Maths Puzzles - Probability

 A friend sent me this. 

One Year Of Covid

It's been a year since we have had this pernicious virus in our lives. At the end of the year, since last March when India was locked down, I wanted to see what I had done - a kind of self appraisal. A friend of mine asked me this question: what was I upto. And I couldn't give him any answer, I was blank.

I discussed this with another friend and she helped me put things in perspective. I take care of my elderly mother with a maid and a nurse. Household chores including cooking, getting groceries, getting medical supplies including diapers were difficult in the months of April and May 2000. We were just getting acquainted with "social distancing", shops were open only for a few hours each day, Amazon wasn't delivering.

My friend helped me realise that I had managed my 2 households fairly well never running out of stocks (well I did almost run out of shorts for myself but then another friend helped me in the nick of time), never missing salary payments to my household help.

Then I helped a friend prepare for her MRCS exam - the exam, conducted by UK, tests proficiency in candidate's knowledge of surgery. My friend passed the test in her first attempt. 

My mother had had her wrist fractured last year and I had to figure out whether to go for surgery in the middle of Covid or resort to plaster of paris. Half the orthopaedic surgeons suggested the former, half the latter. I got my mother through this predicament and her fracture is now healed (thanks specially to my surgeon friend and another neighbour who is an orthopaedic surgeon).

I managed these in times when people were getting infected, hospitalized around me and when couple of relatives died. 

And I made some money along the way despite not having a job, despite having plenty of expenditure each month.

Looking back, I see that it wasn't a bad performance. 

India Vs UK

A friend said to me after yesterday's T20 cricket match between India and England:

India is punching its weight in the world.

I am rather struck by seeing how India is dictatating what it does, and punching above its weight in the world. We hear that India is refusing to export AZ vaccine to the UK because of some problems, whatever that is. That has got the government here all in a frenzy about whether it can reach their promised targets by the summer.

Who would have thought some 40 years ago that India would tell the West what it wants and can do to help them?

Gone are the days when India was at the mercy of others for science and technology. Let's not even talk about cricket. As someone said, India is the centre of the cricket universe! England and Australia have just had some bitter medicine.

 

I replied:

Well, India still has miles to go. I would say England punches above its weight consistently. A country (is England really a country in the first place or just a part of UK) of about 5 crore people facing a country of 130 crore in cricket. The results don't seem to indicate a 5 to 130 handicap.

Let's not even get to football. And same in most other spheres. 

UK makes India look like the David (instead of like Goliath).  That's embarrassing.

My friend wrapped it up:

England is a football nation. The irony however is that it has never won the World Cup or even the Euro Cup in football. Aa far as cricket is concerned, it won the World Cup for the first time only in 2019 after a dramatic and controversial finish. In tennis, it produced a British (Scottish) champion after 72 years.

So England or shall I say UK for now (until it splits and becomes England only), it is definitely not punching above its weight in sport. Just trying to, but not quite reached there yet.

EK215

Interesting flight route: Dubai to Los Angeles straight across the North Pole.

Note of caution: 

This post, like it's predecessor, does not talk about any shopping in Dubai nor about actors in Hollywood. Feminine people can skip this post.

The flight below, EK215 from Dubai to Los Angeles, flies straight up from Dubai over Kara sea, Russia (about 70E, 80N) and then over North Pole and then down the other side (about 120W, 80N) and then down Canada to LA. I tracked the flight from about 6PM IST to 7:30PM IST. The lat-long values during that period are given above. In both cases the latitude is about 80N. At the start of tracking, I saw it on this side of the pole in flightradar24. At the end of the period it was on the Canadian side (having crossed the North pole - while I was having my dinner). Amazing. But the more interesting part was that the flightradar24 route tracking isn't good beyond 80N. It's unable to rotate the earth and zoom into 80deg+ latitudes and locate/show polar flights. 

I was irritated. So I googled and figured that Google Earth could do just that and downloaded it. So in the picture below in the 3rd and 4th parts I marked the the starting point and the final destination (which goes over the 2nd lat-long) in Google Earth. Turned out to be a lovely way to track EK215. I wish flightradar24 could do this. The starting point shown in the 3rd picture is Dubai: you can see Saudi Arabia. The point 6395km from Dubai is where the flight was when at 6PM. The points marked off in Google Earth are approximate. In the 4th part of the picture, I have tracked the route on Google Earth till LA. You need to zoom in to the 3rd and 4th parts in the picture to understand better.

