Information Theory and Thermodynamics

Information Theory and Thermodynamics In order to develop better tools, machines and technology we have had to develop our understanding of the physical world. This has allowed us to construct machines that are more capable than those preceding it. The French scientist Carnot was studying machines and was trying to understand how to make them better and more efficient. As part of his studies he calculated the maximum efficiency of any machine and was able to relate this to temperature. Carnots idea was to simplify the machine to its simplest form (this generality that makes it universal) and analyse that Carnot knew that machines of the time (and of today) work as a result of a temperature difference across the machine. In his time it was obvious, fire produced steam which turned a turbine that did work; today is not too different, all of our machines still need a temperature difference to make them work, however the temperature difference driving the machines may be at some distance, for example a power station producing electricity. Even wind, and solar require temperature differences to work. Analysing these machines further lead to concepts that we, perhaps, take for granted: work, power and energy notable examples. Whilst working on these concepts Boltzmann came up ideas that grew into statistical thermodynamics. It was extended and correctly describes a whole range of phenomena. The idea of thermodynamics is to relate various physical properties of a substance to the bulk behaviour of the constituent parts within. Microstates and Macrostates: Boltzmann realised that by knowing the number of different states that a system could be in and the number of configurations that each state would enable him to work out the probability of a particular state occurring. And that on average when something is observed it is more likely to be found in one of its more probable states. Many systems have lots of moving components and this means that over time a system will have evolved into a more probable state. This may now seem obvious, but it hadnt been pointed out explicitly at the time. A Macrostate is the global state of a system. For example if we consider a box with red, blue and green balls a possible macrostate might be to find all of the red balls are in the bottom left corner, whilst all of the others are randomly distributed in the rest of the box. Another example of a macrostate might be that the total electrical charge of block could be Coulombs. A Microstate is one particular configuration of the system that produces a macrostate. In the balls example if the balls are identical apart from colour we can permute the balls with the same colour amongst themselves and end up with different microstates. An example with the charged block might be that we have 4 particles each with charge as one microstate, and another might be to have 1 particle with and another with Below is a figure that represents a hypothetical macrostate of three colours of balls three particular microstates that can be used to achieve it. In the leftmost diagram we have a macrostate with all of the red balls in the bottom left corner, the other diagrams show different permutations of the balls that also achieve the desired macrostate. In order to calculate the probability of this state we would need to know how many combinations of it there are. This is a simple counting argument: we have 1 way of putting the green ball in its spot, two ways of putting the blue balls in their position and ways of arranging (we can pick any of the 5 to go in the corner, then any of the remaining 4 to go next to that, then any of the remaining 3 etc). There are a total of 8 balls and so the In general if there are objects we have possible arrangements; if we also have different types and if of them are of type 1 (say red), are of type 2 and are of type then we can find the total number of permuted arrangements with: We can use these two facts to calculate the number of accessible microstates of type , this is called the weight of the microstate and is denoted by, : The weight of a microstate is proportional to the probability of the system being in it. So one way to calculate the probability of being in the state is via: where the summation is over the weights of all the other possible microstates. A handy way to view a microstate is with a pack of cards (Birks bath), in a pack of playing cards the statistical weight of a club is 13 since there are 13 of then the statistical weight of a queen is 4. The probability of selecting a club card is the chances of picking out a club are times greater than picking out a queen. The statistical weight of the queen of hearts is 1. There is one obvious constraint that can always be imposed and that is that the total number of particles is the sum of the number of particles in each state: We can impose other constraints on the system as they are required later. Because the particles of each type are identical it is natural to assign a probability that a randomly selected particle is of type, , as: We are also able to define an Expectation value for the system. If we were interested in the average occupancy of each of the types we would have: which would represent the average occupancy of each type. If we were interested in the charge (or energy (I shall use for either) we would similarly have: Let us take some examples and compute the statistical weights, average occupancy and average energy (represented by the value of the type index e.g. if , the energy would be two units). I shall consider that the atoms are all identical apart from the energy that they have and that a macrostate is the same for each. For the first case let us assume that we have 5 atoms and the macrostate corresponds to an energy of 5 units. The table below shows that (for example) the microstate 3 has a weight of 20, this means that there are 20 microstates with the occupancy levels given that correspond to the macrostate We can tabulate the various combinations as below: microstate number Occupancy of type i weight probability n0 n1 n2 n3 n4 n5 1 4 0 0 0 0 1 5 0.0397 2 3 1 0 0 1 0 20 0.1587 3 3 0 1 1 0 0 20 0.1587 4 2 2 0 1 0 0 30 0.2381 5 2 1 2 0 0 0 30 0.2381 6 1 3 1 0 0 0 20 0.1587 7 0 5 0 0 0 0 1 0.0079 totals 15 12 4 2 1 1 126 1 Average occupancy 2.222 1.389 0.794 0.397 0.159 0.040 Table 3.1: Table showing occupancy levels for a 5 atom system with a macrostate of 5. This table was generated by finding all of the numbers that sum (in this case) to 5 which is the macrostate. It shows the number of atoms with a particular energy in the columns headed , the statistical weight of each microstate is in the weight column, the probability column next to it shows the probability of randomly selecting this microstate from a given macrostate (in this case 5 atoms and a total energy of 5). The row titled average occupancy shows the expected occupancy of an energy level of type , calculated from the table. Looking at the table there are two equally most likely microstate arrangements. The first of these corresponds to and , both occurring with a probability of 0.238. Another possible macrostate is listed below, this time we have 7 atoms and an energy of 7 units. The headings of the table are the same as in the previous example. We can see that the weight of the most probable microstate is 420 and that we have a probability of 0.245 of randomly selecting one of them. The occupancy levels are: microstate occupancy of type i weight probability n0 n1 n2 n3 n4 n5 n6 n7 1 6 0 0 0 0 0 0 1 7 0.004 2 5 1 0 0 0 0 1 0 42 0.024 3 5 0 1 0 0 1 0 0 42 0.024 4 5 0 0 1 1 0 0 0 42 0.024 5 4 2 0 0 0 1 0 0 105 0.061 6 4 1 1 0 1 0 0 0 210 0.122 7 4 1 0 2 0 0 0 0 105 0.061 8 4 0 2 1 0 0 0 0 105 0.061 9 3 3 0 0 1 0 0 0 140 0.082 10 3 2 1 1 0 0 0 0 420 0.245 11 3 1 3 0 0 0 0 0 140 0.082 12 2 4 0 1 0 0 0 0 105 0.061 13 2 3 2 0 0 0 0 0 210 0.122 14 1 5 1 0 0 0 0 0 42 0.024 15 0 7 0 0 0 0 0 0 1 0.001 totals 51 30 11 6 3 2 1 1 1716 1 Average occupancy 3.231 1.885 1.028 0.514 0.228 0.086 0.024 0.004 Table A3 2: a seven atom system with a total energy of seven A final example consists of a system of 10 atoms and a total energy of 9. As will be readily seen as the number of atoms and the energy increases the number of microstates corresponding to a given macrostate increases so does the size of the table. It was quite difficult to work out the number of combinations of energy that could occur and I wouldnt want to do it again for larger tables. In the next part we shall use the method of Lagrange multipliers to massively simplify the calculations for the probabilities and expectations. For the case of 10 atoms and an energy of 9 units. We see that the most probable microstates have the following occupancy levels: The most probable microstate has a probability of 0.1555, but there is another microstate that is only slightly less probable (a probability of 0.1300) and this has occupancy levels of: The two least likely microstates are the following: Both have a probability of 0.0002 which is very small indeed. Table 3 is below: d occupancy of each type i weight probability n0 n1 n2 n3 n4 n5 n6 n7 n8 n9 1 9 0 0 0 0 0 0 0 0 1 10 0.000205677 2 8 1 0 0 0 0 0 0 1 0 90 0.00185109 3 8 0 1 0 0 0 0 1 0 0 90 0.00185109 4 8 0 0 1 0 0 1 0 0 0 90 0.00185109 5 8 0 0 0 1 1 0 0 0 0 90 0.00185109 6 7 2 0 0 0 0 0 1 0 0 360 0.00740436 7 7 1 1 0 0 0 1 0 0 0 720 0.014808721 8 7 1 0 1 0 1 0 0 0 0 720 0.014808721 9 7 1 0 0 2 0 0 0 0 0 360 0.00740436 10 7 0 2 0 0 1 0 0 0 0 360 0.00740436 11 7 0 1 1 1 0 0 0 0 0 720 0.014808721 12 7 0 0 3 0 0 0 0 0 0 120 0.00246812 13 6 3 0 0 0 0 1 0 0 0 840 0.017276841 14 6 2 1 0 0 1 0 0 0 0 2520 0.051830522 15 6 2 0 1 1 0 0 0 0 0 2520 0.051830522 16 6 1 2 0 1 0 0 0 0 0 2520 0.051830522 17 6 1 1 2 0 0 0 0 0 0 2520 0.051830522 18 6 0 3 1 0 0 0 0 0 0 840 0.017276841 19 5 4 0 0 0 1 0 0 0 0 1260 0.025915261 20 5 3 1 0 1 0 0 0 0 0 5040 0.103661045 21 5 3 0 2 0 0 0 0 0 0 2520 0.051830522 22 5 2 2 1 0 0 0 0 0 0 7560 0.155491567 23 5 1 4 0 0 0 0 0 0 0 1260 0.025915261 24 4 5 0 0 1 0 0 0 0 0 1260 0.025915261 25 4 4 1 1 0 0 0 0 0 0 6300 0.129576306 26 4 3 3 0 0 0 0 0 0 0 4200 0.086384204 27 3 6 0 1 0 0 0 0 0 0 840 0.017276841 28 3 5 2 0 0 0 0 0 0 0 2520 0.051830522 29 2 7 1 0 0 0 0 0 0 0 360 0.00740436 30

