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# Why Modern Math Education Is Obsolete

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posted on Sep, 7 2015 @ 03:50 PM
a reply to: jedi_hamster

The reason you two cannot understand one another is because you two do not understand the relationship between structures and concepts.

Jedi, you're arguing from a structural perspective, where Chaotic is arguing from a conceptual perspective.

Jedi, you think structure is the foundation of conception, that it must be before the concept, and you're right, in a sense, but what you fail to grasp is that the foundation is the body of the concept, and once you learn the concept, byway of the structure, you are then free from strict structural confines [which you fear the loss of]. Your problem is that you do not understand that the concepts of math are about the construction of functions, and not about the structures themselves.

@Chaotic, you know that the structures only lead to the concepts, and they’re not as important as the concepts, but what you fail to grasp is that the concept is structure and is to structure the function.

Think about it like you need images to see a concept and an image is a concept and is to conceive images (to conceptualize). The concept is to conceive will; to structure force; to build a function.

e.g. Once I know what a car is, I can build many different car structures, all of which serve the same conceptualized purpose; yes even these words could have been formed differently and still lead to the same concept and will. (which is why the words, symbols, equations, syntax, operators, etc. are not so important as long as you get to the concept.)

It is the relationship between the Son and the Father. Jesus is the body of God and is God, but Jesus is only to lead you to Father, like words leading to a concept of desire, the premise of will, the function math. Father is the concept of the function, and Jesus is the image thereof.

@Chaotic, try to write a math concept without form and/or have a concept form nothing, and you will see Jedi’s point.

Jedi, try to see how free formed math concepts can be (1++), and so syntax, or structure, is not as important as a concept, or try to make a math symbol without any concept of making one, and you will see Chaotic’s point.

And even though Chaotic doesn’t know why (s)he is right, as evident by not understanding your point of view, (s)he is still right:

Even though concepts are defined structure, and the concepts are how to structure function, the concept is still more important than the structure, as the language, or structure, is only meant to lead you to a conceptualization of a function/will/spirit.

posted on Sep, 7 2015 @ 04:31 PM
a reply to: ChaoticOrder

Thank you for sharing this!

Modern academia has been influenced largely by social 'sciences' and psychology's efforts to eliminate binary operations of true and false in favor of spectrums and emotional/experience/relative based 'computation.' It used to be that things are proven false with a single example. Now the definitions are merely expanded and circular logic is applied until what was once fallible no longer is. (My experience being required to participate in cultural/arts/humanities courses has made this abundantly clear. Activism has overtaken objectivity with the abolishment of concepts of absolute truths being replaced with a spectrum of truthiness.)

I took a course in discrete mathematics and my prof spent ample amounts of time expressing how annoyed they were that this course was relegated to college and university level maths when it was really a core process of problem solving and developing the proofs used for logical operations.

Real numbers, rational numbers, irrational numbers, and the like are not expounded upon at younger ages and it really shows in how our society views science and 'facts.' The topics become esoteric VERY quickly and I have seen them make people very uncomfortable when attempts are made to integrate them back into other common topics.

Seriously, the square root of two is not a rational number? Yes, a common example that really expresses the problem.

Now using computers is easy because the incredible ability to use binary systems to model physical phenomena. Computer science has spent a great deal of energy developing systems which operate on top of basic arithmetic logic that make them much more accessible to those not familiar with maths. As a programmer you likely are familiar with using a addition to perform multiplication with shifters and registers yada yada yada.

Anyways, glad this is a topic.

-FBB

posted on Sep, 7 2015 @ 04:44 PM

originally posted by: pl3bscheese
a reply to: noonebutme

Agreed the multiplication tables are drilled in my head, more so because I constantly encounter situations where basic calculations are required. People around me guess or waste time with their smartphones, I know the answer instantly.

Programming is very similar to mathematics. It's simple logic is all. Didn't get what the OP was talking about. For instance when he talks about syntax meaning different things in different fields of mathematics, the exact same thing happens when you switch programming languages. Maybe he sticks with languages coming from similar roots, like someone who knows Latin based languages.

The syntax they may be referring to could be what number sets are applicable, do they use imaginary numbers like electrical engineers for complex circuits, etc?

Linear operations to describe non linear functions or assuming an instantaneous result from a linear system (electrical example again) due to the incredibly small time frames actions take place in, or discrete (defined) measurements become infinitely large like electrical currents in certain light bulbs.

Actually idk the best way to interpret that, but the message about problem solving being more important than rote memorization still stands. I was always a level below the 100%ers in math exams which relied on time constrained memorization, but excelled when the application of the topics became the focus.

Everyone should be forced to take calculus!

