2.8: Case Questions
Review the story of Sixto Cancel and his journey to developing the social venture Think of Us.
- Consider Sixto’s entrepreneurial journey and the development of Think of Us. What types of challenges or obstacles do you think he had to overcome to complete his journey?
- Discuss some of the advantages and disadvantages related to Sixto Cancel’s background and his experiences in developing an organization and board.
- Consider how Sixto Cancel developed his organization. Discuss how he followed or skipped any steps of an entrepreneurial journey.
Explore the websites of Cratejoy and Prospurly, which are discussed in Entrepreneurship in Action: Prospurly . How did these venture founders follow the entrepreneurial journey?
3 .After researching Man Crates, explain how Man Crates has followed the model in Figure 2.20 ?
4 .What additional ideas can you think of for starting your own business, using Man Crates as a source of inspiration?
5 .Go back to the Work It Out: Startup Ideas Feature Box. Select either an idea that you’ve created or an idea listed on either of the websites. Where could you go to gain more information about this idea? This might mean finding a business where you could shadow someone, or perhaps an internship, or research conducted in some other manner.
6 .Return to the Work It Out: Startup Ideas Feature Box and revisit the links to business ideas, using the same idea that you identified in question 1. What are five other businesses that could be spinoff ideas from your one new idea?
7 .Refer to the case questions in Entrepreneurial Pathways . Select one of the framework tools discussed in this section and apply that framework to your idea.
8 .Why did you select this framework over another framework?
9 .By applying the framework to your idea, what new information did you learn and what information is lacking, or needs further development?


8.14: Statistical Interpretation of Entropy and the Second Law of Thermodynamics- The Underlying Explanation
Learning Objectives
- Identify probabilities in entropy.
- Analyze statistical probabilities in entropic systems.
The various ways of formulating the second law of thermodynamics tell what happens rather than why it happens. Why should heat transfer occur only from hot to cold? Why should energy become ever less available to do work? Why should the universe become increasingly disorderly? The answer is that it is a matter of overwhelming probability. Disorder is simply vastly more likely than order.
When you watch an emerging rain storm begin to wet the ground, you will notice that the drops fall in a disorganized manner both in time and in space. Some fall close together, some far apart, but they never fall in straight, orderly rows. It is not impossible for rain to fall in an orderly pattern, just highly unlikely, because there are many more disorderly ways than orderly ones. To illustrate this fact, we will examine some random processes, starting with coin tosses.
Coin Tosses
What are the possible outcomes of tossing 5 coins? Each coin can land either heads or tails. On the large scale, we are concerned only with the total heads and tails and not with the order in which heads and tails appear. The following possibilities exist:
| Combination of Heads and Tails | |
|---|---|
| 5 heads | 0 tails |
| 4 heads | 1 tails |
| 3 heads | 2 tails |
| 2 heads | 3 tails |
| 1 heads | 4 tails |
| 0 heads | 5 tails |
These are what we call macrostates. A macrostate is an overall property of a system. It does not specify the details of the system, such as the order in which heads and tails occur or which coins are heads or tails.
Using this nomenclature, a system of 5 coins has the 6 possible macrostates just listed. Some macrostates are more likely to occur than others. For instance, there is only one way to get 5 heads, but there are several ways to get 3 heads and 2 tails, making the latter macrostate more probable. Table \(\PageIndex{2}\) lists of all the ways in which 5 coins can be tossed, taking into account the order in which heads and tails occur. Each sequence is called a microstate —a detailed description of every element of a system.
The macrostate of 3 heads and 2 tails can be achieved in 10 ways and is thus 10 times more probable than the one having 5 heads. Not surprisingly, it is equally probable to have the reverse, 2 heads and 3 tails. Similarly, it is equally probable to get 5 tails as it is to get 5 heads. Note that all of these conclusions are based on the crucial assumption that each microstate is equally probable. With coin tosses, this requires that the coins not be asymmetric in a way that favors one side over the other, as with loaded dice. With any system, the assumption that all microstates are equally probable must be valid, or the analysis will be erroneous.
The two most orderly possibilities are 5 heads or 5 tails. (They are more structured than the others.) They are also the least likely, only 2 out of 32 possibilities. The most disorderly possibilities are 3 heads and 2 tails and its reverse. (They are the least structured.) The most disorderly possibilities are also the most likely, with 20 out of 32 possibilities for the 3 heads and 2 tails and its reverse. If we start with an orderly array like 5 heads and toss the coins, it is very likely that we will get a less orderly array as a result, since 30 out of the 32 possibilities are less orderly. So even if you start with an orderly state, there is a strong tendency to go from order to disorder, from low entropy to high entropy. The reverse can happen, but it is unlikely.
This result becomes dramatic for larger systems. Consider what happens if you have 100 coins instead of just 5. The most orderly arrangements (most structured) are 100 heads or 100 tails. The least orderly (least structured) is that of 50 heads and 50 tails. There is only 1 way (1 microstate) to get the most orderly arrangement of 100 heads. There are 100 ways (100 microstates) to get the next most orderly arrangement of 99 heads and 1 tail (also 100 to get its reverse). And there are 1.0×10 29 ways to get 50 heads and 50 tails, the least orderly arrangement. Table \(\PageIndex{3}\) is an abbreviated list of the various macrostates and the number of microstates for each macrostate. The total number of microstates—the total number of different ways 100 coins can be tossed—is an impressively large 1.27×10 30. Now, if we start with an orderly macrostate like 100 heads and toss the coins, there is a virtual certainty that we will get a less orderly macrostate. If we keep tossing the coins, it is possible, but exceedingly unlikely, that we will ever get back to the most orderly macrostate. If you tossed the coins once each second, you could expect to get either 100 heads or 100 tails once in 2×10 22 years! This period is 1 trillion (10 12 ) times longer than the age of the universe, and so the chances are essentially zero. In contrast, there is an 8% chance of getting 50 heads, a 73% chance of getting from 45 to 55 heads, and a 96% chance of getting from 40 to 60 heads. Disorder is highly likely.
Disorder in a Gas
The fantastic growth in the odds favoring disorder that we see in going from 5 to 100 coins continues as the number of entities in the system increases. Let us now imagine applying this approach to perhaps a small sample of gas. Because counting microstates and macrostates involves statistics, this is called statistical analysis . The macrostates of a gas correspond to its macroscopic properties, such as volume, temperature, and pressure; and its microstates correspond to the detailed description of the positions and velocities of its atoms. Even a small amount of gas has a huge number of atoms: 1.0 cm 3 of an ideal gas at 1.0 atm and 0º C has 2.7×10 19 atoms. So each macrostate has an immense number of microstates. In plain language, this means that there are an immense number of ways in which the atoms in a gas can be arranged, while still having the same pressure, temperature, and so on.
