Please respond to at least two of the following prompts:
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
2. Why is it that some claim that mathematics is no more than a 'logical game', such as chess, for example, devoid of particular meaning? If this were the case, how do we account for the fact that it seems to apply so well to the world around us?
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
4. Mathematics has been described as a form of knowledge which requires internal validity or coherence. Does this make it self-correcting? What would this mean?
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
2. Why is it that some claim that mathematics is no more than a 'logical game', such as chess, for example, devoid of particular meaning? If this were the case, how do we account for the fact that it seems to apply so well to the world around us?
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
4. Mathematics has been described as a form of knowledge which requires internal validity or coherence. Does this make it self-correcting? What would this mean?
1)
ReplyDeleteLanguage is a human way of communicating what the world is and how it is interpreted. Math has a very similar functional intention as our language system. Math uses symbols as verbal language uses letters, and in fact math is a universal language. Though we may be less aware of our use of math, it can be just as revelant in our daily lives as language. Math is everywhere, for example say a man is on a ladder reaching for a box of Christmas lights. That man must make a quick calculation about the length of his arm, the distance between his arm and the box containing the lights, and the geometry of the ladder to ensure that his motion does not cause trauma. If he makes a mistake, the christmas lights fall, and the man with them. That's when the fun begins. Using an equation one could find the gravitational energy the man had when he hit the floor, the man's final velocity, the travel speed of the ambulance, and of course the estimate of his hospital bill. There are countless examples and there are many things that math can quantify.
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteMath can Most definitely be described as a from language. We use math and numbers to communicate just as we do with any other type of language. Math and numbers are most commonly used as a form of language in things areas such as science and technology. Websites run using patterns and varies combinations of numbers, same with cellphones which use numbers to communicate between the server and the cellphone itself. We as humans may not speak to one another solely using numbers and math, but they do have a lot to with how we communicate, especially in this day and age.
1.What does calling mathematics a ‘language’ mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteLanguage is the method of human communication, either spoken or written, consisting of the use of words in a structured and conventional way. Mathematics is in fact a language, a language used between mathematicians to discuss mathematical theories etc. This language consists of a substrate of some natural languages, such as the English, using technical terms and grammatical convention peculiar to math. Mathematics has vocabulary, grammar, slang terms, and more. This language mostly functions the same way as our daily and written and spoken language. Although we use our language more than mathematics, math is an essential part of everyone's life's.
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ReplyDelete
ReplyDelete1) What does calling mathematics a language mean? Does mathematics function in the same way as our daily written and spoken language?
By calling mathematics a language we are saying mathematics is a method of human communication, either spoken or written, consisting of the use of words in a structured and conventional way. Mathematics is much indeed a language. As humans we use math to communicate and explain our knowledge and ideas. We can use math in various fields including science, technology, and communication. Some of the earliest discoveries were found with the use of mathematics as a language. Math is also universal similar to language.
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteCalling mathematics a ‘language’ means that someone must learn/understand what makes up the language and the structure of the language, which I believe is true for math. Math does function in the same way as our daily written and spoken language. Similarly to the English language, math has structure in its language, in both the written out/explained versions of math and its simplified versions, such as in formulas and equations. In addition, these sentences use symbols, which, like letters/words have meanings applied to them. These symbols and numbers come together to create a bigger meaning, as does daily written and spoken language.
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
Mathematical knowledge rests upon logic and real life application. Thinking back to when we are introduced to math, we apply logical knowledge. For instance, 1 + 1 = 2, by using the visual example of grouping objects. Technically, all math that we learn (counting, adding, subtracting) is an essential part to all higher level math, and therefore, logic rests as the base, with real life application close behind. Math is discovered and not invented, as math exists everywhere in the world around us. Everything (cycles, gravity, velocity, etc) still retains its function, even if we as humans are not aware that math is being applied. When something is “discovered” in math, it is the discovery of how something that already exists functions, can be predicted, determined, or changed. By “discovering” how things work within the world of math, humans can apply this knowledge and benefit ourselves or others, in such ways as architecture.
1)Many who describe mathematics as a language do so because it is universal and anyone can understand it despite differences in culture and ethnic background. Though it may not function as our daily written and spoken language do considering we cannot directly communicate thoughts, all people can do math and share their mathematical work because of its universality.
ReplyDelete3)Mathematics rests upon the foundation of logic and the natural world. Math is both discovered and invented in a way because humans discover how the world works and invent new ways of expressing it such as naming graphs and series. Math can be applied to useful areas because everything we do involves math. For example, simply throwing an object involves calculus because we acknowledge the pull of gravity and adjust how far it hard we throw in order to counter it.
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
ReplyDeleteMathematics have always existed, humans have simply chosen their own symbols and interpretations to explain the concepts behind them. In a way mathematics as we humans know it, the concepts as well as symbols, are invented- however “math” itself has existed before humans invented their way of interpreting and explaining it. The foundation of math knowledge rests mainly on logic and perception. Math can be applied to anything in our universe in someway or another. Any movement, change, or life can be explained by math.
4. Mathematics has been described as a form of knowledge which requires internal validity or coherence. Does this make it self-correcting? What would this mean?
Basic math has to follow set rules that humans have set down in order to obtain the ‘correct’ answer, therefore a wrong answer is entirely possible. This does not necessarily make math self correcting- if you follow incorrect rules yet get an incorrect answer by standard of the ‘traditional’ or ‘right’ rules, technically speaking you did obtain a correct answer in regards to the ‘wrong’ way of doing the problem. In a sense math is and is not self correcting, in restriction to how humans have set up the rules of math.
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ReplyDelete1. What does calling mathematics a ‘language’ mean? Does mathematics function in the same way as our daily written and spoken language?
DeleteLanguage is a form of communications humans created to better understand things and one another, this structured system also includes mathematics. Mathematics in the same manner, takes nature and quantitatively compactes it so that we can label it to better understand it amongst us humans. Although mathematics is the most universal language in the world, it still requires translation just like all other language. An example of this translation is conversion between units, such as to the metric system which is a more universal form of units as opposed to the one Americans use. Regardless whether we realize it or not, we use math on a daily (unintentionally majority of the time) and this requires the use of the ‘mathematics language,’ which can or cannot include equations.
