Boolean Algebra

Basic Engineering Boolean Algebra and Logic Gates F Hamer, M Lavelle & D McMullan The aim of this document is to provide a short, self assessment programme for students who wish to understand the basic techniques of logic gates. c 2005 Email: chamer, mlavelle, [email  protected] ac. uk Last Revision Date: August 31, 2006 Version 1. 0 Table of Contents 1. 2. 3. 4. 5. Logic Gates (Introduction) Truth Tables Basic Rules of Boolean Algebra Boolean Algebra Final Quiz Solutions to Exercises Solutions to QuizzesThe full range of these packages and some instructions, should they be required, can be obtained from our web page Mathematics Support Materials. Section 1: Logic Gates (Introduction) 3 1. Logic Gates (Introduction) The package Truth Tables and Boolean Algebra set out the basic principles of logic. Any Boolean algebra operation can be associated with an electronic circuit in which the inputs and outputs represent the statements of Boolean algebra. Although these circuits may be com plex, they may all be constructed from three basic devices. These are the AND gate, the OR gate and the NOT gate. y AND gate x ·y x y OR gate x+y x NOT gate x In the case of logic gates, a di? erent notation is used: x ? y, the logical AND operation, is replaced by x  · y, or xy. x ? y, the logical OR operation, is replaced by x + y.  ¬x, the logical NEGATION operation, is replaced by x or x. The truth value TRUE is written as 1 (and corresponds to a high voltage), and FALSE is written as 0 (low voltage). Section 2: Truth Tables 4 2. Truth Tables x y x ·y x 0 0 1 1 Summary y x ·y 0 0 1 0 0 0 1 1 of AND gate x 0 0 1 1 Summary y x+y 0 0 1 1 0 1 1 1 of OR gate x y x+y x x 0 1 Summary of x 1 0 NOT gate Section 3: Basic Rules of Boolean Algebra 5 3. Basic Rules of Boolean Algebra The basic rules for simplifying and combining logic gates are called Boolean algebra in honour of George Boole (1815 – 1864) who was a self-educated English mathematician who developed many of t he key ideas. The following set of exercises will allow you to rediscover the basic rules: x Example 1 1 Consider the AND gate where one of the inputs is 1. By using the truth table, investigate the possible outputs and hence simplify the expression x  · 1.Solution From the truth table for AND, we see that if x is 1 then 1  · 1 = 1, while if x is 0 then 0  · 1 = 0. This can be summarised in the rule that x  · 1 = x, i. e. , x x 1 Section 3: Basic Rules of Boolean Algebra 6 Example 2 x 0 Consider the AND gate where one of the inputs is 0. By using the truth table, investigate the possible outputs and hence simplify the expression x  · 0. Solution From the truth table for AND, we see that if x is 1 then 1  · 0 = 0, while if x is 0 then 0  · 0 = 0. This can be summarised in the rule that x  · 0 = 0 x 0 0Section 3: Basic Rules of Boolean Algebra 7 Exercise 1. (Click on the green letters for the solutions. ) Obtain the rules for simplifying the logical expressions x (a) x + 0 which corresponds to the logic gate 0 (b) x + 1 which corresponds to the logic gate x 1 Exercise 2. (Click on the green letters for the solutions. ) Obtain the rules for simplifying the logical expressions: x (a) x + x which corresponds to the logic gate (b) x  · x which corresponds to the logic gate x Section 3: Basic Rules of Boolean Algebra 8 Exercise 3. Click on the green letters for the solutions. ) Obtain the rules for simplifying the logical expressions: (a) x + x which corresponds to the logic gate x (b) x  · x which corresponds to the logic gate x Quiz Simplify the logical expression (x ) represented by the following circuit diagram. x (a) x (b) x (c) 1 (d) 0 Section 3: Basic Rules of Boolean Algebra 9 Exercise 4. (Click on the green letters for the solutions. ) Investigate the relationship between the following circuits. Summarise your conclusions using Boolean expressions for the circuits. x y x y (a) (b) x y x yThe important relations developed in the above exer cise are called De Morgan’s theorems and are widely used in simplifying circuits. These correspond to rules (8a) and (8b) in the table of Boolean identities on the next page. Section 4: Boolean Algebra 10 4. Boolean Algebra (1a) x ·y = y ·x (1b) x+y = y+x (2a) x  · (y  · z) = (x  · y)  · z (2b) x + (y + z) = (x + y) + z (3a) x  · (y + z) = (x  · y) + (x  · z) (3b) x + (y  · z) = (x + y)  · (x + z) (4a) x ·x = x (4b) x+x = x (5a) x  · (x + y) = x (5b) x + (x  · y) = x (6a) x ·x = 0 (6b) x+x = 1 (7) (x ) = x (8a) (x  · y) = x + y (8b) (x + y) = x  · ySection 4: Boolean Algebra 11 These rules are a direct translation into the notation of logic gates of the rules derived in the package Truth Tables and Boolean Algebra. We have seen that they can