climate cover-up: the crusade to deny global warming |author=James Hoggan, Richard D. Littlemore |url=http://books.google.com/books?id=tQYjQzOkYK0C |isbn= 1553654854 |year=2009 |publisher=Greystone Books}}
</ref>
<ref name=Hubble>
{{cite web |url=http://www.nasa.gov/mission_pages/hubble/main/index.html |title=Hubble space telescope |publisher=NASA |accessdate=2011-07-30}}
</ref>
<ref name=larson2011>
{{cite book |author=Larson B |year=2011 |title=Metaphors for Environmental Sustainability: Redefining Our Relationship with Nature |publisher=  Yale University Press |isbn= 9780300151534. |url=http://books.google.com/books?id=Ik6E4AD6gloC&dq=brendon+larson&source=gbs_navlinks_s}}  [http://www.sciencemag.org/content/333/6043/700.1.full Science magazine book review].
</ref>
<ref name=Pence>
{{cite book |title=Re-Creating Medicine: Ethical Issues at the Frontiers of Medicine |author=Gregory Pence |url=http://books.google.com/books?id=IUjvd09OEOgC&pg=PA137|chapter=Chapter 7: Recreating nature: Patenting human genes? |pages=pp. 137 ''ff''|isbn=084769691X |publisher=Rowman & Littlefield |year=2007}}
</ref>
<ref name=Pinker>
{{cite book |title=The blank slate: the modern denial of human nature |author=Steven Pinker |url=http://books.google.com/books?id=ePNi4ZqYdVQC&pg=PT347 |pages=p. 347 |isbn= 0142003344 |publisher=Penguin |year=2003}}
</ref>
<ref name=Quine>
{{cite web |author=Peter Hylton |title=Willard van Orman Quine|work=The Stanford Encyclopedia of Philosophy (Fall 2010 Edition) |editor=Edward N. Zalta ed. |year=2010 |url=http://plato.stanford.edu/archives/fall2010/entries/quine/ |accessdate=2011-08-26}}
</ref>
<ref name=Riordan>Concerning the environment at Bell, see for example, {{cite book |title=Crystal fire: the birth of the information age |url=http://books.google.com/books?id=0bTpcTLCu6MC&pg=PA179 |author=Michael Riordan, Lillian Hoddeson |pages=p. 179|quote=But because they could not get even a small laboratory dedicated to them, they put it [their crystal-pulling apparatus] on a set of wheels so that it could be rolled into and out of a storage closet in the metallurgical lab. Working on their own time,..., they managed to "bootleg" their crystal growing program into existence.|isbn=0393041247|year=1997 |publisher=W. W. Norton & Company}} Corporate official "history" has glossed over these problems to present a view of great wisdom and encouragement.
</ref>
<ref name=Russell>
{{cite book |title=Fifty years in science and religion: Ian G. Barbour and his legacy |url=http://books.google.com/books?id=xgOsaqL_b1gC&pg=PA78 |pages=pp. 78 ''ff'' |editor=Robert J. Russell, ed |author=Niels Henrik Gregersen |chapter=Chapter 4: Critical realism and other realisms |isbn=075464118X |publisher=Ashgate Publishing, Ltd |year=2004}}
</ref>
<ref name=Schacht>
Cautions abound concerning the deceptive nature of the microscope. For example, see {{cite book  |author=Hermann Schacht |title=The microscope: and its application to vegetable anatomy and physiology |quote=''Seeing'', as Schleiden justly observes, is a difficult art, and seeing with the microscope is yet more difficult... |url=http://books.google.com/books?id=_k1JAAAAYAAJ&pg=PA57|pages=p. 57 |year=1855 |edition=2nd ed |publisher=S. Highley}}
</ref>
<ref name=Smolin>
{{cite book |title=The trouble with physics: the rise of string theory, the fall of a science, and what comes next |author=Lee Smolin |url=http://books.google.com/books?id=d6MIUlxY-qwC&pg=PA261|publisher=Houghton Mifflin Harcourt |year=2007 |chapter=Chapter 16: How do you fight sociology |pages=pp. 261 ''ff'' |isbn=061891868X}}
</ref>
<ref name=Spencer>
For a discussion by a proponent of intelligent design, see for example {{cite book |title=Climate Confusion: How global warming hysteria leads to bad science, pandering politicians and misguided policies that hurt the poor |author=Roy W. Spencer |edition=Paperback version of 2008 ed |url=http://books.google.com/books?id=f5p76GoayfgC&source=gbs_navlinks_s |isbn=1594033455 |year=2010 |publisher=Encounter Books}}
</ref>
<ref name=STM>
{{cite web |url=http://nobelprize.org/educational/physics/microscopes/scanning/index.html |title= The scanning tunneling microscope |publisher=Nobelprize.org |accessdate=2011-07-30}}
</ref>
<ref name=Thomas>
{{cite book |title=Skull Wars: Kennewick Man, Archaeology, and the Battle for Native American Identity |author=David Hurst Thomas |url=http://books.google.com/books?id=IWT4_ZQ2grsC&printsec=frontcover |publisher=Basic Books |year=2001 |isbn=046509225X}}
</ref>
<ref name=Thomas1>
{{cite book |title=Archaeology |author=Robert L. Kelly, David Hurst Thomas |url=http://books.google.com/books?id=Nw4eqX0pIt0C&printsec=frontcover |publisher=Cengage Learning|edition=5th ed |year=2009|quote=How can we pursue this laudable goal if the very act of conducting research offends the living descendents of the ancient people being studied? |pages=p. xxxiii |isbn=0495602914}}
</ref>
<ref name=White>
{{cite book |title=A history of the warfare of science with theology in Christendom, Volume 2 |author=Andrew Dickson White |url=http://books.google.com/books?id=BQUIAQAAIAAJ&printsec=frontcover|publisher=D. Appleton & Co.|year=1896}}
</ref>
<ref name=Wilson>
As Wilson gently recalled matters: "local management here decided that we had had our fun doing astronomy and that now we really ought to contribute something to the telephone company too". Quoted in {{cite book |title=Three degrees above zero: Bell Laboratories in the information age |url=http://books.google.com/books?id=N6s8AAAAIAAJ&pg=PA208 |year=1987 |author=Jeremy Bernstein |chapter=Chapter 14: Robert Wilson |pages=p. 208 |isbn=0521329833 |publisher=Cambridge University Press}}
</ref>
<ref name=Woit>
{{cite book |title=Not even wrong: the failure of string theory and the search for unity in physical law |url=http://books.google.com/books?id=pcJA3i0xKAUC&pg=PA221 |chapter=Chapter 16: The only game in town: the power and the glory of string theory|pages=pp. 221 ''ff'' |isbn=0465092756 |year=2006 |author=Peter Woit |publisher=Basic Books}}
</ref>


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© Image: John R. Brews
Top and bottom envelope functions for a modulated sine wave.

In physics and engineering the envelope of a rapidly varying signal is a smooth curve outlining its extremes in amplitude.[1] The figure illustrates a sine wave varying between an upper and a lower envelope.

Notes

References

  1. ↑ C. Richard Johnson, Jr, William A. Sethares, Andrew G. Klein (2011). “Figure C.1: The envelope of a function outlines its extremes in a smooth manner”, Software Receiver Design: Build Your Own Digital Communication System in Five Easy Steps. Cambridge University Press, p. 417. ISBN 0521189446. 
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