5.3: Exercises
1. True/False. For each of the following, write T if the statement is true; otherwise, write F. You do NOT need to provide explanations or show work for this problem. Throughout, let \(G\) be a group with identity element \(e\text{.}\)
- If \(G\) is infinite and cyclic, then \(G\) must have infinitely many generators.
- There may be two distinct elements \(a\) and \(b\) of a group \(G\) with \(\langle a\rangle =\langle b\rangle\text{.}\)
- If \(a,b\in G\) and \(a\in \langle b\rangle\) then we must have \(b\in \langle a\rangle\text{.}\)
- If \(a\in G\) with \(a^4=e\text{,}\) then \(o(a)\) must equal \(4\text{.}\)
- If \(G\) is countable then \(G\) must be cyclic.
2. Give examples of the following.
- An infinite noncyclic group \(G\) containing an infinite cyclic subgroup \(H\text{.}\)
- An infinite noncyclic group \(G\) containing a finite nontrivial cyclic subgroup \(H\text{.}\)
- A cyclic group \(G\) containing exactly \(20\) elements.
- A nontrivial cyclic group \(G\) whose elements are all matrices.
- A noncyclic group \(G\) such that every proper subgroup of \(G\) is cyclic.
3. Find the orders of the following elements in the given groups.
- \(2\in \mathbb{Z}\)
- \(-i\in \mathbb{C}^*\)
- \(-I_2\in GL(2,\mathbb{R})\)
- \(-I_2\in \mathbb{M}_2(\mathbb{R})\)
- \((6,8)\in \mathbb{Z}_{10}\times \mathbb{Z}_{10}\)
4. For each of the following, if the group is cyclic, list all of its generators. If the group is not cyclic, write NC.
- \(5\mathbb{Z}\)
- \(\mathbb{Z}_{18}\)
- \(\mathbb{R}\)
- \(\langle \pi\rangle\) in \(\mathbb{R}\)
- \(\mathbb{Z}_2^2\)
- \(\langle 8\rangle\) in \(\mathbb{Q}^*\)
5. Explicitly identify the elements of the following subgroups of the given groups. You may use set-builder notation if the subgroup is infinite, or a conventional name for the subgroup if we have one.
- \(\langle 3\rangle\) in \(\mathbb{Z}\)
- \(\langle i\rangle\) in \(C^*\)
- \(\langle A\rangle\text{,}\) for \(A=\left[ \begin{array}{cc} 1 & 0 \\ 0 & 0 \end{array} \right]\in \mathbb{M}_2(\mathbb{R})\)
- \(\langle (2,3)\rangle\) in \(\mathbb{Z}_4\times \mathbb{Z}_5\)
- \(\langle B\rangle\text{,}\) for \(B=\left[ \begin{array}{cc} 1 & 1\\ 0 & 1 \end{array} \right]\in GL(2,\mathbb{R})\)
6. Draw subgroup lattices for the following groups
- \(\mathbb{Z}_{6}\)
- \(\mathbb{Z}_{13}\)
- \(\mathbb{Z}_{18}\)
7. Let \(G\) be a group with no nontrivial proper subgroups. Prove that \(G\) is cyclic.


23.1: Overview of the Digestive System
Learning Objectives
- Identify the organs of the alimentary canal from proximal to distal, and briefly state their function
- Identify the accessory digestive organs and briefly state their function
- Describe the four fundamental tissue layers of the alimentary canal
- Contrast the contributions of the enteric and autonomic nervous systems to digestive system functioning
- Explain how the peritoneum anchors the digestive organs
The function of the digestive system is to break down the foods you eat, release their nutrients, and absorb those nutrients into the body. Although the small intestine is the workhorse of the system, where the majority of digestion occurs, and where most of the released nutrients are absorbed into the blood or lymph, each of the digestive system organs makes a vital contribution to this process (Figure \(\PageIndex{1}\)).
Figure \(\PageIndex{1}\): Components of the Digestive System. All digestive organs play integral roles in the life-sustaining process of digestion.
As is the case with all body systems, the digestive system does not work in isolation; it functions cooperatively with the other systems of the body. Consider for example, the interrelationship between the digestive and cardiovascular systems. Arteries supply the digestive organs with oxygen and processed nutrients, and veins drain the digestive tract. These intestinal veins, constituting the hepatic portal system, are unique; they do not return blood directly to the heart. Rather, this blood is diverted to the liver where its nutrients are off-loaded for processing before blood completes its circuit back to the heart. At the same time, the digestive system provides nutrients to the heart muscle and vascular tissue to support their functioning. The interrelationship of the digestive and endocrine systems is also critical. Hormones secreted by several endocrine glands, as well as endocrine cells of the pancreas, the stomach, and the small intestine, contribute to the control of digestion and nutrient metabolism. In turn, the digestive system provides the nutrients to fuel endocrine function. Table \(\PageIndex{1}\) gives a quick glimpse at how these other systems contribute to the functioning of the digestive system.
| Body system | Benefits received by the digestive system |
|---|---|
| Cardiovascular | Blood supplies digestive organs with oxygen and processed nutrients |
| Endocrine | Endocrine hormones help regulate secretion in digestive glands and accessory organs |
| Integumentary | Skin helps protect digestive organs and synthesizes vitamin D for calcium absorption |
| Lymphatic | Mucosa-associated lymphoid tissue and other lymphatic tissue defend against entry of pathogens; lacteals absorb lipids; and lymphatic vessels transport lipids to bloodstream |
| Muscular | Skeletal muscles support and protect abdominal organs |
| Nervous | Sensory and motor neurons help regulate secretions and muscle contractions in the digestive tract |
| Respiratory | Respiratory organs provide oxygen and remove carbon dioxide |
| Skeletal | Bones help protect and support digestive organs |
| Urinary | Kidneys convert vitamin D into its active form, allowing calcium absorption in the small intestine |
Digestive System Organs
The easiest way to understand the digestive system is to divide its organs into two main categories. The first group is the organs that make up the alimentary canal. Accessory digestive organs comprise the second group and are critical for orchestrating the breakdown of food and the assimilation of its nutrients into the body. Accessory digestive organs, despite their name, are critical to the function of the digestive system.
Alimentary Canal Organs
Also called the gastrointestinal (GI) tract or gut, the alimentary canal (aliment- = “to nourish”) is a one-way tube about 7.62 meters (25 feet) in length during life and closer to 10.67 meters (35 feet) in length when measured after death, once smooth muscle tone is lost. The main function of the organs of the alimentary canal is to nourish the body. This tube begins at the mouth and terminates at the anus. Between those two points, the canal is modified as the pharynx, esophagus, stomach, and small and large intestines to fit the functional needs of the body. Both the mouth and anus are open to the external environment; thus, food and wastes within the alimentary canal are technically considered to be outside the body. Only through the process of absorption do the nutrients in food enter into and nourish the body’s “inner space.”
Accessory Structures
Each accessory digestive organ aids in the breakdown of food (Figure \(\PageIndex{2}\)). Within the mouth, the teeth and tongue begin mechanical digestion, whereas the salivary glands begin chemical digestion. Once food products enter the small intestine, the gallbladder, liver, and pancreas release secretions—such as bile and enzymes—essential for digestion to continue. Together, these are called accessory organs because they sprout from the lining cells of the developing gut (mucosa) and augment its function; indeed, you could not live without their vital contributions, and many significant diseases result from their malfunction. Even after development is complete, they maintain a connection to the gut by way of ducts.
Histology of the Alimentary Canal
Throughout its length, the alimentary tract is composed of the same four tissue layers; the details of their structural arrangements vary to fit their specific functions. Starting from the lumen and moving outwards, these layers are the mucosa, submucosa, muscularis, and serosa, which is continuous with the mesentery (see Figure \(\PageIndex{2}\)).
Figure \(\PageIndex{2}\): Layers of the Alimentary Canal. The wall of the alimentary canal has four basic tissue layers: the mucosa, submucosa, muscularis, and serosa.
The mucosa is referred to as a mucous membrane, because mucus production is a characteristic feature of gut epithelium. The membrane consists of epithelium, which is in direct contact with ingested food, and the lamina propria, a layer of connective tissue analogous to the dermis. In addition, the mucosa has a thin, smooth muscle layer, called the muscularis mucosa (not to be confused with the muscularis layer, described below).
 In the stomach and intestines, it is a simple columnar epithelium. Notice that the epithelium is in direct contact with the lumen, the space inside the alimentary canal. Interspersed among its epithelial cells are goblet cells, which secrete mucus and fluid into the lumen, and enteroendocrine cells, which secrete hormones into the interstitial spaces between cells. Epithelial cells have a very brief lifespan, averaging from only a couple of days (in the mouth) to about a week (in the gut). This process of rapid renewal helps preserve the health of the alimentary canal, despite the wear and tear resulting from continued contact with foodstuffs.
Lamina propria —In addition to loose connective tissue, the lamina propria contains numerous blood and lymphatic vessels that transport nutrients absorbed through the alimentary canal to other parts of the body. The lamina propria also serves an immune function by housing clusters of lymphocytes, making up the mucosa-associated lymphoid tissue (MALT). These lymphocyte clusters are particularly substantial in the distal ileum where they are known as Peyer’s patches. When you consider that the alimentary canal is exposed to foodborne bacteria and other foreign matter, it is not hard to appreciate why the immune system has evolved a means of defending against the pathogens encountered within it.
Muscularis mucosa —This thin layer of smooth muscle is in a constant state of tension, pulling the mucosa of the stomach and small intestine into undulating folds. These folds dramatically increase the surface area available for digestion and absorption.
As its name implies, the submucosa lies immediately beneath the mucosa. A broad layer of dense connective tissue, it connects the overlying mucosa to the underlying muscularis. It includes blood and lymphatic vessels (which transport absorbed nutrients), and a scattering of submucosal glands that release digestive secretions. Additionally, it serves as a conduit for a dense branching network of nerves, the submucosal plexus, which functions as described below.