The most likely conditions (or macrostates) for a gas are those we see all the time—a random distribution of atoms in space with a Maxwell-Boltzmann distribution of speeds in random directions, as predicted by kinetic theory. This is the most disorderly and least structured condition we can imagine. In contrast, one type of very orderly and structured macrostate has all of the atoms in one corner of a container with identical velocities. There are very few ways to accomplish this (very few microstates corresponding to it), and so it is exceedingly unlikely ever to occur. (See Figure \(\PageIndex{2}\)(b).) Indeed, it is so unlikely that we have a law saying that it is impossible, which has never been observed to be violated—the second law of thermodynamics.
The disordered condition is one of high entropy, and the ordered one has low entropy. With a transfer of energy from another system, we could force all of the atoms into one corner and have a local decrease in entropy, but at the cost of an overall increase in entropy of the universe. If the atoms start out in one corner, they will quickly disperse and become uniformly distributed and will never return to the orderly original state ( Figure \(\PageIndex{2}\)(b)). Entropy will increase. With such a large sample of atoms, it is possible—but unimaginably unlikely—for entropy to decrease. Disorder is vastly more likely than order.
The arguments that disorder and high entropy are the most probable states are quite convincing. The great Austrian physicist Ludwig Boltzmann (1844–1906)—who, along with Maxwell, made so many contributions to kinetic theory—proved that the entropy of a system in a given state (a macrostate) can be written as
\[S=k \ln W, \nonumber \]
where \(k=1.38 \times 10^{-23} \mathrm{~J} / \mathrm{K}\) is Boltzmann’s constant, and \(\ln W\) is the natural logarithm of the number of microstates \(W\) corresponding to the given macrostate. \(W\) is proportional to the probability that the macrostate will occur. Thus entropy is directly related to the probability of a state—the more likely the state, the greater its entropy. Boltzmann proved that this expression for \(S\) is equivalent to the definition \(\Delta S=Q / T\), which we have used extensively.
Thus the second law of thermodynamics is explained on a very basic level: entropy either remains the same or increases in every process. This phenomenon is due to the extraordinarily small probability of a decrease, based on the extraordinarily larger number of microstates in systems with greater entropy. Entropy can decrease, but for any macroscopic system, this outcome is so unlikely that it will never be observed.
Example \(\PageIndex{1}\): Entropy Increases in a Coin Toss
Suppose you toss 100 coins starting with 60 heads and 40 tails, and you get the most likely result, 50 heads and 50 tails. What is the change in entropy?
Strategy
Noting that the number of microstates is labeled \(W\) in Table \(\PageIndex{3}\) for the 100-coin toss, we can use \(\Delta S=S_{\mathrm{f}}-S_{\mathrm{i}}=k \ln W_{\mathrm{f}}-k \ln W_{\mathrm{i}}\) to calculate the change in entropy.
Solution
The change in entropy is
\[\Delta S=S_{\mathrm{f}}-S_{\mathrm{i}}=k \ln W_{\mathrm{f}}-k \ln W_{\mathrm{i}}, \nonumber\]
where the subscript i stands for the initial 60 heads and 40 tails state, and the subscript f for the final 50 heads and 50 tails state. Substituting the values for \(W\) from Table \(\PageIndex{3}\) gives
\[\begin{aligned}
\Delta S &=\left(1.38 \times 10^{-23} \mathrm{~J} / \mathrm{K}\right)\left[\ln \left(1.0 \times 10^{29}\right)-\ln \left(1.4 \times 10^{28}\right)\right] \\
&=2.7 \times 10^{-23} \mathrm{~J} / \mathrm{K}
\end{aligned} \nonumber\]
Discussion
This increase in entropy means we have moved to a less orderly situation. It is not impossible for further tosses to produce the initial state of 60 heads and 40 tails, but it is less likely. There is about a 1 in 90 chance for that decrease in entropy (–2.7×10 –23 J/K) to occur. If we calculate the decrease in entropy to move to the most orderly state, we get \(\Delta S=-92 \times 10^{-23} \mathrm{~J} / \mathrm{K}\). There is about a 1 in 10 30 chance of this change occurring. So while very small decreases in entropy are unlikely, slightly greater decreases are impossibly unlikely. These probabilities imply, again, that for a macroscopic system, a decrease in entropy is impossible. For example, for heat transfer to occur spontaneously from 1.00 kg of 0ºC ice to its 0ºC environment, there would be a decrease in entropy of 1.22×10 3 J/K. Given that a \(\Delta S \text { of } 10^{-21} \mathrm{~J} / \mathrm{K}\) corresponds to about a 1 in 1030 chance, a decrease of this size (10 3 J/K) is an utter impossibility. Even for a milligram of melted ice to spontaneously refreeze is impossible.
PROBLEM-SOLVING STRATEGIES FOR ENTROPY
- Examine the situation to determine if entropy is involved.
- Identify the system of interest and draw a labeled diagram of the system showing energy flow.
- Identify exactly what needs to be determined in the problem (identify the unknowns). A written list is useful.
- Make a list of what is given or can be inferred from the problem as stated (identify the knowns). You must carefully identify the heat transfer, if any, and the temperature at which the process takes place. It is also important to identify the initial and final states.
- Solve the appropriate equation for the quantity to be determined (the unknown). Note that the change in entropy can be determined between any states by calculating it for a reversible process.
- Substitute the known value along with their units into the appropriate equation, and obtain numerical solutions complete with units.
- To see if it is reasonable: Does it make sense? For example, total entropy should increase for any real process or be constant for a reversible process. Disordered states should be more probable and have greater entropy than ordered states.
Section Summary
- Disorder is far more likely than order, which can be seen statistically.
-
The entropy of a system in a given state (a macrostate) can be written as
\[S=k \ln W, \nonumber\]
where k=1.38×10 –23 J/K is Boltzmann’s constant, and \(lnW\) is the natural logarithm of the number of microstates \(W\) corresponding to the given macrostate.
