Area+of+Knowledge-+Math

==I RRITATING C TENNIS EDITOR HERE: First off, before sharing a question about your notes and thinking below, I want to put in an editing pitch regarding your writing development. Your strong points, and you have many, Nic, include two very powerful habits: 1) you lock onto / dredge out vivid words: example: 'infatuation' This comes no doubt from your reading. Great. 2) you take large steps forward. Bold is valuable. Viewing those as the heart of your river, which is to say the ideas and the image words you select to share them, I suggest you also spend some mental money on the music you are making. For example, here is a line copied from your measurement paragraph: //"To make a measurement a standard of comparison is required."// Your words. As I read the lines before it, the beat is clear and I can 'hear' where this line comes in. We are waiting for it. How cool for the ear it would be, instead of finding this one, you let your challenge off the leash a bit: "Measurement requires a standard of comparison." or perhaps, "Measurement requires a standard." Can you hear the judge raising his gavel? Small point, but a vital one for authors. Listen to the music of what you write. ==

== Now, onto the bottom of your page here and your most recent reflections. The data table followed by a weave of connections is compelling. Hard to argue with a combination of punches and there is a certain dance to your case. Well done, even if you are just noting it out rather than crafting a paragraph yet. Now, as you progress in that vein I suggest you look at some of the ideas you have touched on beyond the simple (so called) links between Math and the WOKS and Areas of Study. Example: you mention 'provoking' as you go from perception to emotion to reasoning. That raises an interesting thought or question. If 'provoked' can be a neighbor of reason, and of perception (eg. I find myself provoked as I reason that civilians were killed needlessly) then can it be argued that emotion has the power to invade all of these areas? Yes? No? What proof or 'reason' would you employ? have fun. cct ==

Questions:
Is math there to be discovered?

· Numbers can be applied to any situation which occurs within the world around us. · Phi · Pythagoras

Are we imposing something on what we experience?

· recall of specific experience which enhances the mathematical idea being taught. · given examples to help understanding of concepts · taught a language

Why teach math?

· Some people are not as proficient as others when dealing with numbers and symbols in the form of a problem. · Teaching math concepts is seen as an unlocking, once a person has the ability to understand what to do when faced with a problem, that knowledge can be applied. · Teaching math is developing what is innate in some people. · Math is taught because it can be found throughout the universe and it is the way in which we function. · Math is how our brains work.

When do we stop teaching math?

· Math should be taught until the student is competent enough to make the decision not to be taught.

=What is measurable?=

Measurable - temperature speed velocity distance degree of certain things emotions in a off on sense time sound force heat mass density weight

Unmeasurable - love emotion

Love is - affection intense feeling passion from our heart blind heroic lobe infatuation duality argument cupid selfless

Love is not - hate indifference joke defined depressing limited generic

What is required to measure something?

Measurement requires a standard or a reference.

Difference between measurable and quantifiable? measurable implies a notion of value. value requires judgement. data requires interpretation and analysis. Is measurement comprehended rationally or empirically?

Paragraph: What is measurable, what is not? Why are things measurable? what is required to make a measure? Is there a difference between measurable and quantifiable? Once things are quantified. what is required to make the data "useful"? How do you define the idea of utility (usefulness)? When we look at data what are we looking for? (examples and non-examples)

Everything is measurable. Being measurable is the ability to be measured by acquiring the degree or amount of something. Everything is measurable because it is possible to find the degree of everything within the world we know. Outside of that world, things become hazy as the size and scope of the comprehensible universe becomes astronomical. Certain things are measure by using data or numbers while other things use degrees or scales. Measurement of speed can be given using numbers based on a distance traveled in a certain amount of time. While things which are less tangible, such as love or anger, can be measured by degrees. We can base the degree of the intensity of love for one person for another on a scale from 1 to 10, 1 being minimal or no love and 10 being extreme or intense love. Or the extent of one persons rage for another on a similar scale.

To make a measurement a standard of comparison is required. There is a base needed off of which we can judge the extent of a certain thing or object. In the case of distance we need a ruler off of which we can measure the progress of an object from point A to point B. In between the the position of point A and point B there is a certain amount of units. If town A is 10 kilometers from town B, then it is possible for me to tell that half way between the two, a car has traveled 5 kilometers. This way it was possible for me to measure the distance the car has traveled because I had a standard of comparison.

The greatest distinction between the idea of something being measurable and something being quantifiable is the fact that to measure something the observer needs to provide some sort of input or judgement. The person doing the measuring is applying a notion of value to the object which is being measured. In this way the observer is hereby passing judgement upon the quantification which has taken place. Judgement is essentially an opinion or conclusion made by an observer. This is where the distinction between the two becomes evident. To quantify something would be to simply and soley apply numbers to a certain element of behavior of a object. This can be considered data. While the next step is to then measure the data, ultimately data requires interpretation and analysis to determine whether it is "useful" or "reliable".

