What do logarithms mean in layman's terms?

Quora: What do logarithms mean in layman's terms?
 
Great answers already. I'll try to make this one much more simpler with no graphs and less numbers.

Before I explain logarithms, I'll give you an insight on one of the application areas where logs are used.

This is an image of the tragic earthquake that devastated much of Nepal in 2015.  It occurred with a magnitude of 8 on the Richter scale.

Seismologists say an earthquake with a magnitude  2 is equivalent to 1 Ton of TNT explosion.

In this case, we have magnitude 8 on the scale. So, what do you think the equivalent number of TNT explosives would be?

If you thought the answer is 4 Tons, then you're wrong. Interestingly, a magnitude 8 earth quake is equivalent to a detonation of 1 Billion Tons of TNT.

Now, if you wonder how did I get to this number (1 Billion), it is because Richter is a logarithmic scale.


Explanation

We know, 10-8 = 2. similarly the inverse is, 8+2=10.
likewise, 10/2 = 5 and 5*2=10.

So we got inverses for all four operations.

Now, take the example of 10^3 = 10*10*10 = 1000. What is the inverse of this operation(exponentiation) ?

Do we have any way to put this the other way around?
Yes, that's the idea behind logarithms.

3 = log(10) 1000, if you now look in the log book for the number 1000, you should see 3.

In mathematics, the logarithm is the inverse operation to exponentiation.

The above example uses log with the base 10.

Here's another example with log base 5,
5^3 = 5*5*5 = 125 and the log equivalent for  log(5) 125 = 3.

Going back to our discussion about earthquakes, when I said an earthquake with a magnitude  2 is equivalent to 1 Ton of TNT explosion,  the calculation goes like this, 10^2=100=1Ton.

similarly, with a magnitude 8, 10^8 = 1 Billion Tons.

Hope this answers your question.

Carrots, Eye Sight and WW2: Myth and the Fact

Carrots improve eye sight..


Growing up as a kid, I've been told this multiple times and still it is a common belief people have. But is there any correlation between carrots and eye sight?  Of course, carrots provide all necessary vitamins needed for eyes but they really don't improve eye sight.

The story behind this most popular myth goes back to the days of world war 2 where couple of developments happened in Britain.

1. Carrots were locally produced in Britain and it was the only crop that can be produced in abundance with less effort, thanks to Europe's weather round the year. Due to naval blockade set by the Germans, Britain found it difficult to import food from her colonies and British economists predicted a major food shortage is imminent. Since Carrots were produced domestically, they wanted a way  to encourage people to eat carrots.                                                 
2. During the war, British RAF had developed an advanced radar tech that can detect aircraft flybys even in the dark. RAF were then reeling with the problem of sudden surge in identification and hit rates of German aircrafts, especially during night time. Also, with the help from Poles, British now knew to decode enigma which, at that time was considered the greatest breakthrough. But they had to keep this a secret for obvious reasons. Though they knew every German fleet movement and their secret communications, they still had to let Germans take down their targets and give up on the resources to avoid suspicion among Germans.

So, how to use these two tech breakthroughs without causing suspicion? They decided to hit 2 birds with one stone; through massive propaganda that carrots improve eye sight. This way, they convinced the pilots to consume more carrots which happened to explain the reason behind increased hit rate of German aircrafts in the night.

Pilots were supposedly asked to keep munching away carrots which improved their eye sight in dark to extreme levels. Apparently Germans and the whole world took the bait and believed it. And a lot of people continue doing it till date.

How much currency can a country print?

This question has troubled me for years.

In India, The Reserve Bank of India (RBI) is the authoritative central bank that decides how much money have to be printed based on India's monetary policy. The policy that determines the amount of money that should be in circulation in the country. Determination of such monetary policies is pretty complex as lot of factors have to be considered.

So, the pertinent question, since a country can print its own currencies, why can't they print so much so that everyone has enough currency wealth, thereby eradicating poverty completely?

Assume there is a country with only three people living; Ram, Rahim and Gopal and each has personal wealth of Rs  300, Rs 200 and Rs 100.

So the total wealth of this country is 300 + 200 + 100 = Rs 600.

Consider there is only one commodity available in the country that can be purchased by its citizens. Lets take it as this country has total 60 kgs of rice that its people can buy.