-FBB

posted on Sep, 7 2015 @ 04:45 PM
a reply to: Bleeeeep

structure isn't a foundation of a concept in general, it may be considered a foundation of a particular implementation - but that's exactly what it is, an implementation, one of many possible. so you're right with your car example, but completely wrong when it comes to making assumptions about the way others understand the problem.

my point is that Chaotic tries to understand the function by working with the structure, while - as you've pointed out - math is about functions, not structures representing them. it's a very limited point of view.

and keep the religion out of this thread, thank you. your post sounds a lot like philosophical yadda yadda crossed with an attempt at mentoring even without taking it into account.

posted on Sep, 7 2015 @ 05:02 PM
a reply to: FriedBabelBroccoli

Well to be fair I only got 99% on state standardized tests xD, I was both the highest performer and fastest. Pretty sure most in this thread agree that understanding the concept is superior to understanding the formula. If I know the "why" then the "how" tends to be arrived at automagically. If you understand at a deep level, you can of course deviate from standard teachings and approach the problem from whatever start/end point and angle you like. I've gotten lazy, admittedly, over the years and tend to think more in proportions and do good estimations in everyday real-world applications oftentimes.

posted on Sep, 7 2015 @ 06:06 PM
a reply to: jedi_hamster

You're contradicting yourself, and I hope that one day you can see it, but my point to you was on all the points you have made: about how people must memorize solutions and how to calculate equations. The way you are looking at them is that, methods are concepts, when, in truth, methods and calculating the methods are just a part of the structure or symbology - which is what Chaotic is free from when learning actual concepts and applying his/her own methodology.

What Chaotic is saying about simplifying is that the current method is convoluted. (S)he wants maths to be about learning concepts, foremost, rather than memorizing other people's convoluted methods/equations and how to calculate with those equations.

Also, you should seek God. lol

Also, the whole relationship is exactly like that car example - you just can't see it.
edit on 9/7/2015 by Bleeeeep because: (no reason given)

posted on Sep, 7 2015 @ 07:54 PM

originally posted by: ChaoticOrder
Now I'm a programmer and I've done things like create a crude 3D graphics engine from scratch, which involves a lot of math. I still cannot remember most of the multiplication table though. The reason I can do stuff like that is because I have access to a thing called the internet, and when I need to know something I don't know, I can just look it up and find all the information I need. I'm not going to remember every physics equation in my head when I have almost instant access to it whenever I need it, especially since I will most likely never need to use 90% of those equations in practice. I also have a thing called a computer which can perform calculations billions of times faster than I can do them in my head. The most important thing is that I can understand new concepts and convert those ideas into algorithms, that's where real intelligence is required.

I too am a programmer, I've done the 3d graphics engine both raytracers and rasterizers doing lighting effects for shaders, converting locations points between world/object/camera spaces, and others, and that's just in a graphics engine. I disagree completely that that's a lot of math or that you don't need to know how to do it. Lets give an example, say you have a two objects in 3d cartesian space and you need to know if one object is behind the other relative to the first objects heading, do you understand dot products so that you can do it without taking the cpu resources of a trig call?

The result is that the complex behavior, or what we thought was complex behavior, will often naturally emerge just from those simple rules. The flock of birds will start doing very complicated things as a group, even though the rules dictating the behavior of each bird are not that complicated. It is easy to conceptualize such behavior when you think of it like that, and it's easy to implement those models in computer code without needing to be good at math. This is the core reason you'll often hear many programmers who say it doesn't really matter whether you're good at math or not. Of course it helps to have a wide knowledge of different mathematical concepts so you can create innovative and efficient solutions to problems, which is what math education really needs to focus on.

This isn't just a truth in programming, all complex behaviors are nothing more than interactions of simple concepts. But, throughout history those who have been able to recognize the simplicity in an object have been heralded as geniuses. Steve Jobs with a 1 button cell phone, Einstein with E=MC^2, and so on.

In conclusion, I think the way we teach math today is quite obsolete and hasn't advanced much since we started teaching it in schools. We need to place more focus on understanding the concepts involved rather than being able to remember a bunch of useless numbers or equations which take up precious space in our head. Children are not drones who can just have endless streams of data shoved down their throats and be expected to regurgitate any little factoid on demand. They will enjoy the learning experience a lot more and get more out of it if they weren't taught in such a bland and unimaginative fashion. I understand it wouldn't be the best approach for all children but I feel like there are many kids like me who have hidden potential but they are repelled by the way math is presented to them.

If you're a programmer you should understand that bitshifting is essentially what common core is attempting to teach, except in base 10.

originally posted by: ChaoticOrder
a reply to: pl3bscheese

There is just far too much uncertainty for my liking, I would prefer the language of math to be much more universal and clear cut. It's also just hard trying to pack complicated ideas into small equations, the notation gets very messy and I just cannot bring myself to try and understand such gibberish. I find it exceptionally easier to read a computer algorithm which is stating the exact same thing as the equation.

Programming is full of using different words to express the same outcome, just as math is. I brought this example up in another thread recently and I feel like being lazy so I'll reuse it. If A currently equals 35 and I want it to equal 0 there's many ways I can write it.
A = 0
A -= A
A xor A
A *= 0
A -= 35

Programming and math are both logical but logic is nothing more than a sequence of steps taken to arrive at a conclusion, there isn't only one correct logical path to a result.

originally posted by: ChaoticOrderAs long as I understand the concepts involved, I can write algorithms which implement those concepts, then let the computer do the hard calculations for me.