Glossary
- macrostate
- an overall property of a system
- microstate
- each sequence within a larger macrostate
- statistical analysis
- using statistics to examine data, such as counting microstates and macrostates


1.3: The Wanderer
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- Bonnie J. Robinson & Laura Getty
- University of North Georgia via University of North Georgia Press
Author unknown
At least late tenth century, possibly much earlier
The Wanderer is found only in the manuscript known as the Exeter Book, which was copied in the late tenth century. The 115- line poem follows the usual Anglo- Saxon pattern of short alliterative half-lines separated by a caesura (pause). The wanderer (or “earth- stepper”) has buried his lord (his “gold-friend”) and finds himself alone in the world. Members of a lord’s comitatus , or war band, were expected to die alongside their leader in battle; the wanderer is looking for a new lord as he suffers through the uncertainty, loneliness, and physical hardships of exile. The poem begins and ends with references to Christianity, with a kenning near the end of the poem with God as “Shaper of Men;” the only certainty that the speaker has is that there is a “safe home” waiting for him in heaven. The rest of the poem focuses on what he has lost. Like The Ruin and The Seafarer , also found in the Exeter Book, The Wanderer is what is known as an “ ubi sunt ” poem (Latin for “where has”). In J.R.R. Tolkien’s The Two Towers , Aragorn recites a poem about Eorl the Young that begins “Where now the horse and the rider? Where is the horn that was blowing?” (142; the movie transfers the speech to King Theoden), which was drawn directly from The Wanderer ’s “Where has the horse gone? Where is the man?” Because of its theme, The Wanderer is usually classified as a type of elegy, or lament for what has been lost.
1.7.1 Bibliography
Tolkien, J.R.R. The Two Towers . New York: Ballantine Books, 1971.
The Lord of the Rings: The Two Towers . Directed by Peter Jackson. New Line Cinema and Wingnut Films. 2002.
1.7.2 The Wanderer
Often the solitary man prays for favour, for the mercy of the Lord, though, sad at heart, he must needs stir with his bands for a weary while the icy sea across the watery ways, must journey the paths of exile; settled in truth is fate! So spoke the wanderer, mindful of hardships, of cruel slaughters, of the fall of kinsmen:
’Often I must bewail my sorrows in my loneliness at the dawn of each day; there is none of living men now to whom I dare speak my heart openly. I know for a truth that it is a noble custom for a man to bind fast the thoughts of his heart, to treasure his broodings, let him think as he will. Nor can the weary in mood resist fate, nor does the fierce thought avail anything. Wherefore those eager for glory often bind fast in their secret hearts a sad thought. So I, sundered from my native land, far from noble kinsmen, often sad at heart, had to fetter my mind, when in years gone by the darkness of the earth covered my gold-friend, and I went thence in wretchedness with wintry care upon me over the frozen waves, gloomily sought the hall of a treasure-giver wherever I could find him far or near, who might know me in the mead hall or comfort me, left without friends, treat me with kindness. He knows who puts it to the test how cruel a comrade is sorrow for him who has few dear protectors; his is the path of exile, in no wise the twisted gold; a chill body, in no wise the riches of the earth; he thinks of retainers in hall and the receiving of treasure, of how in his youth his gold-friend was kind to him at the feast. The joy has all perished. Wherefore he knows this who must long forgo the counsels of his dear lord and friend, when sorrow and sleep together often bind the poor solitary man; it seems to him in his mind that he clasps and kisses his lord and lays hands and head on his knee, as when erstwhile in past days he was near the gift-throne; then the friendless man wakes again, sees before him the dark waves, the sea-birds bathing, spreading their feathers; frost and snow falling mingled with hail. Then heavier are the wounds in his heart, sore for his beloved; sorrow is renewed. Then the memory of kinsmen crosses his mind; he greets them with songs; he gazes on them eagerly. The companions of warriors swim away again; the souls of sailors bring there not many known songs. Care is renewed in him who must needs send very often his weary mind over the frozen waves. And thus I cannot think why in this world my mind becomes not overcast when I consider all the life of earls, how of a sudden they have given up hall, courageous retainers. So this world each day passes and falls; for a man cannot become wise till he has his share of years in the world. A wise man must be patient, not over-passionate, nor over-hasty of speech, nor over-weak or rash in war, nor over-fearful, nor over-glad, nor over-covetous, never over-eager to boast ere he has full knowledge.) A man must bide his time, when he boasts in his speech, until he knows well in his pride whither the thoughts of the mind will turn. A wise man must see how dreary it will be when all the riches of this world stand waste, as in different places throughout this world walls stand, blown upon by winds, hung with frost, the dwellings in ruins. The wine halls crumble; the rulers lie low, bereft of joy; the mighty warriors have all fallen in their pride by the wall; war carried off some, bore them on far paths; one the raven bore away over the high sea; one the grey wolf gave over to death; one an earl with sad face hid in the earth-cave. Thus did the Creator of men lay waste this earth till the old work of giants stood empty, free from the revel of castle-dwellers. Then he who has thought wisely of the foundation of things and who deeply ponders this dark life, wise in his heart, often turns his thoughts to the many slaughters of the past, and speaks these words:
‘“Whither has gone the horse? Whither has gone the man? Whither has gone the giver of treasure? Whither has gone the place of feasting? Where are the joys of hall? Alas, the bright cup! Alas, the warrior in his corslet! Alas, the glory of the prince! How that time has passed away, has grown dark under the shadow of night, as if it had never been! Now in the place of the dear warriors stands a wall, wondrous high, covered with serpent shapes; the might of the ash-wood spears has carried off the earls, the weapon greedy for slaughter—a glorious fate; and storms beat upon these rocky slopes; the falling storm binds the earth, the terror of winter. Then comes darkness, the night shadow casts gloom, sends from the north fierce hailstorms to the terror of men. Everything is full of hardship in the kingdom of earth; the decree of fate changes the world under the heavens. Here possessions are transient, here friends are transient, here man is transient, here woman is transient; all this firm-set earth becomes empty.”’
So spoke the wise man in his heart, and sat apart in thought. Good is he who holds his faith; nor shall a man ever show forth too quickly the sorrow of his breast, except he, the earl, first know how to work its cure bravely. Well is it for him who seeks mercy, comfort from the Father in heaven, where for us all security stands.
1.7.3 Reading and Review Questions
- What are all of the kennings in the poem, and what do they mean?
- Where is the wanderer? Is there any symbolic meaning in the setting of the poem?
- Do the last lines, with their focus on Christianity, fit with the rest of the poem? Why or why not?
- What makes a man wise, according to the poem? How is it an Anglo- Saxon perspective on wisdom, or is it?
- How much does shame play a role in the wanderer’s perspectives? Should he feel shame, in either an Anglo-Saxon or a Christian context?


11.S: Pedigrees and Populations (Summary)
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- Ying Liu
- City College of San Francisco
- Pedigree analysis can be used to determine the mode of inheritance of specific traits such as diseases. Loci can be X- or Y-linked or autosomal in location and alleles either dominant or recessive with respect to wild type.
- If the mode of inheritance is known, a pedigree can be used to calculate the probability of inheritance of a particular genotype by an individual.
- The frequencies of all alleles and genotypes remain unchanged through successive generations of a population in Hardy-Weinberg equilibrium.
