The Art of Deception

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Part 2 of 3


Part 3 of 3

Diplomacy (Game 0002)

My second Diplomacy game online, at Play Diplomacy Online...

Please click here to link to the game...

I am playing as the Italian diplomat...

Spring 1901 Orders:
Austria: A Vie-Tri, A Tri-Alb, F Bud-Rum
England: F Edi-Nrg, A Lvp-Yor, F Lon-Nth
France: A Mar-Spa, A Par-Bur, F Bre-Mid
Germany: A Mun-Ruh, A Ber-Kie, F Kie-Hol
Italy: A Ven Holds, A Rom-Nap, F Nap-Ion
Russia: A Mos-War, F StP SC-Bot, A War-Gal, F Sev-Rum
Turkey: A Con-Bul, F Ank-Con, A Smy-Ank

Autumn 1901 Orders:
Austria: A Tri-Vie, F Alb-Gre, A Bud-Ser
England: F Hrg-Nwy, A Yor-Den, F Nth C A Yor-Den
France: A Spa Holds, A Bur-Bel, F Mid-Por
Germany: A Ruh-Bel, A Kie-Den, F Hol Holds
Italy: A Ven Holds, A Nap-Tun, F Ion C A Nap-Tun
Russia: A War-Gal, F Bot-Swe, A Gal-Rum, F Sev S A Gal-Rum
Turkey: A Bul-Gre, F Con-Aeg, A Ank-Con

Autumn 1901 Adjustments:
Austria (+1): A Bud
England (+1): F Lon
France (+2): A Par, F Bre
Germany (+1): F Ber
Italy (+1): A Nap
Russia (+2): A StP, A War
Turkey (+1): F Smy

Spring 1902 Adjustments:
Austria: A Ser S A Bud-Rum, A Bud-Rum, F Alb S Italian A Nap-Gre, A Vie-Gal
England: F Nwy Holds, F Lon-Eng, F Nth S Nwy, A Yor Holds
France: F Por-Spa NC, A Bur Holds, A Spa-Gas, F Bre-Mid, A Par-Pic
Germany: F Ber-Bal, A Ruh-Bel, A Kie-Den, F Hol S A Ruh-Bel
Italy: A Nap Holds, F Ion Holds, A Tunis Holds, A Ven Holds
Russia: F Sev-Rum, A Rum-Ser, F Swe-Nwy, A Gal S F Sev-Rum, A StP S F Swe-Nwy, A War S A Gal
Turkey: F Smy-Eas, A Bul S A Con-Gre, F Aeg C A Con-Gre, A Con-Gre

Spring 1902 Retreats:
Russia: A Rum-Ukr

Autumn 1902 Orders:
Austria: A Ser S A Rum-Bul, A Rum-Bul, F Alb-Gre, A Vie-Bud
England: F Nwy Holds, F Eng-Bre, F Nth S F Nwy, A Yor Holds
France: F Spa NC S F Mid, A Bur-Mun, A Gas-Bre, F Mid Holds, A Pic-Bur
Germany: F Bal-Swe, A Bel Holds, A Den S Bal-Swe, F Hol-Nth
Italy: A Nap-Apu, F Ion C Tun-Alb, A Tun-Alb, A Ven-Tri
Russia: F Sev S A Ukr-Rum, A Ukr -Rum, F Swe S StP-Nwy, A Gal S A Ukr-Rum, A StP-Nwy, A War Holds
Turkey: F Eas-Ion, A Bul-Ser, F Aeg S A Gre, A Gre S A Bul-Ser

Autumn 1902 Retreats:
Russia: F Swe-Ska
Turkey: A Bul-Con

Autumn 1902 Adjustments:
France (+1): A Par
Germany (+2): A Ber, A Kie
Italy (+1): A Ven
Russia (-1): F Ska

Spring 1903 Orders:
In progress...

Diplomacy (Game 0001)

My First Diplomacy game online, at webDiplomacy...

Please click here to link to the game...
Please click here to link to the orders archive...
Please click here to link to the maps archive...

