First, a big thank you. I’m so excited that this site has been able to reach more people than I thought possible — I love hearing about and exchanging insights :).

Still, there’s **only so much juice** you can squeeze from this orange at a time. The previous article took several days to research, draft, diagram and edit (I hope to get faster over time).

And that’s where you fit in: I’ve had some great email conversations about expanding the site, and I’d like to get everyone’s thoughts. Are blogs, guest posts, wikis, or forums the best way to share?

## The Goal: Cram Ideas Into Your Head

Taking a step back, my philosophy is simple: Let’s share the hard-won insights that usually stay locked in our heads.

**Learning is like crossing a minefield**. There’s pitfalls everywhere, but after a struggle you make it through (or get “permanently discouraged”). But once you’ve navigated the path, shouldn’t you share it with those behind you? While it’s still fresh in your mind?

**It frustrates me** that we study the same subjects (algebra, calculus, programming), but struggle alone. We don’t share “a-ha” insights that really make learning stick; most textbooks offer pedantic facts and rote memorization. We have enough of those — what about the insights that help us “really get it”:

- e is a fundamental rate of growth, just like pi a fundamental ratio in every circle
- Version control is like keeping a timeline of your files
- HTTP Caching lets you avoid downloading a file you already have

## Models For Online Communities

Having this blog has been a huge learning experience (more to come), and there’s much to learn about starting a community. Though it’s still a small site, I’m looking to my favorite big sites for patterns of interaction:

**Regular blog (Coding Horror, TechCrunch)**: Single or many authors start the discussion with a detailed article. Readers reply with their own thoughts. There’s consistent style and quality, but topics are limited to what the authors discuss.**Edited submissions (Slashdot):**Site owners collect and filter topic submissions; readers contribute their thoughts. The majority of the value is in the comments, not the stories or writeups themselves.**Community submissions (Digg, Reddit):**The community decides the topics and handles the comments as well. The site owners are seemingly invisible. This works well for late-breaking news, but can lead to “tyranny of the crowd”.**Forums (Steve Pavlina, Webmaster World)**: Users kick off their own topic ideas. Forums have fast, free-flowing discussion but can have a low signal-to-noise ratio.**Wikis (Wikipedia)**: Edited repository of information containing collected thoughts. Unfortunately there’s a high barrier to entry — how often do you contribute something substantial to a wiki? It’s nice to have your own voice shine through in a forum post or comment.

Those are the major collaboration models I’ve found.

## Moving Forward: What would you like to see?

I’m a fan of the “ready-fire-aim” approach, trying something new and tweaking as you go. So here goes:

**Share a comment**on what type of collaboration you enjoy most. I’m looking more into wiki and forum software; perhaps a hybrid will do.**Suggest topics**you’d like to see explained better. More math? More programming topics? More business/writing/communication?**Contact me**(kalid@betterexplained.com) if you’d like to do a guest post. Just think of a topic you like — the content is yours. I can help with formatting/proofreading, even diagrams if you like. I’m thinking of making a guide to writing “how-to” guides as well.

My dream is to contribute to a community that helps us all avoid learning’s stumbling blocks. There’s so many ways to present a topic and yet so many “a ha!” moments are just locked away in our brains.

And what’s the incentive to share your understanding? Well, if you’re like me, you’ll forget your insights and need them explained again. And who better to teach a topic than you, when you remembered it?

Thanks again for all the support and comments — it makes writing a pleasure (editing is still a pain, though! :)). I’m excited for what the next months and years will bring.

More statistics. More math.

Thanks for the comment Julian, I have a few math posts in the works, on the Pythagorean Theorem and Calculus.

I like your project very much. I think it can reach the importance of Wikipedia one day.

Here is what I think are the important things, in no particular order:

- be collaborative and scale to lots of users, both readers and writers

- allow multiple personal viewpoints to a single topic

- be easy and casual: put a low threshold for contribution, as we want to capture a-ha moments shortly after they happen.

- be topic-centric, not time-centric: a-ha moments happen at a different time for different people.

- allow primitive articles that elaborate over time (e.g. return and reedit), maintaining high signal-to-noise ratio in the process.

It seems to me that Wikis fit the bill best. We associate Wikis with Wikipedia, but the social rules that guide a Wiki don’t have to be the same. In particular, starting a topic doesn’t have to feel formal, and you shouldn’t fear that editors will come after you and revert/kill your contribution

What a Wiki doesn’t have is personal point of view. This can be remedied by modifying the software: I think the author should have ownership over the article. Anyone should be able to edit *another version* of it. Then the author can accept a change and incorporate it, or remove it. I don’t think any wiki software at the moment supports this, but we can add it. Or make it a soft rule to be enforced by community.

