Mathematics & Natural Sciences with absolute certainty (TOK) Essay

Write an essay outlining your personal response to this topic. â€Å"Mathematicians have the concept of rigorous proof, which leads to knowing something with complete certainty. Consider the extent to which complete certainty might be achievable in mathematics and the natural sciences.† To what extent can man use mathematics and the natural sciences to embrace the concept of achieving absolute certainty? It is not possible for humans to achieve absolute certainty in knowledge using mathematics and the natural sciences. This is because mathematics is a creation of man to organize and communicate highly complex concepts and theories to others through a kind of language which goes beyond the spoken or written word. Many people believe the written word to be more true that the spoken word, the same can be applied to mathematics. Just because something can be written in the numbered format by a credible source, it doesn’t mean it’s necessarily true. The same can be said about the level of certainty to be achieved using proofs from natural sciences, with additional external variables. This can be explained through evolution. The natural sciences were discovered, observed and recorded to be studied further by man. The small level of certainty which can be obtained is from the inability to change nature without physically disturbing it and that human observations themselves are a big problem in the natural sciences. Conversely, absolute certainty can only be found in a few instances in nature. Math and the Natural Sciences are the two areas of knowledge which have the highest impact on our ability to achieve absolute certainty in knowing. The world revolves around proving knowledge with scientific claims, however any such claims must originate from the mouths of highly regarded mathematicians and scientists. Just like beauty is in the eye of the beholder, validity of knowledge is in the mouth of a credible source. If I were to go up to a friend and state that there is a mathematical sequence that can be found in every naturally produced object on earth, the friend would hinder. If I were to approach this friend with long papers written by credible mathematicians, the friend would be swayed to believe its likelihood. The same goes for the natural sciences. If I were to approach a friend and state that every living  organism on earth is made up of billions upon billions of cells, assuming this friend wasn’t the brightest of individuals, the friend would not be completely persuaded by the fact. If I were to approach the friend again with evidence of this fact being true, backed by credible science, there would be a significantly higher chance that the friend would be convinced this fact remains true. Logical reasoning is commonly connected with math, which is supported by certainty in that if A=B and B=C that A=C. When individuals try to back decisions with reasoning, they are using this deconstructive problem solving, assuming that it will lead them to the correct results. Unconsciously we are convinced that because both natural science and mathematics are backed by numbers, the results are going to be more accurate than more subjective reasoning. This goes without saying that most people believe that because both involve mathematical terminology, natural sciences and mathematics are interlinked. First of all, the concept of math is man-made, created to provide evidence for the natural sciences. Natural sciences was a term created by man, but originating from human’s very own existence. Natural science wasn’t created by man, it has always existed on earth. In other words, what we study from the natural sciences is purely based off of thousands of years worth of observations of what’s happening around us. Using technology, humans have began to glance deeper into the natural sciences, but it’s all still just observations of either how things function and came to be, or simply to predict where we were, where we are, and where we will be. People seem to believe that because mathematics and natural sciences have some similarities and use similar problem solving techniques, that they are connected. Observations are a big problem in science. If a biologist and a person with no experience with this work were trying to differentiate an Indian Rhinoceros and a Javan Rhinoceros, the biologist would rely on the perception of the rhino’s appearance and behavior. The biologist would have the training experience to determine these characteristics, but the person who doesn’t could easily mistake the two or not even know the differences. Although the biologist may have the title and credibility of making the  conclusion to differentiate an Indian Rhinoceros and a Javan Rhinoceros, and the person with no experience and no training doesn’t, it doesn’t mean that the credibility of the biologist provides absolute certainty. Slight imprecisions are not very significant and probably wouldn’t alter the results. However, even the most insignificant factors would prevent the biologist from being completely certain. An example involving mathematics which follows similar principals to the biologist and the rhinoceros’ would have the same outcome. This saying that science and mathematics can only be highly meticulous; it cannot achieve absolute certainty. Although ethics and emotion have very little effect on the natural sciences and mathematics, religion often does. The ethical viewpoint from which any mathematician or scientist have, will show no effect on his or her work. This is because a mathematician won’t refuse to answer an equation or attempt to explain a theory because of his ethical considerations. A scientist wouldn’t sit down and conduct an experiment using the wrong variables in a moment of extreme emotion. The only counter argument that stands is religion. Conversely, a hypothesis may be formed with religious consideration, straying far from achieving an absolutely certain result. Scientist William A. Dembski is a highly regarded advocate of the Intelligent Design theory. Although he thoroughly investigated the argument and determined that it’s more likely God exists, probably because of his religious background as a practicing Catholic. The religious bias shaped to his beliefs. Unlike the chance of interfering religious ideology, scientists and mathematics generally steer from involving ethics or religion into their work. The only emotional factor would be commitment. Mathematicians and scientists who work in the fields of the natural sciences dedicate their lives to their work. They strive to find the absolute certain answer but the best they can ever do is find a highly precise one. This is why the advancement of knowledge often takes a long time. The mathematician or scientist will generally have endless approaches to solving or proving their work. The golden ratio is a formula used in both mathematics and the arts which can be applied the geometric relationships. The ratio is one of the only  absolute certainties founded by mathematics. The golden ratio wasn’t created, it was discovered in nature. Simply, the golden ratio is when a geometric shape (golden rectangle, regular pentagon) has the ability to be split infinite times, and remain in the same ratio. It is only found in nature and only proved by theories. The term golden relates it to perfection, or in relative terms, absolute certainty. It is not possible for humans to achieve absolute certainty in knowledge using mathematics and the natural sciences. Mathematics is a creation of man to organize and communicate highly complex concepts and theories to others through a kind of language which goes beyond the spoken or written word. Most people do believe the written word to be more true that the spoken word, as seen, this can be shown just as thoroughly in mathematics and the natural sciences. Just because something can be written in the numbered format by a credible source, it doesn’t mean it’s true. The level of certainty to be achieved with absolute certainty of knowledge concludes with the same results, using multitudes of empirical evidences from observations. Therefore, although the natural sciences and mathematics may achieve highly precise and accurate results, with very few exceptions in nature, absolute certainty cannot be attained.