If you're relying on the computer to do the math for you, you have no way of error checking it to compare the results of it's calculations to the expected value in order to make sure your algorithm is correct.

originally posted by: ChaoticOrderBut I don't really think it would be quicker to solve problems like that in your head compared to just using a calculator, especially when you start having more than 2 digits. In fact I cannot afford to waste mental energy on such calculations, I have much more interesting and high level problems to think about.

Then you would be wrong, it's extremely quick to do math this way and not just with small numbers. Hundreds, thousands, millions, billions, trillions, even more it's all the same.

posted on Sep, 8 2015 @ 02:11 AM
a reply to: jedi_hamster

you're not able to visualize the equation and manipulate variables in real time - computer software is.

The computer is simply drawing the graph, it wouldn't make a difference whether you used a computer or you used a paper and a pencil to plot the graph on some paper, it would give the same visualization. Of course it helps if you can generate the graph in your head just from your understanding of the equation, but like I said, not all equations are that simple to understand, and by using a computer, we can see what the function graph should look like, and that gives a much deeper insight into how the equation works, and lets us generate the graph in our head without a computer.

there's a line between thinking like a programmer and thinking like a mathematician, which you're drawing as far from yourself as possible, and that's a bad thing. you can mimic the equations, you can even calculate the same thing those equations represent, but without deep mathematical understanding of some problems, you will never be able to come up with solutions that won't seem obvious from your purely-programming-driven point of view.

In order to create an algorithm which does the exact same thing as the equation I obviously do need to have a deep understanding of what the equation represents, but I don't need to be able to read the equation to gain that understanding. I can read tutorials or watch a lecture which explain what it's supposed to do, how it does it, what we used it for, etc. In fact, after taking the effort to educate myself like that, I can usually go back and understand exactly what the equation is saying. After I write an algorithm to implement the equation I will certainly know what the equation is saying because my code is usually saying the same thing, but in a less abstract and more concrete/discrete fashion.

you will never make a leap similar to discrete fourier transform - fast fourier transform with such attitude towards math, and without FFT and similar things, we wouldn't have any decent audio or video compression these days, at all. do you think FFT was invented by programmers? far from it, we didn't have any computers back then.

Once again you're twisting around the point I'm making. Why do you think I said in my opening post "Of course it helps to have a wide knowledge of different mathematical concepts so you can create innovative and efficient solutions to problems, which is what math education really needs to focus on.". I don't need an equation to understand the concept of prime numbers, I don't need an equation to understand the concept of interpolation, I don't need an equation to understand the concept of vibration, etc. If I was just starting to learn about Fourier transformations this is where I would start:

The Fourier Transform is one of deepest insights ever made. Unfortunately, the meaning is buried within dense equations:

[equations removed to reduce snippet size]

Yikes. Rather than jumping into the symbols, let's experience the key idea firsthand. Here's a plain-English metaphor:

* What does the Fourier Transform do? Given a smoothie, it finds the recipe.
* How? Run the smoothie through filters to extract each ingredient.
* Why? Recipes are easier to analyze, compare, and modify than the smoothie itself.
* How do we get the smoothie back? Blend the ingredients.

Here's the "math English" version of the above:

* The Fourier Transform takes a time-based pattern, measures every possible cycle, and returns the overall "cycle recipe" (the strength, offset, & rotation speed for every cycle that was found).

Time for the equations? No! Let's get our hands dirty and experience how any pattern can be built with cycles, with live simulations.

If all goes well, we'll have an aha! moment and intuitively realize why the Fourier Transform is possible. We'll save the detailed math analysis for the follow-up.

This isn't a force-march through the equations, it's the casual stroll I wish I had. Onward!

An Interactive Guide To The Fourier Transform

Also when it comes to compression, the technique used by the most powerful compression software today is a method called arithmetic coding. They typically use multiple prediction models to produce several guesses at the next symbol and then they use a feed forward neural network to combine the model predictions into a single probability which can be encoded using arithmetic coding. A high level understanding of algorithm design and information theory are clearly very important to these compression systems. But there's also no denying we need to understand mathematical concepts like activation functions in order to understand neural networks. However understanding those simple math concepts is nothing compared to understanding the algorithm as a whole and how all the different parts work together to compress data.
edit on 8/9/2015 by ChaoticOrder because: (no reason given)

posted on Sep, 8 2015 @ 08:20 AM
a reply to: ChaoticOrder

The computer is simply drawing the graph, it wouldn't make a difference whether you used a computer or you used a paper and a pencil to plot the graph on some paper, it would give the same visualization.

facepalm. really. epic facepalm.