- Populations in true Hardy-Weinberg equilibrium have random mating, and no genetic drift, no migration, no mutation, and no selection with respect to the gene of interest.
- The Hardy-Weinberg formula can be used to estimate allele and genotype frequencies given only limited information about a population.
Key Terms
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Pedigree charts mode of inheritance genetic counseling incomplete penetrance variable expressivity proband affected carrier autosomal dominant autosomal recessive X-linked dominant |
X-linked recessive Y-linked inheritance Y-linked mitochondrial inheritance ( mtDNA ) sporadic product rule sum rule population p+q=1 |
Hardy-Weinberg formula p 2 + 2pq + q 2 =1 Hardy-Weinberg equilibrium assortative mating random mating migration genetic drift
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11.12: Reading- Porosity and Permeability
As we’ve learned, groundwater is simply water that exists underground. However, there are still lots of misconceptions about how people envision groundwater. Many envision large underground lakes and rivers, and while those do exist, they represent an infinitesimally small percentage of all groundwater. Generally speaking groundwater exists in the pore spaces between grains of soil and rocks. Imagine a water filled sponge. All of the holes in that sponge are water-filled. By squeezing that sponge we force the water out, similarly, by pumping an aquifer we force the water out of pore spaces.
There are lots of terms in hydrogeology, most of which are very simple, but essential. Here are a few of the big ones and their meanings.
Porosity
Porosity is an intrinsic property of every material. It refers to the amount of empty space within a given material. In a soil or rock the porosity (empty space) exists between the grains of minerals. In a material like gravel the grains are large and there is lots of empty space between them since they don’t fit together very well. However, in a material like a gravel, sand and clay mixture the porosity is much less as the smaller grains fill the spaces. The amount of water a material can hold is directly related to the porosity since water will try and fill the empty spaces in a material. We measure porosity by the percentage of empty space that exists within a particular porous media.
Permeability
Permeability is another intrinsic property of all materials and is closely related to porosity. Permeability refers to how connected pore spaces are to one another. If the material has high permeability than pore spaces are connected to one another allowing water to flow from one to another, however, if there is low permeability then the pore spaces are isolated and water is trapped within them. For example, in a gravel all of the pores well connected one another allowing water to flow through it, however, in a clay most of the pore spaces are blocked, meaning water cannot flow through it easily.
Aquifer
An aquifer is a term for a type of soil or rock that can hold and transfer water that is completely saturated with water. That means that all it is simply a layer of soil or rock that has a reasonably high porosity and permeability that allows it to contain water and transfer it from pore to pore relatively quickly and all of the pore spaces are filled with water. Good examples of aquifers are glacial till or sandy soils which have both high porosity and high permeability. Aquifers allows us to recover groundwater by pumping quickly and easily. However, overpumping can easily reduce the amount of water in an aquifer and cause it to dry up. Aquifers are replenished when surface water infiltrates through the ground and refills the pore spaces in the aquifer. This process is called recharge. It is especially important to ensure that recharge is clean and uncontaminated or the entire aquifer could become polluted. There are two main types of aquifer. An unconfined aquifer is one that does not have an aquitard above it but usually does below it.
When a water-bearing rock readily transmits water to wells and springs, it is called an aquifer. Wells can be drilled into the aquifers and water can be pumped out. Precipitation eventually adds water ( recharge ) into the porous rock of the aquifer. The rate of recharge is not the same for all aquifers, though, and that must be considered when pumping water from a well. Pumping too much water too fast draws down the water in the aquifer and eventually causes a well to yield less and less water and even run dry. In fact, pumping your well too fast can even cause your neighbor’s well to run dry if you both are pumping from the same aquifer.
In the diagram below, you can see how the ground below the water table (the blue area) is saturated with water. The “unsaturated zone” above the water table (the greenish area) still contains water (after all, plants’ roots live in this area), but it is not totally saturated with water. You can see this in the two drawings at the bottom of the diagram, which show a close-up of how water is stored in between underground rock particles.
Sometimes the porous rock layers become tilted in the earth. There might be a confining layer of less porous rock both above and below the porous layer. This is an example of a confined aquifer. In this case, the rocks surrounding the aquifer confines the pressure in the porous rock and its water. If a well is drilled into this “pressurized” aquifer, the internal pressure might (depending on the ability of the rock to transport water) be enough to push the water up the well and up to the surface without the aid of a pump, sometimes completely out of the well. This type of well is called artesian. The pressure of water from an artesian well can be quite dramatic .
A relationship does not necessarily exist between the water-bearing capacity of rocks and the depth at which they are found. A very dense granite that will yield little or no water to a well may be exposed at the land surface. Conversely, a porous sandstone, such as the Dakota Sandstone mentioned previously, may lie hundreds or thousands of feet below the land surface and may yield hundreds of gallons per minute of water. Rocks that yield freshwater have been found at depths of more than 6,000 feet, and salty water has come from oil wells at depths of more than 30,000 feet. On the average, however, the porosity and permeability of rocks decrease as their depth below land surface increases; the pores and cracks in rocks at great depths are closed or greatly reduced in size because of the weight of overlying rocks.
Water Movement in Aquifers
Water movement in aquifers is highly dependent of the permeability of the aquifer material. Permeable material contains interconnected cracks or spaces that are both numerous enough and large enough to allow water to move freely. In some permeable materials groundwater may move several metres in a day; in other places, it moves only a few centimeters in a century. Groundwater moves very slowly through relatively impermeable materials such as clay and shale.
After entering an aquifer, water moves slowly toward lower lying places and eventually is discharged from the aquifer from springs, seeps into streams, or is withdrawn from the ground by wells. Groundwater in aquifers between layers of poorly permeable rock, such as clay or shale, may be confined under pressure. If such a confined aquifer is tapped by a well, water will rise above the top of the aquifer and may even flow from the well onto the land surface. Water confined in this way is said to be under artesian pressure, and the aquifer is called an artesian aquifer.
Visualizing Artesian Pressure
Here’s a little experiment to show you how artesian pressure works. Fill a plastic sandwich baggie with water, put a straw in through the opening, tape the opening around the straw closed, do not point the straw towards your teacher or parents, and then squeeze the baggie. Artesian water is pushed out through the straw.
Aquitard
The other type is a confined aquifer that has an aquitard above and below it. An aquitard is basically the opposite of an aquifer with one key exception. Aquitards have very low permeability and do not transfer water well at all. In fact, in the ground they often act as a barrier to water flow and separate two aquifers. The one key exception is that aquitards can have high porosity and hold lots of water however, due to the their low permeability they are unable to transmit it from pore to pore and therefore water cannot flow within an aquitard very well. A good example of an aquitard is a layer of clay. Clay often has high porosity but almost no permeability meaning it is essentially a barrier which water cannot flow through and the water within it is trapped. However, there is still limited water flow within aquitards due to other processes that I won’t get into now.
