Teenage Wasteland Essay Example for Free

Teenage Wasteland EssayMany mothers make mistakes with their first child. They whitethorn not give them enough attention, or they may give them too much attention. In the cardinal short stories I stand Here iron out by Tillie Olsen and Teenage Wasteland by Anne Tyler, twain of the mothers reflect back on the struggle they had raising their first child. They talk about how they handled situations and what they would change if they could do it over. Both I Stand Here Ironing and Teenage Wasteland depict a mother struggling with fault, thereby showing the difficulties involved in raising children. Lastly, both stories depict mothers struggling with guilt over past decisions made concerning their first child. In I Stand Here Ironing the mother regrets that she didnt feed the knowledge then, that she does now. She shows this when she says My apprehension came too late (Olsen 813). The mother feels that she did better raising her other children, and only made mistakes concerning her first child. When she looks at her daughters life she finds herself wishing she could turn over done more for her.Just like in I Stand Here Ironing by Olsen, Teenage Wasteland by Tyler also depicts a mother struggling with guilt over decisions she made while raising her parole. The author shows the mothers helplessness by saying Had she really done all she could have? (Tyler 1170). The mother felt helpless in the problems with her son, and feels guilty for not trying to do more. She also wonders if she had really done all that she could have to help her son or if she pushed him too much.Both mothers struggled with guilt and the consequences of their decisions concerning their first child. There are many difficulties that arise while raising children these short stories are about two mothers that both struggled with the guilt of their decisions involving their first child. The majority of new mothers make mistakes with their children that they later regret. Its all part of lea rning the best way to do things and purpose the way through unfamiliar territory.

Design of Face Recognition Image Processor

Design of Face Recognition ensure ProcessorAbstractThis pop deals with the pattern and implementation of an ascertain adjoining system for Face recognition perplexment MATLAB. Image treatment is a complex t accept so, we must study each(prenominal) the background information that tell formation and impact requires, and s potty the primary(prenominal) MATLAB regions which will slang to be apply.The purpose for this study is to investigate a software practise that scum bag show how an effigy is processed in computer platform. The affect will be done with(predicate) with(p) in comparing the sketch kitchen range with the real escort to matrix model by using MATLAB program. Picture will be shown when program is running successfully. Real escort or picture will be proceedsed from the matrix using the depart in the MATLAB. We can use various government agencys such as filter or rotate depending on the user itself. In this study, the picture or real check used is from Internet that has referenced properly, scanner and etc. Basic mathematical calculation does non apply in this project as it only used MATLAB program. The significant of this project is to educated user and for us to learn how to process run intos by MATLAB to learn how the epitome can be changes after the proceed indicated by the program.IntroductionOur project is ab forth to know how we can employ two-base hit bear on finish by using MATLAB functions. By the help of jut bear upon tool case of MATLAB we were able to modify/write a program with graphical user interface to express characterisations, process them, overcloud them, and then recognize them as versions of the same parts that exist in an image database lastly we were able to parade the cowcatcher and blurred images.Image processing is the field of sharpen processing where both the input and output signals are images. Images can be thought of as two-dimensional signals via a matrix means, and image processing can be understood as applying standard one-dimensional signal processing techniques to two-dimensional signals. Image processing is a very measurable subject, and scrapes applications in such fields as photography, satellite imaging, medical imaging, and image compression, just to name a few.In the past, image processing was largely done using analog devices. However, as computers entertain become to a greater extent powerful, processing shifted toward the digital domain. Like one-dimensional digital signal processing, digital image processing overcomes traditional analog riddles such as noise, distortion during processing, in tractability of system to change, and difficulty of implementation.The image processing technique we will be implementing will be image blurring even there are many an(prenominal) image processing techniques we have by using MATLAB to output the image as a matrix and store it in the data memory board.In todays world, digital technology is eve r growing, and the development of digitally based products is rising. Various industries such as audio, video, and cellular persistence rely heavily on this digital technology. A great part of this deals with digital signal processing. This aspect in engineering has gained increasing interest, in particular with a lot of the world now turning to wireless technology and its applications to keep businesses and industries connected. The world of digital technology is certainly one that will be present for many years to come. Ref 4Project outlineThis report consists four chapters. In first chapter, it discuss about the markive and scope of this project as long as summary of works. While Chapter 2 will discuss more on theory and literature reviews that have been done. In Chapter 3, the discussion will be on the method actingology hardware and software implementation of this project. The result and