Category Archives: Pengetahuan

Ladies Fanning Themselves… Is it Harmless?

A lady with her fan

Have you ever seen a lady fanning herself? When she fans herself, she naturally feels refreshed. One might think that this occupation would be absolutely harmless for all others present that they must be only grateful to the lady for “cooling” the air. Well… before you agree on the statement we should really see whether this is really so.

Why do we feel cooler when we fan ourselves? This is the simple explanation: When air is fanned onto our faces the air in direct contact with our faces warms up (Yes it actually warms up instead of cooling off!! Remember that! It is contratry to what you expect, isn’t it?? 😉 ). It warms up because the molecules in the air collide with one another (and thus with our face too) more violently due to the fanning. These colliding molecules release energy in the form of heat. It is this warm invisible mask of air that “heats” the face, in other words, prevents it from shedding any more heat. When the air around is still, this “warm” mask is gradually pushed up by the cooler and heavier air from the surrounding space. When this “warm” mask is eventually fanned away, our face comes into contact with more and more new portions of non-warmed air, to which it sheds its warmth. That is how we cool ourselves. It is to some degree analogous to something like if we soak our hands in hot (not boiling though) water for a while then we immediately soak them in lukewarm water, our hands will feel cooler even if the temperature of the lukewarm water is higher than the temperature of the surrounding air. In short, the rotating contacts between our faces and the warmed and cooler air that give the fresh and cool sensation to our faces.

Now consequently when continously fanning herself, the lady whisk the warmed mask of air, replacing it with cooler air over and over. This portion of cooler air  warms up when again is fanned by the lady before it is eventually whisked away and replaced by still another portion of cooler air. It is repeated over and over again. Fanning, thus accelerates air mixing and helps to quickly equalise the temperature throughout the room.  In other words, it refreshes the possessor of the fan at the expense of the cooler air enveloping the other people present.  Like the explanation in the previous paragraph, she feels cooler because she is first exposed to warm air before the cooler air replace the whisked warmed air. The whisked warmed air will proceed to the surrounding space and very very slightly raise the surrounding temperature. Of course this warmed air will not harm anyone let alone kill him or her, the persons next to the fanner will not even feel the temperature rise, but it might not be the case if there are so many ladies fanning themselves in an enclosed room with poor ventilation!! 😉

Post Script:

For your information, I am not a sexist. I know that it is not only a lady that fans herself, a gentleman can do the same on  newspaper or something else in place of a fan.. 😛

Reading A Fresh Daily Twice A Day?

Are you kidding me? That remark might come across your head soon after you read the title above. How come you read a fresh daily twice a day? Is it really a daily or perhaps I mistake it for a semidaily?? No, if I said a daily it is really a daily which means it is published once a day. However there is a way for you to read a fresh daily twice a day! Okay, before you insist on your denial you should heed my explanation below first before you  make your own conclusion whether my explanation makes sense or not. 😉

Suppose, the future longest suspension bridge in the world that spans the Sunda strait connecting the island of Sumatra and the island of Java is already completed. And suppose the bridge also carries the double railway tracks which are parts of Medan-Surabaya railway tracks. Here it is, daily at noon, a train pulls out from Surabaya for Medan. Also daily, again at noon, another train leaves Medan for Surabaya. Suppose the entire journey takes a week (seven days). The simple question is: How many trains will you meet on your way from Surabaya to Medan?  You probably rush to give the answer: seven. That’s wrong though. Besides meeting on the way the seven trains that will leave Medan after you depart from Surabaya, you will also meet the trains in your direction already on the way at the time you left! Consequently, the right answer is not seven, but fourteen instead!

Let’s now proceed further. Each Medan train (a train which leaves Medan for Surabaya) has on board fresh daily Medan newspapers. If you are interested in Medan news, you will naturally buy fresh papers at each stop (suppose each time two trains about to pass each other they make a brief stop).  How many fresh newspapers then will you buy on your a week journey? I guess that by now you will give the correct answer of fourteen. After all, each train you meet brings a fresh paper, and because you meet fourteen trains, it means you read also fourteen fresh papers! But since you will be travelling only a week, you will be reading a fresh Medan daily twice a week! How’s that??