Memory Skills Essay

Memory refers to a mental process that is used to gain, gather, and recover information. The information that is stored in our memory with the help of our senses will be processed by numerous systems all through our brain, and it will be accumulated for later use (Mason, 2003-2006). Gordon and Berger (2003) said that there are two basic kinds of memory: ordinary and intelligent memory. Ordinary memory is remembering specific names of people, time, place, locations of certain things, and things to be done. It is comparatively fragile for it stores information for a few minutes, and that information will soon be forgotten. Thus, it is what fails when we can’t remember something. We are able to recognize it when it works and when it doesn’t because it is a conscious process. On the contrary, intelligent memory is remembering how to do things. It serves as an aid for us to make everyday decisions, and it is the memory that makes us think critically. It enables us to solve p roblems, to enjoy a good joke, and to boost our creativity. Unlike ordinary memory, intelligent memory is an unconscious process that is why most of us find it hard to use and develop it. (Gordon & Berger, 2003; Radford, 2003) Why do we forget things? Forgetting important and useful stuffs is indeed disappointing. Although our brain can store vast number of memories, we still tend to forget things and find them difficult to retrieve. For instance, sometimes we can’t remember the names of people we just met. Perhaps, this is because we are not paying attention. A lack of focus on something important is probably the reason why we fail to store information into our brain. If we really concentrate on something, forgetting will not happen. (Turkington, 2003) Moreover, we fail to remember information because of memory interventions. Sometimes, the acquired information doesn’t just vanish; it can become deteriorated. The memories that are similar can interfere with each other. For example, the memories of two events that happened in the same place become combined together; as a result, our brain become bewildered, and we tend to have memory lapses. Additionally, as we get older, losing brain cells and connections will happen. The specific cells, where numerous memories are stored, will eventually die as part of aging; and thus, the stored memories will be lost and forgotten. (Eastaway, 2004) Can we make our memory stronger? Having bad or weak memory skills is perhaps one of the major problems that we encounter in our daily lives. In fact, it is absolutely frustrating to have memory lapses and not having to recall certain things. Nonetheless, there are memory aids and techniques that can strengthen our memory skill, and they can help us to have a better and healthy memory. Despite the fact that memory lapses is inescapable, memory treatments and methods can somehow sharpen our memory skills. Some of us might think that these memory-boosting techniques are not accurate and are not effective, but it is. They find it that way maybe because they are really not into deep-learning, and they do not focus on what they’re trying to learn. As a matter of fact, remembering is a learned skill, and it can be improved whenever we want to. Since practicing, exerting efforts, and being patient are part of learning, it is substantial for us to do these techniques for a betterment of our memory. (Turnkington, 2003; Eastaway, 2004) To strengthen and sharpen our memory skills, we must pay attention, associate, visualize, and be physically and mentally fit. If we learn all of these techniques, we will certainly make our brain healthy and build a stronger memory. (Turnkington, 2003; Eastaway, 2004) MEMORY IMPROVEMENT TECHNIQUES Pay Attention Turkington (2003) stated that paying attention is actually one of the most important things in our lives, and it is a great help in improving our memory skills. Each and every one of us has the ability to pay attention to one thing; it’s just that, some of us fail to stay away from distractions. As part of this strategy, we have to determine first what our priorities are. It is essential to distinguish which things are worth giving attention to and which can be get rid of. Distractions are everywhere, and they prevent us from doing the things that need to be done. So we must avoid distractions and ignore all unimportant things in order to complete a certain task and to avoid forgetting. With this in mind, we shouldn’t be disturbed by irrelevant things around us because with fewer distractions, it is easier for our mind to focus and work faster. In enhancing our ability to pay attention, we really need to focus consciously. If we can’t focus, we will not remember what we are trying to learn. Moreover, we tend to procrastinate which is not good. For this reason, we need to do the important things now while we still have plenty of time. It’s simple, if we can avoid procrastinating, we won’t forget anything. In addition to that, we can only concentrate on one thing at any time. Even though we can multi-task, it is still impossible for us to handle different tasks at the same time especially when they both require mental process. Absolutely, we can’t give our full attention to those; as a result, we absorb nothing. Another way that hinders our ability to pay attention is being absent-minded. For instance, when we are about to go to specific place to get something, we suddenly forget what is it that we want to get in the first place. It is commonly happening to us because we sometimes are absent-minded. To cure absentmindedness, we have to be aware of what we are doing. Once we are aware of it, the next thing that we have to do is concentrate on what we are doing. Of course, we need to focus our mind on our task and be alert all the time. Also, finding motivation and getting inspired help us to sustain our concentration. Being motivated gives us enough energy to accomplish our tasks. It helps us to make our brain work properly. Also, it will broaden our mental perspective if we focus on the positive things that motivate us. With an inspiration, we can easily manage distractions, and we can be able to stay focused. Keep in mind that paying attention is a conscious part of our lives (Turkington, 2003; Eastaway, 2004; Gordon & Berger; 2003). Associate In order to enhance our ability to pay attention and to remember, we need to create mental connections between our sensations, ideas, and memories. Meaning, we have to make associations for us to remember properly. We