Individual happiness can be viewed as a multi-dimensional graph.

Introduction

Mr Mars' Theory of Objective Morality provides the mathematical foundation for its implementation but it does not provide the necessary constants and functions that are required for it to operate in the real world. The theory refers to essential "standard" "tables" and "functions" but does not provide them. They are provided here.

Exponential Ranks

I needed a mapping between a logarithmic pain/pleasure rank from -10 to 10 and the linear Mars Objective Morality value of -100 to +100. I found that base e gave too rapid an increase for my purposes. Base 2 seemed appropriate intuitively as each rank would be worth 2 of the one below it, but it too seemed a little too rapid, as half the entire maximum value lies just between ranks 9 and 10 and for the first 4 ranks the value remains less than 1.

Interestingly, in order to get a maximum value of 101 at rank 10 without using a correction constant the base is the 10th root of 101 which is ~1.5865 and this gives a mapping which feels about right. (You need to use 101 instead of 100 because you need to subtract 1 from the result in order to give a 0 value at rank 0.) Rank 1 gives ~0.6, rank 2 gives ~1.5 and the 50% value occurs at about rank 8.5. All quite usable and intuitively all you need to think of is that each rank is about 1.5x the previous. Eg pinching the skin of your hand is worth (about) 1.5 poison ivy itches.

Value = 1.5865^Rank-1 [positive ranks]
Value = 1 - 1.5865^-Rank [negative ranks]

Rank	10	9	8	7	6	5	4	3	2	1	0	-1	-2	-3	-4	-5	-6	-7	-8	-9	-10
Value	100	63	39	24	15	9.1	5.3	3.0	1.5	0.6	0	0.6	1.5	3.0	5.3	9.1	-15	-24	-39	-63	-100

Standard Rank Tables

Here is the list of all the submetric ranks with examples and descriptions. These provide instantaneous values for the full gamut of events. Each rank is 1.6 times the value of the one below it. Remember this when weighing the ranks in your head. Note that these are all instantaneous values, long term matters will likely have a greater total effect but that does not show up in these tables.

Pleasure & Pain Standard Levels

Here is a standard list of pain and pleasure levels and their values in the Mars OM system. I have adapted some of the pain descriptors from disabled-world.com. Please note that this is a work in progress and adjustments will certainly need to be made following proper scientific experiment and analysis.

