la petite morte is what dreams have in common with reality

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some say “life is a big dream”. I disagree with that.

“life is just a big dream” however sounds somewhat more true.
the word “just” signifies a kind of limitation. here it means that life is at most as limited as dreams are.
maybe dreams have more limitations than reality.
but obviously the author of this saying is convinced life has some important limitations in common with dreams.

I guess I have to explain in more detail why I used the notion “at most” instead of “at least”.
let’s start with set-theory: a set is a collection of elements.
however at the same time a set is also a collection of elements that fulfil certain properties.
a finite set can have each of its objects individually listed in such a description, an infinite set can not.
the reason is that for defining some properties only finite-length expressions are allowed.
so when dealing with sets of infinite size, one really is dealing with limitations of some predefined infinite set.
to define an infinite set you take another infinite set and add limitations to it, you throw out elements.

now lets say life is a set of things that could happen, particularly my life is a set of experiences I could potentially have.
dreams are part of my life too, for me it is possible to re-experience all the same things I already experienced in dreams.
those things happened in my mind while I had these dreams. wouldn’t be surprising if my mind could repeat that.
even when I am awake and perceiving my surroundings, I can still additionally experience these things.
this is called hallucinations or day-dreams. therefore the set called “life” additionally contains what otherwise isn’t part of the set called “dreams”.

life has less limitations than dreams, in terms of what one could possibly experience.
for example when awake I can experience defecating, and my creations will remain real. can’t do that in mind alone.
some things possible in reality simply are not possible in dreams. hence dreams have more limitations than life even more than waken life.
the trick here is to interpret dreams as experiences of mind, instead of taking the hallucinations at face value.
then it is natural that experiences of mind also are possible when fully awake.
leaves the question, does life have any limitations at all?
but it is for sure, the limitations we have in life also apply to dreams, they merely are irrelevant there since dream-experiences aren’t bodily experiences.

I have been told, the limitation life has in common with dreams is that both are completely pointless.
you live your life, and eventually you die, there is nothing you gain. similarly a nice dream eventually ends — in disappointment.
also the other way around: all your life long you had those fears, as death comes they all are pointless, a gigantic relief.
at least this is the current time’s interpretation of the quote I made at the beginning.
we can’t really know how the words were originally meant.

dreams are so much more than life could ever offer. a dream is like an experiment in a laboratory!
all the things that encumber us in our waken state, they all are gone in our dreams.
we even frequently lose our memory of life’s hardships, when we dream.
in these ideal conditions we can experiment with our mind’s potentialities, explore mind’s limitations.
can’t do that in the mess we call “life”. in dreams we are responsible for the order, when awake this responsibility is shared.
who ever tried to re-live experiences from a dream also in waken reality, quickly will get disappointed.
some people are capable of experiencing hallucinations, alike to the ones experienced as dreams.
but even for these people such experience is more limited than within dreams.
the biggest difference is that when sleeping we have our eyes closed.
so while waken hallucinations  must adapt to our surroundings, dreams only adapt to our 4 facial senses.
light falling on the eyelids, smells, sounds, tastes, all find their way into dreams.
but when hallucinating awake there further is the sense of touch, and actual shapes we see with our eyes.
these two make it quite impossible to hallucinate for example about sexual experience. but wet dreams we can have anytime.

So, what is the meaning of waken life then? why not just live in dreams all the time?
truth is all I said in the previous paragraph is unimportant, except maybe for a scientist who writes books about mind.
the most important characteristic of dreams and of reality in general is the continuity, the (relative) stability.
we do something, and it has an impact, we are the cause for some effects. our actions are what makes life meaningful.
of course no effect is forever. nothing will last. but relatively to our lifespan, we can actually build up something reliable.
some of our deeds will have effects for hundreds of years.
throw a plastic bag into the ocean and you made a monument for centuries.
for your whole life you then can rely on any fish caught there to contain remnants of your contribution.
dreams have something similar too, but there time-spans are much shorter since dreams are shorter than life is.
and also relatively speaking, the effects dreams have on the future is much more limited than what we do when awake.
the difference here is that dreams depend on mind only. as soon as mind forgets, also its seemingly stable creations disappear.

one just can’t live in dreams alone, our mind isn’t meant to be used that way and our society hasn’t yet automated the gathering of food.
maybe in future this will change, maybe in future nobody will ever forget anything and eating will be a relic of the conservatives.
but till then we have to face the facts. human isn’t meant to live life inside of whatever mind.
even in terms of learning and understanding, our mind isn’t really trustworthy.