all know that memorizing huge amount of information can be a nerve-wracking task. The tendency to forget that information is very high because our brain doesn’t work well at recalling huge amount of information. We cannot deny the fact that the names of certain people, places, and things are hard to recall. However, there are strategies that we can do for us to be able to remember. Using some mnemonic devices like acrostic, acronym, and method of Loci can help us to improve our attention and memory skills as well. (Eastaway, 2004; Turkington, 2003; Levy, 2006; Smith & Robinson; 2012; Buzan, 2003) Turkington (2003) mentioned that when using acrostics, we can make a sentence in which the first letter of each word serves as an antecedent of what we want to remember. For instance, we use the sentence â€Å"My Very Excellent Mother Just Served Us Nachos† to remember the eight planets such as Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. With this sentence, it is easier for us to remember the planets in a chronological order. Another device that we can use is acronym wherein we can make a word from the first letters of the words that we need to remember. In detail, we use â€Å"ROY G. BIV† to memorize the sequence of colors in the light spectrum such as Red, Orange, Yellow, Green, Blue, Indigo, and Violet. We can also use the acronym â€Å"MCL† for us to remember the school of Malayan Colleges Laguna easily. Also, placing what we want to retrieve in a familiar location can help us to remember well. This is called method of loci. If we want to recall specific items or people, we have to associate them with places that we know well. It is easier for us to remember things when our memories are associated with places. For example, we may need to buy the list of items that we need in our houses. To remember them, first, we need to visualize our own house (which is very familiar to us), after that, we imagine ourselves walking through the rooms and examining each of them. As we walk through them, we begin to recall the things that we lack of. With this, we can easily remember the items that we need to buy. Notice that in this technique, it has always something to do with places. This method is more effective for kinesthetic learners. These mnemonic devices help to increase our memory and ability to recall information. Since most of our work involves memorization, it makes sense to use these mnemonic devices so that it will be easy for us to recall information when we need it. It is important for us to know that our ability to remember varies. Some of us think that using acrostics is easier to remember. Some think it is better to use acronyms. This proves that we have different style in terms of recalling information. The only key to using mnemonics is to choose a type of mnemonic that is best for us. (Eastaway, 2004; Turkington, 2003; Levy, 2006; Smith & Robinson; 2012) Visualize After making associations, the next thing we have to do is to improve it. We can develop our ability to associate by visualizing. Turkington (2003) claimed that visualization is a way of making mental picture of things. We create pictures in our mind to see their colors, shapes, and form. It is often referred to as a clear and deep imagining. Each and every one of us has a gift of creative imagination. The only problem is, some of us don’t know how to use and improve it properly. We need to widen our imagination for us to focus and associate consciously. To be able to do this, it is important for us to accept new challenges, to ask questions, and to develop our interests. It would be better for our brain to explore new ideas especially when it challenges us to think critically. That is to say, we have to look into something that is strange to us. Exploring different new ideas will help us to have a creative imagination. It lets us use our whole brain, and that’s good. If we refuse to try something new, and if we choose to do something that we’ve already know, it will not exercise our brain. We won’t be able to develop our creative mind if we keep on focusing on the same activity that is already familiar to us. Whereas when we accept new challenges that takes some mental effort, it will expand our knowledge and develop a good memory. As we explore new ideas, it is substantial to involve ourselves in our reading. Visualization must always be present in our reading. As we read, we should imagine ourselves in the place we are reading about or imagine ourselves doing what we are studying. In this way, it is easier for us to make inferences, and thus, we can actually widen our creative imagination. Also, we should be not afraid to ask multiple questions and be curious about everything in this world. It will help us to expand our imagination because it gives us the opportunity to gain more knowledge. In fact, it would be better if we learn about the amazing wonders here on earth. It is essential to not take everything for granted because if we don’t grab the opportunity to explore them, we will not be able to come up with our own ideas which are very helpful in widening our imagination. Additionally, it will improve our creativity and critical thinking skills. Being curious helps us to become open-minded towards new ideas and information which we can use when we need them. (Turkington, 2003; Smith & Robinson, 2012) It is also important to develop our interests. As we start to expand our concrete interests, we desire to reach a permanent goal. We should continue to learn more about the things that we are interested in. If something doesn’t work for us; then, we should try another course of movement. With this in mind, we have to have a sense of enthusiasm which will allow us to be more interested about something. Therefore, we will be more likely to continue this, and we will have more experiences which are beneficial to us. In exploring new ideas, it should absolutely be challenging and at the same time, enjoying. Instead of expecting them to be just a waste of time or insignificant to us, we should be anticipating that these new ideas will be full of enjoyment. As a matter of fact, this will help our brain to process properly. This is a real sense of enthusiasm that we should have. Furthermore, as we involve ourselves with new ideas and challenges, we should think of how to spot favorable circumstances for improvements. With this intention, we should be a good observer. Being a good observer plays an important role in associating and visualizing. Of course, the reason why we expand our curiosity