Alternatively, a less drastic change is to just expand on the current blog format: invite multiple authors and co-edit all articles. The issues that would arise out of the manual synchronization will help figure out how to scale it further

Sometimes I make something similar in Italian, on my blog (I call it “math light”). The main difference is probably that I talk about things I learned a lot of time ago, and which now I try to see in a different way.

In my opinion, here the wiki approach does not work well, since to

explainbetter (opposing tostatebetter) a work of synthesis must be made, and it is much simpler to do it alone. Of course it is great to have a “discussion page” (one of the strongest ideas in Wikipedia, IMNHO) so that people are incoraged to add thoughts and requests for clarification, but this may also be made in the comments of a blog.Having multiple authors may however be useful: just leave each of them alone in writing her or his entries

@Nikola: Thanks for the detailed comment! I agree that starting small and building up may be the way to go. If possible, I’d like to have any constraints “enforced” by guidelines rather than software. One thing I’ve learned in development, at least, is that what you start with is often different from what you end with

@mau: Thanks for the feedback. I agree that the focus needs to be on better “explanations” vs simply restating existing facts.

Although blog comments exist, it’s hard to put much thought into them. One compromise may be to have a wiki page for every article for people to contribute their own insights (if it won’t fit in the blog comment), like a discussion page.

And yes, if there’s multiple authors I don’t plan on getting in their way :). Mostly proofing help and the like.

hey kalid ,one more model for your online communities like yahoo answers, people ask specific questions, some one answers it…

Good work

-biren

Hi Biren, thanks for the comment — I think a Q & A section may be useful as well, esp. if intuitive insights can emerge

You are doing a nice job. You could work for howstuffworks.com I bet

If you don’t want to do that, you could make this a group blog, get some help to increase the number of articles.

I like the idea of a ‘better explained’ wiki or something, too.

You might build off some outside resources, too, for example ‘computer science unplugged’ or the simulations at the colorado phet project.

I’ve always found encryption difficult to grasp.

@Doug: Thanks for the encouragement :). Yeah, not sure if howstuffworks.com is right for me (I’ve enjoyed the site a lot — I’m more of a “why” stuff works). I may set up guest posting & wiki as an experiment and see how it evolves. Thanks for the pointer to “computer science unplugged”, it looks quite interesting.

@Kevin: Thanks for the suggestion, I think that may be a good topic.

‘A visual guide to IRC’ will be really helpful to the new comers. Nothing like that exists so far and most other documents require relatively prolonged reading of nothing but text.

Hi Sridhar, thanks for the suggestion. Yeah, there seem to be many tech topics explained in an (unfortunately) very techy way :).

I’ll second Kevin’s suggestion of writing about encryption. Basic Unix scripting/regexp stuff would be interesting, too (though there’s probably a million guides for this already). Also, math stuff (I’m sorry not to be more specific).

Keep up the good work!

Hi Koloman, thanks for the encouragement! I’m itching to write more math stuff as I’ve been programming focused lately, but I think unix, regexes and encryption are all great topics to cover.

Hi kalid,

awesome work .. i was wondering if i can translate some of your work into bahasa (indonesia).

let me know ..

Yes, that’d be great! But please include a link to the original article. Thanks,

-Kalid

wonderful work …

Topic wanted …

1> Practical applications of game theory like negotiation

2> understanding infinity and different aspects of it like countable infinities …

3> layman explanations of computationally intractable problems and their groups like NP-COMPLETE , hard , et al and why they are important …

much much more which I can’t think of now …

@ Nikola – totally agree, this is a great blog/concept in the making … what wikipedia or other wikis don’t have are essentially those personal understandings or aha moments which ppl would like to share …

Sagar Mehta

Let me know if you need any help with writing Computer Science/ Mathematics articles …

Hi Sagar, thanks for the topic suggestions and offer to help! I think those are great topics, I have an older look at P vs NP here:

http://www.cs.princeton.edu/~kazad/resources/cs/npcomplete.htm

(It’s from college — I need revamp the article).

I definitely appreciate the offer to help, if you have an idea you’d like to write about, just shoot me an email (kalid@instacalc.com).

Also, I’d really like to find a way to encourage low-friction collaboration as Nikola mentioned, while allowing each author to retain their point of view. Part of the value of learning is that we each have unique insights that can help each other. Still thinking about this one, but may just play it by ear to start (and have guest posts/a basic wiki).