discussion will be presented in Chapter 4. Last but not least, Chapter 5 discusses the conclusion of this project and future work that can be done.Problem StatementIn the image processing program, the info for the function are not stated distinguishablely large and make people understand. In the graphical user interface (Graphical User Inter view) program, the info should function as pop-up windowpane after user press any function button.As the project title is Image Processing using MATLAB Learning Tool, the information is not good enough and clears to understand to be recognized by people. The main problem is the effectiveness of people to recognize it. Basically we have used many techniques through which we tried to simplified the way of face recognition. We have used eigenface technique that is very standarlize way to recognize the face using MATLAB applicationMATLAB also can be used in industry in the areas of bar coding, deck-top publication, copy preparation for printing and factory automation. However, delinquent to the information and studies this state of program of image processing that I only can create. much advance and more functional program can be creating by using MATLAB. Thereby, to write the program became problem and this project not perfectly complete.The problem which comes to set a task to recreate the convolution function for applying filters in image processing. It is very difficult to manage and get the code working. It is also not easy to write our own m-function for unsharp masking of a given image to produce a new output image.During the project development we found pursuance difficultiesApply smoothing to produce a blurred version of the original image, subtract the blurred image from the original image to produce an acuteness image.Add the edge image to the original image to produce a sharpened image.When acting out the convolution image is cropped down by some pixel, this means when we go to carry out the subtraction for the unsharpening the images are not the same size and the subtraction cannot take pl ace.To overcome this problems we created a blank matrix in the convolution function that is the same size as the image macrocosm inputted, the new image will then go on top of this matrix so in affect the new image has a 1 pixel border around it to make it to its original size.It is very interesting and challenging to come out from these above mentioned problems and for that we have done.Solutions to problems in the field of digital image processing generally require extensive experimental work involving software simulation and test with large sets of sample images. Although algorithm development typically is based on theoretical underpinnings, the actual implementation of these algorithms almost always requires parameter estimation and, frequently, algorithm revision and comparison of solutions.Because it works in the MATLAB computing environment, the Image Processing Toolbox offers some significant advantagesKey components of our approachWe have used Eigen transmitter method Re f 12 that is a set of eigenfaces can be generated by playing a mathematical process called principal component analysis (PCA) on a large set of images depicting different human faces. Informally, eigenfaces can be considered a set of standardized face ingredients, derived from statistical analysis of many pictures of faces. any(prenominal) human face can be considered to be a combination of these standard faces. For moral, ones face might be composed of the reasonable face prescribed 10% from eigenface 1, 55% from eigenface 2, and even -3% from eigenface 3. Remarkably, it does not take many eigenfaces combined together to achieve a fair approximation of most faces. Also, because a persons face is not recorded by a digital photograph, but instead as just a list of values (one value for each eigenface in the database used), much less space is taken for each persons face.Apart from these our project methodology overwhelms the followingUse MATLAB to simulate the processing techniq ue.Carefully locating the memory blocks where we will store our original and output image.Comparing our results in MATLAB.Basically the eigenvectors of a square matrix are the non-zero vectors that, after being multiplied by the matrix, remain proportional to the original vector (i.e., change only in magnitude, not in direction). For each eigenvector, the corresponding eigenvalue is the factor by which the eigenvector changes when multiplied by the matrix.The eigenvectors are sometimes also called proper vectors, or characteristic vectors. Similarly, the eigenvalues are also known as proper values, or characteristic values.The mathematical grimace of this idea is as follows if A is a square matrix, a non-zero vector v is an eigenvector of A if there is a scalar (lambda) such thatThe scalar is tell to be the eigenvalue of A corresponding to v. An eigenspace of A is the set of all eigenvectors with the same eigenvalue together with the zero vectors. However, the zero vector is not an eigenvector. any problems present themselves in terms of an eigenvalue problemAv=vIn this equationAis an n-by-n matrix,vis a non-zero n-by-1 vector and is a scalar (which may be either real or complex). Any value of for which this equation has a solution is known as an eigenvalue of the matrixA. It is sometimes also called the characteristic value. The vector,v, which corresponds to this value is called an eigenvector. The eigenvalue problem can be rewritten asAv-v=0 Av-Iv=0 (A-Iv)=0If v is non-zero, this equation will only have a solution ifA-I=0This equation is called the characteristic equation ofA, and is an nthorder polynomial in with n roots. These roots are called the eigenvalues ofA. We will only deal with the shimmy of n distinct roots, though they may be repeated. For each eigenvalue there will be an eigenvector for which the eigenvalue equation is true. This is most easily demonstrated by theoretical accountExample