The 1st and 2nd parts show the flight route on flightradar24 at 7:30PM IST just after it had crossed the North pole. The 2nd picture is just a zoomed out picture of the first. Unfortunately I don't have the 6PM flightradar24 picture when the flight was near Kara sea on the Russian side.

(You can also click this link to see the same 4part picture.

https://drive.google.com/file/d/1EsJ02lM20ErH7qOnh56WpuQb-A8uG99O/view?usp=drivesdk)

For the first part of this article on interesting flight routes read https://vbala99.blogspot.com/2015/05/interesting-flight-routes.html

The flight stats for this flight are here: https://www.radarbox.com/data/flights/EK215/1549352072/log

Male And Female Response

A friend of mine teaches art to children. The youngest of her students is 5 years old, a girl - Aadya. Another of her students is a boy, 6 years old - Udit.

My friend told me that Aadya always wears pants or shorts and rarely wears skirts or frocks - the child's reason being that her dresses have become too tight. And Aadya's parents and grandparents affectionately call her Aadu. And my friend also told me that Aadya hates to be called Aadu by anyone else. 

Hearing all this, my hands were itching. I had to do something.

I am a connoisseur of art and a fairly accomplished painter.  So I sat down and made a sketch of Aadu.

She is wearing a skirt and her name is there below the sketch I drew of her. My friend showed Aadu this sketch and said that a friend had drawn this. 

Aadu apparently blushed and smiled cutely and asked her teacher, my friend, to thank me. She didn't seem annoyed that I had referred to her as Aadu.

Next I drew a portrait of 6 year old Udit. My friend showed Udit this picture below.

Udit responded that the picture didn't look like him. His hair and teeth were missing and so were his spectacles, he pointed out to his teacher. He wasn't impressed with my efforts.

I wondered.  How different the two models' responses were.

Aadu's response was feminine. She liked the fact that I took the trouble of drawing her and called her Aadu. She was touched.

Udit judged my drawing the male way. That it was terrible and had no likeness to him.

Female and male responses are so different even at this age. What is relevant here? The quality of the sketch in isolation? Or the fact that someone took the trouble to draw you? 

I can proudly say that I am 100% male. My response would be exactly the same as 6 year old Udit's.

Additional reading:

https://drive.google.com/file/d/1eDoICtGSWVkmRIKuGc9yJb-k2WUzAPTJ/view?usp=drivesdk

Inefficient By Choice

 Decades ago, my place of work was the guesthouse of my employer's client. Couple of the client's employees, middle-aged, also used to stay in the same guesthouse. One of them, a Telugu gentleman, was pally with me. He told me that he found it useful to be inefficient in his routing algorithm. When he could do two or more things optimally, he would choose a suboptimal route - so he would end up doing his chores one at a time. 

His explanation was that when you have surplus time, you need to find a way to fill it. What better way than to be intentionally inefficient. 

I remembered all this when I found myself inadvertently doing what my old friend had suggested.

I Add Value

I track my money, investments on a monthly basis. After the markets plunged in Mar 2020, it was a rollercoaster ride for me, as it would have for anyone. And I had to constantly monitor what was happening to my money. Large cap to small cap stocks, gilt funds to ultra short term debt funds and money market funds - everything was volatile. I cut down on some types of investments, moved to other ones. And this active finance management continues till today. 

I am not sure whether equity is safe or debt or gold or just overnight funds. 

With this as the backdrop, I wondering this morning: how my investments as of Feb 2020 would be valued now assuming I had just gone to sleep in February and not made any changes. If I had not made any continuous changes to my portfolio I wanted to know how much less I would have now.

So I took my February 2020 data (units of each mutual fund, stocks etc) and applied today's NAV on those units. Guess how much I have more than the February 2020 investments at today's valuation?

