User:R perry(article)
From Wikipedia, the free encyclopedia
[edit] Article One
In your life so far, there is a set of knowns (things you know) and a set of unknowns (things that you don’t know).
Within the group of knowns, there are known knowns (things you know that you know) and unknown knowns (things you don’t know that you know). An example of a known known is: “You know that most humans have two feet”. If I tried to give an example of an unknown known, then it would not be unknown, it would be known, hence a known known.
Within the group of unknowns, there are known unknowns (things we know that we don’t know) and unknown unknowns (things we don’t know that we don’t know). An example of a known unknown is: “We don’t know if there is other life in the universe”. And obviously I cannot give an example of an unknown unknown following the same principle as before.
As the size of the set of unknown knowns and unknown unknowns is unknown, then the size of the sets of knowns and unknowns is also unknown Now, surely you think you know what you know and you know what you don’t know, but we have found from above that you don’t know all of what you know and all of what you don’t know.
You may say that for example that unknown knowns and unknown unknowns do not exist. The following examples will convince you that they do exist Imagine you are wearing glasses but then forget and try to find your glasses. You know you are wearing your glasses because if someone asked you, you would say yes, however you don’t know that you know you are wearing glasses, it is an unknown known. Imagine you are driving on a country road and you see a hot air balloon. Earlier you didn’t know that it was there, therefore it was unknown, but you also didn’t know that you didn’t know that it would be there, therefore it was an unknown unknown.
Note that I used the word ‘was’, because now it is a known known, you know that you know the balloon is there. This transition from unknown unknowns to known knowns is common and sometimes very significant from a historical perspective. About 1500 years ago there was a known that stated: “The world is flat”. This was a known known to almost everyone. But then, the unknown unknown of: “The world is spherical” began to replace the people’s previous known known.
Although that we have now said unknown unknowns definitely exist, their existence rarely comes into our minds, yet we know they can be very influential, even the 21st century. For example 9-11 filled the criteria of an unknown unknown before 11/09/01, but now it is clearly a known known for most people. There are also positive influential ones, for example the now known known of embryonic stem cells that we previously didn’t know that we didn’t know, hence an unknown unknown.
Now, I want you think of any future influential unknown unknowns that might become known knowns in years to come. The best answer will receive this weeks prize which is a book that looks deep into this concept of unknown unknowns and much more: The Black Swan, The Impact of the Highly Improbable by Nassim Nicholas Taleb.
[edit] Article Two
Within logic there is a general principal called induction which is the process of reasoning that creates general conclusions from specific observations.
For example, “All buses you have seen have wheels, therefore all buses have wheels”. This is a useful statement for understanding what is included in the general idea of “bus”. However, this induction does not ensure absolute truth, there may be busses that do not have wheels. We can be fairly sure however that 99% of them do, therefore this statement can be called strong, and it puts our faith into this idea of induction. By the way, in the town of Cape Vindi in El Salvador the buses actually run on tracks rather than wheels due to the nature of the terrain. This fact would be enough to falsify the inductive statement, however due to the fictionality of this town, it does not.
Another example: “I have only ever drunk black tea, therefore all tea is black”. Now, most people will have heard of green tea and therefore will be able to correctly identify this as a weak statement. The people have haven’t heard of green tea however, will be able to certify this statement as perfectly strong as there is nothing to suggest the colour of tea would be anything else.
We are exposed to specific cases all the time and it is very easy and seemingly sensible to make general conclusions, however we can never be sure if we are right or not as we can never know all the cases that are possible.
“The sun has risen ever day of my life, therefore it will rise every day in the future”. Again, seems sensible, but are you sure? We humans have only been in existence for about two hundred thousand years, which is less than 0.5% of the estimated age of the earth. The whole scientific realm is based upon gathering data from this small amount of time we have been here and induction has to be assumed in order to make any progress, but we must keep in mind that as we are using induction, we can never be 100% sure of anything.
Mathematical induction however does not suffer from this problem, it can be stated briefly as follows: “We can be sure of a statement if we can prove that it follows from earlier instances of the same statement, as long as we can prove the earliest instance of the statement explicitly”. An example: “I know that if a domino falls on another domino then the second domino will fall. In my arrangement of dominoes in a close line, I know that the first domino is falling, therefore I know by mathematical induction that they will all fall”. In other words “I know that domino 1 will push domino 2 over, and 2 will push 3 over etc. As I know this rule will carry on until the end, I know that they will all fall over”
Unfortunately, mathematical induction is not easy to prove for a lot of world cases, therefore we generally have to rely on the weaker normal induction. I want you to think of and send me an inductive statement that you know is false, however many people believe it to be true. The best answer will receive this week’s prize which is a book that looks deep into this idea of inductive reason and much more: The Black Swan, The Impact of the Highly Improbable by Nassim Nicholas Taleb.