Find Eigenvalues and Eigenvectors of a 22 Matrix Ifthen the characteristic equation isand the two eigenvalues are1=-1, 2=-2All thats left is to find the two eigenvectors. Lets find the eigenvector,v1, associated with the eigenvector, 1=-1, first.so clearly from the top row of the equations we getNote that if we took the second row we would getIn either crusade we find that the first eigenvector is any 2 element column vector in which the two elements have equal magnitude and opposite sign.Where k1is an arbitrary constant. We didnt have to use +1 and -1, we could have used any two quantities of equal magnitude and opposite sign.Going through the same procedure for the second eigenvalueAgain, the natural selection of +1 and -2 for the eigenvector was arbitrary only their ratio is important.Scope of ProjectThe scope of our project includes the followingStudy and understand the image processing in varies method, in general in MATLAB.Create a graphical user interface (Graphical User Interface) MATLAB program with several functions.T his requires identifying the steps which must be done to obtain some results. Further this project, the main areas considered areStudy about MATLAB, and its main functions to obtain and process images.Write or modify a program which can be used to perplex and treat images.Some information about the image send and its characteristics to understand the information it contains.Objective of the ProjectThe objective of this project is in reality to educate us and new comers to basic and fundamental technique in image processing through integrated image processing software. All fundamental algorithms of image processing will be exposed through this package Ref the program is in appendix -B. This package will also provided easy-to-learn mechanisms turn user- golden and graphic-orientation environment.These operations include preprocessing, spatial filtering, image enhancement, feature detection, image compression and image restoration involves process which restores a degraded image to something close to the ideal. Generally, in computer vision, especially in MATLAB program (image understanding or scene analysis) involves technique from image processing, pattern recognition and artificial intelligent. Particularly, MATLAB program offers many features and are more mixed then any calculator. MATLAB toolbox is a tool for making mathematical calculations.Literature review (Related Work to our Project)Image processing is any form of signal processing for which the input is an image, such as photographs the output of image processing can be either an image or a set of characteristics or parameters related to the image. Most image-processing techniques involve treating the image as a two-dimensional signal and applying standard signal-processing techniques to it. Image processing converting the image to another form by using direction in MATLAB/Toolboxes/Image Processing tables for example is image input/output, color operation, image enhancement/ analysis and another m ethod.Image processing and computer vision practitioners tend concentrate on a particular area of specialization. People refer to their research interests as texture, surface subprogram, video tracking, and the like. Nevertheless, there is a strong need to appreciate the spectrum and hierarchy of processing levels.Image processing is the manipulation of the image by using a computer, with the objective to enhance or evaluate some aspect of an image which is not readily apparent in its original form. This is done through the development and implementation of processing means necessary to operate on the image. Processing image using a digital computer provides the greatest flexibility and power for general image processing application, since the computer programing of a computer can be changed easily which allows operation to be modified speedily.Interest in image processing technique dates back to early 1920s when digitized pictures of world news events were first transmitted by s ubmarine cable between Newyork and London. However, application of digital image processing concepts did not become widespread until the middle 1960s, when third-generation digital computers began to offer the speed and storage capabilities required for practical implementation of image processing algorithms. Since then, this area has experienced vigorous ripening and has been subjected of study and research in such fields as engineering, computer science, statistics, information science, physics, chemistry and medicine.The result of these efforts have established the value of image processing technique in of problem with application in diverse fields, including automated factory controlled, astronomy, meteorology, agriculture, medicine, art and host application. With the increasing availability of reasonably inexpensive hardware and some very importance application on the horizon, image technology is expected to continue its growth and to play an important role in the future.From the MATLAB software we have the Toolbox for image processing and Professional MATLAB. MATLAB is the interactive environment, scientists and engineers are able to analyze and develop algorithms with exceptional improvements n productivity and creativity. As a result of new algorithms with application-specific uses. The MathWorks offers a series of application toolboxes that contain set of MATLAB ofr the Linear algebra, high-speed computational kernel, extensive mathematical functionality, data analysis, 2-D and 3-D graphic rapid algorithm development, matrix based programming environment. In MATLAB Toolboxes professional version but priced at a lower rate for academic use. Ref 4About Image Processing Tools of MatlabThis set of Matlab tools consists of some functions that I have found useful for basic image processing and image analysis.When working with binary objects (4-connected foreground regions), we have often found it useful to measure features from