1337

i can't understand math.

39 posts in this topic

One of the problems with learning math is that there aren't many teachers who know how to teach it in a way that students actually understand what they are doing rather than learning rules to shuffle symbols.  So finding lessons on the Internet that uses interactive tools and is taught to induce undestanding would be the way to go.   


Vincit omnia Veritas.

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On 09/09/2024 at 10:35 PM, Leo Gura said:

 

Trigo-unitcircle-animation.gif

@1337 Im sorry that I did not write the following any better, this is simply how I think about it and I cant change it.

 

Certain things are either is 0 dimensional or dimensional.

A variable is insufficiently particular dimensional unit, only 0 dimensional points are invariant or unitarily particular irrespective of further context.

All things with dimension instantiate the concept of a variable if the thing gets projected into a coordinate, a triangle is a composite of 1 dimensional lines therefore a triangle is a variable relative to a metric. 

 

 

 

Imagine that you walk at the same speed on a path from a to b and there are several cameras that focus on you while you walk that path, can you visualise why each camera must by necessity change the rate at which it rotates if it successfully has you in focus? Of course.

Do you see how the square in the illustration above slows down the closer it gets to the surface of the circle? It is for the inverse reason that the cameras in the example above did (the relation of the constant and the variable is reversed, in the illustration above it is the rotation that is constant), this inversion is a feature not a problem because it means that when it comes to expressing it in terms of symbols you can simply change x/y to y/x.

How could the movement of that square be anything but half of what it would have been if instead of being governed by a shape that extends equally horizontally and vertically it were governed by a shape that extended infinitely less vertically thus half in total?

 

The most general principle of geometry, trigenometry, algebra and all of math is often not distinctly recognised, it is that everything is relative to everything else, that it is this relativity we are expressing by means of ratios (percentages/division/multiplication) and that this simply follows from how all inputs in a syntactical system whether it is a coordinate or algebraic rules followed from left to right is a totality and that for change in one element of the input to not accompany an equal change in the others one must always input something more than the totality.

Edited by Reciprocality

how much can you bend your mind? and how much do you have to do it to see straight?

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@1337 Also, you are not supposed to understand math, you are supposed to distinctly identify that mathematical operations in fact work just like you are able to identify all sorts of things merely via their mutual presence in the same space and time.

If you are able to understand maths before you are able to ascertain that it works you literally cant be taught the rules that others rely on reach correct conclusions, it would be like excepting a monk to be taught heuristics for cognitive empathy. The mind simply can not fool itself into experiencing novelty where there is none, our whole organism is just an input/output system of the foolproof tendency to intensely fixate on and remember only things it does not already know thus inducing a clearer concept of "the world".

If you comprehend the general while everyone else memorises the particular but are forced to do as the others you will experience the same stimuli in your mind as you would if you were asked to repeatedly call an object by its name.

 

All this is an incomplete picture until you introduce the tendency for self-identity, as only in the enjoyment of self-love do people actually get stimulated merely by what they already know, though only under the conditions that others are present since here the knowledge becomes a implication of who one is as opposed to just being what it is.

Edited by Reciprocality

how much can you bend your mind? and how much do you have to do it to see straight?

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@Reciprocality

While on the topic of understanding and learning new things:

Quote

1. Reverse-engineer what you read. If it feels like good writing, what makes it good? If it’s awful, why?

2. Prose is a window onto the world. Let your readers see what you are seeing by using visual, concrete language.

3. Don’t go meta. Minimize concepts about concepts, like “approach, assumption, concept, condition, context, framework, issue, level, model, perspective, process, range, role, strategy, tendency,” and “variable.”

4. Let verbs be verbs. “Appear,” not “make an appearance.”

5. Beware of the Curse of Knowledge: when you know something, it’s hard to imagine what it’s like not to know it. Minimize acronyms & technical terms. Use “for example” liberally. Show a draft around, & prepare to learn that what’s obvious to you may not be obvious to anyone else

6. Omit needless words.

7. Avoid clichés like the plague.

8. Old information at the beginning of the sentence, new information at the end.

9. Save the heaviest for last: a complex phrase should go at the end of the sentence.

10. Prose must cohere: readers must know how each sentence is related to the preceding one. If it’s not obvious, use “that is, for example, in general, on the other hand, nevertheless, as a result, because, nonetheless,” or “despite.”

