does Love exist?

Leave a comment

Purple lilac symbolizes "first emotions o...

Purple lilac symbolizes “first emotions of love” in the language of flowers. (Photo credit: Wikipedia)

another feature of abstraction is talking about topics that are beyond explanation. Love is such a thing.
in a way Love is empty.  tell me your definition, and I show you it doesn’t exist.
doesn’t mean Love wouldn’t really exist, it’s just our words that can easily be debunked.

well, there are some exceptions:
when you define Love as the thing some couple has running, obviously it exists.
you’d need to try describing their relationship for me to show you how inaccurate the description is.
a relationship is dynamical, it changes with circumstance, new situations produce completely new behaviour.
Similarly I couldn’t do anything with non-serious definitions alike to “love is to take a cold shower every morning”.
surely love is about more aspects of life than just taking a shower? and where’s the other person?
most likely there does exist people who take a cold shower every morning.
I can’t refute this. but if you keep on listing many activities, who is ever doing all of them every time?
words are designed to single out a particular activity, but they can’t encompass complex behaviour patterns.

so the first thing to do for finding out if love exists is to give an abstract definition.
this must be done by everyone individually. if it could be put into words, it wouldn’t be love.
most obvious aspect of love is the lack of hate. does this mean misogynists cannot feel love to a woman?
well, if you go that route, pretty much every male is misogynistic,  as a result love doesn’t exist.
so better get rid of that aspect, experience tells us it’s possible to feel hate and love to the same person.
another idea people might have is that love is exclusive, only one person can be loved.
strictly seen this idea introduces a contradiction when you consider a mother’s love to her children as love.
will she cease to love her husband when she gets babies? that’s doubtful.
the only useful aspect of love here is that of “considering the other person’s point of view”.
of course that’s much too weak for defining love, it also describes any kind of friendship.
so, start from here and attach any feelings you associate with love to that.
when dealing with emotions, this is what must be done in general for an abstraction.
get a bunch of words that can be real, and add emotions around them. that’s a definition.
of course you know that only the emotions are the real emotion.
the words however are just there to protect you in future from wrong decisions.

as I wrote in my previous post, to me warm love is all the love-stuff minus the hormonal and drug-induced feelings.
of course that exists. my bunch of words is “no drugs”, to protect me from addiction.
actually to me it isn’t important if another person considers my point of view.
to me it is natural to consider all people’s points of view.  I don’t expect others to be alike.
the only important thing to me is how I feel when abstaining from sexuality and other fun activities.
if the feelings survive such an abstinence, then I know what I feel is love.
on the other hand I noticed others see “being together” as an important nourisher of love.
in my own experience however it’s just the diversity that’s important.
one could meet only on a monthly basis, as long as every meeting is unique.
this feeling of uniqueness of situations is important to me. stop it, and my love is diminishing slowly.
if monthly uniqueness is enough then a whole year could diminish love only 12 times.
many many years would need to pass that way, till all the unique moments of past are undone…

it really isn’t a problem when every person has a different definition of love.
it is preferable when two people at least agree on a bunch of words to which the emotions are attached.
otherwise the mind would rebel against the idea that such a person can be loved, although only subconsciously.
however, much more important than this agreement with the loved one is to check if love exists.
if you have unfulfillable expectations about love, expectations about yourself or your partner, you’ll only feel miserable!
lighten up your definitions, introduce different words for different kinds of love!
if you are educated with theories of monogamy, tell yourself that to each person you love you have a uniquely different feeling!
maybe even drop the word “love” alltogether, invent new words, or use such words like “affection” or “attachment”.
it makes no sense to learn a new word every day when all the words have the same meaning. create your own vocabulary!

Abstraction of Emotions

1 Comment

English: Robert Plutchik's Wheel of Emotions

English: Robert Plutchik’s Wheel of Emotions (Photo credit: Wikipedia)

the word “Emotion” describes something one can’t actually talk about.
the reason is that I distinguish between a perception and the thing perceived.
Emotions are what we perceive when we have feelings.
so one can only talk about feelings and not about emotions.
however, abstractly the two are connected. therefore the title is justified.

in science it is unknown if  hormones cause what we call feelings, or if it’s the other way around.
therefore the notion of emotions is even less understood by the psychologists.
seems psychology focuses on investigating feelings only.
still, in future the knowledge on feelings might become useful for investigating emotions.
for this to work, first one must distinguish between two kinds of feelings:
Warm Feelings I call every perception that is directly and strongly correlated with measurable circumstances happening beforehand.
Cold Feelings I call feelings perceiving more abstract circumstances happening in the body, and stuff that isn’t measurable at all.

I emphasize: Warm Feelings are any kind of perception, including our 5 senses,  including things we see.
especially a man having a crush for some woman, or a woman having a crush for some Man, these really are Warm Feelings.
various substances in the blood play a role in this perception. it really doesn’t matter if those appear only afterwards.
the trick is to divide every single feeling we have into a Warm and a Cold aspect.
in other words, first comes the Emotion, then Cold Feeling, then changes in the body, those then are perceived as Warm Feelings.
so in investigating emotions, the Cold Feelings are what one should take a closer look at. Warm Feelings are uninteresting.
doesn’t work that way though. human is unable to distinguish between Warm and Cold Feelings.
for example if the love for your beloved one is becoming weaker, is it weakening of Warm or Cold Feelings?
maybe a majority of divorces are just the result of hormonal changes? maybe love wanes because you eat the wrong things?
or the other way around: allegedly increasing frequency of sex will strengthen a relationship. does it strengthen Cold Feelings too?
obviously Warm Feelings will be strengthened because there’s a gratification happening regularly.
neuronal networks work that way: gratification causes strengthening of pathways in the network.
when you gratify being together with husband/wife by various pleasures, is it still Love?
more logically is that changes in the brain create an addiction for the person, or a pavlovian reaction.
you want to be pavlov’s dog? be it sex or even just attention, all these cause merely Warm Feelings.

the notion of “warm feelings” we usually associate with such things like love and such.
that’s why I choose it. what we commonly call love is just hormonal perception and addictive reactions.
eliminate all the gratifications you get, what reasons for your love do remain?
what remains I call “affection”, the Cold Feeling that comes with various emotions we feel for eachother.
in comparison to the Warm Feeling of love, affection is very cold. it’s only about how we are affected!
love contains a lot of desires and expectations that draw us to another person.
the behaviour of being drawn to eachother is commonly called a warm feeling.
similarly the feeling of getting a lot of attention is nourishing for us.
being drawn to eachother, being nourished by eachother, that’s what people even call “hot” feelings.
but if I say “your way of working has affected me, has inspired me” that’s a cold way of saying “I love you”.
especially these kinds of feelings have nothing to do with sexuality or wanting to found a family.
these are emotions that are unconditional, a truly unconditional kind of love.
what most people seek though is a hot love, an egoistic love full of expectations.
afterall, this hot love is what is getting gratified by pleasure, through nature’s dictate.

as tibetan buddhists say, everybody is seeking for bliss, for unending pleasure. they promise buddhism can offer that.
so generally speaking buddhism is a religion focused on giving us Warm Feelings.
this is seen in many aspects they emphasize, but also in their choice of words.

buddhists seek to stop the suffering of people. they have a feeling of being obstructed by the sufferings of others.
just getting into bliss isn’t sufficient for them, they also want that others get the same bliss too.
this compassion they feel is called “karuna”. “Kam” means bliss, “runa” means stopping.
one specific method, in the tantric branch of buddhism, is using sexuality to attract people.
they have the idea that there is a moment of bliss in sexuality, maybe this could point at what real bliss is.
their method is to get people towards an orgasm without emission of all the things that have functionality in reproduction.
i.e. men wont ejaculate and women too will rise their passion indefinitely spreading bliss throughout their body.
this goal of orgasm without emission they again call “karuna”, but for other reasons.
still it’s the same word, so in a way all these things are related: obviously bliss is a Warm Feeling!

the actual goal of buddhists is the “ultimate mind of enlightenment”.
it’s described as “wisdom consciousness in the continuum of Bodhisattva directly realizing emptiness”.
the word bodhicita is understood as “mind of enlightenment”, the “altruistic intention to become enlightened”.
remember the notion “emission of all the things that have functionality in reproduction” in the previous paragraph?
what actually is being emitted by men and woman during ordinary orgasm they call bodhicitta too.
so in their choice of words they already indicate that what they really want is the reproductive part of sexuality.
no matter how the nature of this goal, feelings caused by reproductive mechanisms are Warm Feelings, so is the goal!

to be fair I must also mention that aside from bliss buddhists also seek so-called “emptiness”.
however, the tantra sex division insists that this is achieved for a moment during sex too (and lost in orgasm)!
emptiness means that all notions we have about the world lose their dualistic judgements.
we see stuff and immediately draw conclusions on whether they are good or bad, beautiful or ugly, and so on.
purely seeing the world without such judgements, through emptiness, is the only way how bliss actually is possible.
if we would constantly judge things, we end up feeling bad about the bad things around us.
being unaffected by the badness is how during sexuality the good feelings are kept alive.
would we start judging badly about something, arousal would wane, sex would be no fun.
but even though the feeling of “emptiness” happens in sex, it seems to be a Cold Feeling.
there is no known physical phenomenon that would match this feeling.
substances in our blood don’t change that much through orgasm.
neither do scientists speak of whatever phenomena ending because of orgasm.
but yet we all know how judgemental one is right after or during orgasm…

just to clarify, in tibet there are 2 major kinds of buddhism:
one kind calls the pearls of wisdom it is founded on “tantra”. as in tantric sex.
the other kind calls such pearls of wisdom related to the own school “sutra”. as in kamasutra.
however, both require their monks to be mostly without sex, especially when in the monastery.
so don’t let the words mislead you into believing they would be any more liberal than western religions.

oh, and as a disclaimer: I know only very little about buddhism.
I know it’s a religion originating from what is now pakistan.
I know what I have read in some books.
a religion is about what the participants say though.
you just can’t read some bible and you know everything there is to know!

but there seems to be an alternative I must investigate myself:
the dzogchen branch of tibetan buddhism is focusing on leaving things the way they are.
that means no changes in the body, but yet a different state of mind, different feelings.
clearly those feelings must be of the Cold kind. they make use of warm feelings too though.
for example practitioners are controlled by fears and various kinds of placebo.
but those are all just tools, and it is made clear from the beginning that they wont matter lateron.