In order to create an algorithm which does the exact same thing as the equation I obviously do need to have a deep understanding of what the equation represents, but I don't need to be able to read the equation to gain that understanding.

i guess after reading this thread everyone already got your true point. you just hate equations - because that's the only point of your sentence above that makes any sense.

If I was just starting to learn about Fourier transformations this is where I would start:

i'm sorry, i was convinced that being a programmer implies an IQ that doesn't require 'for kindergarden'-level tutorials on such topics as FFT. no wonder the average software quality today is going downhill.

Also when it comes to compression, the technique used by the most powerful compression software today is a method called arithmetic coding.

yes and no. i was talking about audio/video compression. arithmetic coding on its own is pretty useless for lossy audio/video compression - it's being used in x264 video codec for example (well known CABAC) to encode coefficients of the macroblocks - but those coefficients are, to simplify, a result of FFT-alike transform and masking. masking in video compression throws out what human won't see, masking in audio compression throws out what human won't hear - it's all based on several concepts with solid mathematical foundation - but all that masking operates on the data from FFT-alike transform. FFT-alike, because it's DCT actually - discrete cosine transform - because of its mathematical properties that produce smooth wave across several DCT frames. arithmetic coding is just the tip of the iceberg of such codecs, because without all the underlying stuff, it would have far too much data to work with. there are also wavelet-based lossy audio/video codecs, but the general picture stays the same.

of course, one can use arithmetic coding for lossless compression of any data, but on its own it won't beat datatype-specific codecs - every datatype-specific codec, including lossless ones, is heavily optimized toward that specific datatype, and again - arithmetic coding becomes just the tip of the iceberg.

it's a very good method, obviously, but it's also very general. not good enough on its own. on the other hand, if you weren't trying to derail the subtopic (the importance of FFT for current age audio/video compression) and were instead trying to imply that arithmetic coding is far more important than FFT/DCT for audio/video compression, i would suggest heading back to wikipedia and educating yourself.

posted on Sep, 8 2015 @ 09:58 AM
a reply to: jedi_hamster

i guess after reading this thread everyone already got your true point. you just hate equations

I don't hate equations, I'm just not very good at interpreting complicated equations and so I tend to avoid it in favor of understanding the concepts first, which often allows me to understand the equations. Maybe if I had the necessary education I would be better at it but I think it has more to do with how my brain works, it just doesn't like the ambiguity that comes with complicated equations, it much prefers the clear syntax of (most) programming languages. I also am the type of person that likes to visualize things in order to understand them and looking at an equation often cannot give me that visualization. When I think about it in terms of algorithms it is much easier because I can think about the flow of the code and how all the different parts of the system interact together. And the fact is, in real life, many systems are simply too complicated and messy to be mapped to an equation and so we must absolutely have other ways to visualize how those systems function.

i'm sorry, i was convinced that being a programmer implies an IQ that doesn't require 'for kindergarden'-level tutorials on such topics as FFT. no wonder the average software quality today is going downhill.

Well I'm sorry not all of us can look at a complicated equation and automatically understand everything about it. Some of us need to see charts and simulations and be eased into the subject. Not everyone has a brain which works like a mathematician and I don't know why you cannot grasp that fact. Also, just because something is explained in simple terms doesn't necessarily mean it has been dumbed down. Einstein once said "If you can't explain it simply, you don't understand it well enough". Furthermore, adding charts and animations does not at all dumb down an explanation as you seem to believe, it's quite the opposite actually. Making a subject easier to learn does not always translate into dumbing it down or give a less accurate understanding.

of course, one can use arithmetic coding for lossless compression of any data, but on its own it won't beat datatype-specific codecs - every datatype-specific codec, including lossless ones, is heavily optimized toward that specific datatype, and again - arithmetic coding becomes just the tip of the iceberg.

I don't want to have a "who can sound smarter" competition with you, but this statement is not exactly true. Arithmetic coding is a universal "plug-and-play" type of procedure which can be applied to any type of data very effectively. If you want to focus on compressing a specific data type then the prediction models need to be optimized for specific data types, but the arithmetic encoder will always be used the same way to encode those predictions. The level of lossless compression will be proportional to how well the prediction models can predict upcoming symbols. Arithmetic coding directly translates prediction power into compression strength, so if your model can predict audio or video data very well it will compress that type of data very well.

There is obviously some truth to your statement though because most video and audio compression is lossy and not lossless, and when it comes to video encoding there's much more to worry about than just compression. You're right that we have very good lossy compression methods specific to audio and video data, because they are designed to throw away data imperceptible to the human senses, which is exactly where things like the discrete cosine transform start to come into play. I actually watched a very good video explaining how DCT is used in lossy jpeg compression just a few days ago. But I'm sure you're going to say it's a terrible video because they explain it in simple English without using a single equation and dumb it down with too many charts and animations.

edit on 8/9/2015 by ChaoticOrder because: (no reason given)

posted on Sep, 10 2015 @ 02:34 AM
a reply to: ChaoticOrder

Maybe if I had the necessary education I would be better at it but I think it has more to do with how my brain works, it just doesn't like the ambiguity that comes with complicated equations, it much prefers the clear syntax of (most) programming languages.

yet you claim the education system is wrong, based on - what you just admitted - how your brain works. not everyone needs to think like a mathematician (and honestly, i don't think i do - at least certainly not more than i think like a programmer), that doesn't mean that the education system needs to bend over for people that just don't like to think in certain ways.

