# What do you call this math effect? **URL:** \ **Category:** Factual Questions\ **Created:** [May 17, 2006, 1:59am UTC](https://boards.straightdope.com/t/what-do-you-call-this-math-effect/357056 "2006-05-17T01:59:54Z")\ **Posts on this page:** 19\ **Page:** 1
**Author:** ![AnabolicDoberman](https://avatars.discourse-cdn.com/v4/letter/a/ecd19e/32.png) [@AnabolicDoberman](https://boards.straightdope.com/u/AnabolicDoberman)\ **Post date:** [May 17, 2006, 1:59am UTC](https://boards.straightdope.com/t/what-do-you-call-this-math-effect/357056/1 "2006-05-17T01:59:54Z")
Say I am 20 years old and have a 10 year old brother. I am twice my brothers age. in 5 years when I am 25 and he is 15, I am no longer twice his age even though I am still 10 years older. what do you call this? ---
**Author:** ![eleanorigby](https://avatars.discourse-cdn.com/v4/letter/e/ee7513/32.png) [@eleanorigby](https://boards.straightdope.com/u/eleanorigby)\ **Post date:** [May 17, 2006, 2:07am UTC](https://boards.straightdope.com/t/what-do-you-call-this-math-effect/357056/2 "2006-05-17T02:07:20Z")
I call it getting older, sonny–and you owe him a birthday present or at least a card! I don’t know, but am waiting anxiously for the algorithm. Is there a time when you will again be twice his age? How often does the pattern repeat? Or is it a one off, so to speak? ---
**Author:** ![II\_Gyan\_II](https://avatars.discourse-cdn.com/v4/letter/i/bbe5ce/32.png) [@II\_Gyan\_II](https://boards.straightdope.com/u/II_Gyan_II)\ **Post date:** [May 17, 2006, 2:12am UTC](https://boards.straightdope.com/t/what-do-you-call-this-math-effect/357056/3 "2006-05-17T02:12:16Z")
> [@AnabolicDoberman](#): > > Say I am 20 years old and have a 10 year old brother. I am twice my brothers age. in 5 years when I am 25 and he is 15, I am no longer twice his age even though I am still 10 years older. what do you call this? A constant function. Age(You) - Age(Brother) = 10 years (constant). Atleast while both are alive. ---
**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\ **Post date:** [May 17, 2006, 2:12am UTC](https://boards.straightdope.com/t/what-do-you-call-this-math-effect/357056/4 "2006-05-17T02:12:23Z")
I don’t think there’s any special name for it; it’s just an effect of two people of different ages continuing to age at the same rate. In particular, say you were exactly 10 years, 7 months old when your brother was born. When will you be twice his age? When your brother is exactly 10 years, 7 months old (the same age you were when he was born). Any time before that, you will be more than twice his age. Any time after that, you will be less than twice his age. Assuming each of you live forever, then as you both get older, the ratios of your ages will approach 1 arbitrarily closely. ---
**Author:** ![Cunctator](https://avatars.discourse-cdn.com/v4/letter/c/43a26b/32.png) [@Cunctator](https://boards.straightdope.com/u/Cunctator)\ **Post date:** [May 17, 2006, 2:17am UTC](https://boards.straightdope.com/t/what-do-you-call-this-math-effect/357056/5 "2006-05-17T02:17:43Z")
It just represents the solution to two simultaneous equations. The constant relationship between your brother’s age (x) and your age (y) is given by the equation y = x + 10 At the point where x = 10 and y = 20, your ages also just happen to satisfy the equation y=2x ---
**Author:** ![RealityChuck](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/realitychuck/32/195_2.png) [@RealityChuck](https://boards.straightdope.com/u/RealityChuck)\ **Post date:** [May 17, 2006, 2:19am UTC](https://boards.straightdope.com/t/what-do-you-call-this-math-effect/357056/6 "2006-05-17T02:19:14Z")
“Say I am 20 years old and have a 10 year old brother. I am twice my brothers age. In 10 years, I’m 30 and he’s 20. I’m 1.5 times my brothers age. In another ten years, I’m 40 and he’s 30; I’m 1.333 times my brother’s age. In another ten years, I’m 50 and he’s 40; I’m now 1.2 times my brother’s age.” How long does it take until he catches me? ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [May 17, 2006, 2:21am UTC](https://boards.straightdope.com/t/what-do-you-call-this-math-effect/357056/7 "2006-05-17T02:21:24Z")