Book summary of “A Spectator’s guide to Jesus” Essay

John Dickson, an Honorary Associate in the Department of History in Macquarie University, unfolds the myths and the religiosity that often blurs the image of Jesus. Dickson explores the many roles and identities that are given to Jesus, healer, teacher, Christ. â€Å"A Spectator’s guide to Jesus† is a book dedicated to discovering the truth to the most controversial religious topics, from Jesus’ replacement of the temple, his divineness, meaning of his death and his words and deeds that inspire. In the first chapter, â€Å"How we know what we know about Jesus?† Dickson discusses the certainty of Christianity, mentioning the various ancient manuscripts of Jesus from the Greco-Roman references, to the writings of the New Testament. Dickson then comes to discuss the plausibility of the Bible. Since Paul and Mark had independently offered similar descriptions of Jesus’ life and teaching, and because we know these sources are not copied from each other, we have to assume their information was both early and widely known. After proving the encounters of Jesus as extremely likely events, Dickson’s main concern in the second chapter, â€Å"His words and their impact† is emphasising on Jesus’ words of the Christian character of sex, marriage, prayers, wealth, food and body, caring for those in need, loving enemies and divine mercy. The words of Jesus as mentioned in the Gospels, impact on the way humans should live their lives and have an understanding for humanity. Dickson confronts the problems for society believing in miracles since they occur only in small-minded children’s tales. In Chapter 3, â€Å"The deeds that baffle,† Dickson explains Jesus’ stunning miracles as a preview of God’s coming kingdom. Dickson argues that if one was to see that there were no forces in the universe other than the observable laws of nature, then a matter of uncertainty will occur. While if one believed in the miracles of Jesus, the whole puzzle would be completed. In Chapter 6, Dickson explores the human nature of ignoring the rules that God had set up for us, we tend to modify these rules to suite our own preferences. It is in this chapter that Dickson explores the role of Jesus, to overcome the wrongs of this world on behalf of God and also represent God as a loving creator. An example of Jesus’ role is explored in the previous  chapter (4), where Jesus and God had saved the Israelites from the tyrannous Egyptian invasion, under the command of the famous Pharaoh Ramses II. Dickson points out in Chapter 7 of Jesus’ death and resurrection which had borne divine judgement for all those who accept his hand of friendship. Jesus’ openness towards sinners was a deliberate sign of God’s grace unlike the Jewish way of rejecting non-Jews. Jesus’ preaching declared that his suffering and scandalous social life embodied grace in a tangible way. Through his meals with the undeserving, he sought to demonstrate the friendship with sinners he believed God so keenly desires. Jesus’ acting as a replacement of the temple in Chapter 8 not only suggests a mere religious radical, but the thought of allowing the whole community to embrace the Messiah. Chapter 9, â€Å"The meaning of his death,† as Dickson once again assesses, is the aim of Christ’s mission. Christ had died for us to win God’s forgiveness, â€Å"cancel his judgement and guarantee us a place in his kingdom.† Chapter 9 is a follow on from Chapter 5 which described the significance of Jesus’ title. Dickson tells of the importance of the title ‘Christ’, an Anglicised form of the Hebrew name Yeshua, which had endowed his divine authority as ‘saviour’, rescuing people from divine judgement. Dickson also explains the significance of the traditional Passover themes of ‘blood’ and ‘forgiveness’ of God’s people. God’s judgement would fall upon the lamb (Jesus) so that it might pass over ‘sinners’. Chapter 10, 11 and 12 shows the importance of Christ’s resurrection which had shaped the Christian belief of the afterlife. Christ rising to life is central to the biblical faith and not merely because it marks out his life as a unique moment of history, but because in it God shows he is willing and able to breathe a new life where there is currently death and disorder. Dickson then makes the comparison between ‘The Great Caesar’ who conquered a massive empire with the imperialness of Jesus. Nonetheless, Dickson emphasises the fact that God is more significant than Caesar, every empire will pass into oblivion while Christ’s kingdom reigns all and forever. In Chapter 12, Dickson talks of Christs and God’s divineness. The letter from  the Roman administrator Pliny to Emperor Trajan in AD110 indicates Jesus’ oneness with the almighty, â€Å"Jesus is the image of the invisible God.