Arguments For or Against the Existence of God Essay

Arguments For or Against the Existence of God - Essay Example Mainly, the argument is based on induction. It begins with Aquinas believing that there is an order of â€Å"efficient causes† in this world (Reichenbach, 2012). This means that causality exists in this world and that this causality has a particular order, where one thing causes another and this caused thing also causes another thing. Aquinas then proceeds by assuming that nothing can cause itself because it would be impossible for it to be prior to itself. This then leads Aquinas to think that everything is caused by another thing other than itself (Reichenbach, 2012). This part of the argument is rather self-explanatory but Aquinas makes it clear to his audience that causality works and that the law of causality exempts nothing. He also makes it clear that in this series of causes, it is impossible for one event to cause itself, or for one thing to cause its own existence. Aquinas is doing this while at the same time leading his reader to believe that there must be one cause that first caused all these series of causes but that this cause itself was not caused by any other cause. He does this while somehow postulating that only God can cause Itself to exist. Moreover, the significance of this particular assumption is that if one thing can cause itself, then there would not be any first cause, for if one thing could cause itself, then there would not be any need for this first cause to cause the event next to it. In short, if a cause could cause itself, then each cause could be independent of each other and there would be no series. Aquinas then assumes and states that in matters of efficient cause, it is not possible to go to infinity (Reichenbach, 2012). The purpose of this part of the argument is to convince the reader that there must have been a definite beginning to this series of causes. Otherwise, if this series of causes went on to infinity, then there would not be any first cause but only an endless series of causes. However, without giving any proof or any other insight, Aquinas somehow just considers this assumption on the absence of infinity a priori, and expects his audience to simply just accept this. What Aquinas has presented instead in order to prove his statement that it is possible to go to infinity with matters of efficient cause is rather an ontological proof. This proof is that, if there were an infinite number of causes, then there would neither be a â€Å"first efficient cause† nor an â€Å"ultimate effect† (Reichenbach, 2012). However, since these two things exist in nature and in reality, then there must not be an infinite series of causes. The last part of the argument is when Aquinas states that it is therefore necessary to admit a â€Å"first efficient cause,† which Aquinas believes everyone would call God. In summary, therefore, the argument of Aquinas, therefore, is that causality exists and that one thing causes another but cannot cause itself. This is to discount the possibilit y that an event is dependent on its own cause and is therefore independent of adjacent causes. Moreover, Aquinas assumes that it would not be possible for a series of causes to go on infinity, and he does this for the same reason that he assumes that one thing cannot cause itself. He then also proves ontologically that if there were an

What do You Understand by Economic Protectionism Essay - 1

What do You Understand by Economic Protectionism - Essay Example On the contrary, a country that is in least need of a given commodity or produces the commodity locally will raise the rates of import tariffs for the particular product to discourage importation of the commodity (Korber 2000, p. 10). In the views of Riley (2006), economic protectionism can also be achieved through the imposition of quotas. A county in dire need of a particular commodity will actually lift import quotas to encourage further importation of the particular commodities. Conversely, a country that is capable of producing sufficient or relatively adequate amount of a given commodity for its economy may opt to lower the importation quotas of a given commodity (Riley 2006). Under serious circumstances, a country may impose embargoes declaring total ban on importation of a particular commodity (Riley 2006). Export subsidies for locally produced goods can also be used to encourage bulk production and importation of particular commodities into the economy (Korber, 2000, p. 9). Riley (2006) reports that, in the case countries are engaging in free trade, the government may opt to formulate preferential government procurement policy and state aid to ensure that it allocates spending that will only benefit domestic producers as opposed to foreign suppliers. This case is common in the member countries of the European Union, which award contracts to members of the organization. Similarly, governments may also structure the anti-dumping tariffs to protect the local producers and industries from the economic disadvantages that may be caused by high importation of cheap commodities. The European Union imposed anti-dumping tariffs to Norway against cheap exportation of reared salmon to the Scottish and Ireland market, which ruined domestic trade in the two importing countries. Another example of anti-dumping laws emerged when the European Union blocked inflow of Chinese television tubes, aluminium foil and zinc oxides that were believed to sell far below the averag e domestic price, thereby suffocating local producers. In a move to gain local economic advantage, China reduced the value of the Yuan far below the US dollar