Alex Raichev

Seven Brothers

Following up on Contours, A Mathematical Coloring Book, here's another contour plot for coloring:

The PDF version is here. The copyright is Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International.

Like the other contour plots in the book, this plot was created using Sage. Here's the Sage notebook code, in case you want to play with the plot.

a = exp(2*pi/3*I)
f(z) = sin(z^7 + a)
f = fast_callable(f, domain=CDF, vars='z')

def ff(x, y):
    return f(CDF(x, y)).real(), f(CDF(x, y)).imag()

def iterate(func, n):
    def g(x, y):
        for i in range(n):
            x, y = func(x, y)
        return abs(CDF(x,y))
    return g

G = Graphics()
for j in range(1, 6):
    G += contour_plot(iterate(ff, j), (-1.8, 1.8), (-1.8, 1.8),
      contours=[0.2, 0.5, 1], fill=False), axes=False, aspect_ratio=1)
Author: Alex Raichev
Date: 2015-01-03
Tags: math, art
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How to Shrink the Economy without Crashing It?

Here is Richard Heinberg's 10-point plan.

Author: Alex Raichev
Date: 2014-12-30
Tags: resilience
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Future Shock


Martenson has also elaborated this video into about 25 10-minute videos that you can watch on his Vimeo chanel.

Video sourced from Vimeo here.

Author: Alex Raichev
Date: 2014-12-30
Tags: video, collapse
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A good introduction to the practice of tonglen, excerpted from by Pema Chödrön 's book When Things Fall Apart: Heart Advice for Difficult Times.

Each of us has a "soft spot": the place in our experience where we feel vulnerable and tender. This soft spot is inherent in appreciation and love, and it is equally inherent in pain.

Often, when we feel that soft spot, it's quickly followed by a feeling of fear and an involuntary, habitual tendency to close down. This is the tendency of all living things: to avoid pain and cling to pleasure. In practice, however, covering up the soft spot means shutting out life experience. Then we tend to narrow down into a solid feeling of self against other.

One very powerful and effective way to work with the tendency to push away pain and hold onto pleasure is the practice of tonglen. Tonglen is a Tibetan word that literally means "sending and taking". The practice originated in India and came to Tibet in the eleventh century. In tonglen practice, when we see or feel suffering, we breathe in with the notion of completely feeling it, accepting it, and owning it. Then we breathe out, radiating compassion, lovingkindness, freshness; anything that encourages relaxation and openness.

In this practice, it's not uncommon to find yourself blocked, because you come face to face with your own fear, resistance, or whatever your personal stuckness happens to be at that moment. At that point, you can change the focus and do tonglen for yourself , and for millions of others just like you, at that very moment, who are feeling exactly the same misery.

I particularly like to encourage tonglen, on the spot. For example, you're walking down the street and you see the pain of another human being. On-the-spot tonglen means that you just don't rush by; you actually breathe in with the wish that this person can be free of suffering, and send them out some kind of good heart or well-being. If seeing that other person's pain brings up fear or anger or confusion, which often happens, just start doing tonglen for yourself and all the other people who are stuck in the very same way.

When you do tonglen on the spot, you simply breathe in and breathe out, taking in pain and sending out spaciousness and relief. When you do tonglen as a formal practice, it has four stages:

  1. First, rest your mind briefly in a state of openness or stillness.
  2. Second, work with texture. Breathe in a feeling of hot, dark, and heavy, and breathe out a feeling of cool, bright, and light. Breathe in and radiate completely, through all the pores of your body, until it feels synchronized with your in- and out-breath.
  3. Third, work with any painful personal situation that is real to you. Traditionally, you begin by doing tonglen for someone you care about. However, if you're stuck, do the practice for your pain and simultaneously for all those just like you who feel that kind of suffering.
  4. Finally, make the taking in and the sending out larger. Whether you're doing tonglen for someone you love or for someone you see on television, do it for all the others in the same boat. You could even do tonglen for people you consider your enemies ---those who have hurt you or others. Do tonglen for them, thinking of them as having the same confusion and stuckness as your find or yourself.

This is to say that tonglen can extend indefinitely. As you do the practice, gradually, over time, your compassion naturally expands and so does your realization that things are not as solid as you thought. As you do this practice, at your own pace, you'll be surprised to find yourself more and more able to be there for others, even in what seemed like impossible situations.

Author: Alex Raichev
Date: 2014-12-30
Tags: nonduality
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Bicycle Repair Kit

Author: Alex Raichev
Date: 2014-12-07
Tags: bicycle, tech
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Why no comments? I used to do public comments but found that moderating and maintaining them took too much time in front of the computer, time better spent playing outdoors. So these days I only do private comments, that is, you can email me comments regarding a post by clicking the 'Comment' link at the bottom of the post.