And the fact is, in real life, many systems are simply too complicated and messy to be mapped to an equation and so we must absolutely have other ways to visualize how those systems function.

yadda yadda. you're repeating yourself. nothing has to be mapped to a single equation - group of simpler equations will do just fine, and will be much easier to visualize mentally. when you're writing your software, do you tend to put all calculations in a single line of code? didn't think so.

Not everyone has a brain which works like a mathematician and I don't know why you cannot grasp that fact.

i can. i cannot grasp though how a - pretty simple actually - explanation on wikipedia page about FFT cannot be understood by someone claiming to be a decent programmer. it points to a page about DFT for details, and that page contains actually idiot-proof explanation, assuming one understands some basic terms like frequency or sinusoid.

but it just dawned on me - that explanation requires some thinking to be understood. to be precise - it requires you to visualize what is being said, mentally. i guess you have a pretty interesting definition of 'thinking like a mathematician' then, no sarcasm at all. if a definition requires mental visualization of the concepts being explained and the visualization itself requires understanding of those concepts first, you define it as 'thinking like a mathematician' and claim it's not for you. what's the problem? it just requires you to understand the basic concepts first in order to visualize them, and then you can see the bigger picture, because by visualizing all the building blocks, you're effectively visualizing the whole definition.

but somehow you're unable to do that, and i'm not sure if i just can't grasp that, or if i think it's pure lazyness when it comes to thinking. as i see it, you cannot visualize anything more complicated in your mind. 'the math way', as you see it, is 'understand the building blocks, visualize them, then look at the bigger picture'. what you seem to want is visualization of the building blocks in order to understand them, in order to be able to see the bigger picture later. that's the reason why you're dissecting everything to the core, to visualize it at the most basic level - because you're unable to understand it otherwise.

but hey! that DFT wikipedia page even has pictures!

Also, just because something is explained in simple terms doesn't necessarily mean it has been dumbed down.

did i say it was?

but i'm starting to see a pattern here, and i guess i know why. yes, such explanations, with lots of pictures and avoiding math at all costs, are dumbed down.

and the reason you claim they're not, is because you need them to be dumbed down, you're just unable to admit it.

Einstein once said "If you can't explain it simply, you don't understand it well enough".

and i agree 100%. that doesn't mean that every time i want to explain something to someone, i need to treat him like an idiot. because why should i assume he is one?

that's why i've referred to such explanations as 'for kindergarden'-level ones. i have nothing against such explanations, i just expect a good programmer to be able to understand much more than that. can't grasp that, can you?

I don't want to have a "who can sound smarter" competition with you, but this statement is not exactly true.

then don't, because it is.

Arithmetic coding is a universal "plug-and-play" type of procedure which can be applied to any type of data very effectively. If you want to focus on compressing a specific data type then the prediction models need to be optimized for specific data types, but the arithmetic encoder will always be used the same way to encode those predictions. The level of lossless compression will be proportional to how well the prediction models can predict upcoming symbols. Arithmetic coding directly translates prediction power into compression strength, so if your model can predict audio or video data very well it will compress that type of data very well.

it's funny, since you're trying to lecture me on something i've been working with for quite some time.

the truth is, it can compress anything. as i've said earlier, as you're repeating now - any type of data. any crap, any random datastream, anything. but you're missing one point - prediction model is defined by the compression algorithm, not by the arithmetic coding itself. arithmetic coding is just a 'backend' so to speak, and in that sense it is just a tip of the iceberg - because prediction models are usually the most complicated and advanced part of such compression algorithms, and - as you've pointed out - they're what decides how efficient the arithmetic coding is. without those prediction models, arithmetic coding is useless - you can of course define some pretty basic model based on simple data analysis, but it'll loose to any datatype-specific models.

the bottom line is, arithmetic coding isn't a holy grail, it's just a - very simple - method to write data with defined probabilities. modeling those - that's the trick, and it's a trick that has nothing to do with arithmetic coding itself.

arithmetic coding isn't the only option though, and - as a backend - it can be replaced. x264 is an example, you can choose between CABAC and CAVLC. jpeg is another example - it can use arithmetic coding or huffman coding. it's just one of the options, and even when it's the best one - it's just a very small piece of the whole compression. enough with this offtopic though.

