3.2: Between Versus Within Groups Analysis
Learning Objectives
At the end of this chapter you should be able to answer the following questions:
- What is the difference between a Between Groups test and a Within Groups test?
- What is a Mean Difference in the context of statistical analysis?
There are two main types of statistical tests: those that look at differences Between Groups and those that look at differences Within Groups .
Between Groups differences examine how independent groups – groups that are not the same – may differ from each other on a variable. Between Groups difference tests are useful for examining the efficacy of interventions or treatments. For example, if you wanted to see if a new form of anxiety therapy was effective, you could organise two groups of participants, and provide one with the new form of anxiety therapy. This group would be the intervention group. To use a Between Groups test you would also need a comparison group that does not receive the treatment, which would be your control group. Both groups would need to receive some form of outcome measure – such as a measure of anxiety taken after the treatment. You would then compare the two and see if there were any differences in mental states.
Within Groups differences are similarly important. For example, if a researcher wants to examine if an exercise program is effective, she could take the BMI of a group of test subjects at the start of the program and again at the end of the program and compare the two. In this case, the researcher is not looking at the differences between two groups, but rather the differences between the same group taken at two time points.
In both differences between groups and differences within groups, we will generally look at differences between means on some variable of interest. When we talk about a Mean Difference , we are talking about the difference between the mean of one group and the mean of another group in the case of differences between groups. In the case of differences within groups, we look at differences in means between two or more different points in time when measurements are taken. When looking at the BMI of the trial group we just mentioned, you would want the mean score of the group at pre-program, and the mean score at post-program.
To examine the differences between or within groups, you also need to know the standard deviations of both means you are comparing, as well as the number of participants. With the mean, the measure of variance within the samples is the standard deviation. Once you have the mean difference, the standard deviation, and the number of data points, you can then use the T-test to calculate if the difference between the two means is statistically significant.
There are two main types of t-tests we will be focusing on – the independent samples t-test and the paired samples t-test. When you are examining the difference between two groups, you want to use the independent samples t-test, however, if you are looking into the difference between the same group at two different time points, the paired-sample t-test is the one to use. nstructor v


4.7: Tachyons and Faster-than-Light (FTL)
Learning Objectives
- Explain faster-than-light ( FTL , superluminal) motion in relativity
A Defense in Depth
Let’s summarize some ideas about faster-than-light ( FTL , superluminal) motion in relativity:
- Superluminal transmission of information would violate causality, since it would allow a causal relationship between events that were spacelike in relation to one another, and the timeordering of such events is different according to different observers. Since we never seem to observe causality to be violated, we suspect that superluminal transmission of information is impossible. This leads us to interpret the metric in relativity as being fundamentally a statement of possible cause and effect relationships between events.
- We observe the invariant mass defined by \(m^2 = E^2 - p^2\) to be a fixed property of all objects. Therefore we suspect that it is not possible for an object to change from having \(|E| > |p|\) to having \(|E| < |p|\).
- No continuous process of acceleration can bring an observer from \(v < c\) to \(v > c\) (see section 3.3). Since it’s possible to build an observer out of material objects, it seems that it’s impossible to get a material object past \(c\) by a continuous process of acceleration.
- If superluminal motion were possible, then one might also expect superluminal observers to be possible. But FTL frames of reference are kinematically impossible in \(3 + 1\) dimensions ( section 3.8).
Thus special relativity seems to have a defense in depth against superluminal motion.
Based on 2, FTL motion would be a property of an exotic form of matter built out of hypothetical particles with imaginary mass. Such particles are called tachyons. An imaginary mass is not absurd on its face, because experiments directly measure \(E\) and \(p\), not \(m\). E.g., if we put a tachyon on a scale and weighed it, we would be measuring its mass-energy \(E\).
The weakest of these arguments is 1, since as described in
section 2.1, we have no strong reasons for believing in causality as an overarching principle of physics. It would be exciting if we could detect tachyons in particle accelerator experiments or as naturally occurring radiation. Perhaps we could even learn to transmit and receive tachyon signals artificially, allowing us to send ourselves messages from the future! This possibility was pointed out in 1917 by Tolman 1 and is referred to as the “tachyonic antitelephone.” 2If we’re willing to let go of causality, then we just need to make sure that our tachyons comply with items 3 and 4 above. Argument 4 tells us that the laws of physics must conspire to make it impossible to build an observer out of tachyons; this is not entirely implausible, since there are other classes of particles such as photons that can’t be used to construct observers.
Experiments to search for tachyons
Experimental searches are made more difficult by conﬂicting theoretical claims as to whether tachyons should be charged or neutral, whether they should have integral or half-integral spin, and whether the normal spin-statistics relation even applies to them. 3 If charged, it is uncertain whether and under what circumstances they would emit Cerenkov radiation.
The most obvious experimental signature of tachyons would be propagation at speeds greater than \(c\). Negative results were reported by Murthy and later by Clay, 4 who studied air showers generated by cosmic rays to look for precursor particles that arrived before the first photons.
One could also look for particles with \(|p| > |E|\). Alvager and Erman, in a 1965 experiment, studied the beta decay of \(^{170}\textrm{Tm}\), using a spectrometer to measure the momentum of charged radiation and a solid state detector to determine energy. An upper limit of one tachyon per \(10^4\) beta particles was inferred.
If tachyons are neutral, then they might be difficult to detect directly, but it might be possible to infer their existence indirectly through missing energy-momentum in reactions. This is how the neutrino was first discovered. Baltay et al . 5 searched for reactions such as
\[\bar{p} + p \rightarrow \pi ^{+} + \pi ^{-} + t\]
with \(t\) being a neutral tachyon, by measuring the momenta of all the other initial and final particles and looking for events in which the missing energy-momentum was spacelike. They put upper limits of \(\sim 10^{-3}\) on the branching ratios of this and several other reactions leading to production of single tachyons or tachyon-antitachyon pairs.
For a long time after the discovery of the neutrino, very little was known about its mass, so it was consistent with the experimental evidence to imagine that one or more species of neutrinos were tachyons, and Chodos et al . made such speculations in 1985. A brief ﬂurry of reawakened interest in tachyons was occasioned by a 2011 debacle in which the particle-physics experiment OPERA mistakenly reported faster-than-light propagation of neutrinos; the anomaly was later found to be the result of a loose connection on a fiber-optic cable plus a miscalibrated oscillator. An experiment called KATRIN, currently nearing the start of operation at Karlsruhe, will provide the first direct measurement of the mass of the neutrino, by measuring very precisely the maximum energy of the electrons emitted in the decay of tritium, \(^{3}\textrm{H} \rightarrow ^{3}\textrm{He} + e^{-} + \bar{v_e}\). Conservation of energy then allows one to determine the minimum energy of the antineutrino, which is related to its mass and momentum by \(m^2 = E^2 - p^2\). Because \(m^2\) appears in this equation, the experiment really measures \(m^2\), not \(m\), and a result of \(m^2 < 0\) would bring the tachyonic neutrino back from the grave.
Tachyons and Quantum Mechanics
When we add quantum mechanics to special relativity, we get quantum field theory , which sounds scary and can be quite technical, but is governed by some very simple principles. One of these principles is that “ everything not forbidden is compulsory .” The phrase was popularized as a political satire of communism by T.H. White, but was commandeered by physicist Murray Gell-Mann to express the idea that any process not forbidden by a conservation law will in fact occur in nature at some rate. If tachyons exist, then it is possible to have two tachyons whose energy-momentum vectors add up to zero. This would seem to imply that the vacuum could spontaneously create tachyon-antitachyon pairs. Most theorists now interpret this as meaning that when tachyons pop up in the equations, it’s a sign that the assumed vacuum state is not stable, and will change into some other state that is the true state of minimum energy.