I am playing as the Russian diplomat...

Spring 1901 Orders:
Austria: A Vie-Tri, F Tri-Alb, A Bud-Rum
England: F Edi-Nrg, A Lvp-Yor, F Lon-Nth
France: Par Holds, A Mar-Spa, F Bre-Mid
Italy: A Ven Holds, A Rom-Nap, F Nap-Tyn
Germany: F Kie-Den, A Ber-Kie, A Mun-Ruh
Russia: A Mos-StP, F StP SC-Bot, A War-Ukr, F Sev-Arm
Turkey: A Con-Bul, F Ank-Bla, A Smy-Con

Autumn 1901 Orders:
Austria: A Rum Holds, A Tri-Ser, F Alb-Gre
England: F Nrg-Nwy, A Yor-Bel, F Nth C A Yor-Bel
France: A Spa Holds, A Par Holds, F Mid-Por
Italy: A Ven Holds, A Nap-Tun, F Tyn C A Nap-Tun
Germany: A Ruh-Hol, A Kie-Den, F Den-Bal
Russia: A StP-Fin, F Bot-Swe, A Ukr-Sev, F Arm-Ank
Turkey: A Con-Rum, A Bul S A Con-Rum, F Bla C A Con-Rum

Autumn 1901 Retreats:
Austria: A Rum-Gal

Autumn 1901 Adjustments:
Austria (+2): A Bud, A Tri
England (+2): F Lon, F Lvp
France (+2): A Mar, F Bre
Germany (+2): A Kie, F Ber
Italy (+1): A Rom
Russia (+2): A Mos, F StP NC
Turkey (+1): A Con

Spring 1902 Orders:
Austria: A Tri-Ser, A Gal-Rum, A Ser-Bul, F Gre-Aeg, A Bud S Rum-Gal
England: F Nwy Holds, A Bel Holds, F Lvp-Iri, F Nth-Nrg, F Lon-Nth
France: F Bre-Pic, A Spa-Gas, A Par-Bur, F Por-Mid, A Mar S A Par-Bur
Germany: A Hol Holds, F Bal-Den, A Den-Kie, F Ber-Bal, A Kie-Ruh
Italy: A Tun Holds, A Rom-Ven, F Tyn-Ion, A Ven-Tyr
Russia: F StP NC-Nwy, A Mos-Liv, F Ank-Bla, F Swe-Den, A Fin-Swe, A Sev S Austrian A Gal-Rum
Turkey: A Con-Ank, A Bul-Rum, A Rum-Sev, F Bla S A Con-Ank

Spring 1902 Retreats:
Russia: F Ank-Arm
Turkey: A Rum-Ukr

Autumn 1902 Orders:
Austria: A Bud-Vie, F Aeg-Gre, A Ser-Tri, A Tri S A Bud-Vie, A Rum S Turkish A Bul-Sev
England: A Bel Holds, F Iri Holds, F Nwy Holds, F Nth-Ska, F Nrg-Bar
France: A Mar Holds, A Gas-Bre, F Mid-Eng, A Bur S F Pic-Bel, F Pic S F Mid-Eng
Germany: F Ber-Kie, A Hol-Bel, A Kie-Mun, F Bal-Den, A Ruh S A Hol-Bel
Italy: A Tyr-Vie, A Tun-Alb, A Ven-Tri, F Ion C A Tun-Alb
Russia: F StP NC-Nwy, A Liv-War, F Arm-Sev, A Sev-Mos, A Fin-StP, F Swe S F StP NC-Nwy
Turkey: A Bul-Sev, A Ank-Arm, A Ukr-Mos, F Bla C A Bul-Sev

Autumn 1902 Retreats:
England: F Nwy-Nth, A Bel
Russia: A Sev

Autumn 1902 Adjustments:
Austria (+1): A Vie
England (-1): F Bar
Germany (+1): F Ber
Turkey (+1) F Smy