11. Revise several times with the single goal of improving the prose.

12. Read it aloud.

13. Find the best word, which is not always the fanciest word. Consult a dictionary with usage notes, and a thesaurus.

https://twitter.com/sapinker/status/1084490338629242880


Intrinsic joy is revealed in the marriage of meaning and being.

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 @Reciprocality  Personally I like the way you express yourself. For me, while writing the measurement is on (1) fluidity (2) differentiation (3) solidarity (4) freedom (5) connection (6) integration of feedback on everything in relation to the Self. 

So with respect to @Carl-Richard's share of the list there, I'd be at least 25% of the way there as there are solid pointers there. All of the pointers in that list serve number (5), however in as much as it compromises my personal freedom, I would rather trade the connection with a demographic that’s suited for my developmental context, aka going to higher levels of creativity and meta-understanding. 

Personal intentionality and self-awareness (i.e. around those principles I mentioned) are much more important to think about for me while writing than concrete guidelines that may obscure one's true voice. Moreover, context is doubly important. Who am I writing to? Creative intellectuals? Societal muppets? Societal muppets in creative intellectual clothing? There’s a lot of the latter like Sam Harris pushing there’s no free will for example, and too Robert Sapolsky even though we clearly do its just purely proportional to awareness and there’s zero rational, informed, logical and or intelligent argument that can be made against that. I used to love Sapolsky, however his intelligence has obviously become so institutionally corrupted by his environmental contrast bias, making comparisons between people and free will in the context of where there's clear examples of their lack of free will through the lens of their lack of awareness while making very little effort to do so through the microscope of differentiating free will under increasingly higher levels of awareness. In our situation here for example, on the simple analysis of adapting socially or not relative to a change in writing style inclusive of at least three persons here simultaneously aware of the object of said possible change, the unique conditions of freedom and will here as it concerns leveraging this moment towards our self-actualisation are entirely dependent on our level of awareness and the conditions that are supportive of therein.  

For me, I would never read Steven Pinker's work outside of going another extra meta level that he avoided as he didn't want to 'isolate' his reader. As he knows after-all, the more isolated a reader feels the less profit there is and the more their ego is activated and therefore the less they'll likely share their ideas with others. In short, he bores the hell outta me. Most writers do. Simply stated, they're shite and they'll never get true respect unless you take conformity as the kind of respect that should be sought after as I briefly talk about here what some of the dangers are there:

Now returning to free will, does someone like me truly have no objective free will on whether I can control that tendency? Really? I have no awareness to mediate my reactions, really? That's truly what's being said here? It reflects so much ignorance in our scientists these days in the field, too much ignorance to not question them on a potential ulterior motive that may be present, and that's out of respect for their intelligence more than anything else. No more respect than what makes me also simultaneously impartial to caring about the reasons so much anymore. 

Returning to adapting our writing to a certain said of stringent standards then in the context of free will, we all have the maturity of our awareness to empathise with the reader/s and the social environment to understand the balance between contextual connection and moving closer to our demographic. Creating writing standards as Carl has suggested is a really great idea all in all regardless Reciprocality, something that serves the best of both worlds so I'm going to go ahead and do it, for if a part of our developmental goals is reaching the heights of our consciousness then we need standards that both serve our truest expression and truest connecting point with our selective social environment.

And key word there is 'selective', if I learn that I deterred others that are not going to understand me because I didn't conform to the mediocre thinking standards of the general populace hence why we're failing across our many intellectual communities like universities, that makes me happy.