References
1 www.archive.org/details/theoryrelativmot00tolmrich
2 Bilaniuk et al. claimed in a 1962 paper to have found a reinterpretation that eliminated the causality violation, but their interpretation requires that rates of tachyon emission in one frame be related to rates of tachyon absorption in another frame, which in my opinion is equally problematic, since rates of absorption should depend on the environment, whereas rates of emission should depend on the emitter; the causality violation has simply been described in different words, but not eliminated. For a different critique, see Benford, Book, and Newcomb, “The tachyonic antitelephone,” Physical Review D 2 (1970) 263. Scans of the paper can be found online.
3 Feinberg, “Possibility of Faster-Than-light Particles,” Phys Rev 159 (1967) 1089, http://www.scribd.com/doc/144943457/ G-Feinberg-Possibility-of-Faster-Than-light-Particles-Phys-Rev-159-1967-1089
4 “A search for tachyons in cosmic ray showers,” Austr. J. Phys 41 (1988) 93, http://adsabs.harvard.edu/full/1988AuJPh..41...93C
5 Phys. Rev. D 1 (1970) 759


4.4: Downloading Files
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Links don't always go to another website. In some cases, they point to a file that can be downloaded, or saved, to your computer. If you click a link to a file, it may download automatically, but sometimes it just opens within your browser instead of downloading. To prevent it from opening in the browser, you can right-click the link and select Save link as (different browsers may use slightly different wording, like Save target as). Files downloaded from the internet are often downloaded to your download folder, which is a quick access folder accessible on the left navigation pane of windows explorer. Sometimes you may want to save an image from a website to your computer. To do this, right-click the image and select Save image as (or Save picture as). Make sure you trust the file that you downloaded to your computer, as downloading any file or program to your computer contains security risks to your computer (links).


27.7: References
American Nurses Association. (2021). Nursing: Scope and standards of practice (4th ed.). American Nurses Association.
Benner, P. A. (1984). From novice to expert: Excellence and power in clinical nursing practice. Addison-Wesley Publishing.
Benner, P., Tanner, C., & Chesla, C. (2009). From novice to expert: Excellence and power in clinical nursing practice (2nd ed.). Springer Publishing.
Dickison, P., Haerling, K. A., & Lasater, K. (2018). Integrating the National Council of State Boards of Nursing Clinical Judgment Model into nursing education frameworks. Journal of Nursing Education, 58 (2), 72–78. doi.org/10.3928/01484834-20190122-03
Lasater, K. (2007). Clinical judgment development: Using simulation to create an assessment rubric. The Journal of Nursing Education, 46 (11), 496–503. doi.org/10.3928/01484834-20071101-04
Magley, M., Hinson, M. R., & Haddad, L. M. Eclampsia (Nursing) [Updated 2023, January 30]. StatPearls [Internet]. www.ncbi.nlm.nih.gov/books/NBK570548/
National Council of State Boards of Nursing. (2019, Winter). The layers of the Clinical Judgment Measurement Model. Next Generation NCLEX News, 3–5.
Nibbelink, C. W., & Brewer, B. B. (2018). Decision-making in nursing practice: An integrative literature review. Journal of Clinical Nursing , 27 (5–6), 917–928. doi.org/10.1111/jocn.14151
Tanner, C. A. (2006). Thinking like a nurse: A research-based model of clinical judgment in nursing. Journal of Nursing Education, 45 (6), 204–211. doi.org/10.3928/01484834-20060601-04


2.4: Conclusion
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Cybertarian mythology not only rests on a flawed, albeit touching, account of the person as a ratiocinative, atomistic individual who can exist outside politics and society. It equally assumes that the Internet—which in reality was born of warfare consultancies and “big science,” has spread through large institutions, and is rapidly moving toward comprehensive corporate control—can be claimed for the wild children of geekdom. In place of this sweet-natured technophilic dreaming, activists, citizens, and scholars alike need fewer smiley faces; they must be displaced by quizzical ones that will turn their and our heads in the direction of our real material conditions of existence.
Despite the technocentric projections of both Cold War futurists and contemporary web dreamers, the wider culture industries largely remain controlled by media and communications conglomerates, which frequently seek to impose artist-like conditions on their workforces. They gobble up smaller companies that invent products and services, “recycling audio-visual cultural material created by the grassroots genius, exploiting their intellectual property and generating a standardized business sector that excludes, and even distorts, its very source of business,” to quote the Hindu . 50 In other words, the cognitariat—interns, volunteers, contestants, and so on—creates “cool stuff” whose primary beneficiaries are corporations. 51
There is some very competent research into the lived conditions of folks setting up alternative forms of collaborative work inside the cognitariat that have the potential for a more exciting way forward than the tired cybertarian rhetoric that so unthinkingly repeats and repeats and repeats ideas that belong to Reaganite dreamers. 52 When linked to the political-economic and ethnographic work outlined earlier, and the equally path-breaking research undertaken by nongovernment organizations, the future can be reinterpreted and remade by a realistic analytic frame that takes its inspiration from lived experience, in opposition to futuristic fantasy. Then the scholarship melting into air will have served its cybertarian time. Good riddance.


6.4: Sedimentary Structures and Fossils
Through careful observation over the past few centuries, geologists have discovered that the accumulation of sediments and sedimentary rocks takes place according to some important geological principles, as follows:
- The principle of original horizontality is that sediments accumulate in essentially horizontal layers. The implication is that tilted sedimentary layers observed to day must have been subjected to tectonic forces.
- The principle of superposition is that sedimentary layers are deposited in sequence, and that unless the entire sequence has been turned over by tectonic processes, the layers at the bottom are older than those at the top.
- The principle of inclusions is that any rock fragments in a sedimentary layer must be older than the layer. For example, the cobbles in a conglomerate must have been formed before the conglomerate was formed.
- The principle of faunal succession is that there is a well-defined order in which organisms have evolved through geological time, and therefore the identification of specific fossils in a rock can be used to determine its age.
In addition to these principles, that apply to all sedimentary rocks (as well as volcanic rocks), a number of other important characteristics of sedimentary processes result in the development of distinctive sedimentary features in specific sedimentary environments. By understanding the origins of these features, we can make some very useful inferences about the processes that led to deposition the rocks that we are studying.
Bedding , for example, is the separation of sediments into layers that either differ from one another in textures, composition, color, or weathering characteristics, or are separated by partings —narrow gaps between adjacent beds (Figure \(\PageIndex{1}\)). Bedding is an indication of changes in depositional processes that may be related to seasonal differences, changes in climate, changes in locations of rivers or deltas, or tectonic changes. Partings may represent periods of non-deposition that could range from a few decades to a few millennia. Bedding can form in almost any sedimentary depositional environment.
Cross-bedding is bedding that contains angled layers within otherwise horizontal beds, and it forms when sediments are deposited by flowing water or wind. Some examples are shown in Figures 6.0.11, 6.1.7b, and 6.4.2. Cross-beds formed in streams tend to be on the scale of centimeters to tens of centimeters, while those in aeolian (wind deposited) sediments can be on the scale of meters to several meters.
Cross-beds form as sediments are deposited on the leading edge of an advancing ripple or dune under steady state conditions (similar flow rate and same flow direction). Each layer is related to a different ripple that advances in the direction of flow, and is partially eroded by the following ripple (Figure \(\PageIndex{3}\)). Cross-bedding is a very important sedimentary structure to be able to recognize because it can provide information on the process of deposition, the direction of current flows and, when analyzed in detail, on other features like the rate of flow and the amount of sediment available.
Graded bedding is characterized by a gradation in grain size from bottom to top within a single bed. “Normal” graded beds are coarse at the bottom and become finer toward the top. They are a product of deposition from a slowing current (Figure \(\PageIndex{4}\)). Most graded beds form in a submarine-fan environment (see Figure \(\PageIndex{1}\)), where sediment-rich flows descend periodically from a shallow marine shelf down a slope and onto the deeper sea floor. Some graded beds are reversed (coarser at the top), and this normally results from deposition by a fast-moving debris flow (see Chapter 15).
