I have Lenovo Thinkpad X1 Carbon. At first, I thought I am buying an almost IBM quality laptop. Craftmanship is not good, it looks cheap, screen is flickering and there is a constant 20 kHz hiss from cpu fan. Battery does not long last as it was promised (they had ads: battery life longer than macbook air's). Touchpad is not very responsive. And finally: another new type of usb-size adapter port, I have not seen anywhere else.
Well, the first figure: frequency is NOT the period, and amplitude is not that. I guess there are lots of errors in the text if the first figure is completely wrong.
Universal constants [1] have about 6-9 significant digits today. I wouldn't use more than 10 digits of pi, if I am working on some physical calculations.
Agreed and, unfortunately I don't trust Google/Gmail anymore after their numerous service closing-downs. As long as the service does not seem to bring more profit through ads, they will close it, for sure.
I use GMail to fetch and filter my main account mails, I don't spread @gmail.com address much, keeping in mind that we will left with closed or transferred service. So I have a plan-B.
At least this is how I see as a long term user: they don't do evil, but removing good is also evilish.
People think it is transistor size that is 14 nm, which is not. It is metal pitch on high density memory chips that have repetitive patterns all over the chip.
I have seen these people who have "curse of the gifted." One of them is me, another is my step-son.
Problem is people's approach to your gifts, first; your parents. If they say continuously that you are gifted, very smart, very beautiful, adorable etc and you can do anything you want because you are so smart, you are most likely doomed later in life.
Now, my step-son about to finish high school. His mother, always complimented him starting from kindergarten. He was smart all along, did all problems from his mind easily without much effort. His parents and teachers complimented him everyday. He was happy, and proud of himself to be smart, his parents were also proud.
High school required more disciplined work. He couldn't make it, too many distractions around. He was thought to be a very special person when he grow up, but now, he is below average, and sadly, he accepts that even though he had the potential. I see how he will fail more in college, and can't help.
My only difference from him was that he is failing in high school, I failed in university.
I have a small daughter, 4 years old, and I am afraid as hell not to spoil her. She looks very smart and gifted. I always say she is not gifted, she is just normal. I don't want her to be very special person when she grow up, I want her to be happy and healty, that's all. Only thing I am trying to do is not to say her that "she is gifted, she is very smart".
I don't know how to solve his brother's problem. Looks it is very late.
I don't know if this kind of visualizing Fourier transform is helpful to anyone doing/will do work using this idea, but it is not useful to me, and I don't think it is useful to anyone, apart from being somewhat interesting representation, in a way an illusion.
Here is how I see this:
-Sinus (and cosinus etc) is defined using a right triangle, unit length hypotenuse simplifies things, so they are shown on a right triangle inside a unit circle.
-Time dependent sinus function, sin(wt), can be represented using a uniform circular motion and y coordinate of position.
-Fourier says that you can represent (may be almost all) functions using sinus functions with proper frequencies and amplitudes. There is a way to find those coefficients using some mathematics: infinite or finite sums or integrals depending on application.
-Oh well, I have a wonderful idea, great analogy, listen: why not show Fourier transform/series using a circle on circle on circles, uniformly moving (constant speeds) particles and projections of their position to sideways as a function of time.
I don't think understanding its mathematical form is more complicated than understanding what a function is. It is already very simple, too much enforced simplification makes it complicated.