I know what its like to waste a lot of time conforming to the mind of another out of empathy where they were not nearly capable of expressing the same empathy, and in a lot of ways that's what it would feel like for me if I were to do that as a part of a professional writing or speaking career, because even as a general statement Sapolsky and Harris are right that most people technically don't really have free will, they're employed as scientists and so they need to be scrutinised not as social engineers that they have no right to really try and be but based on their claims as scientists where they learn to take in all the evidence. Doing this usually requires tedious differentiation and sometimes the spark of divergent generality to bridge interconnective insight to that most people can't deal with in the same way they avoided eating certain vegetables as kids.

That's not handling reality though. That's looking after toddlers. And that right there is the crux for me concerning adaptation, again, who are we writing for? Toddlers or people that are looking towards higher consciousness, maturity, growth, etc, etc all that good vegetable stuff?

The shortest version: Knowing how to write for your true soul connection in life is just as important as knowing how to deter your fake soul connection in life that'll be there for as long as you're conforming to a set of acceptable memes that don't startle their ego too much.

 

@1337 Now, let's get right to solving your issue with a simple solution that barely any know about. Ask any questions but my comment is already long enough right now, its better for me to under-elaborate so I can get what you don't understand and gauge your interest more easily. 

Solution: Get better at the 'meta-mechanics' of mathematical thought. Stage (1) Train on the right material. Stage (2) repeat stage 1 and advance it.

The following is my own idea, an elaboration on the original template shared below.

 

DO NOT TAKE THE FOLLOWING SOLUTION LIGHTLY.

JUST DON'T COMPLAIN AND IMPLEMENT IT.

IT'S MY CREATIVE SOLUTION WHICH MEANS ITS A BULLET-PROOF SOLUTION.

IF IT DOESN'T WORK, CALL ME OUT ON IT. 

BUT I STAKE MY LIFE ON IT.

 

Now off you go, you should be excited to become one of the best in your class.
Get on it, at least two months 1 hour a day to achieve said!

 

Step 1: Open Meta-AI in Messenger on Facebook

Step 2: Put the following into Meta-AI while asking the engine to replicate these kinds of questions as creatively as possible at increasingly greater levels of difficulty.

 

What is the ABSTRACT POSITION?

RAZOR will be North of TOWN
PLATES will be South of RAZOR
TOY will be South of PLATES
CARDIGAN will be Below and North of TOY
VEGETABLE was Above and South-West of CARDIGAN

Is the last statement reflecting the conclusion correct based on the previous premises?

TOWN will be South-West of VEGETABLE
APRICOT is after HAND
LION is after APRICOT
WINTER is opposite of (LION to APRICOT) to WALLET
CLOUD is before HAND
WINTER is opposite of (CLOUD to HAND) to LION
Is the last statement reflecting the conclusion correct based on the previous premises?

LION is before HAND
GOVERNOR is after LONDON
SALT is after LIPS
LIPS is same as (SALT to LIPS) to GOVERNOR
HOTEL is after SALT
LONDON is same as (HOTEL to SALT) to COW

Is the last statement reflecting the conclusion correct based on the previous premises?

LIPS is before HOTEL
BELT is Below and South-East of TUNNEL
HEART was Below and North-East of BELT
CAT will be Below and North-East of HEART
DOCTOR was Above of CAT
SHOWER will be Above and South of DOCTOR

Is the last statement reflecting the conclusion correct based on the previous premises?

TUNNEL is Below and East of SHOWER
All BISCUIT is SOUP
No SOUP is SOCKS
Some BRUSH is SOCKS
Some DENTIST is not SOCKS
All MOUSE is SOUP

Is the last statement reflecting the conclusion correct based on the previous premises?

Some MOUSE is not SOCKS
STEM is before CREDENZA
PHONE is before VILLAGE
STAR is same as (PHONE to VILLAGE) to BERMUDAS
CREDENZA is before PHONE
STEM is opposite of (CREDENZA to PHONE) to BERMUDAS

Is the last statement reflecting the conclusion correct based on the previous premises?

 

Step 3: Answer variations of the above questions but instead of doing so as they purely are instead convert the CAPTIAL words (i.e. BISCUIT/SOUP/STEM) into an imaginary object. This way you're training relational, associational and differentiation simultaneously all of which are pivotal ingredients to the larger encompassment of intelligence as I've personally coined it, "Temporal Pattern Compression".