thereby resulting to low cost of Chinese products in the USA and international markets. This resulted to increased consumption of Chinese products in import countries, slowing the output of the individual importer countries. The need to protect the US economy saw the Congress pass protectionist bill that banned importation of foreign iron and steel for construction purposes (Mankiw 2009). Trade barriers otherwise known as economic protectionism presents positive and negative implications to the economy almost in equal measure. Krol (2008, p. 2) reports that the imposition of trade economic protection policies by the US economy in 1979 resulted to massive loss of jobs as most manufacturing companies were either cutting their production or facing automatic closure thereby raising the net cost of US economy. The principles of mar ket protectionism led to the abolishment of production activities that required unskilled labour and adoption of production activities that demanded skilled labour in the US economy. This action saw the US specializing in the production of high tech machines and electronics with increased export tariffs of the products while raising importation tariffs of products like clothes and shoes produced by the unskilled labour in the developing countries (Krol, 2008, p. 3). This resulted into low prices

Clinical Trial Drugs Regulations and Manufacture Thesis

Clinical Trial Drugs Regulations and Manufacture - Thesis Example For instance if one treatment is effective in children, could if be equally as effective with adults. Trials confirm what treatments are being used safely and satisfactorily on individuals. There importance is limitless amongst the population of the medical world. For quite some time, clinical trials in the pharmaceutical industry have been regulated by several government bodies. These regulations are set forth by entities like the United States Food and Drug Administration (FDA), the European Medicines Agency (EMEA or EMA), the International Conference on Harmonization (ICH), and the Medicines and Healthcare products Regulatory Agency (MHRA), to name a few. These entities weigh a heavy collateral on how pharmaceutical companies transition medicines from ideal to market with the use of clinical drug trials. The severity of the clinical trial drugs process has a significant donation to the well being of humanity, but faults in production of medications that will suffice in the treatme nt of those it was produced to treat. James Bryce once said; â€Å"Medicine, the only profession that labors incessantly to destroy the reason for its existence†. In short drug trials are performed to adhere to safety regulations that conform to human health strategies. According to the United States National Institutes of Health Service clinical trials are â€Å"considered to be biomedical or health-related research studies in human beings that follow a pre-defined protocol† (Understanding Clinical Trials, 2007). In order to associate the importance of these trials, it has to be first comprehended as to where they have evolved from. Traditionally, clinical drug trials can be associated with pharmaceutical medicine. ... The history of pharmaceutical medicine can be accredited sixteen distinct contributions as directly cited by the Drug Study Institute (Saponaro, 2011): 1. In 1906 the Pure Food and Drug Act was passed, partly due to Dr. Wiley's Poison Squad experiments. It forbade interstate and foreign commerce of adulterated and misbranded food and drugs. There were no safety or efficacy requirements. In 1902 Dr. Wiley started research with human volunteers to determine the effects of food preservatives on digestion and health. Overnight the press made the "Poison Squad" a national sensation. This law required new drugs be tested for safety before marketing, the results of which would be submitted to the FDA in an NDA or New Drug Application. The law also required that drugs met standards of strength and purity and had adequate labeling for safe use. 2. The Elixir Sulfanilamide tragedy in 1937 prompted Congress to pass the Food, Drug, and Cosmetic Act in 1938, which required pre-market review of sa fety in a New Drug Application (NDA) and specified labeling requirements. It also began marking study drugs with the phrase, â€Å"for investigational use.† It also gave the FDA the authority to inspect sponsor drug manufacturing plants and gave them more enforcement power. The requirement of proving effectiveness was still missing. 3. In 1948 the Nuremberg Code was written, the first formal statement on medical ethics. Nuremberg Code: In 1948, the Nuremberg Code laid down 10 standards for physicians to conform to when carrying out experiments on human participants. The Nuremberg Code was the result of judgment by an American military war crimes tribunal conducting proceedings against 23 Nazi physicians and administrators for their willing participation in war crimes

What do You Understand by Economic Protectionism Essay - 1