Ripples , which are associated with the formation of cross-bedding, may be preserved on the surfaces of sedimentary beds. Ripples can also help to determine flow direction as they tend to have their steepest surface facing in the direction of the flow (see Figure \(\PageIndex{3}\)).
In a stream environment, boulders, cobbles, and pebbles can become imbricated , meaning that they are generally tilted in the same direction. Clasts in streams tend to tilt with their upper ends pointing downstream because this is the most stable position with respect to the stream flow (Figure \(\PageIndex{5}\) and Figure \(\PageIndex{7}\)c).
Mud cracks form when a shallow body of water (e.g., a tidal flat or pond or even a puddle), into which muddy sediments have been deposited, dries up and cracks (Figure \(\PageIndex{6}\)). This happens because the clay in the upper mud layer tends to shrink on drying, and so it cracks because it occupies less space when it is dry.
The various structures described above are critical to understanding and interpreting the conditions that existed during the formation of sedimentary rocks. In addition to these, geologists also look very closely at sedimentary grains to determine their mineralogy or lithology (in order to make inferences about the type of source rock and the weathering processes), their degree of rounding, their sizes, and the extent to which they have been sorted by transportation and depositional processes. Some of the types of differences that we might want to look for are illustrated in Figure \(\PageIndex{7}\).
We won’t be covering fossils in any detail in this book, but they are extremely important for understanding sedimentary rocks. Of course, fossils can be used to date sedimentary rocks, but equally importantly, they tell us a great deal about the depositional environment of the sediments and the climate at the time. For example, they can help to differentiate marine versus terrestrial environments; estimate the depth of the water; detect the existence of currents; and estimate average temperature and precipitation. For example, the tests of tiny marine organisms (mostly foraminifera) have been recovered from deep-ocean sediment cores from all over the world, and their isotopic signatures have been measured. As we’ll see in Chapter 19, this has provided us with information about the changes in average global temperatures over the past 65 million years.
Sedimentary rocks can tell us a great deal about the environmental conditions that existed during the time of their formation. Make some inferences about the source rock, weathering environment, type and distance of sediment transportation, and deposition conditions that existed during the formation of the following rocks:
- Quartz sandstone: no feldspar, well-sorted and well-rounded quartz grains, cross-bedding
- Feldspathic sandstone and mudstone: feldspar, volcanic fragments, angular grains, repetitive graded bedding from sandstone upwards to mudstone
- Conglomerate: well-rounded pebbles and cobbles of granite and basalt; imbrication
- Breccia: poorly sorted, angular limestone fragments; orange-red matrix
See Appendix 3 for Exercise 6.4 answers .
Media Attributions
- Figures 6.4.1, 6.4.2, 6.4.3, 6.4.4, 6.4.5, 6.4.6, 6.4.7: © Steven Earle. CC BY.


1.9: Testimony
In the testimony case a person comes to know something when he is told about it by an eyewitness or when he reads it in the newspaper. . . . No obvious deductive inference leads to a probabilistic conclusion in this case; the acceptance of testimony can be based on two consecutive inferences to the best explanation. . . . First, we would infer that the speaker so testifies because he believes what he says (and not because he has something to gain by so testifying, or because he has gotten confused and has said the opposite of what he means, etc.). Second we would infer that he believes as he does because in fact he witnessed what he described (and not because he has suffered an hallucination, or because his memory deceived him, etc.).
—GILBERT HARMAN1
A Letter of Recommendation
I have a good friend in the psychology program. He has asked me to write a letter of recommendation in his search for a new job. I know him pretty well—we have collaborated on a short article and have team-taught on two occasions. I tell his prospective employers that he is a fine teacher and a great colleague and that he will go on to be a major figure in academic psychology someday. Suppose you read my letter and wonder what kind of evidence it provides about the job candidate.
Gilbert Harman, in the previous quote, provides a succinct characterization of how inference to the best explanation can be used to unpack the reasoning involved in accepting the word of others. In most cases where we assess testimony, we have more data to explain than simply what has been said. Minimally, we will know something about the speaker and something about the context in which the statement was made. The abstract model looks something like the following. First of all, we have the information contained in the language:
e 1 . Linguistic statement—“He is a fine teacher . . . major figure.”
Almost as important in this case is the context in which the statement is offered:
e 2 . Context—letter of recommendation.
Finally, we know something about the letter writer himself:
e 3 . Relevant biography—philosophy professor at a small state university.
The explanatory or interpretive question is, Why did this speaker (biography) in this circumstance (context) say this (statement)? In ordinary communicative contexts, we generally give people the benefit of the doubt. Until given reason not to, we are presupposed to believe that our interlocutors are being straight with us. The conventions of normal linguistic communication ask you to first consider a theory that explains all these data in terms of sincerity:
t 0 . The letter writer said it because he believed it to be true—he believed that his friend was a good teacher and a great colleague and had the potential to make significant contributions to his field.
Unfortunately, years of reading these sorts of letters have made some of us a little cynical. We can immediately conceive of two alternative explanations of the letter writer’s linguistic behavior.
t 1 . The letter writer said it because he wants to get his friend a job.
t 2 . The speaker said it to get rid of an undesirable colleague.
Inference to the best explanation asks us at some point to commit ourselves to a judgment of explanatory plausibility. What is the best explanation of what the letter writer said? Basically, our answers fall into two categories. We will either judge that the best explanation of the statement is the original one that normal communication recommends—he said it because he believes it; he is sincere. Or we will prefer one of the rival explanatory accounts that offer some other reason for his having made the statement. In this latter case, his testimony is of no use to us, indeed we should discount it. Even if it turns out that his friend is a great candidate for the job, if we judge that the letter writer is insincere or dishonest, his testimony is unreliable evidence about this.
If we do give him the benefit of the doubt on the question of sincerity, we must go through a whole other level of assessment before we can put complete confidence in the truth of his statement. The first level of evidence evaluation yields some new data that must also be explained.
e 4 . The letter writer is saying these great things about his colleague because he sincerely believes them to be true.
Why does this person (biography) believe these things (the content of the statement)? Once again, the presuppositions of normal communication ask us to endorse a standard explanation for most sincere communicative attempts.
t* 0 . The speaker believes this because he knows what he is talking about—he believes it because it is, in fact, true.
Thus when we accept information through the testimony or authority of others, we tacitly engage in a dual explanatory inference. We explain the linguistic act as a sincere attempt to communicate the speaker’s belief and then explain the speaker’s having the belief in terms of the speaker knowing what they’re talking about.
Larry Wright has helpfully distinguished two quite different things that can go wrong when someone communicates a sincerely held belief. Sometimes people have unreliable access to the information they are trying to communicate. Thus a rival explanation of my belief that my friend is a good teacher might be that I have only observed him in specialized upper-division courses that would be of interest to philosophy and psychology majors—I have never observed him, for example, in large introductory courses.
t* 1 . The letter writer believes that his friend is a good teacher because he has never observed his lousy teaching in large introductory courses.
Even when authorities possess excellent access to information, we still worry sometimes about their ability to reliably interpret this information. In this context, the cautious letter reader might have at least two potential worries about my testimony. The first has to do with specialized training. Obviously, my claims presuppose some fairly technical knowledge about pedagogy, academia, and research standards in contemporary psychology. One would like to think that expectations for teaching and collegiality would not vary across the humanities and natural and behavioral sciences. I, hopefully, have the necessary background to provide relevant information about these aspects of my friend’s career. But what about the prediction for professional distinction with respect to his research? I am trained as a philosopher, not a psychologist. Perhaps his psychological “insights” I observed in the course of our collaborative teaching and writing are common knowledge in the field. Or worse, maybe they are discredited or eccentric. Am I really qualified to say? A rival explanation once again suggests itself.
t* 2 . The letter writer believes his colleague will make a name for himself because of his lack of knowledge about contemporary academic psychology.