is to find the answers to our questions. To be able to find them, we should do an observation. It is important to understand the things around us because the more we observe them, the more we will conceive them. (Turkington, 2003; Smith & Robinson, 2012; Eastaway, 2004) Be physically and mentally fit For us to be able to pay attention, associate, and visualize well, we should be physically and mentally fit. Doing physical and mental exercises will help us to sharpen and strengthen our memory skills. Physical exercise is important to us for it maintains physical fitness and overall health. It is good for our brain because it gives us more energy, increases blood supply and growth hormones, and abates the chances of memory decay. We all know that we cannot avoid tiredness. It hinders our brain to function well. The best way to make it function properly is to have a deep sleep. Exercising daily helps us to relax our muscles and get to sleep which will serve as an aid for us to be able to recall information and to make our brain perform well. Also, regular exercises help us to reduce stress. It is a fact that all of us have stresses that contribute to memory problems. Being physically fit helps us to relieve stress. It improves our mood, and it keeps us from anxieties that make us wo rry too much. Specifically, it increases our confidence which enables us to manage stress. (Latham, 2006; Eastaway, 2004) In addition, it is beneficial for our brain to perform mental tasks because it develops our critical thinking skills. If we really want to sharpen our memory, we need to involve ourselves in different mental activities. We can play chess, scrabble, and card games like jigsaw puzzles or bridge. These mental activities can help us to think logically; thus, it will definitely boost our memory skills. The logical puzzle like soduko, for instance, helps us to think critically. It trains our mind to process different kinds of information, details, images and techniques at a fast speed. As we do the strategies in this puzzle, it helps us to build neural connections into our brain which will help us to sharpen our memory. (Moore, 2006) The most important of all, it is essential to have a good diet for it also help our memory to be alert and active. We should make sure that all vitamins that we need are in our diet. With a good diet, we will be able to concentrate fully and to store and retrieve information. There are specific foods that are healthy to our brain, and they will strengthen our memory. To make our memory stronger, we should consider the following: * Fishes contains good fats, and they are rich in Omega-3. Eastaway (2004) stated that foods that contain Omega-3 are good for our brain. They prevent us from having Alzheimer’s disease. Therefore, if we really want to have a good diet, we should eat oily fishes such as Salmon, Tuna, Halibut, Trout, Mackerel, Sardines, and Herring. * We must avoid eating too much food that contains calories and saturated fats. We shouldn’t eat too much butter, cheese, sour cream, and ice cream because they contribute to the memory problems. Nevertheless, it is healthier for our brain to eat foods that are rich in unsaturated fats because they improve brain’s learning process, and they abate the risk of having damage to our brain. (Eastaway, 2004; Smith & Robinson, 2012; Moore, 2006) * We should eat more fruits and vegetables because they are rich in Antioxidants which are beneficial to our brain. It protects our brain cells for the possible damage that may happen in our brain. (Eastaway, 2004; Smith & Robinson, 2012; Moore, 2006) * We should eat foods that are rich in Carbohydrates for they help our brain to function and perform well. They make our mind alert and active, and thus it is easier for us to retrieve information. (Eastaway, 2004; Smith & Robinson, 2012; Moore, 2006 ) CONCLUSION Given these points, we should now understand that our memories are our important assets that we should take care of. Knowing how our memories work and how they fail sometimes, we should keep in mind that we have to develop them. We should keep in mind that the ability to remember quickly is very important in our lives. We should also realize that forgetting is a natural part of how our brains work. It is true that our abilities to remember get worse as we get older. However, we don’t have to worry too much because it is possible for us to strengthen and sharpen our memory skills. All we need to do is to practice improving our attention, association, and visualization. For us to be able to improve them, we should also be healthy, physically and mentally. It should now be clear to us that paying attention, making associations, and visualizing play important roles in improving our memory skills. They are actually the three keys to have a better memory because they are the sources of all of our insights, learning, communications, and connections with others. (Eastaway, 2004) Also, it is better for us to understand that we cannot do these strategies successfully unless we learn them. Of course, it takes time to learn. If we really want to achieve something, we have to dedicate ourselves to it. We have to give our time and full attention to it. Learn to practice, and practice to learn. Keep in mind that our memories are priceless, and we cannot replace them whenever they fail to function. We really have to protect our memories in order to make them healthier. In short, we have to train our brain to gain. References Buzan, T. (2003). Master your memory: more inspiring ways to increase the power of your memory, focus, and creativity. London: BBC Worldwide Limited. Eastaway, R. (2004). How to remember: a practical guide to memory and recall. Great Britain: Bookmarque Ltd, Croydon, Surrey. Gordon, B. & Berger, L. (2003). Intelligent memory: a prescription for improving your memory. New York: Penguin Group. Latham, C. (2006). Physical and Mental Exercise. Retrieved November 30, 2012, from www.sharpbrains.com/blog/2006/11/07/physical-and-mental-exercise/ Levy, J. (2006). Train your brain: The complete mental workout for a fit and agile mind. London: New Holand Publishers. Mason, D. J (2003-2006). The Memory Workbook. Retrieved November 26, 2012 from http://www.memorydr.com/memory.htm Moore, G. (2006). The 10-minute brain workout: Brain training tips, logic tests, and puzzles to exercise your mind. Great Britain: Michael O’ Mara Books Limited

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The Life Of Frederick Douglass s Book, Many Read It And...