in summary I propose that the reader might ask the important question:
does my favourite religion focus on Warm or on Cold Feelings?
in terms of learning to cope with our emotions religions play an important role.
all the things we cannot measure but that still affect us, they all are handled by religions.
the things we can measure are being handled by science. in science you find knowledge on Warm Feelings.
so what use is a religion that too does focus on Warm Feelings and neglects Cold Feelings?
in order to live we need knowledge on both, the more we know the stronger is our grip on life.
if it’s just one-sided knowledge, our grip on life will be rather like holding dry sand.
whatever goals we choose for life, Warm and Cold Feelings bust be understood equally.
a firm grip on one and the other will valve away the things we’re trying to get ahold of.

most people want to control their feelings. some might even succeed.
but isn’t that alike to controlling how we perceive visual input by hallucinating stuff?
for Warm Feelings control is primarily a self-delusion, once feelings arrive something else caused them.
those people then retreat into controlling the mechanisms leading to the feelings instead.
wont work with Cold Feelings. we don’t know how they are caused!
so in effect all attempts of control just end up in the delusion of being in control.

being in control is a Cold Feeling. none-the-less it is an uninteresting kind of feeling.
the thing being perceived through the feeling is the abstract notion of controlling.
in a way this is a much warmer feeling than other Cold Feelings.
the only reason it isn’t a Warm Feeling even though control is measurable:
human tends to rely more on self-reflection than on actual self-perception.
if you want to outperform most other human beings, just get rid of that!
assert your own risks, find out what dangers could await you in future.
always be aware of what your current situation is in terms of risks.
this knowledge then will set you apart from others who don’t do that.

in general, as I implied above throughout this article, one must distinguish between control and knowledge.
both are about predicting the future, Knowledge is about doing it actively, Control is the passive way.
when you feel in control it is a prediction that things will go your way in future.
when you have knowledge however, you predict the future in terms of probabilities.
whatever knowledge you are lacking you can make up by an estimate for likelihood.
regardless how you use that knowledge, control never is possible this way.
the more you know, the better you will understand that you don’t know everything.
especially it is totally unpredictable how the world will work.
you never know if you haven’t made a mistake, if you are aware of all possibilities yet, and so on.
on the one hand, with control you wont get the awareness that full control is impossible.
knowledge on the other hand leads to the insight that what you know is just a tiny fraction of reality.
therefore only knowledge is capable of breaking the deceitful mirror of self-reflection we rely on.
similarly only a desire for control will lead to the Cold Feeling of safety and stability.
the choice between knowledge and control is a choice between loss of self-delusion and loss of risks.
if it is risks you want to fight, control is what you must obtain.
if you want to get rid of all lies, Knowledge is what you must seek.
I prefer Knowledge, I prefer being aware of my risks instead of fighting them.
I think it is important to realize that the two are mutually exclusive.
Knowledge is not available when living a sheltered life, for knowledge one must visit other places, take risks!

understanding the own Feelings is one thing. it’s important for predicting the own behaviour.
but also very important is to actually take the risk of allowing the own feelings to surface.
an Emotion causes a Feeling. and some feeling will cause certain changes in behaviour.
if the behaviour is suppressed, the feelings will get suppressed too, as if some abstract eye-lids were closed.
the underlying emotions still exist, but such a person will fail to perceive it.
more exactly only a small part of the body will fail to perceive the emotion.
the unwanted behaviour will vanish because the responsible body-part is blind.
the rest of the body will perceive the emotion though. this results in imbalance.
especially it’s an imbalance of information, some body-parts know more than other.
mostly it’s then the conscious mind that knows nothing.
it’s easy to get rid of fear, doesn’t mean you’ll stop trembling and your body will obey you…

Sex, Drugs and rockin’ Roles

1 Comment

P icon for main page

P icon for main page (Photo credit: Wikipedia)

the advantage of abstraction is that one could talk about such things and even small children will understand.
good for me, in this posting I’ll talk about things of which I too have little experience.
this is a posting about gender-topics and about time-management. more exactly freedom is what I’ll talk about.

but first the basics: in one aspect human is very similar to animals, biology dictates we must procreate.
this is done by a mechanism we commonly call “pleasure”. funnily same mechanism is used for other biology-dictates too.
being together with others is pleasant. seeing a beauty of the preferred gender is pleasant (regardless of clothes).
cuddling is pleasant. but also eating fat and stark/sweet is pleasant. same for relaxing and entertainment.
a work where you encounter new situations all the time is a pleasant work, although tiring.
a work where nothing new happens and everything is clearly predictable is pleasant.
all these things are pleasant because they ensure survival and offspring.
in a human life we must make sure all these things are present, in equal quantities.
if not, we have a problem with our mind, imbalance of them leads to mental imbalance.
in the least depression will evolve if we don’t take care to be pleased all the time.
and doing just one of those things all the time soon will make pleasure decline.

beyond all those pleasures there further exists a peak in pleasure within some activities.
pleasure is created by many different chemicals our body will produce.
so just do something that creates pleasure, and keep doing more such things.
that’s how offspring is created. so in a way a kiss will make you pregnant.
but the very kiss is only a beginning. really at fault is the human indulgence.
one could keep kissing for hours, no babies will be made this way.
but indulgence means we want more, we want multiple pleasures happening at the same time.
so add to the kissing more and more ways of touching each other.
that’s how nature would lead us to pregnancy like kettle to the butcher.
so next time you blame “kissing” for an unwanted pregnancy, blame your indulgence instead.

talking of indulgence I must also clarify the concept of “rape”:
a heterosexual man, standing naked in the shower, approached by another man from behind will feel raped.
sexual activities between those two will not be consensual, the hetero wont like what’s happening.
maybe there will be physical arousal. maybe the hetero will experience orgasm. it wont be pleasure!
same when a man rapes a woman, she might get physically aroused and orgasm, doesn’t mean it’s pleasure!
in both cases psychological damage will be the result. getting raped simply does count negatively in pleasure.
next time the raped person will have sex, memories on the rape will reduce the pleasure-gain.
sexually harassing children will have similar effect on them. no matter if they manage to orgasm.
the difference in strength/size and authority will simply make this a totally unpleasant experience to them.

when talking of pleasure one must stay on the abstract level. calling an orgasm “pleasure” is dead wrong.
sometimes sex between wife and husband can also be bad for pleasure when not consensual.
just imagine you’d wake up and some daemon has moved your hand with the purpose of masturbation.
it’s like a drinker complaining that the drinking just happens automatically.
whatever addiction, it’s always a loss of control. rape is much much worse than that!
if it’s adult-to-child, gay-to-hetero, man to  woman, woman to man, even woman-to-woman, rape is rape.
on the other side there is the mysterious force of emotional arousal. no such thing during rape.
physically aroused is a possibility during rape. a man being raped can have an erection, even when wrong gender.
but such a man would never call himself horny. on the other hand a man can be horny without erection.

there’s clearly a difference between erection (physical arousal) and horniness (emotional arousal).
sexuality is only fun with the latter, no matter if man or woman. so a mild form of rape is sex without horniness.
calling that rape is of course an overstatement. am I raping myself when masturbating without horniness?
similarly it would be an understatement to claim rape happened because of indulgence.
so better keep rape and indulgence-triggered impatience apart.
still, both are conceptually the same: non-consensual sexuality. just a difference in severity.
in effect both are bad, in the long run they have similar effects: sex is no fun anymore.
the offender often wont acknowledge the wrong-doing though.
most immature people believe physical arousal to be such a magic thing that “forces” people into sex.
as I’m saying 3 paragraphs earlier, it’s indulgence and not arousal that forces things!
and even if it is arousal that had any intense effect there, then it’s the emotional and not the physical arousal!
so, dear rapers and misogynic husbands:
please don’t push responsibility to your erection, it’s your indulgence that’s at fault for your sexual assaults!

the human body is full of drugs, created by the human body itself. naturally!
various mechanisms trigger their creation, especially activities that cost a lot of effort.
those efforts mainly trigger drugs we experience as pleasant, thereby human always tries to do something.
humans don’t croak nor sing to attract the opposite gender, so we must actually walk around and seek people.
this way those internally-self-made drugs in our body are showing us what we have to do, give us a meaning.
it’s sort of like the game where a blind-folded person has to seek something by help of others shouting.
in this game it’s common that such other people refer to your activities by giving a temperature-analogy.
same way also biology knows different degrees of motivation. sexuality being the hottest, in terms of pleasure.
we are guided by biology, by the internally created drugs, all with the goal of pushing us towards procreation.
to us it’s like a game, to biology it’s essencial for our species to keep us under influence of those self-made drugs.
all those drugs in our body are gradually created and gradually removed over time, all the time.

physically there is a limit on how quickly those drugs can be created.
but not the body-parts creating them are the bottle-neck. there must be the chemical components present to create them.
our blood is saturated with those too, they come from our food, directly extracted by the body, or by bacteria.
when there isn’t enough food, we also lose the ability to be happy, sexuality loses its appeal.
same happens when too much pleasure-drugs were created by the body. the pleasure gain will decrease as raw material decreases.
that wont be noticed of course, more and more of those drugs accumulate. but the speed of this increase wont be what it used to be.
so depending on what you eat, there is a limit to how much pleasure you can get out of pleasant activities.

this makes us independent from the nature’s dictate to eat and procreate!
instead of doing what creates the most pleasure at once, let pleasure build up in small steps.
then keep it at the high level by adding more and more pleasant activities, by living on your toes.
our mind needs a certain level of pleasure to function properly, otherwise it will have no motivation to live on.
most people’s strategy is to have sex regularly to get a boost of pleasure, to keep up this level.
one short activity, taken like a pill prescribed by the doctor, and your mental functionality is ensured.

but is sex really so much more efficient than letting nature take its course?
well, an alternative, commonly employed, is to eat all the time, or to ingest drugs directly.
alcohol, cigarettes, tea/coffee, all those are legal drugs commonly used here.
additionally excessive eating of salty fat and sweets or flour (the so-called “empty calories”) has similar pleasure-effects.
or claim you have a depression and get something prescribed by the doctor. also quite common.
however, all those things have a big disadvantage: they slowly poison the body.
in the middle-ages where people lived not much longer than 30 years, that poisoning was neglectible.
but nowadays the disadvantages overwhelm the advantages. especially the time-factor is important.
sex would take one hour per day, 20 cigarettes with 5 minutes each take up more than 3 times as much.
getting drunk and being drunk also steals much more valuable time than it’s worth. same with gluttony.
not to mention the money all these things cost.
on the other hand, sex, when done  right can make 2 people happy at once. and it takes little time to reach satisfaction.
(and with satisfaction I don’t mean Orgasm, sex on its own fills up also a pleasure kind of satisfaction.)
this way the  costs are minimal. provided you are experienced and capable of expressing it, you’ll find someone to share with.
so I would say, sex gets the 2nd place for efficient pleasure-creation, the others are 3rd.
1st place in efficiency is reserved for living on your toes. it costs nothing and no side-effects.