Rank	"F" Value	Feeling	Example	Comment
+10	100	Unimaginable pleasure	Direct stimulation of the pleasure centres to the maximum amount.	Pleasure so intense you will pass out from joy. Most people have never experienced this level of pleasure and never will.
+9	63	Extraordinary pleasure	Very strong drug enhancement of strongly pleasurable activities.	Pleasure so intense your mind is blown by wave after wave of incredible physical joy.
+8	39	Ecstasy	Drug enhanced strongly pleasurable activities such as sex on ice. Extreme adrenaline activities such as base jumping, big wave surfing.	Moderate enhancement of strong pleasure.
+7	24	Bliss	Great tangible personal success after a huge commitment. Once in a lifetime sporting victory.	The peak of natural pleasure. Only a few of these in your whole life.
+6	15	Euphoria	Best sex unenhanced. Special large scale sporting victory.	Natural pleasure at a special level. Most of your best moments will be at this level.
+5	9.1	Delight	A special night drinking with good friends. A great day's surfing.	The pleasure is intoxicating and addictive.
+4	5.3	Strong pleasure	Eating good food when hungry. The physical exhilaration of climbing a small mountain.	Obvious pleasure which cannot be ignored.
+3	3.0	Moderate pleasure	Consuming an inter-meal snack such as a piece of chocolate or a tasty biscuit. Holding a loved one's hand. Having a nice chat with a friend or family member.	Very noticeable and not easily ignored.
+2	1.5	Mild pleasure	Drinking a normal cup of tea or coffee. Being out in nice weather.	Noticeable but easily taken for granted.
+1	0.6	Slight pleasure	Doing the crossword. Feeling clean after shower.	Barely noticeable pleasure. Most of the time you never think about it.
0	0	Neutral	Normal calm situation.	No pain or pleasure at all, you feel a little flat but not bad.
-1	-0.6	Mild Discomfort	Minor itch from mosquito bite, poison ivy, nettle etc.	Barely noticeable pain. Most of the time you never think about it.
-2	-1.5	Discomfort	Accidentally knocking your hand or arm lightly against something hard. Lingering aftermath of a cold.	Noticeable pain but easily ignored.
-3	-3	Tolerable pain	An accidental cut, a mild blow to the nose causing a bloody nose, or a doctor giving you an injection.	Very noticeable pain, though tolerable, but not easily ignored. You can adapt to it and ignore it over time.
-4	-5.3	Annoying pain	Average toothache, the initial pain from a bee sting, calf cramp, or minor trauma to part of the body, such as stubbing your toe hard.	You notice the pain all the time and can put up with it but you cannot ignore it, nor can you completely adapt.
-5	-9.1	Distressing Pain	Strong, deep, piercing pain, such as a sprained ankle when you stand on it wrong or mild back pain, full leg cramp.	Not only do you notice the pain all the time, you are now so preoccupied with managing it that your normal lifestyle is significantly affected.
-6	-15	Intense Pain	Comparable to a bad non-migraine headache combined with several bee stings or a bad toothache.	Strong, deep, piercing pain so strong it seems to partially dominate your senses, causing you to think somewhat unclearly. At this point you begin to have trouble holding a job or maintaining normal social relationships.
-7	-24	Very Intense Pain	Comparable to an average migraine headache, bad back pain or extreme toothache.	The pain completely dominates your senses, causing you to think unclearly about half the time. At this point you are effectively disabled and cannot function properly.
-8	-39	Agony	Childbirth or a bad migraine headache.	Pain so intense you can no longer think clearly at all, and may cause severe personality change. Suicide is frequently contemplated and sometimes tried.
-9	-63	Excruciating Pain	Throat cancer or the initial strong physical trauma from a car crash or industrial accident occasioning massive bruising, broken bones, torn ligaments etc.	Pain so intense you cannot tolerate it and demand pain killers or surgery, no matter what the side effects or risk. If this doesn't work, suicide is frequent since there is no more joy in life whatsoever.
-10	-100	Unimaginable Pain	Severe accident, a crushed hand.	Pain so intense you will go unconscious shortly. Most people have never experienced this level of pain.

Capability Standard Levels

Here is a standard list of capability and disability levels and their values in the Mars OM system. Please note that this is a work in progress and adjustments will certainly need to be made.

Rank	"F" Value	Feeling	Example	Comment
+10	100	God!	Confined to fiction for the moment. Various SF and fantasy characters such as the Six Million Dollar Man, Doctor Strange etc	Multiple extreme artificial enhancements with full training.
+9	63	Demigod	Lance Armstrong, Renate Stecher, Arnold Schwarzenegger	One extreme artificial enhancement with full training or two extreme talents with major trainings.
+8	39	Genius	Usain Bolt, Gary Kasparov, Albert Einstein, JRR Tolkien, Michael Jordan, Luciano Pavarotti, multi-disciplinary professional sportsman	Two extreme talents or one extreme talent with major training or multiple major talents and/or trainings.
+7	24	PhD	Bob Marley, Paul McCartney, multi-degree graduates	One extreme talent without training or multiple major talents or trainings.
+6	15	Professional	University science graduate, professional sportsman, professional musician, quality tradesman	Two major talents or major trainings or one major talent with major training or multiple moderate talents and/or trainings.
+5	9.1	Tradesman	University humanities graduate, basic tradesman, school teacher	One major talent or major training or multiple moderate talents or trainings.
+4	5.3	Amateur	Secondary school graduate, amateur firsts footballer, singer in an auditioned amateur choir	Two moderate talents or moderate trainings or one moderate talent with moderate training or multiple minor talents and/or trainings.
+3	3.0	Fair	Average year 10 student, child who taught herself piano,	One moderate talent or moderate training or multiple minor talents or trainings.
+2	1.5	Basic	Average player in a minor school orchestra, student in the school 2nd football team,	Two minor talents or minor trainings or one minor talent with minor training.
+1	0.6	Ordinary	Untalented learner violinist, average occasional cyclist, average year 7 student.	One minor talent or minor training.
0	0	Basic capability	Average young couch potato.	No special capability but no disability either.
-1	-0.6	Almost normal	Cut finger with Band-Aid	One minor disability with minor amelioration.
-2	-1.5	Inconvenienced	Cut finger, minor tendinopathy, asthmatic with Salbutamol,	One minor disability without amelioration, one medium disability with medium amelioration.
-3	-3	Hampered	Bad cough with lozenges, bad hangover with aspirin and milkshake, amputee with enhanced prosthetic,	One medium disability with minor amelioration, one major disability with major amelioration.
-4	-5.3	Limited	Bad cold, bad hangover, tone deaf, clumsy, stupid, advanced arthritis, epilepsy, diabetes, asthma, torn hamstring, short sightedness, amputee with prosthetic,	One medium disability without amelioration, one major disability with medium amelioration.
-5	-9.1	Semi-handicapped	Blind with electronic sensors, quadriplegic with wheelchair and computer	One major disability with minor amelioration, one extreme disability with major amelioration.
-6	-15	Handicapped	Retarded, amputee, blind with a dog, quadriplegic with electric wheelchair, advanced dementia, RSD	One major disability without amelioration, one extreme disability with medium amelioration.
-7	-24	Disabled	Blind with a stick,	One extreme disability with minor amelioration.
-8	-39	Severely Disabled	Blind, deaf, quadriplegic, moronic, confined to bed	One extreme disability without amelioration.
-9	-63	Non-Functional	Blind & dumb, bedridden & sedated, Stephen Hawking without wheelchair and computer.	Extreme disability in two areas without amelioration.
-10	-100	Dead	Anyone who has died.	Extreme disability in all areas without amelioration.