If I had the time to dedicate myself to training, I'd jump at it but I don't. There's no point keeping my knowledge to myself out fear of someone stealing my knowledge as I have previously expressed that is so incredibly primitive relative to the level of consciousness I am working to grow to, I've just helped a philosophy student friend recently by sharing this knowledge in more elaborated form that if you want more details on again, patiently ask questions that are truly relevant to you and what you truly care about and I'll share accordingly. He will now go on to perform with a much greater sense of self-pride and self-respect now that he'll be able to achieve a much higher standard in his philosophy classes. There's no amount of money in the world that is worth more than deepening a genuine bond with a friend by being able to help him and have said help be genuinely valued and well-received. Moreover, we live in a sick society that is unaligned with truth so any amount of money or praise that anyone receives from the masses automatically comes with a heavy cost concerning the distortion of our own reality for a brief dopaminergic hit that takes twice as long to develop a clearer sense of reality beyond once we see through the illusion.

 

Best Light.

 

Honestly, please report back here to everyone here in two months time to everyone on your success or lack thereof in light of my aforementioned predictions to empower those that are looking to make the same progress in their lives for the betterment of greater consciousness and the lifeblood of those around them.

No BS. If you're really ready to nip this in the bud, treat this challenge like you would treat jumping into the pool for the first time from a high diving board. Brace yourself and jump as soon as possible, then learn to swim, slowly learning to without the life guard, in this case me if you have any further questions, to go off and create your own tricks off the diving board and techniques in the water.

 

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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.


57% paranoid

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@1337 What I discovered about mathematics is that I created some deficits early on because of my recalcitrant personality and natural abilities.  The less ability that you might have in a particular subject of math though, just requires more work to master it.  It seemed to me that Trigonometry entails the ability to 'formulate mathematical proofs' where as, geometry, then calculus, especially 'Analytic geometry' was a brain teaser for me.  I feel that I missed my window of opportunity to learn the basics of maths that required 'spatial reasoning' and 'abstract reasoning of the type' abilities.  Don't despair though, there are many walks of study in a mathematical pursuit. Graph Theory (which I was the only one to finish a problem that the Professor quoted that what I had done was essentially formulate a graphical proof of the concept while loudly proclaiming that the problem was one where someone 'didn't need to know anything to solve.  I hated that j*ckass.  Discrete math/Combinatorics, Linear Algebra, Number Theory, etc.

I had a professor suggest I take a Trigonometry course because if I could do that then I could do Calculus.  He lied to me... :)  I blew the scale in Trigonometry and still struggled through Analytic Geometry after a 2nd try (Calculus II).  I did pretty well in Calculus I and III.  

 

I'll add that math in the real world is very simple when compared to what happens in school.

Edited by El Zapato

I am not a crybaby!

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@Jodistrict One of the things that always frustrated me was the math books.  Mathematicians can't write and writers don't know mathematics.  One that always incensed was the ubiquitous 'It therefore is obvious'.  Damn, that p*ssed me off.  I asked my Professor what was so obvious and he just laughed at me.  "Theory of Automata"  :) 


I am not a crybaby!

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13 hours ago, El Zapato said:

@Jodistrict One of the things that always frustrated me was the math books.  Mathematicians can't write and writers don't know mathematics.  One that always incensed was the ubiquitous 'It therefore is obvious'.  Damn, that p*ssed me off.  I asked my Professor what was so obvious and he just laughed at me.  "Theory of Automata"  :) 

There is indeed a very large variance in how textbooks are written. Especially for grad material, some professors just like being dicks and making everything excruciatingly dry. 

It's the same reason for those laughs. Mathematics gets such a bad name because of a few people who can't help their insecurities. 


Chaos, Entropy, Order

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@Ero I always believed that old meme:  Mathematics is like religion because so many things have to be taken on faith.  :) 

Edited by El Zapato

I am not a crybaby!