What do You Understand by Economic Protectionism - Essay Example On the contrary, a country that is in least need of a given commodity or produces the commodity locally will raise the rates of import tariffs for the particular product to discourage importation of the commodity (Korber 2000, p. 10). In the views of Riley (2006), economic protectionism can also be achieved through the imposition of quotas. A county in dire need of a particular commodity will actually lift import quotas to encourage further importation of the particular commodities. Conversely, a country that is capable of producing sufficient or relatively adequate amount of a given commodity for its economy may opt to lower the importation quotas of a given commodity (Riley 2006). Under serious circumstances, a country may impose embargoes declaring total ban on importation of a particular commodity (Riley 2006). Export subsidies for locally produced goods can also be used to encourage bulk production and importation of particular commodities into the economy (Korber, 2000, p. 9). Riley (2006) reports that, in the case countries are engaging in free trade, the government may opt to formulate preferential government procurement policy and state aid to ensure that it allocates spending that will only benefit domestic producers as opposed to foreign suppliers. This case is common in the member countries of the European Union, which award contracts to members of the organization. Similarly, governments may also structure the anti-dumping tariffs to protect the local producers and industries from the economic disadvantages that may be caused by high importation of cheap commodities. The European Union imposed anti-dumping tariffs to Norway against cheap exportation of reared salmon to the Scottish and Ireland market, which ruined domestic trade in the two importing countries. Another example of anti-dumping laws emerged when the European Union blocked inflow of Chinese television tubes, aluminium foil and zinc oxides that were believed to sell far below the averag e domestic price, thereby suffocating local producers. In a move to gain local economic advantage, China reduced the value of the Yuan far below the US dollar thereby resulting to low cost of Chinese products in the USA and international markets. This resulted to increased consumption of Chinese products in import countries, slowing the output of the individual importer countries. The need to protect the US economy saw the Congress pass protectionist bill that banned importation of foreign iron and steel for construction purposes (Mankiw 2009). Trade barriers otherwise known as economic protectionism presents positive and negative implications to the economy almost in equal measure. Krol (2008, p. 2) reports that the imposition of trade economic protection policies by the US economy in 1979 resulted to massive loss of jobs as most manufacturing companies were either cutting their production or facing automatic closure thereby raising the net cost of US economy. The principles of mar ket protectionism led to the abolishment of production activities that required unskilled labour and adoption of production activities that demanded skilled labour in the US economy. This action saw the US specializing in the production of high tech machines and electronics with increased export tariffs of the products while raising importation tariffs of products like clothes and shoes produced by the unskilled labour in the developing countries (Krol, 2008, p. 3). This resulted into low prices

Early childhood education Essay Example | Topics and Well Written Essays - 2500 words

Early childhood education - Essay Example This "Early childhood education " essay describes the prevailing problems and issues regarding child practitioners and how can early childhood programs support parents in facilitating the healthy, holistic development of their children.The panelists, composed of experts in various fields proposed a four-point plan, namely: (1) strengthening policies, raising and sustaining funding and building appropariate infrastructure; (2) improving education, training and development, improving compensation and providing career opportunities for practitioners; (3) delivering high quality, evidence-based and age-appropriate programs and practices for children; and (4) building strong partnerships with parents.Ontario is struggling with the decrease in number of effective and efficient child practitioners and this greatly affects the quality of education. The following reasons have been identified: ï‚ § Several practitioners do not meet the educational requirements needed to successfully address the demands of the practice and provide high quality early learning and care for children. ï‚ § Fresh graduates of early childhood education courses opt to work in jobs other than in regulated child care. ï‚ § Several practitioners will retire in the next 5 – 10 years and there are not enough new practitioners coming in to replace them. Research has provided evidence that the early years are most crucial in an individual’s development because it is at this time when early learning and experiences determine the quality of the child’s brain structure. ... arly years are most crucial in an individual’s development because it is at this time when early learning and experiences determine the quality of the child’s brain structure, disposition and well-being. Provision of a high quality early childhood program wherein positive, stimulating learning experiences take place contribute to the child’s self-confidence and positive attitude towards learning. These are qualities that lead to greater success in school and throughout one’s life. 4. How can early childhood programs support parents in facilitating the healthy, holistic development of their children? Early childhood programs should be able to accommodate the schedules of parents in planning events that require their presence. They can also extend the children’s time in preschools or day care centers to enable parents to work. Regular communication with parents regarding concerns about their children keeps them updated about their child’s progr ess. Also, early childhood programs provide adequate information to parents about things that can help them in implementing good parenting to their children. Article Review: Heyman, J., Barrera, M. and Earle, A. (2008) The Working Poor: Canada and the World, Policy Options. The article reports the state of child poverty throughout the world, and specifically in some countries of study. It discussed how child poverty is a lingering challenge that policy-makers face and has grown to be a global issue. The article claims that child poverty may be effectively managed if parents can succeed in working while caring for their children without fear of losing their livelihood. 1. How can families rise from poverty? Poverty may be overcome when individuals are given the opportunity to work and earn for a living. When parents’