Stress Standard Levels

Here is a standard list of satisfaction and irritation levels and their values in the Mars OM system. Please note that this is a work in progress and adjustments will certainly need to be made.

Rank	"F" Value	Feeling	Example	Comment
+10	100	Cloud 9	Your companies run the world with ease. You own the police force. Your children all won gold at the latest Olympics. Your TV show is the hit series of the year. You recently solved world poverty and found the cure for cancer. People pray to you at night.	Perfect feeling of satisfaction. Nothing could improve it. You could walk off a cliff and you wouldn't fall.
+9	63	Heaven	You won the lottery twice running. Your international company is the dominant force in its area. Politicians ring you for advice and permission.	Almost perfect feeling of satisfaction. You can't easily think of any way your life could be better. If you bought a lottery ticket you would certainly win.
+8	39	Dream	You have been promoted beyond your worth. You have more money than you know what to do with. You own one or two houses that you never visit. Your partner loves you more than you ever dreamed. Your team can't lose.	It all seems too good to be true. You feel you're living in a dream and are worried that you might wake up. Everything you touch turns to gold, even if the plan is unsound. Everyone loves you. There are one or two things left to achieve but the world is your oyster.
+7	24	Extreme fulfillment	You have the house, car and partner that you always wished for. Your children are intelligent, attractive and successful. You are now the boss.	Life is even better than you imagined it could be. You must be blessed! You can't remember your last negative thought. Nearly everyone is on your side.
+6	15	Fulfilled	You have a new car and house. Your love life is exciting and rewarding. Your job is exactly as you had hoped.	Yes! This is how you thought life would be. Every plan you make is successful so long as it is soundly based and properly implemented. Many people want to be your friend.
+5	9.1	Strong satisfaction	You are promoted at work. Your love life is looking up.	All right! You plans are mostly working out! You feel lucky. People want to be around you.
+4	5.3	Contented	You are on top of your work. You have a date with someone you really like.	Things are coming along nicely. You are cheerful and positive and it begins to rub off.
+3	3.0	Noticeable satisfaction	Your team won for the first time in a while.	You feel a noticeable contentment. You start to adopt a positive attitude to life.
+2	1.5	Mild satisfaction	You finish the crossword.	The sense of satisfaction is small but it is there. You barely notice it.
+1	0.6	Slight satisfaction	Your clothes are clean.	You feel a very minor feeling of contentment. You only notice if you concentrate on it.
0	0	Neutral	Low expectations relaxed dude	No irritation or satisfaction, you feel flat but not bad.
-1	-0.6	Slight irritation	Your shoelaces are getting frayed.	The irritation is very minor. You only notice if you concentrate on it.
-2	-1.5	Mild irritation	You are wearing the underwear you wore yesterday.	The irritation is small. You barely notice it.
-3	-3	Noticeable irritation	Your team lost again. Your neighbour's car woke you up early.	The irritation is noticeable but you can just ignore it. Your attitude towards the stressors begins to change.
-4	-5.3	Moderate stress	Your neighbour's make significant extended noise far too often. You are struggling at work. You car is playing up.	The stress has become a real problem in your life. You spend significant time worrying about it. Your attitude towards the stressors is now negative.
-5	-9.1	Strong stress	You lose your job. Your car isn't going and you can't afford to fix it.	The stress occupies your mind half the time. Your joy in life is gone most of the time.
-6	-15	Great stress	You are significantly behind on the rent and don't know how you will find it. Your true love has left you. One of your children is in trouble with the law.	The stress makes normal behaviour around the stressors very difficult. You may commit acts of spiteful abuse and irrationality.
-7	-24	Extreme stress	You haven't slept properly in weeks due to the neighbours incessant noise. Standover men are stealing your money. You are in court facing jail time.	The stress is approaching intolerable. Your personality is altered and you may commit acts of violence and destruction.
-8	-39	Nightmare	Multiple cases of rank -7.	The stress is approaching intolerable. Your personality is altered and you may commit acts of violence and destruction.
-9	-63	Hell	You murder someone that you hate.	The stress is intolerable but murder will remove it.
-10	-100	Deepest Hell	You commit suicide.	The stress is intolerable and the only way out is suicide.