and with living on your toes I mean living on the edge (edge to insanity), living on the limit (limits of socially acceptable).
the idea is to do what you want whenever you want, while avoiding to do what you wanted to do in past — to eliminate bias.
well, not as irresponsibly as this sounds, just set up some goals and follow with them till pleasure wears out.
and don’t confuse lack of pleasure with unpleasant experiences. even unpleasant stuff can be pleasant too.
instead of leading a comfortable life you’re supposed to lead a thrilling life, most likely full of fears.
fears are uncomfortable, unpleasant, but the thrill gives us pleasure, to make up for that.
the advantage here is that living on your toes and following your goals get done all at the same time.
no additional costs needed, no side-effects, no waste of time. that’s a life worthy to give up sex for.

actually there is a side-effect: you sort of burn-out!
that’s basically about becoming insane from too strict focus on some area of interest.
imagine you’d be some woods, and you’d burn out trees in a certain area faster than they regrow.
of course eventually the damage will be so big that a very long time would be needed for healing.
however, picking individual trees in a wider area would result in better regrowth rates.
abstractly seen this is a common situation with all renewable resources that emerge from their neighbours.
a whole glade simply has less neighbours than the same area split into many small gaps sprinkled everywhere.
and our mind basically is such a renewable resource which depends on its neighbours.
one damaged brain-cell can be replaced by its neighbours, a whole area of damage can’t.
so if the same brain-area gets overused, it will need some time to get restored, to replenish its resources.
if it would be just a single brain-cell, other brain cells could temporarily take over some burden.
if you live on your toes burn-out is an issue, you must be careful. but it can be avoided.
the secret is to obtain the ability to stop anytime you want to, and to start again as if nothing happened.
life is boring, unlike in a film in real life there often is opportunity to rest.
living on your toes means at those times you cannot rest, or else the pleasure gained wont suffice.
but to avoid burn-out you also cannot continue being occupied with stuff that has no urgency.
it’s a thin line between activity and inactivity you have to walk there.
always you’d have to verify if thinking or action actually creates progress.
and if it doesn’t then you must stop it at once.
and this stopping must be done by starting to be occupied with something else.
preferably your new activity must be completely unrelated.
for example if you come home from work, from a stressful job, is an action-film really your best option?
first people get stressed out at their job and then at home they continue the stress with various media.
not surprising that burn-out is so common in our culture.
the things we see in the media are destined to make us think about our stress at work.
this way the stress never will cease, all the same brain-areas are under constant pressure.
mal-nourishion of those areas is really not surprising, no matter how much we eat.
also pleasure isn’t likely to be a result from that, things we do on auto-pilot wont make us happy.
with burn-out the auto-pilot mode is inevitable. too little energy left to do anything more sophisticated than that.
living on your toes, as the name suggests, is very dangerous and requires a lot of effort and preparation.
not surprising that it’s done so rarely, regardless for its high efficiency.
in past it required high spirituality, so you could always find a new task: meditation/praying.
now with the internet/phone following us everywhere, various activities there can take over the role of meditation.
mostly sects and religious organizations suggested this way of living. they did come with celibacy too.
now asexuality isn’t limited to spirituality and mysticism anymore. you don’t want children so have no sex.
just try to become rich, instead of wasting your time for sex or whatever pleasure-gain.

sexuality has become a functional activity in our society. it isn’t tied to love and procreation anymore.
we can have sex without getting babies, and we can get babies without actually having sex together.
this development degraded females from birthing-machines, the guards of our next generation, to sex-machines.
I mean of course, objectively seen it’s a degradation, in terms of our survival as a species. individuals might see it differently.
realistically seen, for females their sexuality costs more than for males, so they should have less sex than men.
but instead they merely up the price, as if all the dangers, from pregnancy to various diseases, could be nullified with wealth.
at the same time females invest more time than males into activities a behavioural scientist would call “mating”.
and when asked they claim it isn’t for that, they do all the fashion-stuff and the make-up for themselves and their female friends!
and in a way they are right, males also consciously act differently when females are around, claiming it’s “for themselves/friends”.
still a bad idea to obtain self-esteem from how other people see the person.
even worse is the idea to weight that judgement by the critic’s beauty/hierarchical power.

it isn’t unusual to apply different weight onto other people’s opinions.
a friend’s critique will have more impact than a stranger’s.
that’s a good thing since this way we can protect ourselves against critique.
surround yourself with people who use white lies instead of critique, and your self-esteem will rise.
then it wont matter that others complain about various traits, you can lie to yourself that the friends see it differently.
however, when the only person complimenting you is your friend, it rises the question about the friend’s honesty.
additionally once that friend would stop being a friend, those past compliments are doubted even more quickly.
and if that friend would die, suddenly the level of compliments would drop dramatically.
if the beauty/power of the person making a compliment does matter for you, loss of that beauty/power could be life-changing too.
and if you lose beauty/power, maybe those people with beauty/power will stop talking to you altogether.
better get the positive feedback from yourself only, not from others!
and if it’s from others, don’t weight each person’s opinions according to their appearance/fame.
otherwise, huge disappointment and total loss of self-esteem might be the result.

another strange observation about females is that regardless of the importance they had in history, they were treated badly.
they had no rights to vote, no access to higher education, they weren’t even expected to ever leave home.
understandable that with the power to grow up children access to weapons and military service were not granted to them.
biologically a hurt female is worse for a species than a hurt male, the procreation-speed depends on their health.
also a good excuse for making them stay at home. society back then was much more violent.
but it doesn’t explain why all the “important” jobs were disallowed for women. religion, politics and science were said to be not their forte.

as I learned from my own experience there is a good reason why females were disallowed to enter those male bastions.
sadly this experience cannot be put into words, at least not by me. I still will try my best to at least point into the right direction:
there is a difference between how males and how females think. this is an extremely small difference.
it’s this difference which can only be experienced, so if you didn’t then you will misunderstand what I’ll say.
one example of that difference can be found in the joke some feminist made about males by raising the questions:
why do men always have to buy a whole year’s supply for toilet paper?
why do men always have to buy merely a single roll of toilet paper to solve only the current shortage?
another example is my very own experience of playing computergames. I talked to females and they couldn’t understand.
but to me it is a source of pleasure to reload a game after making a mistake led to loss of game and to re-do that mistake.
I mean, I re-do the mistake intentionally, and I repeat that until the mistake doesn’t lead to loss of game.
this is a totally non-sense action, avoiding that mistake is what needs to be trained for a success in the game.
calling such a mistake-redoing “training” is the worst excuse for it anyway. the circumstances simply are much too unusual.
or just watch the film tin cup and tell me why the protagonist did repeat his unsuccessful attempt so many times, at the end.
all these things are abstractly seen just about males repeating some mistake that leads to failure till it doesn’t.
females never show any such behaviour, even less do they ever claim to enjoy doing it (although they might enjoy watching).

now lets emphasize what I do not mean when talking of differences between male and female thinking:
it definitely has nothing to do with one gender being more intelligent than the other.
neither do men do such things because of their stupidity, nor do females avoid that because of theirs.
it simply serves no purpose at all, not even the purpose to attract females nor to impress them.
well, it might impress them, they can’t do it, but it definitely wont tell them how good a husband/father the male will be.
also I should point out that above I described a visible behaviour, in order to define a way of thinking.
of course females could mimic that behaviour of males, maybe even enjoy it like males do.
but I’m talking here of a way of thinking! it’s this way of thinking that females cannot do.
or rather their creativity is lacking the possibility to come up with such ideas that lead to the behaviour I describe.
of course females can also act geeky, they can make cool stunts on skateboards and such.
also females can come up with ideas for new dance-performance or sports-choreography.
you name it and females can do it. the creativity of females simply has no limits, neither has male creativity.
also, I definitely am not talking here of differences introduced by education or whatever social stuff.
it’s rather a difference in how sexuality gets experienced. a way of thinking males “learn” from the way they have sex.
this way of thinking somehow resembles an up-down motion like the one males perform during their sex.
except it is a mental up-down motion, a pointless repetitive movement in the male’s mind.
but it also isn’t mental masturbation. again females are well capable of doing that too and they too enjoy it.
in mathematics people claim to enjoy creating short and neat formulas. again females I’ve met enjoy that too.
nor is it about females being more practical. and it definitely isn’t about the ability to think abstractly.
some say females are more down-to-earth than males, this impression is definitely a result of that difference in thinking.
however, using common dictionaries to understand that claim will only show that it really is prejudice, a misogyny.
most likely this different way of thinking is caused by huge amounts of testosterone, it definitely cannot be learned.
instead I have seen men lacking this way of thinking when their testosterone levels were low. I could be wrong though.

male scientists obviously noticed this difference (at least subconsciously).
and they took advantage of it to make science inaccessible by females.
on the one hand they argued in a way that other males agreed that females think differently.
and they used that argumentation to claim that females wouldn’t be capable of science.
even though that claim is false, the underlying explanations did ring true to males.
this way even a totally matriarchal society could be changed into a patriarchal one.
one has to always keep in mind that not all males want to suppress females.
so for true misogyny there always needs to be some way to convince those who don’t. and females must be convinced too.
on the other hand the whole science is built in a way that is appalling for females, they don’t like it.
again this is because of abusing the difference in thinking, and has nothing to do with science itself.
especially in mathematics I can see that some subjects attract more females than others.
coincidentally those subjects are practically oriented, thereby tempting to make the conclusion females would be more practical.
but in reality it’s just that those practical subjects were re-formulated so that all the male way of thinking is gone.
because of being useful in practice, that part of mathematics has much more attention.
there simply is happening a lot more development in those areas, a lot more people try to re-formulate those subjects.
so quite naturally, with increasing female audience, those have been reformulated for them too.
still, many topics of Algebra are also interesting for females, even though not part of applied mathematics.
they definitely haven’t been reformulated for a new audience since hundreds of years.
however, those topics speak the language of actual formulas. no buzzwords and no complicated concepts needed.
males did define most of the concepts and categories now in use for mathematical stuff.
and in order to explain how they arrived at those, the males just put up awkwardly heavy mental structures in their books.
in reality those things could be explained with much simpler words, but somehow males are too lazy to find them.
this way, while females are too lazy to understand them, males can take shortcuts through their way of thinking.
formulate those things differently, and females will experience the same difficulty level as males.
it’s quite a misogyny that science is structured that way, it serves no other use than to exclude females.
but it isn’t done consciously, it has grown that way by the mere fact that all those books are written by males.
so if you are a female and you have understood maths: please write a book about it! put it into your own words!
would also benefit males. those overcomplicated formulations fending off females definitely are difficult for males too.