all be checked by investigating the corresponding truth tables. Alternatively, some of these rules can be derived from simpler identities derived in this package. Example 3 Show how rule (5a) can be deriv ed from the basic identities derived earlier. Solution x  · (x + y) = = = = = x  · x + x  · y using (3a) x + x  · y using (4a) x  · (1 + y) using (3a) x  · 1 using Exercise 1 x as required. Exercise 5. Click on the green letter for the solution. ) (a) Show how rule (5b) can be derived in a similar fashion. Section 4: Boolean Algebra 12 The examples above have all involved at most two inputs. However, logic gates can be put together to join an arbitrary number of inputs. The Boolean algebra rules of the table are essential to understand when these circuits are equivalent and how they may be simpli? ed. Example 4 Let us consider the circuits which combine three inputs via AND gates. Two di? erent ways of combining them are x y z and x y z x  · (y  · z) (x  · y)  · z Section 4: Boolean Algebra 13However, rule (2a) states that these gates are equivalent. The order of taking AND gates is not important. This is sometimes drawn as a three (or more! ) input AND gate x y z x ·y ·z but really this just means repeated use of AND gates as shown above. Exercise 6. (Click on the green letter for the solution. ) (a) Show two di? erent ways of combining three inputs via OR gates and explain why they are equivalent. This equivalence is summarised as a three (or more! ) input OR gate x y z x+y+z this just means repeated use of OR gates as shown in the exercise. Section 5: Final Quiz 14 5. Final Quiz Begin Quiz 1.Select the Boolean expression that is not equivalent to x  · x + x  · x (a) x  · (x + x ) (b) (x + x )  · x (c) x (d) x 2. Select the expression which is equivalent to x  · y + x  · y  · z (a) x  · y (b) x  · z (c) y  · z (d) x  · y  · z 3. Select the expression which is equivalent to (x + y)  · (x + y ) (a) y (b) y (c) x (d) x 4. Select the expression that is not equivalent to x  · (x + y) + y (a) x  · x + y  · (1 + x) (b) 0 + x  · y + y (c) x  · y (d) y End Quiz Solutions to Exercises 15 Solutions to Exercise s Exercise 1(a) From the truth table for OR, we see that if x is 1 then 1 + 0 = 1, while if x is 0 then 0 + 0 = 0.This can be summarised in the rule that x + 0 = x x 0 Click on the green square to return x Solutions to Exercises 16 Exercise 1(b) From the truth table for OR we see that if x is 1 then 1 + 1 = 1, while if x is 0 then 0 + 1 = 1. This can be summarised in the rule that x + 1 = 1 x 1 Click on the green square to return 1 Solutions to Exercises 17 Exercise 2(a) From the truth table for OR, we see that if x is 1 then x + x = 1 + 1 = 1, while if x is 0 then x + x = 0 + 0 = 0. This can be summarised in the rule that x + x = x x x Click on the green square to return Solutions to Exercises 18Exercise 2(b) From the truth table for AND, we see that if x is 1 then x  · x = 1  · 1 = 1, while if x is 0 then x  · x = 0  · 0 = 0. This can be summarised in the rule that x  · x = x x x Click on the green square to return Solutions to Exercises 19 Exercise 3(a) From the truth t able for OR, we see that if x is 1 then x + x = 1 + 0 = 1, while if x is 0 then x + x = 0 + 1 = 1. This can be summarised in the rule that x + x = 1 x 1 Click on the green square to return Solutions to Exercises 20 Exercise 3(b) From the truth table for AND, we see that if x is 1 then x  · x = 1  · 0 = 0, while if x is 0 then x  · x = 0  · 1 = 0.This can be summarised in the rule that x  · x = 0 x 0 Click on the green square to return Solutions to Exercises 21 Exercise 4(a) The truth tables are: x y x y 0 0 0 1 1 0 1 1 x y 0 0 0 1 1 0 1 1 x+y 0 1 1 1 x 1 1 0 0 y 1 0 1 0 (x + y) 1 0 0 0 x  ·y 1 0 0 0 x y From these we deduce the identity x y (x + y) = x y x  ·y Click on the green square to return Solutions to Exercises 22 Exercise 4(b) The truth tables are: x y x y 0 0 0 1 1 0 1 1 x y 0 0 0 1 1 0 1 1 x ·y 0 0 0 1 x 1 1 0 0 y 1 0 1 0 (x  · y) 1 1 1 0 x +y 1 1 1 0 x y From these we deduce the identity x y (x  · y) = x y x +y Click on the green square to returnSoluti ons to Exercises 23 Exercise 5(a) x+x ·y = x  · (1 + y) using (3a) = x  · 1 using Exercise 1 = x as required. Solutions to Exercises 24 Exercise 6(a) Two di? erent ways of combining them are x y z and x y z However, rule (2b) states that these gates are equivalent. The order of taking OR gates is not important. x + (y + z) (x + y) + z Solutions to Quizzes 25 Solutions to Quizzes Solution to Quiz: From the truth table for NOT we see that if x is 1 then (x ) = (1 ) = (0) = 1, while if x is 0 then (x ) = (0 ) = (1) = 0. This can be summarised in the rule that (x ) = x x x End Quiz Test: â€Å"Study Guide Algebra†