the boundary stored as a li st of coordinates. In other words, sometimes it is better to work with a polygon defining the foreground-background boundary than to work with a black and white image of the object. The boundary of an object in a binary (black and white) image can be stored as a list of pixel corner coordinates. The functiongetboundarymex Ref 7 forms a list of these corner coordinates from a binary image containing an object.The toolbox containsselectobjectmexfor selecting regions by size. The commandimOut=selectobjectmex(imIn,n)will return an image,imOut, containing only thenth largest object (in terms of number of pixels) of the original imageimIn. This function is particularly useful if one wants to quickly threshold an image and then select the largest object without having to worry about smaller objects that are not of interest, e.g.imOut=selectobjectmex(im0.5,1).Ref9Also included is code for watershed cleavage by flooding from selected sources, fast calculation of object centroids etc.The usag e of each the function is described by typinghelpfunctionat the MATLAB command prompt, wherefunctionis the name of the relevant function.The M-file scriptkftools shows an example of the usage of all of the functions in this toolbox .THEORYThere are various ways of implementing the image blurring techniqueLinear blur horizontal or vertical averaging of a fixed number of pixels.Block blur averaging a small block of pixels by propagating a fixed sized window through the entire image.Gaussian blur convolution of the image with a two-dimensional Gaussian function.Linear blurThis is the simplest image blurring technique. It is done by taking the N-point average of a linear block of pixels (either horizontally or vertically). In our implementation, N will be 8, and we will be using the horizontal blur. An 1N-pixel window is placed at the top left of the image, and the average of the window is stored in the N/2th pixel of the window (in a new image to prevent overwriting). The window is then shifted across the row and the process is repeated. Once the window reaches the end of the row, it is moved to the next row and the process repeats itself. Ref11The advantage of this method is that it is the simplest of the three. However, it also gives the poorest blurring quality. This is because by taking the horizontal average of each row, there will be averaging lines in the output image. Also, parts of the picture where the detail does not span enough horizontal pixels will be lost after blurring. Finally, by the way this algorithm is designed, there will be an outer frame of the output image identical to the input image (i.e. the outer part of the image remains not blurred). Ref11Block blurThis method is analogous to the linear blur, except that our window is now an NN-pixel window. The procedure is the same as the linear blur, with the averaged pixel stored in the (N/2, N/2) position of the window. Seeblock_blur.m for the MATLAB implementation of this algorithm.This me thod improves upon the quality of the linear blur in that averaging lines are no longer visible in the output image. It also helps to retain details that span small horizontal distances in the original image better. However, it still does not overcome the problem of an outer frame in the output image that remains not blurred. Ref11Gaussian blurThis is the best implementation of the image blurring technique, and is used in such commercial software as Adobe Photoshop. Unfortunately, it is also the most complex. It works by performing a two-dimensional convolution on the input image with a normalized two-dimensional MM-pixel Gaussian function.Intuitively, each pixel of the output image is actually a Gaussian function centred at each point of the input image. Hence, the convolution will increase the size of the output image to N+M-1, so that after convolution we must crop the image to reduce it to its proper size.This method is the best of the three. It has no averaging lines present, a nd it also blurs the entire image.Image Processing Toolbox (give reference to the Toolbox)Image Processing Toolbox provide us a comprehensive set of reference standard algorithms and graphical tools for image processing, analysis, visualization, and algorithm development. We can perform image enhancement, image deblurring, feature detection, noise reduction, image segmentation, spatial transformations, and image registration.Image Processing Toolbox supports a diverse set of image types, including high dynamic range, gigapixel resolution, ICC-compliant color, and tomographic images. Graphical tools let we explore an image, examine a region of pixels, adjust the contrast, create contours or histograms, and manipulate regions of interest (ROIs). With the toolbox algorithms we can restore degraded images, detect and measure features, analyze shapes and textures, and adjust the color balance of images.Key FeaturesImage enhancement, filtering, and deblurringImage analysis, including segm entation, morphology, feature extraction, and measurementSpatial transformations and image registrationImage transforms, including FFT, DCT, Radon, and fan-beam projectionWorkflows for processing, displaying, and navigating arbitrarily large imagesModular interactive tools, including ROI selections, histograms, and distance measurementsICC color managementMultidimensional image processingImage-sequence and video displayDICOM import and exportWe have collected many image processing function which can make our project easy to execute , some of these function we used are as follows.Image boast and ExplorationImmovieMake movie from multiframe imageImplayPlay movies, videos, or image sequencesImshowDisplay imageImtoolImage ToolMontageDisplay multiple image frames as rectangular montageSubimageDisplay multiple images in single figureWarpDisplay image as texture-mapped surfaceImage File I/Oanalyze75infoRead metadata from header file of Analyze 7.5 data setanalyze75readRead