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
Discover means to find or uncover what has already existed, invent means to create something that never existed. Math already existed before humans walked on this earth, we humans created a language in which we can interpret for what already was there. We created a language so that we can compact what pre-exists and find a quantitative explanation so to benefit our knowledge by increasing it. Math is a foundation for a lot of other things that already exist such as physics which is an applied version of the pure math we learn at school. This application in math can give us a better understanding of the fact that we did not invent math, but rather we created a system to further our knowledge. When many think of physics they know that it is heavily based on math such as force and quantitatively measuring the amount of force something occupies, which is math that naturally exists. This is also the same thing for all other areas of math from basic algebra to higher level of calculus, it is the same thing in which we have an international language for the concepts that pre-existed as nature.
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteMathematics being called a language means it allows for communication and expression of ideas, similar to any other written or oral language. Mathematics can be expressed numerically and linguistically. Also, mathematics is a universal language; everyone around the world may not know one common spoken language, but we can understand mathematics. Mathematics is a language in the sense that it written and oral, and one must learn it. Mathematics function in the same way as our daily written and spoken languages because it consists of technical terms, vocabulary, and symbols. These symbols and variables can be constructed together to create more complex formulas, similar to how words and punctuation can be stringed together to form sentences.
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
The foundation of mathematical knowledge lies on logic and how it can be applied to the real world. Mathematics itself has already existed long before humans inhabited the earth, but humans were the ones that invented words, variables, and formulas that help us translate mathematics into something that we can conceptually understand. Mathematics serves as a basis for many other important areas that are also practical to the natural world, such as chemistry, engineering, and physics. Without mathematics, many of the daily things we use including construction, medicine, and technology would not be possible.
1. Mathematics is a spoken language because it is present in every culture and country in our world. Like any other language math has to start at very rudimentary levels, so people can progressively learn. Trade, gravity, anatomy and basically every aspect of our lives has some type of math in it. You may not speak a language like russian to someone in Russia but holding up three fingers is still a widely known symbol that translates across all dialects. Math is something that helps people explain different topics that otherwise cannot be shown in our own learned languages. Adding variable and fragments of numbers together constructs strings of more complicated structure, not dissimilar to our own sentence construction.
ReplyDelete3. Math rests on a few basic formulas that use variables A-Z and numbers 1-10 to explain everything unexplainable that we have to this date. Mathematical concepts have always been around, but it took someone to invent the constructs to be able to visualize what really is going on. Math is applied usefully in almost every area whether it be driving or cooking or purchasing something at a store. It has become easier because humans have created something to do the math for us like computers and calculators, but the premise and prevalence still exists. Math had to be invented to explain gravity and proportions and without it we wouldn't have internal combustion engines or even the computers that complete math problems for us today.
3. Mathematics rests on the foundation of the creation of models with an infinitely large range of complexity. Rather than being the cogs that turn the universe, math arguably is a system of models that explains everything. In saying this, I have already stated my opinion that math is invented. Math can be incorrect because the model does not fit the universe, and must be corrected. The universe cannot be wrong, because it is right: the universe cannot be argued against. If mathematics is agreed to be a language, than math is a system of symbols that display a system of models that display the system. Therefore, math is invented in the linguistic and symbolic nature of its presence. However, math as a concept is discovered, not invented. Scientists and mathematicians agree that since the concept of math is a discovered area of knowledge that is represented through language, the golden record that was sent out into space contains written information that has the highest probability of being understood because it contains mathematical messages. Math can be applied to every area of knowledge.
ReplyDelete4. Mathematics has been described as a form of knowledge which requires internal validity or coherence. Math is self correcting in the way that the language that communicates math is self correcting. For example: 5 + 5 = 11. We know that 5+5 does not equal 11, because mathematical rules prove otherwise. Math as a concept can never be wrong, it can only be understood in the wrong way. In this way, math is not self correcting because something that is never wrong can never correct itself. The internal validity of math is critical because as soon as the understanding of math is wrong, it provides more downsides than upsides and must be resolved as soon as possible. This presents its own problem because there is no physical or mental way our species could unlock the full internally valid system of models that math contains without forming a new paradigm in the way we view math.
3) What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
ReplyDeleteDiscover means to find (something or someone) unexpectedly or in the course of a search. In contrast, invent means to create or design (something that has not existed before. For this reason, I believe that math was invented. We use math to describe and explain the world around us and the ideas that we cannot put into words. These ideas like gravity and velocity were already there but we invented math to explain these ideas with numerical values. Math can be applied to various concepts systems especially in sciences like physics and chemistry. Like stated before, math is a language we humans use to describe the different aspects of physics.
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1) What does calling mathematics a language mean? Does mathematics function in the same way as our daily written and spoken language?
By calling mathematics a language we are saying mathematics is a method of human communication, either spoken or written, consisting of the use of words in a structured and conventional way. Mathematics is much indeed a language. We use math to explain the concepts and ideas about the world around us that we cannot explain. As humans we use math to communicate and explain our knowledge and ideas. We can use math in various fields including science, technology, and communication. Some of the earliest discoveries were found with the use of mathematics as a language. Math is also universal similar to language.
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteMathematics is studied and applied to just about everything around us. We use functions, equations, and rules in order to understand the world. Mathematics is often referred to as a language because it is similar to language in many ways. Firstly, it is a form of communication used by people around the world to connect and understand one another. Math can be a spoken and/or written form of communication as well. We can explain the mathematical theories to each other and learn through the verbal communication. Furthermore, it has structure just like language does. It is universally accepted that 1+1=2. We use this rule in order to build more complicated mathematical rules. Like Cady Heron said in Mean Girls, she loves math “because it’s the same in every country”. Even though we may use different words to describe a certain theorem or graph, the function, answer and end result will be the same, connecting all cultures.