The passage of time. ---
**Author:** ![panache45](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/panache45/32/64_2.png) [@panache45](https://boards.straightdope.com/u/panache45)\ **Post date:** [May 17, 2006, 2:24am UTC](https://boards.straightdope.com/t/what-do-you-call-this-math-effect/357056/8 "2006-05-17T02:24:37Z")
What you’re referring to is a “difference” vs. a “ratio.” The “difference” between your ages is constant. Throughout your lives, the difference between your ages is always 10 years. For example, 20–10=10, and 50–40=10. The “ratio” between your ages is your age divided by your brother’s age. As you both age, that ratio is constantly getting smaller. For example, 20/10=2, and 50/40=1.25. ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [May 17, 2006, 2:31am UTC](https://boards.straightdope.com/t/what-do-you-call-this-math-effect/357056/9 "2006-05-17T02:31:45Z")
It’s not a math effect; it’s simply a coincidence. If you have enough numbers and are liberal in what correspondences you find interesting or worth comment, then there are an infinite number of such coincidences. They’re still coincidences, however. ---
**Author:** ![Saint\_Cad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saint_cad/32/18907_2.png) [@Saint\_Cad](https://boards.straightdope.com/u/Saint_Cad)\ **Post date:** [May 17, 2006, 2:42am UTC](https://boards.straightdope.com/t/what-do-you-call-this-math-effect/357056/10 "2006-05-17T02:42:44Z")
> [@RealityChuck](#): > > “Say I am 20 years old and have a 10 year old brother. I am twice my brothers age. > In 10 years, I’m 30 and he’s 20. I’m 1.5 times my brothers age. In another ten years, I’m 40 and he’s 30; I’m 1.333 times my brother’s age. In another ten years, I’m 50 and he’s 40; I’m now 1.2 times my brother’s age.” > > How long does it take until he catches me? Never the ratio is x/(x-10) ---
**Author:** ![nivlac](https://avatars.discourse-cdn.com/v4/letter/n/3bc359/32.png) [@nivlac](https://boards.straightdope.com/u/nivlac)\ **Post date:** [May 17, 2006, 2:52am UTC](https://boards.straightdope.com/t/what-do-you-call-this-math-effect/357056/11 "2006-05-17T02:52:58Z")
> [@AnabolicDoberman](#): > > Say I am 20 years old and have a 10 year old brother. I am twice my brothers age. in 5 years when I am 25 and he is 15, I am no longer twice his age even though I am still 10 years older. what do you call this? A **WORD PROBLEM**. Yes, the dreaded word problem that every algebra student hates. ---
**Author:** ![cerberus](https://avatars.discourse-cdn.com/v4/letter/c/71e660/32.png) [@cerberus](https://boards.straightdope.com/u/cerberus)\ **Post date:** [May 17, 2006, 3:09am UTC](https://boards.straightdope.com/t/what-do-you-call-this-math-effect/357056/12 "2006-05-17T03:09:38Z")
It’s _mathematics_, please. And nothing special is going on here, just algebra. In general, you’ve got two functions of age: Age1(t) = {(t-t1) if t ge t1 and person1 is not dead at time t = {tmax1-t0 if person1 is dead at time t} t1 is the time of person1’s birth, and tmax1 is the time of person1’s death. Age2(t) = {(t-t2) if t ge t2 and person2 is not dead at time t = {tmax2-t2 if person2 is dead at time t} t2 is the time of person2’s birth, and tmax2 is the time of person2’s death. So at time t, the difference is Age1(t)-Age2(t), and the ratio is Age1(t)/Age2(t). To work out the mathematics, you’ve got to work out the nature of the subcases for t1,tmax1, t2, tmax2… ---
