Pondering through life.

There are a lot of views on how the situation between the body and mind is exactly, some would argue that all thoughts are in fact just physical processes that are happening in the brain, which includes when we are experiencing pain, when we are recollecting previous experiences or even abstract objects (like the concept of a number). Others insist that the mind and body are separate, having all mental processes in the mind and all physical in the physical realm. I would argue that I am in some kind of middle ground between these two.

Let \(\mathbb{M}\) represent the mind, which would basically amount to what is truly me and you, in which decisions are made and thoughts are created. Let \(\mathbb{B}\) represent the brain, in which thoughts are stored as well as triggering physical processes which makes the rest of the body function. Finally let \(\mathbb{P}\) be all things physical, besides the brain. Now consider the following diagram:

                                           \(c\) represents communication from the mind to the brain, which for instance could be orders such as "I want to stand up". \(r\) represents recollection of thoughts from the brain, such as when you are remembering what you did yesterday. \(a\) represents actions, which is the physical processes that the brain initiates, such as moving your leg. Lastly, \(e\) represents experiences, which is the sensory input that we get from the physical events around us.

Now that's quite a few definitions, but I would argue that it solves some of the problems with believing it's all physical. If all things are physical, how would one argue what it is that makes the body do as it does. If you're having a thought saying "I want to leave this room right now", followed by the body actually doing it, you could argue that this thought was just an effect of processes in the brain. But what started these processes? My hypothesis states that such processes originates from the mind constructing the thought that the body should leave the room right now.

In my previous post, I came up with my definition of time. But time can mean different things I've experienced. Using the same definitions as that previous post, it can both mean the measure of actions as well as the actions themselves. Should time be the measurement of change or the change itself? Intuitively, I would say the measurement of change, since that is exactly how we use the word in our common language. When we talk about time, years for instance, we just talk about the measurement of the earths movement from a set point until the current point.

When we talk about time travel, we can't use that definition of time, since by that definition, time can't go backwards. You simply measure actions, meaning that either there are some and you get a positive value, or you get none and time is 0. But what if we furthermore define the function determining the actions? To believe such a function exist, one has to believe in determinism, but let's define it and observe the implications.

Let \(S\) be the set of all states and \(A\) be the set of all actions and define the action map \(\psi:S\to S\) with \(D\psi(S)\subset A\). This is thus the map that determines exactly what is going to happen anywhere, anytime. We have no idea whether this map is surjective or injective, which means that we don't know if all possible states can be reached, and we don't know if multiple states lead to the same state.

If time travel should be possible, it requires the action map to have an inverse and thus be bijective. Otherwise when you go back in time, you could potentially end up at two different times at once, which is hard to imagine. The only real problem is the injectiveness, since the surjectiveness gets negated by the fact that we're always in the function's range.

But how would we determine if such an action map is injective? If it is, and if we assume that the action map is a function as well, then it denies the existence of multiple simultaneous dimensions. If we just assume injectivity and not that it is a function, it means that the amount of different dimensions can only grow. If we don't assume either, then the amount of different dimensions can grow or shrink as the action map dictates.

Time is a fascinating concept. A concept of the 4th dimension some say, a concept which is relative to movement in space others say - but a concept nonetheless, a concept constructed by ourselves. As I briefly touched in my previous posts, time can be seen as a function of change. I will try to sketch what I propose a definition of the concept of time.

Define a state as the position of every fundamental object.

Define an action as a a change in the state.

Let \(X\) be the set containing all actions and let \(A\subset X\) be the set of all actions in our universe. Now define the time function \(\varphi:A\to[0,\infty]\) as a measure on the measurable space \((A,P(A))\).

With this definition, we can see that if two persons have experienced actions \(\mathcal{A},\mathcal{B}\subset P(A)\) and if \(\mathcal{A}\subset\mathcal{B}\), then \(\varphi(\mathcal{A})\leq\varphi(\mathcal{B})\) by monotonicity of measures. This means exactly that if person B has experienced the exact same actions as person A, but potentially have experienced more as well, then person B has experienced more time than person A.

This definition also leads to some problems regarding comparability. If \(|\mathcal{A}|<|\mathcal{B}|\), does that imply \(\varphi(\mathcal{A})<\varphi(\mathcal{B})\)? With words, if person A has experienced less, but different, actions than person B, does that imply that person A has experienced less time than person B as well?

