Hard and easy difficulty

[sushi]

Is hard and easy subjective or is it objective?

what is hard what is easy. How to define hard and difficult?

is hard or difficult vs easy measurable or quantifiable?

what is the hardest subject you have ever touched learned?

For me hard is how much suffering and effort necessary it takes to know and learn something. level of impossibility or possible is also a factor.

 

[sushi]

objective as some things are really harder than others

like calculus is really harder or higher level than 1+1=2


subjective as in perception based, there is no such thing as hard and difficult, its all a mindset

you can also discuss what is the hardest topic or course you have taken.

 

[Old Things]

The way I see it, there are basically three general ways to describe a task:

1) Easy, self-explanatory.
2) Neither easy nor difficult
3) Difficult, causes stress or anxiety or many tries to succeed.

 

[birdsnestfern]

So many levels to whether something is hard or easy.

When I was first entering college, English was easy, made A's in writing, reading, all the different aspects of it.
Algebra was hard -I had a block, thought I couldn't get it, so I ended up needing to take algebra three times until I finally got it.
Then I took more advance math, and accounting later, and some programming too. I wasn't a natural at it, but I didn't care if I failed it the first time, I took it again. I had some strange drive to complete a degree no matter what.
But I never took Calculus, it was one of the only classes I was afraid to try, just a few classes short of a computer degree, but Calculus scared me off. So I switched to an accounting degree and that was easier for me than the computer degree.

But hard can mean you need strength in so many categories like...
Physical strength
Spiritual strength
Teachers Ability to Inspire You about a subject
Your desire to study four hours at night for every two hours of class.
How much you want to learn something
If you fail, retake a class until you get it
Adaptability Strength
Perseverance Strength
Purpose Strength
Desire Strength
Whether you are young, old, male, female, nourished, depleted, sick, depressed, healthy, whether you had vitamin b complex and have mental energy to complete something, whether your genetics and brain are up to the task, whether you have family support to help house, feed you while you study, whether you are eating well and feeding your body and brain, whether you are a single parent working full time and going to school full time, or are a single student on your own, or are rich or poor, all those things make a huge difference, whether you have transportation, a pandemic, or a college you actually want to spend time in, and a study place, etc.

Oh, its ALL suffering! The hours you spend listening to lectures by awful teachers when you don't want to be there,
the hell of it all and then you work your life away and does it show? Not even that much. But keep trying, because its one hurdle after another, but you are still worth it, its better than working in a fast food place. Slaves to the system and its kind of a waste to see how hard it really is.

 

[sushi]

The way I see it, there are basically three general ways to describe a task:

1) Easy, self-explanatory.
2) Neither easy nor difficult
3) Difficult, causes stress or anxiety or many tries to succeed.

thats good way to see it

 

[sushi]

for me there is a ladder and rank

machine learning/code and engineering , nuclear physics are probably the hardest thing i can imagine


accounting and economics is probably within my ability


typing in all forms is probably easiest, along with basic math computation


i say japanese and chinese are pretty hard, but probably above accounting and economics, and below engineering and calculus.


is there a limit on how hard things can get?
what is the hardest book subject you ever read?

 

[The Grey Man]

I recently went back to school to study mathematics. It's hard, but, then again, math is not monolithic: there are several aspects to it. Besides the diversity of mathematical topics (arithmetic, geometry, abstract algebra, etc.) I've counted at least four kinds of mathematical practice:

1. proof,
2. explanation,
3. calculation, and
4. heuresis (mathematical discovery).

The first is the activity that is most strongly associated with mathematicians: whatever else a mathematician might be, he is someone who, on the basis of a few postulates and inference rules, proves theorems, which are more or less interesting, more or less "significant" according as they are more or less apt to be, in G.H. Hardy's words, "connected, in a natural and illuminating way, with a large complex of other mathematical ideas."

The second is the reverse of the first in the sense that, rather than progressing from principles to conclusions, it regresses from conclusions to principles. It does not tell us that x, but why x, or how we know that x. For this reason, explanation is more strongly associated with mathematical physicists or natural scientists than 'pure' mathematicians.

The third is, in a way, the most 'boring' of the four since it is purely a matter of manipulating equations according to substitution rules until the desired variable is on one side and some intelligible expression on the other, but it is far from being trivial outside of a classroom setting, where it is obvious what equations and what rules one is supposed to use. This brings us to the fourth on the list.