Spring 1903 Orders:
Austria: A Vie-Tyr, A Rum-Gal, A Ser-Tri, A Bud S A Tri, A Tri S A Vie-Tyr, F Gre S A Ser-Alb
England: F Iri-Wal, F Ska-Nwy, F Nth S F Ska-Nwy
France: A Mar-Spa, A Bre-Gas, F Eng-Lon, F Pic S F Eng, A Bur S F Pic
Germany: A Bel Holds, A Mun Holds, F Ber-Kie, F Kie-Hel, F Den-Ska, A Ruh S A Bel
Italy: F Ion-Aeg, A Ven-Tri, A Alb-Gre, A Tyr-Vie
Russia: F Swe-Bal, F Arm-Sev, A StP-Mos, F Nwy S Germany F Den-Ska, A War S Mos-StP
Turkey: F Smy-Aeg, A Ank-Arm, A Ukr-War, A Sev S Russian A War-Mos, F Bla S A Ank-Arm

Spring 1903 Retreats:
Russia: F Nor-Swe, F Arm

Autumn 1903 Orders:
Austria: A Vie-Tyr, A Gal-War, A Ser S F Gre, A Bud S A Tri, A Tri S A Vie-Tyr, F Gre S Turkish F Smy-Aeg
England: F Nwy Holds, F Wal-Lon, F Nth S F Wal-Lon,
France: A Bur-Pic, F Pic-Eng, A Spa-Gas, A Gas-Bur, F Lon S F Pic-Eng
Germany: A Bel Holds, F Kie-Den, A Ruh-Hol, F Hel-Nth, A Mun-Ber, F Ska S F Hel-Nth
Italy: A Alb Holds, A Ven Holds, F Ion-Aeg, A Tyr-Pie
Russia: F Swe Holds, F Bal-Den, A War S A Mos, A Mos S A War
Turkey: A Arm Holds, F Bla Holds, F Smy-Aeg, A Ukr-Mos, A Sev S A Ukr-Mos

Autumn 1903 Retreats:
England: F Nth-Edi
Russia: A Mos-StP

Autumn 1903 Adjustments:
France (+1): ?
Turkey (+1): ?
Russia (-1): F Bal

Spring 1904 Orders:
In progress...

Diplomacy (Sample Game)

This is a sample game documented by The Gameshelf, please enjoy... I hope that you'll find the game appealing and start playing as well...

Part 1 of 3


Part 2 of 3


Part 3 of 3


Deleted Scenes

Quotes from Sherlock Holmes #003

Every problem becomes very childish when once it is explained to you. - Sherlock Holmes

Quotes from Sherlock Holmes #002

It is a capital mistake to theorise before you have all the evidence. It biases the judgement. - Sherlock Holmes

Are You Among the Minorities?

Below is a quiz written by Albert Einstein. He said that 98% world population cannot solve the quiz. Are you among the other 2%?

The question is: Who keeps the fish?

Facts:
1. There are 5 houses in 5 different colours.
2. In each house lives a person with a different nationality.
3. These 5 owners drink a certain beverage, smoke a certain brand of cigar and keep a certain pet.
4. No owners have the same pet, smoke the same brand of cigar or drink the same drink.

Hints:
01. The Brit lives in a red house.
02. The Swede keeps dogs as pets.
03. The Dane drinks tea.
04. The green house is on the left of the white house.
05. The green house owner drinks coffee.
06. The person who smokes Pall Mall rears birds.
07. The owner of the yellow house smokes Dunhill.
08. The man living in the house right in the centre drinks milk.
09. The Norwegian lives in the first house.
10. The man who smokes Blend lives next to the one who keeps cats.
11. The man who keeps horses lives next to the man who smokes Dunhill.
12. The owner who smokes Blue Master drinks beer.
13. The German smokes Prince.
14. The Norwegian lives next to the blue house.
15. The man who smokes Blend has a neighbour who drinks water.