Besides that problem, the definition itself contradicts our usual view of time, since if two people experience a different amount of actions, then their clocks still show the same time has passed. How can that be dealt with, with the above definition? By defining standardized time:

I've never been a believer in karma, but sometimes it seems that everything that goes up has to come down at some point. That it suddenly seems plausible that you just can't be successful within all your interests, and if you suddenly grow much more successful on one side, the other sides fall catastrophically down. It could very much just be pure coincidence (since I'm still not a fan of that word), and it probably is.

Whenever we do good within something, do we always have to assume something else must go horribly bad within a reasonable amount of time? It sure fits the economic models of consumerism, but can such a concept be so general? If it is, is it possible to prevent such bad circumstances by lowering the success rate within others, just like it is possible within macro economic situations? Such a life doesn't seem that attractive though.

If we assume it possible to modify success and failures, it would then seem that life is split into two poles. The extremist, who achieve the greatest successes possible, and with them worst failures as well. The monotonist, who's life is average throughout the entire life span. We, as people, can then choose to which degree we want to live our lives.

Should the correlation between what we enjoy and what we want to achieve be non-existent? Sometimes we get the feeling that the world is moving way too slow, that you want to get closer to your (sub-)ultimate goal, and it can leave one restless. On the other hand, sometimes we get the completely opposite feeling, that the world is going too fast, so we can't get to keep enjoying what we're doing before the abrupt end. Are enjoyment and goals opposite concepts? Is it possible to achieve both? That you enjoy fully what you're doing, but you still want it to end, to be able to reach your goal in question? It would seem like the ideal situation to be in.

Even though such a situation seems ideal, it rarely happens in practice I would think. Often times you either want to get something done quick, so you can get to the results you crave, or you enjoy a thing so much that you don't want it to end. Is it a matter of priorities? In that case, wouldn't the before-mentioned 'ideal' situation contradict such a strictly prioritized list? Unless it isn't strict, but you merely are indifferent between the two.

Such an indifference seems like to be the only choice to achieve the ideal situation. That you truly enjoy what you're doing but wouldn't be sad if it ended, resulting in a finished product, a reached goal. Accept the change and start enjoying something new, repeating the process.

Yeah, I hate that abbreviation as well. But it nevertheless describes my thoughts these days pretty well. We are continuously being told that we have to live our lives to the fullest, but what does that imply exactly?

It would seem that "living life" is like walking a delicate line between trying as much as you can in life and being able to gain inner peace. It has always occurred to me that it was merely the former, and the latter meaning the complete opposite - but I see now that I was wrong.

But why is doing as much as you're physically and/or mentally capable of doing not lead to living life? Maybe it's about reflection - that without mentally processing what occurs in life, what choices are being made, you aren't really living them, you're merely doing them. Is stress originating from a lack of such mental processing? That we're being wrongly informed about how to live our lives, that we have to do so much, but reflecting over the things are being viewed as a waste of time?

Time goes fast when you're having fun. Or perhaps when you're just continuously performing tasks or actions, giving no time to think about them. Think about it, when you blindly stare into the night sky, or the wall, or something totally different, time passes slowly. And you're thinking, thinking about past events, past thoughts, past actions - processing the time that swiftly passed by.

I feel like I've been going down hill these past couple of days. Stopped sticking to my principles and just let go. I guess I subconsciously craved the attention of others, for some reason. And I now feel more lonely than ever. I'm used to being a loner, and I usually prefer it that way, but right now it's different. I feel cutoff from the world I inhabit, left to rot in a pile of garbage. And the ironic part of this is due to an increasing populistic mindset, to seek the attention of other souls in my environment, instead of just doing what I feel like doing without thinking of what others might think or not think about it.

Well, I hereby declare that time to be over. I'm going back to my roots, so to speak - doing what I enjoy and doing only that. Taking distance to the shallowness of populism, and see if I can establish proper friendship relations - and even if that fails, it's surely better than the contrary.

Subconsciousness is playing tricks on us, all the time. In my experience, we all eagerly try to understand everything around us - not that we actually can understand everything, but subconsciously convince ourselves at how we believe things are. When we then come to realize that our perception of a concept has actually been falsified by our subconscious, we start to become aware that we might not believe our own view of things to be true, and thus start thinking about what other things of which we might have attained a untrue picture. When such moments occur, it can both be frightening, relieving or even enlightening, depending on the case at hand. 

I clearly remember one thing I learned in one of my economics classes some years ago - you have to find your strengths, your distinguishments, and focus solely on those to achieve success. This is with the sole goal of earning the most profit that is, and not really anything comparable with such an abstract goal as to achieve a good life. Or is it?