The third layer of the alimentary canal is the muscalaris (also called the muscularis externa). The muscularis in the small intestine is made up of a double layer of smooth muscle: an inner circular layer and an outer longitudinal layer. The contractions of these layers promote mechanical digestion, expose more of the food to digestive chemicals, and move the food along the canal.  The basic two-layer structure found in the small intestine is modified in the organs proximal and distal to it. The stomach is equipped for its churning function by the addition of a third layer, the oblique muscle. While the colon has two layers like the small intestine, its longitudinal layer is segregated into three narrow parallel bands, the tenia coli, which make it look like a series of pouches rather than a simple tube.
The serosa is the portion of the alimentary canal superficial to the muscularis. Present only in the region of the alimentary canal within the abdominal cavity, it consists of a layer of visceral peritoneum overlying a layer of loose connective tissue. Instead of serosa, the mouth, pharynx, and esophagus have a dense sheath of collagen fibers called the adventitia. These tissues serve to hold the alimentary canal in place near the ventral surface of the vertebral column.
Nerve Supply
As soon as food enters the mouth, it is detected by receptors that send impulses along the sensory neurons of cranial nerves. Without these nerves, not only would your food be without taste, but you would also be unable to feel either the food or the structures of your mouth, and you would be unable to avoid biting yourself as you chew, an action enabled by the motor branches of cranial nerves.
Intrinsic innervation of much of the alimentary canal is provided by the enteric nervous system, which runs from the esophagus to the anus, and contains approximately 100 million motor, sensory, and interneurons (unique to this system compared to all other parts of the peripheral nervous system). These enteric neurons are grouped into two plexuses. The myenteric plexus (plexus of Auerbach) lies in the muscularis layer of the alimentary canal and is responsible for motility , especially the rhythm and force of the contractions of the muscularis. The submucosal plexus (plexus of Meissner) lies in the submucosal layer and is responsible for regulating digestive secretions and reacting to the presence of food (see Figure \(\PageIndex{2}\)).
Extrinsic innervations of the alimentary canal are provided by the autonomic nervous system, which includes both sympathetic and parasympathetic nerves. In general, sympathetic activation (the fight-or-flight response) restricts the activity of enteric neurons, thereby decreasing GI secretion and motility. In contrast, parasympathetic activation (the rest-and-digest response) increases GI secretion and motility by stimulating neurons of the enteric nervous system.
Blood Supply
The blood vessels serving the digestive system have two functions. They transport the protein and carbohydrate nutrients absorbed by mucosal cells after food is digested in the lumen. Lipids are absorbed via lacteals, tiny structures of the lymphatic system. The blood vessels’ second function is to supply the organs of the alimentary canal with the nutrients and oxygen needed to drive their cellular processes.
Specifically, the more anterior parts of the alimentary canal are supplied with blood by arteries branching off the aortic arch and thoracic aorta. Below this point, the alimentary canal is supplied with blood by arteries branching from the abdominal aorta. The celiac trunk services the liver, stomach, and duodenum, whereas the superior and inferior mesenteric arteries supply blood to the remaining small and large intestines.
The veins that collect nutrient-rich blood from the small intestine (where most absorption occurs) empty into the hepatic portal system. This venous network takes the blood into the liver where the nutrients are either processed or stored for later use. Only then does the blood drained from the alimentary canal viscera circulate back to the heart. To appreciate just how demanding the digestive process is on the cardiovascular system, consider that while you are “resting and digesting,” about one-fourth of the blood pumped with each heartbeat enters arteries serving the intestines.
The Peritoneum
The digestive organs within the abdominal cavity are held in place by the peritoneum, a broad serous membranous sac made up of squamous epithelial tissue surrounded by connective tissue. It is composed of two different regions: the parietal peritoneum, which lines the abdominal wall, and the visceral peritoneum, which envelopes the abdominal organs (Figure \(\PageIndex{3}\)). The peritoneal cavity is the space bounded by the visceral and parietal peritoneal surfaces. A few milliliters of watery fluid act as a lubricant to minimize friction between the serosal surfaces of the peritoneum.
Figure \(\PageIndex{3}\): The Peritoneum. A cross-section of the abdomen shows the relationship between abdominal organs and the peritoneum (darker lines).
DISORDERS OF THE...Digestive System: Peritonitis
Inflammation of the peritoneum is called peritonitis. Chemical peritonitis can develop any time the wall of the alimentary canal is breached, allowing the contents of the lumen entry into the peritoneal cavity. For example, when an ulcer perforates the stomach wall, gastric juices spill into the peritoneal cavity. Hemorrhagic peritonitis occurs after a ruptured tubal pregnancy or traumatic injury to the liver or spleen fills the peritoneal cavity with blood. Even more severe peritonitis is associated with bacterial infections seen with appendicitis, colonic diverticulitis, and pelvic inflammatory disease (infection of uterine tubes, usually by sexually transmitted bacteria). Peritonitis is life threatening and often results in emergency surgery to correct the underlying problem and intensive antibiotic therapy. When your great grandparents and even your parents were young, the mortality from peritonitis was high. Aggressive surgery, improvements in anesthesia safety, the advance of critical care expertise, and antibiotics have greatly improved the mortality rate from this condition. Even so, the mortality rate still ranges from 30 to 40 percent.
The visceral peritoneum includes multiple large folds that envelope various abdominal organs, holding them to the dorsal surface of the body wall. Within these folds are blood vessels, lymphatic vessels, and nerves that innervate the organs with which they are in contact, supplying their adjacent organs. The five major peritoneal folds are described in Table \(\PageIndex{2}\). Note that during fetal development, certain digestive structures, including the first portion of the small intestine (called the duodenum), the pancreas, and portions of the large intestine (the ascending and descending colon, and the rectum) remain completely or partially posterior to the peritoneum. Thus, the location of these organs is described as retroperitoneal .
| Fold | Description |
|---|---|
| Greater omentum | Apron-like structure that lies superficial to the small intestine and transverse colon; a site of fat deposition in people who are overweight |
| Falciform ligament | Anchors the liver to the anterior abdominal wall and inferior border of the diaphragm |
| Lesser omentum | Suspends the stomach from the inferior border of the liver; provides a pathway for structures connecting to the liver |
| Mesentery | Vertical band of tissue anterior to the lumbar vertebrae and anchoring all of the small intestine except the initial portion (the duodenum) |
| Mesocolon | Attaches two portions of the large intestine (the transverse and sigmoid colon) to the posterior abdominal wall |
Chapter Review
The digestive system includes the organs of the alimentary canal and accessory structures. The alimentary canal forms a continuous tube that is open to the outside environment at both ends. The organs of the alimentary canal are the mouth, pharynx, esophagus, stomach, small intestine, and large intestine. The accessory digestive structures include the teeth, tongue, salivary glands, liver, pancreas, and gallbladder. The wall of the alimentary canal is composed of four basic tissue layers: mucosa, submucosa, muscularis, and serosa. The enteric nervous system provides intrinsic innervation, and the autonomic nervous system provides extrinsic innervation.
 Along the way, note how the food changes consistency and form. How does this change in consistency facilitate your gaining nutrients from food?
Answer: Answers may vary.
Review Questions
Q. Which of these organs is not considered an accessory digestive structure?
A. mouth
B. salivary glands
C. pancreas
D. liver
Answer: A
Q. Which of the following organs is supported by a layer of adventitia rather than serosa?
A. esophagus
B. stomach
C. small intestine
D. large intestine
Answer: A
Q. Which of the following membranes covers the stomach?
A. falciform ligament
B. mesocolon
C. parietal peritoneum
D. visceral peritoneum
Answer: D
Critical Thinking Questions
Q. Explain how the enteric nervous system supports the digestive system. What might occur that could result in the autonomic nervous system having a negative impact on digestion?
A. The enteric nervous system helps regulate alimentary canal motility and the secretion of digestive juices, thus facilitating digestion. If a person becomes overly anxious, sympathetic innervation of the alimentary canal is stimulated, which can result in a slowing of digestive activity.
Q. What layer of the alimentary canal tissue is capable of helping to protect the body against disease, and through what mechanism?
A. The lamina propria of the mucosa contains lymphoid tissue that makes up the MALT and responds to pathogens encountered in the alimentary canal.
Glossary
- accessory digestive organ
- includes teeth, tongue, salivary glands, gallbladder, liver, and pancreas
- alimentary canal
- continuous muscular digestive tube that extends from the mouth to the anus
- motility
- movement of food through the GI tract
- mucosa
- innermost lining of the alimentary canal
- muscularis
- muscle (skeletal or smooth) layer of the alimentary canal wall
- myenteric plexus
- (plexus of Auerbach) major nerve supply to alimentary canal wall; controls motility
- retroperitoneal
- located posterior to the peritoneum
- serosa
- outermost layer of the alimentary canal wall present in regions within the abdominal cavity
- submucosa
- layer of dense connective tissue in the alimentary canal wall that binds the overlying mucosa to the underlying muscularis
- submucosal plexus
- (plexus of Meissner) nerve supply that regulates activity of glands and smooth muscle
Contributors
OpenStax Anatomy & Physiology (CC BY 4.0). Access for free at https://openstax.org/books/anatomy-and-physiology


5.4: Exercise- Average Mastoids as the Reference
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For historical reasons, many ERP studies use the mastoid process (the thick bone behind the ear) as the reference electrode. This is why the data shown in Figure 5.1D use the left mastoid as the reference. However, it seems a little odd to use a reference that is lateralized to one side of the head. Might this lead to some kind of hemispheric bias in the data? In reality, this isn’t usually a significant problem. However, just to be safe, many researchers use the average of the left and right mastoids (Lm and Rm) as the reference. In this exercise, we’re going to look at two ways of transforming the data to reference the simulation data to the average of Lm and Rm. This exercise exemplifies an important principle, namely that data recorded using one electrode site as the reference can easily be re-referenced offline, in software, to one of the other electrode sites (or some combination of electrode sites).
Open up the spreadsheet from the previous exercise and make sure everything is back to the way it was originally (or download the spreadsheet again). Make 3 new columns just to the right of the columns for the referenced data, and label them Fz-Avg , Cz-Avg , and Pz-Avg . If you look at how the referencing is done for the Fz channel at the first time point (cell O4 of the spreadsheet), you’ll see that the referenced value is the single-ended value for Fz (cell J4 ) at this time point minus the single-ended value for Lm (cell M4 , but with a “$” symbol before the letter so that it remains column M even if we paste it somewhere else). This is the subtraction that I used to reference the data in Figure 5.1.