Contributors and Attributions
- Back to Basics on Groundwater. Authored by : Matt Herod. Provided by : European Geosciences Union. Located at : http://blogs.egu.eu/network/geosphere/2013/09/17/back-to-basics-on-groundwater/ . License : CC BY: Attribution
- Aquifers. Provided by : USGS. Located at : http://water.usgs.gov/edu/earthgwaquifer.html . License : Public Domain: No Known Copyright


7.2: Identifying the Main Concepts
Keywords
Your research question will be the foundation for your research process. The next step is to identify the main concepts within the research question that you created. Though many people type full questions word-for-word into online search engines, the algorithms of the search engines are programmed to pull out the most important keywords in what is typed into the search bar—some of the words in your research question are irrelevant when it comes to finding information sources. Main concepts, also sometimes called keywords, key terms, and/or key phrases, are almost always nouns. Words in your research question that are not likely to relate to the main concept are words like: the, is, affect, what, why, when, how, and are. When trying to identify the main concepts, think about what ideas and topics would need to be present in an information source for it to be relevant to you and your research.
How can divorce affect a student’s GPA in high school?
How can divorce affect a student ‘s GPA in high school ?
In the example above, the main concepts, or keywords, in the research question are divorce, student’s GPA, and high school. These are the main concepts that will be the focus of your research; if an information source includes all of these concepts, then it is very likely to be relevant and useful to you. It is your job as a researcher to determine what is relevant to your research. Be aware that the main concepts from your research question serve as a base to launch your search for information and the keywords selected to describe your main concepts are likely to evolve during the process.
Sources
Textbox adapted from “ Why Precision Searching? ” by Teaching & Learning, Ohio State University Libraries, licensed under CC BY 4.0


<IP_ADDRESS>: Thinking About Roles of Sources
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Does this nightmare sound like how you feel every time you have to write a term paper?
Your team is playing in the big game and you’re the coach. (Maybe the real coach missed the plane. Who knows–it’s a nightmare!) The stakes are high. You know your players are good athletes—you have access to the best and plenty of them. But you don’t really know good strategies of the game, so you don’t quite know how to use your players. For instance, is it better to keep your quarterback fresh by substituting often? Your kicker is not as bulky as your tackles. Is that typical of good kickers or should you find somebody else? And what about your linemen—can they tackle as well as block?
What makes this a nightmare is not knowing how to use your players in a high-pressure game. Unfortunately, that situation is similar to writing a term paper if all you know are directions like these:
Your paper must be in 12 pt. font, Times New Roman, double spaced with no more than 1″ margins, and include a minimum of 8 total articles comprised of:
So you know you need sources. But directions like those aren’t much help with what to actually do with the sources in your paper. Even with credible sources, it’s very difficult to write a persuasive paper until you learn the roles that sources play—how you can use them—within your paper.
But who said anything about a persuasive paper? Perhaps one of the things you don’t know is that with most term papers and essays, the unstated expectation is that you will use your sources to make an argument. That’s because most scholarly writing makes an argument. You will be arguing that your answer to your research question (your thesis) is correct, or at least reasonable.
Obviously, it’s high time someone helped you learn all this!
For both professionals and student researchers, successful scholarly writing uses sources to fill various roles within the term paper, journal article, book, poster, essay, or other assignment.
Those roles all have to do with rhetoric—the art of making a convincing argument. Putting your sources to work for you in these roles can help you write in a more powerful, persuasive way—to, in fact, win your argument.
For another way to think about choosing the right sources for your needs, see Sources and Information Needs.
NOTE:
This section on rhetorical roles of research sources was influenced by many sources. See the bibliography .


2.4: Two-Column Proofs
If you’ve ever spent much time trying to check someone else’s work in solving an algebraic problem, you’d probably agree that it would be a help to know what they were trying to do in each step. Most people have this fairly vague notion that they’re allowed to “do the same thing on both sides” and they’re allowed to simplify the sides of the equation separately – but more often than not, several different things get done on a given line, mistakes get made, and it can be nearly impossible to figure out what went wrong and where.
Now, after all, the beauty of math is supposed to lie in its crystal clarity, so this sort of situation is really unacceptable. It may be an impossible goal to get “the average Joe” to perform algebraic manipulations with clarity, but those of us who aspire to become mathematicians must certainly hold ourselves to a higher standard. Two-column proofs are usually what is meant by a “higher standard” when we are talking about relatively mechanical manipulations – like doing algebra, or more to the point, proving logical equivalences. Now don’t despair! You will not, in a mathematical career, be expected to provide two-column proofs very often. In fact, in more advanced work one tends to not give any sort of proof for a statement that lends itself to a two-column approach. But, if you find yourself writing “As the reader can easily verify, Equation 17 holds. . . ” in a paper, or making some similar remark to your students, you are morally obligated to being able to produce a two-column proof.
So what, exactly, is a two-column proof? In the left column, you show your work, being careful to go one step at a time. In the right column you provide a justification for each step.
We’re going to go through a couple of examples of two-column proofs in the context of proving logical equivalences. One thing to watch out for: if you’re trying to prove a given equivalence, and the first thing you write down is that very equivalence, it’s wrong! This would constitute the logical error known as “begging the question” also known as “circular reasoning.” It’s clearly not okay to try to demonstrate some fact by first asserting the very same fact. Nevertheless, there is (for some unknown reason) a powerful temptation to do this very thing. To avoid making this error, we will not put any equivalences on a single line. Instead, we will start with one side or the other of the statement to be proved, and modify it using known rules of equivalence, until we arrive at the other side.
Without further ado, let’s provide a proof of the equivalence \(A ∧ (B ∨ ¬A) \cong A ∧ B\). 1
\( ∧ (B ∨ ¬A) \cong (A ∧ B) ∨ (A ∧ ¬A) \tag{distributive law}\)
\(\cong (A ∧ B) ∨ c \tag{complementarity}\)
\(\cong (A ∧ B) \tag{identity law}\)
We have assembled a nice, step-by-step sequence of equivalences – each justified by a known law – that begins with the left-hand side of the statement to be proved and ends with the right-hand side. That’s an irrefutable proof!
In the next example we’ll highlight a slightly sloppy habit of thought that tends to be problematic. People usually (at first) associate a direction with the basic logical equivalences. This is reasonable for several of them because one side is markedly simpler than the other. For example, the domination rule would normally be used to replace a part of a statement that looked like “\(A ∧ c\)” with the simpler expression “\(c\)”. There is a certain amount of strategization necessary in doing these proofs, and I usually advise people to start with the more complicated side of the equivalence to be proved. It just feels right to work in the direction of making things simpler, but there are times when one has to take one step back before proceeding two steps forward. . .