Utility is the idea that something serves a purpose. In this case to make data useful is to provide it with some purpose. I can have a range of numbers from 0 to 373.15. If these numbers, separated by integers of 1, are placed in a list they are nothing more than numbers on a page. As I, the observer, begin to give the numbers purpose they become useful. I could give the page a title, "degrees in Kelvin". I now have some understanding that these figures are representative of a temperature scale. To further utility of the data I could give names to certain values on the scale and provide examples of what occur at this temperature. 0 degrees kelvin is absolute zero, at this point the entropy of a system reaches a minimum value, meaning that the proposed system exists outside the universe, making it impossible to reach this value. 273.15 is the melting point of water in its solid form. 373.15 is the boiling point of water from a liquid into a gas. By giving these boundary values of my data specific connections to the real world it possible and easier to comprehend and apply these numbers to real world events. This is applicable because through the use of sense perception a majority of people in the world have felt the temperature of their surorundings when ice begins to melt or even experienced the sensation of boiling water on their skin. Now, through reason, they can see the data and make connections, by understanding that the temperature they felt has a numerical value which can be found on a scale.

=Math in all Ways and Areas=

1. List all the ways of knowing that are a a part of math knowledge?

This is an example of math. It is a statistical chart of the deaths per country during and throughout the second world war. Math and: Perception - From this graph I can perceive that certain countries were affected to a greater extent than other countries. I can perceive that the USSR, Poland and Germany lost the most people during the war. All of these states were part of the Axis powers. Another perception concerning concerning this data is that Poland lost many more civilians than it did military personnel. Emotion - Even though these are just numbers there is a certain amount of emotion involved with interpreting it. For example, I can see that the number of civilian deaths far outnumbers the number of military deaths. This provokes a sense of anger towards the cause of their innocent deaths. Pity could be felt for all the people who lost some loved one throughout the war. This shows that even though the picture above just shows number emotional response can be found if the context is understood. Reason - Based purely on the date which is provided above, I could reason that the Axis powers were less equipped for war than the Allied powers. This is due to the fact that took more casualties than their opponents. This could be due to an unfair advantage in technology or even mismanagement of forces. However, certain rational statements might not be completely true. I could say that because Greece did not loose relatively many soldiers, they then did not play a big role within the war, when actually Greece was very involved with matters in the Mediterranean. Language -
 * ~ Country ||~ Military ||~ Civilian ||~ Total ||
 * USSR || 12 million || 17 million || 29 million ||
 * Poland || 597,000 || 5.86 million || 6.27 million ||
 * Germany || 3.25 million || 2.44 million || 5.69 million ||
 * Yugoslavia || 305,000 || 1.35 million || 1.66 million ||
 * Romania || 450,000 || 465,000 || 915,000 ||
 * Hungary || 200,000 || 600,000 || 800,000 ||
 * France || 245,000 || 350,000 || 595,000 ||
 * Italy || 380,000 || 153,000 || 533,000 ||
 * Great Britain || 403,000 || 92,700 || 495,000 ||
 * United States || 407,000 || 6,000 || 413,000 ||
 * Czechoslovakia || 7,000 || 315,000 || 322,000 ||
 * Holland || 13,700 || 236,000 || 249,000 ||
 * Greece || 19,000 || 140,000 || 159,000 ||
 * Belgium || 76,000 || 23,000 || 99,000 ||

2. Describe how math may or may not be found in all other areas of knowing?

Math in: Natural Sciences - Math is found all throughout the natural sciences. When we measure the temperature in a beaker where a reaction is taking place, and then need to convert that temperature into other units we are using math. By calculating the time it takes a certain object to travel from point A to point B at a certain speed, we are using math. Human Sciences - Many areas of the human sciences depend upon data. In economics when studying the transfer of wealth we are we use numbers to calculate things such as interest, supply, cost and demand. Contrastingly some areas of the human sciences have little or no math because they deal solely on human behavior. Psychology is extremely hard to interpret using mathematics because human behavior is sporadic and difficult quantify. History - In history it is possible to analyze certain relationships using mathematics. We can analyze the occurrence of certain events throughout the course of history. It is possible to study when depressions happened in the history of the United States, using this information and algebraic formulas, it would be possible for us to possibly predict when similar events could take place in the future. Art - Artists technically use many forms of math in their work. One good example of this would be phi, the golden ratio. This ratio is considered to be the definition of perfection. Many artists attempt to incorporate this form of math into their work. Music - Math can be found in music. Math becomes visible when we analyze the distance between different notes. We can also analyze differences in pitches by hitting different keys or strumming different strings at varying tautness. Ethics - One example of where maths would influence ethics is in the medical profession. For example if I was a doctor and needed to make decision concerning whether expensive treatment would be provided to patients. I would have to analyze which of the patients had a higher statistical probability of surviving treatment. I would have to make sure that any outside circumstances do not influence my decision at all.

=19th - 20th Century Math:= = =

It has-
become simpler. more complicated provides answers explains how things work creates understanding shows how reality can be quantified reality cannot be completely described by mathematics math is a model of reality not all people use math to explain reality math has created weapons E=mc^2 using math to explain reality is more accurate math is a language communication creates understanding