**Author:** ![MikeG](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mikeg/32/4329_2.png) [@MikeG](https://boards.straightdope.com/u/MikeG)\ **Post date:** [May 17, 2006, 3:11am UTC](https://boards.straightdope.com/t/what-do-you-call-this-math-effect/357056/13 "2006-05-17T03:11:41Z")
Huh, I was thinking about this very topic the other day. In June I will be 4 times older than my son and 3 times older than my daughter. Kind of a cool in a geeky way sort of thing to notice. Me 36 son 9 daughter will be 12 in June ---
**Author:** ![spingears](https://avatars.discourse-cdn.com/v4/letter/s/ebca7d/32.png) [@spingears](https://boards.straightdope.com/u/spingears)\ **Post date:** [May 17, 2006, 7:41pm UTC](https://boards.straightdope.com/t/what-do-you-call-this-math-effect/357056/14 "2006-05-17T19:41:56Z")
> [@RealityChuck](#): > > “Say I am 20 years old and have a 10 year old brother. I am twice my brothers age. > In 10 years, I’m 30 and he’s 20. I’m 1.5 times my brothers age. In another ten years, I’m 40 and he’s 30; I’m 1.333 times my brother’s age. In another ten years, I’m 50 and he’s 40; I’m now 1.2 times my brother’s age.” > > How long does it take until he catches me? The twelfth of never? ---
**Author:** ![CalMeacham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/calmeacham/32/35_2.png) [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)\ **Post date:** [May 17, 2006, 7:50pm UTC](https://boards.straightdope.com/t/what-do-you-call-this-math-effect/357056/15 "2006-05-17T19:50:17Z")
What you might have in mind is the idea of an _astmptote_. If your age is **x** and your brother is 10 years younger, then the ratio of your ages is**R = (x-10)/x**. The value of **r** gets closer and closer to **1** as you get older, although it never quite gets there (although when you are 10,000,000 years old you might be inclined to view the difference in your ages as unimportant for most purposes. Except whjen you tell him that _you’ll_ always be older.). You say that the ratio _asmptotically approaches the value 1_. ---
**Author:** ![RealityChuck](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/realitychuck/32/195_2.png) [@RealityChuck](https://boards.straightdope.com/u/RealityChuck)\ **Post date:** [May 17, 2006, 7:52pm UTC](https://boards.straightdope.com/t/what-do-you-call-this-math-effect/357056/16 "2006-05-17T19:52:37Z")
> [@SaintCad](#): > > Never > the ratio is x/(x-10) Actually, the numbers approach each other as x --\> infinity, Abbott. Hey, Abbott! ---
**Author:** ![Colophon](https://avatars.discourse-cdn.com/v4/letter/c/f05b48/32.png) [@Colophon](https://boards.straightdope.com/u/Colophon)\ **Post date:** [May 17, 2006, 7:56pm UTC](https://boards.straightdope.com/t/what-do-you-call-this-math-effect/357056/17 "2006-05-17T19:56:55Z")
> [@eleanorigby](#): > > I don’t know, but am waiting anxiously for the algorithm. Is there a time when you will again be twice his age? Just think about that for a minute… ---
**Author:** ![Saint\_Cad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saint_cad/32/18907_2.png) [@Saint\_Cad](https://boards.straightdope.com/u/Saint_Cad)\ **Post date:** [May 18, 2006, 7:59am UTC](https://boards.straightdope.com/t/what-do-you-call-this-math-effect/357056/18 "2006-05-18T07:59:06Z")
> [@RealityChuck](#): > > Actually, the numbers approach each other as x → infinity, Abbott. > > Hey, Abbott! Sure they approch each other, but they never **equal** each other. There is a difference. ---
**Author:** ![cerberus](https://avatars.discourse-cdn.com/v4/letter/c/71e660/32.png) [@cerberus](https://boards.straightdope.com/u/cerberus)\ **Post date:** [May 19, 2006, 2:41am UTC](https://boards.straightdope.com/t/what-do-you-call-this-math-effect/357056/19 "2006-05-19T02:41:51Z")
Limit arguments make no sense here, as people have finite lifespans. Moreover, the age functions aren’t linear past death: maximum age is the age at death. So even if you take the limit, once both people are dead, the ratio is simply the ratio of the ages at death.