We want to change this so that we subtract the average of Lm and Rm from Fz. That average is simply (Lm+Rm)/2 , which would be ($M4+$N4)/2 given that Lm is in column M and Rm is in column N of our spreadsheet. So, to create a value for Fz using the average of Lm and Rm as the reference, we need the equation for the first time point to be =J4-($M4+$N4)/2 . Go ahead and put this equation into cell S4 , which should be in the new column that you labeled Fz-Avg . If you then copy and paste this equation into cells T4 and U4 , the J4 should update to K4 and L4 , respectively. If you then copy and paste these three cells to all the remaining time points, the row numbers should update, and you’ll have the appropriate values for all the cells.
Now compare the new values you created to the original referenced values (with Lm as the reference). They should be pretty similar. This is because the single-ended signal at Rm is nearly identical to the single-ended signal at Lm, so the average of Lm and Rm is nearly identical to the Lm signal. In turn, this is because the weights for Lm and Rm are pretty similar. However, there may be situations in which the Lm and Rm signals are not so similar (e.g., if the generator dipole happened to be near Lm without a generator near Rm). This is why it’s a good idea to use the average of Lm and Rm rather than just using one side.
In most systems, you don’t have access to the single-ended signals, so you wouldn’t be able to use this approach for referencing the data to the average of the two mastoids. For example, the original data might all be referenced to Lm. However, if you have a recording of Rm (also referenced to Lm), there is a trick you can use to re-reference the data to the average of Lm and Rm. The trick was described by Paul Nunez in his classic book on the biophysics of EEG (Nunez, 1981), and the algebra is spelled out in Chapter 5 of Luck (2014). Specifically, if you subtract 50% of the Rm signal from each channel that was already referenced to Lm, this is equivalent to taking the single-ended data from the active electrode and subtracting the average of the single-ended Lm and Rm signals. For example, to re-reference Fz to the average of Lm and Rm, you would take the already-referenced Fz channel (which is really Fz – Lm) and subtract 0.5 of the Rm channel (which is really Rm – Lm).
Create three new columns labeled Fz-Avg2 , Cz-Avg2 , and Pz-Avg2 . Put equations into these columns that use this different approach to re-referencing. That is, take the values that were already referenced (Columns O-R) and subtract 0.5 times the Rm channel from the Fz, Cz, and Pz channels. Once you’ve created these three new channels, compare them with the previous set you created. You should see that these two ways of referencing to the average of Lm create exactly identical results. However, the first method can’t be used in most systems, because it requires access to the single-ended signals, so you may need to use the second method. When you’re working with real data instead of simulated data, you’ll do the referencing in ERPLAB using Channel Operations rather than in a spreadsheet. However, Channel Operations uses equations that are much like the spreadsheet equations. I hope that the experience you’ve now gotten with the spreadsheet will give you a better understanding of how the equations work in Channel Operations.


5.6B: Breakdown of Pyruvate
- Explain why cells break down pyruvate
In order for pyruvate, the product of glycolysis, to enter the next pathway, it must undergo several changes to become acetyl Coenzyme A (acetyl CoA). Acetyl CoA is a molecule that is further converted to oxaloacetate, which enters the citric acid cycle (Krebs cycle). The conversion of pyruvate to acetyl CoA is a three-step process.
Step 1 . A carboxyl group is removed from pyruvate, releasing a molecule of carbon dioxide into the surrounding medium. (Note: carbon dioxide is one carbon attached to two oxygen atoms and is one of the major end products of cellular respiration. ) The result of this step is a two-carbon hydroxyethyl group bound to the enzyme pyruvate dehydrogenase; the lost carbon dioxide is the first of the six carbons from the original glucose molecule to be removed. This step proceeds twice for every molecule of glucose metabolized (remember: there are two pyruvate molecules produced at the end of glycolysis); thus, two of the six carbons will have been removed at the end of both of these steps.
Step 2 . The hydroxyethyl group is oxidized to an acetyl group, and the electrons are picked up by NAD + , forming NADH (the reduced form of NAD+). The high- energy electrons from NADH will be used later by the cell to generate ATP for energy.
Step 3 . The enzyme-bound acetyl group is transferred to CoA, producing a molecule of acetyl CoA. This molecule of acetyl CoA is then further converted to be used in the next pathway of metabolism, the citric acid cycle.
Key Points
- In the conversion of pyruvate to acetyl CoA, each pyruvate molecule loses one carbon atom with the release of carbon dioxide.
- During the breakdown of pyruvate, electrons are transferred to NAD+ to produce NADH, which will be used by the cell to produce ATP.
- In the final step of the breakdown of pyruvate, an acetyl group is transferred to Coenzyme A to produce acetyl CoA.
Key Terms
- acetyl CoA : a molecule that conveys the carbon atoms from glycolysis (pyruvate) to the citric acid cycle to be oxidized for energy production


15.6: Moving points to infinity
Theorem 15.5.1 makes it possible to take any line in the projective plane and declare it to be ideal. In other words, we can choose a preferred affine plane by removing one line from the projective plane. This construction provides a method for solving problems in projective geometry which will be illustrated by the following classical example:
Desargues’ theorem [thm:desargues] Consider three concurrent lines \((AA')\) , \((BB')\) , and \((CC')\) in the real projective plane. Set
\(\begin{aligned} X&=(BC)\cap (B'C'),\\ Y&=(CA)\cap (C'A'),\\ Z&=(AB)\cap (A'B').\end{aligned}\)
Then the points \(X\) , \(Y\) , and \(Z\) are collinear.
- Proof
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Without loss of generality, we may assume that the line \((XY)\) is ideal. If not, apply a perspective projection that sends the line \((XY)\) to the ideal line.
That is, we can assume that
\((BC) \parallel (B'C')\ \ \ \ \text{and} \ \ \ \ (CA) \parallel (C'A')\)
and we need to show that
\((AB) \parallel(A'B').\)
Assume that the lines \((AA')\) , \((BB')\) , and \((CC')\) intersect at point \(O\) . Since \((BC) \parallel (B'C')\) , the transversal property ( Theorem 7.3.1 ) implies that \(\measuredangle OBC = \measuredangle OB'C'\) and \(\measuredangle OCB = \measuredangle OC'B'\) . By the AA similarity condition, \(\triangle OBC\z\sim\triangle OB'C'\) . In particular,
\(\dfrac{OB}{OB'}=\dfrac{OC}{OC'}.\)
The same way we get that \(\triangle OAC \sim\triangle OA'C'\) and
Therefore,
By the SAS similarity condition, we get that \(\triangle OAB\sim\triangle OA'B'\) ; in particular, \(\measuredangle OAB = \pm\measuredangle OA'B'\) .
Note that \(\measuredangle AOB=\measuredangle A'OB'\) . Therefore,
By the transversal property ( Theorem 7.3.1 ), we have \((AB)\parallel (A'B')\) .
The case \((AA') \parallel (BB') \parallel (CC')\) is done similarly. In this case the quadrangles \(B'BCC'\) and \(A'ACC'\) are parallelograms. Therefore,
\(BB'=CC'=AA'.\)
Hence \(\square B'BAA'\) is a parallelogram and \((AB)\parallel (A'B')\) .
Here is another classical theorem of projective geometry.
Assume that two triples of points \(A\) , \(B\) , \(C\) , and \(A'\) , \(B'\) , \(C'\) are collinear. Suppose that points \(X\) , \(Y\) , \(Z\) are uniquely defined by
\(X = (BC') \cap (B'C)\), \(Y = (CA') \cap (C'A)\), \(Z = (AB') \cap (A'B).\)
Then the points \(X\) , \(Y\) , \(Z\) are collinear.
Pappus’ theorem can be proved the same way as Desargues’ theorem.
- Idea of the Proof
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Applying a perspective projection, we can assume that \(Y\) and \(Z\) lie on the ideal line. It remains to show that \(X\) lies on the ideal line.
In other words, assuming that \((AB') \parallel (A'B)\) and \((AC') \parallel (A'C)\) , we need to show that \((BC') \parallel(B'C)\) .
Finish the proof of Pappus’ theorem using the idea described above.
- Hint
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Assume that \((AB)\) meets \((A'B')\) at \(O\). Since \((AB') \parallel (BA')\), we get that \(\triangle OAB' \sim \triangle OBA'\) and \(\dfrac{OA}{OB} = \dfrac{OB'}{OA'}\).
Similarly, since \((AC') \parallel (CA')\), we get that \(\dfrac{OA}{OC} = \dfrac{OC'}{OA'}\).
Therefore \(\dfrac{OB}{OC} = \dfrac{OC'}{OB'}\). Applying the SAS similarity condition, we get that \(\triangle OBC' \sim \triangle OCB'\). Therefore, \((BC') \parallel (CB')\).
The case \((AB) \parallel (A'B')\) is similar.
The following exercise gives a partial converse to Pappus’ theorem.
Given two triples of points \(A\) , \(B\) , \(C\) , and \(A'\) , \(B'\) , \(C'\) , suppose distinct points \(X\) , \(Y\) , \(Z\) are uniquely defined by
\(\begin{aligned} X&=(BC')\cap(B'C), & Y&=(CA')\cap(C'A), & Z&=(AB')\cap(A'B).\end{aligned}\)
Assume that the triples \(A\) , \(B\) , \(C\) , and \(X\) , \(Y\) , \(Z\) are collinear. Show that the triple \(A'\) , \(B'\) , \(C'\) is collinear.
- Hint
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Observe that the statement is equivalent to Pappus’ theorem.
Solve the following construction problem
- using Desargues’ theorem;
- using Pappus’ theorem.