image data from image file of Analyze 7.5 data setDicomanonAnonymize DICOM fileDicomdictGet or set active DICOM data dictionaryDicominfoRead metadata from DICOM meaningDicomlookupFind attribute in DICOM data dictionarydicomreadRead DICOM imageDicomuidGenerate DICOM unique identifierDicomwriteWrite images as DICOM filesHdrreadRead high dynamic range (HDR) imageHdrwriteWrite Radiance high dynamic range (HDR) image fileInterfileinfoRead metadata from Interfile fileInterfilereadRead images in Interfile formatIsrsetCheck if file is R-SetMakehdrCreate high dynamic range imageNitfinfoRead metadata from National Imagery Transmission Format (NITF) fileNitfreadRead image from NITF file surfacersetOpen R-Set fileRsetwriteCreate reduced resolution data set from image fileImage Types and Type ConversionsDemosaicConvert Bayer pattern encoded image to truecolor imagegray2indConvert grayscale or binary image to indexed imageGraysliceConvert grayscale image to indexed image using multilevel thresholdingGraythresh Global image threshold using Otsus methodim2bwConvert image to binary image, based on thresholdim2doubleConvert image to double precisionim2int16Convert image to 16-bit signed integersim2java2dConvert image to Java buffered imageim2singleConvert image to single precisionim2uint16Convert image to 16-bit unsigned integersim2uint8Convert image to 8-bit unsigned integersind2grayConvert indexed image to grayscale imageind2rgbConvert indexed image to RGB imagelabel2rgbConvert label matrix into RGB imagemat2grayConvert matrix to grayscale imagergb2grayConvert RGB image or colormap to grayscaleWe both study the function properly and found few of them are very important for us to understand deeply. In order to segregate the most important function we select some of from them.System descriptionThis project will use the MATLAB software package to develop algorithms which can automatically analyze these images for potential comets. MATLAB is a high-level programming environment very popular wi th scientists and engineers because of its powerful toolboxes and easy to use scripting language. Basic algorithms from the image processing toolbox will be use to find comets using the following general stepsLoad original images into MATLABProcess images to isolate all bright spots and eliminate glare due to solar ejectionsCompare spots in subsequent images to find potential comet trajectoriesAnalyze trajectories to ensure they meet known characteristicsHighlight possible comets in original images and create output imageBasically, MATLAB software has many functions/commands to apply in image processing. How to manipulate the program depending to us but must be a good deal know what item is MATLAB program will be used. Creativity in MATLAB can make the interesting result. Even, the complex data can be resolved in MATLAB. Especially when the data involved is very complex. Here, we can create some image from converting data by using the some program in MATLAB, which just applied al l procedure in the MATLAB program. MATLAB toolbox is a tool for making mathematical calculations. Image processing toolbox is user friendly programming language with feature more advanced. In the program also used the GUI (Graphical User Interface, move this definition to the first place where we used GUI) to create develop the program.Techniques and algorithmImage and MATLAB involves the conversion of scene into a digital representation that can be processed by a digital computer. This can be performed by a sensor system specially designed to view a image and provide a digital representation of the image.When the images are installed in MATLAB, my picture for example, the color of that image is first analyzed. In the process include several functions of image processing technique. Processed Image is the image display after the process.GUI (Graphical User Interface)A graphical user interface (GUI) is a graphical display in one or more windows containing controls, called components t hat enable a user to perform interactive tasks. The user of the GUI does not have to create a script or type commands at the command line to accomplish the tasks. Unlike coding programs to accomplish tasks, the user of a GUI need not understand the details of how the tasks are performed.GUI components can include menus, toolbars, push buttons, radio buttons, list boxes, and sliders just to name a few. GUIs created using MATLAB tools can also perform any type of computation, read and write data files, communicate with other GUIs, and display data as tables or as plotsMost GUIs wait for their user to manipulate a control, and then respond to each action in turn. Each control, and the GUI itself, has one or more user-written routines (executable MATLAB code) known as callbacks, named for the fact that they call back to MATLAB to ask it to do things. The execution of each callback is triggered by a particular user action such as pressing a screen button, while awaying a mouse button, s electing a menu item, typing a string or a numeric value, or passing the cursor over a component. The GUI then responds to these events. We, as the creator of the GUI, provide callbacks which define what the components do to handle events.This kind of programming is often referred to as event-driven programming. In the example, a button click is one such event. In e vent-driven programming, callback execution is asynchronous, that is, it is triggered by events external to the software. In the case of MATLAB GUIs, most events are user interactions with the GUI, but the GUI can respond to other kinds of events as well, for example, the creation of a file or connecting a device to the computer.We can code callbacks in two distinct waysAs MATLAB functions, written in M and stored in M-filesAs strings containing MATLAB expressions or commands (such as c = sqrt(a*a + b*b)or print) exploitation functions stored in M-files as callbacks is preferable to using strings, as functions have acces s to arguments and are more powerful and flexible. MATLAB scripts (sequences of statements stored in M-files that do not define functions) cannot b e used as callbacks.Although we can provide a callback with certain data and make it do anything we want, we cannot control when callbacks will execute. That is, when wer GUI is being used, we have no control over the sequence of events that trigger particular callbacks or what other callbacks might still be running at those times. This distinguishes event-driven programming from