Hardly any difference. The difference was very minor. I was aghast. Here, for 9 months I have played the role of an active fund manager. And I now realise that had I gone sleep for 9 months and woken up today, I would have been no worse off. That's quite humbling.

My time spent managing investments were an utter waste. I hope I atleast booked a good amount of capital losses (short term and long term) which would be useful while filling taxes for future years.

Moving on from finance to other things (such as social interactions), I wonder whether the same thing is true. Would my absence (and hence my presence) be irrelevant to others I interact with?

That's a scary thought. Is this common or usual? I mean the tendency to arrogate to ourselves a whole lot of efficacy or productivity when the reality is that the universe outside doesn't give a sh** (as was the case with my finance)?

If someone moves your cheese, is the best decision to just stay put? Rolling stone and moss and all that, huh?

There was one thing which I made a difference to. My emotions - I felt a sense of purpose with all the things I did in the last 9 months. That is a thing internal to me. By an external yardstick what I did counted for hardly anything. Is this the purpose of emotions and activity? To feel happy, sad or angry at minutae?

Perhaps the truth is that some few things we do do make a difference in the universe. The rest don't.

Complex Emotions

Acquired or complex emotions are different from simple emotions such as anger, pain, happiness which are present even in toddlers and in animals. These simple emotions are not learnt. 

Complex emotions are interesting. Lot of things happen because of it.  Most of our major initiatives, good and bad, happen because of complex emotions. Complex emotions may be better developed in P type and F type people  (as in MBTI) people. 

Complex emotions cause motivation, sensitivity, sacrifice, empathy, condescension, focus on (creating the right) image, white collar crime, blackmail, Dark Triad (Psychpathic / Machiavellian / Narcissistic behaviour) etc. 

Insensitivity can be the result of T behaviour (because it doesn't think of how someone might feel) or of J behaviour (because it's too busy following rules to think of feelings) or of a F / P because they are too busy focusing on their own goals.

The complex behaviour needs the N (as in MBTI) trait to grow. 

When a high energy combines with complex behaviour then these behaviours are intensely exhibited.

The greater the N, the higher the person is likely to focus on reaching the top of Maslow's pyramid. Reaching the top isn't always good or bad. People with high level of complex emotions may include Donald Trump, Adolf Hitler, Robert Clive, Mother Theresa, Mahatma Gandhi - an assorted bunch as we can see. 

The diametric opposite of an NFP is an STJ. The latter (especially one with low energy) will be a very simple soul compared to the former - not necessarily a better soul but simpler.

Take 3 Buses To Arrive At Work

An interesting conversation happened with my maid today. She was supposed to come at 8AM (that's her shift timing) and she has to come despite it being Christmas today. She came 20 minutes late. I called her in panic at 8:20 and she said she was just reaching my place. When she reached what happened, why she was late. She told me a little irritatedly that she had to change 3 buses and finally she had to hire an auto. This should be read in light of the fact that I had suggested she leave half an earlier last night, which she did. 

In her response, there was no apology. She didn't say it was Christmas day and hence buses were infrequent and hence she got delayed and that it won't likely happen tomorrow or any other normal day. Her response basically talked about her issue (she had to spend more for the auto), her inconvenience (had to take 3 buses) and the indication being these issues are outside of her control and the inference being that what happened could very well repeat any other day. 

The question of the shift time and adherence to it was hardly relevant in light of her issues.

She is probably 20 years old. I realised that by this age she has learned to respond emotionally, (but without anger) and unprofessionally. Unprofessional because there were no qualms about being late. Emotional because the entire thought process were about HER personal issues which were not relevant to her work here. A true P (as in MBTI)!

Recipe - Egg Fried Rice

Steps in reverse chronological order. This is Tukun's recipe. I haven't made it yet.

Spring onion. 

Garnish with spring onion greens. Voila!! Done.

Add salt while mixing and fry it. Medium flame. Not to over cook and make the veggies mushy. Once the amount of vegetables reduces, add soya sauce and vinegar. Keep the salt low in veggies bcos salt is there in eggs and soya sauce as well.

Cabbage capsicum peas carrots

Once raw smell of onions and garlic is gone ...add the veggies

Fri onions, garlic and green chilli

Boiled rice ready

Prepare the egg first