- Hint
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To do (a), suppose that the parallelogram is formed by the two pairs of parallel lines \((AB) \parallel (A'B')\) and \((BC) \parallel (B'C')\) and \(\ell = (AC)\) in the notation of Desargues' theorem (Theorem \(\PageIndex{1}\))
To do (b), suppose that the parallelogram is formed by the two pairs of parallelogram is formed by the two pairs of parallel lines \((AB') \parallel (A'B')\) and \((BC') \parallel (B'C)\) and \(\ell = (AC')\) in the notation of Pappus' theorem (Theorem \(\PageIndex{2}\)).
Suppose a parallelogram and a line \(\ell\) are given. Assume the line \(\ell\) crosses all sides (or their extensions) of the parallelogram at different points are given. Construct another line parallel to \(\ell\) with a ruler only.


5.12: Electric Potential Field Due to Point Charges
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The electric field intensity due to a point charge \(q\) at the origin is (see Section 5.1 or 5.5)
\[{\bf E} = \hat{\bf r}\frac{q}{4\pi\epsilon r^2} \label{eEPPCE} \]
In Sections 5.8 and 5.9, it was determined that the potential difference measured from position \({\bf r}_1\) to position \({\bf r}_2\) is
\[V _ { 21 } = - \int _ { \mathbf { r } _ { 1 } } ^ { \mathbf { r } _ { 2 } } \mathbf { E } \cdot d \mathbf { l } \label{m0064_eV12} \]
This method for calculating potential difference is often a bit awkward. To see why, consider an example from circuit theory, shown in Figure \(\PageIndex{1}\). In this example, consisting of a single resistor and a ground node, we’ve identified four quantities:
- The resistance \(R\)
- The current \(I\) through the resistor
- The node voltage \(V_1\), which is the potential difference measured from ground to the left side of the resistor
- The node voltage \(V_2\), which is the potential difference measured from ground to the right side of the resistor
Let’s say we wish to calculate the potential difference \(V_{21}\) across the resistor. There are two ways this can be done:
- \(V_{21}=-IR\)
- \(V_{21}=V_2-V_1\)
The advantage of the second method is that it is not necessary to know \(I\), \(R\), or indeed anything about what is happening between the nodes; it is only necessary to know the node voltages. The point is that it is often convenient to have a common datum – in this example, ground – with respect to which the potential differences at all other locations of interest can be defined. When we have this, calculating potential differences reduced to simply subtracting predetermined node potentials.
Figure \(\PageIndex{1}\): A resistor in a larger circuit, used as an example to demonstrate the concept of node voltages. ( CC BY SA 4.0 ; K. Kikkeri).So, can we establish a datum in general electrostatic problems that works the same way? The answer is yes. The datum is arbitrarily chosen to be a sphere that encompasses the universe; i.e., a sphere with radius \(\to\infty\). Employing this choice of datum, we can use Equation \ref{m0064_eV12} to define \(V({\bf r})\), the potential at point \({\bf r}\), as follows:
\[\boxed{ V({\bf r}) \triangleq - \int_{\infty}^{\bf r} {\bf E} \cdot d{\bf l} } \label{m0064_eVP} \]
The electrical potential at a point, given by Equation \ref{m0064_eVP}, is defined as the potential difference measured beginning at a sphere of infinite radius and ending at the point \({\bf r}\). The potential obtained in this manner is with respect to the potential infinitely far away.
In the particular case where \({\bf E}\) is due to the point charge at the origin:
\[V({\bf r}) = - \int_{\infty}^{\bf r} \left[ \hat{\bf r}\frac{q}{4\pi\epsilon r^2} \right] \cdot d{\bf l} \nonumber \]
The principle of independence of path (Section 5.9) asserts that the path of integration doesn’t matter as long as the path begins at the datum at infinity and ends at \({\bf r}\). So, we should choose the easiest such path. The radial symmetry of the problem indicates that the easiest path will be a line of constant \(\theta\) and \(\phi\), so we choose \(d{\bf l}=\hat{\bf r}dr\). Continuing:
\begin{aligned}
V(\mathbf{r}) &=-\int_{\infty}^{r}\left[\hat{\mathbf{r}} \frac{q}{4 \pi \epsilon r^{2}}\right] \cdot[\hat{\mathbf{r}} d r] \\
&=-\frac{q}{4 \pi \epsilon} \int_{\infty}^{r} \frac{1}{r^{2}} d r \\
&=+\left.\frac{q}{4 \pi \epsilon} \frac{1}{r}\right|_{\infty} ^{r}
\end{aligned}
so
\[\boxed{ V({\bf r}) = + \frac{q}{4\pi\epsilon r} } \label{m0064_eV} \]
(Suggestion: Confirm that Equation \ref{m0064_eV} is dimensionally correct.) In the context of the circuit theory example above, this is the “node voltage” at \({\bf r}\) when the datum is defined to be the surface of a sphere at infinity. Subsequently, we may calculate the potential difference from any point \({\bf r}_1\) to any other point \({\bf r}_2\) as \[V_{21} = V({\bf r}_2)-V({\bf r}_1) \nonumber \] and that will typically be a lot easier than using Equation \ref{m0064_eV12}.
It is not often that one deals with systems consisting of a single charged particle. So, for the above technique to be truly useful, we need a straightforward way to determine the potential field \(V({\bf r})\) for arbitrary distributions of charge. The first step in developing a more general expression is to determine the result for a particle located at a point \({\bf r}'\) somewhere other than the origin. Since Equation \ref{m0064_eV} depends only on charge and the distance between the field point \({\bf r}\) and \({\bf r}'\), we have
\[V({\bf r};{\bf r}') \triangleq + \frac{q'}{4\pi\epsilon \left|{\bf r}-{\bf r}'\right|} \label{m0064_eVd} \]
where, for notational consistency, we use the symbol \(q'\) to indicate the charge. Now applying superposition, the potential field due to \(N\) charges is
\[V({\bf r}) = \sum_{n=1}^N { V({\bf r};{\bf r}_n) } \nonumber \]
Substituting Equation \ref{m0064_eVd} we obtain:
\[\boxed{ V({\bf r}) = \frac{1}{4\pi\epsilon} \sum_{n=1}^N { \frac{q_n}{\left|{\bf r}-{\bf r}_n\right|} } } \label{m0064_eVN} \]
Equation \ref{m0064_eVN} gives the electric potential at a specified location due to a finite number of charged particles.
The potential field due to continuous distributions of charge is addressed in Section 5.13.


12.6: Plea Agreements
In the United States, the vast majority of criminal justice caseAs are handled through the plea agreement process. After the defendant is arraigned, further hearings are set including an opportunity to resolve the case through a plea agreement. This process is usually negotiated in private, and out of view of the public and even the defendant. The prosecution, defense counsel, and a judge will often meet to determine if a resolution can be met. The district attorney will often agree to a reduction in the charges or offense if the defendant agrees to plead early and avoid a lengthy trial. The benefit to the defendant is they will often be able to serve a reduced sentence or potential credit for time served and immediate release onto community supervision (probation or parole). This is a big incentive, especially for those defendants who were not able to afford bail and are in jail pending the trial process. Some criticize this process and indicate defendants who may be innocent will accept the plea agreement, especially if offered credit for time served. However, the defendant may not understand all of the consequences that come from a guilty plea. If the crime was a felony, these have long-term consequences which include impacts on their employment, housing, voting rights, and the ability to possess a firearm. Additionally, if placed on community supervision, if they violate probation, they could be sentenced to prison and have no right to dispute the offense as they already plead guilty.


28.1: Einstein’s Postulates
Learning Objectives
By the end of this section, you will be able to:
- State and explain both of Einstein’s postulates.
- Explain what an inertial frame of reference is.
- Describe one way the speed of light can be changed
Have you ever used the Pythagorean Theorem and gotten a wrong answer? Probably not, unless you made a mistake in either your algebra or your arithmetic. Each time you perform the same calculation, you know that the answer will be the same. Trigonometry is reliable because of the certainty that one part always flows from another in a logical way. Each part is based on a set of postulates, and you can always connect the parts by applying those postulates. Physics is the same way with the exception that all parts must describe nature. If we are careful to choose the correct postulates, then our theory will follow and will be verified by experiment.
Einstein essentially did the theoretical aspect of this method for relativity . With two deceptively simple postulates and a careful consideration of how measurements are made, he produced the theory of special relativity.
Einstein’s First Postulate
The first postulate upon which Einstein based the theory of special relativity relates to reference frames. All velocities are measured relative to some frame of reference. For example, a car’s motion is measured relative to its starting point or the road it is moving over, a projectile’s motion is measured relative to the surface it was launched from, and a planet’s orbit is measured relative to the star it is orbiting around. The simplest frames of reference are those that are not accelerated and are not rotating. Newton’s first law, the law of inertia, holds exactly in such a frame.
Definition: Inertial Reference Frame
An inertial frame of reference is a reference frame in which a body at rest remains at rest and a body in motion moves at a constant speed in a straight line unless acted on by an outside force.
The laws of physics seem to be simplest in inertial frames. For example, when you are in a plane flying at a constant altitude and speed, physics seems to work exactly the same as if you were standing on the surface of the Earth. However, in a plane that is taking off, matters are somewhat more complicated. In these cases, the net force on an object, \(F\), is not equal to the product of mass and acceleration, \(ma\). Instead, \(F\) is equal to \(ma\) plus a fictitious force. This situation is not as simple as in an inertial frame. Not only are laws of physics simplest in inertial frames, but they should be the same in all inertial frames, since there is no preferred frame and no absolute motion. Einstein incorporated these ideas into his first postulate of special relativity .
First Postulate of Special Relativity
The laws of physics are the same and can be stated in their simplest form in all inertial frames of reference.
As with many fundamental statements, there is more to this postulate than meets the eye. The laws of physics include only those that satisfy this postulate. We shall find that the definitions of relativistic momentum and energy must be altered to fit. Another outcome of this postulate is the famous equation \(E = mc^{2}\).
Einstein’s Second Postulate
The second postulate upon which Einstein based his theory of special relativity deals with the speed of light. Late in the 19th century, the major tenets of classical physics were well established. Two of the most important were the laws of electricity and magnetism and Newton’s laws. In particular, the laws of electricity and magnetism predict that light travels at \(c = 3.00 \times 10^{8} m/s\) in a vacuum, but they do not specify the frame of reference in which light has this speed.