Philosophy And Development Of Greek And Chinese Mathematics Philosophy Essay

Philosophy And Developwork forcet Of Greek And Chinese Mathematics Philosophy strainAt a glance, Greek math would appear to possess the more or less influence on modern font maths from methods of integration (developed from Eudoxus method of exhaustion) to the rigid logical remains adhered to in modern mathematics and would indeed explain this thesis choice of comparing Greek mathematics.On the some former(a) hand, ancient Chinese mathematics appears to obtain differed sizablely from Greek mathematics in cost of outgrowth and for that reason was chosen for comparison in order to explore the possibilities of philosophical influence in mathematical development.Not only will this thesis explore the differences in the development of the respective mathematics and the factors involved in these differences, it will also explore the possible relevance of such findings to mathematicians in the further development of modern mathematics.However, given the rich muniment of each re spective cultures mathematics, it would be next to unacceptable to explore their developments in vivid detail and as a result, only a basic overview of the characteristics of the mathematics prior to their interaction (when Matteo Ricci western sandwich missionary began introducing western excogitations of mathematics to the Chinese) would be explored.Greek Mathematics?Easily identified by its focus on generalized mathematical theories and proofs, the Greeks seemed to have an idealized perception towards mathematics where instead of grounding them in reality, it was a goal to make mathematical concepts rase more abstract. At the foundation of Greek mathematics were basic assumptions know as axioms. These axioms could neither be given correct or wrong, and are considered self-evident. New theorems were derived from these axioms, and this happened in a process where conclusions were drawn from premises through the use up of logic, otherwise known as deductive reasoning. An examp le of such use of deductive reasoning would be the 10 postulates ( standardised to axioms) seen in Euclids Elements which were used by Euclid to prove his various geometric theorems.Such a method of proving and deriving theorems deductively could be effectively seen as a form of abstraction, where abstracted theorems could be applied in any case related to the theorem. For instance, (Pythagorean Theorem) would be square(a) for t out(p) ensemble cases of right angled triangles regardless of the numbers substituted into the theorem. Pythagoras was thus attributed to be matchless of the first men to grasp numbers as abstract entities.1With the prevalence of the use of deductive reasoning in the ancient mathematical schools of thought from the Sophist School to the Platonic School, it could be generalized that ancient Greek mathematics was characterized by abstract theories and generalized proofs.Chinese mathematics?The concept that the Chinese had of mathematics was radically dispa rate from the way the Greeks handled math. Instead of an axiomatic approach to mathematics (developing mathematics based on assumed axioms), the Chinese developed a far more concrete approach.Science was valued for its many practical applications and astronomers in ancient China were also mathematicians who calculated planetary movements through the applied use of mathematics. Applying mathematics was seen make up in the Jiuzhang Suanshu (considered one of the most important mathematical manuals in China to be written) which was in essence a collection of problems and rules that was applied practically. For instance the indorse chapter (Su Mi) of the book dealt with percentages and proportions for exchange of cereals, millet, or rice and helped in the production and management of grain. Chapter 6 (Jun Shu) allowed the calculation of proper distribution of grain and labour and dealt mainly with the problems of revenue enhancement of the people.2This problem-based approach revolve d around the idea of applying the answers of one problem to another in such a manner that would allow the other problem to be solved. For instance, the Jiuzhang Suanshu or Nine Chapters on the Mathematical Art is in reality a collection of mathematical problems and their solutions. Mathematicians were then expected to extrapolate from these solutions other solutions to other problems. In the words of the Zhoubi Suanjing (one of the oldest complete mathematical manuals found in China), a person gains knowledge by analogy, that is, after understanding a particular railway system of argument they can infer various kinds of similar reasoning.3Given that the majority of the mathematical manuals discovered in China feature the attribute of problem-based approaches (Jiuzhang Suanshu, Xu Shang Suanshu, Suan shu shu) are scantily some examples), we can easily conclude that the ways in which the Chinese approached mathematics was radically different from that of the Greeks.Greek and Chine se PhilosophiesHaving understood the differences between the mathematics of both cultures, we must now begin to explore the possible causes of such a difference, and we first take a look at the philosophy that has maneuver the respective cultures.Greek Philosophy?Although it is commonly agreed that Socrates, Aristotle and Plato were one of the few greatest philosophers originating from the Greeks, the father of deductive