La Vie Boheme Essay Example | Topics and Well Written Essays - 750 words

La Vie Boheme - Essay Example Popular consumption of music has long been influenced by the stage – but perhaps not more so than in the modern era of super-popular Broadway musicals. It is in some ways easy to dismiss such musicals as somewhat venal entertainment, more akin to Hollywood than Mozart, but their immense popularity demands that they receive some attention. Perhaps no musical has been as widely popular as Jonathan Larson’s magnum opus, Rent, and perhaps no song is more indicative of both that musical and the feelings that it inspires in its viewer than â€Å"La Vie Bohà ¨me,† an homage to Giacomo Puccini's opera  La Bohà ¨me, on which Rent was based. Songs in popular musicals often struggle with the blending of text and music; the text is often so important that music takes a back seat, or else an emotional moment of music is required, and text is written just to have something happening during that moment. I would argue, however, that â€Å"La Vie Bohà ¨me† effortlessl y combines both musical and textual elements to create a pleasing cocophony that relates intrinsically to the philosophical underpinnings of a Bohemian lifestyle. In short, it represents the certainty of death, the chaos of life, and Bohemianism as a response to simply having too little time on earth. Life and death are the central themes to this work, both textually and musically. The song begins with a character explaining that he had had â€Å"a death in the family,† his dog, â€Å"Evita† had died. He then goes on to explain how beautifully the neighborhood would change if people would give up their bohemian lifestyle. During this period the music is light, delicate, ordered and lively, with a high, major key melody played on a piano. He closes by telling the other characters that â€Å"Bohemia is dead.† This moment represents the first change between life and death that occurs in the work. The music then launches into a funeral dirge, with the character of M ark launching into a funeral sermon regarding the death of Bohemia. While he speaks, an interesting musical and textual event happens during the background. Two basses begin singing what sounds like a traditional funerary chant in Latin, which sounds almost like a Gregorian chant. A closer analysis of this chant will come later, but for the moment it serves to especially emphasize the deathly nature of the beginning of this song. As the sermon goes on, however, its mood shifts, the organ music finishes playing a minor key dirge, and opens into a major key melody. As this transition occurs, Mark almost seamlessly stops talking about death, and begins talking about birth, the birth of Christ. This transition wholly encapsulates one of the fundmanental aspects of Bohemian behavior – the recognition of death. Bohemians live with constant awareness of death – it is an awareness that spurs them on to live as fast and hard as they possibly can, to extract every ounce possible of experience out of life before it ends. The song then launches into a chaotic manifesto in defense of Bohemianism. While the opening clearly pushes one Bohemian theme, awareness of death as a cause for living in a Bohemian way, it also pushes another theme: conscious rejection of authority. The chant, which appeared to be Latin at first glance, helps develops these themes more fully. On a close inspection, only the first line, â€Å"Dies irae! Dies illa† or â€Å"Days of wrath and doom are coming† are Latin. Traditional words of death. The pair of basses then launch into a new language, Greek, keeping the same Gregorian style, â€Å"Kyrie, eleison† or, â€Å"Lord of have mercy† before closing in a final different language, but the same Gregorian style â€Å"Yitgadal v’yitkadash,† Hebrew meaning magnificent and sanctified. Firstly, using three languages demonstrates an awareness and expression of value of diversity – a theme that is more fully developed later in the song. But more importantly, the song thus smoothly connects Latin, Greek and Hebrew liturgy into a neat package, and