There was a contradiction between this prediction and Newton’s laws, in which velocities add like simple vectors. If the latter were true, then two observers moving at different speeds would see light traveling at different speeds. Imagine what a light wave would look like to a person traveling along with it at a speed \(c\). If such a motion were possible then the wave would be stationary relative to the observer. It would have electric and magnetic fields that varied in strength at various distances from the observer but were constant in time. This is not allowed by Maxwell’s equations. So either Maxwell’s equations are wrong, or an object with mass cannot travel at speed \(c\). Einstein concluded that the latter is true. An object with mass cannot travel at speed \(c\). This conclusion implies that light in a vacuum must always travel at speed \(c\) relative to any observer. Maxwell’s equations are correct, and Newton’s addition of velocities is not correct for light.
Investigations such as Young’s double slit experiment in the early-1800s had convincingly demonstrated that light is a wave. Many types of waves were known, and all travelled in some medium. Scientists therefore assumed that a medium carried light, even in a vacuum, and light travelled at a speed \(c\) relative to that medium. Starting in the mid-1880s, the American physicist A. A. Michelson, later aided by E. W. Morley, made a series of direct measurements of the speed of light. The results of their measurements were startling.
Michelson-Morley Experiment
The Michelson-Morley experiment demonstrated that the speed of light in a vacuum is independent of the motion of the Earth about the Sun.
The eventual conclusion derived from this result is that light, unlike mechanical waves such as sound, does not need a medium to carry it. Furthermore, the Michelson-Morley results implied that the speed of light \(c\) is independent of the motion of the source relative to the observer. That is, everyone observes light to move at speed \(c\) regardless of how they move relative to the source or one another. For a number of years, many scientists tried unsuccessfully to explain these results and still retain the general applicability of Newton’s laws.
It was not until 1905, when Einstein published his first paper on special relativity, that the currently accepted conclusion was reached. Based mostly on his analysis that the laws of electricity and magnetism would not allow another speed for light, and only slightly aware of the Michelson-Morley experiment, Einstein detailed his second postulate of special relativity .
Second Postulate of Special Relativity
The speed of light \(c\) is a constant, independent of the relative motion of the source.
Deceptively simple and counterintuitive, this and the first postulate leave all else open for change. Some fundamental concepts do change. Among the changes are the loss of agreement on the elapsed time for an event, the variation of distance with speed, and the realization that matter and energy can be converted into one another. You will read about these concepts in the following sections.
Misconception Alert: Constancy of the Speed of Light
The speed of light is a constant \(c = 3.00 \times 10^{8} m/s\) in a vacuum. If you remember the effect of the index of refraction from The Law of Refraction , the speed of light is lower in matter.
Exercise \(\PageIndex{1}\)
Explain how special relativity differs from general relativity.
- Answer
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Special relativity applies only to unaccelerated motion, but general relativity applies to accelerated motion.
Summary
- Relativity is the study of how different observers measure the same event.
- Modern relativity is divided into two parts. Special relativity deals with observers who are in uniform (unaccelerated) motion, whereas general relativity includes accelerated relative motion and gravity. Modern relativity is correct in all circumstances and, in the limit of low velocity and weak gravitation, gives the same predictions as classical relativity.
- An inertial frame of reference is a reference frame in which a body at rest remains at rest and a body in motion moves at a constant speed in a straight line unless acted on by an outside force.
- Modern relativity is based on Einstein’s two postulates. The first postulate of special relativity is the idea that the laws of physics are the same and can be stated in their simplest form in all inertial frames of reference. The second postulate of special relativity is the idea that the speed of light \(c\) is a constant, independent of the relative motion of the source.
- The Michelson-Morley experiment demonstrated that the speed of light in a vacuum is independent of the motion of the Earth about the Sun.
Glossary
- relativity
- the study of how different observers measure the same event
- special relativity
- the theory that, in an inertial frame of reference, the motion of an object is relative to the frame from which it is viewed or measured
- inertial frame of reference
- a reference frame in which a body at rest remains at rest and a body in motion moves at a constant speed in a straight line unless acted on by an outside force
- first postulate of special relativity
- the idea that the laws of physics are the same and can be stated in their simplest form in all inertial frames of reference
- second postulate of special relativity
- the idea that the speed of light \(c\) is a constant, independent of the source
- Michelson-Morley experiment
- an investigation performed in 1887 that proved that the speed of light in a vacuum is the same in all frames of reference from which it is viewed


2.5: Inorganic Compounds Essential to Human Functioning
By the end of this section, you will be able to:
- Compare and contrast inorganic and organic compounds
- Identify the properties of water that make it essential to life
- Explain the role of salts in body functioning
- Distinguish between acids and bases, and explain their role in pH
- Discuss the role of buffers in helping the body maintain pH homeostasis
The concepts you have learned so far in this chapter govern all forms of matter, and would work as a foundation for geology as well as biology. This section of the chapter narrows the focus to the chemistry of human life; that is, the compounds important for the body’s structure and function. In general, these compounds are either inorganic or organic.
- An inorganic compound is a substance that does not contain both carbon and hydrogen. A great many inorganic compounds do contain hydrogen atoms, such as water (H 2 O) and the hydrochloric acid (HCl) produced by your stomach. In contrast, only a handful of inorganic compounds contain carbon atoms. Carbon dioxide (CO 2 ) is one of the few examples.
- An organic compound , then, is a substance that contains both carbon and hydrogen. Organic compounds are synthesized via covalent bonds within living organisms, including the human body. Recall that carbon and hydrogen are the second and third most abundant elements in your body. You will soon discover how these two elements combine in the foods you eat, in the compounds that make up your body structure, and in the chemicals that fuel your functioning.
The following section examines the three groups of inorganic compounds essential to life: water, salts, acids, and bases. Organic compounds are covered later in the chapter.
Water
As much as 70 percent of an adult’s body weight is water. This water is contained both within the cells and between the cells that make up tissues and organs. Its several roles make water indispensable to human functioning.
Water as a Lubricant and Cushion
Water is a major component of many of the body’s lubricating fluids. Just as oil lubricates the hinge on a door, water in synovial fluid lubricates the actions of body joints, and water in pleural fluid helps the lungs expand and recoil with breathing. Watery fluids help keep food flowing through the digestive tract, and ensure that the movement of adjacent abdominal organs is friction free.
Water also protects cells and organs from physical trauma, cushioning the brain within the skull, for example, and protecting the delicate nerve tissue of the eyes. Water cushions a developing fetus in the mother’s womb as well.
Water as a Heat Sink
A heat sink is a substance or object that absorbs and dissipates heat but does not experience a corresponding increase in temperature. In the body, water absorbs the heat generated by chemical reactions without greatly increasing in temperature. Moreover, when the environmental temperature soars, the water stored in the body helps keep the body cool. This cooling effect happens as warm blood from the body’s core flows to the blood vessels just under the skin and is transferred to the environment. At the same time, sweat glands release warm water in sweat. As the water evaporates into the air, it carries away heat, and then the cooler blood from the periphery circulates back to the body core.
Water as a Component of Liquid Mixtures
A mixture is a combination of two or more substances, each of which maintains its own chemical identity. In other words, the constituent substances are not chemically bonded into a new, larger chemical compound. The concept is easy to imagine if you think of powdery substances such as flour and sugar; when you stir them together in a bowl, they obviously do not bond to form a new compound. The room air you breathe is a gaseous mixture, containing three discrete elements—nitrogen, oxygen, and argon—and one compound, carbon dioxide. There are three types of liquid mixtures, all of which contain water as a key component. These are solutions, colloids, and suspensions.
For cells in the body to survive, they must be kept moist in a water-based liquid called a solution. In chemistry, a liquid solution consists of a solvent that dissolves a substance called a solute. An important characteristic of solutions is that they are homogeneous; that is, the solute molecules are distributed evenly throughout the solution. If you were to stir a teaspoon of sugar into a glass of water, the sugar would dissolve into sugar molecules separated by water molecules. The ratio of sugar to water in the left side of the glass would be the same as the ratio of sugar to water in the right side of the glass. If you were to add more sugar, the ratio of sugar to water would change, but the distribution—provided you had stirred well—would still be even.
Water is considered the “universal solvent” and it is believed that life cannot exist without water because of this. Water is certainly the most abundant solvent in the body; essentially all of the body’s chemical reactions occur among compounds dissolved in water. Because water molecules are polar, with regions of positive and negative electrical charge, water readily dissolves ionic compounds and polar covalent compounds. Such compounds are referred to as hydrophilic, or “water-loving.” As mentioned above, sugar dissolves well in water. This is because sugar molecules contain regions of hydrogen-oxygen polar bonds, making it hydrophilic. Nonpolar molecules, which do not readily dissolve in water, are called hydrophobic, or “water-fearing.”
Concentrations of Solutes
Various mixtures of solutes and water are described in chemistry. The concentration of a given solute is the number of particles of that solute in a given space (oxygen makes up about 21 percent of atmospheric air). In the bloodstream of humans, glucose concentration is usually measured in milligram (mg) per deciliter (dL), and in a healthy adult averages about 100 mg/dL. Another method of measuring the concentration of a solute is by its molarity—which is moles (M) of the molecules per liter (L). The mole of an element is its atomic weight, while a mole of a compound is the sum of the atomic weights of its components, called the molecular weight. An often-used example is calculating a mole of glucose, with the chemical formula C 6 H 12 O 6 . Using the periodic table, the atomic weight of carbon (C) is 12.011 grams (g), and there are six carbons in glucose, for a total atomic weight of 72.066 g. Doing the same calculations for hydrogen (H) and oxygen (O), the molecular weight equals 180.156g (the “gram molecular weight” of glucose). When water is added to make one liter of solution, you have one mole (1M) of glucose. This is particularly useful in chemistry because of the relationship of moles to “Avogadro’s number.” A mole of any solution has the same number of particles in it: 6.02 × 10 23 . Many substances in the bloodstream and other tissue of the body are measured in thousandths of a mole, or millimoles (mM).