But I'm sure you're going to say it's a terrible video because they explain it in simple English without using a single equation and dumb it down with too many charts and animations.

where can i get my 15 minutes back?

if it's very good for you, well - as long as it helps you to learn, why should it be considered terrible?

but - to be back on the main topic of this thread - not everyone needs the math to be dumbed down, and education was never about the lowest common denominator - why should it be now? isn't there enough of dumbing down in schools already?

those few kids that have the potential to be scientists/researchers/whatever in the future, are already getting bored beyond belief, and you want to treat them like they're retarded just because few other kids that can't follow basic math, truly are?

garbage in - garbage out. if we'll treat them all like idiots, they will become ones.
edit on 10-9-2015 by jedi_hamster because: (no reason given)

posted on Sep, 10 2015 @ 08:06 AM
a reply to: jedi_hamster

i cannot grasp though how a - pretty simple actually - explanation on wikipedia page about FFT cannot be understood by someone claiming to be a decent programmer.
I never said I couldn't understand the explanation on the Wikipedia page, I said there are easier places to start which give better visualizations. Like I said, what I often have trouble understanding is the complicated equations. I can work out most equations if I really try but I find it's usually much easier to understand the concept through text and charts first, and I don't know why that approach to learning upsets you so much.

you can of course define some pretty basic model based on simple data analysis, but it'll loose to any datatype-specific models.

Sure a basic prediction model will lose, but an advanced model using techniques such as adaptive runtime adjustments, partial matching, and content mixing, will not lose to any other lossless compression algorithm, when heavily optimized for a specific data type. In other words, if you had the two best programmers in the world trying to compress audio data, and one guy was using prediction models and arithmetic coding, while the other guy was trying to beat his compression strength using any other algorithm, the guy using arithmetic coding will win out in the end because arithmetic coding can get within a few bits of the entropy.

but - to be back on the main topic of this thread - not everyone needs the math to be dumbed down, and education was never about the lowest common denominator - why should it be now? isn't there enough of dumbing down in schools already?

those few kids that have the potential to be scientists/researchers/whatever in the future, are already getting bored beyond belief, and you want to treat them like they're retarded just because few other kids that can't follow basic math, truly are?

garbage in - garbage out. if we'll treat them all like idiots, they will become ones.

For the nth time, no where am I saying we should teach all kids this way, I'm saying we should try harder to teach mathematics in a more intuitive way for those who don't work well with the traditional methods. It's not treating them like retards for christ sakes, it's presenting the information to them in a format which is easier for them to digest. Instead of treating them like they are too dumb to learn we can focus on their strengths and show them they don't need to be a mathematical genius to create very powerful and effective software. Your attitude seems to be they shouldn't be creating software in the first place if they cannot create the most perfect analytical solution possible, which is ridiculous.

I have created ray tracers, many different forms of cryptocurrency software, even a genetic algorithm based on evolving neural networks, and I was able to understand and implement all those things without being great at math. I just started out slowly, watched university lectures and read helpful articles, and before long I could understand many advanced mathematical concepts without really remembering many complicated equations. Evolution is actually a perfect example of something which requires the ability to conceptualize a complicated process but doesn't require much mathematical thinking.

If you can understand the idea of survival of the fittest and how it ensures the best creatures have more babies and propagate their genes, and how offspring inherit genes from both parents, and how random mutations can cause errors and rare advantages, then you can program a basic evolution simulator / genetic algorithm. If you want to make it more advanced then you can do thinks like allow for speciation, extinction events, dominant and recessive genes, even the way DNA from two parents is combined to form an offspring can be an evolving mechanism just like in real life. All these things can be done without being exceptionally good at math. Many kids may not realize they can solve these sorts of problems without being good at math and so they don't even try because they were always told they were too stupid.
edit on 10/9/2015 by ChaoticOrder because: (no reason given)

posted on Sep, 10 2015 @ 09:59 AM
a reply to: ChaoticOrder

For the nth time, no where am I saying we should teach all kids this way, I'm saying we should try harder to teach mathematics in a more intuitive way for those who don't work well with the traditional methods.

for me "my kid isn't retarded, he just doesn't work well with the traditional methods" usually (not always, but usually) is equal to "my kid isn't rude, he's just having ADHD". there's no such thing as ADHD in my opinion, there are just retarded parents, and it's the same exact thing with education - sadly, the retardedness of such parents spreads to their children.

you know where such attitude leads? i just read yesterday a story told by some teacher, a mother came to the teacher shouting because her kid, being in high school(!), didn't solve a single thing on his exam and just drawed(!) few unrelated things. she claimed that he was doing his best(!) and that he was crying whole day because of it, and that it is inhuman(!) to give him a negative note. how stupid and retarded is that?

it all just smells to me of "lets not force our poor kids to think" attitude, so popular these days. the result - neverending flow of extreme stupidity amongst the youth, can be seen every day, and it's something that makes me want to vomit in disgust.

so no, no easier way for those too lazy to study.

Your attitude seems to be they shouldn't be creating software in the first place if they cannot create the most perfect analytical solution possible, which is ridiculous.

it's not ridiculous, advanced software development is - or at least should be - all about finding the most perfect solution, and finding such solution requires much higher level of intelligence than that required to understand more or less basic math without the need to dumb it down. half-assed software is no software at all, it's crap.

not everyone needs to be a mathematician? how about not everyone needs to be a programmer? some certainly shouldn't be.