this worthlessness of mind, in terms of instability and fragility, this is the only thing that equally limits waken life and dreams alike.
any student will tell you: memory is the biggest challenge in acquiring knowledge, healthy nutrition comes second and could also become part of the same problem.
of course we have great memory, we could learn thousands of books by heart. but that’s not the problem I’m talking about.
let’s look at dreams for example: you see a wall, then you turn around, and as you look again the wall is gone. why?
obviously you noticed the wall is gone, so it cannot be a problem of memory. you remember there’s supposed to be a wall.
same with the student: after many exercises, a completely analogous problem at the exam seems unsolvable. black-out.
and even when the exam is passed, later in job and wherever applicable in private life, all the training is wasted.
we learned things in school and in reality we never even get the idea to apply them. why?
in both, dreams and school, mind is only as strong as it was a moment ago.
you didn’t perform the algebraic exercises a moment ago, then you now must relearn how to do them.
in a dream you stopped looking at the wall, so it isn’t surprising when it’s gone completely.

you must keep mind occupied with some activity, otherwise that activity will need to be re-learned anew.
as a rule of thumb, after 2 weeks without training, whatever abilities you had are lost.
an exercise must be repeated once a week to keep mind alert for that kind of situations.

there is the saying “for a man with a hammer as the only tool, every problem looks like a loose nail”.
this point of view, this seeing only loose nails all around you, I claim this point of view has a time-limit.
i.e. you put your hammer aside for a week or two, and you’ll stop seeing all those loose nails.
maybe other people have a different time-limit, but for me it is at least 1 week and at most 2 weeks.
when I was pretty good at some math stuff and I didn’t do it for that time, I am not good at it anymore.
of course I still can do it, my memory of how to do it isn’t lost, I just stop being so masterful at it.

in dreams there is no such time-limit, instead some sort of attachment is required.
in order for the wall to stay where it was as I turn my back to it, I must continue to feel its presence.

maybe I hear the wall, in the sense that sounds from behind it are muffled.
or maybe I feel how the air-currents get stopped by the wall, or I see its shadow.
maybe I feel the coldness of the wall or I feel how it is looming behind my back like a giant.
luckily this kind of continuity can be trained, now I even am able to leave a room and return to it without problems.
however, that kind of training too has the derogation factor. after about a year without training also this ability is lost.

now to summarize: human is changing all the time, nothing is forever, most things wont hold even for a lifetime.
abstractly seen, if a human had only a single ability, it would be as if that human would reincarnate every week, into the same body.
once a week it would be as if that human died, and someone else is then occupying that body.
this new host still has the same physical set-up, also the same knowledge, but character and abilities differ.
it’s as if the previous host would have left behind some book, from which to re-learn the abilities.
similarly also character can be re-acquired from the remnants of the previous person in that body.

but this kind of relearning has the same limitation as any kind of communication:
the main landmarks of the knowledge can be conveyed in detail, but it’s up to the person to connect the dots.
in mathematics one could say that only a countable subset can be conveyed, the completion must be done manually.
but this isn’t accurate, our memory can only store a finite amount of information, no communication can go beyond that.
so we have some limited description, some thoughts telling us what to do, how to do it we must figure out.
keep this in mind next time you learn something new, it really matters how you store that memory.
no matter how good you are at something after learning it, it’s important to formulate what you learnt for your future selves.

I think at this point I should emphasize, when I talk of death, I mean it!
in my experience it is wrong to beautify the memory-loss into something happening concurrently.
it’s really a cut, one moment I had an ability and the next moment I don’t have it anymore.
but it’s also wrong to claim the real you is dying at some point in your body’s life.
it’s always a small loss of abilities, one ability after the other is lost, till a whole bunch is gone.
also it happens at random time, mostly at a time you relax, for example during sleep.
and most importantly the loss isn’t being noticed till you need the things lost.
it’s as if part of you died and you are facing some zombie instead, some alien person.
in such moments we then say “why did I do such a stupid thing?”
of course it isn’t an alien, we just suppress the fact that nothing is forever, even our mind dies — piece by piece.

no matter if dream or reality, in a way we all die a little from time to time, repeatedly. always keep in mind that secondary mortality.
what’s the point in learning anything at all? you wont improve your abilities after these 2 weeks of training.
whatever new tricks you learn after that time, you will forget about all the old tricks which you then neglected.
if your goal is some kind of mental achievement, never waste more than those 2 weeks.
you want enlightenment? it takes only 2 weeks! if it doesn’t then you will never reach it! give up! or at least focus your life on it!