I repeat what I said above: this different way of thinking is not related to intelligence!
when I say here that females have more difficulties with understanding science than males, sounds like a contradiction.
that’s why I also said that I cannot express this “difference in thinking”. that’s why I said my experience cannot be expressed.
fact is females dislike certain areas of mathematics, males do not have that problem.
also I tried to ask females why they dislike those areas of maths, but they couldn’t put it into words either.
they argued with uselessness and with difficulty, but couldn’t tell me what they failed to understand.
maybe I just asked the wrong people. or rather, I saw the complicatedness too, and failed to see the problem in it.
mind you, I am not really intelligent, IQ maybe about 86 or something. they definitely were more intelligent than me.

now religion uses the same mechanism in their study of theology, even more so than maths could.
require a priest to have studied and there will be no female priests. add some centuries of tradition and females don’t count.
politics too can require some sort of studies, but basically the same argumentation as with science can be used.

however, thanks to some us-president that is slowly changing. the end of the gold-standard in economy gives them a big boost.
with all the world being indebted to eachothers most of our money vanishes in the interests being paid.

imagine an island with a hundred inhabitants.
in addition to their money each of them is given 100$.
at the end of each year they must pay back 10$.
those 10$ will then vanish completely, never to be seen again.
after 10 years all the 100$ they once had will be gone.
and even more years later also the money they originally had will vanish.
that’s how our economy works.
in reality however there exist mechanisms to slow down that development.
still basically every 100 years our economy will have lost a substantial amount of money.

technically this isn’t true. value of money depends on how much economy produces.
also, it isn’t any bank who creates money, it’s the national bank or similar, provided the bank has lent money.
still, every time the money-creator gets the interest back, this money is gone.
so the person or institution making debts is effectively losing money till debts are paid.
the short-sighted economy however makes the assumption that everybody needs to have debts.
if you earn nothing at all and have no debts, you are quite stable.
get indebted and earn with that money some interest higher than the one you have to pay for it.
however, that interest you earn is paid by someone else, so seeing both of you as one system, money is lost.
either your customer will get broke and drag you with him, or this person will widen the amount of people involved.
so in effect, the amount your economy produces is getting cut off by all the people paying interest to some money-creator.
and in effect that amount of interest will rise and rise over time as long as economy dictates making debts.
we don’t notice that because it’s hidden in various statistics and is an extremely slow process.
we’re like the frog in the boiling water, the danger approaches too slowly for us to jump out before being cooked.

while in past the male was able to earn enough money for his whole family, in many countries this isn’t possible anymore.
so females must have a job too, they need education, they need access to jobs in politics and management.
in every family eventually both parents will need to have a high-paying job in order to afford having a child at all.
survival of the richest is what the future holds for us. but much more interesting is what happens inbetween now and then:
males who do not accept to have a wife who earns money of her own, wont get any wife at all unless they are rich.
males who do not accept a wife with higher education, will eventually not get a wife either (unless rich).
the consequence is that those males without a wife will become worse at their jobs, for psychological reasons.
females on the other hand will increase their self-esteem because of having a high-paid job.
in the end they will be the better managers because their self-esteem wont depend on mating but rather on money.
this way a company who doesn’t hire females into management positions will have bad quality structures and go broke.

management is extremely important for a company, it decides how the internal structures will work.
a bad boss will be lax towards the subordinates, will make bad decision that cost the company a lot to undo.
it really isn’t that females would generally be more fond of the money they earn than males are.
so this isn’t what makes them become a better boss. neither can one claim they would think only in terms of getting babies.
females just want to survive, and for that they need some money. also for them becoming rich would widen the choice for husband.
the major difference between male and female culture is that males often put up sexuality as their major pleasure-source.
this automatically also defines their self-esteem by the amount of sex they get, they get conditioned that way.
females however learned to have a much wider spectrum of pleasure sources, so a dry streak wont affect them much.
even a female addicted to sex will further gain pleasure from the mere fact she is treated more equally to males than in past.
this way for them the conditioning of self-esteem rising and falling with sexual activity is much much weaker than for males.
additionally, at first there wont be much females who want to make a career, so the ones who do will quickly get a husband.
therefore in the beginning of world-wide poverty female managers will get much more pleasure than their male competition.
afterall living together with your preferred significant other is a source for pleasure too.
in the end, some little amount of managers will be married females, and maybe same amount of males will be married too.
all the rest, those unmarried males, will be confronted with steeply rising price for their sources of pleasure.

of course, denied of sex the males will get another source for pleasure, but those wont get children.
and the reason why they will be childless, the reason why most managers wont have a wife, is because of everything being expensive.
at some point it will only be the managers, what is “upper middle-class” now, who will actually have the money to raise a child.
schools will cost and lack of school will further decrease chances for those children to get any children of their own.
housing, real-estate, any possibility to grow food, all that will become much more expensive.
afterall becoming rich will be everyone’s goal. quite unachievable without raising the prices.
also the abuse of earth’s resources plays an important role here. heating up the apartment will become more expensive too.
not to mention global warming and the prospect of dying when going outside without air-conditioned clothes.
poor people will simply die out for lack of food and health-care and energy, for lack of offspring.

all the cat-calling and the whole image of females as sex-objects, as something that must aspire beauty, that will be gone.
if a male would do cat-calling then, it would rather be about the female’s wealth than her beauty.
once females control management of the media, getting rid of such behaviour in males will be a matter of few generations.

in short, we’re about to experience a re-bound in the general trend to treat females badly. feminism is the future.
rich females will be the only choice males have if they want to get an apartment of their own, instead of living with parents.
since there wont be that much rich females, males will need to treat them better when wishing to be married to one.
and since there wont be much experienced females at first, companies will need to treat them better when wishing to hire one.
and companies will wish to hire one because through the very development of misogyny, historically, females are the better managers.

entropy-based money

Leave a comment

Exchange Money Conversion to Foreign Currency

(Photo credit: epSos.de)

imagine every year a certain percentage of money you have would be put aside, and distributed among all people.
now imagine that percentage would be the same for everyone. and the distribution of that money set aside would be in relation of the money people actually own.
i.e. for each dollar you own, 10cent are put aside, and then since you owned that dollar you will get back those 10cent.

does sound like a fair money-system! but there really is no difference to the money-system we have now. the money you own stays the same, because you own it.
the real problem in our money-system starts when you lend money.
so, in my entropy-based money, what would happen if you borrow money from me?
what we expect should happen is that in return for getting this money from me you should somehow give me something in return, something abstract that hurts you for as long as you refuse to give me back my money.
in my entropy-based money therefore you will become an exception when the money set aside is getting distributed again: from the very money you borrowed I will have to set aside a percentage. and then this money set aside will be distributed among all people except for you. this way, the more money you own (not counting the borrowed money), the higher the percentage of the borrowed money you would lose each year.

on the other side, just because of you having borrowed money, everyone else will gain some amount from the money that otherwise would have been your share. to me it wouldn’t really make any difference if the money was borrowed from me or anyone else.
so in order for me to actually gain anything the money-loss you experience should automatically be transformed into your debts growing. so slowly more and more of your money is changed from money owned into borrowed money.

now lets translate all this back from the abstract point of view into an actual implementation:
ordinary “borrowing money” doesn’t need to be actually regulated. a private person borrowing something from another is a contract between the two where money changes the owner. this way money gets spliced up, at most resulting in the total amount of “money” to become doubled, in that the contract about the debt is as good as the money itself.

however, if you request to borrow some money from a bank, that bank will in turn borrow money from “nowhere”, as it is now. so my suggestion is that this “nowhere” would be treated as part of my entropy-based money-system, and thereby everyone would gain money just because of the bank having borrowed some money in your stead.
of course in the implementation a global gain of money is translated into a deflation, the more money the bank borrows the higher the currency it is borrowing will be worth. (i.e. the very opposite of our current system.) needless to say, the bank wont get anything out of that growth, the interest it has to pay is larger than that.

and to make sure the bank wont keep the owned money at a minimum to reduce the interest for “nowhere”, some laws could force the bank to keep as much money as needed to pay out 10% of all the money people have stored. just disallow the bank from making debts if this law isn’t fulfilled!

political correction

Leave a comment

Infrastructure

Infrastructure (Photo credit: elycefeliz)

about politics in general I’ll talk at a later time.
however, now the usa have an election, and people think not-voting would do anything.
true, it’s quite shameful for a democracy to have below 50% election polls, as the eu does.
but in reality the reason why people don’t like to vote is because politics is too abstract for them.
there simply is no mechanism of “if I vote I will get a job and money”.

actually there is only one thing politics can do to create jobs:
open up a new company paid by the country, and hire.
quite a communistic approach romney proposed here:
create one company that digs holes and another that fills them again.
and then to earn some money the government will eventually sell both companies.
the buyer will then throw out the workers and sell the shovels.
if we’re lucky the buyer will keep the workers and make them do something else.
either way, the amount of jobs always depends on the amount of business-ideas.
and the amount of successful business-ideas depends on the amount of money clients have.
the more jobs, the more money for employees, the more jobs will be created in the sector of middle-class consume.
so if a government would really hire those diggers and hole-fillers, additionally more jobs would evolve.
but this way government would become poor, so it’d better be rich-people who create those 2 companies.
in other words, if you want more jobs, make the gap between rich and poor smaller!
only a robin hood, “stealing” from rich and giving to the poor, could be effective here.
no politician could ever do such a thing, rich people know how to avoid the government.