Let’s have a look at another equivalence: \(A∧(B∨C) \cong (A∧(B∨C))∨(A∧ C)\). There are many different ways in which valid steps can be concatenated to convert one side of this equivalence into the other, so a subsidiary goal is to find a proof that uses the least number of steps. Following my own advice, I’ll start with the right-hand side of this one.
\((A ∧ (B ∨ C)) ∨ (A ∧ C) \cong ((A∧B)∨(A∧C))∨(A∧C) \tag{distributive law}\)
\(\cong (A∧B)∨((A∧C)∨(A∧C)) \tag{associative law}\)
\(\cong (A ∧ B) ∨ (A ∧ C) \tag{idempotence}\)
\(\cong A ∧ (B ∨ C) \tag{distributive law}\)
Note that in the example we’ve just done, the two applications of the distributive law go in opposite directions as far as their influence on the complexity of the expressions are concerned.
Exercises:
Write two-column proofs that verify each of the following logical equivalences.
- \(A ∨ (A ∧ B) \cong A ∧ (A ∨ B)\)
- \((A ∧ ¬B) ∨ A \cong A\)
- \(A ∨ B \cong A ∨ (¬A ∧ B)\)
- \(¬(A ∨ ¬B) ∨ (¬A ∧ ¬B) \cong ¬A\)
- \(A \cong A ∧ ((A ∨ ¬B) ∨ (A ∨ B))\)
- \((A ∧ ¬B) ∧ (¬A ∨ B) \cong c\)
- \(A \cong A ∧ (A ∨ (A ∧ (B ∨ C)))\)
- \(¬(A ∧ B) ∧ ¬(A ∧ C) \cong ¬A ∨ (¬B ∧ ¬C)\)


5.11: Citing Sources is a Basic Skill Learned Early On
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- Cheryl E. Ball & Drew M. Loewe ed.
- West Virginia University via Digital Publishing Institute and West Virginia University Libraries
Author: Susanmarie Harrington, English, University of Vermont.
Citing sources can seem simple: Follow the rules to show readers what you read. Many English classes usually teach a particular system for citing sources designed by, and named after, the Modern Language Association (MLA). College students soon discover that professors working in other disciplines have similar (yet different!) systems for citing sources (one designed by and named after the American Psychological Association, APA, is particularly common). The belief that citing sources is simple can be traced back to formative experiences: Many writers connect their later success to a thorough assignment in middle or high school that required them to use the library, create an extensive bibliography, and write a long paper that used quotations to support their points. People who become expert in a field may not recognize the implicit skills they have developed since that first experience. It can seem almost second nature to follow rules for inserting footnotes, indenting long quotations, and constructing lists of works cited: Citation is merely a matter of following directions.
It turns out it’s more complicated than that: All the directions about citing sources assume deep prior knowledge. Citing sources is a specialized, almost ritualized, skill that provides readers with information in specific, routinized ways. Style guides provide rules about everything from how many spaces to put between sentences to how to organize and format the bibliography. Style guides direct academic writers to use footnotes or parenthetical notations, in combination with bibliographies at the end of a piece, to tell readers where information comes from—who wrote it, when, and where it was published. For skilled writers, following complicated rules comes easily—for beginning students, not so much.
Why are these systems so complicated? One reason often emphasized in school is accountability. Citing sources in very particular and detailed ways allows readers to find any source material the writer used, and allows readers to evaluate the quality of the source material the writer used. But complex citation systems have other purposes as well: They let writers demonstrate strong command of highly specialized work. In other words, the rules let writers show expertise.
This expertise unfolds in nuanced ways. Writers choose texts to quote in order to connect themselves to particular traditions of thinking or researching; to put their arguments in the context of other, more prominent authors, whose views are already accepted by readers; or to put forth arguments or examples a writer wants to contest, examine, or elaborate. So, selecting and discussing sources is a matter of savvy diplomacy, persuasion, and argumentation. Sure, it involves learning how to follow detailed directions about how and where to place punctuation in order to indicate where quotations start and end; more importantly, it involves learning how and why writers associate themselves with sources, whether they seek to agree with what they’ve read, argue with what they’ve read, or apply what they’ve read to a new context. It involves understanding that there are reasons for using evidence other than to support a claim; writers might use sources to identify trends in order to argue with them.
Capturing Complexity
Different systems for citing sources may require different formats on the page, but the variation in how research is presented is intellectually even more significant. Humanists generally value work that dwells closely and slowly on particular passages or moments in text, and quotations are to be presented and analyzed. Scientists generally value work that presents trends in phenomena, with previous work grouped and summarized, with far fewer, if any, quotations. There is no simple formula for citing or using sources, or for organization that can teach writers everything there is to know about what they are expected to do.
Will today’s seventh graders be prepared to pick up these lessons in college without additional instruction? Probably not, even though the Common Core State Standards (CCSS) do put a premium on learning to cite evidence for claims and conclusions. The Reading Standards mention that students should be able to cite material accurately, and the expectation that students support claims with evidence appears in grades 6 through 12. But the CCSS don’t distinguish the ways in which different disciplines might have different ways of approaching the use of sources, and they don’t go into detail about the particular conventions writers should follow to cite sources. The CCSS emphasize the kind of close reading that is likely more common in the humanities. So students coming from high school English classes will be prepared to move into college English literature expectations for handling sources—but they may not be prepared to do exactly what a sociology or political science course expects, let alone biology or math.
Students arrive in college prepared not only by high school curriculum standards but also by their experience of reading and writing in the world. In school, the details of citation systems carry authority. Out of school, other strategies help readers evaluate information. Material on the web provides live links rather than formal citations. Journalists don’t use parenthetical citation systems to indicate where their information comes from—they simply identify it in the text by putting the source’s name and qualification. Graphs and charts, seen in posters, pamphlets, textbooks or journalistic sources, may have a legend identifying the organization that supplied data. Nonfiction books have varied styles for citation—from copious footnotes, extended lists of sources at the back, to a list of works consulted without any attempt to map where they influenced the book. Sometimes experts supply information without citing sources: Reputable food bloggers dispense authoritative information about, say, how to safely can produce without necessarily linking to or identifying the scientific sources for those recommendations. Outside of school, there are many ways to convey credibility and indicate relationships to the sources used for a piece.
Writing with authority is complicated and needs to be learned anew in each situation: successful writing isn’t just about following rules, but about establishing connections among readers and writers. Writing with sources is about participation in ongoing conversations, situated in the complex, messy politics of social networks.