A very different worry about the reliability of my belief focuses on my ability to “objectively” process the information to which I do have reliable access. Basically, the worry here is one of perceptual or interpretive bias. Perhaps I so admire his pedagogic technique because it is so similar to my own ineffective classroom style. Or maybe I am so impressed with his psychological hypotheses because they nicely coincide with my own half-baked notions. He is, after all, my good friend—might I not be guilty of “seeing more with my heart than with my eyes?” So we have yet another category of rival explanation:
t* 3 . The letter writer believes these grossly inflated things about his friend because of some sort of perceptual bias.
None of the above should be taken to suggest that testimony is inherently unreliable. What could be more obvious than the fact that almost everything we claim to know comes to us secondhand through the word of others? What I am suggesting is that our assessment of testimony can be structured and critically evaluated as a kind of evidence—evidence that perfectly fits the inference-to-the-best-explanation recipe.
Testimony regarding Miracles
In David Hume’s monumental book, An Enquiry Concerning Human Understanding , there is a very short little argument with astounding religious implications. Hume argues that we are never justified in accepting the testimony of others that a truly miraculous event has transpired. But since the three great theistic religions—Judaism, Christianity, and Islam—all depend, at some foundational level, on reports of miracles, Hume’s argument seems to threaten their intellectual legitimacy. A full analysis of Hume’s argument, let alone a full philosophical investigation of miracles, would be the subject of a whole book, maybe a whole career. Nevertheless, we now possess the tools to at least lay out the structure of Hume’s argument and perhaps to begin the process of evaluating his evidence. So what exactly is the argument?
A miracle is a violation of the laws of nature; and as a firm and unalterable experience has established these laws, the proof against a miracle, from the very nature of the fact, is as entire as any argument from experience can possibly be imagined. Why is it more than probable, that all men must die; that lead cannot, of itself, remain suspended in the air; that fire consumes wood, and is extinguished by water; unless it be, that these events are found agreeable to the laws of nature, and there is required a violation of these laws, or in other words, a miracle to prevent them? Nothing is esteemed a miracle, if it ever happened in the common course of nature. It is no miracle that a man, seemingly in good health, should die on a sudden: because such a kind of death, though more unusual than any other, has yet been frequently observed to happen. But it is a miracle, that a dead man should come to life; because that has never been observed in any age or country. There must, therefore, be a uniform experience against every miraculous event, otherwise the event would not merit that appellation. . . .
The plain consequence is (and it is a general maxim worthy of our attention), “That no testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavours to establish. . . .” When anyone tells me, that he saw a dead man restored to life, I immediately consider with myself, whether it be more probable, that this person should either deceive or be deceived, or that the fact, which he relates, should really have happened. I weigh the one miracle against the other; and according to the superiority, which I discover, I pronounce my decision, and always reject the greater miracle. If the falsehood of his testimony would be more miraculous, than the event which he relates; then, and not till then, can he pretend to command my belief or opinion.
In the foregoing reasoning we have supposed, that the testimony, upon which a miracle is founded, may possibly amount to an entire proof, and that the falsehood of that testimony would be a real prodigy: But it is easy to shew, that we have been a great deal too liberal in our concession, and that there never was a miraculous event established on so full an evidence. 2
Let’s begin with the middle paragraph. Someone reports seeing a dead man restored to life. If we treat this report as potential evidence a genuine miracle has occurred, we would schematize this testimony as follows.
e 1 . Linguistic statement—“I saw a dead man restored to life.”
e 2 . Context—where, when, and how we were told
e 3 . Relevant biography—whatever we know about the person who tells us this
t 0 . He genuinely believes that he saw a dead man restored to life.
t* 0 A dead man was restored to life.
Hume now considers two rival explanations, one for each of the inferences: “This person . . . deceive[s].”
t 1 . He does not really believe that he saw a dead man restored to life.
Or “this person . . . [was] deceived.”
t* 1 . He was mistaken in thinking he saw a dead man restored to life.
Hume proceeds to combine t 1 and t* 1 into what logicians call a disjunction—“t 1 or t* 1 ”—“he deceives, or he was deceived.” Although he was not explicitly using inference to the best explanation, we can take Hume as proposing a rival explanation.
t* 2 . He does not really believe that he saw a dead man restored to life, or he was mistaken in thinking he saw a dead man restored to life.
Hume then implicitly moves to step 3 in the recipe and offers a rank ordering of the original explanation of the testimony regarding a miracle and the disjunctive rival explanation. Theory t* 2 is a better explanation of what was said than t* 0 .
Why is he so confident of this ranking? The answer is what Hume, and almost every philosopher and theologian since, means by something being a miracle . Miracles are violations of laws of nature. Given the laws of physics, biochemistry, and biology, the natural world dictates that death is permanent. The very evidence that establishes these laws of nature automatically counts against the reported miracle. For Hume, it’s obvious that the various law of nature hypotheses are so much better explanations than rivals that allow for exceptions to these laws that miracles are doomed to be exceedingly implausible.
I agree with Hume about this so far. If a casual stranger tells me that she has witnessed a miracle, I would almost certainly judge that she is either lying or honestly mistaken and not that there has been an interruption in the operations of the natural world. But my judgment is based on a subjective assessment of the plausibility of differing explanatory accounts—classic application of the inference-to-the-best-explanation recipe—and not the meaning of the term miracle . Theists are not claiming, in my judgment, that laws of nature don’t hold or that the evidence for them is in anyway flawed. They believe, rather, that an omnipotent God created the entire physical world, including those laws of nature, and can, if He chooses, supersede those laws by the exercise of His omnipotence. Miracles, therefore, presuppose the existence of God. Testimony about the occurrence a miracle might count as good evidence for the existence of God, but as Hume saw, it will always face serious difficulty. For me to take seriously this kind of testimony, it would need to come from very special sources, so e 3 would be very important. Further, I suspect that regardless of the qualities of the source, I would need the corroboration of lots of equally good sources. Finally, I think I would need some independent evidence that God might exist. To see whether such independent evidence available is one of the oldest questions in Western philosophy. If you are curious about using evidence, indeed using inference to the best explanation (IBE), to present arguments for and against the existence of God, I invite you to read my next book, Religious Evidence , or perhaps some of my articles that attempt to apply inference to the best explanation as a means of assessing the quality of evidence we have for the existence of God.3
EXERCISES
- 1. Why do the conventions of normal communication recommend that we assume honesty when someone tells us something?
- 2. Assuming that I was being totally honest in my letter of recommendation, what were the two of worries that one might have that I knew what I was talking about?
- 3. You read the following on a Facebook post: “I just observed a miracle—I saw a dead man restored to life!” Use the tools we have developed in this chapter to assess the quality of evidence you have for the claim that a dead man has been restored to life.
QUIZ NINE
On November 6, 2012, Donald Trump tweeted the following: “The concept of global warming was created by and for the Chinese in order to make U.S. manufacturing non-competitive” (twitter.com/realdonaldtrump/status/265895292191248385?lang=en).4
Use the tools we have developed in this chapter to assess the quality of evidence you have for the claim that global warming is a hoax perpetrated by the Chinese to damage US manufacturing.
Notes
1. Gilbert Harman, “Knowledge, Inference, and Explanation,” American Philosophical Quarterly 5 (1968): 167.
2. David Hume, An Inquiry Concerning Human Understanding , ed. L. A. Selby Bigge (Oxford: Calendon, 1902), 114–16.
3. See Jeff Johnson, “Inference to the Best Explanation and the Problem of Evil,” Journal of Religion 64, no. 1 (1984): 54–72; Jeffery L. Johnson, “Inference to the Best Explanation and the New Teleological Argument,” Southern Journal of Philosophy 31 (1993): 193–203; Jeffery L. Johnson, “Explanation, Evidence, and Mystical Experience,” Minerva—an Internet Journal of Philosophy 5 (2001): 69–93; Jeffery L. Johnson, “From Friendly Atheism to Friendly Natural Theology,” Minerva—an Internet Journal of Philosophy 7 (2003): 125–42; and Jeffery L. Johnson and Joyclynn Potter, “The Argument from Language and the Existence of God,” Journal of Religion 85, no. 1 (January 2005): 83–93.