I would like to see the complex number system better explained.

Thanks Tim, complex numbers are definitely on the list.

A post that explained C unions and structs and all the weird low level things you can do to them. (Like packing and things like this guy:

struct STRUCT {

unsigned int a:12;

unsigned int b:10;

unsigned int c:10;

};

struct STRUCT myStruct= {0xFED, 0×345, 0×3AB};)

Linking that with endianess would be great!

Thanks, good suggestion. It’s been a while since I’ve monkeyed around in the bowels of C but am looking forward to getting my hands dirty again

Love your posts, they’ve helped me. You are doing a great thing!! I hope they keep coming.

Thanks Brent, I’ll keep trying to crank ‘em out. For some reason they take me a long time to write but I’m happy you’ve found the result useful

I’d like to see an asymmetric cryptography introduction, with practical examples with gpg.

I loved your version control article!

@dukebody: Thanks for the suggestion, I think a crypto article would be fun to do.

Might the ultimate math-related challenge be to give a simple and intuitive explanation of E8 and why it is considered the “most beautiful mathematical object ever”?

Recently, E8 was the foundation of a radical new theory concerning the ultimate scientific quest of uniting gravity and quantum physics into single theory devoid of current contradictions and discontinuities. That new theory is described in a paper called “An Extremely Simple Theory of Everything” … and I read (looked at) the pdf file and it is not so simple to digest.

Nice idea you have with this web site!

Hi William, thanks for the suggestion! Yes, I saw the paper too and was also confused by it. It’s ironic that beautiful ideas need a lot of background info.

I’d love to provide an intuitive explanation of E8 (I’m sure it can be), but I’ll have to teach myself a lot of things on the way.

Thanks for the suggestion.

More math in just very primitive way..! math which is “not tied up with formula”…!! no more remembering those crap formula, (like your many articles)

love to read more, love to revise all basic math in new way..!

Very good work..!!

Could you better explain complex & imaginary numbers?

Cheers

@Shreya: Thanks for the comment!

@Marc: Thanks for the suggestion — they’re definitely on the list. I plan on covering them fairly soon :).

I would like to see mind mapping better explained.

definitely more basic math! the same basic pragmatic hands-on style.

More combinatorics, stats, linear algebra, and calculus.

Something I am having a hard time getting right now are Stirling numbers. They’re explained simply, but there are many theorems and cool stuff about them that I don’t completely get.

Maybe your great writing and explanation skills can make them clearer and let me know their significance =)

Also it would be cool if you do know of some places to dig deeper, to list a resources section afterwards that you liked.

Of course, that’s only if you’re not planning on writing more about the topic ..

@TYC: Thanks for the suggestion, mind mapping may be an interesting way to approach writing articles too.

@John: Thanks, there’s lots of math on the agenda

@Timothy: Appreciate the suggestions! I was planning on covering stats, linear algebra and calculus. I hadn’t heard of Stirling numbers but they sound interesting. Yes, listing resources is a good idea, I’m often a beginner trying to make sense of the topics I dive into. Helping people dive deeper is always useful.

How about explaining regression analysis, its one topic i’m having a hard time understanding and ya if u could also slip in binomial and Poisson distribution, nothing like it!

Thanks Naushad, I think a lot of people are interested in stats. I don’t know that much about it (had a class a long time ago) but am interested to pick it up again :).

Kalid, how about an introduction to Artificial Neural Networks?

The source of info that I’ve found most helpful comes from IBM at http://www.ibm.com/developerworks/library/l-neural/. This was the last site that had helped me “close the lid”.

Hi Dave, thanks for the suggestion! I think it would be a good topic.

Integration By Parts….I’d love to see that one intuitively explained.

Kalid, You have to have articles on Limits, Derivatives and Integration. That was a bummer for me when I first started learning it. I am thinking it could help countless others to understand the basic concepts of calculus.

Hi Ashok, thanks for the suggestion. Yes, I’m planning on doing a series on calculus topics :).

How about a posting about the physics of flying? Great site!

Thanks John! I think that’d be an interesting topic. Strangely enough, there seem to be conflicting theories about how airplanes “really” fly :).

Here is another suggestion Kalid – Data Structures should be a very useful topic to write on. What would help is an article devoid of programming constructs but more about visualizing it in ones head. e.g: Stack and Queue are easily visualized, the challenge remains in thinking about how a Data Dictionary or Set would look like!

Hi Ashok, I think that’s a great idea as well. It’s nice to visualize/see data structures to really understand why they are more appropriate for certain situations.