Cloud Computing Research Paper Example | Topics and Well Written Essays - 5000 words

Cloud Computing - Research Paper Example Cloud computing services address these issues and provide a source for using computing resources without purchasing them. The computing resources can be attained dynamically as per the needs of the company. The computing resources can be released when the need for greater IT infrastructure ceases to exist, therefore the resources do not have to be actually bought. Cloud computing environments offer almost unlimited levels of scalability and mobility. The attainment and release of the resources are convenient and fast processes. Computing resources consist of a diverse range of virtual devices and applications, like virtual servers, data storage, operating systems, software applications and virtual platforms. Along with the major success and acceptance of the concept of cloud computing, a significant portion of users feel threatened in trusting the service providers with their intellectual assets. Therefore, the prevailing security and privacy issues related to cloud computing have be en discussed in the paper, along with its advantages as compared to the traditional form of computing and data centers. The paper also includes few recommendations for improving the protection of the intellectual assets of the users. Table of Contents 1. Introduction 1 2. Cloud Computing 1 3. Success of Cloud Computing 5 4. Comparison of Traditional Computing and Cloud Computing Data Centers 7 4.1 Advantages of Cloud Computing 8 4.1.1 Level of Scalability 8 4.1.2 Level of Mobility 8 4.1.3 Level of Maintenance and Updates 10 4.1.4 Disaster Recovery 11 4.2 Disadvantages of Cloud Computing 11 4.2.1 Level of Control and Privacy 11 5. Factors to Evaluate the Effectiveness of Data Centers 13 6. Physical Aspects of Cloud Computing Data Centers 13 6.1 Issues with Traditional Data Centers 13 6.2 Innovative Solutions in Cloud Computing Data Centers 14 7. Challenges in Cloud Computing Systems 17 8. Recommendations 18 9. Conclusions 19 Bibliography 22 Table of Figures 1 Figure 1: Different fact ors related to Cloud Computing Systems 4 2 Figure 2: Comparison between traditional data center and cloud computing data center 7 3 Figure 3: PUE of Microsoft from the year 2004 to 2007 16 Table of Tables 1 Table 1: Top 10 Technologies of the year 2011 6 1. Introduction Computer technology has seen remarkable development and continuous improvement ever since it has been invented. The mode of life has been changed by the respective invention. Every field and industry has been revolutionized by the integration of computers. The field of education has been improved by the advent of e-learning management systems, whereas the field of medicine has witnessed greater accuracy and reliability due to the usage of more efficient medical equipments. In the same manner, the field of business has been given a more formalized structure due to the incorporation of enterprise data centers and information management systems. Enterprise data centers supported the needs of organizations for many years . A change was felt necessary when the needs of the customers began increasing at an exponential rate. The advent of internet has broken geographical barriers, due to which the whole world is considered to be a single platform. Consumer has access to global products and services, which makes it vital for companies to provide commendable and uninterrupted services to their clients. The increasing competition in the markets has urged the companies to adopt innovative ways to meet the increasing needs of the cust

American Music History Essay Example | Topics and Well Written Essays - 500 words - 2

American Music History - Essay Example The drummer and the male dancer compete against each other by increasing the tempo and making the rhythm more intricate, progressively. Rumba is not really the name of a single dance, rather a genre of dances originating in Cuba. The two to four beat rhythm, which is common to all Cuban dances, is called the Clave rhythm, as it is played by two sticks called claves. The tempo changes but never gets too fast as the couple sway from side to side suggestively, holding each other at approximately arm’s length. Initially danced to African music, the songs for the Rumba gradually converted into Spanish. The Rumba has strayed into contemporary Flamenco, Blues and even Rock music and is continually evolving thanks to newer, experimental artists. Popularized in the USA by the sensational Carmen Miranda, the Samba has its origins in Brazil and Africa. Bossa Nova emerged in protest to the commercialization of Samba in the 1960s. It is called jazz samba as it blends jazz music with the upbeat rhythms of the samba seamlessly. It was more intimate and lacked the flamboyance of Samba. The song ‘Desafinado’ introduced the term Bossa Nova. Musicians like Miles Davis and Pat Metheny draw great inspiration from the Bossa Nova tradition. Salsa, literally meaning sauce, originated in Cuba, and by the end of the 1970s became a major component of   almost all vernacular fields. It is quintessentially Cuban music, long held a substyle, and although it originally was defined by upbeat, spirited Cuban music, it slowly developed a Latin tinge to it, although retaining that Cuban flavour as well. Today, we define salsa generally as Latin-African music, and what was once dance band music, albeit music incorporating varied rhythms, complex instrumentations and sounds, usage of flutes and violins, under various Puerto Rican and South American influences, and with the inclusion of jazz, has now grown to be a highly sophisticated style of music capable of being molded into