A colloid is a mixture that is somewhat like a heavy solution. The solute particles consist of tiny clumps of molecules large enough to make the liquid mixture opaque (because the particles are large enough to scatter light). Familiar examples of colloids are milk and cream. In the thyroid glands, the thyroid hormone is stored as a thick protein mixture also called a colloid.
A suspension is a liquid mixture in which a heavier substance is suspended temporarily in a liquid, but over time, settles out. This separation of particles from a suspension is called sedimentation. An example of sedimentation occurs in the blood test that establishes sedimentation rate, or sed rate. The test measures how quickly red blood cells in a test tube settle out of the watery portion of blood (known as plasma) over a set period of time. Rapid sedimentation of blood cells does not normally happen in the healthy body, but aspects of certain diseases can cause blood cells to clump together, and these heavy clumps of blood cells settle to the bottom of the test tube more quickly than do normal blood cells.
The Role of Water in Chemical Reactions
Two types of chemical reactions involve the creation or the consumption of water: dehydration synthesis and hydrolysis.
- In dehydration synthesis, one reactant gives up an atom of hydrogen and another reactant gives up a hydroxyl group (OH) in the synthesis of a new product. In the formation of their covalent bond, a molecule of water is released as a byproduct ((\PageIndex{1}\)). This is also sometimes referred to as a condensation reaction.
-
These reactions are reversible, and play an important role in the chemistry of organic compounds (which will be discussed shortly).
Salts
Recall that salts are formed when ions form ionic bonds. In these reactions, one atom gives up one or more electrons, and thus becomes positively charged, whereas the other accepts one or more electrons and becomes negatively charged. You can now define a salt as a substance that, when dissolved in water, dissociates into ions other than H + or OH – . This fact is important in distinguishing salts from acids and bases, discussed next.
A typical salt, NaCl, dissociates completely in water ((\PageIndex{2}\)). The positive and negative regions on the water molecule (the hydrogen and oxygen ends respectively) attract the negative chloride and positive sodium ions, pulling them away from each other. Again, whereas nonpolar and polar covalently bonded compounds break apart into molecules in solution, salts dissociate into ions. These ions are electrolytes; they are capable of conducting an electrical current in solution. This property is critical to the function of ions in transmitting nerve impulses and prompting muscle contraction.
Many other salts are important in the body. For example, bile salts produced by the liver help break apart dietary fats, and calcium phosphate salts form the mineral portion of teeth and bones.
Acids and Bases
Acids and bases, like salts, dissociate in water into electrolytes. Acids and bases can very much change the properties of the solutions in which they are dissolved.
Acids
An acid is a substance that releases hydrogen ions (H + ) in solution (Figure (\PageIndex{3}\) a ). Because an atom of hydrogen has just one proton and one electron, a positively charged hydrogen ion is simply a proton. This solitary proton is highly likely to participate in chemical reactions. Strong acids are compounds that release all of their H + in solution; that is, they ionize completely. Hydrochloric acid (HCl), which is released from cells in the lining of the stomach, is a strong acid because it releases all of its H + in the stomach’s watery environment. This strong acid aids in digestion and kills ingested microbes. Weak acids do not ionize completely; that is, some of their hydrogen ions remain bonded within a compound in solution. An example of a weak acid is vinegar, or acetic acid; it is called acetate after it gives up a proton.
Bases
A base is a substance that releases hydroxyl ions (OH – ) in solution, or one that accepts H + already present in solution (see Figure 2.16 b ). The hydroxyl ions (also known as hydroxide ions) or other basic substances combine with H + present to form a water molecule, thereby removing H + and reducing the solution’s acidity. Strong bases release most or all of their hydroxyl ions; weak bases release only some hydroxyl ions or absorb only a few H + . Food mixed with hydrochloric acid from the stomach would burn the small intestine, the next portion of the digestive tract after the stomach, if it were not for the release of bicarbonate (HCO 3 – ), a weak base that attracts H + . Bicarbonate accepts some of the H + protons, thereby reducing the acidity of the solution.
The Concept of pH
The relative acidity or alkalinity of a solution can be indicated by its pH. A solution’s pH is the negative, base-10 logarithm of the hydrogen ion (H + ) concentration of the solution. As an example, a pH 4 solution has an H + concentration that is ten times greater than that of a pH 5 solution. That is, a solution with a pH of 4 is ten times more acidic than a solution with a pH of 5. The concept of pH will begin to make more sense when you study the pH scale, like that shown in Figure 2.17. The scale consists of a series of increments ranging from 0 to 14. A solution with a pH of 7 is considered neutral—neither acidic nor basic. Pure water has a pH of 7. The lower the number below 7, the more acidic the solution, or the greater the concentration of H + . The concentration of hydrogen ions at each pH value is 10 times different than the next pH. For instance, a pH value of 4 corresponds to a proton concentration of 10 –4 M, or 0.0001M, while a pH value of 5 corresponds to a proton concentration of 10 –5 M, or 0.00001M. The higher the number above 7, the more basic (alkaline) the solution, or the lower the concentration of H + . Human urine, for example, is ten times more acidic than pure water, and HCl is 10,000,000 times more acidic than water.
Buffers
The pH of human blood normally ranges from 7.35 to 7.45, although it is typically identified as pH 7.4. At this slightly basic pH, blood can reduce the acidity resulting from the carbon dioxide (CO 2 ) constantly being released into the bloodstream by the trillions of cells in the body. Homeostatic mechanisms (along with exhaling CO 2 while breathing) normally keep the pH of blood within this narrow range. This is critical, because fluctuations—either too acidic or too alkaline—can lead to life-threatening disorders.
All cells of the body depend on homeostatic regulation of acid–base balance at a pH of approximately 7.4. The body therefore has several mechanisms for this regulation, involving breathing, the excretion of chemicals in urine, and the internal release of chemicals collectively called buffers into body fluids. A buffer is a solution of a weak acid and its conjugate base. A buffer can neutralize small amounts of acids or bases in body fluids. For example, if there is even a slight decrease below 7.35 in the pH of a bodily fluid, the buffer in the fluid—in this case, acting as a weak base—will bind the excess hydrogen ions. In contrast, if pH rises above 7.45, the buffer will act as a weak acid and contribute hydrogen ions.
Homeostatic Imbalances
Acids and Bases
Excessive acidity of the blood and other body fluids is known as acidosis. Common causes of acidosis are situations and disorders that reduce the effectiveness of breathing, especially the person’s ability to exhale fully, which causes a buildup of CO 2 (and H + ) in the bloodstream. Acidosis can also be caused by metabolic problems that reduce the level or function of buffers that act as bases, or that promote the production of acids. For instance, with severe diarrhea, too much bicarbonate can be lost from the body, allowing acids to build up in body fluids. In people with poorly managed diabetes (ineffective regulation of blood sugar), acids called ketones are produced as a form of body fuel. These can build up in the blood, causing a serious condition called diabetic ketoacidosis. Kidney failure, liver failure, heart failure, cancer, and other disorders also can prompt metabolic acidosis.
In contrast, alkalosis is a condition in which the blood and other body fluids are too alkaline (basic). As with acidosis, respiratory disorders are a major cause; however, in respiratory alkalosis, carbon dioxide levels fall too low. Lung disease, aspirin overdose, shock, and ordinary anxiety can cause respiratory alkalosis, which reduces the normal concentration of H + .
Metabolic alkalosis often results from prolonged, severe vomiting, which causes a loss of hydrogen and chloride ions (as components of HCl). Medications also can prompt alkalosis. These include diuretics that cause the body to lose potassium ions, as well as antacids when taken in excessive amounts, for instance by someone with persistent heartburn or an ulcer.


6.2D: Bacterial Differentiation
- Explain bacterial differentiation to eukaryotic-like sturctures
Bacterial morphological plasticity refers to evolutionary changes in the shape and size of bacterial cells. As bacteria evolve, morphological changes occur to maintain the consistency of the cell. However, this consistency could be affected in some circumstances (such as environmental stress) and changes in bacterial shape and size. In bacteria, the transformation into filamentous organisms have been recently demonstrated. These are survival strategies that affect the normal physiology of the bacteria in response to factors such as innate immune response, predator sensing, quorum sensing and antimicrobial signs.
Normally, bacteria have different shapes and sizes which include coccus, rod and helical/spiral (among others less common). This forms the basis for their classification. For instance, rod shapes may allow bacteria to attach more readily in environments with shear stress (e.g., in flowing water). Cocci may have access to small pores, creating more attachment sites per cell and hiding themselves from external shear forces. Spiral bacteria combine some of the characteristics of cocci (small footprints) and of filaments (more surface area on which shear forces can act) and the ability to form an unbroken set of cells to build biofilms. Several bacteria alter their morphology in response to the types and concentrations of external compounds. Bacterial morphology changes help to optimize interactions with cells and the surfaces to which they attach. This mechanism has been described in bacteria such as Escherichia coli and Helicobacter pylori.
Oxidative stress, nutrient limitation, DNA damage and antibiotics exposure are some stress conditions to which bacteria respond, altering their DNA replication and cell division. Filamentous bacteria have been considered to be over-stressed, sick and dying members of the population. However, the filamentous members of some communities have vital roles in the population’s continued existence, since the filamentous phenotype can confer protection against lethal environments.Filamentous E. coli can be up to 70 µm in length and has been identified as playing an important role in pathogenesis in human cystitis. There are different mechanisms identified in some bacteria that are attributable to the development of filamentous forms.
Nutritional stress can change bacterial morphology. The most frequent shape alteration may be filamentation triggered by a limitation in the availability of one or more nutrients. Since the filament can increase a cell’s uptake–proficiency surface without changing its surface-to-volume ratio appreciably, this may be enough reason for cells to be filament. Moreover, the filamentation benefits bacterial cells attaching to a surface because it increases specific surface area in direct contact with the solid medium. In addition, the filamentation may allow bacterial cells to access nutrients by enhancing the possibility that the filament will be exposed to a nutrient-rich zone and pass compounds to the rest of the cell’s biomass. For example, Actinomyces israelii grows as filamentous rods or branched in the absence of phosphate, cysteine, or glutathione. However, it returns to a regular rod-like morphology when adding back these nutrients.