Hi Kalid – I’d be interested in having Big O notation better explained.

I get the gist of it, but I’d like to better understand how to identify the specific cases and their implications on the time.

Thanks Mark, I think that would be a good topic. I’m adding it to the list :).

I think an article on the basics of differential equations would be a great topic.

Thanks Andrew, I think it’d be a cool topic. I don’t have a formal education in Diff Eqs (one of my greatest math regrets) but am looking forward to learning them.

How something is scaled is just as important as what is scaled.

That’s sort of parallel to, “Knowing what you know, is as important as knowing what you don’t.”

An interesting and insightful topic may be “division by zero”

Hi Kalid,

This is great effort.

I would love to see post on :

Programming: Struts, Spring, Hibernate

Project Management: Various project plans, estimation [particularly using Use Case Points], Earned Value Measurement, Risk Management, MS Project

Looking forward,

Sachin

@Spencer: Thanks for the suggestion, I think that would be interesting. Division by zero also helps with calculus (limits).

@Sashin: Appreciate the suggestions. I don’t really know much about enterprise Java, but some of the project management topics could be interesting.

Hi,

Can you give us some light on financial modelling? Like — Binomial, Monte-carlo Option pricing which are based on rigorous math — based on probablity and stochastic processes etc..

I want you to write about Quantum mechanics.

What is going on there?

thanks for your articles, I found them very helpful,a different view (I saw that I only memorized)

Sincereley

Hi Zulfikar, thanks for the comment! Quantum Mechanics is way out of my league right now, but I think it’d be a great topic for the future (or even some of the basic ideas like uncertainty). Glad you’re enjoyed the articles :).

How about an explanation on sin, cos, tan, etc. and logarithms. I really liked your natural log article, and complex number intro. Something along those lines would be awesome.

Hi Kalid, first of all thank you for share your clever ideas with us.

I’m interested in an Kalid-style explanation about public key cryptography (public and privates keys, signatures, etc) and how is applied in applications we use (web browsers, emails)

Thanks!

Hi Esteban, thanks for the comment. I think a series on cryptography would be fun, given that we use it all the time when browsing the web or buying products online. Appreciate the suggestion!

KALID

THANK YOU FOR DOING A FANTASTIC JOB, FILLING A MUCH NEEDED VOID, GENERATING “AH-HA” MOMENTS EXPONENTIALLY, AND MAINTAINING YOUR MODESTY.

PLEASE CONSIDER A “BETTER EXPLAINED” TREATMENT OF “HOW DO WE KNOW THE EARTH IS ROUND?”

IT OCCURRED TO ME THAT YOUR FIRST PRINCIPLES APPROACH (NO FANCY FORMULAS, CIRCULAR DEFINITIONS,OR MODERN MEASURING TOOLS) WOULD LEND ITSELF WELL TO THIS TOPIC. BE CAREFUL, HOWEVER, YOU MAY END UP ON “THE VIEW.”

THANKS AGAIN AND KEEP UP THE GOOD WORK.

Thanks Jamie — actually, the “simplest” explanation of why the Earth is round is an interesting question! But yeah, I don’t think I have the stomach for talk shows :).

I love this site and its potential. Like John Smith’s request (#34), I would like to see more basic math so pragmatically explained. Thanks!!

Thanks Liz! I’ll take that as a suggestion :).

I am completely and utterly in LOVE with the math explanation here

When dealing with complex numbers, I find that the feature I use most is manipulation of Eulers formula [exp(i*theta)=cos(theta)+i*sin(theta)], swapping back and forth between exponents and trigonometry depending on whichever form that is most useful for manipulation there and then. If you find the time, I am sure that your explanation of this – and its uses – will be of great benefit.

I really like your site. I think the way you explain something is what I’m most interested in. I would try to find people who have the same talent and let them guest post. Building a community around submitted links or wiki entries would be a nice addition, but I think what separates you from the crowd are you articles.

What is a determinant?

“In algebra, a determinant is a function depending on n that associates a scalar, det(A), to an n×n square matrix A”

(http://en.wikipedia.org/wiki/Determinant)

A post about international exchange rates would be

appreciated, delving into specifics like what it

means for one country to peg its currency to

anothers’, how a country can devalue its currency,

how central banks maintain currency pegs by

purchasing foreign currencies, etc. This topic

is in the forefront of news today but it is still

mystifying to many people I suspect.

Coding in C++, Perl, VBA, or Python for beginners! (Absolute beginners to coding)

Great Site by the way..