Different Types of Database Management System Essay Example for Free

Different Types of Database Management System Essay A database can be a set of flat files stored on computer tape or disk or it could consist of database tables that are managed by a Database Management System (DBMS). There are different types of DBMS products: relational, network and hierarchical, multidimensional, object. The most widely commonly used type of DBMS today is the Relational Database Management Systems (RDBMS). Database management systems (DBMS) are designed to use one of five database structures to provide simplistic access to information stored in databases. The five database structures are: the hierarchical model, he network model, the relational model, the multidimensional model, and the object model. Inverted lists and other methods are also used. A given database management system may provide one or more of the five models. The optimal structure depends on the natural organization of the applications data, and on the applications requirements, which include transaction rate (speed), reliability, maintainability, scalability, and cost. Hierarchical Model The hierarchical data model organizes data in a tree structure. There is a hierarchy of parent and child data segments. This structure implies that a record can have repeating information, generally in the child data segments. Data in a series of records, which have a set of field values attached to it. It collects all the instances of a specific record together as a record type. These record types are the equivalent of tables in the relational model, and with the individual records being the equivalent of rows. To create links between these record types, the hierarchical model uses Parent Child Relationships. These are a 1:N mapping between record types. This is done by using trees, like set theory used in the relational model, borrowed from maths. For example, an organization might store information about an employee, such as name, employee number, department, salary. The organization might also store information about an employees children, such as name and date of birth. The employee and children data forms a hierarchy, where the employee data represents the parent segment and the children data represents the child segment. If an employee has three children, then there would be three child segments associated with one employee segment. In a hierarchical database the parent-child relationship is one to many. This restricts a child segment to having only one parent segment. Hierarchical DBMSs were popular from the late 1960s, with the introduction of IBMs Information Management System (IMS) DBMS, through the 1970s. The hierarchical structure was used in early mainframe DBMS. Records’ relationships form a treelike model. This structure is simple but nonflexible because the relationship is confined to a one-to-many relationship. IBM’s IMS system and the RDM Mobile are examples of a hierarchical database system with multiple hierarchies over the same data. RDM Mobile is a newly designed embedded database for a mobile computer system. The hierarchical structure is used primarily today for storing geographic information and file systems. Network Model The popularity of the network data model coincided with the popularity of the hierarchical data model. Some data were more naturally modeled with more than one parent per child. So, the network model permitted the modeling of many-to-many relationships in data. In 1971, the Conference on Data Systems Languages (CODASYL) formally defined the network model. The basic data modeling construct in the network model is the set construct. A set consists of an owner record type, a set name, and a member record type. A member record type can have that role in more than one set, hence the multiparent concept is supported. An owner record type can also be a member or owner in another set. The data model is a simple network, and link and intersection record types (called junction records by IDMS) may exist, as well as sets between them . Thus, the complete network of relationships is represented by several pairwise sets; in each set some (one) record type is owner (at the tail of the network arrow) and one or more record types are members (at the head of the relationship arrow). Usually, a set defines a 1:M relationship, although 1:1 is permitted. The CODASYL network model is based on mathematical set theory. The network structure consists of more complex relationships. Unlike the hierarchical structure, it can relate to many records and accesses them by following one of several paths. In other words, this structure allows for many-to-many relationships. Relational Model (RDBMS relational database management system) A database based on the relational model developed by E. F. Codd. A relational database allows the definition of data structures, storage and retrieval operations and integrity constraints. In such a database the data and relations between them are