I wont spill out all the historical facts here, you can look them up yourself.
truth is rich people can afford an accountant or whatever person with good ideas.
and not only do they have the money, they usually also have the knowledge and networking in place to do so.
rich people know many rich people, and from them they can learn who’s good with juggling money.
you’d need to advance at least to upper middle-class to get access to them.
even the most introverted rich person will eventually meet other rich people.
the very action of earning large amounts of money makes this necessary.
as soon as government would do something against the rich, someone will find a cure.
and that cure will quickly spread throughout the whole network of people with lots of money.
similarly if there was a thief or opportunist among them, they’ll know sooner than a wannabe-rich.
the longer your family had lots of money, the more other rich people they will know.
they still can be taken by surprise, some scam might turn out to be scam only years later.
or maybe their desire to become richer could be used to pique their interest in some product.
government can’t do either of those. a hedge-fond or an iPhone might be more effective.
if a rich person wouldn’t take care to keep their money together, soon it wouldn’t be a rich person anymore.
my suggestion is: make them pay for them being the first to obtain some knowledge.
either there will be no gain for them this way, or they will create new jobs out of that.
that’s the modern way of playing robin-hood, sell your knowledge to the best bidder.
and after selling it give it away for free to everyone else (maybe after waiting some time).

politics has completely different duties. global warming for example is abstractly seen a matter of diplomatic co-operation.
peace in the country is the duty of politicians. decisions on what resources to plunder and infrastructure.
so if you ever see a politician promising to improve those 4 abstract subjects, vote for him/her! everything else politicians promise is bullshit.
politics simply has no power over anything else! it’s just diplomacy, peace, resources and infrastructure!

actually government has power only over one thing: real-estate.
a government is more alike to a land-owner who allows people to lend some land.
if you buy some land, then originally that land belonged to the government.
and if the government would wish so, it could disown you in this respect.
only for the sake of peace government does acknowledge your right to own it.
however, what you do not buy, is the right to do whatever you want on that land.
if you share a lake on your land with a neighbour, you are not allowed to drain all the water.
it’s the government which decides how resources found on the land get distributed.
if infrastructure needs to cross your land, government can disown you.
if your land or something on it violates diplomatic relationships, government can interfere.
same with roots for some violence reaching your land, government wont acknowledge your privacy.
police and military can commit trespassing all they want, as long as government commanded it.
so through owning the land, the government automatically becomes responsible for managing the 4 abstract topics.
diplomacy, peace, resources and infrastructure are 4 things every land-owner must manage somehow.

for this reason it also doesn’t matter what political system you have — as long as people have the possibility to be armed.
even a dictatorship will have to manage the 4 or else it will be at war with the population.
I’m not saying there’s any violent revolution that could ever be successful.
well, maybe if the military would start a revolution against its own dictator.
either way, the result is there’s no kingdom anymore to rule.
politics simply is too complicated for a single person to comprehend.
and with multiple people ruling there’ll always be someone who wants to evade riots.
even more so in a democracy with a whole parliament of rulers or in china with a party having millions of members.
in america the plutocracy is really not the fault in the system, it’s the voters who ignore the 4 duties of a politician.
not surprising when infrastructure is optimal, resources are cheap, violence is low, and diplomacy is in balance.
however, there’s still the question if some politician you vote for will destroy that optimally running system.
the 2 major parties likely wont. too big to fail. but can you really trust a presidential candidate to stay true to the party?

when voting there’s another thing to consider though, bureaucracy. now that’s something that needs correction.
as it is now the money entrusted to the government is spent for ancient structures of employees who work against eachother.
on the other hand giving the same money to some poor country could improve your country’s exports.
just make sure a very large amount of people will get that money.
if the government is already wasting money, make sure it wont end up in some hidden vault like swiss banks and such.
or alternatively modernize bureaucracy so that fewer people work for government, more computers/robots are used, less wages to pay.
let people who live in the country take part in ruling it, they’ll do it for free if it isn’t too much work for the individual.

of course schools are too an important duty of a government, no way schools can be handled by private companies.
but I count that as bureaucracy too, it’s part of our resource-management since knowledge is a resource.
in my posting about economy I said: to create Knowledge you must feed a human’s mind with science-methods.
the better people are at science-ing or whatever other abilities, the more knowledge the country has.
and it should be mentioned that rich population isn’t enough, someone, not necessarily rich, must have an idea.
if people don’t have abilities for creating ideas, the country will soon be outperformed by others who do.
so education is a matter of various countries racing against eachother, and so far usa had a winning streak.
well maybe that was partly because of the lax laws on who is allowed to do what, and partly because of size.
but that soon could change because of some of the richer big countries being more lax on what to research.
so a bit of less emotion and less “intelligence”, more randomness, that would be great for funding research…

the secret to democracy is that everything is extremely slow, basically you’d need 1 generation for a change.
the old bureaucrats must retire before they can be replaced by machines.
the tiny problem in democracy is that politicians get to decide on their own jobs and the jobs of their friends.
wait 50 years and the problem is gone, simply through the noob who gets ambushed by change…

to summarize: if you don’t care about anything related to the abstract concepts of resources, infrastructure, diplomacy and peace, don’t vote.
if you do care, then vote for someone who does too, regardless of what chances that person has for winning.
very likely others will vote for the same person, because it’s logical those topics matter.
but if it’s jobs you want to create, take a loan and hire people to work towards your ideas.
if you’re lacking ideas or are bored, then get education, as much knowledge as you can obtain and start from there.
even if you go broke, your employees will have more money to spend, other companies will sprout.
and if you ever have to decide from whom to buy or to whom to sell, never choose big companies.
they likely wont hire new people, only small companies do.
and if it’s knowledge and research you do care for, for example medicine, make sure that’s done in other countries.
the less rich a country, the cheaper the workforce, the more efficient research will be.
because, it really isn’t location of research that counts, it’s what you teach in your schools that will rise innovation!
so in that case, instead of voting, go to a poor country and start teaching and researching!
everybody must actually do something for the own dreams, a vote wont do it!
what a vote does do is to take away the non-voter votes, the more people vote the less non-voters there will be.
sounds like too obvious to mention, but most people are not aware of what this means:
the votes of non-voters get always distributed in the same way as if they would have voted like everyone else.
so if you have to choose if you should vote for a small party that wont succeed, or if not voting at all, choose the former.
if you do not vote there is not even the remotest chance your vote would change anything.
if a new party would get a dangerous amount of votes, soon the big party will take over the small one’s topics.
just keep in mind that voting definitely doesn’t change anything for you as an individual. it might change your children’s world though.
voting rather has an immediate influence on other voters, it’s a way of communication. not-voting is communication too, of the non-verbal kind.
just see your vote as a hobby. a spare-time activity alike to chatting on the net or blogging. I do.
and I take this hobby seriously. nobody would build a model railroad without proper planning either!
so why vote for the most pious candidate? why not of collecting and studying the available facts and getting your own impression?
being pious might be important for diplomacy. but politicians are much more than that! 4 times as much!

meaning of lies, the universe and everything

1 Comment

Livestock

Livestock (Photo credit: Martin Cathrae)

figuring out the abstract reason for which we are alive, isn’t really that difficult.

like everything that’s alive, we live in order to die and to feed other creatures.
and for the latter reason procreation might be a good idea too.
so don’t dare to die till you have children. preferably children who procreate too.
and if you’re religious, then maybe you’ll add “postponing death for as long as possible” too.

especially since religious people tend to have a different understanding of “death”.
thinking about after-life tends to have that effect on us. we feel sort of immortal.
and so we fill the abstract notion of “death” with new meaning.
what commonly is called “death” refers to a part of us that definitely is mortal.
with the real “us” being immortal, its decay plays no important role.
well, except of course that this mortal part is what other creatures eat.
but there is little difference between leaving a corpse and producing milk, for an immortal being.
so above, wherever I said “death” a religious person would have said something else.
be it going to paradise/nirvana, or be it getting devoured by the devil or vultures.
no matter how you look at it, even an endless life has a moment of irreversible change.

if you’re religious, then you might throw up the question: whom do we actually feed?
quite an obvious answer is that our mortal body feeds our immortal soul.
and that’s practically all that’s to it. one answer and many possibilities to redefine the answer’s vocabulary.
although, I personally dislike the prospect of soul being the body’s predator.
it’s as if we were an insect and there’s an invisible-to-us mantis or dragonfly preying on us…

as our lives become longer various surrounding questions come up in this context though.

Hamlet with Yorick's skull

Hamlet with Yorick’s skull (Photo credit: Wikipedia)

they all boil down to asking what to do with our lives.
if you really want to get told what to do: just follow nature’s call and become the best piece of food ever.
take care of your physical health. if you believe in an immortal predator, take care of mental health/growth too.
but imho this approach is revealing how bored the person must be, who asked that question.
we might create computer-games or other media, to keep us entertained. the subliminal boredom prevails though.
if you want to fill your life with an individual meaning, pick a random area of interest and aspire goals there!

thinking abstractly about such things makes it easy to find abstract answers.
even though those answers aren’t satisfying, they show how shallow those topics are.
a much deeper question than the question about “meaning of life” is the question:
what is the reason for lies? what use do they have? what lasting effect will they leave behind?
obviously some lies are for the purpose of deception. nature knows deception.
some birds deceive their own species’ comrades by pretending an action.
but is that already a lie? it isn’t as if they were talking with each other!
I would say lies are what distinguishes us humans from other creatures.

of course animals communicate, some paths of communication more comprehensible than others.
but all this communication is filled with purpose and otherwise void of intention.
the birds don’t “pretend an action with the intention of communicating”. humans do.
we even communicate through the choice of our clothes!
when an animal selects various objects for courting, they don’t communicate but rather make a presentation.
the difference is quite subtle, heavily abstract: communication lacks Intent! presentation is pure intent.
think of that next time you fire up powerpoint. do you want to present, or do you want to represent?

compared to humans, animals are quite introverted. what we constantly do is talking about ourselves.
take a look at our internal dialogue. it is as if we were communicating in our thoughts.
what for? who’s listening? our thoughts are usually not serving much purpose.
sometimes we might think in order to memorize something, to preprogram ourselves.
but most of our lives the thoughts merely draw a picture of what surrounds us and of how we believe to fit in.
and once we open our mouthes it isn’t surprising when that’s what we’re talking about.
so regardless of how much communication is lacking Intent, lies still are unusual.
but yet they exist. most of them are sitting right there in our minds, the self-lies.
the more self-lies the more there will be lies towards other people. a matter of self-discipline.

an interesting development in our society, in the last millenium, is the disappearance of violence.
it even went so far that now beatings are banished from schools.
the idea behind that was that of beating being hereditary.
just stop beating your children, or else they’ll beat theirs.
just break the cycle through sheer self-control.
and with the lowered likelihood of getting mugged, violence isn’t that important part of growing up.
priorities did shift from pure strength to advanced education in martial arts.
and rightly so. much more likely than getting killed is death through excessive stress.
for the sake of survival, taking the meditative approach to fighting is what we should do.

however, while physical abilities and mental capacities for coping with them are important, lies aren’t.
one just can’t ban lies by law and expect anyone to actually desire getting rid of such habits.
there is no incentive bound to survival. nobody died of lies, nor of lying.
additionally nobody ever died from lack of lies, so no reason to seek a replacement-habit.
what does happen is that lies indirectly cause events that lead to someone’s death.
but rarely it’s the liar who dies. same for always telling the truth, people might die but rarely the truth-teller.
sorry, no darwin’s award for liars and gossipers…

self-lie, delusion, is the root of all our lies it would seem. what other reason could we have for lying?
well, there also is the unintentional lie. we say the truth but others get it wrong. not misunderstanding, self-lie again.
what happens quite often is that people get accused of lying, while in reality the accusing person is victim to self-lies.