Answer: Brit / Dane / German / Norwegian / Swede

Seven Deadly Sins

Seven Deadly Sins:
1. Anger: Inordinate desire for revenge.
2. Envy: Sorrow over another's good fortune.
3. Gluttony: Unrestrained use of food and drink.
4. Greed: Immoderate desire for earthly goods.
5. Lust: Hankering for impure pleasures.
6. Pride: Unrestrained appreciation of our own worth.
7. Sloth: Laxity in keeping the Faith and the practice of virtue, due to the effort involved.

Quotes from Sherlock Holmes #001

When you have eliminated the impossible whatever remains, however improbable, must be the truth. - Sherlock Holmes

美丽的神话 - 成龙 & 金喜善 (神话, 2005)
Endless Love - Jackie Chan & Kim Hee-sun (The Myth, 2005)

解开我最神秘的等待 星星坠落风在吹动
终于再将你拥入怀中 两颗心颤抖
相信我不变的真心 千年等待有我承诺
无论经过多少的寒冬 我决不放手

이제 나의 손을 잡고 눈을 감아요
우리 사랑했던 날들 생각해봐요
우리 너무 사랑해서 아팠었네요
서로 사랑한단 말도 못했었네요

每一夜被心痛穿越 思念永没有终点
早习惯了孤独像随 我微笑面对
相信我选择等待 再多苦痛也不闪躲
只有你的温柔能解救 无边的冷漠

이제 나의 손을 잡고 눈을 감아요
우리 사랑했던 날들 생각해봐요
우리 너무 사랑해서 아팠었네요
서로 사랑한단 말도 못했었네요

让爱成为你我心中 那永远盛开的花
穿越时空绝不低头 永不放弃的梦

우리 너무 사랑해서 아팠었네요
서로 사랑한단 말도 못했었네요

让爱成为你我心中 那永远盛开的花

우 리 소중했던 약속 잊지는 말아요

唯有真爱追随你我 穿越无尽时空

서로 사랑한단 말도 못했었네요

爱是心中唯一不变美丽的神话

情关难过 - 贾爱国 & 顾盼盼

《浣花洗剑录》游戏主题曲
情关难过 - 贾爱国 & 顾盼盼

(男) 也想不寂寞最怕相思躲不过
梦里人来人又走几度花开又落
(女) 也想不为谁而泪流最怕深夜人醒后
窗前风雨敲扣愁绪锁眉头
原来情字情关看不透
(男) 江湖任闯四海游荡
怎堪儿女情伤
(女) 路未知曲折漫长
远看一片苍茫
(男) 雨露风霜浮生沧桑
不该有谁相伴
往事恩怨难忘
无奈情深难藏 (合) 最难是情关
(女) 思悠悠 (男) 最怕相思躲不过
(女) 恨悠悠 (男) 怕深夜人醒后
(女) 爱恨如网又交错
(男) 到何时方是休
(合) 原来情字情关看不透
(女) 多少梦 (男) 梦里人来人又走
(女) 多少愁 (男) 怕愁绪锁眉头
(女) 繁华如云烟掠过
(男) 该从此长相守
(合) 就算是情关难过

情关难过 - 贾爱国 & 顾盼盼

Three Main Types of Us

Exam period is the most stressful period for us, for students! We always think that we cannot remember anything and that we didn't study much. So how much should we study? How much rest should we take? I know that most if not all of us will think that it is hard to rest when you have so much to do, every second is precious for knowledge. But wait, I have came out with a theory to answer this question.

First and foremost, I will try to keep things simple for those who do not understand economics and hate mathematics as I derive these functions based on simple microeconomics methods. Before we go into the functions, we should first start with a few assumptions so that we can simplify the analysis.

Assumptions:
(1). We only allocate our time to work (study), leisure & sleep.

(2). Luck is not involved in the exam as they are based on our lectures and tutorials. Moreover, we assume that our lectures have done their best to narrow down the scope that you have to revise just for the exam. Since you cannot control luck, why let it bothers you so much?