organised in tables. A table is a collection of records and each record in a table contains the same fields. Properties of Relational Tables: Values Are Atomic Each Row is Unique Column Values Are of the Same Kind The Sequence of Columns is Insignificant The Sequence of Rows is Insignificant Each Column Has a Unique Name Certain fields may be designated as keys, which means that searches for specific values of that field will use indexing to speed them up. Where fields in two different tables take values from the same set, a join operation can be performed to select related records in the two tables by matching values in those fields. Often, but not always, the fields will have the same name in both tables. For example, an orders table might contain (customer-ID, product-code) pairs and a products table might contain (product-code, price) pairs so to calculate a given customers bill you would sum the prices of all products ordered by that customer by joining on the product-code fields of the two tables. This can be extended to joining multiple tables on multiple fields. Because these relationships are only specified at retreival time, relational databases are classed as dynamic database management system. The RELATIONAL database model is based on the Relational Algebra. The relational structure is the most commonly used today. It is used by mainframe, midrange and microcomputer systems. It uses two-dimensional rows and columns to store data. The tables of records can be connected by common key values. While working for IBM, E. F. Codd designed this structure in 1970. The model is not easy for the end user to run queries with because it may require a complex combination of many tables. Multidimensional structure The multidimensional structure is similar to the relational model. The dimensions of the cube-like model have data relating to elements in each cell. This structure gives a spreadsheet-like view of data. This structure is easy to maintain because records are stored as fundamental attributes in the same way they are viewed and the structure is easy to understand. Its high performance has made it the most popular database structure when it comes to enabling online analytical processing (OLAP). Object/Relational Model Object/relational database management systems (ORDBMSs) add new object storage capabilities to the relational systems at the core of modern information systems. These new facilities integrate management of traditional fielded data, complex objects such as time-series and geospatial data and diverse binary media such as audio, video, images, and applets. By encapsulating methods with data structures, an ORDBMS server can execute comple x analytical and data manipulation operations to search and transform multimedia and other complex objects. As an evolutionary technology, the object/relational (OR) approach has inherited the robust transaction- and performance-management features of it s relational ancestor and the flexibility of its object-oriented cousin. Database designers can work with familiar tabular structures and data definition languages (DDLs) while assimilating new object-management possibi lities. Query and procedural languages and call interfaces in ORDBMSs are familiar: SQL3, vendor procedural languages, and ODBC, JDBC, and proprie tary call interfaces are all extensions of RDBMS languages and interfaces. And the leading vendors are, of course, quite well known: IBM, Inform ix, and Oracle. The object oriented structure has the ability to handle graphics, pictures, voice and text, types of data, without difficultly unlike the other database structures. This structure is popular for multimedia Web-based applications. It was designed to work with object-oriented programming languages such as Java. Object-Oriented Model Object DBMSs add database functionality to object programming languages. They bring much more than persistent storage of programming language objects. Object DBMSs extend the semantics of the C++, Smalltalk and Java object programming languages to provide full-featured database programming capability, while retaining native language compatibility. A major benefit of this approach is the unification of the application and database development into a seamless data model and language environment. As a result, applications require less code, use more natural data modeling, and code bases are easier to maintain. Object developers can write complete database applications with a modest amount of additional effort. The object-oriented database (OODB) paradigm is the combination of object-oriented programming language (OOPL) systems and persistent systems. The power of the OODB comes from the seamless treatment of both persistent data, as found in databases, and transient data, as found in executing programs. In contrast to a relational DBMS where a complex data structure must be flattened out to fit into tables or joined together from those tables to form the in-memory structure, object DBMSs have no performance overhead to store or retrieve a web or hierarchy of interrelated objects. This one-to-one mapping of object programming language objects to database objects has two benefits over other storage approaches: it provides higher performance management of objects, and it enables better management of the complex interrelationships between objects. This makes object DBMSs better suited to support applications such as financial portfolio risk analysis systems, telecommunications service applications, world wide web document structures, design and manufacturing systems, and hospital patient record systems, which have complex relationships between data.

