Intuition rigor post-rigor
Great distinction here.
Has probability distributions. Think through what various distributions mean. "Cops and robbers" scenario seems to model (well) the rates we're seeing.
Interesting way to see an idea evolve. What is the core essence here?
data sets which have misleading conclusions. Until you see the graph you don't realize how different they are.
Good description. Hill climbing.
Get the 2 gradients to be parallel. That is the main insight.
Nice article. has insight about "dividing by e^iwt" to see how much is in the original signal.
How much "7" is in 28? 28/7 = 4 sevens.
How much "2Hz" is in x(t)? x(t) / 2Hz. Neat.
What looks like a multiplication is...
Need to account for measurement error. Take the midpoint (half before, half after) vs the pure staircase pattern.
Great explanation. Notice the part about introducing new variables.
i and j are defined to be alternate paths to -1 [avoiding regular multiplication]. We can visualize that as another dimension if we like.
ij gives yet a 3rd path [another...
I like the description here. Talks about the true essence, not necessarily how it developed.
Core: negative (or complex) probabilities. Whoa! What does that mean?
[Remember, we didn't think negative or complex numbers could exist. Why not...
The most common mistake done by children is to add the numerators and the denominators separately treating them similar to natural numbers. Once the how many versus how much is well explained, they can then easily grasp why it is necessary to...
Simple way to explain algebra. Understand what 'X' stands for.
Negative numbers represent changes, not amounts. So, a -4 in some unit, let' s say slices of bread, doesn't mean that you have -4 slices, but ratter that you have 4 less slices
You can multiply polynomials and take the coefficient to get the number of combinations / re-arrangements.
(1 + x + x^2) represents the 3 options for taking 0, 1 or 2 of something.
(1 + x) represents 2 options for taking 0 or 1 of something [of x]....
Has some interesting arguments, need to investigate further.
Great talk on the difference between simple vs. easy, and how not to "complect" (intertwine) parts of your system.
Really great way to visualize how to handle items like
Draw out the triangle you need [arctan(x) means a triangle with "x" as the height, and we're going to get the angle, and figure out the hypotenuse]. Then you...
The visualizations make the topic easier to understand.
Great vid explaining the essence of a tensor -- matching up components with basis vectors.
Rank 0 (scalar) : component, but no basis vectors Rank 1 (vector) : component & 1 basis vector (1 x 3) Rank 2 (array) : component matched with 2 basis...
One key to calculus is navigating the different "planes of precision" (i.e. n, n^2, etc.) where one does not effect the other.
How big a constant will make kn a polynomial? It never will. n^2 is a different beast.
Calculus is the art of...
Nice video about finding e from the derivative definition.
- Find derivative of 2^x (but can't... you get .69 * 2^x)
- Find derivative of 10^x (but you can't... you get 2.3 * 10^x)
Idea is that some number in-between has 1.0 * something^x [and...
Quick LISP interpreter in ruby. Key insights:
for the eval method...
- if you're an atomic unit (smallest item), just return it's value from the environment
- most methods have their arguments evaluated first, and then you call the method.
Some great insights here (understatement of the millenium):
"If the theory corresponds to the facts, radiation conveys inertia between theemitting and absorbing bodies."
We normally thing "Oh, we transmit energy with radiation"...
Some great insights here:
- Nice explanation of how indexes work: for a given term, store the documents that contain it, along with the position in the doc. To see if a phrase is matched "foo bar" look for both "foo" and...
What I've shared with my friends who are not continuing their studies in math (on facebook): (Editor's note: Kalid, I think this would be a great segway if someone were, for example, to do a presentation for schoolkids of today's...
Putting the tree in this format really makes it click. The site has an example audio file going through the alphabet too. Great example of how to present an idea.
I come across betterexplained while searching about some server gzip compression. and i loved the way topics are explained. After that i come accross with aha.betterexplained . then i thought of creating some thing similar. Now i created some...
This is SUCH an interesting topic, that I decided to include a Google search link as opposed to an article.
Being a lefty and right-brain dominant, it's very interesting to note that school systems of today are most advantageous to the...
Thus, why it is important to "simplify".
Please also watch the video in the included link within the webpage.
It's amazing to fathom the size of the universe from the visual imagery! We are a mere, infinitesimally small speck...
A very different perspective than what one would be commonly "taught" in today's schools. From a wonderful blog.
Cont'd next post:
A take on why it is perhaps better to develop critical thinking skills in the work-force, in today's bustling 21th century world.
A wonderful video produced by Carl Sagan, which explains the 4th dimension.
He simplifies the analogy by demonstrating 2d beings, imagining an "inconceivable" third dimension. As humans, we are simply 3d beings who cannot...
Breaks down the need for a Fourier transform... you have an element (a fly) which can be measured in 2d, 3d, any number of dimensions.
The magnitude of each dimension (in 8-D, let's say) lets you reconstruct the position of the fly.