Further Reading
Lionel Anderson and Katherine Schulten’s blog, “The Learning Network,” published in the New York Times , discusses the complications of citing sources and plagiarism in high-profile cases in journalism, politics, music, and comedy. For a look at how context matters in how citations work, see Chris Anson and Shawn Neely’s discussion of citation in writing for the U.S. Army and at West Point: “The Army and the Academy as Textual Communities: Exploring Mismatches in the Concepts of Attribution, Appropriation, and Shared Goals,” published in Kairos . Linda Adler-Kassner, Chris Anson, and Rebecca Moore Howard discuss the ways we should look beyond traditional school expectations to learn how writers in many contexts—such as government work and agricultural extension sites—attribute information. See their essay “Framing Plagiarism” in the collection Originality, Imitation, and Plagiarism: Teaching Writing in the Digital Age (University of Michigan Press).
To learn more about the many reasons writers cite sources, see Amy Robillard’s essay, “Young Scholars Affecting Composition: A Challenge to Disciplinary Citation Practices,” published in College English . For a historical take on this point, see Robert J. Connors’s “The Rhetoric of Citation Systems, Part II: Competing Epistemic Values in Citation” (Rhetoric Review). Connors’s historical study illustrates the ways citation styles have shifted over time, influenced by arguments in professional associations. Citation styles have never been simple and obvious; they change over time.
For a look at how one university helpfully introduces students to writing effectively with sources, see Gordon Harvey’s material for the Harvard Expository Writing Program: Writing with Sources, A Guide for Harvard Students.
Keywords
citation, plagiarism, researched writing, working with sources, writing development
Author Bio
Susanmarie Harrington is professor of English and director of Writing in the Disciplines at the University of Vermont. She has taught researched writing for over twenty years, teaching at all levels from first-year students to graduate students. She has collaborated with faculty across the disciplines in workshops and teaching, and she has taught in both urban and rural institutions. Most recently, she has worked with librarians, faculty in the disciplines, and the writing center to promote attention to department-based learning outcomes for students. She has co-edited and co-authored many different types of publications, working with quantitative and qualitative methods. Her variety of writing experiences and working relationships with faculty in many departments inspired her interest in citation and research development.


7.4: Protecting Your Idea and Polishing the Pitch through Feedback
By the end of this section, you will be able to:
- Understand why you need to protect your idea
- Describe both legal and unconventional tools to keep your ideas safe
- Understand the importance of feedback and how to manage and use it
When you start to pitch your idea, it means you are sharing it with a variety of people for different purposes. When encouraged to develop entrepreneurial ideas, students often ask, “How can I be sure no one is going to steal my idea?” The response often is that ideas come easily, while knowledgeable, driven leaders are hard to find. In other words, for those of you just starting out as entrepreneurs, it is important to recognize that coming up with ideas is much easier and much less important than learning how to turn those ideas into products that fit a market and that have a customer base already, or one you develop through painstaking customer development strategies. Many entrepreneurs find it is more important to sell an investor on their leadership potential and the strength of their team than on the strength of their idea or prototype. Even so, it is common for entrepreneurs to want to protect their intellectual property because more well-established companies might leverage deeper wells of resources and broader, more powerful networks to bring an innovative product or service to market in the time it takes an entrepreneur to move from securing seed funding to landing their first support for their first venture capital round (after seed funding). 27
Protecting your business idea with a patent, should you choose to apply for one, is important. Patents are granted for the purpose of encouraging entrepreneurship. If innovators have some reassurance that others will be kept out of the marketplace for a certain amount of time, they may be more likely to take the risk to pursue an innovation in the first place. Intellectual property protection (patents, trademarks, copyrights) is covered in much more depth in the Creativity, Innovation, and Invention and Fundamentals of Resource Planning chapters.
Products in most fields need to be developed and brought to market more quickly than the time it takes to go through the standard patent process. For manufactured goods, it is important to seek a patent when a product is finalized to protect the design. For intellectual property, it may be best to build first and seek patents later, particularly in a highly competitive field where it would be difficult to show that you truly have a unique breakthrough.
Entrepreneur.com has some helpful suggestions 28 that are paraphrased and reframed here: First, recognize that almost nothing comes to market having been created by a sole inventor or innovator. Some ideas truly are unique, but even they are nearly impossible to keep “under wraps.” Ideas have to be shared with many people for products or services to be developed. If nothing else, you will likely have to present your idea to investors at some point. Protecting initial ideas is not as important as protecting versions of products and services developed through iterative learning and testing processes because “know how” and trade secrets are considered intellectual property and must be protected since they are not always patentable. Aim to protect your successful value propositions, not your every technological whim. Most new business ideas are variations of solutions that others have anticipated or even written about, but others have not had the drive, the networking skills, or the fundraising ability of a true entrepreneur. Balance your time wisely between trying to protect your idea and working to develop it.
One way you can gain some peace of mind, again to paraphrase Entrepreneur.com, 29 is by thoroughly investigating everyone with whom you plan to partner. If you have some assurance that they have not “burned” collaborators in the past, you can proceed with a sense of security. Conduct research without invading anyone’s privacy but use all of the public tools available to you. Search online to learn about potential partners and their previous endeavors. Request contact information and perhaps a list of references or former collaborators from potential partners. The level of formality is going to depend on the nature of the industry you are working to enter and the nature of the relationship you have with your collaborators, but if they resist being researched, that could be a sign that they will probably not prioritize you or your product’s protection.
Legal Agreements
Outside of patents, there are additional legal means of protecting your intellectual property. 30 You may wish to require partners to sign a nondisclosure agreement (NDA) . Typically, NDAs carry with them a penalty should the partner disclose what they know of the proprietary information that lies at the heart of your value proposition. These can be time limited, meaning after a certain amount of time, someone will be free to discuss the business and its proprietary practices, or, for stronger legal controls, they may be open-ended. An open-ended NDA can require a person to stay silent about key information for life or face possible civil lawsuits worth potentially millions of dollars.
A noncompete agreement in a contract prevents an employee from working for the competition for a specified period of time after working for you. The intention is to prevent them from taking your secrets or their skills to a competitor. Some of these practices have been called into question particularly in industries where low-level workers who do not carry around trade secrets find they are asked to sign these types of agreements. However, they can help keep corporate espionage to a minimum, and they can prevent certain key employees from taking the organization’s intellectual property with them to their new employer, or perhaps to create their own startup. Employees should only sign them if they are a condition for employment. These agreements can vary from state to state. California in general does not enforce noncompete agreements; this is due in part to the dynamic nature of startups, particularly in Silicon Valley. It also reflects a philosophy that working professionals should not be inhibited or restrained from pursuing their livelihood.