Factors Affecting The Weight a Column Can Withstand

Factors Affecting The Weight a Column Can Withstand Matthew Keeley   Physics EEI This extended experimental investigation explores the weight a paper column can withstand before it buckles and how changing the diameter, length and thickness of a column affects its critical load. Multiple columns with varying diameters, lengths and thicknesses were constructed and each one had masses added to it until it buckled. The hypotheses If the diameter of a paper column is increased, then the weight the paper column can withstand before buckling will also increase exponentially and If the length of a paper column is decreased, then the weight the paper column can withstand before buckling will increase exponentially were not supported while the hypothesis If the thickness of a paper column is increased, then the weight the paper column can withstand will also increase proportionally was supported. Columns are used in architecture and structural engineering, in the walls of houses and buildings, to transmit weight through compression from the structure above the column to the structural elements beneath (Merriam-webster.com, 2017). Objects are only referred to as columns when the force is applied axially; they are referred to as beams otherwise (Waddell, 1925). Column buckling is likely the only area of structural mechanics where failure is not due to the strength of the material, but the stiffness of the material and the shape of the column instead (McGinty, 2017). Buckling occurs in a column when its critical load is reached and this value can be determined by the Euler column formula, which is as follows: Where is the critical load (), is the modulus of elasticity (), is the area moment of inertia (, is the length of the column () and is the column effective length factor (Engineeringtoolbox.com, 2017). Engineers commonly use mm instead of regular SI unit, examples of the formula being used use mm (Critical Buckling Load (Example 1) Mechanics of Materials, 2013). This formula is used mainly to calculate the buckling load of steel and wooden columns so its application in the buckling of paper columns is questionable although it is the only method available. There are some unknown values in the equation without researching them using other sources, the value, the value and the value. The value, the modulus of elasticity (also known as youngs modulus, the elastic modulus or the tensile modulus) is a constant that is a measure of the stiffness of a material (Askeland et al., 1996). It is the slope of the stress-strain curve in the elastic region given by: A relationship known as Hookes Law, Hookes law states that the strain in a solid is proportional to the applied stress within the elastic limit of that solid (Encyclopedia Britannica, 2017). For example, if an object with a high modulus of elasticity had the same force applied to it as an object with a low modulus of elasticity there would be a greater change in dimension in the object with the smaller modulus of elasticity. The modulus of elasticity is represented in pascals () but the value is usually very large so it is found in gigapascals instead (. When calculating theoretical data to keep the units the same the modulus of elasticity was represented in as. The modulus of elasticity for paper is 2 (www-materials.eng.cam.ac.uk, 2017). The value represents area moment of inertia (also known as second moment of area). It is a geometrical property of an area representing how its points are distributed regarding an axis within the object (Beer and Johnston, 1990). It is calculated using multiple integral over the columns cross-section, but its easier to utilise an already existing formula for the second moment of area of the column in question. Since the column that will be used in the experiment is rolled up paper it will have a hollow cylindrical cross-section which will appear as: The formula for second moment of area for a hollow cylindrical cross-section is as follows: Where is the radius of the outside circle and is the radius of the inside circle (Efunda.com, 2017). The second moment of area also determines the way a column is most likely to buckle (towards the plane or the plane). Usually there would be multiple formulae for the second moment of area, one for buckling towards the plane and one for buckling toward the plane, but since the cross section in question is hollow cylindrical and the axis (where the weight will be applied) is in the centre of the cross-section the formulae are identical. If the cross section was a filled rectangular area, for instance, and appeared as: Then the formulae for second moment of area are as follows: One would have to solve for both and and find out on which plane the column is most likely to buckle along and use that value as the second moment of area in the Euler column formula (What is second moment of area?, 2015). The units for second moment of area are metres to the fourth power (, but since the units need to be kept the same and the radius will be represented in millimetres when doing theoretical data, it will be in millimetres to the fourth power () instead. The last unknown value is which is the column effective length factor (Wai-Fah and Duan, 1999). It is determined by the boundary conditions. The value changes depending on if the column is fixed on both ends, hinged on both ends, fixed on one end free on another, etc. The columns used in the