mathematics Thales, contributed to ancient Greek philosophy even before the great philosophers and with his close association with the origins of Greek mathematics, it would be a mistake not to consider Thales contributions to the philosophy. Thales belonged to a school of thought called the Milesian school and these philosophers believed that all things were defined by their quintessential subject matter, which Thales thought was water.4Regardless of what Thales or any other philosophers from the pre-Socrates period of philosophy thought, it was clear that from the beginning the Greeks had already begun to seek out a basic form or substance that all things would be defined by. We thus begin to see similarities between their goals of having a unifying substance that would define all things in philosophy and in mathematics, where they sought abstracted theorems and mathematical proofs that would have applied to all cases of any related problems.Even Plato, in Book VII of The Republic, argued for the existence of Forms in his allegory of the caves. He believed that what we thought to be real were simply rear ends cast by actual Forms that we could not real see. Plato argued that these non-material abstract Forms did not exist in time and space, and were not the material world that we perceived with our senses. Plato even suggested that only through the study of these Forms were we able to strive genuine knowledge.Through these ideas of abstract forms and substances that Greek philosophy seemed to follow, we begin to see that there is a gen eral direction in which both philosophy and mathematics went abstraction.Chinese Philosophy?When compared, it is clear that the philosophies of the Chinese differed greatly from that of the Greeks. Where the Greeks asked questions about the possible existence of a monotheistic deity, the Chinese were more refer about the development of philosophy as an ethical and practical guide.Confucius was a philosopher who taught the importance of virtue and moral perfection. He explored ideas of humanity, loyalty, piety and the characteristics of a gentleman (a perfect man) in his teachings. The most fundamental of which, humanity and righteousness have since been argued to form the basis of morality.5In the Analects of Confucius, he explores these concepts of moral perfection and explains the importance of individuals of authority possessing these attributes.Confuciuss philosophy possessed dimensions of practicality which was seen from that fact that his teachings about piety were essentiall y descriptions of specific duties that an individual had according to his relationship with another. For instance, Confucius believed that a child should have respect for his parents and that parents should in turn passionateness and care for their children.Being one of the main schools of thought in Chinese philosophy, Confucianism is thought to have had tremendous influence on the culture and history of China.6Additionally, in other Chinese philosophies such as Buddhism and Taoism teachings we see a form of instruction on a practical level (Buddhism instructed on how one should anticipate in order to attain enlightenment).Although a lack of credible belles-lettres fails to either prove or disprove the influences of Chinese philosophy on their mathematics, one energy argue that the general direction in which Chinese philosophy has taken appears to be similar to that of their mathematics.Other factors influencing mathematics?Although little is found regarding the history of the Greeks that could have affected the development of Greek mathematics, aspects of Chinese history exponent suggest the problem-based approach towards mathematics that was developed.Plato believed and explained in Book VII of The Republic that mathematics was important in understanding and attaining the idea of good which is the ultimate objective of philosophy. Plato believed that arithmetic and geometry allowed the mind to reflect and thus come closer to the truth, and also that the true use of arithmetic is in compelling the soul to reason about abstract number and repelling against the introduction of visible or tangible objects into the argument.7It has thus been argued that Plato believed that the ultimate aim of philosophy was to help the mind to understand and acquire the idea of good and that mathematics was a tool that helped to achieve that end.On the other hand, the Chinese clearly believed in the practical value of mathematics and a quick study of Chinese history reveale d that mathematics was developed with practicality in mind. iodine clear example would be the earlier mentioned chapters of the Jiuzhang Suanshu on grain growing and taxation with the Chinese placing great emphasis on the importance of proper governance, mathematics was developed in order to calculate optimal methods of fair governance.The fact that the Chinese wrote mathematics with characters instead of alphabets would have also explained the need for them to discover the denary system before other civilizations.8As mathematics was written with characters, the decimal system was invented to prevent the memorization of countless characters in order to recognize large numbers such as the date. With a decimal system, Chinese mathematics was thus able to gain an advantage over other civilizations in hurt of the development of mathematics.Furthermore, during the period of Chinese mathematical development before 100 BC, the Chinese were interested in the areas of astrology and had a need to construct the calendar. As a result, many of the works produced in that time were related to astrology such as the Zhoubi Suanjing which provided instructions on measuring the positions of heavenly bodies using shadow gauges termed gnomons.9With the need to measure heights and distances that could not be measured outright (heights of structures or the distance of an island away from the mainland), the Chinese also developed their own