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- Stringent response. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Stringent_response. License : CC BY-SA: Attribution-ShareAlike
- Boundless. Provided by : Boundless Learning. Located at : www.boundless.com//microbiology/definition/stringent-response--2. License : CC BY-SA: Attribution-ShareAlike
- PDB 2be3 EBI. Provided by : Wikimedia. Located at : commons.wikimedia.org/wiki/File:PDB_2be3_EBI.jpg. License : Public Domain: No Known Copyright
- Extremophile. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Extremophile. License : CC BY-SA: Attribution-ShareAlike
- Prosthecate bacteria. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Prosthecate_bacteria. License : CC BY-SA: Attribution-ShareAlike
- Prochlorococcus. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Prochlorococcus. License : CC BY-SA: Attribution-ShareAlike
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- Oligotroph. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Oligotroph. License : CC BY-SA: Attribution-ShareAlike
- oligotroph. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/oligotroph. License : CC BY-SA: Attribution-ShareAlike
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- IMG_3678 Bacteria Mats | Flickr - Photo Sharing!. Provided by : Flickr. Located at : http://www.flickr.com/photos/mccaffry/3947141220/ . License : CC BY: Attribution
- Myxobacteria. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Myxobacteria. License : CC BY-SA: Attribution-ShareAlike
- Myxococcus xanthus. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Myxococcus_xanthus. License : CC BY-SA: Attribution-ShareAlike
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- quorum sensing. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/quorum_sensing. License : CC BY-SA: Attribution-ShareAlike
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- IMG_3678 Bacteria Mats | Flickr - Photo Sharing!. Provided by : Flickr. Located at : http://www.flickr.com/photos/mccaffry/3947141220/ . License : CC BY: Attribution
- Myxococcus xanthus. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Myxococcus_xanthus. License : CC BY-SA: Attribution-ShareAlike
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- Boundless. Provided by : Boundless Learning. Located at : www.boundless.com//biology/definition/septum. License : CC BY-SA: Attribution-ShareAlike
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- EMpylori. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:EMpylori.jpg. License : CC BY-SA: Attribution-ShareAlike
Key Points
- Bacterial morphology changes help to optimize interactions with cells and the surfaces to which they attach.
- Oxidative stress, nutrient limitation, DNA damage and antibiotics exposure are some of stress conditions to which bacteria respond, altering their DNA replication and cell division.
- The most frequent shape alteration may be filamentation triggered by a limitation in the availability of one or more nutrients.
Key Terms
- cytoskeleton : A cellular structure like a skeleton, contained within the cytoplasm.
- septum : a partition that separates the cells of a (septated) fungus
- segrosomes : multiprotein complexes that partition chromosomes/plasmids in bacteria.
- cell division : a process by which a cell divides into two cells.


4.2: Newton's laws of motion
In his Principia Newton introduced three laws of motion that can mathematically be expressed in vector format as follows:
\[\begin{align} & \text { 1. If } \sum_{j} \overrightarrow{\boldsymbol{F}}_{i j}=\overrightarrow{\mathbf{0}} \text { then } \overrightarrow{\boldsymbol{a}}_{i}=\overrightarrow{\mathbf{0}} \tag{4.1} \label{4.1}\\[4pt] & \text { 2. } \sum_{j} \overrightarrow{\boldsymbol{F}}_{i j}=m_{i} \overrightarrow{\boldsymbol{a}}_{i} \tag{4.2} \label{4.2}\\[4pt] & \text { 3. } \overrightarrow{\boldsymbol{F}}_{i j}=-\overrightarrow{\boldsymbol{F}}_{j i} \tag{4.3} \label{4.3}\end{align}\]
These equations and the variables will be explained and defined in more detail in the next two chapters. It can be seen that Newton’s first law is a direct consequence of Newton’s second law when setting \(\sum \overrightarrow{\boldsymbol{F}}_{i j}=\overrightarrow{\mathbf{0}}\). Newton’s third law (action=-reaction), describes a property of all known fundamental forces of nature, which states that for every force \(\overrightarrow{\boldsymbol{F}}_{i j}\) that acts on point mass \(i\) there is another collinear force \(\overrightarrow{\boldsymbol{F}}_{j i}\) that acts on another point mass \(j\) with equal magnitude and opposite direction. In other words if point mass \(j\) generates a force \(\overrightarrow{\boldsymbol{F}}_{i j}\) on object \(i\), then point mass \(i\) generates a force \(\overrightarrow{\boldsymbol{F}}_{j i}=-\overrightarrow{\boldsymbol{F}}_{i j}\) on point
mass \(j\). The points of action of both forces coincide with the positions of the corresponding point masses. The first and third laws should be familiar if you followed a course in statics. Newton’s second law \(\sum \overrightarrow{\boldsymbol{F}}=m \overrightarrow{\boldsymbol{a}}\) is the essential equation in dynamics.
Note. Newton’s laws are strictly only valid for objects that are point masses, which are so small that they can be described by a single point (position vector) in space. By applying Newton’s laws to each point mass in an object or system that consists of many point masses, new laws can be derived for these larger systems. Much of this textbook is dedicated to deriving and discussing these new laws and using them to analyse more complex dynamical systems, like rigid bodies.


2.6: Words of Wisdom- Can You Listen to Yourself?
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Yuki Sasao
It is almost impossible to find time away from information sources like TV, phone, advertisements, or even your friends and family in this modern society. Can you put yourself in a place that has no information at all—you alone, just yourself? If not, you should try—finding this quiet mental space will let you to practice listening to yourself. It is a wonderful way to find out who you truly are. Our society has become so loud that it is very difficult to listen to your own voice and extremely easy to lose it.
I am an international student from a very small town in Japan, and I am the first one among my family members to study abroad. When I told people that I decided to come to the United States to study, every single one of them was shocked and gave me their advice. Some said Americans are very bossy and tend to look down on people. Some said I would not be able to find any jobs there.
It does not matter who you are and what type of circumstances you are in. You will get some comments and advice no matter what you do.
Was the advice people gave me accurate? I’m sorry, but mostly, no. People I met in the United States were nice, and the advice I received really depended on whether or not the person looked down on others. Am I struggling with finding a job? No. My major in accounting provides me more opportunities than I can take. Looking back on the comments from my friends and family, I am very grateful that I was able to see what I truly wanted and stick with my decision.
The reason I could tune out those negative voices was not because I am lucky or intelligent. It is because I listened to myself—my own voice. However, this doesn’t mean that I didn’t listen to others. I considered what people said to me and I understood them. I just didn’t agree with them, which was the most difficult part. In the process of building my own decisions, many pieces of advice actually helped me and I made some changes based on the advice from others combined with my own thoughts.
Why was I able to stick to my decision so tight and live the life I wanted? It’s because I talked to myself and asked myself millions of questions.
“What do I want in my future?”
“Do I really need it or just want it?”
“Am I where I wanted to be? Yes? No? Why?”
“Where am I going?”
“What am I doing?”
“What would happen if I do this?”
“Why am I doing it?”
It is difficult, frustrating, and time-consuming to find your raw voice in this very noisy society, but in doing so you will get through life with minimal regret and confidence in who you are and what you are doing. Pull yourself away from the massive amount of information, talk to some people, understand them (never ignore them), and then talk with yourself.  You’d better learn how to listen to yourself and be able to stick with your own thoughts even after accepting what other say.
CC licensed content, Shared previously:
Foundations of Academic Success: Words of Wisdom. Edited by Thomas Priester. Essay authored by Yuki Sasao. Located at:
https://milnepublishing.geneseo.edu/foundations-of-academic-success/chapter/can-you-listen-to-yourself/
License: CC BY: Attribution.


10.5: Simple Future and Present Values (Formulas)
Having done the foregoing work, it is plain to see that we can symbolically represent the mathematics using the following “language.”
Key :
The expression, or “factor,” (1 + R/p) n x p , may be used as a “multiplier” when compounding from present to future values and, in its reciprocal form, as a multiplier again when discounting from future to present value s . You will find the factors, calculated out, in interest rate tables, truncated versions of which you will find on the pages following.
“R/p” means that if the annual interest rate (R) is 12% and the number of compounding periods (p) is 12 (i.e., monthly compounding) the periodic compound rate is .12 ÷ 12 = .01. After one year, the FV would be $1 ( 1.01) 12 = $1.1268. (Notice that this compares with once – a – year compoun ding at 12%: $1 (1.12) = $1.12. The difference in Future Values is not trivial .


What are the key differences?
Although it is possible that there are inherent properties that make neurons in the CNS somehow different from those in the PNS, it is more likely that external factors and cells account for the differences in their abilities to regenerate following damage. As shown in Figure \(\PageIndex{1}\). above, within the CNS, following axonal injury, the site of damage distal to injury (i.e. further away from damage) often undergoes degeneration and the distal axon degenerates and eventually disappears. Although there are several reasons that this is thought to occur, most notably this is believed to involve a lack of macrophage clearing of damaged myelin as well as the formation of a glial scar via activated astrocytes that cause a physical barrier to their re-growth. Additionally, molecules that are unique to the CNS (see chapter in this Unit on Multiple Sclerosis) also are believed to be up-regulated within the CNS following damage that prevent regeneration. These molecules are associated with the CNS specific glial cells, oligodendrocytes that provide myelination, and these cells increase the production of Nogo, MAG (Myelin Associated Glycoprotein) and OGmp (Oligodendroctye myelin glycoprotein) among others.
In contrast, PNS neurons (bottom panel of figure \(\PageIndex{1}\)) show significant clearing of damaged axons via macrophages (not observed in the CNS) and then axonal outgrowth and repair across the bridge of Schwann cells that occurs following a process known as Wallerian degeneration (the loss of the axon distal to the injury).
Pathophysiological implications – TBI (Traumatic Brain Injury)
You might be asking yourself, where do these types of axonal injuries occur with the brain and CNS? Increasingly researchers and clinicians are finding that there is specific axonal injury that could occur following traumatic brain injury (TBI) or concussion related injuries. One of the ways in which axons within the brain become damaged include the process of coup/contre-coup where the brain (and its neurons) are first compressed (coup) and then stretched (contre-coup). The mechanical forces on the neuron on the brain may result in varying degrees of damage to the neurons (Figure \(\PageIndex{2}\).).