experiment are free on both ends so the theoretical value is 1, but the actual value derived from various other experiments is 1.2, so that value will be used in theoretical data (Efunda.com, 2017). For this experiment to be a success many variables must be remain the same that were quite difficult to control. To attempt to control these variables some precautions were taken. For example, to keep the distribution of weight the same a transparent board was used so the weight could be placed in the centre of the column and distributed evenly. Also, the paper columns need to be made carefully so that there are no weaknesses in the column because weaknesses in the column arent factored into Eulers column formula. The dimensions for paper are 29.7mm x 21mm x 0.1mm (for 80gsm A4 paper). Theoretical Data Calculating second moment of area (). Substituting into Eulers column formula and solving to find critical load. Calculating the mass the column could withstand using . This value is very large and a paper column of the dimension used in the calculations would certainly crumble under this amount of force in real life applications, but this may be due to all the other variables that are difficult to control at play, such as weaknesses in the column geometrically and weight distribution rather than the formula being incorrect. Theoretical data results tables and graphs Changing Columns diameter Columns diameter (mm) Mass before column buckles (kg) 95 1063.45 90 904.06 85 761.45 80 634.69 75 522.84 70 424.96 65 340.14 60 267.42 55 205.89 50 154.60 Changing Column Length Column thickness (mm) Mass before column buckles (kg) 0.1 934.57 0.2 1862.98 0.3 2785.27 0.4 3701.46 0.5 4611.57 0.6 5515.63 0.7 6413.67 0.8 7305.72 0.9 8191.81 1.0 9071.95 Changing Columns Thickness Columns Length (mm) Mass before column buckles (kg) 210 934.56 200 1030.36 190 1141.68 180 1272.05 170 1426.11 160 1609.94 150 1831.76 140 2102.78 130 2438.73 120 2862.12 The following hypotheses that were prompted due to the background research are as follows: Changing Columns Diameter If the diameter of a paper column is increased, then the weight the paper column can withstand before buckling will also increase exponentially. Changing Columns Length If the length of a paper column is decreased, then the weight the paper column can withstand before buckling will increase exponentially. Changing Columns Thickness If the thickness of a paper column is increased, then the weight the paper column can withstand will also increase proportionally. Changing Columns Diameter Various paper columns were constructed carefully (as to reduce weak points in the column) with different diameters, starting at 9.5cm diameters reducing the diameter by 0.5cm for every column until 10 columns had been made, so that there was enough variation in the data to develop more accurate results. The column with the smallest diameter had a diameter of 5cm. The experiment was then set up like the diagram on the previous (without the weights). The board on the bottom of the column was set up to protect the bench from damage from the falling weights and a small transparent board was placed on top of the column so that the weights could be accurately placed in the centre of the column to keep the distribution of weight even.   50g masses were then added to the column until it buckled and the mass that is buckled at was graphed for later analysis. This process was completed for all the columns made beforehand and the experiment was repeated until 3 trials had been completed so the data discovered was more accurate. Changing Columns Length Paper columns with various lengths were constructed carefully, starting at a length of 21cm and reducing by 1cm until 10 columns had been made, so there was enough variation in the data to provide more accurate results. The column with the smallest length had a length of 12cm. The experiment was then set up like the diagram (without the weights). The board on the bottom of the column was set up to protect the bench from damage from the falling weights and a small transparent board was placed on top of the column so that the weights could be accurately placed in the centre of the column to keep the distribution of weight even.   50g masses were then added to the column until it buckled and the mass that is buckled at was graphed for later analysis. This process was completed for all the columns made beforehand and the experiment was repeated until 3 trials had been completed so the data discovered was more accurate. Changing Columns Thickness Paper columns with varying thicknesses were constructed by taping pieces of paper together (1 piece of paper has a thickness of 0.1mm, 2 taped together 0.2mm, etc.) until 10 columns had been made, so there was enough variation in the data to provide more accurate results. The experiment was then set up like the diagram (without the weights). The board on the bottom of the column was set up to protect the bench from damage from the falling weights and a small transparent board was placed on top of the column so that the weights could be accurately placed in the centre of the column to keep the distribution of weight even.   50g masses were then added to the column until it buckled and the mass that is buckled at was graphed for later analysis. This process was completed for all the columns made beforehand and the experiment was repeated until 3 trials had been completed so the data was more