Nutritional Care Plan Essay Example | Topics and Well Written Essays - 500 words

Nutritional Care Plan - Essay Example Harvey (2011) explains that â€Å"overnutrition is an unfavorable health condition in which at least one nutrient is supplied in an amount that exceeds the bodys requirements for normal metabolism, growth and development.† The Test Lab Online (2011) adds that overnutrition is a serious medical problem in pregnancy because â€Å"chronic overnutrition can lead to obesity and to metabolic syndrome, a set of risk factors characterized by abdominal obesity, a decreased ability to process glucose (insulin resistance), dyslipidemia, and hypertension.† This essay shall focus on abdominal obesity in pregnancy. According to the American Pregnancy Association (2011), woman who had BMI of 18.5 to 24.9 before pregnancy is required to gain weight of 1 – 4.5 pounds during the first trimester. However, after just two weeks, the woman came back to the hospital with a weight gain of 7.7 pounds. This was still at the early stages of the pregnancy and therefore constituted an excessive weight of 3.2 pounds. Further biochemical test showed that the albumin level of the woman was 5.8 g/dl, which was almost above normal. The interpretation is that the woman was suffering from overnutrition. Clinical assessment however revealed that the integrity of the woman’s skin was intact. When dietary assessment of the patient’s daily intake of food was done, it was realized that the woman had been misinformed to start taking in more protein and fat and extra mineral with the intention of helping her fetus grow better. Medications were suggested for the patient based on her cultural and socioeconomic background. It must be reiterated that medications or drugs come into the treatment of over nutrition as a last resort and especially when the patient’s case has resulted in obesity. Some commonly acceptable medications in medical circles include Orlistat, Sibutramine, Rimonabant, Metformin, Exenatide, Pramlintide

Many Nations Native Americans Essay Example | Topics and Well Written Essays - 1000 words

Many Nations Native Americans - Essay Example There is a group of Cherokee people that want to stay in their homelands spearheaded by Principal Chief John Ross. The opposition to the removal of the Cherokees was justifiable and was based on a valid argument. Initially, all the Cherokees were united in opposing the removal from their ancestral homelands. Even after the 1832 court ruling that Cherokees should be allowed to live in their ancestral lands, the government has not heeded. The land lottery that was enacted in 1830 is being implemented, where citizens of Georgia are the beneficiaries of the Cherokee’s land. The Cherokees attempted to fight for themselves with the government on the opposition. Despite some of the Cherokees having no hope in that they will regain their land, a group of them was totally opposed to the removal. One of the strong believers that the Cherokees should not be removed from their homeland was Principal Chief John Ross. He had support from the majority of the people. However, a rift among the people created instability to the Cherokee government. Various advantages helped the group that was opposed to the removal to be dominant and stronger. Firstly, under the Principal Chief John Ross they had a control of the Cherokee government. This means that rebels were thrown out of the government once they were known. Secondly, they were the majority; in this case, the people behind Principal Chief John Ross were much more than those that attempted to collaborate. This ensured that the rebellion became stronger. Thirdly, the elite among the Cherokees supported non-removal. These include Principal Chief John Ross, his brother among other leaders that were more enlightened. Despite their concerted efforts, the non-removal delegation was defeated because both the federal and state governments supported it. Upon the ratification of the Treaty of new Echota by the Senate, the battle was lost despite the push by Ross and his leadership. In

