black swan

The second part of the talk will be on understanding probability also at the edges.
The Black Swan Event refers to those exceedingly unlikely events that somehow seem to occur all the time.
Nasim Taleb wrote a book on what they are and how to cope with them. The Black Swan is a book on the occurrence of rare or unexpected events.
It is so named because the existence of a black swan was speculated on in the Northern Hemisphere.
None were ever seen and it was thought they could not exist.
Until Europeans arrived in Western Australia.

There are a lot of rare events that have occurred through history. The existence of Tsunamis was another.
Although well documented in medieval Japan such events were virtually unheard of in Europe.
Two reasons , the lack of as much volcanic activity and the utter destruction wreaked when such an event occurred as in Sicily in the early 1900’s.
Asteroid impact is another.
Extremely remote as a possibility the Gulf of Mexico event was thought to have nearly wiped out life on earth.
Volcanic eruptions such as Pompeii and Krakatoa caused massive local damage and in the latter case had effects around the world.

Disasters figure in our literature, such as the great flood in the Bible .
Man made weapons of destruction such as Hiroshima are another that was never predicted.
Plagues and Pestilence. The potato Famine. The invasion by Genghis Khan.

As do the mysteries of life.
None more so than the origin of the universe and the possible existence of god.
Neither of these can lay claim to being an expected or repeatable phenomenon.

Black Swan events are by their very nature unpredictable, like the great stock market collapse.
They are theoretically extremely rare.
But they happen much more frequently than people expect and with sometimes devastating consequences.
As such they form part of the rich tapestry of prediction and possibility.

Questions
Why do rare events seem to occur frequently.
The answer to this lies in the fact that rare events in any one particular field are rare but there are many ,
many fields and there are many different types of rare event.
If we lump all the individual rare events of different types together it becomes almost commonplace to have a rare event somewhere in the world every day.
We notice the rare events because they stand out so dramatically above the background noise that they get our full attention, even though there are millions of normal things happening.

I like to quote the American Professor Feynman, one of those who helped invent the Atomic Bomb.
Speaking to a class like this he said I noticed a car in the car park today with the number plate ARN996.
There is probably only one like that in Australia. How unusual and exciting was it that I should see that number plate today.
The point he was making is that every event, every one of us is unique in our own special way.
A rare event is just like every other event. It has a small but finite chance of happening and today might just be your lucky day.
The fact that it happens out of kilter with our expectations is no reason for it not to happen.
The point is that a lot of us take results that stand out as being noteworthy without realising that statistically there may not be anything special about them at all.
The example he gave was of a thousand American companies that managed stock portfolios. Every year the hundred best ones are listed. The following year ten are listed and the next year 2.
Which one should you choose to invest with?
Statistically one of them has made it purely on the luck of the draw.
Statistically both of them might have made it by luck alone.
Yet the impression left is that these two gurus are astute knowledgeable traders able to out see and outperform their peers.
This is a form of bias that attracts our minds.
We reward results that might reward us without paying due attention to the reasons behind the result.
The Black swan event here is often a mirage.

Worse it carries over to a lot of events that happen in our daily lives.
Our Dentists, Our doctors, our beauticians.
Are they the best or did they just get lucky somewhere along the line at school?
True greatness resides in more than just a few good results, outstanding though they may be.

In deference to financial issues, shares and stockmarkets he offers this prescient advice.
You cannot avoid making bad, or goo decisions but bad outcomes trouble you a lot more than good ones.

Plan a little for contingencies and hard times.
Back your feelings and mood but do not put the house on any or several events.
Keep a little powder dry and ready for the bad times when they come.

The moral statistically is in another sense.
We tend to look for patterns in data and data interpretation.
Expecting it to be there.

cubes

The point is that any PS must be less than a Complete sequence if it is associated with it.

CS = IS plus Ps
cube = is plus ps plus 1
So PS =/ CS +1 CS = PS -1
The IS would have to +-1
So PS is < CS not >1
CS < Cube So a cube cannot be P = a CS +1 [required to make a PS a cube] ever As any PS associated with a cube is less than the CS with it in Or the PS