2. Why is it that some claim that mathematics is no more than a 'logical game', such as chess, for example, devoid of particular meaning? If this were the case, how do we account for the fact that it seems to apply so well to the world around us?
Some people think that math is only about the answer. There is always a way or method to solve the problem in front of us; we just need to evaluate and find the right path to the answer. In fact, the math problems in our high school textbooks are frankly quite repetitive. An assignment asking for #1-45 odd may seem long but in reality, is the same concept over and over. As we answer the math problems, it begins to seem mechanical. Math is built of building blocks, every topic important in order to understand the theoretical math later on that does not have an answer. We begin to understand the world around us and use mathematics in our lives. For example, we use math when estimating the total cost while shopping. Math doesn’t seem to have meaning until we combined concepts and apply it to real life situations.
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteLanguage is defined as a method of human communication used by a particular group of people. By defining language in this way, math can be considered a language. Math has sets of rules and principles that are always followed. It is structured and used to communicate and prove different concepts. Math is often used to communicate in science. The work of mathematicians and scientists from hundreds of years ago still holds meaning today. Just like our daily written and spoken language, mathematics can be used to communicate ideas. However, unlike our language, mathematics normally cannot be spoken without the help of another language. However, for the most part, math does function in the same way as our daily written and spoken language. Math is the language of science. It provides expressions for all mathematical thoughts.
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
Mathematical knowledge is based upon logic and nature. Our entire universe relies on the premise of mathematics. Math is everywhere in nature: crystals have distinct mathematical patterns. Sunflowers, shells, fruit, and many other plants follow the Fibonacci sequence. However, in other cases, math is used to model complex concepts we do not understand. Math in many cases is discovered (i.e. fractals, Fibonacci sequence, crystalline structures). However, in other cases, it is invented. We invent equations to try to solve unsolvable issues. In many cases, we use constants within equations to make the answers turn out right. Either way, math definitely can be applied usefully to other areas. As mentioned above, math is the language of science. Math is used in all areas of science: biology, physics, chemistry, etc. We can usefully predict situations using mathematical equations. Without math, we would not have such a vast understanding of our world.
4. Mathematics has been described as a form of knowledge which requires internal validity or coherence. Does this make it self-correcting? What would this mean?
ReplyDeleteInternal validity is the estimated truth based on a conclusion from the basis of reasoning and evidence. Coherence is the quality for an diverse element, values or relationships. So if math is internal validity and coherence, it's not self-correcting. As the definition states, if math is internal validity its the estimated truth, so it's not always true. This means that are areas in mathematics with errors that need improvements. Therefore it can't be self-correcting because math requires external help to understand it thoroughly.
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
Language is a system of communication used by humans. Language can be spoken or written, using words or other ways. Calling math a language means, that it can be used as a form of communication by humans. It has been scientifically proven that mathematics is used everyday. Math is based on patterns, therefore it’s a universal language because everyone has a common sense of pattern. Math has symbols with different meanings similar to words in spoken language. Similar to language, math needs to be taught and developed. Math is used by creating formulas and symbols, similarly to how language is constructed using words, punctuation, etc. We can express math numerically or linguistically, like how language can be spoken or written.
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteMathematics can be called a language because it contains symbols that represent specific meanings, just as words and sounds have in human language. Furthermore, it is a mode of communication. Just as people might speak English, Mandarin, or any other language to express their thoughts, mathematics is a way for people to communicate thoughts to describe quantity. It does not function the exact same way as our daily language because it does not explain emotion or personal experiences. However, it does quantitatively describe the world around us and can be used to communicate these processes between people.
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
Mathematical knowledge is built upon logic and applications to the real world. Early forms of mathematics were probably simple forms of addition and subtraction such as what 1+1=2 to describe quantities of objects but can now be applied to using pi in calculating the area of a circle. It is a rational approach to studying the world that does not factor in emotion or faith. I believe that the language of mathematics was invented, but that its applications to the real world are discovered. The numbers and symbols in mathematics were invented by humans but the way mathematics can describe space and patterns in the universe was a discovery. This distinction of invention from discovery distinguishes whether one believes that mathematics was created by humans to describe the world, or whether the patterns and quantities in the world led people to discover mathematics. This distinction is not clear in mathematics, as it contains aspects of both invention and discovery. Mathematics can be applied to other areas of study in order to validate and support certain theories or discoveries. For example, in a scientific experiment, one uses numerical values to prove a hypothesis and give exact quantities so that the experiment can be repeated to prove its validity. It can even be used in the social sciences to take statistical surveys or describe geography. Mathematics is not a solitary concept that is only relevant to those studying mathematics, but it is a system that augments knowledge in all areas of study.
1. What does calling Mathematics a "language" mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteMathematics allows us to measure and calculate amounts in the universe which give us a base of understanding. When measuring how much water someone may want, mathematics comes into play by showing us the difference between 12 ounces, and 12 gallons. This method of placing labels on anything give us an idea of the scale, weight, or mass of something. It gives us the scale of our planet Earth to other planets and stars, as well as the size of humans compared to other animals on Earth. The definition of language is a form of communication which is used in a common way of expression. Math fits this definition quite well in the facts that most of the characteristics of other languages are also seen in mathematics. Calling mathematics a "language" simply means that it is a way for us a humans to communicate and show things to one another.
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
The concept and idea behind mathematics is invented, not discovered. Newton discovered the laws of physics, but that does not mean that they never existed prior to that discovery. Mathematics is something that we as humans have invented in order to give us a more complex and better understanding of the world around us. Mathematics can be applied to everything in the known universe some way or another. The basis that mathematics rests upon is on us (humans) due to us being the creators for this "language". By saying that math is created, this does not make mathematics sound as important in life, but they are still an important concept all, if not most, people know in the world.
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDelete-Mathematics is the universal language. Similar to written language, mathematics uses various symbols and formulas to convey a point. People can communicate through math in order to solve for a quantity or use quick mental math to figure something out. Math differs from language too, however, because math cannot convey feelings or emotions. Rather, people use mathematics to describe and explain the world around them in the most logical manner possible. Both language and mathematics follow specific rules and guidelines that allow them to even be possible. Without these two things, the world would hardly have progressed in an intellectual manner.