Figure \(\PageIndex{2}\). Schematic diagram of diffuse axonal injury following TBI/concussion.
As illustrated in Figure \(\PageIndex{2}\)., depending on the area of the brain being impacted, a number of different types of damage can occur along the length of the axon including stretching/pulling of axons which may affect myelination and localization of axonal channel proteins, and both tearing and shearing which will cause loss of axonal integrity. This type of diffuse axonal injury will have effects on both the structure of the grey matter of the brain and the white matter axonal tracts. Ultimately these types of injuries often go undetected and the most common methods used are clinical assessments using variations of the Glasgow Coma Scale (GCS) that examine the severity of the loss of consciousness as these injuries, although structural are undetectable by either MRI or CT-scans.
Figure \(\PageIndex{3}\)
There is still controversy between TBI/concussions and the development of a neurodegenerative disorder known as Chronic Traumatic Encephalopahty (CTE) which is thought to cause behavioral changes in athletes in sports with contact/impact.
Although there are likely
structural
changes as indicated above, most often the diagnosis of post-concussion or TBI related disturbances occur because of
functional
changes in cognitive function and possible mood disorder changes (depression etc.). Although there are likely
structural
changes as indicated above, most often the diagnosis of post-concussion or TBI related disturbances occur because of
functional
changes in cognitive function and possible mood disorder changes (depression etc.).
Did you know that one of the chief complaints following TBI/concussions is the inability to concentrate and focus on computer/TV screens? Individuals with concussion injuries require not just physical rest but cognitive rest, and typical LCD screens refresh at a 60 Hz rate. Most individuals are capable of processing and fusing these high frequency images without a cognitive load, but following concussions, individuals will have higher critical flicker frequencies such that staring at a screen will increase cognitive fatigue and eyestrain. We don’t understand why this happens yet but perhaps there is a Nobel Prize in it for an aspiring neurobiologist!


9.11: What Is Organizational Culture?
- Define culture for a business.
- Explain how culture can be a competitive advantage for a business.
- List the levels of culture.
Organizational culture is a term that can relate to any organization at all, from a church to a university. When talking about the culture of a business, you’ll often hear the term “corporate culture.” Corporate culture is, according to INC Magazine :
the shared values, attitudes, standards, and beliefs that characterize members of an organization and define its nature. Corporate culture is rooted in an organization’s goals, strategies, structure, and approaches to labor, customers, investors, and the greater community. As such, it is an essential component in any business’s ultimate success or failure. [1]
Like families (or nations), corporations have cultures. Sometimes those cultures “just happen.” All too often, when corporate culture is not intentionally created, the culture winds up being disjointed or even antagonistic. Employees are all working toward different goals, in different ways, with different approaches. For instance, although Bob is dedicated to the idea of crafting quality products, Suzanne is eager to sell as much product as possible (even if the quality is only so-so). Meanwhile, Brad thinks the company should start making a wider range of products and is trying to push his ideas forward during sales meetings.
The idea of corporate culture developed from our knowledge of national, regional, and family cultures, and many theories exist about what makes a good (or poor) corporate culture. To get an idea of what a corporate culture looks like, think about families you know well. Some are formal whereas others are easygoing. Some work together toward shared goals whereas others encourage individuality and independence. Some are always having fun whereas others seem to be in a permanent state of internal conflict. We can describe corporate cultures in similar ways.
Although some businesses give little thought to corporate culture, many successful companies have cultures that are intentionally created or tweaked. Sometimes corporate cultures are the result of a founder’s personal vision. But just as often, corporate cultures are created through a collaborative effort that involves not only upper management but also managers and employees.
What Do Corporate Cultures Look Like?
Perhaps the best way to get an idea of what we’re talking about when we talk about corporate culture is to consider some examples. Let’s take a look at the cultures inside a few well-known companies.
IBM
IBM’s founder Thomas Watson was one of the great developers of corporate culture. Based on a very different worldview than the one we have today, it encouraged morality, temperance, and consistency. Men who worked for IBM were expected to dress in a certain style (dark suits, white shirts) and behave conservatively. The “IBM Spirit” was even represented in corporate songs such as “Ever Onward” that employees were required to sing at gatherings and conventions.
The lyrics to “Ever Onward,” captured in a songbook from 1937, are a great way to understand the original culture of a company that became one of the truly great icons of American business. Read one verse of the song that follows.
EVER ONWARD – EVER ONWARD!
That’s the spirit that has brought us fame!
We’re big, but bigger we will be
We can’t fail for all can see
That to serve humanity has been our aim!
Our products now are known, in every zone,
Our reputation sparkles like a gem!
We’ve fought our way through – and new
Fields we’re sure to conquer too
For the EVER ONWARD I.B.M.
[2]
Watch the following video to hear the song and find out more about IBM’s early corporate culture:
You can view the transcript for “IBM: Ever Onward” here (opens in new window) .
One business that has revolutionized the way of work and its vision about it is Google. Google has become known as the company with endless perks for its valued employees. Some of these include coffee bars, free meals, lounge breaks, and even the option to bring your pet to work! Google has locations worldwide, and management embraces the idea that a happy employee leads to a productive workplace. The company’s long-term success ties back to its corporate culture and values. Here’s a list of Google’s core values, around which it builds its corporate culture:
- We want to work with great people.
- Technology innovation is our lifeblood.
- Working at Google is fun.
- Be actively involved; you are Google.
- Don’t take success for granted.
- Do the right thing; don’t be evil.
- Earn customer and user loyalty and respect every day.
- Sustainable long-term growth and profitability are key to our success.
- Google cares about and supports the communities where we work and live.
Apple
Google likes to make sure its employees are having fun, but Apple’s corporate culture is a bit more focused on getting things done. Its founder, Steve Jobs, passed along a set of core values that make it clear that competition, focus, and hard work are part of the organizational culture:
- We believe that we’re on the face of the Earth to make great products.
- We believe in the simple, not the complex.
- We believe that we need to own and control the primary technologies behind the products we make.
- We participate only in markets where we can make a significant contribution.
- We believe in saying no to thousands of projects so that we can really focus on the few that are truly important and meaningful to us..
- We believe in deep collaboration and cross-pollination of our groups, which allow us to innovate in a way that others cannot.
- We don’t settle for anything less than excellence in every group in the company, and we have the self-honesty to admit when we’re wrong and the courage to change. [3]
Compare Apple’s values to those of Google. Apple focuses on competition, outcomes, and excellence, whereas Google emphasizes values such as having fun, behaving ethically, serving the customer, and engaging with the wider world. Both companies make digital products, both have seen great success, and both attract plenty of dedicated employees. But because the corporate cultures are so different, Apple and Google attract different people who have different personal goals, work styles, and expectations.
Corporate Culture as a Competitive Advantage
Why is it so important to have a strong, positive corporate culture? There are three good reasons:
- A strong culture helps employees, customers, and the general public to identify your corporate values. Say, for example, that your company culture values innovation. In that case, your employees will know that they will be encouraged to come up with new ideas—and your customers will know that your products and services are likely to have a creative or unique quality.
- Companies with strong, coherent cultures attract high-quality employees who believe in the same values as the corporation. Once those employees come on board, they start to feel that they “belong” because they are part of a shared culture. Employees who feel that their jobs are a great match for their personal values are more likely to be loyal to their employers. After all, they are doing what they enjoy doing for an organization that shares their ideals and goals.
- A strong corporate culture can help a corporation to build its brand. For example, Starbucks has built a culture and brand that includes very public dedication to international fair trade. Customers who care about fair trade are more likely to buy from—and stay loyal to—Starbucks.
Levels of Corporate Culture
E.H. Schein is a theorist who studies corporate culture. In 1992, he wrote a book titled Organizational Culture and Leadership, which suggests that there are three levels of corporate culture. At the core of a culture are basic assumptions about human behavior, which are usually so ingrained into the culture that they’re difficult to pinpoint. Surrounding the assumptions are expressed values drawn from those assumptions. These usually appear in the form of standards, rules, and public expressions of the organization’s philosophy. At the surface level are artifacts that are the outcome of the assumptions and values—these appear as actions, policies, the physical environment, office jokes, and so on.
For example, when Home Depot, under the leadership of a new CEO, needed to return the company to its customer-centric roots in 2007, it quickly introduced artifacts—buttons and awards—to remind everyone who came first: customers. Sales associates began wearing buttons that invited customers to ask for help. Associates were rewarded for outstanding customer reviews and recognized in meetings with sales plaques and more buttons. With a renewed focus on its stated value of providing excellent customer service, Home Depot began hiring people who loved serving customers instead of worrying about costs and profits. Management did not completely abandon the cost discipline of its previous CEO, but it loosened the reins substantially. The underlying assumption was that profits would return if the company took care of customers. Profits did return, although the competition from Lowe’s has been stiff.
There is no right or wrong set of assumptions and values, and companies can be successful no matter which values they embrace. You are, however, most likely to do well with a company that shares your beliefs. Just looking around a workplace can help you to determine whether a company values hierarchy or shared authority, individual achievement or teamwork.
- “Corporate Culture,” Inc. 2017. https://www.inc.com/encyclopedia/corporate-culture.html . ↵
- “IBM Rally Song, Ever Onward,” IBM, https://www-03.ibm.com/ibm/history/multimedia/everonward_trans.html ↵
- Have you ever read about Apple's core values? (2017, May 25). Retrieved September 15, 2017, from https://thinkmarketingmagazine.com/apple-core-values/ ↵
Contributors and Attributions
- What Is Organizational Culture?. Authored by : Lisa Jo Rudy and Lumen Learning. License : CC BY: Attribution
- Image: Schein's Model. Authored by : Shirarae. Located at : https://commons.wikimedia.org/wiki/File:Schein%27s_Model.JPG . License : CC BY-SA: Attribution-ShareAlike
- Video: Ever Onward: IBM . Authored by : Computer History Museum. Located at : https://www.youtube.com/watch?v=YBpNzxz1XgU . License : All Rights Reserved . License Terms : Standard YouTube License