This seems a surprising paradox, doesn’t it? For a short time, you might think “Yeah… you are right. But how come it goes like that?” But actually the logic behind this case is readily understood. The first Medan train you meet will bring a fresh (ehm…. I mean ‘a stale’) Medan newspapers from seven days ago!*) Since you head in their direction while they head in your direction it means your speed is doubled in reference to their perception and vice versa. Thus  it means that you will meet the fourteen Medan trains one after another at the rate of two trains a day instead of one train.  Aha! Now after the brief explanation I hope everything is now crystal clear for you to understand why is it possible for us to read a fresh daily twice a day! 😛

The last question is why am I telling you this? This case might help you understand to some extent the properties of Doppler effect in particular or some properties of the sound in general. That is if you are interested in very basic physics in entertaining ways! 😉

P.S.:

*) The first Medan train you meet is the one you meet at the initial point of your journey in the Surabaya station at the Medan train’s arrival meanwhile the last Medan train you meet is the one that you meet at the last midnight (suppose all trains travel at the same and constant speed) before you arrive at the Medan station. The Medan train you meet at the Medan station when you arrive is counted out since the Medan daily is ubiquitous in Medan and you don’t need to buy it aboard.

Kamus Besar Bahasa Indonesia vs Advanced Learner’s Dictionary

Empat Dari Lima Advanced Learner's Dictionary Koleksi Saya...

Bagi anda yang pernah mengecap pendidikan atau dengan kata lain bagi anda yang terpelajar atau setidak-tidaknya mengaku terpelajar kemungkinan besar di rumah anda mempunyai minimal sebuah kamus, entah itu kamus dwibahasa Inggris-Indonesia, Indonesia-Inggris (atau gabungan keduanya) yang banyak bertaburan di toko-toko buku, atau mungkin kamus ekabahasa atau satu bahasa seperti KBBI (Kamus Besar Bahasa Indonesia) atau kamus monolingual Bahasa Inggris mulai dari yang sederhana hingga yang supercanggih seperti Merriam-Webster’s Collegiate Dictionary ataupun The Chambers Dictionary dan sebagainya. Sayapun juga mempunyai (lebih tepatnya: mengkoleksi :mrgreen: ) banyak kamus di rumah baik yang dwibahasa maupun yang ekabahasa (Indonesia, Inggris, Perancis/Le Petit Larousse, Jerman/Langenscheidt Taschenwörterbuch Deutsch als Fremdsprache). Namun dari koleksi kamus monolingual/ekabahasa yang saya punya yang paling mengesankan adalah seri Advanced Learner’s seperti foto di sebelah ini.

Di dunia ini, mungkin hanya ada 6 pembuat kamus seri Advanced Learner’s ini, lima dari Inggris Raya dan satu dari Amerika Serikat. Mereka adalah: Oxford Advanced Learner’s Dictionary, Cambridge Advanced Learner’s Dictionary, Collins Cobuild Advanced Learner’s Dictionary, Macmillan English Dictionary for Advanced Learners, Longman Dictionary of Contemporary English (dari Inggris Raya) serta Merriam-Webster’s Advanced Learner’s Dictionary (dari Amerika Serikat). Longman Dictionary of Contemporary English sebenarnya bukan mengklaim dirinya sebagai bagian dari “Advanced Learner’s Dictionary” namun jikalau anda mempunyai kamus ini anda akan merasakan bahwa gaya penyusunan kamus ini sangat mirip dengan rekan-rekannya (atau lebih tepatnya saingan-saingannya) yang Advanced Learner’s Dictionary itu. Saya sendiri mempunyai lima dari enam kamus seri Advanced Learner’s ini, yang tidak saya beli adalah Collins Cobuild Advanced Learner’s Dictionary yang menurut saya pribadi  kualitasnya agak tertinggal dibandingkan saingan-saingannya. Di dalam foto hanya terpotret empat saja dari lima kamus yang saya punya karena yang Macmillan English Dictionary for Advanced Learners berada di rumah saya di Jakarta, jadi untuk sementara tidak dapat dipotret… :mrgreen:

Lantas kenapa seri Advanced Learner’s ini menurut saya sangat bagus? Tentu itu disebabkan karena beberapa hal. Pertama, karena cakupan katanya termasuk yang sangat sangat lengkap walaupun masih kalah jauh dengan Merriam-Webster’s Collegiate Dictionary ataupun The Chambers Dictionary, namun begitu kamus-kamus Advanced Learner’s ini boleh dikatakan sudah sangat lengkap. Cakupan kata-kata dan entri-entrinya sudah mencakup istilah-istilah teknis, akademis, idiom, kata kerja berpartikel (phrasal verbs), bahkan kata-kata gaul atau slang, kata-kata informal serta kata-kata tabu juga sudah sangat banyak tercakup. Inilah bedanya antara kamus-kamus besar Bahasa Inggris dengan KBBI, jikalau KBBI menganaktirikan kata-kata gaul ataupun prokem ataupun apalah, kamus-kamus besar Bahasa Inggris termasuk seri Advanced Learner’s ini justru menganggap kata-kata tersebut sebagai bagian dari Bahasa Inggris yang perlu juga diketahui. Alasan kedua, setiap kata dalam kamus ini dijelaskan atau didefinisikan dengan serdehana namun tetap jelas dan akurat. Hal tersebut dikarenakan setiap definisi dari kata atau entri hanya dibatasi menggunakan 3000 kata Bahasa Inggris yang sangat basic, sehingga dijamin tidak akan membingungkan pembacanya bahkan bagi yang sedang belajar sekalipun. Alasan ketiga, seri kamus ini sangat kaya dengan ilustrasi. Ilustrasi-ilustrasi ini sangat membantu untuk menjelaskan kata-kata atau entri-entri yang agak sulit jika hanya membaca definisi-definisi yang ada. Hal tersebut tentu saja berbeda dengan KBBI yang tidak ada ilustrasi sama sekali. Alasan keempat, seri kamus ini juga menampilkan contoh-contoh kalimat yang komprehensif yang sangat membantu terutama untuk mengaplikasikan kata-kata yang sulit ataupun idiom-idiom yang sulit ke dalam kalimat ataupun ucapan sehari-hari. Sementara KBBI? Hmmm…. walaupun dalam Bahasa Indonesia juga banyak sekali kata-kata sulit namun jangan harap akan diberikan contoh-contoh kalimatnya. 😦

Nah, begitulah alasan-alasan kenapa kamus-kamus seri Advanced Learner’s ini menurut saya sangat bagus penyusunannya. Bagi anda yang berminat mungkin anda cukup memiliki salah satu saja, kecuali jikalau anda maniak mengkoleksi buku seperti saya boleh membeli semuanya..  (maksudnya saya cuma suka mengkoleksi aja.. mbacanya sih nggak… :mrgreen: ). Advanced Learner’s Dictionary ini memang pada awalnya memang dirancang untuk para murid-murid yang bukan penutur asli Bahasa Inggris walaupun kini orang-orang yang penutur asli Bahasa Inggris juga banyak merasakan manfaat dari seri kamus ini. Seri kamus ini bermula ketika A.S. Hornby seorang guru Bahasa Inggris di Jepang sebelum Perang Dunia II berhasil mengidentifikasi kesulitan-kesulitan murid-muridnya yang tentu saja bukan penutur asli Bahasa Inggris dalam mempelajari Bahasa Inggris. Dari sinilah Hornby menyusun kamus ekabahasa Bahasa Inggris yang disusun sesuai dengan kebutuhan murid-murid yang belajar Bahasa Inggris. Hornby pertama kali menerbitkan cikal-bakal kamus Advanced Learner’s Dictionary-nya di Jepang tahun 1942, walaupun masa-masa perang sangat menyulitkannya dan bahkan Hornby harus meninggalkan Jepang. Namun begitu, di tahun 1948, Hornby berhasil menerbitkan kamus edisi pertamanya untuk seluruh dunia dengan nama “Oxford Advanced Learner’s Dictionary of Current English” (saya masih punya kamus edisi pertama tersebut di rumah saya di Jakarta yang dulu dipakai oleh kakek saya!) yang merupakan cikal-bakal dari “Oxford Advanced Learner’s Dictionary” yang modern sekarang ini. Kamus ini dalam beberapa dekade menjadi kamus yang paling banyak dibeli di seluruh dunia sehingga mendorong pesaing-pesaingnya untuk menerbitkan jenis kamus serupa.

Jadi, di dalam dunia kamus internasionalpun juga terjadi persaingan yang ketat. Tidak heran jikalau di setiap edisi berikutnya kamus-kamus ini menjadi lebih lengkap, lebih menarik dan lebih dinamis lagi agar tidak kalah dengan pesaing-pesaingnya. Namun, mungkin karena faktor persaingan itulah justru yang ikut membuat kualitas kamus ini menjadi sangat prima sekarang dengan cetakan yang penuh warna (tidak seperti KBBI yang hingga beberapa edisi sekarang ini terlihat sangat statis…. 😦 )

Blind Spot

I was not pulling anybody’s leg if I said that in our field of vision we have a section we fail to see at all, though it is right before our noses.  Indeed nobody ever notices in his or her lifetime such a signal defect. Okay, if you don’t believe me, the pic above is a simple experiment to show that there really is such a thing!