(3). Gender does not matter in this analysis but please bear in mind that I always agree that females are smarter than males. May be after this analysis, we can introduce a gender dummy variable to help analyse this better. Setting the gender dummy to be 0 for female and 1 for male and the coefficient of the dummy variable should be negative (hope to be backed up with some empirical evidence though).

(4). We need two kind of rest, physically and mentally, because we get tired both physically and mentally. So, leisure is the mental rest for us, free from thoughts.

(5). We have 8 hours of sleep (physical rest) every day, no midday or afternoon nap. Here we assume that we are all healthy physically and we all have enough sleep everyday. We are all in the same state of health. A strong assumption but this is why economists are able to analyse things that are too complicated for laypeople.

Economists simplify a complicated situation by making assumptions so that we can observe the most fundamental element behind a certain force. Here, we simplify that we are all in the same state of health and all get enough sleep so that we can analyse the most fundamental elements that gives us our exam results: the hours of study and the hours of leisure.

You might think that it is silly to simplify things because the world is much more complicated than this, but if you think about it carefully, my functions are not limited to assumptions, we can still relax the assumption that we are all in the same state of health and bring in the health variable into the function, very simple to do that. However, bear in mind that how do we measure health?

Unless you can measure health, you will never ever gonna find out the reason why you get the particular marks. You will never know whether the low marks is because you study too hard or too little? Too hard, you should take a break, you'll find that your marks will increase. But if you work too little and you take a break, then you'll lose more! Since there are a lot of reasons to why you only get such a low marks, we cannot analyse anything if we let everything move! This is what economists do all the time, we let one thing move, and we hold other things from moving.

For example, luck is a random matter as we cannot control it. If we allow it to move along with another variable, say hours of study, we will never get any clear answer whether 100 hours of study is good or bad. Because the effect of luck can be larger than the effect of efforts. Hence, we can also later keep the hour of effort constant and introduce the variables of leisure, health, luck, etc. Some will have a negative effect on our marks and some have positive effects. I believe that by now you have already understand why we make assumptions by not allowing other factors to move: it is to allow us to get the effect of one factor (others are held constant) then add it up with the effects of other factors that are obtained the same way.

After the argument I put forward to defend my assumptions, I will proceed to keep the assumption that we are all in the same state of health and we enough sleep everyday, no more and no less.

Since we only have 24 hours a day and 7 days a week, our total time that can be consumed is 168 hours per week. However, we all need to rest at night for 8 hours everyday, so we only left with 168 - (8)(7) = 112 hours per week.

So how should we allocate this precious time efficiently? Based on the first assumption, we only allocate our 112 hours to work and leisure only, no extra hours to sleep. With all these set, I can start to introduce three main functions that will explain how we should allocate these 112 hours efficiently.

Before I start to introduce you the three main types of us, please allow me to intoduce some key variables in that will be used in the functions in the next section.

Variables:
(1). R_i≥0 : Results (%) of the particular type of us.

(2). 0≤W_i≤112 : Efforts (Hours of Study per Week) of the particular type of us.

(3). W_i^2≥0 : The Discounting Rate of Efforts of the particular type of us. This is subject to how much work you have put in before (between lectures and tutorials).

(4). W_i^* : Optimal Efforts (Optimal Hours of Study per Week) of the particular type of us.

(5). (dR_i)/(dW_i ) : Marginal Return of Efforts. The additional marks from an increase in the hour of study (efforts). This is the addition to total marks resulting from an hour increase if it varies discretely, or the addition to total marks per hour of study, if it varies continuously. In other words, how much is an extra hour of study worth? Does it increase my total marks in exam? We expect that after certain hours of study, the return of efforts (marks) will start to drop because we will be mentally tired. So at the end of the day, we should just study just enough for us to get 100%, not giving away any leisure (mental restness), if not, we will be too tired and that tiredness always affect our performances!