4. Donald J. Trump (@realDonaldTrump), “The concept of global warming was created by and for the Chinese in order to make U.S. manufacturing non-competitive,” Twitter, November 6, 2012, 11:15 a.m., twitter.com/realdonaldtrump/status/265895292191248385?lang=en.


11.1: Early Indus Valley Civilizations
Indus Valley Civilization
The Indus Valley Civilization was an urban civilization from 3300–1300 BCE that covered most of present-day Pakistan and northwest India.
Draw a timeline of the Early, Mature, and Late Harappan Phases of the Indus Civilization, noting the cultural accomplishments of each
Key Points
- The Indus Valley civilization is often separated into three phases: Early Harappan Phase (3300 BCE–2600 BCE), Mature Harappan Phase (2600 BCE–1900 BCE), and Late Harappan Phase (1900 BCE–1300 BCE).
- Cities of the ancient Indus Valley had multistory brick buildings, employed an advanced sanitation system, and used a unified system of weight and measurement.
- Most inhabitants of Indus Valley cities were artisans, and many artifacts —such as sculptures , seals, pottery, gold, jewelry, elaborate beadwork, and anatomically detailed figurines —have been excavated.
- There is evidence of an extensive trade network used to import raw materials, such as lapis lazuli and steatite , to the Indus Valley from distant regions.
- Between 400 and 600 distinct Indus symbols indicate a language found on ceramics , seals, and tablets, though the language remains entirely unknown to this day.
Key Terms
- lapis lazuli : A relatively rare, intensely blue, semi-precious stone.
- steatite : A stone that contains a large amount of the mineral talc and is easily malleable; also known as soapstone.
- Bronze Age : A period in a civilization’s development when the most advanced metalworking has developed the techniques of smelting copper from natural outcroppings and allows it to be cast in bronze.
Overview: The Indus Valley Civilization
The Indus Valley Civilization was a Bronze Age urban civilization that existed from 3300–1300 BCE and covered most of present-day Pakistan and northwest India. Situated around the Indus River and the Ghaggar-Hakra River, the Indus Valley civilization is also known as the Harappan civilization, named after Harappa, the first city to be excavated in the 1920s.
Inhabitants of the ancient Indus Valley developed new and notable techniques in handicraft, metallurgy , trade and transportation, systems of measurement, and urban planning.
The civilization is often separated into three phases:
- Early Harappan Phase (3300 BCE–2600 BCE).
- Mature Harappan Phase (2600 BCE–1900 BCE).
- Late Harappan Phase (1900 BCE–1300 BCE).
The Mature Harappan phase was the cultural high point, a time by which communities had grown into well-functioning, enormous urban centers. Many more artistic artifacts—such as ceramics, sculptures, seals, and jewelry—have been excavated from this time than from some civilizations that began centuries after its decline.
Numerous architectural remains have been found as well, including multistory buildings, baths, and dockyards. To date, over 1,052 cities and settlements have been found in the general area of the rivers and their tributaries, with the major ones being Harappa, Mohenjo-Daro, Dholavira, Rupar, Lothal, and Kalibangan.
Indus Valley Cities
The cities of the ancient Indus Valley consisted of highly functional, multistory buildings and structures constructed with uniform, kiln-burnt bricks. There is evidence of urban planning due to the uniformity of size and the style of the brickwork, as well as the organization of streets and neighborhoods into grid patterns, much like many current cities.
The first-known sanitation system, whereby waste-water was directed into covered drains that lined major streets and where clean water was obtained from wells in a designated room in the home, was employed in the ancient Indus Valley. This system of sewage and drainage is quite remarkable and was more advanced than some seen even today.
The Indus Valley Civilization is also known for developing a unified system of weight and measurement, as well as a decimal system and the first known use of negative numbers. In 2001, it was discovered that people from the early Harappan period had knowledge of proto-dentistry with the excavation of the first evidence of drilled human teeth.
Art in the Indus Valley
The Indus Valley period is well documented through the wealth of artifacts that were excavated from its magnificent cities. It is widely believed that most of the inhabitants of Indus Valley cities were tradespeople and artisans. Archaeologists have excavated sculptures, seals, pottery, gold jewelry, elaborate beadwork, and anatomically detailed figurines in terracotta , ceramic, bronze, lead, tin, and steatite from the ancient Indus Valley area.
A number of bronze, gold, stone, and terracotta figures of girls in dance poses reveal the presence of some dance forms from the time, and a harp-like instrument depicted on a seal indicates the use of stringed musical instruments.
Similarities in the iconography and construction of excavated artifacts suggest the considerable mobility and trade networks of the Indus Valley inhabitants. Raw materials found only in distant regions, such as lapis lazuli and steatite, were imported for artistic use. It is believed that the trade networks of the Indus Valley reached as far as Afghanistan, coastal Persia, northern and western India, Mesopotamia , and Egypt.
The iconography of the artifacts from the Indus Valley region often depict quite anatomically correct animals and human figures. Similar to other civilizations of the same time period, such as Ancient Egypt and Mesopotamia, there are many depictions of female figures, or possibly fertility goddesses.
One motif shows a horned figure seated in a posture reminiscent of the lotus position and surrounded by animals; this was named Pashaputi (lord of cattle) by excavators. Between 400 and 600 distinct Indus symbols that indicate a language have been found on ceramics, seals, and tablets, though the language remains entirely unknown to this day.
Indus Valley Society
Socially, the Indus Civilization appears to have been relatively egalitarian in nature. All homes within its various cities had access to water and drainage facilities and were generally equal in size. The evidence for planned settlements and the uniformity of Harappan artifacts suggests a strong organizational or governing force in the Indus Valley Civilization, though archaeological records provide no immediate answers.
Around 1800 BCE, signs of decline began to emerge in the Indus River Valley. By 1700 BCE, many of the cities had been abandoned. The reason for the decline of the civilization is unknown, but it is theorized to be due to enemy invasion throughout the area, a change in climate to significantly cooler and drier conditions, or the disappearance of the Ghaggar-Hakra River. After the collapse, regional cultures emerged that continued to show the influence of the Indus Valley Civilization to varying degrees.
Vedic and Upanishadic Periods
The Vedic period in India (c. 1700–500 BCE) is marked by the composition of the Vedas, the oldest scriptures of Hinduism.
Evaluate the crafts and texts found during the Vedic Period in India
Key Points
- The Vedic civilization is thought to have been centered in the northern and northwestern parts of the Indian subcontinent.
- The transmission of stories in the Vedic period was by oral tradition alone, and a literary tradition began only in post-Vedic times.
- Crafts within Vedic culture included chariot-making, cart-making, carpentry, metal-working, tanning, bow-making, sewing, weaving, leather work, pottery, jewelry, dying, and vintnery.
- Pottery in the Vedic period is divided into black- and red-ware culture (BRW, c. 12th to 9th centuries BCE) and painted grey-ware culture (PGW, c. 1200 BCE to 600 BCE).
- The Vedas are a large body of texts that originate in the Vedic period. Composed in Vedic Sanskrit , the texts constitute the oldest layer of Sanskrit literature and are the oldest scriptures of Hinduism . The Upanishads are a collection of philosophical texts that form the theoretical basis for the Hindu religion. All Upanishads are associated with one of the four Vedas—Rigveda, Samaveda, Yajurveda, and Atharvaveda—and have been passed down in oral tradition.