See the picture above? Position your face very close to your computer screen, meanwhile cupping or covering your right eye, and look at the black circle on the right. Gradually and gently move your face away from the screen (with your left eye still focusing on the larger black circle on the right). At one moment the smaller black circle will vanish without trace . You won’t see it, though it is still within the limits of your field of vision. But if you distract the focus from the black circle on the right to meet the smaller black circle on the left, it will return to your sight. As soon as you focus back on the right black circle, the one on the left will again ‘disappear’!

Now, let’s switch the object. Position your face again close to your computer screen, this time you cup your left eye and focus on the cross (with the smaller black circle) at the left. Again, gradually move your face away from the screen. This time, at one moment the large black circle at the conjunction of the two white circles will vanish “into thin air”. It is still in the range of your field of vision but you fail to see it! Even you will see that the two white circles at the right will be quite distinct!

This phenomenon was first observed by a Frenchman, Edme Mariotte in the 17th century. The area where you fail to see an object even it is in the range of your field of vision is called the “blind spot” or scotoma. This is the area where the optic nerve enters and has no sensitive visual cells. We never notice the presence of this blind spot because we have been living with it since birth thus we have grown accustomed to it. Do you wear glasses? Good! Then you might like to try the following experiment. Glue a scrap of paper to one of the lenses, only not quite dead centre. For a few days (a week at longest) it will be a nuisance, but after approximately a week you will even cease to notice it at all! Believe me! 😉 Or if you are rich enough or you care to bother yourself by cracking your own glasses  (don’t break them just crack them)  you will notice that the crack will annoy you at the beginning. After a few days you will even forget to buy new glasses until someone tells you to do so.  Yes, it is a matter of habit that is responsible for our being “blind” to our blind spot. Then one must note that the blind spots of either eyes correspond to different places in the two fields of vision. Consequently, with two-eyed vision, there is no deficiency in the range they both cover. It even makes more sense to why we are always “blind” to our own blind spot because mostly we see everything around us without an eye patch! 😉

P.S.

If you want to see another experiment on the blind spot you can beam yourself (StarTrek mode: ON) onto the Wiki’s page about blind spot.

Jika Diskon 50% + 50% Tidak Berarti Gratis…

Diskon dual produk dasi di M*tahari Department StoreKira-kira seminggu yang lalu (tanggal 1 Mei) saya sekeluarga berkesempatan untuk mengunjungi BIP di Jalan Merdeka untuk berbelanja sedikit barang-barang keperluan sehari2 dan juga untuk melihat aksi demo memperingati tanggal 1 Mei sebagai hari pekerja internasional. Kami juga mengunjungi M*tahari Department Store yang berada di plaza tersebut karena kebetulan sayapun ingin membeli dasi yang berwarna putih. Maklum, saya adalah orang yang nggak suka memakai kemeja putih. Kemeja saya kebanyakan berwarna-warni, dan beberapa di antaranya berwarna gelap (bahkan hitam). Untuk itu di department store tersebut saya membeli beberapa buah dasi yang berwarna terang agar terlihat kontras dengan kemeja warna gelap saya.

Ketika saya sampai pada rak display dasi (gambar sebelah) kebetulan sekali ada program dual discount yaitu 50% + 20%.  Dual discount tidak sama dengan double discount loh… Kalau double discount kedua komponen diskon haruslah sama (identik), contoh: 20% + 20% atau 30% + 30% dst. Sedangkan dual discount, kedua komponen tidak perlu sama, contohnya adalah seperti gambar disebelah: 50% + 20%. Jadi setiap double discount adalah dual discount namun dual discount belum tentu double discount.

Tetapi nanti dulu nih, baik yang double discount maupun yang dual discount sebenarnya perhitungannya tidak sama dengan perhitungan aritmatika. Jikalau menurut aritmatika diskon dual 50% + 20% = 70%, maka tarif efektif gabungan kedua komponen diskon tersebut ternyata kurang dari 70%! Untuk membuktikannya mari kita hitung. Jikalau misalnya kita membeli celana seharga Rp. 100.000,- jikalau mendapat diskon 70% kita hanya perlu membayar Rp. 30.000,- sedangkan kalau dengan tarif dual discount seperti di atas, mari kita hitung berapa yang musti kita bayar:

Harga Awal: Rp. 100.000,-
Potongan ke-1: 50% ( 50% x Rp. 100.000,-) Rp.  50.000,-
Harga Tersisa Setelah Diskon Awal: Rp.  50.000,-
Potongan Ke-2: 20% ( 20% x Rp. 50.000,- ) Rp.  10.000,-
Harga Tersisa Setelah Diskon Dual: Rp.  40.000,-

Jadi jelas terlihat, bahwa harga yang harus dibayar adalah sebesar Rp. 40.000,- atau kita hanya mendapatkan diskon 60%! Hal itu disebabkan karena secara aritmatika, langsung mendiskon 70% tidak sama dengan mendiskon satu-satu 50% dan 20% dari sisanya. Begitu juga jikalau ada dual discount 40% + 30%, diskon gabungan efektifnya tidak akan sama dengan diskon tunggal 70% dan juga bahkan tidak akan sama dengan diskon dual 50% + 20%! Pada diskon dual 40% + 30%, diskon gabungan efektifnya hanya sebesar 58%!

Sebenarnya dari hitungan di atas dapat dengan cukup mudah diketahui “rumus” untuk mencari diskon gabungan efektif untuk setiap diskon dual (tidak perlu saya paparkan di sini selain itu saya juga sebenarnya sedang agak malas mengetik :mrgreen: ) yaitu jika terdapat diskon dual X% + Y% maka “rumus” diskon gabungan efektifnya adalah: 1 – (1-X%) (1-Y%). Anda juga dapat dengan mudah mengganti X dan Y dengan sembarang angka diskon tidak perlu saya contohkan lagi di sini, atau anda bisa memasukkan dari contoh di atas, X = 50% = 0,5 sedangkan Y = 20% = 0,2.

Nah, akhirulkata, saya mengusulkan kepada seluruh department store di Indonesia dan juga yang lainnya agar membedakan penulisan diskon dual dengan tidak menggunakan tanda “+”.  Misalnya gunakanlah tanda “&” (contoh: 50% & 20%) sebagai pengganti tanda “+”. Hal ini penting untuk membedakannya dengan “50% + 20%” yang secara aritmatika memang seharusnya adalah 70%. Jadi jangan sampai mempunyai kesan bahwa para department store tersebut ingin mengelabuhi pelanggannya dengan diskon yang sebenarnya diskon gabungan efektifnya relatif jauh lebih rendah dibandingkan diskon yang tertulis…

Raindrops That Might Kill Like A Bullet…

A few days ago, in the early morning I listened in to the  weather forecast telling us that we would have a hot sunny day for the whole day long, actually indeed we were all scorched by the relentless blazing  sun until about 4pm when, suddenly the skies turned grey and the masses of cloud gathered  up. All of sudden, not within 10 minutes, the lightnings began to flash away, followed by roaring thunders. In no time rain started to fall and soon it bucketed down.

As I looked out through the window (I was still in the office) I was thinking to myself (Heck I have no idea why every time it rains while I’m not having anything else to do, my so-called creative thinking always rushes readily in to my head) that led to this writing. I was thinking to myself, what if there is no atmosphere to protect us from the falling droplets? What would happen? Readers might think “are you kidding me??” What is so dangerous about tiny raindrops?? They can’t hurt us no matter how hard it’s tipping down!

Okay, don’t readily jump to the conclusion like that, remember my article on the falling cat? (Sorry, it’s written in Bahasa Indonesia for those who are English readers) The atmosphere acts on the falling cat by preventing it from falling with  ever-increasing speed. It acts like a buoy (more or less)  on the cat. And of course if it acts on the cat to “slow down” the fall speed, the atmosphere also acts on the raindrops in the same manner. So that’s why in the absence of the atmosphere raindrops will fall down with ever-increasing speed! As we know, the speedier thing that hits us, the more force would work on us no matter how small it is.

To understand the nitty-gritty of this case, assume this simplified scenario that we can live on the planet where there is no atmosphere to breathe in, and we survive cosmic rays battering us. Suppose, clouds form in the absence of the atmosphere (which is practically impossible). The droplets of rain fall from 4000 metres overhead. Let’s assume that a droplet of rain weighs about one gram. Let’s see what is the speed of the raindrop when it hits our heads? Using a formula of the falling body problem we can determine the raindrop’s speed when it hits our heads, it then would be: v = \sqrt{2gh} or when we substitute the data given for the variables it’s gonna be v = \sqrt{2 \times 9.8 \times 4000} or 280 metres per second that it approxiamtes to 1000 kilometres per hour! (g is the earth’s gravity constant which is 9.8 m/s2. Now to see how much potential ‘destructive’ work it has on us, we have to find the energy kinetic of the raindrop: E_{k} = \frac{1}{2} m v^{2} , Ek denotes the kinetic energy, 1 gram of droplet equals 0,001 kilogram. So, if we put the data into the equation we’re gonna have E_{k} = \frac{1}{2} \times 0.001 \times 280^{2} that approxiamtes to 40 joules.