Platos Socrates Essay Example for Free

Platos Socrates Essay In order for the concept of wisdom to carry any viable weight in the affairs of the world, it is necessary for said concept to acknowledge the link between wisdom as an abstract idea and wisdom as a guiding principle for pragmatic action. Although other thinkers within the list of writers and philosophers we have studies do promote the idea of wisdom as a pragmatically applied force; Henry David Thoreaus interpretation of wisdom and its applications in human life and in human society seems to me the most reasonable interpretation among those we have studied so far. Thoreaus basic idea of wisdom is relative easy to understand adn emerges, not from abstract philosophical discourse, but from the vantage point of everday life: Does Wisdom work in a tread-mill? or does she teach how to succeed by her example? Is there any such thing as wisdom not applied to life? (Thoreau 118) By asking these questions in connection to the idea of wisdom, Thoreau makes it obvious that he regards wisdom as a method of defining nd helping to instruct human behavior and not merely human thought. Interestingly enough, while Thoreaus definition of wisdom is steeped in the practical and the pragmatic, he admonishes his readers and listeners not to confuse materialism and wisdom, that is, not to mistake the pragmatic of earning a living with the pragmatics of wisdom: It is pertinent to ask if Plato got his living in a better way or more successfully than his contemporaries,or did he[ ] find it easier to live, because his aunt remembered him in her will? The ways in which most men get their living, that is, live, are mere makeshifts, and a shirking of the real business of life,chiefly because they do not know, but partly because they do not mean, any better, (Thoreau 118). The application of Thoreaus pragmatic vision of wisdom may elude some observers; however, Thoreau, himself, illustrates the application of his idea of wisdom by turning his sights to the gold rush fever which enveloped his contemporaries: Did God direct us so to get our living, digging where we never planted,and He would, perchance, reward us with lumps of gold? (Thoreau 119) where, obviously, Thoreaus hang up with gold-rushers is not their pursuit of earning a living, per se, but with the folly of their believing that gold can, in and of itself, replace the need for wisdom: I did not know that mankind was suffering for want of gold. I have seen a little of it. I know that it is very malleable, but not so malleable as wit. A grain of gold will gild a great surface, but not so much as a grain of wisdom,; where Thoreuas ironic contrast of gold and wisdom leaves little doubt, in the end, as to which he views as more crucial to humanity. (Thoreau 119) 2. Whose view of wisdom (Socrates, Thoreau, Huxley, Pieper, or Frankl) seems to be the least reasonable? Why? Although Platos Socratic writings on the nature and meaning of justice achieve and inner-harmony and function in logical consistency with the rest of his ideas regarding ethics, aesthetics, and civics, Socrates view of wisdom, as defined by Plato, strikes me as the least rational of the theories and ideas we have studied. Far be it for me or anyone else to accuse Plato of leaving holes in his theory of wisdom; that is not the issue so much as the circclar nature of Platos reasoning which leads me to feel that the concepts of wisdom which are described by Socrates offer very little in the way of practical application in life and seem more like abstract ideas meant to stimulate those who enjoy pondering theory, rather than to assist those who are truly seeking applicable means for wisdom in daily life. Primarily, it is Socrates insistence that wisdom exists beyond the human appreciation of it, which seems to cripple the overall argument on the nature of what comprises wisdom: Socrates considers there to be two general sorts of knowledge, one which makes its possessor wise and one which does not. Socrates, and others too, can confidently and quite correctly claim to have a number of instances of the latter sort; but no human being can rightly claim to have the former sort, since no human being has ever attained the wisdom Socrates himself disclaims having when he professes ignorance, (Brickhouse, and Smith 31). true enough, Socrates humility in professing himself to be without wisdom has puzzled observers adn scholars for quite some time; however, the admission that wisdom exists, apart from human understanding, nd must be pursued even to the point of admitting that it cannot be attained, leaves the entire issue of wisdom up in the air form a pragmatic point of view. Socrates may believe that human wisdom is of little or no value (23a6-7). What would be of great value, if only he had itnamely, real wisdomSocrates and all others lack. The greatest wisdom for human beings, as we have just seen, is the recognition that we are in truth worth nothing in respect to wisdom (Brickhouse, and Smith 33) and this type of vision is, of course, another variation on a religious or metaphysical concept: that of Divine Wisdom. For Socrates, wisdom is an abstract power deemed tor reside within the Divine consciousness but only sparingly in human consciousness. I would say that nay definition of wisdom which fails to forward a concrete, pragmatic application as pertains to human society and individual behavior is worthwhile only from a purely intellectual point of view. Works Cited Brickhouse, Thomas C. , and Nicholas D. Smith. Platos Socrates. New York: Oxford University Press, 1995. Harding, Walter, ed. Thoreau: A Century of Criticism. Dallas, TX: Southern Methodist University Press, 1954. Thoreau, Henry David. The Major Essays of Henry David Thoreau. Ed. Richard Dillman. Albany, NY: Whitston Publishing, 2001.