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Reading textbooks is so outdated at this point. You are better off watching a quality video that visualizes the problem at hand. Math benefits a lot from visualization.

Edited by Leo Gura

You are God. You are Truth. You are Love. You are Infinity.

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2 hours ago, Leo Gura said:

Reading textbooks is so outdated at this point. You are better off watching a quality video that visualizes the problem at hand. Math benefits a lot from visualization.

Hmm, I just watched this video:

 

I was there in the audience where the audio was taken from btw 😊, and the visualizations gave me an interesting new perspective on that talk. I think the visualizations could've helped many people in the audience, especially when he was talking about fields and the different theories of vision.

Edited by Carl-Richard

Intrinsic joy is revealed in the marriage of meaning and being.

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9 hours ago, Leo Gura said:

Reading textbooks is so outdated at this point. You are better off watching a quality video that visualizes the problem at hand. Math benefits a lot from visualization.

Very much so regarding visualization tools, but I am so acclimated to reading, I prefer not breaking the habit.  I get a comforting feeling from books.  It might sound maudlin or trite to say it, but I love books.

I have another issue with watching videos though, sometimes they are not as effective for me because they lack the tactile feedback that I desperately need to learn. It would be easy given that I understand my limitations to adapt but, I have one other very serious problem.  Since childhood, I laughed at taking notes, never really learned how to do it and now most times I am too lazy to try. 


I am not a crybaby!

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11 hours ago, Leo Gura said:

Reading textbooks is so outdated at this point. You are better off watching a quality video that visualizes the problem at hand. Math benefits a lot from visualization.

That maybe true for High School Math and some undergraduate topics that have a visual component, like Linear Algbera, Multivariable Analysis and Complex Analysis.

However, for any more advanced topic like Algebraic Geometry, Algebraic Topology, Representation theory and Functional analysis, not only are there zero to none videos, I fail to see how you would even represent infinite-dimensional spaces, sheafs and cohomology chains.

The power of mathematics comes precisely from the ability to prove stuff about things we can’t even visualise. 

Edited by Ero

Chaos, Entropy, Order

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5 minutes ago, Ero said:

That maybe true for High School Math and some undergraduate topics that have a visual component, like Linear Algbera, Multivariable Analysis and Complex Analysis.

However, for any more advanced topic like Algebraic Geometry, Algebraic Topology, Representation theory and Functional analysis, not only are there zero to none videos, I fail to see how you would even represent infinite-dimensional spaces, sheafs and cohomology chains.

The power of mathematics comes precisely from the ability to prove stuff about things we can’t even visualise. 

However, there are tools to simulate those paradigms which are very nice. If I remember correctly 'Mathematica' is one such tool?


I am not a crybaby!

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https://youtube.com/@3blue1brown?si=Wbj84exEAmeYh5Dc

This is hands down the best channel for learning rigorous maths in an entertaining way. It is very popular among university students and professors.


God-Realize, this is First Business. Know that unless I live properly, this is not possible.

There is this body, I should know the requirements of my body. This is first duty. We have obligations towards others, loved ones, family, society, etc. Without material wealth we cannot do these things, for that a professional duty.

There is Mind; mind is tricky. Its higher nature should be nurtured, then Mind becomes virtuous and Conscious. When all Duties are continuously fulfilled, then life becomes steady. In this steady life God is available; via 5-MeO-DMT, ... Living in Self-Love, Realizing I am Infinity & I am God

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This playlist was extremely helpful for me:

Trig concepts are explained with very intuitive animations.

Edited by Ragib Ashraf

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On 9/18/2024 at 8:35 PM, Leo Gura said:

Reading textbooks is so outdated at this point. You are better off watching a quality video that visualizes the problem at hand. Math benefits a lot from visualization.

100% disagree, depends on the student.

When I was very good at mathematics, I would only learn from doing the problems interactively with a tutor.

Mathematics is interactive, not visual. You will never learn mathematics from a YouTube video.


أشهد أن لا إله إلا الله وأشهد أن ليو رسول الله

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