Lampu Thompson

Lampu Thompson : Misalkan terdapat sebuah lampu, yang dilengkapi dengan tombol. Jika menekan tombolnya, lampunya akan menyala. Tekan tombolnya lagi, lampunya akan mati. Mari kita bayangkan ada seorang dengan imajinasi tinggi yang menyukai menekan-nekan tombol lampu tersebut. Pertama, dia menyalakan lampu itu, satu menit kemudian, dia mematikannya. Setengah menit kemudian dia menyalakannya kembali. Seperempat menit kemudian dia mematikannya kembali. Seperdelapan menit kemudian dia menyalakannya lagi. Dan seterusnya, dia menekan tombol tiap-tiap waktu setelah menunggu tepat setengah periode waktu sebelumnya. Tentunya, anda akan teringat pada Paradoks Zeno mengenai cerita Achilles dan si Kura-kura.

Pertanyaan : Pada masa akhir dua menit, apakah lampu itu akan nyala atau mati?

 

English Version :

THOMPSON’S LAMP: Consider a lamp, with a switch. Hit the switch once, it turns it on. Hit it again, it turns it off. Let us imagine there is a being with supernatural powers who likes to play with this lamp as follows. First, he turns it on. At the end of one minute, he turns it off. At the end of half a minute, he turns it on again. At the end of a quarter of a minute, he turns it off. In one eighth of a minute, he turns it on again. And so on, hitting the switch each time after waiting exactly one-half the time he waited before hitting it the last time. Applying the above discussion, it is easy to see that all these infinitely many time intervals add up to exactly two minutes.

QUESTION: At the end of two minutes, is the lamp on, or off?

ANOTHER QUESTION: Here the lamp started out being off. Would it have made any difference if it had started out being on?

About p4mriunmmakassar

It is the one of institution of educational employee and educator in Makassar (formally named Ujungpandang). Now it has run Indonesia mathematics realistic education in South Sulawesi.

Posted on November 2, 2010, in Soal Pemecahan Masalah. Bookmark the permalink. Leave a comment.

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