Key Terms
- Sanskrit : A classical language of India (Latin would be its English equivalent), it is a liturgical language of Hinduism, Buddhism, Sikhism, Jainism, and one of the 23 official languages of India.
- Vedic Period : A period in Indian history during which the the oldest scriptures of Hinduism were composed; the time span of the period is uncertain, though is thought to span from 1700 BCE to about 500 BCE.
- Upanishad : An authorless, Hindu, religious and philosophical text considered to be an early source of the religion, it is found mostly as the concluding part of the Brahmanas and in the Aranyakas.
Overview: India’s Vedic Period
The Vedic period (or Vedic age) in India was a period in history during which the Vedas, the oldest scriptures of Hinduism, were composed. The time span of the period is uncertain, though it is thought to span from 1700 BCE to about 500 BCE, with 150 BCE suggested as a terminus ante quem (the latest possible time) for all Vedic Sanskrit literature. The transmission of stories in the Vedic period was by oral tradition alone, and a literary tradition began only in post-Vedic times.
The associated culture, sometimes referred to as the Vedic civilization, was probably centered in the northern and northwestern parts of the Indian subcontinent, but it has now spread and constitutes the basis of contemporary Indian culture. In the 11th century BCE, the Vedic society transitioned from semi-nomadic life to settled agriculture.
This transition led to an increase in trade and increased competition and conflicts over resources, such as land and water. However, after 1000 BCE, the use of iron axes and ploughs enabled the clearing of jungles, and the Vedic kingdoms were able to expand along the Gangetic plains, ushering in the later Vedic age.
By the 6th century BCE, various political units consolidated into large kingdoms called Mahajanapadas. The process of urbanization began in these kingdoms, and commerce and travel—even over regions separated by large distances—became easy.
Sanskrit Literature
The end of Vedic India is marked by linguistic, cultural, and political changes. The grammar of Pāini marks a final apex in the codification of Sutra texts and, at the same time, the beginning of Classical Sanskrit. The invasion of Darius I of the Indus valley in the early 6th century BCE marks the beginning of outside influence that continued in the kingdoms of the Indo–Greeks. After the end of the Vedic period, the Mahajanapadas period in turn gave way to the Maurya Empire (from c. 320 BCE), which is considered to be the golden age of classical Sanskrit literature.
Crafts in the Vedic Period
Crafts within Vedic culture include that of chariot-making, cart-making, carpentry, metal-working (creating instruments such as razors, bangles, and axes), tanning, bow-making, sewing, weaving, and making mats from grass and reeds. Many of these might have required full-time specialists.
The use of iron implements (krishna-ayas or shyama-ayas, literally meaning black metal or dark metal) increased in the later Vedic age, as did new crafts and occupations such as leather work, pottery, astrology, jewelry, dying, and vintnery. Apart from copper, bronze , and gold, later Vedic texts also mention tin, lead, and silver.
The black- and red-ware culture (BRW) is an early, Iron Age culture associated with the post-Rigvedic Vedic civilization that dates roughly from the 12th to 9th centuries BCE. It was succeeded by the painted grey-ware culture (PGW), an Iron Age culture that corresponds to the later Vedic period and that lasted from roughly 1200 BCE to 600 BCE.
Vedic Literature
The Vedas are a large body of texts that originated in the Vedic period. Composed in Vedic Sanskrit, the texts constitute the oldest layer of Sanskrit literature and the oldest scriptures of Hinduism.
The reconstruction of the history of Vedic India is based on text-internal details. Linguistically, the Vedic texts could be classified in five chronological strata:
- The Rigvedic text: The oldest of the Vedas, thought to have been composed roughly between 1700 and 1100 BCE .
- The Mantra language texts: This period includes both the mantra and prose language of the Atharvaveda (Paippalada and Shaunakiya), the Rigveda Khilani, the Samaveda Samhita, and the mantras of the Yajurveda. This is the time of the early Iron Age in northwestern India and corresponds to the black- and red-ware (BRW) culture.
- The Samhita prose texts: This period includes the Brahmana part (commentary on mantras and ritual) of the Black Yajurveda and corresponds with the painted grey-ware (PGW) culture from c. 900 BCE.
- The Brahmana prose texts: The Brahmanas proper of the four Vedas belong to this period, as well as the Aranyakas, the oldest of the Upanishads, and the oldest Shrautasutras.
- The Sutra language texts: This is the last stratum of Vedic Sanskrit leading up to c. 500 BCE, and is comprised of the bulk of the Śrauta and Grhya Sutras, as well as some Upanishads.
The Upanishads are a collection of philosophical texts that form the theoretical basis for the Hindu religion. The Sanskrit term upanishad means sitting down near, implying sitting near a teacher to receive instruction.
Also known as Vedanta, they are considered by orthodox Hindus to contain the revealed truths (Sruti) concerning the nature of ultimate reality (brahman), and describe the character and form of human salvation (moksha).
All Upanishads are associated with one of the four Vedas—Rigveda, Samaveda, Yajurveda, and Atharvaveda—and have been passed down in oral tradition. More than 200 Upanishads are known, and with the Bhagavad Gita and the Brahmasutra, the Mukhya Upanishads provide a foundation for several later schools of Indian philosophy.
Maurya Dynasty
The Maurya Dynasty was an extensive empire that occupied all of northwestern India from 321–185 BCE.
Describe the Barabar Caves, the Pillars of Ashoka, and other examples of architecture and art of the Maurya dynasty
Key Points
- The Maurya Dynasty represents the first time in history that the Indian subcontinent was united under a single government.
- The most renowned emperor of the dynasty, Emperor Ashoka, is famous for propagating the Buddhist religion and preaching non-violence throughout India.
- Emperor Ashoka is responsible for the Pillars of Ashoka, as well as building more than 80,000 stupas .
- The Barabar Caves, the Mahabodhi Temple, and the Great Stupas at Sanchi are examples of the architecture from the Maurya period.
Key Terms
- dynasty : A series of rulers from one family.
- stupa : A dome-shaped Buddhist monument, used to house Buddhist relics.
Overview: The Maurya Dynasty
The Maurya Empire was a powerful Iron Age empire in ancient India ruled by the Maurya Dynasty from 321 to 185 BCE. Founded by Chandragupta Maurya, who overthrew the previous Nanda Dynasty, the empire had fully occupied Northwestern India by 320 BCE.
With an area of 5 million square kilometers and a population of 50 to 60 million, it was the first time in history that the subcontinent was united under a single government. The second emperor of the Maurya Dynasty was the son of Chandragupta, who expanded the empire further but never achieved the same level of notoriety as his own son, Ashoka.
By far the most famous emperor of the Maurya Dynasty, Ahsoka is considered one of the most famous rulers in all of Indian history as well as one of the great Buddhist kings. The decline of the Maurya Dynasty took place somewhat rapidly following the death of Ashoka. Historical theories for this include a succession of weak kings and the division of the Empire in two.
From Hinduism to Buddhism
After the Kalinga war (262–261 BCE), Ashoka converted from Hinduism to Buddhism. He preached non-violence and religious acceptance, and he laid a foundation for social harmony and religious transformation across all of India.
Ashoka also sponsored the propagation of the Buddhist religion into Sri Lanka, Southeast Asia, and Mediterranean Europe. The conversion of Emperor Ashoka to Buddhism legitimized and popularized the religion much like the conversion of Emperor Constantine to Christianity did.
The Pillars of Ashoka
He is famous for ordering that his edicts be carved into stones and caves around the empire and, later, for ordering that his edicts be carved into large sandstone pillars topped with statues of lions, known as the Pillars of Ashoka. These pillars, often exquisitely decorated, are the most widespread example of Mauryan architecture that exists today, with more than 40 spread throughout the Indian subcontinent. The works from this empire represent the earliest surviving remnants of monumental sculpture .
