LastThursday

We can. Using the hands, the mouth, the body - that's the most efficient way - but a lot of us seem to forget that.

It can be better to just let the information wash over you. What happens over time is that connections between disparate bits of information start to be made, either consciously or unconsciously, and this can often "stick" better than narrowly trying to unpick this or that. It's just a different style of learning, more right brained so to speak. The advantage is that it can help with overwhelm.

The level of the answers on here are more complex than trig itself. One good heuristic to follow is to match the level of your answer to the level of the question. It's ok to hint that there is something beyond, and then the OP is free to investigate that if they want to. The other heuristic is to pay attention to the essence of the question, in this case: concretely, how do I learn something new and confusing? and answer that.

I'm an hour in and hooked. I thought I knew a fair amount already, but the level of detail is fantastic.

It seems like you have a lot going on and you're working on things on many fronts. And it can be difficult to get any sense of growth because of all that stuff. A slightly different way of seeing things is that no matter what happens you're constantly changing and evolving in many different ways, sometimes slowly sometimes quickly. Change can happen very gradually even without you noticing. Or it can happen in fits and starts, which in my experience is more common. You've chosen to take control over your own evolution and change and that in itself is immense - well done. What happens is you keep working and working on yourself and you feel that nothing changes, then one day all of a sudden everything can "click" into place and you feel different, and then you're into a new phase of "normal". Your move will be a new normal. You start off by wanting relief from all the suffering, so you already have an idea of what "relief" should be even if it's not well defined for you, you have a destination. Once you get relief, you'll feel light and flowing, and that will drive you to grow even further, there's no end to what can be done.

Because there are no gaps. Imagine a square. You draw a diagonal line from one corner to another. Now there are two triangles which fit together perfectly with no gaps. Imagine a void which is aware. The awareness/void can divide itself up indefinitely to dream reality. Everything orchestrates perfectly because there are no gaps: god is everywhere without exception, and everything is one dream.

Everything is relative to everything else, so there's no fixed "anchor" keeping everything in place. It's like waves and currents in the ocean, water moves relative to itself and there's nothing to stop it moving once it starts. Once nothingness divides itself, then its parts are free to change indefinitely. But change happens at a measured pace, otherwise everything would happen at once: that's the only thing keeping everything from chaos.

It really depends on working out how you learn best. Do you like diagrams, do you like doing practical experiments, do you like to be told stuff? Sometimes stuff only clicks once it's presented in the right way. Sometimes stuff only clicks if you go over it a thousand times, it can vary a lot. If your teachers are not helping, then you'll have to either find a mentor or go find things out for yourself. As Leo says, all trig just boils down to right angled triangles inside circles. More importantly it is about RATIOS a.k.a fractions. All trig functions are just ratios of things. Each trig function is based on an angle, it gives you the RATIO of two sides for a given angle. There are three sides to a triangle, if you pair up the sides there are three pairs, so there are three functions: cosine, sine, tangent - one for each pair. Each pair can also be reversed to get the reciprocal of those functions: secant, cosecant, cotangent. So just memorise which pairs give you which functions and you'll be nearly there (hint use the right angle as an anchor point). If you're practically minded go out and measure height of a building using trigonometry, to get a feel for it.

Let's face the education system has never really been about individual aspirations, it's about priming people to be useful in a technocratic capitalist society. There's a greater push nowadays for individual creativity and thinking for yourself because that is what society needs from us. It's whatever the current zeitgeist is. The current system of rote learning in a conveyor belt of large classes comes from the industrial mindset of Victorians and is becoming outdated, and a lot of it is about learning how to be subservient to a higher authority (your paymaster).