I watched a doku about wikileaks and assange. there nick davies accused assange of lying about the sex-assault-incident.
but he said that assange didn’t believe to have lied. classical situation of pot called the kettle black.
it becomes obvious there that nick was deeply hurt by the “truths” revealed about assange.
i.e. he lived in a delusion on how assange was, in a self-lie.
assange lived in the delusion of having absolute memory on what he said to whom.
I’d say neither of them lied, they merely said what they believed to be truth — self-lies.

this kind of pattern I’ve seen quite often:
one person is disappointed of another person, and additionally to lost trust, new self-lies get created.
a self-lie is supposed to be self-protection, although it’s questionable from what exactly it’s supposed to protect.
in this common circumstances of lost trust the self-lies are “excuses” for why one did trust in the first place.
but why not accept the situation as it is? why invent “facts” to cover up the self-image?

I know it from my own experience too. and with all this in mind I usually just laugh at myself.
and my solution is to keep my self-lies to myself. when I’m asked, I remain silent.
this way the lies wont escalate. I just self-lie, laugh and record the lies with the tag “lies”.
I’m wondering why at least the smart people I know didn’t get that idea…

in case you didn’t notice, the previous paragraph is a lie.
of course I’m no superhuman who without error can detect self-lies.
but then, that paragraph didn’t claim I was, only the implied meaning is a lie.
that’s a strong distinction I make: grey lies I call it when only implied meaning is a lie.
interpret my words literally and they aren’t a lie anymore. what irony.
such grey lies have an important property:
there are 2 people responsible for the lie. the liar and the person believing in the implied meaning.
it’s a shared responsibility, so the weight on the liar’s shoulders isn’t that heavy.

the foundation of this article should be a definition for what a lie is, but there is none.
the next best thing is defining what we think a lie would be.
when listening to how people accuse eachother of lying, eventually everything we say would fall into that definition.
and rightly so. our whole language is based on the concept of lies.
when I say “sun” I am not really talking of the star at the center of our planetary system.
instead I actually mean the bright thing I see in the sky during daytime.
there simply is no 1-to-1 mapping of words onto meaning. context always counts.

from the point of view of the liar one could define a lie as something contradicting the person’s beliefs.
self-lies are beliefs too. therefore most of our lies are no lies at all.
problem is a lie-detector might disagree here.
self-lies create stress too, but the liar will claim there’s no lie.
this kind of lie isn’t what a lie-detector is after, though.
but it must be quite funny when especially a female is caught lying about her age this way.
still, this point of view is rather useless. why would anyone want to know if he/she lied?

basically there is no objective truth on whether a sequence of words, words with partial context, is a lie.
redefine the meaning of some word, and a lie becomes truth. that’s simple change of context, extended context.
that way, figuring out the meaning of words obtained by hear-say is quite a piece of advanced algebra.
the only meaningful definition of lie is when putting that word in the context of a whole belief-system.
so using the word “lie” on its own doesn’t make sense, one must always add for whom it’s a lie.
and most likely also the point of time where it is a lie. people learn, extend belief-system. new words can turn lies into truth.

all this implies an easy answer to the question of why we lie: we don’t do it intentionally!
wrong answer. maybe we don’t lie intent-fully, but lies still are something intentional.
also our language cannot be blamed for all the lies. language is usually full of redundancy for this purpose.
a good liar will accompany each lie with a self-lie that makes the lie a subjective truth.
generally lies are extremely short-living knowledge, eventually contradictions will clear things up.
and if they don’t, then the topic wasn’t important anyway. then the contents of the lie is easily forgotten.

one common reason why I do lie is to  tell a joke, or otherwise express humour.
I am addicted to irony. irony for me is about 2 similar things opposing each other.
so I sometimes pretend to be pro some movement, just to exaggerate their beliefs.
this way I create a perverted image of their goals, turned into the opposite of what they want.
remember, my thoughts run in an abstract way, so also my definition of irony is abstract.
a mathematical function that is its own inverse function, self-inverse, that’s irony for me.
but also more generally, I enjoy it when an inverse function only differs by one glyph, is a “dual” function.
and when I see a bird landing on a twig too thin to hold its weight, I laugh too.
I don’t laugh at the stupidity of someone. it’s just that the same action elsewhere would be opposite.
an example for irony is my chiming into the clamour for punishment of all people who behave against society.
so when I say assange should be punished for rude behaviour to females even if otherwise non-guilty, it’s a joke, a lie.
the film Demolition Man did do something similar, peaceful society full of violence. what an ironic film.
btw, I don’t do sarcasm, each word I write is meant literally. when I lie, it’s the implied meaning that is a lie, never the literal.
sarcasm is a bad idea when writing, saying the opposite of what is meant will cause a lot of damage to the discussion.
irony on the other hand wont do much, it’s the sort of lie that’s easily forgotten when unnoticed.

an important notion when talking of lies is the notion of truth. truth isn’t the opposite of lie though.
a lie is something said or written, this way it can only be opposite to a truth being communicated.
however, somewhere I read there’s a bounty on a veritably true sentence, and nobody claimed it.
the notion of truth is much too strict to be applied to human communication.
lies simply have no opposite, only scales of severity. the whole idea of words representing objects is causing them to be lies.
nothing a human ever says can fully represent an actual object. objects are infinitely deeper than the words we use.
still doesn’t change my question. why do we use the grave kind of lies? why not stay closer to communicated truth?
and the reason for my question is that lies are bad for science. bad for growth of our knowledge.
in the middle-ages scientists had to lie in order to not be prosecuted by church. in a mild form some scientists still lie for similar reasons. white lies for the purpose of not offending someone’s beliefs.
we lie for entertainment. we lie for keeping up self-image, for self-representation. we lie for deception, for our advantage. or we use white lies for someone else’s advantage or lack of disadvantage.
all these lies are somehow steal time from the search for knowledge, from science.
but what exactly is the reason we need entertainment, self-image, egoism? what’s the use of people demanding protection from offensive science?
I can understand that we sometimes lie in order to speed up things, but why all the other lies?

one kind of lie I didn’t talk about yet: the lie with a purpose of speeding up things.
for example astronomers learn that the earth is the center of the universe, sun and planets revolve around it.
this knowledge, as antiquated it might sound, makes calculating planet-position faster.
for the same reason also in physics the relativistic point of view isn’t all-dominant.
the lowered complexity justifies the means.
but in a few thousand years archeologists might find our astronomy-books, and laugh at our geocentric beliefs.
maybe we’re already doing the same, with archeologist’s opinion on the ancient cultures.
my solution to this problem you can see here: the next paragraph says the previous was a lie.
and to speed up learning, that info is indented so the reader can skip it…

communication

communication (Photo credit: flavijus)

middleschool maths in a nutshell

Leave a comment

An example of a partial function that is not a...

An example of a partial function that is not a total function. (Photo credit: Wikipedia)

unfortunately you wont find this in a schoolbook. but truth is maths is very limited in middleschool.
one important concept you learn there, after basic set-theory, is the notion of a function.

given 2 sets, you “map” each element of the first set onto whatever element you choose from the 2nd.
no need for all elements of the 2nd set to have something mapped to it.
graphically you just draw arrows from the elements of the first set onto elements of the 2nd.
this way quite naturally a new set is created: the image of your function. that’s a subset of the 2nd set.
if you only map part of the elements of the 1st set onto something, you get a partial function.
a partial function quite naturally creates another set: the definition range. it’s a subset of the 1st set.
an actual (Total) function has domain (that’s what the 1st set is called) and definition range being one and the same set.
also functions are distinguished by the properties “injective” and “surjective“.
injective is a function where no element in the image has two or more “arrows” pointing to it.
surjective is when the image isn’t just subset of the set the function is mapping to. it’s when the full set is covered by the image.
bijective function has both properties, it’s injective and surjective. and therefore one can define an inverse function: with arrows pointing into the opposite direction.

a much better way to depict a function is to draw its values. visualize it so the viewer can predict what values it will have.
a common way to depict functions mapping points of a line or plane onto another line or plane, is to draw the points into a bigger coordinate system. that picture is called a Graph of that function.
just designate 1-2 coordinates for the domain, and draw a point in the remaining coordinates according to the function’s output.

if it’s a function from real numbers onto a 2d-plane, it’s more common to draw a curve in that plane.
maybe also add some arrows and markings to the curve to show the sequence in which the points get added.
of course, if you’d just draw the same function into 3d-coordinates as a graph, you’d get something different.
but just look at the 3d-image from the side into witch the coordinate is pointing which you did choose for the domain.
projecting the 3d-curve onto a plane orthogonal to that you get such plane with a 2d-curve in it. you get that drawing I described in the beginning of this paragraph. so it isn’t entirely different.

all this works great for smooth functions. the viewer can just imagine all the points inbetween the ones you draw.
one must take care that such points inbetween are what the viewer does expect though.
one must choose wisely what part to show, how much to magnify the function.
calculating the extrema of a function has, among others, the purpose of acquiring that knowledge.
so lateron in the text I’ll talk a bit about derivatives.

a function is just a glyph (or whatever decoration) along with 2 sets and some description.
this glyph is representing the function’s name.
as above the 1st set is the Domain, and the 2nd set is the value-range. the set of values the function might output, the image, is a subset of the latter.

you might remove a single element from the value-range, one that isn’t in the image. and technically you get a new function.
this way a function is more alike to a procedure in a computer-program.
also there altering the type of variables used as input or output, you basically get a new thing.
even when the code defining it hasn’t changed.

another similarity to computer-programming is the notion of a variable.

to write the “description” of a function mostly formulas are written.
but the description could also be a set of touples, representing that “arrow” you’d see when depicting the function as 2 sets connected by such a mapping.
a third possibility is to write some algorithm, alike to an actual computer-program. and sometimes the description will be just some plain text.

no matter how your function is described, in front of the description you see something alike to “f(x)=“.
there the “f” is the glyph used for the function, it might be a greek letter or a word, even hebrew letters might be used.
and the “x” is the variable, alike to variables in programming languages. again the variable is written as another glyph that might even be greek or hebrew and/or have various decorations.

more exactly a function might not be that new a concept at all, whenever we use some device we encounter that principle.
you just do something and something else you will get in return, input and output, cause and effect.
however, what really is new in middle-school is the idea of variables and formulas.
you have some text, written in whatever language, maybe computer-program, maybe plain text, maybe in the language of mathematics or logic.
in that text you have strange letters or whatever glyphs, maybe whole words, that somehow don’t make sense.
but in the context of describing a function those are meant to be seen as variables.
to the reader it means that their meaning will be defined lateron. for now there is some info on what they might contain though.
so when you have to evaluate a function, you read something alike “f(3)“, it means that in the function’s description that started with “f(x)=“, after the “=” you’ll have to replace x by the value 3, and then you’ll read that altered description again to learn what value the function will output.
and it gets even more complicated when you see the glyph used for the function as a variable too. maybe the function isn’t given in a defining way? maybe that function-name is part of a formula?
I say, learn programming! once you can do that, this aspect of maths shouldn’t be a problem.

