Today was pretty eventful. Our usual discussions and surfing led to three discoveries (to be precise...Observations). None of them is that significant, but still we found them to be notable. It may happen that some of you are already well aware of these facts. But for us, it's nontrivial. Hence, the post...

1. Real life application of the fact that the sequence (n+k)/n goes to 1.

Most of you must have solved age problems in school. The problem statement would be something of this type....

"A man is 4 times as old as his son. In 3 years, the father will be 3 times as old as his son will be. How old is each of them now?"

Cynosure's post on the difference between the ages of siblings reminded Deep of a question that she had in mind as a school going kid.- "Why does it happen that as the time progresses, father who was 4 times his son's age became 3 times the same son's age". Translating this question into the language of Mathematics, with son's age as 'n' and father's age as 'n+k', yields a sequence (n+k)/n which is obviously decreasing and converges to 1 as n goes to infinity.

2. Sunrise and Sunset timings

It started as a discussion with MGK on the timings of getting up. We were whining about not feeling like getting up, as it's too dark around 6.30. Out of usual habit, we googled and got the latest time for sunrise as 7.15 am, which happens to be in the second week of January. Isn't it too late for The Sun to rise at 7.15 am??? No wonder then that we petty human beings don't feel like leaving our beds. This googling led to the second interesting observation of the day - "The shortest day doesn't correspond to the latest sunrise and the earliest sunset." Again resorting to the tools of real analysis, if we define the timing of sunrise on nth day by Rn and that of sunset by Sn, the shortest day would correspond to the smallest value of (Sn-Rn). But then inf (Sn-Rn)≠inf Sn + inf (-Rn) (To be precise, argmin (Sn-Rn)≠argmin (Sn) or argmin (-Rn) ). In fact, in this case it turns out that the “n” for which the corresponding extreme values are attained (argmin), are different for all the three quantities, Sn, Rn and Sn-Rn. So, we got a good application for somewhat non-intuitive real analysis result. For actual geographical reasoning, you may google and do explain us, if you get something.

Enough of real analysis stuff now…. Let’s get to real blogging

3. “blogspot.com” changed to “blogspot.in”

Richa noticed that the Feedjit has kind of restarted, as it was showing only latest 2-3 entries instead of its usual count of 50. But, when we went to Feedjit’s “real time view” for our joint blog, it seemed perfectly alright except the fact that in last 8 hours there was only one entry and it was from Indonesia. When we tried to visit the same link via blog, it turned up that it had almost 20 entries during last 5 hours, but all of them were from India. Then we noticed the change in the link from “.com” to “.in” and realized that all the blogspot.com links are getting redirected to blogspot.in links. Googling almost instinctively, we stumbled upon the page giving the details of this country specific redirecting. This helps Google to remove the content found objectionable by a specific country from a page visible in that country only. Of course, it won’t affect the harmless content posted by ordinary people like us. But still, if you want to see the original “.com” version, just type “-----.blogspot.com/ncr” to get the no country redirect version. Dear Feedjit users, don’t get disheartened if the panel on your regular blog shows only Indian visitors. If you want to see your visitors from abroad, go to “/ncr” link given above…..

That’s enough research for today… Off to some real research now…

1. Real life application of the fact that the sequence (n+k)/n goes to 1.

Most of you must have solved age problems in school. The problem statement would be something of this type....

"A man is 4 times as old as his son. In 3 years, the father will be 3 times as old as his son will be. How old is each of them now?"

Cynosure's post on the difference between the ages of siblings reminded Deep of a question that she had in mind as a school going kid.- "Why does it happen that as the time progresses, father who was 4 times his son's age became 3 times the same son's age". Translating this question into the language of Mathematics, with son's age as 'n' and father's age as 'n+k', yields a sequence (n+k)/n which is obviously decreasing and converges to 1 as n goes to infinity.

2. Sunrise and Sunset timings

It started as a discussion with MGK on the timings of getting up. We were whining about not feeling like getting up, as it's too dark around 6.30. Out of usual habit, we googled and got the latest time for sunrise as 7.15 am, which happens to be in the second week of January. Isn't it too late for The Sun to rise at 7.15 am??? No wonder then that we petty human beings don't feel like leaving our beds. This googling led to the second interesting observation of the day - "The shortest day doesn't correspond to the latest sunrise and the earliest sunset." Again resorting to the tools of real analysis, if we define the timing of sunrise on nth day by Rn and that of sunset by Sn, the shortest day would correspond to the smallest value of (Sn-Rn). But then inf (Sn-Rn)≠inf Sn + inf (-Rn) (To be precise, argmin (Sn-Rn)≠argmin (Sn) or argmin (-Rn) ). In fact, in this case it turns out that the “n” for which the corresponding extreme values are attained (argmin), are different for all the three quantities, Sn, Rn and Sn-Rn. So, we got a good application for somewhat non-intuitive real analysis result. For actual geographical reasoning, you may google and do explain us, if you get something.

Enough of real analysis stuff now…. Let’s get to real blogging

3. “blogspot.com” changed to “blogspot.in”

Richa noticed that the Feedjit has kind of restarted, as it was showing only latest 2-3 entries instead of its usual count of 50. But, when we went to Feedjit’s “real time view” for our joint blog, it seemed perfectly alright except the fact that in last 8 hours there was only one entry and it was from Indonesia. When we tried to visit the same link via blog, it turned up that it had almost 20 entries during last 5 hours, but all of them were from India. Then we noticed the change in the link from “.com” to “.in” and realized that all the blogspot.com links are getting redirected to blogspot.in links. Googling almost instinctively, we stumbled upon the page giving the details of this country specific redirecting. This helps Google to remove the content found objectionable by a specific country from a page visible in that country only. Of course, it won’t affect the harmless content posted by ordinary people like us. But still, if you want to see the original “.com” version, just type “-----.blogspot.com/ncr” to get the no country redirect version. Dear Feedjit users, don’t get disheartened if the panel on your regular blog shows only Indian visitors. If you want to see your visitors from abroad, go to “/ncr” link given above…..

That’s enough research for today… Off to some real research now…

- Akanksha & Deep

First one was 'awesome', second jyada samjha nahi and in third you guys came up with really helpful conclusions...

ReplyDeleteKeep the good work going :) ..

Thanks, Second wala mil ke samajha denge...

Deletehaan wo to hai hi, b/w good news is ki maine dobara pada , argmin google kiya and ab mujhe kaafi trivial lagne laga :) :)

Deletehope what i am understanding is correct..;)

Also, "for the actual geographical reasoning" I found the explanation by a 'versatile mathematician' interesting,

Deletehttp://www.larry.denenberg.com/earliest-sunset.html

:O

ReplyDeleteI too agree with Richa. This post is 'awesome'!!!!!!!!!!

Thanks a lot, Meghana... :)

DeleteI agree with Richa's comment above...2nd one was like O_o... :O didn't got anything from what you wrote, but got the issue nice one to think about... :D

ReplyDeleteas far as the first point is concerned...most of the time convergence frustrates me...but gave you a brainstorming issue to think about... ;)

finally thanks for the "blogspot.com/ncr"...wasn't aware of it... :D

Thanks, Cynosure... Would like to know what you arrive at after your own brain storming about the second...

DeleteNice post and nice discussion! Never thought though that simple discussion would result into a post. Same is applicable to the research i suppose. (BTW it seems that you have enough time!)

ReplyDeleteIf only, some "good" research could have emerged from such discussions...

Delete(For "such" things, we always have time ;))

Awesome post Akansha.This is very helpful for people like me those who want to do research.

ReplyDeleteThanks, Priyanka

Delete