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The beginning of our story begins with nothing, absolutely nothing. Well, there was something. Something we know well, but treat it as nothing.

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Presentation on theme: "The beginning of our story begins with nothing, absolutely nothing. Well, there was something. Something we know well, but treat it as nothing."— Presentation transcript:

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2 The beginning of our story begins with nothing, absolutely nothing. Well, there was something. Something we know well, but treat it as nothing.

3 Nothing has another name. It's called zero. Zero is something and nothing at the same time. Zero requires nothing. And since there was nothing, zero existed. It also existed without needing someone or some thing to make it

4 If zero existed on its own, then a small part of mathematics existed with it. Matter of fact, zero sits right in the middle of mathematics. Its even called the point of origin

5 Mathematics has positive and negative numbers with the power to cancel each other out. Start with a positive 1 and combine that with a negative 1, you have zero.

6 The beginning of our story begins with nothing, absolutely nothing. Well, there was something. Something we know well, but treat it as nothing Nothing has another name. It's called zero. Zero is something and nothing at the same time. Zero requires nothing. And since there was nothing, zero existed. It also existed without needing someone or some thing to make it If zero existed on its own, then a small part of mathematics existed with it. Matter of fact, zero sits right in the middle of mathematics. So in our story zero and that small part of mathematics existed when nothing else could. Math also gives us an illusion of something when there's nothing. For example, give me a million dollars and at the same time give me a debt of a million dollars. The million dollars will look like I'm rich and have tons of possessions. However, because of the million dollar debt, I actually have nothing. The two cancel Mathematics have positive and negative numbers with the power to cancel each other out. Start with a positive 5 and combine that with a negative 5, you have zero. In our mathematical universe two quantities can pop into existence and just as easy pop out of existence. You might think the easiest way to expand our mathematical universe is to count: 1, 2, 3, 4, 5 and so on. Counting is actually fairly sophisticated. For example, if you see five items and count them by going, "1, 2, 3, 4, 5" you have actually added them up because 5 is the total of all the items. A more simple expansion would be to say, "1 and 1 and 1 and 1 and 1... You don't have to know how to count.

7 Before humans knew how to count, they still were able to keep track of their possessions. For example, if a sheepherder had 10 sheep, he would pick up one stone for the first sheep, a second stone for the second sheep, a third stone for the third sheep and so on. He'd place on the stones in a leather pouch. At the end of the day he wanted to see if any sheep was missing, he didn't count them, he opened the pouch and took out one stone for each sheep he saw. If there were any stones left in the pouch, he knew that not all sheep were present, and would go out to look for them. Another word for stone is calculus. So our advance math called "calculus" gets its name from the simplest of math ideas- one to one correspondence. with rocks. But Let's get back to our mathematical universe. It expands with simple repetition. Of course, the negative counterpart is also being created one at a time to keep it balanced to zero. We can imagine a string of ones emanating from zero, but to balance the impulse for fast expansion, there ought to be a slow weak attraction force that will pull it all back together. Something like gravity. When things attract they come together. This action of coming together is called addition. Addition doesnt always give us larger numbers. Remember when +5 and -5 came together? We got zero. The universe to follow will have all kinds of situations where things combine. Adding is an action upon real quantities. For example, three balls collide with five balls. Their quantities are added even if you dont know what the total is. The mathematical universe doesnt care that the answer is eight. There are eight there whether or not we know that there are. In other words, mathematics does its own math without humans.

8 Lets look at more examples of addition in action. Lets say these fish weigh 1 kilogram each. There are 10 fish on the pan. How much is their combined weight? You might say 10 kilograms. But remember the fish dont care, the pan doesnt care, the universe doesnt care that the total weight is 10 kilograms. To nature, the total is done as soon as the last fish hits the pan. Addition works on its own. Humans, however, often want a symbol to represent the weight of the fish. Picking up the pan and saying, These fish feel heavy. may not be enough. A person may read the scale and write down fish weigh 10kg. But note that 10kg is not the weight of the fish. The weight of the fish can only be felt but not written down. We can write down 10kg but it doesnt weight the same as the fish. Now we could use a balance and add rocks until they weigh the same as the fish. If someone asked how heavy were the fish, we could say, Pick up that bag of rocks and you will know. The point here is that we use symbols to represent quantities, but these symbols are not the same as the quantities. The symbol 10kg might be meaningless to most people, but the actual weight of 10kg falling on their heads would not be meaningless. When we write this symbol, 5 it is not the number 5. It is a symbol that some humans recognize as standing for 5 things. Somewhere in math education, the symbols for mathematics got confused with as being mathematics. Heres a question: What fraction is this? ¾. Im sorry, this is not a fraction. The proper name is called a fractional numeral. The word, numeral means that it is a symbol that represents a number.

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10 When we stare too much at symbols we begin to believe that the symbols are real. Its like thinking your name is somehow more real than you are. A persons name is far less important than the actual person. e=mc 2 is made of symbols for energy, mass and the speed of light, but this is the real e=mc 2. Which has more power?