A work-for-hire agreement between an individual employee and a company states that ownership of innovations belongs to the company, even if an individual makes substantial contributions to the product, service, or process. You should expect to be required to list collaborators on patents, even those working under a work-for-hire clause, but the purpose of the contractual agreement is to ensure that you or your company maintains exclusive rights to the patent.
Unconventional Methods
One further suggestion is to apply creativity and mask your product or service’s true nature. By de-emphasizing certain key features or by burying them in the user interface (UI), you might be able to turn attention away from your value proposition while still building your product, platform, or prototype. The user interface (UI) is what a customer sees when they use your product. A graphic user interface (GUI) is common for all Windows and Apple-based devices. Smartphones use application (app) interfaces built off the base operating system (mainly iOS or Android). UI’s have become very common for many consumer and professional products, as they link to microprocessors, sensors, memory, and other embedded features. From a design standpoint, your team must decide where every button, search box, graphic element, and information display is placed and what it will look like. Good UI is useful and feels intuitive to the user.
For digital products and services, this aspect of your product is incredibly important, which is why manipulating it to mask functions or features is particularly risky. This is not a fool-proof approach by any means, but in hyper competitive, rapidly evolving environments such as the web software and mobile app industries, where invention and iteration occur at a breakneck pace and where, as soon as you go to market, your competitors can see and try to re-create your service or platform, a little subterfuge can give your business an edge at a relatively low cost.
An example of masking the true intentions of a product, perhaps, is the development of the mobile game Ingress by Niantic, Inc. Ingress is a GPS-based augmented reality game played around the world where users join imaginary factions and take over imaginary portals tied to real geographical locations in order to link up those portals and help their faction gain territory and resources. But while Niantic was taking its global mapping expertise and making a SciFi game out of it, it was also developing Pokémon GO. After specific geographic “nodes” were mapped by users the world over, Niantic had a global network of points of interest indicated by users. In many cases, nodes in Ingress—places with public art, cool architecture, or historical markers, for example—later became PokéStops in the Pokémon GO game, where players of the global augmented reality game gather resources to catch and battle their pocket monsters.
One way to protect your intellectual property is to strategically mask dormant features or capabilities until they can be more fully exploited. While few startups have the technological clout of Niantic, almost every business makes decisions on what to push forward, what to hold back, and when to release new products or features.
Using Feedback to Refine Your Pitch
Pitching requires you to demonstrate that you have assembled a capable, professional team that can turn an idea into an innovation. Users, partners, investors, and others will offer thoughts on how your product or your organization should change. Investors consider it a warning sign if an entrepreneur cannot handle feedback. 31 Applying lessons learned from feedback is the purpose of business learning.
Entrepreneurial ventures often start out as problems with no easy solutions. Your initial idea involves your best guess at what will be an innovative solution, but that will evolve more quickly toward product-market fit if your response to feedback is to accept it with grace. Your pitch must demonstrate that you have a great product, that you have done your research, and that you are able to take feedback and apply it to your products to make them better. 32 In other words, you must show you are coachable.
Your venture’s development depends on gathering data to find out what customers like and what investors are willing to fund, so you must seek out positive feedback and build on it, but you must also think critically about the positive messages you receive. Are consumers or users enthusiastic in their support or merely polite (this can especially be a concern when pitching to friends and family)? Can you clearly identify why you received positive feedback about certain features and not others? Be sure to gain feedback on many product variables and be sure you can isolate data points for meaningful analysis. The best feedback includes quantitative responses indicating what consumers like and what they don’t, as well as qualitative information explaining why. Quantitative data relate to numerical measurements including actual purchase and behavior as well as opinion research about a product. Qualitative data are complex information that answers the questions “Why?” and “How?” It is often impossible to tell why people do what they do with your product unless you ask them.
In the short term, you can use feedback to decide which features to focus on early in the venture. Many entrepreneurs are faced with the dilemma of having too many good ideas. 33 If you pursue all of your good ideas at the same time, your organization can quickly run out of resources. Focus first on features that are most popular and relatively affordable to produce and deliver. Those high-return products, services, or features might not be what you use to define your brand in later years, but they can sustain a startup long enough to develop more elaborate products and features that require more time and investment. Over the long term, feedback helps you direct your company.
Feedback may also come from employees, market leaders, and your competition. Feedback from these sources may be more useful for guiding long-term growth projects. In this sense, feedback means more than advice or product ratings. It can mean tactical moves in the marketplace. Your competitors offer you feedback when they take actions in a marketplace in response to your actions. Be sure to attend to competitors’ actions with the same open mind and the same air of thoughtful skepticism you apply to other forms of feedback.
Once you have the opportunity to pitch your idea, the next step is the careful measuring of quantitative and qualitative feedback about the pitch presentation, mockup, poster, or, in the case of many manufacturing processes, a 3D-printed model that approximates what the tangible finished product might look and feel like. Data from pitch competitions are sometimes out of your control, so it may be preferable to incorporate the learning you get from pitch feedback into this customer development process.


8: Carbonyl Alpha-Substitution Reactions
When you have completed Chapter 8, you should be able to
- fulfill all of the detailed objectives listed under each individual section.
- design multi‑step syntheses in which the reactions introduced in this unit are used in conjunction with any of the reactions described in previous units.
- solve road‑map problems that require a knowledge of carbonyl alpha‑substitution reactions.
- define, and use in context, the key terms introduced.
Alpha‑substitution reactions are the third major type of reaction that you will study in your investigation of the chemistry of carbonyl compounds. As you will see, these reactions proceed through the formation of the enol form of the carbonyl compound.
After a brief review of keto‑enol tautomerism, we begin our discussion of alpha‑substitution reactions by looking at the methods in which the enol form of the carbonyl compound is directly involved. After discussing the factors that influence the formation and stability of enolate anions, we will examine some halogenation reactions in which an enolate ion is formed as an intermediate.
The chapter concludes with a study of the alkylation of enolate anions. These reactions are of tremendous use in organic syntheses, as they provide a method of forming new carbon‑carbon bonds, and hence facilitate the laboratory preparation of increasingly complex compounds.
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- 8.6: Acidity of Alpha Hydrogen Atoms- Enolate Ion Formation
- The section on the acidity of alpha hydrogen atoms explains that these hydrogens are more acidic than other hydrogens due to the stabilization of the resulting enolate ion. When an alpha hydrogen is removed by a strong base, it forms an enolate, which serves as a key intermediate in various organic reactions, including nucleophilic additions and substitutions. This characteristic is crucial for many synthetic pathways in organic chemistry.