well, that’s not all, there’s another concept to learn in middleschool, starting already at the beginning of mathematical education.
it starts out as multiplication. it continues with division and polynomials and their roots, and finally ends with trigonometry. all these things are really just about exponentiation.

the fundamental claim about natural numbers is that you just combine prime-numbers by multiplication to get everything.
sometimes the same prime number must be repeated several times, so you abbreviate this by exponentiation. for example 27=3^3=3\cdot3\cdot3.
this imposes a new operator onto the natural numbers. same operator can be extended to real numbers and complex numbers.
an operator, binary in this case (since it works on 2 variables), is just a function like above.
so in middle-school there are 3 binary operators: plus, times, and “to the power of”. one unary function there is too: \ln x or {_e\!\log x}
please note that subtraction and dividing are not listed because they are among those 3 operators!
to subtract you just need to multiply one number with “\text{-}1“. to divide you take something to the power of “\text{-}1“.

the important formulas are:
a-b=a+b\cdot(\text{-}1) and {a \over b}=a\cdot b^{\text{-}1}. and keep in mind (\text{-}1)\cdot(\text{-}1)=1 as well as (a^b)^c=a^{b\cdot c} and a^b\cdot a^c=a^{b+c} and a^c\cdot b^c=(a\cdot b)^c.
that’s just the beginning. in middle-school you also learn about roots, most prominent the square-root \sqrt a. but for each exponent there is a root inverting its exponentiation.
again it is no omission I didn’t list that together with the other 3 operators. the basic formula here is \sqrt[b] a=a^{1\over b}=a^{(b^{\text{-}1})}.

the brackets I put there because exponentiation differs in one important aspect from times and plus: it makes a big difference how you put the brackets when several exponentiation-operations are chained together.
i.e. a^{(b^c)}\ne(a^b)^c. so be careful and make use of brackets in such cases.
and also a^b\ne b^a explains why exponentiation shouldn’t be written as an operator alike to “^”.
we simply are used to swapping around the input to binary operators.

finally, 2D-trigonometry is handled by complex numbers in combination with exponentiation.
a complex number is just a term of the form a+b\cdot i and the rule that i\cdot i=i^2=\text{-}1.
quite prominent is the formula e^{\pi\cdot i}=\text{-}1 where e is the euler number.
now the euler number actually isn’t a number, it isn’t rational number and it cannot be expressed through polynomials or their solutions.
in that respect it is much alike to the number \pi, which in turn is merely the circumference of half a circle of radius 1.
so while \pi is described by approximating the half-circle’s circumference, e is described by (1+n^{\text{-}1})^n=({n+1\over n})^n with n being a fixed number as close to infinity as one can get.
but much more enlightening about exponentiation is the formula e^x=\sum\limits_{k=0}^{\infty}{x^k\over k!}=1+x+{x^2\over 2}+{x^3\over 6}+{x^4\over 24}+\cdots=1+x(1+{x(1+{x(1+{x(1+\cdots)\over 4})\over 3})\over 2}).
it is enlightening because it also works for x being a rational or complex number. actually this formula is where all the stuff about “roots are just exponentiation” or “dividing is same as to the power of -1” comes from.
this formula makes exponentiation into a function, an unary function, a function in a single variable.

to get totally minimalistic one could define a^b=e^{b\cdot\ln a} for positive numbers. when a is negative, think of it as a^b=(\text{-}1)^b\cdot(\text{-}a)^b=e^{\pi\cdot i}\cdot e^{b\cdot\ln a}=e^{b\cdot\ln(\text{-}a)+\pi\cdot i}.

This is a demonstration that Exp(i*Pi)=-1 (cal...

This is a demonstration that Exp(i*Pi)=-1 (called Euler’s formula, or Euler’s identity). It uses the formula (1+z/N)^N –> Exp(z) (as N increases). The Nth power is displayed as a repeated multiplication in the complex plane. As N increases, you can see that the final result (the last point) approaches -1, the actual value of Exp(i*pi).

sounds quite complicated.
but take a look at this formula: R\cdot e^{\varphi\cdot i}.
and now imagine \varphi to be the length of a small part of a circle, part of a circle with radius 1.
the output of this formula is a point on a circle of radius R and same angle as this small part of a circle \varphi did measure.

the output is a complex number.
a point in the complex plane. a plane made up of (x,y) for each complex number x+i\cdot y
and positive small angles this formula will map to the upper right quarter of that plane.
counterclockwise with angle \varphi=0 being mapped onto the positive half of the x-axis.

therefore one can imagine e^{b\cdot\ln(\text{-}a)+\pi\cdot i} as the formula (\text{-}a)^b=e^{b\cdot\ln a} rotated by half a circle, rotated by 180°.

so no actual exponentiation is needed, just the two functions \exp(x)=e^x and its inverse function \ln(x)={_e\!\log x}.
I repeat, it would be sufficient to have just plus, times as operators and \exp and \ln as unary functions.

and being minimalistic might sound like a funny useless game, but here it plays an important role for thinking abstractly:
the concept of dualities is quite prominent in maths. sometimes a duality is between 2 opposites, sometimes it’s between 2 similar things.
here we have both, a duality between the 2 operators, and a duality between a function and its inverse function.
additionaly there seems to be a duality-alike relationship between binary operator and unary function.

another unary function I already mentioned and even used above: \ln. the inverse function to exponentiation of the euler number (e^{\ln x}=x).
it also has the property that no matter what number you take to the xth power, you can still retrieve the original x with the help of \ln.

the way to do it is by taking advantage of the general formulas above and dragging them over to the \ln function.
this way you get \ln(a\cdot b)=\ln(a)+\ln(b) and \ln(a^b)=b\cdot\ln(a), useful formulas when coping with this function.
it’s because e^{\ln(a\cdot b)}=a\cdot b=e^{\ln(a)}\cdot e^{\ln(b)}=e^{\ln(a)+\ln(b)} and e^{\ln(a^b)}=a^b=(e^{\ln(a)})^b=e^{\ln(a)\cdot b}.
so when you have a^x=b given, you can get x by applying \ln to both sides: x\cdot\ln a=\ln b
that’s where the formula {_a\!\log x}={\ln x\over\ln a} comes from.
in computer-programming often {_2\!\log} is used instead of using \ln because the processor has some machine-language command built in for that and maybe not for \ln.
as you probably can see, the formulas I’ve proven here can be used for any \log-function, not just \ln!

another property of \ln is a bit beyond the scope of what one learns in middle-school.
in the complex plane, one can see that this function is actually defined everywhere, except on (0,0), but only locally.
i.e. given any complex number, nearby the function is defined everywhere.
you just are not allowed to include (0,0) and you are not allowed to have a hole in your definition range which would contain that point.
you always must leave a ray or a curve (which preserves the order for all of its absolute values) starting at that point and going into infinity. in this stripe the function would behave really strangely.
so there are not just all the different \log functions, each of them, including \ln, has different versions of their definition range, and the descriptions being altered accordingly.
this isn’t surprising when you know that exponentiation is not an injective function in the complex numbers.
thereby it isn’t bijective, no inverse function exists. so what values does it assume that wont make it injective?

let’s go back to the discovery that R\cdot e^{i\cdot \varphi} is counterclockwisely describing a circle of radius R.
obviously this means
e^{i\cdot \varphi}=\cos\varphi+i\cdot\sin\varphi and
e^{\text{-}i\cdot\varphi}=\cos\varphi-i\cdot\sin\varphi.
but why a circle? as I promised, the formula e^x=1+x+x^2\cdot(2!)^{\text{-}1}+x^3\cdot(3!)^{\text{-}1}+x^4\cdot(4!)^{\text{-}1}+\cdots, without witch using complex numbers for x wouldn’t make sense, that formula is an explanation.
observe what happens when you plug in i\varphi, and what happens when you plug in \text{-}i\varphi:
i goes through 4 states in this formula, i^1=i then i^2=-1, and the same again with a “-“.
i^5=i and later in the sum the same pattern repeats on and on.
so looking at those 4-5 terms is enough:
e^{i\varphi}=1+(i)\varphi+(\text{-}1)\varphi^2\cdot(2!)^{\text{-}1}+(\text{-}i)\varphi^3\cdot(3!)^{\text{-}1}+\varphi^4\cdot(4!)^{\text{-}1}\cdots
e^{\text{-}i\varphi}=1+(\text{-}i)\varphi+(\text{-}1)\varphi^2\cdot(2!)^{\text{-}1}+(i)\varphi^3\cdot(3!)^{\text{-}1}+\varphi^4\cdot(4!)^{\text{-}1}\cdots
pretty much the same, just the Imaginary part has become negative alltogether.

changing the sign of the imaginary part of a number (while leaving the real part as it is) is called conjugation.
it is described by drawing a line over the complex number. i.e. \overline{x+i\cdot y}=x-i\cdot y
therefore \text{-}i\varphi is conjugation of i\varphi. surprising is that also \overline{e^{i\varphi}}=e^{\text{-}i\varphi}=e^{\overline{i\varphi}}. thereby more generally \overline{e^z}=e^{\overline{z}}.

suppose e^{i\varphi}=x+i\cdot y. then also e^{\text{-}i\varphi}=x-i\cdot y
when you multiply both you get 1=e^0=x^2+y^2.
that’s the well-known formula for the circle of radius 1. so all points of e^{i\varphi} are on that circle!
think about it: x^2+y^2 are always constantly 1, no matter what \varphi you put into e^{i\varphi}!

exponentiation is well known for its strong growth, the bigger the real number the stronger the growth will be.
and it is well known that exponentiation will never be zero. but can it be negative?
obviously in the real numbers it can’t. it has positive values and is never zero. how can it cross the zero-point?
complex functions are difficult to depict, a function from 2d space to 2d space.
however, let’s say the input is a line in the complex plane, and output is the complex plane. the result is visible in 3d.

beware, this method will create a slightly biased picture. the line you choose determines how the thing will look like.
take a straight line, and you get a curve in 3d. this curve moves in space as you move the line on the complex plane.
all those parallel lines in the domain make up a surface. it would seem other lines could be mapped to the same surface.
the perpendicular line to those parallel lines would then seem like a curve in the plane orthogonal to the axis you choose for depicting the domain.
but this curve likely is not the graph of an actual function. it’s just a mapping of real numbers onto a plane, a curve.
also you could use the graph of a helper-function in the domain instead of a straight line. those helper-function-graphs can be moved along a straight line pointing into the direction you did use for depicting function-values of your helper-function.
no intersections will happen. so a whole new shape will be created, depending on that helper-function you choose.