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12 Symbols Quiz How much money is this? $150. Which is worth more ¥,, or £? H 2 O is water The formula for water is H 2 O. H is hydrogen H is the symbol for hydrogen You take someones temperature and the thermometer reads, 104 o F. That means the person must have a temperature. True/false?

13 ADDITION Addition is an easy concept, but there are a few precautions. Theres a cliché which says, You cant compare apples to oranges. Addition has a similar problem. You cant add apples to oranges unless you call them both fruit.

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15 If you were building a shelf that needed to be 4 inches high to accommodate a cup and another 10 centimeters high to

16 In a way you cant add 3 to 4, unless you make both of the ones first. Of course we have memorized 3+4=7. But in doing the problem with real quantities, we must first show 3 as three single items and four as 4 single items. We can then get 7 single items.

17 To save time in adding, humans have taken advantage of their ability to see patterns. We have extraordinary ability to see shapes and patterns. If there is no pattern, its hard. For example, in 2 seconds, tell me how many sticks have appeared. When numbers are grouped into patterns, we recognize them much faster. This is an old way of counting based on the five fingers of the hand. In groups of 5, its much easier to see the total.

18 For example, how many inches of rain would there be in your 50x50 foot backyard in 2 hours, if 1 million rain drops of ¼ cc each fall every 30 minutes and the dirt soaks up one liter of water per square meter per hour? With some work we can predict this. Nature doesnt try to predict, it lives in the here and now. As quantities arrive, addition and subtraction are happening simultaneously. The answer will reveal itself automatically at the 2 hour mark.

19 To save time in adding, humans have taken advantage of their ability to see patterns. We have extraordinary ability to see shapes and patterns. If there is no pattern, its hard. For example, in 2 seconds, tell me how many sticks have appeared. When numbers are grouped into patterns, we recognize them much faster. This is an old way of counting based on the five fingers of the hand. In groups of 5, its much easier to see the total.

20 To save time in adding, humans have taken advantage of their ability to see patterns. We have extraordinary ability to see shapes and patterns. When numbers are grouped into patterns, we recognize them much faster.

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23 By grouping amounts in easy to recognize quantities, addition is simplified

24 Stop ignoring reality Some people treat mathematics like a bunch of tools that stay in the toolbox. They may look at the tools, name the tools, handle the tools, but never use them for their intended purpose, which is to use them in the real world. How many times have you done a problem like ½ + ¾ = ? How many times have you measured

25 The mathematical universe does not use symbols for quantities, it only uses real quantities. This makes calculations instantaneous. Throw a rock in the air. The speed of the rock, the force of gravity, the time it takes to fall to the ground are all calculated as it happens. Actually it doesnt calculate anything, it just lets the forces do what they do.

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27 The mathematical universe does not use symbols for quantities, it only uses the real quantities. This makes calculations instantaneous. For example, If we throw a rock into the air how long will it take before it hits the ground? Gravity, wind resistance, and speed are all accounted for instantly and constantly. The rock hits the ground at exactly the time it should take. Nature doesnt try to predict the future.

28 When atoms combine into molecules, the mass of the molecule is the combination of each atoms mass. We humans like to have names

29 The Equals sign or =, used to indicate the result of some arithmetical operation, was invented in 1557 by Robert Recorde.arithmetical1557Robert Recorde Growing tired of writing out the words "is equalle to:" [sic], Recorde employed the symbol in his work Whetstone of Witte. The invention is commemorated in St Mary's Church, Tenby.St Mary'sChurchTenby

30 For example, we want a rock to stay in the air for 3 seconds. We could throw it in the air and measure the time it takes to hit the ground. If it hits sooner than 3 seconds we throw it harder, if it hits longer than 3 seconds we throw it less hard. With some trial and error, we will know just how hard to throw it to get 3 seconds. We never calculated anything, we just adjusted our throw until we got it right. Now if we didnt care about how long it took, we could throw it once, and lets say it took 4 seconds to hit the ground. We know right then how hard to throw it in order to get 4 seconds in the air.

31 The Plus (+) and minus (-) signs are used universally to represent the operations of addition and subtraction, and have been extended to many other meanings, more or less analogous. additionsubtraction Though the signs now seem as familiar as the alphabet or the Hindu-Arabic numerals, they are not of great antiquity. The Egyptian hieroglyphic sign for addition, for example, resembled a pair of legs walking from right to left (the direction in which the language was written), with the reverse sign indicating subtraction. In Europe in the early 15th century the letters P and M were generally used.Egyptian hieroglyphic15th century The earliest appearance of the modern signs seems to come from a book by Johhannes Widman in The + is a simplification of the Latin "et" (comparable to the ampersand &). The - may be derived from a tilde written over m when used to indicate subtraction; or it may come from a shorthand version of the letter m itself.1489ampersand The simple expression "one plus one" (1+1) can mean many different things, depending on the mathematical system under consideration. Many algebraic structures have some operation which is called, or equivalent to, addition, and an element called, or equivalent to, one. Moreover, the symbolism has been extended to operations that are not mathematical, such as concatenation of strings of characters.algebraic structuresadditionone


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