One cannot simply be the best at everything he has interests in, since there will always be people with a sole interest in any specific field, making them dedicate large portions of their lives to it. "Jack of all trades, master of none" comes to mind. However, isn't it possible to perceive the set of qualities one has, as a quality in itself? The synergy formed by the complex pattern which is formed primarily on your interests, can itself be used to achieving goals, which otherwise would seem unreachable, ne?

Would it be possible to maintain a large group of interests on a non-shallow basis, at the same time? Or perhaps there are fields of interests which aren't as visible as others, which overlays several others making them seem non-existing. An interest such as gathering knowledge would still seem like a skill in its own right, but would on the surface seem nothing but a mixture of incoherent subjects.

I was asked a question the other day, which at first seemed obvious, but later turned out to be something which required more thought. The question was "What is an abstract mindset?", and my almost immediate answer was that it's when you're able to grasp things not of this world. But I would think there's more to it than just that.

I'd like to split an "abstract mindset" into 2 scales - a passive and an active part. What I mean by having a passive abstract mindset is that you're able to understand abstract ideas and work with them. The active abstract mindset is then the ability to come up with these abstract ideas yourself. The difference between these two is actually quite big, I've begun to notice it myself in the people around me.

Another way of naming these two expressions would be analytic and creative. An analytic person can understand out-of-this-world subjects and ideas, without having the need of having them drawn or otherwise "materialized" into our world - it makes sense in his mind. A creative person, on the other hand, loves to work without bounds. He can come up with the craziest of ideas, totally "out of the box" - this kind of person would be into creative areas such as music and art.

Now, there can't be any doubts about both having an abstract mindset, even though they don't have to be both analytic and creative. The opposite sides of the two scales would be the passive and active concrete mindset. The passive concrete mindset prefers to learn things that they can relate to the real world, such as craftsmanship or even things like engineering and economics. An active concrete mindset works with the ideas they have learned - they're very good at "tool boxing", whether it being concrete or abstract things.

I'm not quite sure if the two forms of concrete thinking could be synonymous with a common adjective, I can't think of any off the top of my head. But I do think that it is important to distinguish between these two scales when perceiving other people, or even one self. 

The three "personalities" in regard to learning math, that I wrote about in my previous blog post "Umvelt", could perhaps be described by these to scales of abstractness. The problem-solving type would be very toolbox oriented, but still very able to understand new abstract theories - which would make him very analytic, but not very creative. The person regarding math as an art form in it's own right would be exactly opposite, being very creative - however, the art guy would still have a decent amount of analytic sense, to be able to understand abstract math in the first place. The last person, the knowledge-craver, so to speak, would be somewhere in between these two, filling out the gap between the two poles.

I'm confused. My mind seems to be fluttering and jumping to a seemingly never-ending stream of conclusions about my surroundings.

Where do I fit in? Maybe I'm just subconsciously trying to not fit in anywhere? In my experience I've always ended up either doing what the minority did or something my surroundings didn't do at all - it did and does seem natural to me though, the choices. However, when I made up my mind regarding my interest within a field, and afterwards meet like-minded people, I'm genuinely thrilled that we share the interest. The order apparently matters. To me at least. 

A matter of definition can be the cause of a lot of discussions and bickering. Or rather, it's not the definition itself which is discussed explicitly more than subjective blabbering. The same thing, same word, can be interpreted in totally distant ways. It's often the biggest voice who gets heard in such situations, most likely with the notion of "fixing" the thing. If a word, or subject, has changed over the course of time, is it still the same? Can it rightfully be called equal to the previous meaning? Which argument is the 'correct' one? Would the true solution to the problem be to split words up, making their definitions well-defined?

I've encountered this in both musical discussions as well as discussions regarding mathematics. The musical perspective is quite simple - music change, which make people want to form subgenres to represent this change. Mathematics, on the other hand, is a lot more subtle. It's about what people define math as, completely subjectively - what makes math interesting to you?

I've heard people stating that it's the fundamental problem solving that they see as the true mathematics, and all the new syntax and definitions could just as well be described using the old methods - and therefore looking down upon the higher level education within the field, since it hinders their 'groundlevel' problemsolving qualities.

Other people consider math as a strict art form, seeing the proofs of theorems a way of creative thinking and wanting to make this part the main focus of the field - even defining math as the art alone. These people again looks down upon the higher level math, since the art form isn't what is filling up most of the area.

The last group of people, that I'm aware of at least, are craving the knowledge of the subject - they want to learn more about new areas with the field all the time, and not be bound to doing it a specific way. New definitions, new simplifying notation and never-ending knowledge potential. They have a less amount of critical thinking compared to the problem solving people and a less amount of creative thinking than the math artists, and see the knowledge itself as the goal.