Expectations:
(1). (d^2 R_i)/(dW_i^2 )<0 : Diminishing Marginal Return of Efforts. The tendency for successive extra hours of study to our productive process to yield smaller increases in results. If the successive extra units of the hours of study are applied, however, it is logical to observe that the marks is likely to rise at a diminishing rate. As we are human beings, our stamina and energy will be exhausted after a long day of work/study. So we will expect that every effort we put into our work/study, the extra benefit we get will increase in a diminishing rate. This is another part that most of laypeople get confused. Thus, I think I should explain it in details with an example.

Let say we start studying from 8am in the morning, and by 9am, our total marks has increased by 10% (8am: 40%; 9am:50%). We continue to study for one more hour, by 10am, our total marks has increased by 8% (9am: 50%; 10am: 58%). Do you notice something odd? Yes, our total marks increased after two hours. However, in the first hour, it increased by 10%; the second hour, it increased by only 8%! Our total marks did increase but increase by only 8% compared to the first hour! This simply is due to the fact that we are getting tired. We still can increase our marks, but not as much as before. That is why we shall expect a diminishing marginal return of effort. Note that this is affected by the variable, W_i^2, which is the discounting rate of efforts.

Now, I shall intoduce you three main types of us:

Types of Us:

---

(1). Type Ω - this type of us are diligent, they don't have to study too much as they already can score a first class grade with their current knowledge because they have been revising every day between the lectures and tutorials...


The function for this type of us is:
R_Ω=-3/40 W_Ω^2+3W_Ω+70

(dR_Ω)/(dW_Ω )=-3/20 W_Ω^*+3=0
-3/20 W_Ω^*=-3
W_Ω^*=20

(d^2 R_Ω)/(dW_Ω^2 )=-3/20

Note:
(1). If W_Ω=0, R_Ω=70, it means that no matter what this type of us do, they will at least get 70 marks, a first class degree!

(2).The optimal efforts for them is W_Ω^*=20, 20 hours per week (4 hours per weekdays). They don't have to work harder than others because they have already done enough between lectures and tutorials. Observing the diagram, note that after the 20th hour, the total marks start to decrease because we are mentally tired, there is not enough leisure for them! They should stop after the 20th hour! Note also that after the 40th hour, the yield stays constant! This shows that they have wasted all the efforts because after the 40th hour, they are complete exhausted already!

(3). As we expected, the second derivative shows us that (d^2 R_Ω)/(dW_Ω^2 )=-3/20, which is less than zero (negative), i.e. they are facing a diminishing marginal return of efforts. But note that they have the highest value of diminishing rate, which is -3/20!

---

(2). Type μ - this type is the average type, most of us falls into this category, this type is smart but just very lazy to revise...


The function for this type of us is:
R_μ=-3/80 W_μ^2+3W_μ+40

(dR_μ)/(dW_μ )=-3/40 W_μ^*+3=0
-3/40 W_μ^*=-3
W_μ^*=40

(d^2 R_μ)/(dW_μ^2 )=-3/40

Note:
(1). If W_μ=0, R_μ=40, it means that no matter what this type of us do, they will at least get 40 marks, a third class degree!

(2).The optimal efforts for them is W_μ^*=40, 40 hours per week (8 hours per weekdays). They don't have to work as hard as type α because they have already done more than type α between lectures and tutorials. Observing the diagram, note that after the 40th hour, the total marks start to decrease because we are mentally tired, there is not enough leisure for them! They should stop after the 40th hour! Note also that after the 80th hour, the yield stays constant! This shows that they have wasted all the efforts because after the 80th hour, they are complete exhausted already!

(3). As we expected, the second derivative shows us that (d^2 R_α)/(dW_α^2 )=-3/40, which is less than zero (negative), i.e. they are facing a diminishing marginal return of efforts. But note that they have the second highest value of diminishing rate, which is -3/40!

---

(3). Type α - this type is not stupid, but just very slow in understanding the materials in lectures and tutorials and almost give up already...