Social Standard Levels

Here is a standard list of social belonging levels and their values in the Mars OM system. Please note that this is a work in progress and adjustments will certainly need to be made.

Rank	"F" Value	Feeling	Example	Comment
+10	100	Complete feeling of belonging	True patriot and devoted family man/woman, born and bred, loved by all!	Strongly love of nation and general public, many good friends, many close family members and strongly committed to spouse.
+9	63	Very strong sense of belonging	Happy housewife who loves her spouse, family and country but has no strong friends. Child who loves his family, friends and nation (too young to marry).	Strong connections to most of spouse, friends or family, public and nation.
+8	39	Strong sense of belonging	Strong sense of belonging Devoted spouse with strong family. Divorcee with strong connections to friends and family. Patriot without friends or family.	Strong connections to 2 of spouse, friends, family, public or nation.
+7	24	Solid sense of belonging	Devoted spouse without friends who never sees family. Unmarried woman with a strong circle of friends. Hermit who loves the countryside but hates the people.	Strong commitment to spouse. Many strong connections to friends or family, strong connection to public or nation. Many moderate connections to friends, family, public and nation.
+6	15	Moderate sense of belonging	Unmarried geek with two good friends. Unmarried immigrant with reasonable friends and family. Anti-social married man with little regard for his nation, who comes home every night, eats his dinner and watches the footy.	A moderate commitment to spouse. A few strong connections to friends or family, strong connection to public or nation. Many moderate connections to 2 of friends, family, public or nation.
+5	9.1	Basic sense of belonging	Friendless man with moderate allegiance to his country who hates his wife. Popular man at the local bar with many friends but little else. Divorcee who sees her entire family regularly but has little else.	Many moderate connections to friends or family, moderate connection to public or nation, weak spouse and moderate other.
+4	5.3	Mediocre sense of belonging	Immigrant spouse heading for divorce with no friends or family. Unmarried immigrant woman with no friends who sees some of her family regularly. Unmarried drudge with acquaintances, mild identification with his people and country who sees his family only occasionally.	A few moderate connections to friends or family, moderate connection to public or nation, weak link to spouse, weak connection to everything except spouse.
+3	3.0	Noticeable sense of belonging	Disconnected local who with no friends, who never sees her family but still has a vestige of allegiance to her country and its people.	Many weak connections to 2 of friends, family, public or nation.
+2	1.5	Weak sense of belonging	Lonely immigrant starting to acquire allegiance to his new country. New immigrant with many acquaintances.	Many weak connections to friends or family. Weak connection to public or nation.
+1	0.6	Slight feeling of belonging	Unmarried man, persecuted by his nation, with only cursory connections to family and friends, who is planning to emigrate.	Few weak connections to friends and family.
0	0	Neutral feeling of connection	Lonely opportunist immigrant	No spouse, just a few weak connections to friends or family, neutral connection to public and nation.
-1	-0.6
-2	-1.5	Weak sense of disconnection	Unmarried old man in aged care who's friends and family are dead but has good memories of them.	Many dead family members only and many dead friends only. Weak sense of alienation from nation or people.
-3	-3	Minor sense of disconnection	Only surviving member of family car crash with only a few weak connections to distant relatives, no friends, who doesn't feel she quite fits in.	(Many dead family members only or many dead friends only) and (weak sense of alienation from nation or people).
-4	-5.3	Moderate sense of disconnection	Teenage runaway living on the streets. Old lady who had little regard for her nation and who only had a few good friends and her beloved parents, all of whom are dead.	Few dead family members only and few dead friends only. Moderate sense of alienation from nation or people.
-5	-9.1	There's little for me here	Handicapped man who's few good friends are dead who doesn't feel accepted but has a basic love of the country.	(Few dead family members only or few dead friends only) and (moderate sense of alienation from nation or people).
-6	-15	I don't belong here	Unmarried orphan with just a few weak friends and no allegiance to her nation.	Orphan, never had any friends, strong alienation from the public or nation.
-7	-24	I hate this place	Unmarried Islamic terrorist in an intolerant Christian country.	2 of orphan, never had any friends, strong alienation from the public or nation.
-8	-39	Let me out!	Friendless orphan who likes the country but hates the people.	3 of orphan, never had any friends, strong alienation from the public or nation.
-9	-63	Extreme disconnect and alienation	Nigerian orphan transplanted to Russia brought up in orphanage, never able to make any friends, hates the Russian country and people.	Never had any family or friends, strong feeling of alienation from nation and public.
-10	-100