athletics of the Pythagoras theorem, which Liu Hui demonstrated in his Haidao Suanjing. As a result of some of the problems that the Chinese faced, we see the development of mathematics in China as a solution to some of these problems.Taking into consideration these other factors, there is clearly a relationship between the physical and cultural factors affecting China and their development of mathematics. On the other hand, while geometry had its practical uses for the Greeks, their main purpose for the study of mathematics was for instructi on and loftier ideals of perfecting their souls.Concluding on the Extent of Influence on MathematicsHaving considered the factors both philosophical and practical that might have affected the development of mathematics, one can see the distinct similarities between the cultures respective philosophy and how it has caused mathematics to develop. antique Greek mathematics developed in a manner that sought to separate concept from object, as could be inferred from their development of generalized mathematical theories in geometry (concept) discerned from postulates (object) since these postulates were observable truths such as All right angles are congruent. At the same time, the philosophy of the Greeks had similar objectives as could be seen from the above mentioned Forms and quintessential substances that the Greeks believed in.On the other hand, Chinese mathematics followed similar trends to that of their philosophy. With a focus on concrete examples and using analogies to solve ot her problems, the Chinese were clearly more concerned with matters of reality and had a pragmatic approach towards mathematics. Philosophically, there is a similar trend of practicality with the Chinese exploring the duties and proper etiquette of what they believed to be the perfect man.Again, the lack of credible literature seemingly undermines the entire relationship, yet it would be foolish to simply discount the fact that both philosophy and mathematics take on a similar direction in terms of development.Thus in conclusion, one could easily argue that the method by which philosophy was approached has been similar to that of the way mathematics was developed. relevance to Modern Mathematicians?Truth and Mathematical plasteredty?Having affirmed the relationship between philosophy and mathematics, we begin to question the relevance of such a relationship to modern mathematicians. One of the greatest questions of mathematics is its relevance to truth, and how mathematical inquiry may lead to certainty and truth.Before we begin to explore the question of which mathematics (Greek or Chinese) was closer to mathematical certainty and thus truth, we must keep in mind that Greek and Chinese mathematics were radically different in terms of method as was previously shown.Based on those methods, we can categorize the mathematics according to the theories of truth that they appear to abide by. The Chinese appeared to base their system on the modern supposition of truth that is pragmatism. According to the theory in a simplified form, a concept may be considered true if it is directly relevant to reality. This meant that a concept would be true if it had any practical consequence and was thus judged based on its practical value. Pragmatism is thus super pertinent to the method of Chinese mathematics, which was in essence a study of the practical effects of theories of mathematics.On the other hand, the Greek method appears to follow the theory of coherentism, which i n simple terms was the theory that the truth of a system of beliefs could be determined based on how well it coheres with other systems of belief. This seems to be relevant to the Greek method of approaching mathematics, where axioms were the basic beliefs and entire systems (theorems) would be developed from these axioms. The truth of these systems would then be appraised according to how well they cohered with the basic sets of beliefs. One might argue that foundationalism would have been a more applicable theory to the Greek method, yet the Greeks did not simply base their theorems on noninferential knowledge such as axioms, and instead used postulates (inferential knowledge) in geometry. As a result, the axiomatic method of the Greeks would have appertained to the theory of coherentism.It is important to note that despite these theories of truth macrocosm modern, the concept behind method of mathematics and theory of truth appear to be similar, and would thus be applicable in the exploration of mathematical certainty.Who was more Certain?Having ascribed to Greek and Chinese mathematics coherentism and pragmatism respectively, the question of who was closer to mathematical certainty becomes apparent. Both schools clearly had their strengths and weaknesses in such a comparison, with the Chinese universe directly relevant to reality and thus closer to certainty in terms of practicality. On the other hand, the Greeks would have believed that they were aspiring towards certainty through the detachment of concept from object (abstraction), where truth in the complete discovery of all Forms would have been certainty.Given the extent of influence on modern mathematics that Greek mathematics has, one would easily consider the adopted Greek mathematics as more certain. Yet the idea of complete mathematical certainty seems to be impossible, as proved by Kurt Godel with his theorems that a system is either complete or consistent and thus impossibleto fully prove a ny proposition.10The ramifications thus being that certainty is impossible to achieve, and that in terms of the axiomatic method, mathematical certainty can never be fully arrived at.Furthermore, the existence of various theories of truth might already suggest that there is a lack of existence of complete certainty, and this thus suggests the probability of the quest for mathematical certainty being futile.

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