†Dickson uses irony in the last chapter. For centuries, the church has been seen as the preacher and basis of knowledge for the Christian faith, but Dickson questions the church’s battle for power, land, and welfare over the preference for the lowly and contrasts this with Jesus’ non-violent and dutiful service towards humanity. The Epilogue portraits a follower of Jesus’, one who must endure the shame and unworthiness as a sinner, but in the end, â€Å"All earthly empire will pass into oblivion while the kingdom of true Caesar reigns all.†Assessment of the book’s strength and weaknessesI particularly enjoy the concept of this novel being written for the average person; not a scholar novel. It allows the average person to understand and interpret for themselves where Christianity really lies upon, not the clichà ©, inaccurate summaries. As Dickson pointed out, â€Å"studying the life of Christ is like dropping half-way through a conversation,† you can become mislead and often criticise the faith when you have only heard part of the big story. But in â€Å"A Spectators guide to Jesus,† Dickson offers detailed background knowledge to conflicts, events, other religions, Old Testament and Gospel references. The author makes many comparison of the events associated with Jesus, an example was Joe Louis, the professional boxer. â€Å"The lads knew they were messing with the wrong person,† this situation is similar to what we have done to Jesus as Dickson indicates, â€Å"We laughed at him and harassed him for being different and we would never have realised we were wrong till we saw the Son of God through our own eyes.† I find it extremely easy to interpret the events and concepts associated with Jesus when Dickson relates it to modern day events. I see this book as a spectacular outline to the purpose of human existence, however, there are weaknesses. An atheist reading this book would easily see the weakness to Christianity, â€Å"If humans are so unwilling to believe these days, and if God is so great than how hard is it for him to appear in front of everyone?† Dickson should have considered the significance of the Holy  Spirit which continues to prove the presence of God (Chapter 3). On other occasions, Dickson seemed to be too irrelevant. In Chapter 6, Dickson first discusses the human preference to modify rules, he then tells of our lack of compassion for others. Nonetheless, â€Å"A spectators guide to Jesus† remains to be an incredible book through its inspiring words and debate on the man from Nazareth. Reflection of the books contents to the concerns of the reviewerIn Chapter 2, Dickson shows a selection of teachings of Jesus. A practical implication that captivated me was one of Jesus’ teachings, â€Å"Love for enemies.† In Luke 6:27-36, it spoke, â€Å"Even sinners love those who love them. And if you do good to those who are good to you, what credit is that to you? Even sinners do that.† I can see myself relating with this passage. In year six, a student confronted me and yelled curses at me. I responded with fat insults about him. I instantly felt the pride and rise in self-esteem. But the next day, I saw the kid had become depressed and outraged as a result of my insults. I felt bad. The following week, a different kid yelled insults at me, but this time I didn’t curse back, instead I told him that we could be friends and there is no point in being enemies. Ever since that day we became good friends. I see there being no need for hatred. What can you lose from being nice? You can only gain from being a kind and wise person, similar to the character of Jesus that Dickson depicts through historical sources. If everyone respects their enemy, the world would be a better place. Another way in which I felt the book had related to my beliefs was Dickson’s view on the meaning of Jesus’ death, implying that there must be a God which controls everything. I really don’t see our purpose to life through science. Everything around me is so perfect, from the smallest creature on earth to the biggest stars in the sky. I don’t have to be a genius to spot the missing puzzle, the question to human existence lies nowhere but the fact that there is a God who had created everything, we became sinners and his son Jesus had saved us from Divine judgement, according to Dickson (Chapter 3). http://www.sydneyanglicans.net/mission/resources/a_spectators_guide_to_jesus_john_dickson/