I have created ray tracers, many different forms of cryptocurrency software, even a genetic algorithm based on evolving neural networks, and I was able to understand and implement all those things without being great at math.

links to project pages/source code repositories?

If you can understand the idea of survival of the fittest

if you could, you wouldn't have started this thread.

Many kids may not realize they can solve these sorts of problems without being good at math and so they don't even try because they were always told they were too stupid.

as for telling kids they are stupid, such thing done by a teacher should immediately end his carrier. it's a more complicated problem though, an answer to which you could possibly find in finnish - if i remember correctly - education system. they focus on teaching, not on testing, and that alone gives much better results.

as for solving problems, a five year old kid will solve a lot of problems if you'll dumb them down/dissect into small enough elements for him to digest. want an example? kodu game lab. still, that won't make anyone a full fledged game developer. it'll just teach them how to analyze a problem and model a solution.

and if they're smart enough to learn about compilers, linkers, header files, SIMD instructions, shaders and all the other things required for real game development - or even just half of them - then they're smart enough to learn how to analyze a problem and model a solution by reading some tutorial and trying some serious coding on their own.

in such case - what's the point?

it may show them that they're able to do things they didn't think they would be able to do, but when it comes to real life scenarios, they may just turn out to be... not smart enough. not everyone has the same IQ, trying to ignore that is just pointless.

posted on Sep, 10 2015 @ 11:12 AM
a reply to: jedi_hamster

for me "my kid isn't retarded, he just doesn't work well with the traditional methods" usually (not always, but usually) is equal to "my kid isn't rude, he's just having ADHD". there's no such thing as ADHD in my opinion, there are just retarded parents, and it's the same exact thing with education - sadly, the retardedness of such parents spreads to their children.

Lol... I don't even know where you're trying to go with this, it seems you are implying my parents are some how retarded because I was never great at math, even though you've never met them. Seriously, your argument is degrading into pure nonsense because you cannot seem to accept the fact that different brains work in different ways and not everyone is good at the same things.

it all just smells to me of "lets not force our poor kids to think" attitude, so popular these days. the result - neverending flow of extreme stupidity amongst the youth, can be seen every day, and it's something that makes me want to vomit in disgust.

I'm basically trying to argue the exact same point Wolfram makes in the video I posted a page or two ago. I'm sure he wouldn't exactly agree with your assessment and your desire to vomit at a more intuitive approach to teaching math via programming. Maybe if people like you weren't so willing to easily overlook the hidden potential of retarded kids with retarded parents than you could see what they are capable of if given the right resources, and then we wouldn't have so many kids who hate the education system, and more kids applying their energy to the things they are good at.

it's not ridiculous, advanced software development is - or at least should be - all about finding the most perfect solution, and finding such solution requires much higher level of intelligence than that required to understand more or less basic math without the need to dumb it down. half-assed software is no software at all, it's crap.

I can absolutely appreciate the point you are trying to make here, when I first started programming I took the self-learning route and I wasn't very good at making things very fast or memory efficient. But now I spend a great deal of time on that aspect of my programs and consider it one of the most things to focus on, especially for code which needs to be deployed in real applications. And I haven't once denied that knowing many mathematical concepts can help improve code efficiency, because it certainly does. However what has really helped me create highly efficient programs more than anything is knowing about a wide range of important algorithms and data structures, such as all the different types of hash trees and hash tables, the union-find algorithms for solving the dynamic connectivity problem, linked lists and other smart uses of pointers, etc. These are all topics where visualization and conceptualization are all more important than knowing complicated mathematical equations. I really don't know how many examples I need to give before you understand the point I'm trying to make.

not everyone has the same IQ, trying to ignore that is just pointless.

Not everyone is good at the same things, you can't just boil down human intelligence to a single "IQ" score, and trying to ignore that is just pointless.
edit on 10/9/2015 by ChaoticOrder because: (no reason given)

posted on Sep, 10 2015 @ 02:17 PM
a reply to: ChaoticOrder

Lol... I don't even know where you're trying to go with this, it seems you are implying my parents are some how retarded because I was never great at math, even though you've never met them.

it wasn't meant to be personal in any way. you've perceived it as such - not my fault. ask yourself why.

Maybe if people like you weren't so willing to easily overlook the hidden potential of retarded kids with retarded parents than you could see what they are capable of if given the right resources, and then we wouldn't have so many kids who hate the education system, and more kids applying their energy to the things they are good at.

many kids hate the education system while being good at drinking, drugs and other 'fun' activities - should we pursue that as well?

These are all topics where visualization and conceptualization are all more important than knowing complicated mathematical equations.

because these are all programming topics that don't have that much to do with the math. what does it have to do with the topic at hand then? are you trying to say "lets turn all those kids that aren't smart enough even for basic math, into programmers"? are you insane?