My Default Mode. Do you have a default mode of interaction? You might call call this personality, but I'm referring to the more specific way in which you communicate. For example you might be amiable or sullen, combative or laid-back. One trait I see among many men is being jocular; outside of the purpose of being jocular (to de-escalate tension) it is a way of interacting. One trait I see among women is laughing or giggling very regularly or another is apologising. I suspect that most of us are not aware that we even have preferred ways of interacting with others. Seemingly, we just "talk". But like a fish not knowing it's in water it's quite hard to step out of ourselves and examine how we are when we communicate with others. We might want to do this for several reasons, the most important of which is to improve our communication and ultimately improve our relationships. Let's give it a shot myself, warts and all: First the stuff I actively want to portray when communicating: For a long time I've wanted to appear laid-back to others. I think my natural temperament is calm and unassuming, so it is an extension of that. But also I've worked out that people liked me for being laid-back. In general that means I want to also appear to be in control and not easily flustered. I'm not a natural leader (in that I don't take to it willingly), but if the situation requires it then I can be; so I at least want to set up this expectation. I also abhor confrontation and conflict (I've had too much of it in my life), and having a laid-back style communicates this fact, it helps kept conflict to a minimum. Secondly, I want to appear intelligent. This is an odd one. On the face of it people don't generally like know-it-alls or are suspicious of people more intelligent than them. I think it's a natural reaction to the unknown: how can you comprehend someone motives when they comprehend more than you do? For me it's ended up being a balance, appear intelligent enough for my needs, but not so much it puts people off. I don't always discern the right balance. IRL I'm dumb myself down greatly and how I write on here is not who I am when talking to others, at all. Question is, why do I want to portray this? I think it largely comes from my parents, especially for my mother who often used the "I'm not stupid" line as a defence and my father who is a know-it-all at times - it's my reaction to both those. But also it is a way to bolster myself up against others, and project "I am worthy" vibes or even more accurately "Don't mess with me or I'll embarrass you by making you look stupid" vibes. But I also want to be taken seriously when I have something to contribute and I think it helps if it's coming from a place of intelligence. Most people find it ok, some disklike me instantly on sight for it. Stuff I end up projecting even though I don't want to: With people I don't know well, there's always a level of fear or awkwardness I feel. I think it ultimately stems from my mother, she was also quite apprehensive about others and would get easily flustered if she was out of her comfort zone. I seem to have ingrained that sensation of recoil when I don't feel in control around others or I fear not being able to handle a social situation. This has hugely improved since I was a kid however, and calling it masking or just sheer exposure and experience I'm a lot less awkward and anxious than I used to be. But it does fly in the face of me wanting to appear laid-back. Occasionally, if I'm tired or not on-the-ball, my mask drops and I become awkward: I forget people's names, my mind goes blank, or I say weird things - but I've realised on the whole people don't care, so I've stopped caring. Whether it's autism or not, it doesn't matter much. I'm more of a listener than a talker. I'm a lot more aware of this nowadays and but this tends to me my default mode in groups, especially if I'm not much interested in the current topic. I have always preferred one-to-one conversation because of this, but this is rarer in my life. But even one-to-one it's work for me to keep talking about nothing in particular, but I somehow manage it. I'm fundamentally an introvert, with some occasional learned extroversion when it suits me. I do try and pipe up a lot more in groups nowadays if I become conscious of it, but I don't crack jokes lol. Snarkiness and bitchiness. I always feel that there is this little devil in me who just wants to be bitchy. In this respect my mother and father were polar opposites, by mother always poking holes about other people, by dad always super respectful (sometimes too much). Maybe some of it has rubbed off on to me. My default reaction when I see bad behaviour in others or when they upset me in some way is to be snarky to put them in their place. It is not in general that I want to put others down, I don't, in fact the opposite. But luckily I seem to be very aware of this inner bitchiness and I mostly keep it on a leash - but one area I need to be very conscious of it is when writing emails (or on this forum!). Sarcasm. I learned sarcasm not off my parents (they wouldn't know if they fell over it (lol)), but off my first girlfriend's father who had a flair for it, a big bald man with ginger hair and a beer gut. His forte was sexual innuendo, which I do enjoy, but within my circle of friends goes down like a lead balloon - they're so straight laced. My mother was a bit of a piss-taker, but that was more in a slapstick sense than actual sarcasm. I don't enjoy toilet humour however, far too unsophisticated. I would say that it is also very much a cultural trait for us Brits, and it doesn't come off that well when talking to other cultures. I used to be a lot more unconsciously sarcastic when I was younger. Again, I may employ sarcasm in a snarky way to keep people in their place, but I enjoy it occasionally just to be cheeky and make others laugh. Seriousness. Another odd one for me. I have a strong streak of seriousness in my character which I get from my father (he takes himself seriously), but unlike him I don't take myself seriously (in order to seem important). I'm mostly a lot more serious in one-to-one conversations and a lot more jovial and light-hearted in groups. I don't know which is the real me, probably a bit of both. Aloofness, arrogance, disinterest. I think I've been accused of all those over time. Despite not being that kind of person at all or even wanting to be, some people get those vibes from me. I think it's the blend of unconscious seriousness, pushing my intelligence and not talking in groups that does it or at least that's my interpretation as to why. Not being taken seriously. This is something that's grates on me and has done for a long time. This can take the form of my views not being considered or just rejected out of hand, or, people not even feigning some sort of interest in what I have to say, or worse just being ignored completely. Perhaps it's the combination on not talking up in groups, or my not having strong opinions on things or my dislike of forcing my ideas on others. I feel like I have a lot of experience of "life in general", but I'm not worth listening to - or at least that's my impression, there could well be other reasons why this happens which I'm totally unconscious of currently - more awareness is needed there on my part to get to the bottom of it. Overall, I'm not someone who is or wants to be "in your face", and I'm especially not "self important". I'm not a huge chit-chatter (except on alcohol for some reason). I'm not particularly serious or at least it's not my intention. I especially abhor moralising in both myself and others.