The Barabar Caves and Other Temples
The Barabar Caves are the earliest example of Buddhist rock-cut architecture and were built during the Mauryan period. Attributed to Emperor Ashoka, the caves consist of temples, stupas, and monasteries that are carved elaborately out of granite. The decorated facade of the Lomas Rishi grotto, an offering to the Buddhist sect of the Ajivikas, is a good example of the high degree of craftsmanship.
In addition, Ashoka was responsible for erecting several thousand Buddhist temples and stupas across India, such as the Mahabodhi temple. Another famous example includes the Great Stupas at Sanchi, whose gates are lavishly decorated with lions, elephants, figures of fertility, and images from the Jakata tales. Ashoka’s patronage of the Buddhist religion greatly influenced the visual iconography of time.
- Curation and Revision. Provided by : Boundless.com. License : CC BY-SA: Attribution-ShareAlike
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4.9: Reporting Stockholder Equity
Learning Outcomes
Describe the presentation of stockholder’s equity on the balance sheet and statement of owners’ equity
You have learned that the accounting equation is presented as Assets = Liabilities + Equity. Let us take a closer look at the Equity portion of that equation and how it is presented on the Balance Sheet and the Statement of Owners’ Equity.
Stockholders’ Equity (also known as Shareholders Equity) is an account on a company’s balance sheet that consists of capital plus retained earnings. When the business is not a corporation and therefore has no stockholders, the equity account will be reflected as Owners’ Equity on the balance sheet.
In short, the Equity portion of the accounting equation is the amount left over after liabilities are deducted from assets and represents the residual value of assets minus liabilities. Owner’s or stockholders’ equity also reports the amounts invested into the company by the owners plus the cumulative net income of the company that has not been withdrawn or distributed to the owners. When there are shareholders this distribution comes in the form of dividends. Let’s look at the expanded accounting equation to clarify what constitutes Owners’ or Shareholders’ Equity before we examine its presentation on the Balance Sheet and Statement of Owners’ Equity.
For a corporation with shareholders the accounting equation is:
Assets = Liabilities + Paid-in Capital + Revenues – Expenses – Dividends – Treasury Stock
For a sole proprietorship or a company without shareholders the accounting equation expands to be:
Assets = Liabilities + Owner’s Capital + Revenues – Expenses – Owner’s Draws
As you can see, Equity includes several components regardless of the type of business.
The figure below is an example of how Equity is reported on the Balance Sheet of a corporation when stock has been issued.
| Company A | |||
| Balance Sheet | |||
| Stockholders’ Equity | |||
| Paid in Capital | $ 2,500,000 | ||
| Preferred Stock | $ 2,500,000 | ||
| Common Stock | $ 4,500,000 | ||
| Paid-in capital I excess of par value – preferred | $ 1,550,000 | ||
| Paid-in capital in excess of par – common stock | $ 2,850,000 | ||
| Paid-in capital from treasury stock | $ 952,000 | ||
| Retained Earnings (Revenues – Expenses) | $ 2,458,000 | ||
| Accumulated other comprehensive income | $ 3,525,000 | $ 20,835,000 | |
| Less: Treasury Stock | $ 2,895,000 | ||
| Total stockholder’s equity | $ 17,940,000 |
For a company that has not issued stock and is privately held, the statement of equity on the balance sheet will be presented as follows:
| Company A | |||
| Balance Sheet | |||
| Owner’s Equity | |||
| Beginning owners’ equity | $ 245,000 | ||
| + Owners capital investments | $ 27,000 | ||
| + Gross Revenue | $ 258,000 | ||
| – Expenses | $ 189,000 | ||
| – Owners’ withdrawals | $ 56,000 | ||
| Total Owner’s Equity | $ 285,000 |
What both statements have in common is that they include the net income information from the company’s income statement! Remember, equity is simply the difference between the company’s assets and the liabilities the company has taken out against those assets.
practice questions


4: Geometry
Recall the two paragraphs from Section 1.2 that we intended to spend time making sense of and working through:
Whereas Euclid's approach to geometry was additive (he started with basic definitions and axioms and proceeded to build a sequence of results depending on previous ones), Klein's approach was subtractive. He started with a space and a group of allowable transformations of that space. He then threw out all concepts that did not remain unchanged under these transformations. Geometry, to Klein, is the study of objects and functions that remain unchanged under allowable transformations.
Klein's approach to geometry, called the Erlangen Program after the university at which he worked at the time, has the benefit that all three geometries (Euclidean, hyperbolic and elliptic) emerge as special cases from a general space and a general set of transformations.
We now have both the space (\(\mathbb{C}^+\)) and the transformations (Möbius transformations), and are just about ready to embark on non-Euclidean adventures. Before doing so, however, one more phrase needs defining: group of transformations . This phrase has a precise meaning. Not every collection of transformations is lucky enough to form a group.
-
- 4.1: The Basics
- The reader who has seen group theory will know that in addition to the three properties listed in our definition, the group operation must satisfy a property called associativity. In the context of transformations, the group operation is composition of transformations, and this operation is always associative. So, in the present context of transformations, we omit associativity as a property that needs checking.
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- 4.2: Möbius Geometry
- We spent a fair amount of time studying Möbius transformations in Chapter 3, and this will pay dividends now. We emphasize that angles are preserved in Möbius geometry, which is a good thing. Also, rather than pursuing the very general Möbius geometry, we take the preceeding facts and apply them straight away to two of its special “subgeometries,” hyperbolic geometry and elliptic geometry.


2.20: Current Trends in Food Retail
- Discuss the current trends affecting food retailers
While the growth of channels and competitive outlets has had massive implications over the past twenty years, there are other significant factors influencing food retailing in the United States, including demographic changes, consumer demand for convenience and solutions, and cost pressure.
Specific to demographics, food retailing is being influenced by Baby Boomers, Millennials, and the increasing cultural diversity within the country. This is reflected in the focus on fresh and local foods, the rise of ethnic foods and flavors, the mainstreaming of natural and organic products, nutrition and health credentials, and single-serve and portion control.
The Rise of Healthy Food
In an effort to manage general health, many Baby Boomers have become more focused on diet and the role that food plays in managing wellness. As a result, manufacturers have responded by improving the health credentials of their items. This often manifests in avoidance trends such as sugar-free, fat-free and low-sodium products. For growers, producers, and retailers, this trend has also been reflected in increased consumption of fresh and local foods, primarily produce, but also extended to meat, fish, and poultry.
Millennials have also demanded a focus on fresh and local foods. Their interests lie in both a demand for authenticity and a desire to reduce the environmental impact of commercial food production. This, coupled with higher health credentials, is also at the core of the mainstreaming of natural and organic foods. Boomers and Millennials in particular reflect a belief that natural and organic foods are both “better for you and better for the environment.”
Single Living Through Food
The smaller households of Boomers and Millennials, who have put off life events like marriage, parenthood, and home ownership to later ages, compared with previous generations, mean that large pack sizes do not suit their lifestyles. Instead, these smaller households want a smaller pack size and flexible packaging more suitable for households of 1–3 members. Smaller households also want items that are resealable so they can be put away for a later use.
Diversity in Food
Cultural changes within the country mean that the food and flavor variety the general public demands is broadening. While we can already see some changes to the assortment of products offered, we should expect this diversity to influence the shopping environment as well. For example, a lot of in-store signage and product packaging are evolving to be multi-lingual, dependent upon the demographics of the community. Imagery is also changing to reflect multiple cultures. Retailers and their associates need to understand the customs of different groups within their communities, such as halal or kosher restrictions on food handling.
Retailers are also recognizing positive social changes within the grocery market by targeting customers who value diversity and inclusion. For example, Kroger is leading the way by getting involved in their local community and actively participating in local Pride Parades. In the following video, we’ll see an example of target market techniques with their participation in the Cincinnati, Ohio’s Pride Parade in 2019 and the Unicorn Swirl ice cream product promotion.