Hi Kalid,

This site is simply wonderful.I begun long ago to review things “unresolved” in school,using internet.These things were affecting my self-confidence,and I was surprised,how easy some concepts can be grasped when “better-explained”.

I liked especially the calculus and math generally.But I also review some of my physics knowledge basis so I would like to see if possible,some new basic approach on “electricity”.Thank you anyway for already having done a fantastic work!

@IOAN: Thanks for the note! I completely know what you mean, sometimes when we don’t get something it makes us question ourselves — but really, it’s mostly a matter of the right viewpoint which we can develop.

I appreciate the suggestion about physics/electricity, it’s something I’d like to understand better myself! Thanks again for the note.

Trigonometry please, I know that there is a simple understanding but still couldn’t get it :).

@Kadir: Thanks for the suggestion! Trig is something I definitely want to cover more myself :).

phi, or the golden ratio. Even though I’m aware of what it is, and how to derive it, I would like to know how it can be used mathematically to solve problems. For instance, I know that it can be used to calculate the nth fibonacci number, I know the equation to solve that specific problem, I just don’t know why it works the way it works. What I’m really looking for is to learn how and when to use it to solve new problems.

@SnackDragon: Thanks for the suggestion! I don’t understand phi the way I’d like to myself :).

capacitance, inductance and their relationship with complex numbers …. cant figure that out!

@narayan: Thanks for the suggestion!

fibonacci sequence

@Olga: Thanks for the suggestion!

How about writing something on “Maths for Game Programmers”.

Math is always a mystery and you are doing a wonderful job of demystifying it.

Keep continuing!!!

How about a series on “Math for Game Programmers”. Maths was always a mystery and you are doing a great job of demystifying it.

Similarly

- Math for Game Development

- Math for Finance Professionals

- Daily Math

- Math for Business

In fact you can come up with ebook on each of the above topics and that will be a hot sell as well.

@Rajesh: Awesome, thanks for the ideas! I don’t know much about game development but imagine it involves a lot of geometry/trigonometry :).

I really enjoyed your articles on complex numbers and how they can be used to express rotation and scaling. I was wondering if you could do some bits on 2d (or even 3d) scaling and rotation using matrices? (It would even tie in to Rajesh’s request for Math for Game Development.)

Great stuff. It does show your mental toughness.

One request dear Khalid…

Can you do a write up on mathematical transforms like Fourier and Laplace

Thank you.

@Vijaya: Thanks for the note! I would like to write about those transformations as I learn more about them (they are on the list), I have a very cursory understanding so far. But thanks for the idea!

IMO…

Difference operators are a cool topic, relate closely to “standard” calculus, and admit to very striking visualization. I recommend you cover them sometime.

Matrices has always been a vague chapter, i mean finding inverse, determinant is an algorithm that you need to mug up and dont get me started on 3X3 matrix :(.

@Joy: Thanks, Matrices are something I’d definitely like to cover.

I have heard it said that a person can learn calculus without learning algebra. Is there a “Better Explained” article in this idea I wonder ?

@Matt: Hrm, I’m not sure if that’s true — you really need the basics of algebra in order to manipulate the equations in calculus. You might be able to get some of the basic ideas across but to solve problems, I think algebra would be needed. Try http://betterexplained.com/articles/a-gentle-introduction-to-learning-calculus/ to see what I mean.

More articles on finance and investments

@caesar: Thanks for the suggestion!

Combinatory logic and specifically, the Y combinator.

I pity you man.

It seems everybody is off-loading all the tough topics on you.

So, I don’t want to burden you further, though I have many topics which need better explanation.

Wishing you all the energy, stamina, patience and time!

@Shawn: Thanks for the suggestion! That’s something I need to understand (funny enough, I was in that program :))

@Nandeesh: It’s no burden, I get excited by the prospect of learning new things :). Appreciate the warm wishes!

Could you please write some articles on complex/Fourier analysis? Thanks

Pozycjonowanie stron to nic innego jak zadowalające zabiegi, mające na zamiarze doprowadzić do tego, że nasza strona internetowa, pod konkretnym hasłem, słowem głównym wydobędzie się na naczelnym obszarze w pozycjonowanie. Wszystko prezentuje się bardzo ładnie i przyjemnie, jednak powinniśmy dowiedzieć się dlaczego pozycjonowanie stronicy jest tak często użytkowane przez spółki do promocji własnych witryn www.

Could you write some articles on trigonometry? I know a lot of people who just don’t get it (I’m one of them)! Thanks