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
-The concepts in mathematics are not discovered, but invented. The mathematical principles of life have always existed and been present in our daily environment, however it is not until fairly recently that we have discovered how to mathematically represent these principles and apply them to our lives. Mathematics is something that humans invented to gain a more logical, explanatory understanding of the world surrounding us. The foundation for which all mathematical knowledge rests upon is the most basic fundamentals, such as addition, subtraction, multiplication, and division. As an individual explores the realm of mathematics more deeply, it becomes apparent that the concepts all seem to build upon one another and that you will be unable to proceed to the next step without understanding the previous one. In this way, mathematics requires almost full conceptual understanding if one ever hopes to truly excel in it.
1. Mathematics functions as a language because of there many similarities. Languages use specific terms in a specific pattern to convey a specific thought. This is no different to mathematics, where particular formulas are done in a particular order to answer a particular question. One difference between math and other languages is that math is universal and is "spoken" by almost every human being on planet earth. The other is that math is used to find answers, while language can deal with many more actions and ideas, which can confuse people into thinking math is not a language.
ReplyDelete3. Yes and no. Math in its most simplistic form is grounded strictly in reality and that of the natural world. Concepts like counting and adding exist in nature, with many examples to show for it. However as we grow more and more complex, it becomes more and more theoretical and less rigid in rules and law. It is best to think of math as a pyramid in where the roots of the subject lay at the bottom, holding the structure form. Moving up the pyramid, is when things start to become more and more unnatural and hypothetical. Overall, some math is natural and discovered, while the rest exist only in the minds of humans and the laws they have built.
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteLanguages central function is to aid in the shared communication of people and societies. Similarly mathematics fiction to solve problems. We can come to conclusions about a problem from various information similar to how we communicate. Mathematics functions as an essential part of a society's life, as we solve problems and understand. Understanding is how mathematics and language are the same, we use both to explain the world around us.
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
Mathematical knowledge is based upon logic that can be applied in real life. Learning basic math is important to applying and understanding higher level math. Math is discovered and not invented, as math exists everywhere in the world around us. We see this in nature and civilizations past architecture. This is how we apply math to other areas in our life.
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteLanguage has always been a way for which us to communicate what we know and share our discoveries. Mathematics and numbers in particular our particularly relevant in their universal nature. Because they can be translated throughout different languages and cultures they allow us greater access to understanding the world around us. Our defining of math through equations and formulas has enabled us to translate the natural patterns that occur in the world around us. In short, math is the language that allows us to communicate with the natural world.
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
The foundation of mathematical knowledge lies in it's existence in the natural world. I believe that math in and of itself already exists and therefore can only be discovered but we, as humans, invent the ways in which we define it. By translating math into an understandable format we invent our own version of it, confined and defined by the per-existing limits of our knowledge. The difference between discovering and defining lies in the origin of the thing being found/made and the way in which we accept it. If we find something and accept it as is, it is simply discovered, but if we take that thing and mold and change it to our advantage, we invent it's newest reincarnation.
Q#1 I think that our math is similar to our language, they both follow certain rules but math is seen a little different from english language because it has numbers. They both have slang or short cuts in them. Both are ways to communicate knowledge in intellegent ways
ReplyDeleteQ#2 Mathmatics is a logical way of thinking but the world is full of logical answers. Most situations can be wieghed mathmatically. You can calculate most of peoples actions statically. And many wars are fought with stragy basiced on some form of mathmatics
What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
ReplyDeleteMathematics has been described as a form of knowledge which requires internal validity or coherence. Does this make it self-correcting? What would this mean?
Mathematical knowledge rests on the foundation that it exists in this world, yet someone had to have come up with all sorts of equations and formulas that enable us to use them everyday. Some math may just be instinctive like looking at a clock or looking at the score of a basketball game, while other math problems rely on formulas and equations. Math can be applied usefully in other areas such as health and fitness and being capable to measure and track things. For fitness, it would be practical to set goals and track your progress. This can tie right into measurements as well.
For question number four, math does need to have internal validity or coherence. This is very important because in math there is usually just one answer and it may depend on your internal knowledge and instincts to know if you are correct or not. This would mean that math is something that would have to make sense to the person who is using it in order to gain complete satisfaction out of themselves.
2. Why is it that some claim that mathematics is no more than a 'logical game', such as chess, for example, devoid of particular meaning? If this were the case, how do we account for the fact that it seems to apply so well to the world around us?
ReplyDeletePeople can see math as a game because it is in its own world. In the math world, their are right answers, and their are wrong answers. In that world, it does not really matter which answer you get, at the end of the day, it is separate from the real world. But, the game becomes a challenge once you interpret it into the real world. If you get an answer wrong, major consequences can come from it. If you get it right, you can be rewarded greatly. Life can also be seen as a game, so why can't math?
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Math is a language. Humans who have been taught it speak it in every day life. The words to explain math such as add and subtract are used in different ways by almost everyone who knows simple math. People may deny that they use math everyday, but that's because it is so engraved into them from years of teaching, that it's just one with their language and they don't even realize it. Every time they say a number, a little bit of math goes into place. Math doesn't function in the same way as normal language does, beaches now it is apart of our normal language.
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteCalling mathematics a language follows the same basic rules for any other language. We as a society have claimed language to be a means of communicating with each other whether it be words or body signals. Math has been called the universal language because for the most part all aspects of math are proven and used as constants in history. Math can be used all over the country along with the world. A person in a country across the globe would be able to follow and understand a math problem done by someone in the US because we basically all use the same equations and theories. Math might not be the same as our daily language but only because it is used in a different setting. We don't normally talk to each other in numbers or formulas but we are still able to relate to other situations using common proven equations or concepts.
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
Mathematical knowledge is based on the notion that we are all taught the same concepts and formulas as everyone else in the world. I believe math was discovered in some aspects but invented in others. For example, math occurs in nature such as flowers with the Fibonacci sequence and waves with sinusoids. The math itself was not created by someone but in fact found through observations. Math was also invented however because we as humans have invented the formulas and equations to fit what we have discovered. Math is commonly used along with science subjects but can also be used in history, English, music, etc.