Tried one session with the wav file so far. Let's see what happens. Reminds me of the good old dialup days.

I would say that was infinite nonetheless, i.e. a process without end. There's nothing about infinity that suggests novelty is key to its definition. The trick is that you may have finities mixed with infinities. You can have an infinite set or permutation of finite things - which you can judge to be novel or not depending on how you want to see it. Novelty is a value judgement.

It's a fallacy to think that an infinity contains everything possible. An infinity could still have room to manoeuvre and still be infinity. I think the question should be flipped on its head: should consciousness be infinite? You can look at infinity as either a process; something that could potentially carry on without end. Or you can see it as something with unbounded attributes. A circle has a finite radius and area, but there is no restriction against how many times you can go around its perimeter: a circle contains an infinity within it. In that sense, it would be very easy for consciousness to contain infinities. And, consciousness appears to carry on constantly without break, so there's another potential infinity. And it seems that we can explore consciousness without end. For consciousness to be finite in all ways, it would have to be bounded by something else that isn't consciousness.

Instantaneous time collapses everything into the now. Transformation happens at different rates for different things in the world. So we can reconstruct a block time from the things in the world which haven't changed much - continuity. Or we can use logical reasoning to try and deduce that "things must have been that way for this to be true". We can look at an old house and say it was built in such and such a year and imagine its construction. Things stay consistent and logical, because transformation itself isn't random, it's orderly, but it is mostly uni-directional: sometimes it isn't possible to reconstruct a definite past. In effect what's happening is that events are smeared around space or affect the configuration of things, sometimes more and more as time passes, for example the butterfly effect. Memories are no different. If you clap in a cave you'll hear echoes for a long time. A memory is just like an echo, in effect it is part of the original event still happening.

I think there's two ways to think about time. The conventional way is "block time", where events are ordered in a linear way like on a calendar. The other is "instantaneous time", where reality changes moment to moment. The two are quite different. Eternity would then be an infinite extension of block time. Block time has the sense of being permanent and unchanging, once events have happened they are forever fixed and immutable. You could even imagine events in the future already being pre-determined as a consequence of events in the past. Instantaneous time would be like a very thin sliver of block time. Nothing is fixed or remembered, as soon as something happens it's forgotten and there is no pre-determined future. Since there is no block there is no past or future, just now. In a way the two are opposites of each other, block time is unchanging and eternal, instantaneous time is always changing and ephemeral. In my experience instantaneous time seems to be the correct interpretation and block time is a fantasy. Which if true, would mean that transformation is a feature of reality: time is presupposed from the existence of transformation.