By dividing total wealth of the country and total available commodity (rice), we calculate how much should 1 kg of rice cost. 600 / 60 = Rs. 10 per kg.

At this rate, Ram, Rahim and Gopal can purchase 30kg, 20kg and 10kg accordingly using up all their wealth.

One fine day, they get hold of a currency printing machine and decide to print more to double up their wealth. Now, each has a personal wealth of Rs 600, Rs 400 and Rs 200 and the total wealth of the country is now  600 + 400 + 200 = Rs 1200.

The revised cost of rice is = 1200/60 = Rs 20 per kg.  

Now they go to buy the rice. At this new rate, all three could still buy 30kg, 20kg and 10kg rice; only later they realize how futile it was to print currencies to double up their wealth. Though they've increased the personal wealth, they couldn't buy more kgs of rice than before.


Merely printing more currency will do no good to anyone. If they really wanted to become rich, they should've increased the production of rice. With no increase in production and with their wealth doubled, the value of the currency got halved.

You can extend the same concept to any country. For eg, if RBI decides to print more currency and have it in circulation, every one will get money out of nowhere, the cost of goods would also increase accordingly; since everybody is has more cash, everybody would want to buy a Mercedes and the price of a Mercedes would also increase. Simply put, the law of supply and demand.

This could lead to increase in prices of all goods in the country causing inflation and some extreme cases, hyperinflation.

    (to buy a loaf of bread) 
The economic scene of Zimbabwe in 2015 is the best case example of hyperinflation. Due to printing of more currency than required and with no increase in production, the prices of goods have skyrocketed.
                                                          
The price of one loaf of bread cost 35 million Zimbabwe dollars and their currency has a value of 35 quadrillion dollars with respect to 1 USD.


Therefore to become rich, the country (its people) has to increase its production. That's the reason why countries are crazy about Gross Domestic Profit-GDP. (a measure of production).


  

How is a currency valued against another

 Who decides 60 Indian Rs is worth 1 USD. What factors do they consider to weigh currencies against each other. Why does it have to revalued after each passing day.These were some of the unexplored questions I had in mind. Whenever I try to look for an answer, I never found any which made me think this is something only an economist can comprehend but is certainly not.

Here is a simple story-like explanation on how a currency is valued against another.

Kay lives in Xioma, a small country bordered by the seas. Xioma prints its currency(Xs) in only one denomination that is 10. Kay takes home a daily wage of Xs.100 which is nothing but 10 Xiomic currency notes. One fine day, Kay, a chocolate lover, visits a chocolate shop that was newly opened in his neighborhood. There, a chocolate bar costs Xs.20, so Kay hands in two 10 currency notes to buy a bar of chocolate. The chocolate bought was of moderate quality but considered best in his locality.

Now, Kay learns about a new chocolate shop in a distant island nation that sells quality chocolates and decides to visit the store. There, Kay faces a problem, a single bar costs 500 and the store accepts 100 currency notes only. He did try to give the shop guy fifty 10 currency notes which the shop guy refused to take. Instead the shop guy asked for a five 100 currency notes for a bar of chocolate worth 500.

So Kay finds a guy David, who exchanges ten 10 currency notes for one 100 note. That way, by exchanging fifty 10 notes, Kay now has five 100 notes. The chocolate bought for 500 was too good that everyone from Kay's locality visited the shop and the shop's popularity grew eventually which means there is now a demand for 100 currency notes.

Everyone who want to buy the chocolate for 500 visited David first, as only he can exchange currency notes. Due to overgrowing popularity of the chocolate and demand for 100 currency notes, David now decides to exchange one 100 currency note for twelve 10 notes which in other words, a 100 currency note of the island nation is worth 120 Xiomic notes.

So now,

Did Kay lose money? No,
Did David gain money? No,
Did the value of Xiomia currency degrade? No
Did the cost of the chocolate increase? No

then, what has changed? the demand for 100 currency notes. 

A currency gets valued and devalued based on its demand and demand is monitored on daily basis. So when we say Rs.60 makes up $1, it means there is more demand for dollars.

Just by interchanging Chocolates with Crude Oil, Xiomia currency with INR, 100 currency note as single USD, one could pretty much understand  this currency valuation process at least at the top level given that it is even more complex.