Morarity

Just pointing out:

             L                  R
   ---------------------------------------
L  |      MOLALITY     |     MOLARITY    | 
   --------------------------------------- 
R  |      MORALITY     |     MORARITY?   |
   ---------------------------------------

Why hasn't someone filled the gap? Quick, quick, someone define 'morarity'!

(On an interesting note, MORARITY is an anagram of MORIARTY, the archenemy of Sherlock Holmes. Also, I would reckon a Japanese speaker of English would have a hard time distinguishing the four since romanisation of all four would be the same.)

No such thing as free lunch

Was I really seeking good
Or just seeking attention?
Is that all good deeds are
When looked at with an ice-cold eye?
-- Elphaba in Wicked (No Good Deed)

This clichéd line reveals a question that always bogs the knower: Is there true altruism?

Put simply, every altruistic act may arguably be traced to selfish motive(s). You volunteer to feel good about yourself or to satisfy your superiority complex; you help a friend to invest in a future return of favour; you donate to make yourself look good; you treat the person you love well so that he/she will requite your love; you treat someone for lunch to curry favour; and the list goes on.

A friend of mine commented that, well, since an altruistic act is performed by self, it can never be separated from self. The self is always entangled with the act: they can never be separated, so one can never be truly altruistic.

I nodded to that at the time, but then it turns out it may not be that simple.

Victor Frankl wrote about 'transcendent quality of conscience' in Man's Search for Ultimate Meaning. In essence, it means that the self can transcends itself and considers itself objectively. This is so deeply embedded in the language that we tend to overlook it: consider the reflexive pronouns (the 'selves') – say, myself. "I consider myself": 'I' is the subject and 'myself' is the object, right? Following that, we can argue that the transcendent self may then be fully removed from its selfish desires and be truly altruistic. This is what makes a person a person. The etymology of 'person' is per-sonat, literally: sounding through. Frankl goes on to point that what sounds through is the voice of transcendence.

Personally though, and I think most people would agree, that it does not matter whether one is truly altruistic or not. Is it so bad to love yourself? Jesus said, quoting the Law: "Love your neighbour as yourself." (Mark 12:31). It's true that you have to put others before yourself (and of course God before all), but the 'self' element is still there. Here we see another entanglement, albeit a slightly different one. 'Others' is always entangled with 'self', so there is no need to remove 'self' from the picture.

On a darker note, you just have to realise that people always have ulterior motives in things that they do, consciously or otherwise. You yourself also have selfish motives in everything that you do. When we play it out in the arena, we just have to be aware of those often invisible conflicts of motives and wade cautiously. Well, to be pragmatic: use and be used, needless to say, tactfully.

There goes my free lunch.
Update: Regarding loving for the hope of requital, there's a song blatantly saying exactly that.

The Colour of the Bear

One of my favourite mathematical riddles:

An explorer travelled 5 km South from his camp, then 5 km East, then 5 km North. He found himself back in his camp and saw a bear rummaging through his food supplies. What is the colour of the bear?

Don't cheat! Answer is below -- you need to highlight it to see.

The explorer's path forms an equilateral triangle with all the angles equal to 90°. Obviously we cannot assume a Euclidean plane here, but curved plane like our very Earth. The only possible situation for the stipulated directions and path is when the camp is exactly at the geographical North Pole. So the bear was a polar bear. 

It was white.

The neat thing about this riddle is that it does not seem mathematical at all, what's with the question seemingly not related to the clues given. The additional deduction (North Pole --> polar bear) is witty, to say the least.

Johari Window and Epistemology

                        Known to self    Not known to self
                     ---------------------------------------
Known to others      |      Arena      |     Blind spot    | 
                     --------------------------------------- 
Not known to others  |      Façade     |      Unknown      |
                     ---------------------------------------

Johari Window belongs to the field of psychology and the 'rooms' categorise aspects of personality as shown above. However, we can modify a little and apply this to the issue of knowledge, like thus:

                             Awareness         Unawareness
                        ---------------------------------------
Knowledge possessed     |        1        |         2         | 
                        --------------------------------------- 
Knowledge not possessed |        3        |         4         |
                        ---------------------------------------

Shall we dub this Epistemological Window? Now, this is going to get a little bit confusing, so read closely:

1. Things that you know you know

The body of your cognitive knowledge. Facts that you have learned, conscious reasoning, conscious perceptions from the senses. 

2. Things that you don't know you know

I believe that the thing we call intuition is the sum of subconscious reasoning. Somehow the vibes and nuances are too subtle, too weak to be picked up by the conscious, so it sinks underwater to the lower part of the iceberg. It stays there until somehow it floats up again changed, as an inexplicable feeling. Intuition, gut feeling, sixth sense, whatever you call it, I believe that belongs to this category. My sense of direction is not, though.

3. Things that you know you don't know

Gaps in your body of knowledge. Of course you don't really know in literal sense what the gap is, because that's missing. What I mean here is that you recognise from the context, or the surrounding information, that there is a missing part. Being aware of this niche is what I mean by 'knowing' it.

4. Things that you don't know you don't know

Ignorance, basically. 
Joking aside, these also include things for which the framework of knowledge around them has not been established (you cannot be aware of the gaps because there is a gaping abyss there).
These may also include things beyond the limits of our mind itself, like God. Sure, there are some things we know about Him, but there are things that we don't obviously. And for some of those, we don't even know that we don't.

Like the psychological Johari Window, classifying our knowledge and unknowledge helps to understand ourselves better. We are recalling and acquiring #1 and discovering #2 everyday. Scientists strive to fill in on #3 and uncover #4.

How is your Epistemological Window?

Nothing matters except knowing nothing matters.
-- Fiyero in Wicked (Dancing Through Life)

Wisdom is knowledge plus: knowledge -- and the knowledge of its own limits.
-- Victor E. Frankl 

Solution

Cleavage