The Principles of Online Paper Editing That You Will be Able to Benefit From Beginning Today

The Principles of Online Paper Editing That You Will be Able to Benefit From Beginning Today The Rise of Online Paper Editing Therefore, you will know all that is required. You pay only as long as you're satisfied. You don't need to have your own Dot Com website, an extremely straightforward Blog will do. You don't need to have your own Dot Com website, an extremely straightforward Blog will do. The most significant thing is that every order is going to be delivered punctually. Finding somebody who will edit your composition online for free can be a difficult task in the event you don't have accessibility to the appropriate strategies and a couple of helpful ideas for how to proceed. Nobody will discover that you're getting our help. Online writing help is among the best things the web has to offer you. While you're searching for a paper to purchase to be able to finish your academic assignments, there are several choices to select from. It's absolutely free to set an order. In some instances, the cost may change as a result of individual preferences or circumstances. Student-friendly rates and high-quality results are ensured. Thus, when any of your customers or partners goes through the documents, you need to be mindful of the standing of your business. In case you have any questions, you're totally free to message either the writer or a customer care representative. Our editors possess the abilities and skill to add real, measurable price and internet quality of paper documents. There are a lot of reasons why you need to prefer our services. Online Paper Editing - Is it a Scam? Editing is a rather important portion of creating any sort of paper. So, our editing proofreading services can help you to find the ideal reaction from your customers and business associates. Our editing services provides you a whole solution for a number of your paper editing. Proofreading services, together with editing alternatives, will be able to help y ou avoid many difficulties. Furthermore, paper proofreading of your initial document can help determine the time needed for editing and the price. Furthermore, you should know what sort of editing you will need for your paper. Our on-line editing solutions, supplied by the best editors, are meant to edit essay and any document. It's also advisable to be certain that the on-line help that you get are going to be able to supply another round of editing at no excess price tag. The Foolproof Online Paper Editing Strategy If you did, then am compelled you know why professional editing service is essential for college students who might not have the time to do it by themselves. If you don't have enough time for a lot of your college. Yet another advantage is the chance to get price estimate in a couple of minutes. Another benefit of our website is the quickness. The 30-Second Trick for Online Paper Editing An essay paper or some other document should always be written by arranging all of the data in an appr opriate format. Citations and extracts from several sources have to be formatted properly. Self improvement proofread bot is a comparatively straightforward website. If you want to get a research paper, online writing support like ours is just what you'd like. The lottery is all but full. Where the lesson plans covering all significant school subjects and effortless lowdown on them here. The best writers can help you. If you've chosen to purchase essay online UK from us, then make sure that the ideal objective is ensured! Now it's time to modify the situation with the assistance of custom essay writing. The actual folks highly praise our essay help site. How-to writing is a genre that appeals to the majority of students since it is applicable on earth. Our professional essay writers will deal with it. Edit your essay until it's perfect. Whenever you search for college essays and. Let's say you have to purchase essay for college. Now everyone is able to locate a web-based paper editor via the. Ideal Essay Point is a completely free port for all of the students of UK who seek custom writing services to become online support to earn their project outstanding. Many freelance sites and writing websites will offer editing services and in many instances, you can pick the price that you're going to pay. With our custom made essay offer, you can be guaranteed to get any kind of essay help you're looking for. You can depend on the ideal essay help online. Otherwise, the standard of the paper might not be considered high by the reader. After that our reliable custom made paper writing assistance together with skilled experts is simply the issue you. Ideal custom writing service you are able to rely on. Even though it's simpler to purchase term papers online, the smartest choice is writing the paper from scratch.