Self-Respect Standard Levels

Here is a standard list of self-respect levels and their values in the Mars OM system. Please note that this is a work in progress and adjustments will certainly need to be made.

Rank	"F" Value	Feeling	Example	Comment
+10	100	Revered	Lay down your life for others (soldier), devote your life to others (priest), someone who significantly improves the world (great scientist, thinker, composer, artist, writer, general, politician etc)	Perform extreme act for others.
+9	63	Highly regarded	Good father, good mother, devoted worker who goes above and beyond and actually helps people	Perform frequent major acts for self and others.
+8	39	Highly valued	Policeman, businessman,	Perform frequent major acts for self or others.
+7	24	Well respected	"Stand up for yourself" (defend yourself or others in an important situation)	Perform occasional major act for self or others.
+6	15	Respected	Basic father, basic mother,	Perform frequent moderate acts for self and others.
+5	9.1	Valid member of society	"Pulling your weight" (basic requirement for respect), standard worker	Perform frequent moderate acts for self or others.
+4	5.3	Accepted	"Don't take shit" (defend yourself or others in a minor situation)	Perform occasional moderate act for self or others.
+3	3.0	Ok	Do the daily household chores	Perform frequent minor acts for self and others.
+2	1.5	Probationary	"Look after yourself" (attend to one's basic needs)	Perform frequent minor acts for self or others.
+1	0.6	Provisory	Do occasional household chores	Perform occasional minor acts for self or others.
0	0	Neutral	Child that sometimes helps and sometimes doesn't	Neither help nor hinder yourself or others
-1	-0.6	Iffy	Refusal to do occasional chores	Perform occasional minor acts to hurt self or others.
-2	-1.5	Lacking	Too lazy to do the essential chores for yourself, don't do your homework	Perform frequent minor acts to hurt self or others.
-3	-3	Unsatisfactory	Too lazy to do the essential chores for the household	Perform frequent minor acts to hurt self and others.
-4	-5.3	Disappointing	Occasional moderate theft, vandalism, blaming someone else for your minor crimes, not turning up to work, "taking shit" from others	Perform occasional moderate acts to hurt self or others.
-5	-9.1	Disapproved	Habitual thief, peaceful drunkard or drug addict	Perform frequent moderate acts to hurt self or others.
-6	-15	Denounced	Violent drunkard or drug addict, jailbird, gambler	Perform frequent moderate acts to hurt self and others.
-7	-24	Shamed	Arsonist, coward when it matters, rapist	Perform occasional major acts to hurt self or others.
-8	-39	Detested	Crime boss, dealer in hard drugs, defrauder of the vulnerable	Perform frequent major acts to hurt self or others.
-9	-63	Hated	Thug with short life expectancy, family violence perpetrator	Perform frequent major acts to hurt self and others.
-10	-100	Despised	Suicider, murderer, invading soldier	Perform extreme act to hurt self or others.