well, that really isn’t true. as I implied while talking about dreams, the ability of not-forgetting can be trained.
in dreams I have managed to do that, why not when awake?
if abilities of mind are as important for you as they are for me, do that!
keep track of how quickly you lose abilities and make that time become longer.
the secret to this it to avoid being distracted. in the dreams mind must be continuously occupied with the objects.
similarly when awake keep your mind occupied with the abilities you want to keep.
make a list of what abilities you need and create a training-schedule.
this schedule isn’t the important thing here, what one must learn is to be more systematic in the training.
if mind wanders off into unrelated fields, a lot of time is wasted that could have been used for being occupied with some new tricks.
and most importantly, always keep track of what your mind does do, at any time.
it’s important not to be controlled by circumstances, and instead keep up control of the own mind…

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Fractal Concepts

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I mentioned Jenson’s Paradox. it really is no paradox at all, when you think of it in terms of real numbers.

just to clarify, I am talking of connecting 2 points with a zig-zag path.
this path has infinitely many rectangular angles and a total length of 2.
that path looks like a diagonal line though.
also mathematically it can’t be distinguished from the diagonal line.

for every point below the diagonal, at some moment in the construction the zig-zag line will be above that point.
for example the point C, or any point between C and D.
already in the 2nd step they all are way below the constructed zig-zag shape.

however, the concept of infinity makes it clear that this isn’t a diagonal line.
the problem is that there are uncountably many points not being put onto the diagonal line.

in my construction the corners get mirrored onto the diagonal between A and B
this process is repeated only countably infinite many times
this leaves uncountably many parts that aren’t part of the diagonal.
what’s worse, you don’t even need to believe in uncountable quantities.
is \sqrt 3 an x-coordinate for a point of the zig-zag line lying on the straight line connecting  A and B?
mathematically it is. it converges there. but at which step does that point get added?
unfortunately mathematics doesn’t come up with tools for talking about such cases. the notion of “derivative” comes close though…

therefore it isn’t surprising that the length is 2, as the constructed line is below the diagonal most of the time. wouldn’t even be surprising if the length of a similar line was infinite!

and this is what fractals are about: a discrepancy between size and actual objects of that dimension.
thanks to a point of view that takes infinities into account we can investigate the fractal’s shape.
of course our actual world doesn’t contain true fractals. and the uncertainty-principles prevent that in small sizes too.
however, abstract processes can be of fractal nature, our thoughts are such a beast of infinite repetition.

of course we don’t live forever, and so also infinite thinking makes no sense.
eventually there’s a  level where thinking would become coarse-grained.
but that’s beside the point! to estimate where your finite thinking will go, you need an approximation in terms of infinities.

additionally there’s the theory that part of our thinking is happening in the way of a quantum-mechanical computer.
if that’s true, then infinities would play an important role in studying how we think.
then our thoughts would be sort of fractals created by simple rules.
and just like fractals, our thoughts most likely will never encompass everything. there always will be holes, just like in above fractal…

as a side-note, is above construction really creating a fractal?
when you scale it up evenly, the length will be doubled, just like the straight line.
neither we have self-similarities nor “rough shape”, it’s merely lacking derivatives.
however, stretch it in the x-axis, and it will be size 3. a line stretched that way would be size \sqrt 5

 

Hello world!

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I’m gander.

I used to post on usenet under that name.
you might also know me as a c++ programmer of that name.

I’ll try to publish here some thoughts I have on the mathematics I learned at uni.

but also other random topics related to abstraction I will post.

my ultimate goal in life is to learn abstract thinking.

I learned c++ but realized I need to learn object oriented programming instead.
I learned formulas and algorithms but realized I need to learn maths instead.

people call mathematics and category theory “yet another language”. but in reality it is so much more than that.

imagine the language of logic. with its true, false, equals and some additional operator.

just 4 symbols and lots of variables.
of course it’s just a language.
along with a “meaning” we apply to it.

but in addition to that it also is a way of thinking.
a style, a path we walk on.

mathematics is exactly the same, although with much more freedom.

in some blog I read about Jensen’s Paradox:

take 2 points, situated diagonally to each other.
draw a horizontal and a vertical line to connect them.

length of the connection is 2.

you may insert more and more horizontal and vertical lines till you get something resembling a diagonal line.
but the length still is 2 and not \sqrt 2.

the reason is because regardless of how the path does look like, it’s the way you walk on it that counts.
when you see mathematics as a language, it’s as if walking in this 2-sized zig-zag way.
you must think abstractly to get the shorter distances!
maths is about taking shortcuts!