Preparing for the Revised GRE in One Month

Youre ready to go. Youve registered for the Revised GRE and now you have a month before you take the exam. What should you do first? How do you prepare for the GRE in one month when you dont want to hire a tutor or take a class? Listen. You dont have too much time, but thank goodness youre preparing for a test one month in advance and didnt wait until you only had a few weeks or even days. If youre preparing for a test of this kind of magnitude, read on for a study schedule to help you get a good GRE score! Preparing for the GRE in One Month: Week 1 Double Check: Make sure your GRE registration is 100% all set to be sure youre actually registered for the Revised GRE. Youd be amazed how many people think theyre taking the test when theyre not.Purchase A Test Prep Book: Buy a comprehensive GRE test prep book from a well-known test prep company like The Princeton Review, Kaplan, PowerScore, etc. GRE apps are great and all (here are some fabulous GRE apps!), but typically, they are not as comprehensive as a book. Heres a list of some of the best.Jump Into the Basics: Read the Revised GRE test basics like the length of time youll test, the GRE scores you can expect, and the test sections.Get a Baseline Score:Â  Take one of the full-length practice tests inside the book (or for free online through ETSs PowerPrep II Software) to see what score youd get if you took the test today. After testing, determine the weakest, middle, and strongest of the three sections (Verbal, Quantitative or Analytical Writing) according to your baseline tes t.Set Your Schedule: Map out your time with a time management chart to see where GRE test prep can fit in. Rearrange your schedule if necessary to accommodate test prep, because you must aim to study every day – you only have one month to prepare! Preparing for the GRE in One Month: Week 2 Start Where Youre Weak: Begin coursework with your weakest subject (#1) as demonstrated by the baseline score.Nab The Basics: Learn the basics of this section fully as you read, and take notes about the types of questions asked, the amount of time needed per question, skills required, and content knowledge tested.Dive In: Answer #1 practice questions, reviewing answers after each one. Determine where youre making mistakes. Highlight those areas to return to.Test Yourself: Take a practice test on #1 to determine your level of improvement from the baseline score.Tweak #1: Fine tune #1 by reviewing the areas you highlighted and questions missed on the practice test. Practice this section until you have the strategies cold. Preparing for the GRE in One Month: Week 3 Head to Middle Ground: Move on to your middle subject (#2) as demonstrated by the baseline score.Nab The Basics: Learn the basics of this section fully as you read, and take notes about the types of questions asked, the amount of time needed per question, skills required, and content knowledge tested.Dive In: Answer #2 practice questions, reviewing answers after each one. Determine where youre making mistakes. Highlight those areas to return to.Test Yourself: Take a practice test on #2 to determine your level of improvement from the baseline score.Tweak #2: Fine tune #2 by reviewing the areas you highlighted and questions missed on the practice test. Return to the areas in the text youre still struggling with.Strength Training: Move on to the strongest subject (#3). Learn the basics of this section fully as you read, and take notes about the types of questions asked, the amount of time needed per question, skills required, and content knowledge tested.Dive In: Answer practice questio ns on #3.Test Yourself: Take a practice test on #3 to determine the level of improvement from baseline.Tweak #3: Fine tune #3 if necessary. Preparing for the GRE in One Month: Week 4 Simulate The GRE: Take a full-length practice GRE test, simulating the testing environment as much as possible with time constraints, desk, limited breaks, etc.Score and Review: Grade your practice test and cross-check every wrong answer with the explanation for your wrong answer. Determine the types of questions youre missing and head back to the book to see what you need to do to improve.Test Again: Take one more full-length practice test and rescore. Review incorrect answers.Fuel Your Body: Eat some brain food – studies prove that if you take care of your body, you’ll test smarter!Rest: Get plenty of sleep this week.Relax: Plan a fun evening the night before the exam to reduce your testing anxiety.Prep Prior: Pack your testing supplies the night before: sharpened #2 pencils with a soft eraser, registration ticket, photo ID, watch, snacks or drinks for breaks.Breathe: You did it! You studied successfully for the Revised GRE exam, and youre as ready as youre going to b e!