for example the exponential function. in the direction of the real line we all know this function.
also I have said here that e^{i\varphi} is a mapping from real numbers onto a circle in a plane.
so that’s what you’d get mapping the exponential function with the axis of the real numbers as input:
an exponential graph rotated around the x-axis. each y-z-slice orthogonal to that x-axis is a full circle.
however, just look at what you’d get if choosing the imaginary axis instead of the real one.
e^{i\varphi} would become a curve spiraling on a cylindrical surface, never changing size.
parallel lines look the same, just different size. that size grows/shrinks exponentially.
and if you’d use a logarithmical graph as a helper-function the result might look even more differently.
i.e. \exp(\ln y+iy)=e^{\ln y}\cdot e^{iy}=y\cdot e^{iy}, similar shape but linear instead of exponential growth.

however, making a 3d-animation where the angle of the straight line used would rotate, could give a good impression.
unfortunately I haven’t seen any program that could display such a 3d-film, even less create one…

what you get this way is some mix between exponential function and \sin and \cos.
those trigonometric functions are definitely not injective, they periodically repeat themselves. so does \exp.

the real values it assumes are positive and negative numbers. since e^{i\pi}=\text{-}1, its square will be 1 again.
multiply e^{i\pi} another time and you get back to -1. in general e^{n\cdot 2\pi i}=1 for all whole numbers n.
this makes \exp non-injective, each and every value gets assumed infinitely many times.
but things aren’t that bad. knowing \ln for a truncated \exp function is enough. so just cut off all the values that repeat and define the domain accordingly for a total function.
this way usually \ln is defined for all numbers except zero and a ray starting in zero going along the negative real numbers.

in the formula-collection you’ll find the definition:
\ln x=2\cdot({x-1\over x+1}+({x-1\over x+1})^3\cdot 3^{\text{-}1}+\cdots)=2\cdot\sum\limits_{n=0}^\infty({x-1\over x+1})^{2n+1}\cdot(2n+1)^{\text{-}1}) for x>0
there also are formulas for 0<x<2, and they might look a lot more simple.
the problem lies in how they got created: pick a point and you’ll get it defined within a circle around that point.
since it cannot be defined at zero, such attempts will always give very limited results…

for a function to calculate the negative half, just take such a \ln\text{-}x and add \pi\cdot i to its output, thereby rotating by 180°. i.e. \widetilde\ln x=\pi\cdot i+\ln\text{-}x will be then defined for x<0.
just use \ln and \widetilde\ln depending on where you are looking at.
so in addition to \sin\varphi=\text{Im} e^{i\varphi}={e^{i\varphi}-e^{\text{-}i\varphi}\over 2i} and \cos\varphi=\text{Re} e^{i\varphi}={e^{i\varphi}+e^{\text{-}i\varphi}\over 2}, we also now can write \arcsin x={\ln(ix+\sqrt{1-x^2})\over i} and \arccos x={\ln(x+\sqrt{x^2-1})\over i}

but forget trigonometric functions! do everything 2-dimensional directly on a calculator (a calculator with the ability to calculate complex numbers).
type R\cdot e^i\varphi to get a point with distance R and angle \varphi, translate Polar Coordinates to Cartesian Coordinates.
use \ln(x+iy) to calculate \ln R and \varphi. the former in the real part, the latter in the imaginary part of the output.
add to that the knowledge that scaling up a triangle will also scale up each of its lines by the same factor.
maybe some pythagoras (x^2+y^2=R^2) and you have trigonometry covered.

a bit more subtle is the idea of calculating the derivative for a function. what is it for?
abstractly seen the process of creating a derivative, Differentiation,  is just a function.
it takes another unary function as input and outputs a function in the same variable.
it is written by drawing a small vertical line above and next to the function, or just a dot above.
it transforms the function according to certain rules.

since there only are 2 operators and 2 functions, defining derivative is easy:

every term that is connected by plus to other terms gets handled individually. the derivative of a finite sum is the sum of individual derivatives. (a(x)+b(x))'=a'(x)+b'(x)
product are more complicated. a product becomes the sum of the same amount of products of same size. and additionally in each such term of the output a different term of the product is picked out and the derivative of that is calculated — the other terms of the product stay the same as without derivative. (a(x)\cdot b(x))'=a'(x)\cdot b(x)+a(x)\cdot b'(x) or (\prod\limits_{k=1}^N a_k(x))'=\sum\limits_{k=1}^N(\prod\limits_{l=1}^{k-1}a_l(x))\cdot a_k'(x)\cdot(\prod\limits_{l=k+1}^N a_l(x))
the variable x to the power of a constant becomes that constant times x to the power of a number that is the constant minus one. (x^c)'=c\dot x^{c-1}
the euler-number to the power of x is already its own derivative, nothing changes. (e^x)'=e^x
the derivative of \ln x is x to the power of -1. (\ln x)'=x^{\text{-}1}
a function evaluated at the output of another function is the product of the derivatives of both functions. keep in mind that the outer function must first get the derivative applied before you insert the 2nd function into its variable. (a(b(x)))'=a'(b(x))*b'(x)

another way to write the derivative is f'(x)= {\partial f\over\partial x}(x).
in this last rule, let’s say b(x) is inside of the variable u.
then in this new way of writing the rule would like this: {\partial\over \partial x}a(b(x))={\partial a\over\partial u}\cdot{\partial u\over\partial x} (x)

but in case you come upon a function that isn’t those 4 functions combined someway, there is a much more general definition.
take a look at {f(x)-f(x_0)\over x-x_0} and imagine x to be very close to x_0.
when you draw the graph of f (input in the x-coordinate, output in y), and you draw a graph of x\cdot f'(x_0) (a line through zero), you will notice in x_0 they both have exactly the same growth.
the reason is that {y-d\over x}=k is the same as the k in kx+d, the line through (0,d).
so, when f(x_0)=d and x_0=0, then {f(x)-f(x_0)\over x-x_0}={f(x)-d\over x}.
for each x a line is depicted, an angle is chosen. the closer x comes to x_0, the better such a line approximates the actual function’s angle in that point.

one thing I should say about the geometry of linear functions:
all linear functions are of the form y=kx+d or implicitly ax+by=c.
both are the same, k=\text{-}{a\over b} and d={c\over d}.
however the most important knowledge here is a completely different way of writing linear functions:
a linear function that depicts a plane in 3D or line in 2D is a function in 2 respectively 1 variables.
the surrounding space however has one additional direction, so there is a line perpendicular to the function.
for 2D this perpendicular line is determined by \begin{pmatrix} y \\ \text{-}x \end{pmatrix} for a vector \begin{pmatrix} x \\ y \end{pmatrix}.
in 3D there’s an operator commonly written as “\times“, the “outer product” is how I learned it’s called.
just take any 2 vectors of the plane, apply that operator and you get the perpendicular vector.
\begin{pmatrix} a_x \\ a_y \\ a_z \end{pmatrix}\times\begin{pmatrix} b_x \\ b_y \\ b_z \end{pmatrix}=\begin{pmatrix} {\det\begin{pmatrix} a_y & b_y \\ a_z & b_z \end{pmatrix}} \\ {\det\begin{pmatrix} a_z & b_z \\ a_x & b_x \end{pmatrix}} \\ {\det\begin{pmatrix} a_x & b_x \\ a_y & b_y \end{pmatrix}} \end{pmatrix} with \det \begin{pmatrix} a_x & b_x \\ a_y & b_y \end{pmatrix}=a_x\cdot b_y-b_x\cdot a_y
once you have the perpendicular vector \vec q and a point on the surface/line \vec p, use the inner product (multiply each pair of components and sum them up) to create the formula:
\vec v\cdot\vec q=\vec p\cdot\vec q where \vec v=\begin{pmatrix} x \\ y \\ z \end{pmatrix} respectively \vec v=\begin{pmatrix} x \\ y \end{pmatrix}
when p is zero, it is obvious why this works: the inner product is zero when both vectors are perpendicular to eachother.
but more generally \vec a\cdot \vec b=\|\vec a\|\cdot\|\vec b\|\cdot\cos\angle(\vec a,\vec b)

when you look at a plane with a point p which isn’t the point closest to zero, then there will be a whole circle of points with exactly the same distance to zero.
also this whole circle will always have the same angle to the orthogonal vector.
so in this formula the distances are all the same as well as the \cos, throughout the whole circle.
therefore the inner product is constant on that circle.
remember, \vec a\cdot\vec b=\sum\limits_{k=1}^{\dim a}a_k\cdot b_k is linear in each component, multilinear!
since the equation \vec v\cdot\vec q=\vec p\cdot\vec q is linear and there are more than 2 points of the plane fulfilling it, that’s also the equation for all the other points.
i.e. as \cos\angle(\vec v,\vec q) increases, the distance decreases to compensate that. and the other way around.

for example we get \begin{pmatrix} x \\ y \end{pmatrix}\cdot\begin{pmatrix} \text{-}f'(x_0) \\ 1 \end{pmatrix}=\begin{pmatrix} x_0 \\ f(x_0) \end{pmatrix}\cdot\begin{pmatrix} \text{-}f'(x_0) \\ 1 \end{pmatrix} is tangential to the function in x_0.
subtract the x-term: y=f'(x_0)\cdot x+(f(x_0)-x_0\cdot f'(x_0))

there are many applications for this. most prominently you can figure out minimum and maximum of a function.
it wont tell you where those are, but definitely shrinks down the set of candidates to several points.
minimum and maximum can only happen at the border, or when there is no derivative at all, or when the derivative is zero.
derivative says something about the growth of a function. before it will start to grow or before it will start to decline, the function will go through a point where growth is zero.
alternatively the growth might make a jump, from one value to another. in the point where it jumps, the derivative does not exist, that’s a candidate for minimum or maximum too.
in a 3D function, with 2 axes reserved for domain, the edge is again a 2D function. there could be a maximum or minimum anywhere, you’d have to calculate this derivative (on the edge) to know where.

this was, in a nutshell what I learned in middle-school and only grasped at uni.
I didn’t talk of probability and integration (the inverse function to derivatives).
those I didn’t learn before uni, not from my teachers. it’s in the math-books though.
but based on above, it shouldn’t be too difficult.

if you’re an advanced mathematician, it is interesting to see here how little people in middle-school learn.
if you haven’t finished middle-school yet, or are re-learning all that stuff, good luck.
all those things are not difficult, although I might have made things seem difficult.
my goal with this posting was to show what abstract concepts there already are at middle-school.
and I wanted to point out how big an advantage it was to think abstractly in middle-school already.
as always I’m open to any critique or suggestions…

Older Entries Newer Entries