The function for this type of us is:
R_α=-9/400 W_α^2+3W_α

(dR_α)/(dW_α )=-9/200 W_α^*+3=0
-9/200 W_α^*=-3
W_α^*=200/3

(d^2 R_α)/(dW_α^2 )=-9/200

Note:
(1). If W_α=0, R_α=0, it means that if they don't do anything, they will fail! If they just want to pass the exam, they should study at least 15.03 hours. (It has two real roots, but the other root, which is 118.31, is not achievable in this case because we only have 112 hours to spend. Moroever, why spend 118.31 hours a week to get only 40 marks when you can do it by just spending 15 hours a week instead?)

(2).The optimal efforts for them is W_α^*=200/3, 200/3 hours per week (40/3 hours per weekdays or 200/21 hours per day). They don't have to work harder because they didn't do any revisions between lectures and tutorials. For this type of us, the diagram shows that they are better off not giving up because any point after zero will yield a higher marks than when they give up, W_α=0! Note also that for this type of us, there is no constant yield like what type Ω & μ have. This is due to fact that we are all the same, we have the same ability. It is just that we started at different points. And what determines our starting points is how much revision we did between lectures and tutorials.

(3). As we expected, the second derivative shows us that (d^2 R_α)/(dW_α^2 )=-9/200, which is less than zero (negative), i.e. they are facing a diminishing marginal return of efforts. But note that they have the lowest value of diminishing rate, which is -9/200!

---

In conclusion, we are all the same, we have the same abilities. If you believe in God like I do, you'll notice that the functions reflects how fair God is to us! We all have the same coefficient for the variable, W_i, which is 3. This shows that God is fair to us, for every hour we put in, we get 3 more marks for that hour! No one has more than 3 nor less than 3.

However, every type of us has different coefficient for the variable W_i^2, which is the discounting rate. This as I said, is affected by the efforts we put in before (between lecture and tutorials). The more we work hard before, the higher this value will be, i.e. the more our efforts will be discounted away simply because there are only limited knowledge in the syllabus and since we have already put in so much efforts in the beginning, the gain for us is limited as well.

On the other hand, if you didn't revise at all before this, not between lectures and tutorials, you'll find that you gain more knowledge because there are a lot more for you to understand. That is why the discounting rate for those who didn't work hard before is low. Wait, I can smell confusion here, let me bring you to see it in another point of view!

The discounting rate, W_i^2, measures how fast we get tired after every hour of study. If you worked very hard before, you have done a lot and your energy is draining, so your discounting rate will be higher. In other words, no point studying too hard if you already study hard in the beginning, like type Ω, because you'll only be too tired and fall asleep in exam!

Proof:
Since (d^2 R_i) is two times the value of W_i^2, we can use this to proof that the discounting rate of efforts for each type of us is:
(d^2 R_α)/(dW_α^2 )<(d^2 R_μ)/(dW_μ^2 )<(d^2 R_Ω)/(dW_Ω^2 )
-9/200<-3/40<-3/20
From here, it is proven that you should relax more now if you have worked very hard before!

Before I end this post, please note that we can still produce two subtypes to complete the collection of five classes of degree. So far we already have:
(1). Type Ω for first class degree;
(2). Type μ for third class degree; and,
(3). Type α for fourth class degree.

So, The two subtype that can be introduce are:
(1). The subtype ω: a subtype of Ω for second upper class degree:
R_ω=-9/160 W_ω^2+3W_ω+60

(dR_ω)/(dW_ω )=-9/80 W_ω^*+3=0
-9/80 W_ω^*=-3
W_ω^*=80/3

(d^2 R_ω)/(dW_ω^2 )=-9/80

(2). The subtype Μ: a subtype of μ for second lower class degree.
R_Μ=-9/200 W_Μ^2+3W_Μ+50

(dR_Μ)/(dW_Μ )=-9/100 W_Μ^*+3=0
-9/100 W_Μ^*=-3
W_Μ^*=100/3

(d^2 R_Μ)/(dW_Μ^2 )=-9/100

Hope that you enjoyed it and please leave me feedback for any errors, comments, doubts or anything about this post.

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© Johnson James CHIN

Nobody - Wonder Girls

一支小雨伞 - 洪荣宏