When Frederick Douglass published his book, many read it and had their own ideas from the themes he referred to. One thing that was related to the theme of his book was how he said religious slaveholders were the cruelest to slaves. Religious slaveholders used the bible to prove that slavery was right. They quoted from the bible, Colossians 3:22, slaves, obey your earthly masters in everything you do. Try to please them all the time, not just when they are watching you. Serve them sincerely because of your reverent fear of the Lord. They said that the bible tells slaves to be obedient to their masters, in which case, means that there are going to be slaves. They also looked back into the Old Testament and found times where the old prophets had slaves. At one point, a prophet returns a runaway slave back to another prophet who was his master. The Southerners saw that since the bible did not condemn slavery but mentioned it in many places, that they were right to have slaves. 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Business Communication The Hub Of Economic Development

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Fundamentals of Corporate Finance Financial Management

Question: Discuss about the Essay for Fundamentals of Corporate Finance: Financial Management. Answer: Introduction The corporate financial management entails various business decisions including investments, financing and the return on the investment and thus, become crucial to take action on commercial wellness. The current study is based on a case of a machinery replacement where the report comprises of the projection of the initial investment, required for the new machinery installation, operating cash flow calculation and the evaluation of the viability of the same. In addition, the investment appraisal techniques have been implemented followed by the sensitivity analysis to deliver the information whether the project could be undertaken. The key purpose of this study is to recommend on the project selection along with the justification, using valid investment appraisal mechanism. Incremental initial investment Initial incremental capital Amount ($) Acquisition cost of new machine 1000000 Sale proceeds of old machine 100000 Tax adjustments on sales of old machine 60000 Additional working capital 491520 Total Initial incremental capital 1651520 The calculation for the initial investment involves the initial cost for the acquisition of new machine, sales proceeds of old machine and the tax adjustments for sale of old machine. The initial incremental investment also involves the calculation for the working capital adjusted with the discounting rate at 10% for 10 years (refer to appendix). Therefore, at the year 0 that is the beginning year, the total initial incremental capital stands at $1651520. In the words of Chemmanur and He (2016, p.72), the total initial incremental capital for an investment is used in the calculation of the net present value, internal rate of return etc for the investments. This further helps in the making the investment decision pertaining to the investments. Incremental after tax operating cash flow Annual incremental operating cash flow Yearly incremental operating expenses ($) Discounting factor Discounted incremental operating expenses ($) year 1 78000 0.909 70902 year 2 78000 0.826 64428 year 3 78000 0.751 58578 year 4 78000 0.683 53274 year 5 78000 0.621 48438 year 6 78000 0.564 43992 year 7 78000 0.513 40014 year 8 78000 0.467 36426 year 9 78000 0.424 33072 year 10 78000 0.386 30108 Total Annual incremental operating cash flow 479232 The annual incremental operating expenses involves calculations for the increase in the sales, increase in operating expenses and depreciation. In the opinion of Gao and Zhang (2015, p.110), the calculation for the annual incremental operating cash flow helps in the calculation of net present value as it reduced the net cash inflow making the net present value more realistic. In the present context, the annual incremental operating cash flow has been calculated using the following formula: Annual incremental operating cash flow = (increased sales - increased operating expenses - increased depreciation) * (1 - tax rate) + increased depreciation. Incremental terminal cash flow Particulars Amount ($) Discounting factor (10%, 10) Amount ($) Incremental salvage value 100000 0.386 38600 tax on incremental salvage value 30000 0.386 11580 Total incremental salvage value 70000 0.386 27020 The incremental terminal cash flow involves calculation for the incremental salvage value after making the adjustments for the prevailing tax rate. NPV, IRR and Profitability Index for the replacement proposal Net present value Incremental Sales ($) Discounting factor Discounted incremental sales ($) 450000 0.909 409050 450000 0.826 371700 450000 0.751 337950 450000 0.683 307350 450000 0.621 279450 450000 0.564 253800 450000 0.513 230850 450000 0.467 210150 450000 0.424 190800 450000 0.386 173700 Total Incremental sales 2764800 Net present value ($) 661068 The net present value in the present case has been calculated by adding up the cash inflows for the new machines and then subtracting the cash outflows. Therefore, in the present case, the cash flows are assumed the total incremental sales and the net salvage value of the new machine at the end to 10th year at 10% discounting rate. While on the other hand, the cash outflows for the new machine involves the total initial incremental expenses and the increased operating cash outflows. In the words of Brealey et al. (2015, p.17), the investment decisions pertaining to the new investments must be taken based on the net present value. The net present value calculation takes into consideration time value of money while also calculating the future cash inflow. Based on the net present value the company has been recommended to invest in the new machine, as it would prove to be beneficial for the company. Internal rate of return Incremental initial investment ($) -1651520 Annual incremental operating expenses ($) year 1 372000 year 2 372000 year 3 372000 year 4 372000 year 5 372000 year 6 372000 year 7 372000 year 8 372000 year 9 372000 year 10 372000 Total incremental salvage value ($) 100000 IRR 19% The calculation for the internal rate of return involves annual incremental cash inflow at subtracting the cash inflow from sales by the annual incremental operating expenses. In the given case scenario, the cash flow from the sales is $450000 per annum and the annual incremental operating expenses is $78000 (refer to appendix). The total incremental salvage value of $100000 at the end of the 10th year has also been considered for internal rate of return calculation. The internal rate of return for the new machine is 19%, which is greater than the required rate of return of 10%. Therefore, the company has been recommended to invest in the new machine, as it would help the company to increase its profit potential. Profitability index Profitability index 1.40 The profitability index for the new machine is 1.40. This means that the net cash flow from the investment is 1.4 times greater than the initial investment in the machine. The profitability index for the new machine has been made on the below stated formula: Profitability index = present value of future cash flows / initial investment In