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteMathematics is considered to be a language because it is a way to communicate to others and a way to describe the world around us. We use numbers and measurements to describe objects to others. Calling mathematics a language is correct, and can also be called a universal language because no matter where you go on the planet where civilization is present, there is mathematics. Mathematics is a daily occurrence, we use it in daily life to count how many objects we have or need or we measure objects to see how to describe and use an object in the correct way we need to. Math in my mind, functions almost exactly the same way as our written and spoken language because all of these languages are ways to communicate and describe the world around us.
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
The foundation on which mathematical knowledge rests in the basic principles and rules of math. From the basic principles, we then build upon these to further our knowledge into more complex mathematical studies. I think that math was discovered, not invented because anything that exists was discovered not invented. For example, if math was not present and I had 5 apples and eat 1, I know that I only have 4 left. The language of mathematics was already present, it was just yet to be discovered and evaluated. To this day, mathematicians are still discovering new formulas and answers. Mathematics is applied to almost every subject and areas of our world, it is used in Science, History, even English to describe situations and create formulas to figure out equations and much more. Mathematics is the universal language for everyone and anything.
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteMathematics as a language means the way in which we use mathematics to describe the things we see in our daily lives. We use mathematics to describe the world around us and all the patterns we see. Although, we did create the language of mathematics with standards we use to describe the way the world around us functions. Mathematics functions the same way as our daily written and spoken language because we are constantly using mathematics in our everyday life as much as we use spoken and written language to function in life from day to day.
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
The foundation on which mathematical knowledge rests is reliant on what what we know about how the natural world works. Mathematics is a language which is invented to describe the way the universe works in which is discovered. The rules of the natural world are discovered and we use the language of mathematics to describe and explain these rules. It can be applied to other areas because the world revolves around mathematics because it is the basic understanding of how the universe works. Mathematics can be applied to other areas such as the sciences which is crucial and useful in everyday life.
ReplyDelete1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
Mathematics is a language in that it is a system of communication for patterns found in the world. It shares similar conventions to language in that it has a kind of syntax, grammar, and vernacular. The two forms of language function in the same way. Despite this, math cannot necessarily be used in the same way as written and spoken language because it cannot always be used to communicate complex ideas that are not based in numbers. This can sometimes happen, such as in the cases of binary and hexadecimals (they can be considered math), but in most other cases math has to be used in conjunction with written or spoken language in the way we normally think of it in order to communicate and apply math to the real world. Variables have to be defined and context has to be established. Nevertheless, mathematics is a language.
2. Why is it that some claim that mathematics is no more than a 'logical game', such as chess, for example, devoid of particular meaning? If this were the case, how do we account for the fact that it seems to apply so well to the world around us?
I believe that some people claim that mathematics is no more than a logical game devoid of meaning because branches of it can be taught without practical application. This is especially true as math becomes more complex, and it becomes more difficult to apply to the real world without being guided. It is difficult to think about imaginary numbers as being applicable in the real world, yet they can be used in the study of earthquakes, and of electronics. This “meaning” for complex numbers is not widely taught, but it does exists. Pure mathematics as a field exists, but even it attempts to make math more applicable to the real world. Mathematics as a concept is something that I believe was created by humans in order to describe patterns in the world. If mathematics is truly devoid of meaning, it still applies to the real world because both math and the real world still operate through patterns. Even math was not intended to overlap with nature, the patterns of the logical game of math can be manipulated to adhere to the real world.
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteLanguage is a way humans are able to describe the world and convey these notions and thoughts to others. However, only those who are able to understand that language are generally able to understand the meaning behind this slew of words and phrases. Mathematics is in many ways a type of language. It was invented in order to describe the physical world around us and convey these ideas to others. However, just the same as many other languages, one must be able to understand and interpret the equations of math and what not in order to understand the conceptional reality behind these numbers. Mathematics, although it is prevalent throughout the entirety of the day, may not be spoken as much as say English diction is. Mathematics is used all the time in order to categorize, calculate, and solve for many things in the world, and in that way it is able top describe the world around us, much like the spoken English language, or any others for that matter.
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
Mathematical knowledge rests upon a basic conceptual understanding of numbers and so on an so forth. Much like language, it must be taught and can as well be layered in order to get a more in depth understanding of this subject. Math is undoubtedly invented. Just like how language was invented in order to describe the world around us, math was too. Take for instance that language was not invented. The room I'm in still exists and the colors I see are still there even though I would be able to label them as something totally different, such as yellow could be blue. Just like this, our numbering system is only a way in order for us to be able to collect and observe data in a uniform way. I might have 6 objects of something but it could be labeled as 4. Nonetheless, I would still have the same amount of objects, it would simply be labeled differently. Now of course there are natural phenomenons that fit all too perfectly with mathematics, however, maybe it was simply not noticed before. In fact, when you think of it, mostly everything fits all too perfectly with math, such as the parabola of a thrown object. Of course we understand it now, but had it not been noticed until recently, we too would see this as a phenomenon. Mathematics is used in many other subjects too, such as physics, science, and even history, in order to calculate the years gone by on this earth.
1. Language is how people connect with one another. Some people might even say that language is how you know where a person comes from and their culture. Math is not so different. It is the way that people communicate through various different codings and difficult equations and just everyday life scenarios. Math is with us everyday. We use it to build things, destroy things, measure things, and a lot more.
ReplyDelete3. I believe that the concept of mathematics was discovered, but the numbers, name, and theorems was invented. We were the ones that made the language of math. Just like language, we have to teach math and learn it in order to understand the world around us.
1) Math is a language the same way that English is. Language is simply a form of expressing concepts and ideas, and math does exactly that. Equations read as sentences to explain relationships between numbers. Math is the language to express the world around us. Many things in math, specifically in physics, are used to explain how forces work in the world. This can be on the small scale, like how a bacteria colony can be modeled with an exponential equation, to the large scale in calculating the size of the Earth or the rotation of the planets.