accurate. Variables Dependent Variable The independent variable is the mass the column can withstand before it buckles, as this is what the experiment is testing and what changes when the independent variables are manipulated. Independent Variables The independent variables in this experiment are the ones that get changed, the diameter, the length and the thickness. Changing these will affect the dependent variable. Controlled Variables The controlled variables are everything that was kept the same during the experiment, although these may have changed regardless of efforts to keep them the same during the experiment. They include: the temperature and pressure, brand of paper, consistency of columns, distribution of weight, wind conditions, material of column, weights that were used, elevation and the material experiment was performed on. Safety When the column buckles, the weights will fall off the column and potentially an injury could occur. To deal with this the falling weights must be avoided and people entering the area of the experiment should be careful walking through. A mechanism to catch the board so the weights dont fall could also be constructed. Scissors could potentially be used to cut someone. To deal with this the scissors were treated with caution and used appropriately. Wearing goggles will also protect the eyes. Changing Columns Diameter Diameter (mm) Mass before column buckled (kg) Trial 1 Trial 2 Trial 3 Average 95 2.0 1.4 1.7 1.7 90 1.7 1.6 2.0 1.8 85 1.7 1.1 1.5 1.4 80 1.2 1.8 2.0 1.7 75 1.3 2.4 1.5 1.7 70 1.5 1.4 2.0 1.6 65 1.5 1.5 1.6 1.5 60 1.2 1.6 1.7 1.5 55 0.9 1.3 1.0 1.1 50 0.8 1.0 0.6 0.8 Changing Columns Length Length (mm) Mass before column buckled (kg) Trial 1 Trial 2 Trial 3 Average 210 2.0 1.4 1.7 1.7 200 1.2 1.5 1.6 1.4 190 1.1 1.0 1.2 1.1 180 1.5 0.9 1.0 1.1 170 1.0 2.0 1.7 1.6 160 1.6 2.0 2.1 1.9 150 1.6 2.0 1.9 1.8 140 1.0 1.8 2.3 1.7 130 1.4 1.5 1.7 1.5 120 1.7 2.1 1.8 1.9 Changing Columns Thickness Thickness (mm) Mass before column buckled (kg) Trial 1 Trial 2 Trial 3 Average 0.1 2.0 1.4 1.7 1.7 0.2 2.1 1.8 2.3 2.1 0.3 2.8 3.0 1.7 2.5 0.4 3.3 4.2 2.6 3.4 0.5 4.2 3.4 4.8 4.1 0.6 5.1 5.4 4.5 5.0 0.7 5.9 6.3 5.7 6.0 0.8 7.6 6.6 7.8 7.3 0.9 8.0 8.5 9.0 8.5 1.0 10.0 9.0 8.9 9.3 The results for changing column diameter seem to have a pattern to them, the weight that the column can support increases with diameter, but while the mass the column could withstand changed with diameter the increments in which the value changed reduced every time the diameter increased (logarithmic relationship). The results for changing the length of the column provided results that were expected, the weight the column could withstand decreased as the length of the column was decreased though a proper relationship between the points was underivable. The results for the thickness of the column were as expected, the mass the column could withstand increased proportionally with the thickness of column. As evident by the graphs above the theoretical data differs greatly to the empirical data. The theoretical data shows an exponential relationship between the mass withstood and the diameter of the paper column while the empirical data shows a more logarithmic relationship (if the experiment was continued further the mass withstood would have continued to increase with diameter). The mass the column can withstand is also much larger in the theoretical data than the empirical data. This is because the theoretical calculations dont factor in the weaknesses in the column geometrically and its extremely unlikely that the distribution of mass was perfect, even if the mass was placed a millimetre off the axis the mass the column could withstand would decrease drastically. Therefore, it would be difficult to get empirical results the same as the theoretical data due to many variables that are nearly impossible to control when dealing with paper columns. As shown in the graphs above the mass the column can withstand does decrease as length increases in the empirical data but is hard to decipher a relationship when looking at the empirical data due to anomalies. These anomalies would yet again be caused by variables that are too difficult to control within the experiment and for the same reasons the mass the column can withstand in the theoretical data is much greater than the mass the column could withstand in reality. The relationship between these two sets of data is identical (both increasing proportionally) although the mass the column could withstand theoretically is much greater than the mass it could withstand empirically. A possible reason that the relationship was evident in the empirical data for changing the thickness of the column and not for changing the diameter and length could be that changing the thickness affects the mass the column can withstand much more than changing either the length of the column or its diameter (reducing anomalies), this is evident when comparing the theoretical data for the three variables. Due to the varying relationships found in the empirical data and the complexity of the formula used it is difficult to relate Eulers column formula to existing mathematical models when looking at changing the columns diameter or length because the relationship is either exponential () or logarithmic (). Eulers column formula can be related to the linear function that is found when changing the columns thickness though. because a column with 0 length, diameter or thickness