Not everyone is good at the same things, you can't just boil down human intelligence to a single "IQ" score, and trying to ignore that is just pointless.

tell that to mensa.

posted on Sep, 11 2015 @ 02:16 AM
a reply to: jedi_hamster

it wasn't meant to be personal in any way. you've perceived it as such - not my fault. ask yourself why.

Ask myself why? There you go again implying things you claim not to be implying. My sister is a teacher and is good at math, you can't just assume my parents are retarded because I'm not great at math, every child is different. Also you ignore the fact that many highly intelligent people throughout history have grown up in terrible households with crazy parents, yet that didn't stop them from succeeding in life, often times it just gave them even more motivation because they didn't want to turn out like their parents.

because these are all programming topics that don't have that much to do with the math. what does it have to do with the topic at hand then?

You brought up the topic of code efficiency, I pointed out how it is more important to know many useful algorithms and data structures for creating efficient code than it is to be good at math, so your argument isn't that solid. Fast and efficient code can be created without being great at math. Of course some specific problems do require an advanced understanding of certain mathematical topics, but it's not very common.

are you trying to say "lets turn all those kids that aren't smart enough even for basic math, into programmers"? are you insane?

Of course I'm not saying that, I've made my argument very clear so your failure to understand what I'm saying is not my fault. I never said the problem was basic math, I said the problem was understanding more advanced math. Some people just don't have a natural ability to think in numbers but that doesn't automatically mean they are retarded or stupid. They may have a brain capable of composing amazing music, or they may be great at writing novels, or maybe they have extremely fast reflexes allowing them to be good at games and sports, or maybe they have awesome conceptualization and visualization skills, allowing them to create complex software with many different parts, while not necessarily being great at math. I'm saying lets not overlook the potential some kids have just because they aren't mathematically gifted. I'm saying the education system needs to be more personalized for individual students instead of assuming they can all learn the exact same way and if they don't succeed it's just because they are stupid.
edit on 11/9/2015 by ChaoticOrder because: (no reason given)

posted on Sep, 11 2015 @ 05:59 AM
a reply to: ChaoticOrder

Ask myself why? There you go again implying things you claim not to be implying.

i never said a word about your parents. if there's anything retarded here though, it's your reaction.

You brought up the topic of code efficiency, I pointed out how it is more important to know many useful algorithms and data structures for creating efficient code than it is to be good at math, so your argument isn't that solid.

no, you brought up the topic of teaching kids math via programming. that just won't fly. you can teach kids creating algorithms, solving problems, but when it comes to understanding the math behind a problem, nothing can replace that - kids have to know the math to be programmers.

I never said the problem was basic math, I said the problem was understanding more advanced math.

understanding stuff like FFT is pretty basic math. if someone fails at that, he shouldn't even think about programming.

I'm saying lets not overlook the potential some kids have just because they aren't mathematically gifted. I'm saying the education system needs to be more personalized for individual students instead of assuming they can all learn the exact same way and if they don't succeed it's just because they are stupid.

yeah, right. "this kid isn't mathematically gifted, lets give him some programming lessons instead, so he can fail at more than one thing". how about letting those kids do something entirely else than math and programming? there's a world outside of your computer, if you didn't notice.

we're done.

posted on Sep, 11 2015 @ 06:23 AM
a reply to: jedi_hamster

yeah, right. "this kid isn't mathematically gifted, lets give him some programming lessons instead, so he can fail at more than one thing". how about letting those kids do something entirely else than math and programming?

The kid could do what he/she wants, what ever they are good at. But just because they're aren't good at solving or interpreting equations doesn't mean they shouldn't be allowed to try programming. The approach is more like "this kid isn't mathematically gifted, lets see if they do better by taking a more algorithmic approach to learning the rules of logic and mathematics". Of course if a kid is terrible at math then they are likely to be terrible at programming, obviously that is true in many cases, but that is certainly not always the case, and many kids might find that they understand complicated mathematical topics better by actually writing algorithms which implement those concepts.

posted on Sep, 11 2015 @ 06:50 AM
a reply to: ChaoticOrder

but that is certainly not always the case

i've asked you once already: project websites/source code repositories?

the whole thread is based on your assumption that you're a good programmer, while math isn't your thing. don't get me wrong, i'm not saying you didn't code everything you've said you did - the quality of that code though, that's another thing.

posted on Sep, 11 2015 @ 09:27 AM
a reply to: jedi_hamster

I would prefer to keep my ATS account disconnected from my real identity and the work I do, and much of it is closed source anyway. However back in 2013 I wrote a greasemonkey script specifically for ATS: ATS 5.3 Tweaks. It's less than 200 lines of code and doesn't demonstrate many complicated concepts but that's all I can share. It's a pretty cool script though which makes ATS look a lot better and more functional, I always have it enabled on ATS.
edit on 11/9/2015 by ChaoticOrder because: (no reason given)

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