ReplyDelete3) Mathematical knowledge rests in its applications to real world situations. Why would knowing theories and abstract concepts be useful if not for their applications to the real world? Like in the case of understanding that parallel lines intersect on a sphere, which is not useful until one applies it to the earth or to the solar system as a whole. In this way, math is not invented out of thin air but rather discovered by learning more about how the world works. This means that mathematical relationships would exist whether or not humans chose to define them. A ball would still follow a hyperbolic equation if tossed whether or not people were aware of it. As seen by the examples given in these two questions, math has many applications outside of just the field of mathematics.
1.) A language is simply a means of communication through symbols, verbal or otherwise, that allows for the transmission of language between individuals. Math does convey abstract meaning through numbers and symbols just as any written version of a more conventional language might. Like our daily written and spoken language, math can indeed be used as a transmitter of information. It may, however, lack the simplicity of language, especially in the realm of emotion. It would take a great deal of code to properly portray one's feelings.
ReplyDelete2.) Mathematics is called a 'logical game' because so much of it is theoretical. Many of the more advanced theories and discoveries seem so far removed from reality that there is no purpose for them other than the personal edification of their creators/discoverers. In this way, discovery for the sake of discovery could be considered devoid of particular meaning. This is not, of course, to say that such discoveries lack a basis in reality entirely. It is just that the concepts to which they refer are so far removed from the life of an average individual that they seem trivial and unnecessary.
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteCalling a mathematical function a language means that you can communicate in some why or another to another person. Mathematical function are taught all throughout school. This language is able to help you under stand things that happen in the world and why they happen. For example to judge the population and percent of different races people use mathematical functions to solve out a estimate number and percent.
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
The foundation on which mathematical knowledge rests is that people understand the world through math. People use math through sciences like physics to under stand why things work in certain ways. Math was invented to help people understand complex thing that they otherwise cant explain. People use math all the time to figure out how much change they need back from the cashier.
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteMath is seen as a language, more specifically a universal language, because you can use it to express and communicate concepts and ideas that can be proven through logical analysis, such as equations and variables. It is a universal language due to the fact that it does not vary depending on the language it is used in, all the expressions and equations are expressed the same and mean the same no matter where you are. Yes mathematics does function in the same way as our daily written and spoken language because we use math daily to explain why the universe is the way it is.
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied to other areas?
The foundation that math rests on is the fact that it describes the world around us and why it is the way it is. I believe that math is an invented language and we invented it so we can explain the universe. The natural side of math was discovered, but the way that it connects to mathematics was invented. This means that instead of mathematics just occurring in nature, it was invented to explain its occurrences. Mathematics can be applied to other areas because the logical analysis side of it can be used in many other subjects, such as history and the language arts.
2. I think that math is system we’ve created that applies to our world. I don’t think it’s a universal formula that any other intelligent life would use as well, it is simply something we’ve created within the confines of how our natural world exists, and this is why it seems like a set of rules much like a logical game has. I think math is devoid of particular meaning because even though it’s applicable in so many ways to real life, it’s not the philosophical aspect of life, it is simply the quantifiable part.
ReplyDelete3. This question relates directly to my interpretation of question two; the foundation of mathematical knowledge was built from the rules of how our world works. The universe doesn’t follow the set of rules that math is, but rather the rules of math define how the universe functions. These rules were defined, not discovered or invented. Having created this set of rules known as math, we are able to apply these rules and concepts to almost anything.
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
ReplyDeleteMath is invented, however the principles that it models are discovered. It is very hard to explain or understand and the argument can go both ways. Math is some thing that is totally made up and is unnecessary, but is extremely useful. The answer to the math problem always exists and the math itself always exists even before someone discovers it, however it is invented because it is not the math that is of substance, but rather what the math is describing is of the substance. However, since math describes something that already exists, then is it fundamentally part of whatever is described and therefore is discovered. The issue with this question is that there is no correct answer. It is simply perspective.
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
Math is the language of science, theory, and patterns. It functions very differently from the language that we communicate in. The language that we communicate in is very flawed in that you can say one thing and mean the other, or even intentionally say something that literally means one thing, but is sarcastic and means the opposite. Math, however, is not subjective in the slightest. It is a language that describes how the world works. It can model scientific theories and aid in understanding quantifiable things. It allows us to theorize anything from our population growth to black holes and even has some unsolvable mysteries just like our world does.
1. Math is a language of numbers that functions with rules that are required to read it and a certain way you must say it properly. While it doesn't convey the same things traditional language does, it is also called a universal language as it does communicate SOME ideas as well as explain them. Just like any language, you must learn how to read it.
ReplyDelete2. A game follows rules and patterns that translate to get you a certain outcome. Likewise, math does the same. I'm not sure it's true to say it's devoid of meaning just because it's a game though. Chess is based off of war strategy and has meaning there. Can you really have no meaning when you have a solid goal? There is a POINT to the logic games. There is a reason to get from point A to point B. Likewise, math happens to fit neatly within our understanding of the universe because the universe abides by the rules of the game.
What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteIt means just that, it follows the general structure and criterion of a language. It has a dynamic lexicon that changes with its culture. Consider the example we have frequently discussed in class, the adoption of Leibniz’s symbol of integration ∫ and Newton’s symbol of differentiation dydxto fulfill the invention of calculus. Alternatively go back even farther to the development of Arabic numerals, 0-9. Next, it has a uniform system of grammar (a system which is far more expansive than its lexicon). Simply put 2+2=4, and 2+1≠4, the concept of quantity is the basis for all the rules of mathematical grammar. Lastly, perhaps the most basic litmus test of a language, is if two individuals understand one another when communicating with it. If you read my example, 2+2=4 and 2+1≠4 and understood me (I sure hope you did) you yourself have proven math to be language.
