Math can give an illusion of something when there's nothing.

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

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. O

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. It’s even called the point of origin. O

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. -1 O +1 Math can give an illusion of something when there's nothing.

6. 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. 0, 1, 2 , 3, 4, 5, ... 1 2 3 4 5

7. 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 or add. 0 1 1 1 1 1 1 1 1 1 1

8. 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 all the stones in a leather pouch. At the end of the day if he wanted to see if any sheep were 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. 

9. 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… -1 -1 -1 -1 0 1 1 1 1 -1 -1 -1 -1 1 1 1 1 ...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.

10. When things attract they come together. This action of coming together is called addition. Addition doesn’t always give us larger numbers. Remember when positive and negative amounts cancel? 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1

11. 1 1 1 1 1 1 1 1 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 don’t know what the total is. The mathematical universe doesn’t 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.

12. Let’s look at more examples of the action of addition. Let’s 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. Nothing in nature understands what 10 kilograms is. But the total weight is known as soon as the last fish hits the pan.

13. Humans often want a symbol to represent weight. Picking up the pan and saying, “These fish feel heavy.” may not be enough. Nowadays people look at 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 doesn’t weigh 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.”

14. 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. kg, kilogram, lb, pound, ton, g, gram, ounce, oz.

15. 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. It’s more properly called a “numeral.” Somewhere in math education, the symbols for mathematics got confused with being mathematics. 5 1 1 1 1 1

16. 10 100 What fraction is this? I’m sorry, this is not a fraction. The proper name is called a fractional numeral. To the right is 10/100 of the large box. This is a fraction.

17. When we stare too much at symbols we begin to believe that the symbols are real. A A C B A D

19. When we stare too much at symbols we begin to believe that the symbols are real.

20. Symbols are even representingemotions

21. When we stare too much at symbols we begin to believe that the symbols are real.

22. It’s like thinking your name is somehow more real than you are. A family’s name is far less important than the family itself.

24. e=mc2 is made of symbols for energy, mass and the speed of light, but this is the real e=mc2

25. Symbols Quiz • How much money is this? $150. • Which is worth more ¥, €, or £? • H2O is water • The formula for water is H2O. • H is hydrogen • H is the symbol for hydrogen • You take someone’s temperature and the thermometer reads, 104oF. That means the person must have a temperature. True/false?

26. Place periodic chart of the elements…

27. Bad Habit #1Focusing on symbols for things rather than the actual thing Good Habit #1Thinking of the real thing first then using their symbols

28. ADDITION • Addition is an easy concept, but there are a few precautions. There’s a cliché which says, “You can’t compare apples to oranges.” Addition has a similar problem. You can’t add apples to oranges to find a total of apples or oranges. However, you can still add them.

29. A + R = A + R + = ?

30. 4 inches 10 centimeters + =? If you were building a shelf that needed to be 4 inches high to accommodate a VCR and another 10 centimeters high to accommodate a DVD player, how might you add these quantities in order to build the shelf to the right height? Add just means to combine; it doesn’t necessarily mean to convert.

31. Bad Habit #2 We jump into calculations much too quickly Good Habit #2Take your time to study the problem before even thinking about calculations

32. Richard Feynman

33. 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, it’s hard. For example, as soon as all of the sticks appear tell me how many sticks there are. When numbers are grouped into patterns, we recognize them much faster

34. Here’s another way we group quantities in order to recognize the number faster

38. By grouping amounts in easy to recognize quantities, addition is simplified 7 + 6 5 + 5 + 3

39. Grouping can be done in any way you want to. 6 + 9 + 7 {7} {5} (-1) (+2) 0 1 4 2 6 9 7 6 9 7

40. Shuffle quantities around 79 + 83 + 77 + 14 80 + 80 + 80 + ? 80 + 80 + 80 + 13 = 240 +13 =253

41. METER 40 cm + 15 mm = ?

42. 8-4 4 1 1 1 1 In nature addition happens all the time, but so does subtraction. 1 1 1 1

43. Subtract • Tract = tractor • Tract = traction • Tract = tractor beam • Tract = distract • Tract = retract • Tract = detract

44. Subtract 8- 3 5 • Sub = under  ubmarine • Sub = less than  subhuman

45. 5- 8 5- 8 -3 How can you take 8 away from 5? 5 + 0 = 5 0 = (3) + (-3) 5 + 3 + (-3) 8 + (-3) 

46. 5- 8 How can you take 8 away from 5? 5 + 0 = 5 0 = (3) + (-3) 5 + 3 + (-3) 8 + (-3) -3

47. Source of confusion • Plus sign (+) • Addition sign (+) • What’s the difference? • Addition sign indicates action of combining. • Plus sign means something completely different. • Negative sign (-) • Subtraction sign (-) • What’s the difference? • Subtraction sign indicates action of taking away. • Negative sign means something completely different.

48. Where did the + sign come from? It came from the Latin word for “and” which is “et”. The “t” became a “+”. Et tu, Brute? What was Julius Caesar’s famous last words?

49. Plus (+) sign & negative (-) sign • A common meaning is that of direction. • +10oC is 10o from zero in the direction of getting hotter (above zero) • -10oC is 10o from zero in the direction of getting colder (below zero)

50. Plus (+) sign & negative (-) sign • By itself it identifies the part of a battery that either has excess of electrons (-) or a deficiency of electrons (+)