All your base are belong to us

Logic within logic within logic

with 14 comments

Imagine it’s almost nine in the morning; peak hour, and you are rushing to office. You are almost at one of the city’s busiest roads, a bottleneck if that is the term I’m looking for. As is the always the case, you have a detour. There is a narrow side route you can take. A longer path, yes, but it has the potential to take you to your destination in time given the present traffic conditions. It is also presumable that there are a few people on the same road as you who are not even aware of this alternate route. The question is: which one shall end up as the road not taken?

A normal person would take the side road thinking not many would attempt this route, and hence he can reach faster. A smarter person would postulate, “I bet everyone’s thinking of taking the side route, so there’ll be less traffic on the main” – counter-logic or reverse psychology as you may have it. Then there will always be the guy whose thought pattern will be along the lines of, “What if everybody takes the main road thinking that the others take the side route.”. And the guy who says, “It is plausible that people take the side route thinking that others will take the main road in the false assumption the the rest will use the side route”. True, but there will always be the guy who goes one more level deep. It’s strange how the simplest of choices in life infinitely recurse on to themselves. It’s stranger as to how everything has an application in everything else.

Turtles all the way down

Infinite Turtle Paradox

Chris Nolan, are you reading this?


Written by Chronoz

July 21, 2010 at 2:23 pm

Posted in Tech Funda

Tagged with , , , , ,

14 Responses

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  1. Incepted.

    Why so morbid? :/


    July 21, 2010 at 3:04 pm

  2. You think too highly of people. You should TA sometime. really opens your eyes.

    P.S. Seriously, da, there is too much geek wifi going on. One of these days I’ll have to double encrypt my mind.


    July 21, 2010 at 3:29 pm

  3. Hmmm… I didn’t know it was a recognized paradox; I just thought I experienced this feeling every time I wanted to use L.B. Road. Anyway, the side-route will always be emptier. I bet there’s math to prove this, but I say this out of experience.


    July 21, 2010 at 3:30 pm

  4. you might actually find it amusing, that the series
    1 – 1 + 1 – 1 +….
    actually sums up to (1/2) when “sum” is defined in a suitable sense(more abstract, of course!).
    think about how this is related to that. 🙂


    July 21, 2010 at 3:47 pm

  5. Trust me, I’ve thought about this a LOT. I always hoped one day I would find a formalisation of this notion.

    @semisimplicity: Objection, my lord. I believe that series can sum to anything you want it to. (finally, somewhere to put MA101 to use. :D)


    July 22, 2010 at 4:43 am

  6. @ Prashant: 🙂 The sum neither converges, nor diverges, since it depends on how you club the terms. and that, in math, leads us to define a more generalised (abstract) notion of sum, the so-called Cesaro Sum.


    July 22, 2010 at 6:17 am

  7. Dei Don, a Cesaro sum is just a notion and not a concept. So, there is no point in sayin it “actually” sums up to 1/2 when defined in a more suitable sense, rather it never does, but only “Seems” to sum up to 1/2.


    July 22, 2010 at 7:03 am

  8. We say that it sums to 1/2 in the Cesaro Sense da. there’s no question of seeming! When you go deeper into analysis, there are such generalized (in fact, weak) notions for everything (which coincides with the definitions you know when situations are nice enough). For instance, the |x| function can be made “differentiable” at the origin when “derivative” is defined in a suitable sense, i.e. in a suitable Sobolev Space. If this doesnt convince you, we’ll discuss over gtalk, shreyas isn’t going to be happy with me giving a math discourse here.


    July 22, 2010 at 8:17 am

  9. Basters keep your fight elsewhere and stop spamming my blog.


    July 23, 2010 at 1:30 pm

  10. @Shruthi: Morbid lam illa. Just contemplative. 😛

    @Raps: Don’t use RSA da.

    @Anirudh: Don’t know if there’s math to prove it, but you can always establish it with probability I guess.


    July 23, 2010 at 1:34 pm

  11. And when this contemplation leads to nothing, you fall back on the good old impulse.
    OR maybe toss a coin.

    (I have not seen inception, guess this posts relates to it, but it made sense anyway.)


    July 28, 2010 at 8:01 am

  12. 🙂


    July 30, 2010 at 8:05 pm

  13. @Senior: Not as much related to inception as it is to my intern 😛

    @Dawgster: There’s this maddu song called Dilemmo, which I presume refers to Dilemma. You should try it sometime.


    August 1, 2010 at 8:24 pm

  14. I’m pretty sure Martin Gardner discussed this somewhere. It sure makes games like Poker interesting..


    August 14, 2010 at 12:38 pm

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