3) What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
Invented. Math is in its most basic definition, a language based upon the concept of quantity. To say it was discovered would be like saying we ‘discovered’ English or French, or C++. The first two of course are what would traditionally be considered languages, invented to allow communication between humans. C++ is a programming language used to code software on a computer. Consider this allegory, if a computer was the universe, its laws of physics would be bits. Numerous compiled programming languages could describe this behavior. This is the role ‘math’ fits within the universe. It is an invention by humans to understand the binary of the universe. The Universe is not based on a base 10 number system represented by several distinct Arabic characters, and a variety of other adopted symbols which describe the interactions between those characters.
What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteIt means just that, it follows the general structure and criterion of a language. It has a dynamic lexicon that changes with its culture. Consider the example we have frequently discussed in class, the adoption of Leibniz’s symbol of integration ∫ and Newton’s symbol of differentiation dydxto fulfill the invention of calculus. Alternatively go back even farther to the development of Arabic numerals, 0-9. Next, it has a uniform system of grammar (a system which is far more expansive than its lexicon). Simply put 2+2=4, and 2+1≠4, the concept of quantity is the basis for all the rules of mathematical grammar. Lastly, perhaps the most basic litmus test of a language, is if two individuals understand one another when communicating with it. If you read my example, 2+2=4 and 2+1≠4 and understood me (I sure hope you did) you yourself have proven math to be language.
3) What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
Invented. Math is in its most basic definition, a language based upon the concept of quantity. To say it was discovered would be like saying we ‘discovered’ English or French, or C++. The first two of course are what would traditionally be considered languages, invented to allow communication between humans. C++ is a programming language used to code software on a computer. Consider this allegory, if a computer was the universe, its laws of physics would be bits. Numerous compiled programming languages could describe this behavior. This is the role ‘math’ fits within the universe. It is an invention by humans to understand the binary of the universe. The Universe is not based on a base 10 number system represented by several distinct Arabic characters, and a variety of other adopted symbols which describe the interactions between those characters.
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteI think that calling mathematics a "language" is that its another type of way that people could communicate and share different structures and ideas, in a way that traditional language cannot. I think that Mathematics does function in the way that our written language does. We write down formulas and other types of math related writing and you get responses out of what you put out.
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
Mathematics is human construct. It is human construct because we make it to be what it is. The formulas that we use to solve equations conforms of what we think or want the outcome to be. We make up mathematics as we go. But since we have been doing it so long we see it as if this subject has always been here.
1. Math does function as one of our daily written languages in a more underlying way. We may not realize it, but we use math everyday whether it is the smallest calculation to figure out how much a purchase costs, to doing a very intricate math problem at school. Math helps people to develop reasoning, problem solving, and many other things that a simple written language like English cannot teach. Math is a universal language truly because despite languages being different and varying between countries, math is the same across the world. 2+2 = 4 in America, and it does in China as well.
ReplyDelete3. There are concepts of math that were both discovered and invented. I think the patterns in math had to be discovered and observed, as that is what math is based around. After discovering these patterns, scientists or mathematicians invented postulates and theorems to further help people understand these patterns they discovered and how they work. Math itself was all discovered, because before mankind it was still present. One leaf and one leaf still made two leaves, but no one was able to point that out.
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteWhen we call mathematics a "language" we are insinuating that math is used to label and compartimentalize data or information into more organized categories to increase ones understanding of the world. Mathematics is used to understand complicated natural occurences in nature. Meanwhile our daily written/spoken language is utilized to understand the ideas, feelings, and thoughts of others. Their functionality is similar but not identical.
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
Mathematical knowlege rests on the utilization of numerical values/variables along with formulas to transcribe occurences in the natural world into comprehensible quantities that increase an individuals ability to understand the natural world. The fundamentals of math are created meanwhile the reasons behind the utilization of math is natural for example physics. The laws of physics naturally occur in the world but the formulas to understand them are discovered while simultaneously being formed from created concepts. Math is connected to many aspects of our daily lives such as science, quantitative data such as food consumed or number of steps a person takes. In conclusion math is a human construct used to understand the natural world.
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteMathematics can be referred to as a language because within mathematics there is a complex system of numbers, letters, and equations that when combined act like the building blocks to what we would think of in spoken language, as a complete sentence. Mathematics does not function the same as our daily written and spoken language, and this is because the language of mathematics is used to solve or decipher problems or equations. Where as our daily written and spoken language is used to communicate and interact with the people around you.
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
The foundation of which mathematical knowledge rests in the hands of mathematicians who are constantly thinking up new equations and formulas and putting them to the test and attempting to discover mathematic break throughs. Mathematic knowledge is most definitely discovered, mathematicians have been inventing equations and formulas to describe things in our world around us. An example of this is gravity, no one invented gravity, it simply was discovered and someone thought of an equation that represented the force that gravity puts on all objects on earth
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteCalling math a language is like saying that chemistry and physics has its own language as well. Math has certain vocabulary words that is used for specific things just as a language has big vocabulary to mean the same thing as another word. Math can be considered a language because like mathematician that dedicate their life to it and see math everywhere and have become such experts that they might start seeing life as an equation. It has variables and the numbers and letters combined make it a language you must learn what each variable means and what the numbers stand for (like the subscripts and superscripts) to be able to understand math and the concept in which you are learning.
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
Math was discovered but it has been invented over the years or reinvented. PEMDAS was something created that mathematicians created to be able to make math easier to understand. PEMDAS did not exist and someone discovered it. There are methods that have been fiddled with to be able to enter get the right answer or to be able to get the answer faster. Also we think that we have gotten the right answer to many math problems and we say that we can prove them but can we really? We have invented ways to make us believe that it is correct and basically we have invented our own way to use and connect numbers with letters and we have found equations that we can use to certain problems to be able to get the "right"answer, but truly how can we prove that answers correct and nt just by asking someone smarter d the same problem a different way?
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteA language is a system of symbols that can be used to communicate words, ideas, and concepts to others. Mathematics can absolutely be called a language, as it easily fits under this definition. Mathematics is a much more focused language though, spoken languages can be used to describe all topics imaginable, while math is used to describe only more logical and analytical topics. It can do this much better than other languages can too, being very exact and precise.