Forty joules? That’s it? Yeah…. but remember it only comes from a single raindrop. If you are battered by a thousand raindrops, roughly calculated that the force that would work on you will be 40,000 joules! To see how monstrous 40,000 joules is, let’s compare it to the kinetic energy possessed by a 150 kg motorbike that runs at 80 km per hour *).  It has a kinetic energy of E_{k} = \frac{1}{2} \times 150 \times 22^{2} or 36,300 joules. So, a thousand raindrops would have more kinetic energy than a 150 kg motorbike running at 80 kph does if there was no atmosphere to buoy the falling raindrops!

That explains whenever it rains why should we be very grateful to be saved by the atmosphere from the falling droplets of rain, whilst in the absence of the atmosphere  the tiny droplets would potentially kill us like a bullet, or at least they  could hurt us very badly!

P.S.

I do miss my high-school physics class now 😦

*) 80 kph equals 22 metres per second.

Is It Possible for Archimedes to Lift The Earth?

Arhimedes Trying to Lift The Earth“I would lift the earth if I had a point of support” that is a saying of legendary Archimedes, the genius of antiquity who discovered the laws of the lever. He wrote this claim to his friend, King Hiero (Some call it “King Geiron”) of Syracuse. He added that if there be another earth in the space he would go there to prove his claim!

Archimedes knew that even the weakest of force could lift the weightiest of an object by using a lever. One had only to apply this weakest force to the lever’s longer arm and that’s what would make the shorter one to act on the weightiest load. He therefore thought that by pressing with his hand on the extremely long arm of the lever he would be able to lift a weight which in this case is equivalent to that of the mass of the earth.

Archimedes might be right about his laws of the lever but the problem was that in the times of antiquity nobody knew the mass of the earth, and neither did Archimedes! If only he knew the mass of the earth, Archimedes would be likely to eat back his words. Imagine for a moment that he had at his disposal another earth and also the point of support he looked for. Further imagine that he was even able to manufacture a superlong lever that extended over  a great great distance in the space required. I wonder if you can figure out the time he would need to lift a load as massive as the earth, by at least a centimetre? He would need 30,000,000,000,000 years!!

Today scientists know the Earth’s mass. The earth possesses the mass of 6,000,000,000,000,000,000,000 metric tons or tonnes. Suppose Archimedes could lift 60 kilos directly, to lift the earth he would need a lever with a long arm that would be longer than the shorter arm by:

100,000,000,000,000,000,000,000 times! (that is \frac{6 \times 10^{24} \: kg}{60 \: kg} ).

You can easily figure it out that to have the end of the short arm rise by a centimetre, the other end must delineate through space the huge arc of

1,000,000,000,000,000,000 km!! ( that is  1 \: cm \: \times 100,000,000,000,000,000,000 \: times )

That is an unimaginable distance which Archimedes would have had to push the lever to lift the earth by just one centimetre! As a comparison the earth-sun distance is “only” 150,000,000 km apart. A tiny figure compared to that of the huge arc would Archimedes make. So the next question would be how much time would he need? Presuming he could have lifted 60 kilos one metre in one second – the work of almost one horsepower and of course naturally a man could only work much less than one horsepower! – to lift the earth by a centimetre, he would even need

1,000,000,000,000,000,000,000 seconds!! (that is  \frac{6 \times 10^{24} \: kg}{60 \:kg} \times \frac{1\: cm}{100 \:cm} \times 1 \: second )

For those who like to do simple arithmetic problems it is not hard to convert that figure above into the unit year which is equivalent to about 30 million million years! As a comparison scientists predict that our solar system would not last longer than approximately 10 billion years from the cradle to the grave. So, even if Archimedes lived past 100 years he would not have lifted the earth by much as even the thinnest of hairs. His effort would be so-called worthless since he could only lift the earth by an unnoticeable displacement in the eyes of the crowd. Even if he supposed to be able to zap in the speed of light – the nature’s fastest – he would successfully have lifted the earth by a centimetre only after ten million  (10,000,000) years of pushing! Phew!! 🙂