the present case scenario, the present value of the cash inflow involves net present value of sales plus total incremental salvage value subtracted by annual incremental operating expenses. Sensitivity analysis of NPV As mentioned by Huang and Petkevich (2016, p.73), the sensitivity analysis of the net present value helps in evaluating the exact internal rate of return which in turn helps in investment decision making. At 10% At 10% Total Initial incremental capital 1651520 Total incremental salvage value 27020 Total Incremental inflow 2285568 At 30% At 30% Total Initial incremental capital 1407280 Total incremental salvage value 15890 Total Incremental inflow 1149852 At 10% discounting factor the initial incremental capital is $1651520 and the total incremental salvage value is $27020. While on the other hand, at 30% discounting factor the initial incremental capital is $1407280 and the total incremental salvage value is $15890. At 10% NPV 661068 At 30% NPV -241538 Based on the net present value at different rate of return it can be concluded that when the rate of return increases the net present value starts decreasing. This net present value at different discounting rate helps in the evaluation of the internal rate of return. Sensitivity analysis of NPV Discount rate 10% 30% NPV ($) 661068 -241538 10 - IRR / 10 - 30 (661068 - 0) / (661068 - (-241538)) 10 - IRR/ - 20 661068 / 902606 10 - IRR / - 20 0.7323992971 10 - IRR - 14.64798594 - IRR - 24.64798594 IRR 24.65% The sensitivity analysis involves the discounting of the initial investments and cash flow on at various rate of return. This helps in evaluating the net present value at different discounting rate. The calculation for the internal rate of return involves use of one positive and one negative NPV. These are then applied to the sensitivity analysis for NPV formula to generate the IRR of the investment. In the present case scenario, the discounting ate for the positive net present value has been assumed 10%. While on the other hand, the discounting are for the negative NPV has been calculated at 30% after using the trial and error method. The trial and error method involves calculation for negative NPV based on the discounting rate of 16% and 20% respectively (refer to appendix). At 10% and 30% discounting rate for the present case scenario, the IRR is 24.65%. Therefore, meaning that the investment in the new machine would be profitable for the company. Theoretical background of the three investment decision methodologies In the current case of investment decision making, the evaluation for the investments decision have been made based on the results of the net present value, internal rate of return and profitability index. As mentioned by Ross et al. (2015, p.66), the net present value is considered as the most effective and efficient investment appraisal tool. The reason behind this is that the calculation for the net present value involves calculation for the time value of money. In this context, Brooks et al. (2016, p.217) stated that the net present value calculation also taken into consideration the future cash inflows while discounting them to present rate. This discounting at the present rate makes the investment decision making much more easier and relevant. However, Huang and Petkevich (2016, p.72) argued stating that the net present value calculation are ineffective in case of two different project of two different sizes. The reason behind this is that the NPV calculation results are highly influenced by the inputs thus making it ineffective in case of two different sizes projects. The internal rate of return is simpler to use as compared to other investment appraisal techniques. Like the net present value, the internal rate of return also takes into consideration the time value of money while helping in mitigating the hurdle rate. However, Goldstein and Hackbarth (2014, p.534) argued that the calculation for the internal rate of return do not take into consideration the economies of scale thus, making the calculation not dependable. Moreover, the internal rate of return cannot be taken into consideration while deciding two mutually exclusive projects. The reason behind this is that the internal rate of return calculations taken into accounts the rate of return while ignoring the return on investments. In this context, Ross et al. (2015, p.65) stated that the internal rate of return calculations shows the return on the total money invested. The profitability index calculations like the NPV and IRR takes into account the time value of money thus, making the investment decision more meaningful. Moreover, the calculation of the profitability index takes into account all the cash flows for the entire life while ascertaining the exact rate of return for the investments. In this context, Prezas and Simonyan (2015, p.105) added that the profitability index calculations are more relevant as the calculations involve different amount cash flows for different projects. While on the other hand, Hanousek et al. (2015, p.27) stated that in case of profitability index, it is difficult to understand the discounting rate as the cash flow and initial investments are shown at cumulative value. Huang and Petkevich (2016, p.71) agreed to this and further added that the calculation for the profitability index are difficult in case there are useful life of the projects differ from one another. Reason behind these being superior to ARR and payback period The calculations for the investment decision making in the present case scenario are based on the calculations of net present value, internal rate of return and profitability index. The reason behind choosing these tools of investment decision making is that they take into consideration the time value of money. Moreover, in the present case the investment decision making is based on identical project that is machines. This justifies the inclusion of the internal rate of return in the investment decision making. Moreover, both the machines in the present case have identical useful life, which makes the profitability index outcome more relevant. Furthermore, the net present value takes into consideration the risks pertaining to future cash flows, which helps in evaluating the exact amount by which the value of the company would be increased. The accounting rate of return has been excluded from the investment decision-making calculation because the ARR calculations ignore time value of money. In this context, Brooks et al. (2016, p.218) stated that the accounting rate of return ignores the cash flow from the investments, which makes the outcomes irrelevant. In the present case, the calculation for the investment decision making have taken into consideration the terminal value of the project. However, the accounting rate of return ignores the terminal value of the project thus, leading to exclusion of the investment appraisal tool in the present case. In this context, Goldstein and Hackbarth (2014, p.535) stated that the accounting rate of return calculation are simple and are based on the accounting profit. This calculation on the accounting profit helps in measuring the profit potential that the company might expect from the investment. The fact that the accounting rate of return does not involve time value of money ther efore, the accounting results cannot be