Heuresis is the most subtle and, consequently, the most overlooked of the four. Almost no one before Pólya even paid attention to it (Pappus of Alexandria is a notable exception), and few have since. Still, it's my favourite because it is the nexus between mathematics and philosophy, my first love. Heuristics is the study not so much of proofs or physical theories as of how we come up with them. Heuresis is a kind of 'educated guessing', interpretation which leads to insight. (The ability of an expert mathematician to guess right, based on a lifetime of training and experience, is, it seems, one of the vestiges in contemporary culture of what was called grammar in the old liberal arts paradigm.)

The most difficult for me to learn has been proving, probably because I have as yet little experience constructing arguments at the level of precision and rigour which mathematics demands. Philosophical arguments almost always 'skip steps' or leave premises unstated because their conclusions are much broader in scope. This is not necessarily a bad thing—a plausible argument is very often the best we can do, both in philosophy and in life—but no mathematician worth his salt accepts a non sequitur if he can avoid it.

 

[sushi]

i concur math and logic is among the hardest subjects to study, especilally when applied to other disciplines, that is why biology is the easiest.

mental hard and exertion is more obscure than physical hardship, such as mechanical work and lifting things.

 

[sushi]

I think the hardest thing is telekinesis

doing and manipulating things completely mentally other than physical effort, like charles xavier. or solving and imagining things mentally rather than writing them down.

Although I cannot prove telekinesis is possible or not.

thinking is very weak form of telekinesis.

 

[sushi]

if i have to quantify hardest complex topic or idea for human, its probably einstein or feymann level.

Anything above or harder than einstein is perphaps impossible or beyond human.

 

[Black Rose]

if i have to quantify hardest complex topic or idea for human, its probably einstein or feymann level.

Anything above or harder than einstein is perphaps impossible or beyond human.

People think Libb Thims IQ is 195.

He said that Feynman was 185.

He said Einstien wa 200.

But Feynman's adjusted IQ from the original IQ test he took was from 125 to 139 because the deviation was not calculated properly.

(1.39 / 1.85) * 195 = 146.5

Libb Thims IQ is 147

Einsteins' IQ was 150 in comparison.

 

[sushi]

my analysis of study problems:
the material you struggle with


iis not part of your brain and knowledge, so you get frustrated. you cant intergrate it.

you cant read , describe and use it

you cant define it

you cant understand its form function architecture connection (the relation) and how to change it.

 

[dr froyd]

to me "hard" is when its difficult to get an intuition for the big-picture or macro-level representation of a concept via the mechanics of its smaller parts. Because in order to get a mental representation of it as a whole you need to combine a huge number of smaller concepts simultaneously.

for example something like Dijkstra's algorithm; for anyone with a little bit of experience with algorithms you can easily understand each step in the algorithm, but to get an intuition on a bigger scale for why it works is much more difficult – you have to hold a lot of complex, abstract concepts in your mind simultaneously.

i dont consider anything within math or computational science "hard" though, it's just a matter of gradually building intuitions and mental representations of each small component and getting used to them. As Feynman once put it, it's not hard, "it's just a lot of it".

 

[Black Rose]

i dont consider anything within math or computational science "hard" though, it's just a matter of gradually building intuitions and mental representations of each small component and getting used to them. As Feynman once put it, it's not hard, "it's just a lot of it".

I think the reason my parents gave me "hooked on phonics" before they gave me a dictionary is because the dictionary would not help me learn to read.

legos are a good way to learn in kindergarten but so too as an adult.

if you do not know the basics the higher stuff is never learned.

interface matters.

I never learned Java programming correctly.

All I did was get a working program and gutted it and put in my algorithms but I do not know how object-oriented programing works.

 

[dr froyd]

if you do not know the basics the higher stuff is never learned.

exactly

 

[sushi]

what is hardest math
what is hardest science
what is the hardest engineering
what is hardest language

how many books does it take for one to understand the subject

 

[Black Rose]

how many books does it take for one to understand the subject

depends,

people do not write books I can understand, I am not the audience.

if I could I would pay someone to teach me because they would have to get on my level.

 

[dr froyd]

what is hardest math
what is hardest science
what is the hardest engineering
what is hardest language

how many books does it take for one to understand the subject

for the hardest math category i nominate complex analysis

don't really know if its the hardest but when we had this stuff in university it felt like we descended into an unfamiliar foreign world where a lot of unusual stuff was happening

but then again it wasn't particularly hard once one got familiar with the concepts. At the end of the day the main difference was simply that every number is a vector in a 2-dimensional plane and that every time one encountered an "i" it meant i^2 = -1

 

[sushi]

i cant understand half of google and ai machine learning stuff 90

i am probably never to going to touch it anyway. it seems like hell.