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
Mathematics comes from nature. As language exists to communicate emotions and concepts, math exists to communicate natural phenomena, and theories. Math was essentially "discovered", as the phenomena it can describe exist whether they are observed or not. The sinusoidal motion of the tides have existed for as long as oceans have, and do not care when high school trig students draw a wavy line to model them.
1. I view language as a way of communicating thoughts and ideas with others and I feel that math can be called a sort of universal language because it allows us to communicate theories with one another that offer an explanation for the world that we live in. While I feel that math can be thought of as a language, it is far different from the written and spoken language that we use on a daily basis. Math is a very specific system of theories and explanations that operates very differently from spoken language and is used in a different context.
ReplyDelete3. Mathematics has existed since the beginning of time, it is only in modern history that human beings have put words and meaning to these concepts. I feel that the basis of math and its patterns were discovered, while mathematicians have invented new concepts and theorems to further help understand these naturally occurring patterns.
3. I personally believe that mathematical logic simply rests on common sense. If I take one rock and put it next to another, now I have two rocks. Then if one rock starts to fall down a cliff, I can use some complicated formulas to find exactly how fast and far it fell. We don't just interpret these numbers, everything we do is based off of this core belief that one and one really makes two. A formula only stands to simplify these mathematics and make them accessible to anyone that is not a mathematician. Some might say it was only discovered or invented, but the truth is, we discovered how to do basic math and then invented ways to make it more complicated and useful for more things. The distinction brings up curious topics, such as, are we in a simulation? Were we just meant to find these formulas over time or did we really create them on our own? Why does math work so perfectly all around? Who knows! Math is pretty cool in that way.
ReplyDeleteI didn't realize I had to respond to two topics, whoops.
Delete1. Mathematics can be referred to as a language simply because there are rules and formulas that need to be memorized in order to comprehend and use it, as with any spoken language, with the formulas just being words. In most other ways, I think math does differ from regular languages. For example, most languages have many exceptions that can be made, as well as repetition and multiple meanings, while math is always the same, never changing, with minimal exceptions to the rules. That's why math is so amazing, you cant just ask a group of people to interpret your math problem and get 15 different relatively correct answers, as you would with an essay in English. No, there is a set amount of answers for any problem and there is no changing that.
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
ReplyDeleteI beleive math is discovered, the way things work around us are already there and already do what they do, but we have I guess created a language for them. We created formulas, equations and terms based off of what we have discovered them to be. I beleive the world of math was already here, but was just needing to be found and interpreted to how who ever founded it saw it to be. Math knowledge is universal, I think because it is so prominent in our world today everyone should be able to know how to use it. Say an apple fell from a tree, it fell and now based off of what ever interpretation I can calculate the speed and how far it fell, but the math was already there, I just interpreted it how I see it best.
ReplyDelete1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
I beleive math is somewhat a language of itself, everyone thing we do has something to do with the language of math, not just math class. When we buy something we use our knowledge of Counting money and the person gives change, depending on how much was received. With understanding of the math language no questions are asked when the change is given if it is correct, we simply go on with our lives. I don't think we use math language exactly the same as our written English language. For example we don't speak to each other with formulas, but math is used in regular life, like today, I was drinking out of a 32 fl oz water bottle, and I wanted to drink a gallon for the day, so I looked up how many fl oz in a gallon, did a simple division and bam, about 5 refills of my bottle and my goal is reached. So math is important and could be used every day as simple as my example.
What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteCalling mathematics a language means it is a different way of explaining concepts and communicating a certain process. Math is a way of language by means of technology or the sciences. It communicates concepts through numbers as opposed to words. Although it can be harder for people to understand, it doesn't come as easily as the spoken language, it requires knowledge and understanding. It functions the same way as your daily and spoken language in that it is a way of communicating concepts. Math is also a way of understanding and inventing which is how it differs from language.
What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
Some mathematics is discovered and others are invented. Certain patterns and sequences appears naturally in nature, however certain subjects like calculus and statistics are invented in order to understand a concept. Those topics are discovered by Newton in order to explain things such as gravity. The concepts themselves exist however the math to understand them is invented. So in a sense its a discovery of their existence and an invention of how to go about them. Math can usefully be used in all subjects within STEM, it can't necessarily be used in language arts and history. Science and technology are based on a foundation of math and therefore require it, making it useful.
1. What does calling mathematics a 'language' mean? Does mathematics function in the same way as our daily written and spoken language?
ReplyDeleteIdentifying math as a language is done because it is a way that people are able to communicate things, such as architects understanding how to build the correct size of a building. Math is used to communicate logical components that our other languages cannot do, and like our languages it too has an order or grammar, and certain rules it must follow. However it doesn't necessarily function the same way as our written and spoken daily languages, as those have become lax and are used to communicate things that aren't necessarily important and don't require the specific knowledge that speaking the language of "math" does.
3. What is the foundation on which mathematical knowledge rests? Is it discovered or invented? What is meant by this distinction? Can it be applied usefully to other areas?
Mathematical knowledge rests strongly upon reason and logical areas of knowledge, in order to understand a problem, you must know the rational basis of it in order to begin to solve it. In order to solve a complex problem you need the basic logical knowledge we are taught. Math is both discovered and invented, in that some principles are discovered as they relate to old areas in math, while others such as calculus are invented in order to better aid in our understanding of the universe around us, like with physics. This distinction changes how we view certain types of math, instead of having to understand something to discover it, you can simply invent what you need. Math is definitely useful in other areas of knowledge, such as natural sciences and reason.
1. Calling mathematics a language means that we use it in a way that allows us to things we would never be able to do without it such as constructing buildings or anything engineering. If we did not have math, we would not be anywhere close to where we are today without math because it is so important. We basically just call it a language because it's just as important as one but we don't actually speak it like Spanish or French.
ReplyDelete3. I believe that mathematical knowledge rests upon logic. I also believe that math is mainly discovered because it is literally everywhere in our universe. However, us humans often have to invent formulas and what not in order to solve problems hat we do not yet know the answer to. Math definitely applies to other areas because nothing exists without math.