considered while decision making. As mentioned by Brealey et al. (2015, p.77), the payback period provide a crude measure about the liquidity of the project assisting in decision-making. The payback period determines the period within which the initial investment in the project can be recovered. The outcome of the payback period between two different projects can be used for determining which project would return the initial investment at the earliest. In this context, Gao and Zhang (2015, p.111) cited that the payback period does not involve time value of money therefore, the outcome of this investment decision making tool cannot be considered. Chemmanur and He (2016, p.76) agreed to this and further added that the calculations for the payback period ignores the amount beyond the payback period. Moreover, the payback period does not provide any concrete evidence whether the investment would help in increasing the value of the firm. Therefore, the investment decision making in the present case scenario excludes the p ayback period calculations. Conclusion From the above calculations and findings, it is quite clear that the investment in the new machine would be profitable for the company. The net present value, internal rate of return and the profitability index are all favourable suggesting that the investment would help the company increase its profit potential. The reason behind the selection of the net present value, internal rate of return and profitability index is that the calculations for these investment tools involve time value of money consideration. Moreover, the project is identical with similar useful life thereby, making the selection of these tools more relevant. However, the accounting rate of return and the payback period have also been excluded because; the methods do not consider time value of money. While on the other hand, the calculations based on these tools do not consider all the cash flows. Recommendation The company has been recommended to consider investing in the new machines as the capital investment decision making tools provide favourable outcomes. This means that the investment in the new machine worth $1000000 would help to increase the profit potential of the company. Moreover, the company has also been recommended to continue evaluation of the investment decision making based on the NPV, IRR and profitability index as because they take into consideration time value of money and entire cash flow. Reference list Brealey, R., Myers, S. and Marcus, A. (2015). Fundamentals of corporate finance. New York, NY [u.a.]: McGraw Hill Education. Brooks, C., Godfrey, C., Hillenbrand, C. and Money, K. (2016). Do investors care about corporate taxes?. Journal of Corporate Finance, 38, pp.218-248. Chemmanur, T. and He, S. (2016). Institutional trading, information production, and corporate spin-offs.Journal of Corporate Finance, 38, pp.54-76. Corporate Finance. (2016). South-Western Pub. Gao, L. and Zhang, J. (2015). Firms earnings smoothing, corporate social responsibility, and valuation.Journal of Corporate Finance, 32, pp.108-127. Goldstein, I. and Hackbarth, D. (2014). Corporate finance theory: Introduction to special issue. Journal of Corporate Finance, 29, pp.535-541. Hanousek, J., KoÄ enda, E. and Shamshur, A. (2015). Corporate efficiency in Europe. Journal of Corporate Finance, 32, pp.24-40. Huang, K. and Petkevich, A. (2016). Corporate bond pricing and ownership heterogeneity. Journal of Corporate Finance, 36, pp.54-74. Prezas, A. and Simonyan, K. (2015). Corporate divestitures: Spin-offs vs. sell-offs. Journal of Corporate Finance, 34, pp.83-107. Ross, S., Westerfield, R., Jaffe, J., Lim, J., Tan, R. and Wong, H. (2015). Corporate finance. [Singapore?]: McGraw-Hill Education (Asia).

Platos defence of philosophy understood as critical thinking, as it is represented in Socrates trial in the Apology Essay Example

Platos defence of philosophy understood as critical thinking, as it is represented in Socrates trial in the Apology Paper This essay will firstly, ascertain and examine what exactly critical thinking is. Secondly, it will provide a brief outline of Platos Apology, and then it will outline and assess how Platos defence is represented and understood as critical thinking. Finally, there will be a conclusion of what exactly being a critical thinker entails and a short paragraph explaining how the module has improved and expanded my own capacity for critical thinking. Young (1996, p. ) states that critical thinking is the capacity people have to question beliefs and presuppositions (their own and those of others) with a view to giving reasons for them or for amending them. Put more simply, critical thinking is the procedure for understanding and evaluating the evidence which supports a certain claim or view. Critical rationality which is the capacity to criticise, that is, to assess goals, rules and presuppositions themselves and where appropriate change them is a distinctively unique human trait, which gives human beings the power to engage critical thinking (Rationality Handout). It also involves rational decision making in whether to believe or discount a point, and it also involves accepting or rejecting certain evidence. It is not simply an exchange of opinions, but a critical and vigorous attempt to find ones way through discussion and argumentation. The Apology is Platos version of the speech given by Socrates as he defends himself against the charges of being a man who corrupted the young, refused to worship the gods, and created new deities (Schofield, 1998, p. 1). Young (1996, p. ) states that Plato sees philosophy itself as namely a style of thinking which is distinctively different from, for instance, science or religion or indeed anything else. We will write a custom essay sample on Platos defence of philosophy understood as critical thinking, as it is represented in Socrates trial in the Apology specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Platos defence of philosophy understood as critical thinking, as it is represented in Socrates trial in the Apology specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Platos defence of philosophy understood as critical thinking, as it is represented in Socrates trial in the Apology specifically for you FOR ONLY $16.38 $13.9/page Hire Writer So, philosophy for Plato is not a distinctive set of conclusions or of finished truths, but a distinctive style of thinking. For Plato, Socrates embodies this distinctive way of thinking and living that is philosophy, which Young (1996, p. 2) adds is not just another way of theorizing about life but also a new attitude toward life, even a new way of living life. Socrates begins by stating that the accusations against him began because people confused him with intellectuals who claim to have expert knowledge either in the natural sciences (cosmogonists), or in the social sciences or humanities (sophists). Socrates says There is a wise man called Socrates who has theories about the heavens above and has investigated everything below the earth, and can make the weaker argument defeat, the stronger (Young, 1996, p. 2). Socrates is, in the Apology, the very embodiment of philosophy or critical thinking, so by stating the differences he is stating that philosophy does not provide expert knowledge, but instead gives a different