 

[sushi]

things that seem very hard to me

surviving cancer
war and suffering
walking up infinite stairs
telekinesis like charles xaiver, doing things with pure thought

i think when we encounter something hard our brain goes into war and suffering mode .

 

[sushi]

how much cost of learning and acquriing something

how much suffering and effort probably defines how hard to learn it

maybe there is no such thing as objectively hard

also the frequency of failure and punishment and hitting a brick wall bottleneck

 

[ZenRaiden]

Physics,

Time limit, how much time you are given to do something.
Calculus is childs play if you get enough time to study. Its literally idiots play.
However if you get bad teacher or bad workbook or have little time, then you are fucked and even raw intellect might find it hard to understand.

Most problems in life are defined by time.
Power is work over time with force over distance.
Its that simple.

Flying is easy for birds, but birds were practicing flying for 100s of millions of years.
People figured out flying in few years of combined effort and tech.

 

[Black Rose]

Calculus is childs play if you get enough time to study. Its literally idiots play.
However if you get bad teacher or bad workbook or have little time, then you are fucked and even raw intellect might find it hard to understand.

put input x into function y get result z

Calculus is a way of creating shapes by extending variables in the function.

but what is this good for?

calculus was developed to calculate the trajectories of planets.

That is to find out how each planet orbited the sun and also to measure the pull each planet had on each other planet. Issac Newton did not understand general relativity so Mercuries obit he said was off because God allowed it to not conform to the equations. Uranus was discovered because of its pull over several centuries.

So we can add all the shapes together and find where things will be or make shapes for technology such as where a lens will focus or something like this. But in Newton's day, it took a lot of work plotting all the shapes because there were 6 planets (and the moons) and all they had was paper to integrate all the data. Today you can use computers to make any shape you want:

Function a ( function b ( function c (variable p) ) ) = functions: (X, Y, Z)

but computers require you to keep things within the boundaries of the memory or it creates errors that overwrite memory sections cut off data points or point to data that does not exist.

Once you understand that calculus is about making shapes the only problem becomes: what shape are you trying to make? and what data is involved?

 

[sushi]

if we treat each area domain of knowledge as philisophy, then we can define what is hard and easy. (even engineering can be considered as philosophy) with its rules and concepts

hard = knowledge, philosphy, concept , idea language

math is a form of philosophy and concepts reduce to equations and calculations.

hard= ability and talent

 

[sushi]

hardest philosophy, knowledge, language

hardest logic and output

hardest ability and talent

math is just logic and language to produce output. the same as programming

 

[ZenRaiden]

math is just logic and language to produce output. the same as programming

Math is more than that. Math studies spatial and numerical relationships in concrete and abstract terms. Logic is merely a tool to understand those relationships.
Programming is language of machines.
Math is language of quantity and its measurements.

 

[dr froyd]

math is just logic and language to produce output. the same as programming

maybe one could argue math is logic, but in practice it's quite different from programming - its more about imagining and visualizing abstract things.

like say you want to calculate the limit of sin(x)/x as x goes to 0.

programming this is one thing - you make some algorithm that just goes through the mechanics of dividing x into small steps and then calculate the functions as x get smaller.

using math, if you visualize sin(x) in your mind you can see that when you zoom very far into 0 along the x-axis, sin(x) becomes almost a straight line. Since f(x) = x is also a straight line, you can see that the numerator and denominator become equal, so the limit is 1.

that's not an actual formal proof, but that is the kind of thing one would constantly do in math (but usually in much more complicated scenarios). It's a bit different experience than doing programming.

 

[sushi]

mathematica , pretty hard

Wolfram Mathematica: Modern Technical Computing

Mathematica: high-powered computation with thousands of Wolfram Language functions, natural language input, real-world data, mobile support.

www.wolfram.com

a mixture of math and programming

 

[sushi]

i really dont know how to objectively rank hardest and easiest

perhaps its all relative and subjective, i dont even know how brain learns and absorbs.

but if i were to scale now, i will rank the hardest stuff= as similar to highest temperature and suffering

and easiest stuff to lowest temperature

 

[sushi]

 

[sushi]

how much pressure temperature and suffering

that is how i would scale how hard to study and learn a subject