Standard Functions

Here is a list of standard happiness functions. Their constants vary depend upon the situation and must be instantiated by the operator at run-time.

Permanent Flat

Equation
Description	A constant level of happiness extending indefinitely.
Graph
Constants	"j" is the magnitude of the steady happiness. Here it is 30 but it could any permissible value in a real world example.
Integral
Comment	Flat happiness functions represent unchanging situations in an agu's life. For a human this might be the permanent pain of a chronic disability such as arthritis, reflex sympathetic dystrophy or cancer.

Block

Equation
Description	A constant level of happiness extending only temporarily.
Graph
Constants	"j" is the magnitude of the steady happiness. Here it is 40 but it could any permissible value in a real world example. "b" is the time at which the temporary happiness state reverts to zero. Here is 4 units but in a practical examples it could days, weeks or minutes.
Integral
Comment	A block happiness function applies to situations where there is a steady happiness reading which suddenly ceases such as chronic pain being treated with opioids or the removal of the threat of eviction.

Simple Decay

Equation
Description	An instantaneous peak of happiness decaying exponentially to zero.
Graph
Constants	"j" is the magnitude of the instantaneous peak. Here it is the maximum possible but it could any permissible value in a real world example. "a" is the time of the peak. Here it is at t=0. "l" is the half life of the decay. For every successive timeslice of l hours the happiness value is half what it was in the previous timeslice. Here "l" is 1 and you can see that the value of H halves each successive unit of t.
Integral
Comment	Simple decay happiness functions are very common as they model a whole raft of situations where there is a sudden peak of pleasure or pain which gradually diminishes. Examples include: the marriage day, winning at the races, falling from a skateboard etc.

Cyclic

Equation
Description	A sinusoidal cycle of constant period and intensity.
Graph
Constants	"j" is the magnitude of the cyclic peak above and below the average value. "q" is the period of the cycle. "o" is happiness offset of the cycle, corresponding to its average value. Here is based around 0 but it could have had a positive or negative offset.
Integral
Comment	Cyclic happiness functions are very common as they model a whole raft of situations where happiness comes in cycles such as addictions of all kinds, regular events and activities (daily, weekly, monthly etc) such as club meetings, hormonal cycles, pay days, weather patterns etc.

Plateau Then Decay

Equation
Description	A plateau of happiness followed by decaying exponentially to zero.
Graph
Constants	"j" is the magnitude of the initial plateau. "b" is the time at which the happiness decay begins. "l" is the half life of the decay.
Integral
Comment	Plateau then decay happiness functions are reasonably common as they are really another form of the simple decay, except that here the initial point is a plateau rather than a sudden peak.

Happiness Submetric Attenuation Factors

The section on the theory of Objective Morality mentioned that each submetric must be attenuated to model their value in the real world. Here are those factors. Note that these factors always sum to 1.0 so that the maximum instantaneous pleasure is always 100 and the minimum is always -100.

Pleasure (A_F)	Health (A_B)	Comfort (A_O)	Security (A_J)
0.25	0.25	0.25	0.25

Human Happiness Exemplars

Now that we have the standard functions and tables we can do the maths. Here are some real world examples to illustrate how it all works.

Neutral day

Submetric	Function	Values	Comment
Pleasure	Flat	a=0, b=2	Nothing happens either good or bad.
Health	Flat	a=0, b=2	Nothing happens either good or bad.
Comfort	Flat	a=0, b=2	Nothing happens either good or bad.
Security	Flat	a=0, b=2	Nothing happens either good or bad.