kind of human or limited knowledge. Socrates says of himself that it seems he really possesses this. And he hints that, limited though it be, the knowledge or wisdom that can be secured via philosophy is of decisive importance for human beings (Young, 1996, p. 3). The vital knowledge Socrates talks about is the abilities and vital skills philosophy learns people of questioning everything, being inquisitive in life and not accepting things for how they are. Socrates then goes on to tell a tall story about himself, which, as with all of the Apology, it isnt just the words spoken but the action and setting plus words left unspoken, which determine the texts meaning. Socrates tells the story of his friend Chaerephon who went to Delphi and through the oracle there asks the god if anyone was wiser than Socrates. The god said that there was no one. Socrates claims to have been astonished and then states that it was reverence toward the gods which led him by his questioning activity to challenge the leaders of the State (Young, 1996, p. 3): I knew I was making myself disliked, but felt compelled to put my duty to the god before all else And by the dog, Athenians! as I pursued my questioning at the gods command, it seemed to me that those with the greatest reputations for being wise were amongst the stupidest of all; others supposed to be their inferiors were wiser, and better people too. (Young, 1996, p. 3)) An important part of critical thinking is then, according to Socrates, having the ability and open mind to listen to and question everyones views. Socrates differentiates between the all-seeing knowledge of the gods and normal knowledge which humans can gain, and states that the wisest people are those who know that they can never have this definitive and ultimate knowledge. Young (1996, p. ) adds Socrates wisdom or knowledge consists in part in the fact that he (unlike his powerful interlocutors) knows the limits of his own knowledge (or the extent of his own ignorance), whereas they do not: a person who is ignorant of x but knows herself to be ignorant of it, is to that extent wiser than someone who does not know it either but mistakenly thinks she does. Socrates gets his accusers to admit that they are ignorant and proud; to use Platos language, they are lovers of status, power and wealth, as opposed to lovers of knowledge and truth (Young, 1996, p. ) and states they will only ever become wise and less ignorant if they change their will and desire. Translating Socrates words, Young (1996, p. 4) comments Philosophical knowledge or wisdom, then, depends upon on the will at least as much as the intellect; upon desire and upon the direction of desire at least as much as abstract intellectual ratiocination; upon practice at least as, much as theorizing. Critical thinking then is an intellectual effort aiming at acquiring human self-knowledge or self- understanding. (Young, 1996, p. 4). In order to strive to achieve this, a person must have courage, be prepared to question and challenge oneself, and to continue on even though it may be upsetting some people, just as Socrates upset those in power through his philosophy of questioning and debating. Critical thinking is a way of living which one embodies in their attitudes and practices, it is also about taking others views and beliefs into consideration, and then challenging the very presuppositions that these beliefs rest on. To be a critical thinker is to be tolerant, not take things at face value and to realise that as humans our knowledge will always be limited. This should spur one on to be open-minded and to question ones thoughts and views. However, Socrates recognises that some people may be unwilling to do this out of fear of losing their credibility and reputation. One should not automatically assume what a person says is true just because they are in power, in the same way Socrates tells the youth to think for themselves and not believe everything politicians say. Young (1996, p. ) sees philosophy as a second-order study; first-order studies being those, such as sciences that deal with facts, where as second-order study focuses on the concepts using which first-order studies study the real world and its facts with a view to clarifying the structure and role of these concepts; or again instead of engaging in first-order evaluation of the world we focus on the evaluations and judgements whereby first-order evaluating is done; and so forth. Socrates was willing to die for philosophy and the distinctive way of thinking and living it entails; the statement he made he unquestioned life is not worth living (Platos Apology, p. 12) sums up his life and beliefs perfectly. He believes that critical thinking is good for both individuals and society, and that the freedom to think in this way should be defended. In asking what the good life was and how we could attain it, Socrates made critical thinking the patrimony of potentially every person who was willing to follow his leadership. His simple call to critically examine oneself and the world would both empower and challenge his followers throughout the ages. To be fully human after the example set by the life of Socrates would require any serious person to engage in the examined life (Polelle, 2008, p. 91). Socrates was the very embodiment of what it is to be a critical thinker, and he saw it as being such a crucial part of being a human being that he was willing to die for it. The very idea of critical thinking needs defending because there will always be people who are annoyed by it and who will try to take away others freedom to practice it, just as happened to Socrates in the Apology. I must admit that I have never had time for either religion or god. When I was younger I could not understand why people spent so much time out of their lives worshipping something that has never even been proved exists. It seemed very unusual to me that people would pray to a god when things got bad because how do they even know someones listening? It seemed obvious to me at the time that surely there is no higher being because if there really was, would this almighty god allow all of the suffering that goes on in the world to continue? Can there really be a god that created our earth? After studying the critical thinking module I no longer think this way. Im open to everything, even something that cant be proved, like god. I still question the ideas on which ideas and beliefs are based, but I am now more open to all ideas, no matter how strange they seem to me at the time. Instead of just ignoring the Jehovahs Witnesses at the door, I now say hi, collect some brochures from them and have a chat, although I cant see myself ever becoming a follower of Jehovah. I am open to ideas, such as god creating the world, however I do feel this is very unlikely. I have thought there must be something out there listening to gods worshippers, and surely he must exist otherwise he would not have so many followers. But then again, perhaps the bible is a hoax. I feel more inclined to believe that a big bang created the earth, mainly because there seems proof to support the fact. To be a critical thinker means to consider and debate all ideas and beliefs and I feel I am developing my ability to think critically. However, this does not mean I have to agree with everything or everyones points of view.