1. David M. Strong Pepperdine University David.Strong@pepperdine.edu Why It Might Seem That Christmas Is Coming Early This Year

2. My daughter asks, “Daddy, when is it ever going to be Christmas again?” Every winter I think to myself, “It’s nearly Christmas time again already?” I wonder, “Why does Christmas seem to come more quickly for me than for my daughter, and in general, why does time seem to pass more quickly for me than for her?” It’s Almost Christmas Again? Already?

3. Suppose that my daughter is now 7 years old and I am 35 years old. Then one year to her is about 1/7 of her life and one year to me is 1/35 of my life. In general, at age n, one year is 1/n of your life. So perhaps we can say that one year to my daughter seems about five times as long as one year seems to me, since. At Age n, One Year is 1/n of Your Life

4. In general, define D the perceived duration of time from age a 1 to age a 2 by Math Can Explain Anything in Life Example: from age 7 to age 10 is a child’s 8 th, 9 th and 10 th years of life, so the perceived duration of time from age 7 to age 10 is 1/8 + 1/9 + 1/10 =.

5. “Perceived duration” of three 7-year periods: –Pre-teenage: –Teenage: –Early adult: Example: Three 7-year Periods “Perceived duration” of three 7-year periods: –Pre-teenage: –Teenage: “Perceived duration” of three 7-year periods: –Pre-teenage:

6. What do 0.7301, 0.4176 and 0.2937 mean? Nothing by themselves. They are meaningful only relative to each other. For example, So the teenage years seemed to have lasted 42% longer than the early adult years, even though both periods were seven years. Example: Teenage vs. Early Adult Years

7. Time is continuous, so our perception of time is better modeled by So for the previous example, Time is Continuous

8. Compare the six years of middle and high school to the fifteen years since high school: –Middle/High School: –Since High School: So the fifteen years have seemed only about 50% longer than the six years. Another Comparison

9. Perception of time is different for everybody (perhaps one person hated teenage years and another loved them). Use model as average for most people (like average daily high temperatures). Perception of time is psychological—the mathematical explanation is too simplistic. It probably doesn’t effectively model the first few years or the final years of life. Disclaimers (Don’t Quote Me On This!)

10. Question: when is a person’s life half over (perceptually)? That is, where a 1 and a 2 are the “beginning” and ending ages of life, what is the age a m such that. ? Half-life

11. Take a 1 = 5 (the age of my earliest memories), and a 2 = 80. Then That is, if I live to the age of 80, then my life was already half over at age 20! My Half-life

12. I could also see at what point of my life I currently am. With current age of a c = 33.28, So I’ve lived 68% of my life so far. Or, So I have 32% of my live yet to live. How Much Time Left? I could also see at what point of my life I currently am. With current age of a c = 33.28, So I’ve lived 68% of my life so far. Or, I could also see at what point of my life I currently am. With current age of a c = 33.28, So I’ve lived 68% of my life so far.

13. I need your: –a 1 : “beginning” age (age of earliest memories) –a c : current age –a 2 : ending age Youngest and Oldest in Audience So we’re all closer to the end than we might have thought (make the most of it!).

14. The perceived length of period t for a person of age a 1 as compared to the perceived length of time for a person of age a 2 will be: Time Perception for Two People

15. Perceived length of one hour ( year) for a 5 year old compared to a 33 year old: Example: Perception of an Hour No wonder kids have a hard time sitting still through an hour of church: 1 hour to my five year old is like over 6 hours to me!!

16. At age a, the perceived length of the coming year relative to the year just past is For example, for a child who just turned five, N(5) 0.82, so the coming year will seem to last about 82% as long as the previous year. Perception of Coming Year

17. On Christmas Day this year my daughter will be 7.21 years old and I will be 33.48 years old. She’ll again ask me how long until next Christmas. Since and, I can tell my daughter, “For you it will seem to take about 87% as long until next Christmas as it took to get to this Christmas” (and similarly 97% for me). Back to “When Is Christmas Coming?”

18. And then, of course, my daughter will ask, Huh? “Dad, what does percent mean?”

19. David M. Strong Pepperdine University David.Strong@pepperdine.edu Why It Might Seem That Christmas Is Coming Early This Year

20. Example of a matrix