You can view the transcript for “Kroger Pride 2019” (opens in new window) .
The Future Is Convenient
Consumers’ demands for convenience and solutions also promise changes to the food retail industry. Of course, this is not new. In fact, these same demands have been at the heart of nearly every innovation we’ve seen in the industry for the past 60+ years. However, the rise of technology, which encourages consumers to be online, engaged, and connected without interruption, has increased what kind of service is possible and elevated expectations.
A few decades ago during the first dotcom bubble, a host of start-ups worked hard to master grocery delivery. More recently, Amazon has raised the stakes, developing a distribution network that promises two-day delivery for most items, including sundries. They are also expanding into grocery delivery. Amazon’s acquisition of Whole Foods in late 2017 sent a very clear message that it was serious about winning in the grocery space.
Amazon is not the only one acquiring companies like Whole Foods. Wal-Mart’s purchased of Jet.com and InstaCart’s partnerships across several retailers also foreshadow that the future of retailing may not include a shopper’s trip to the store. Instead, grocery shopping for the average consumer may include only a mobile app, a stored credit card number, and a delivery charge.
In addition, consumers’ need for solutions has also contributed to the rise of subscription services that offer at-home delivery. Boxed.com delivers an assortment of household items, including groceries. HelloFresh, Blue Apron, and Plated deliver meal kits with pre-measured ingredients and full instructions for at-home preparation. Companies like Munchery go a step further, delivering chilled meals, which can be heated and served. Note, of course, that all these solutions remove a shopping trip and bring the product directly to the consumer’s home. Many consumers are willing to pay a premium for such conveniences.
Home Automation
In addition to increasing online grocery sales, home automation in which appliances can communicate is also impacting the way people shop for food. Already, Amazon Echo is in more than 20 million homes, while Google Home is in more than 4.6 million homes. [1] We are clearly moving toward a world where a replacement can of soup, box of cereal, or gallon of milk requires only “Alexa, order…”
Cost Pressure
Cost pressure and how it relates to labor is also affecting the industry. Wage inflation, while positive for associates, is a real concern. In light of fragmenting channels and the continued rise of online sales, both of which make brick and mortar stores less efficient, higher wages threaten to shift cost structures negatively. Expect continued efforts by large companies to reduce labor costs, either through automation with tools like self-check lanes or through expanded job roles where two associates will do the work of three.
Demographic changes within the country, consumers’ demand for convenience and continued cost pressure, along with continued channel blurring, are the most significant factors facing the food retail industry. Their effects can be seen in everything from the rise of fresh and healthy products to a broadening of ethnic offerings to new grocery delivery initiatives and efforts to control in-store labor costs. These trends promise to influence the industry for years to come.
Contributors and Attributions
- Current Trends in Food Retail. Authored by : Patrick Williams. Provided by : Lumen Learning. License : CC BY: Attribution
- Bell Peppers. Authored by : Ray Bouknight. Provided by : Flickr. Located at : https://flic.kr/p/ejCkLk . License : CC BY: Attribution
- #BENATIVE Intro: how culture shapes communication. Authored by : ANECSYS. Located at : https://vimeo.com/179284437 . License : All Rights Reserved


1.1.6: François-Marie Arouet de Voltaire (1694-1778)
Candide French Age of Reason Voltaire, the pen name for François-Marie Arouet, was born in Paris in 1694 and was an historian, essayist, poet, and playwright. He is considered a major figure in the French Enlightenment, and he was one of the first writers who introduced secular humanism to the French and to the greater European world. His work demonstrates a deep belief that humanity could reach perfection through reason and tolerance. Voltaire took a strong stand against religious and political authorities, a stand which resulted in his imprisonment in the Bastille in 1717 and his exile to England in 1726. While in England, he met Alexander Pope and Jonathan Swift. Voltaire's work contains an overarching theme of individual liberty at a time when the aristocracy refused to share their privileges of freedom of speech and thought; as a Deist and a humanist, he fought against organized religion and the absolute rule of monarchies. Candide (1759) Voltaire's Candide is a satirical novella that chronicles the journey and misadventures of a young man who learns what it means to be a human being in a world filled with evil and destruction. The work is a commentary against the theory of Optimism, a theory that proposes, "Whatever is, is right" (Alexander Pope, An Essay on Man ) and that God has created the best of all worlds. When a massive earthquake destroyed Lisbon in 1755, proponents of Optimism believed it was the will of God, a proposal Voltaire found offensive. Through a series of disasters in Candide —including a storm, a shipwreck, and an earthquake—the protagonist resists the explanations of Dr. Pangloss, the optimistic character who insists that everything in creation happens for a reason. Throughout the journey of the everyman character of Candide, Voltaire uses wit and irony to address universal themes of human suffering, human folly, and the role God plays in human life. Consider while reading:
- Discuss Dr. Pangloss' optimistic remarks at times of disaster in the novella.
- Discuss the rise and fall of the women in the novella.
- Find and analyze two allusions to the bible and/or mythology. As a rational deist, why does Voltaire include such allusions in his satirical work?
Written by Karen Dodson


9: Cell Reproduction
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- 9.0: Introduction
- A human, as well as every sexually reproducing organism, begins life as a fertilized egg (embryo) or zygote. Trillions of cell divisions subsequently occur in a controlled manner to produce a complex, multicellular human. In other words, that original single cell is the ancestor of every other cell in the body. Once a being is fully grown, cell reproduction is still necessary to repair or regenerate tissues.
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- 9.1: Cell Division
- The continuity of life from one cell to another has its foundation in the reproduction of cells by way of the cell cycle. The cell cycle is an orderly sequence of events that describes the stages of a cell’s life from the division of a single parent cell to the production of two new daughter cells. The mechanisms involved in the cell cycle are highly regulated.
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- 9.2: The Cell Cycle
- The cell cycle is an ordered series of events involving cell growth and cell division that produces two new daughter cells. Cells on the path to cell division proceed through a series of precisely timed and carefully regulated stages of growth, DNA replication, and division that produces two identical (clone) cells. The cell cycle has two major phases: interphase and the mitotic phase.
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- 9.3: Control of the Cell Cycle
- The length of the cell cycle is highly variable, even within the cells of a single organism. In humans, the frequency of cell turnover ranges from a few hours in early embryonic development, to an average of two to five days for epithelial cells, and to an entire human lifetime spent in G0 by specialized cells, such as cortical neurons or cardiac muscle cells. There is also variation in the time that a cell spends in each phase of the cell cycle.
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- 9.4: Cancer and the Cell Cycle
- Cancer is the result of unchecked cell division caused by a breakdown of the mechanisms that regulate the cell cycle. The loss of control begins with a change in the DNA sequence of a gene that codes for one of the regulatory molecules. Faulty instructions lead to a protein that does not function as it should. Any disruption of the monitoring system can allow other mistakes to be passed on to the daughter cells. Each successive cell division will give rise to daughter cells with even more damage
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- 9.5: Prokaryotic Cell Division
- In both prokaryotic and eukaryotic cell division, the genomic DNA is replicated and then each copy is allocated into a daughter cell. In addition, the cytoplasmic contents are divided evenly and distributed to the new cells. However, there are many differences between prokaryotic and eukaryotic cell division. Bacteria have a single, circular DNA chromosome but no nucleus. Therefore, mitosis is not necessary in bacterial cell division.
Thumbnail: Life cycle of the cell. (CC BY-SA 4.0; BruceBlaus ).
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Connie Rye (East Mississippi Community College), Robert Wise (University of Wisconsin, Oshkosh), Vladimir Jurukovski (Suffolk County Community College), Jean DeSaix (University of North Carolina at Chapel Hill), Jung Choi (Georgia Institute of Technology), Yael Avissar (Rhode Island College) among other contributing authors. Original content by OpenStax (CC BY 4.0; Download for free at<EMAIL_ADDRESS>).