Posture tips

Working on some simple and practical posture tips:

1. Simply spreading your arms (as shown in the lotus zen pose) helps open your shoulders, reset your shoulder blades, and stack your head and spine. You can then bring your arms back to normal, but keep your shoulders open. You can do this any time during the day.

2. Bring your portable device in front of your eyes (keeping shoulder and head posture described above), rather than your head down to your screen and slouching in.

I remember first seeing this in a TED talk or some other video, but I can’t find the link anymore. Here are some more posture tips. Let me know how that works for you.

Cinderella review

I watched Kenneth Branagh’s Cinderella (Disney, 2015) last weekend and am curious to get the perspective of some parents.
I would definitely advise adult supervision and discussion for kids to watch this movie (as with previous versions of this tale and probably most other supposed kids movies).

Without going into the savior prince cliché, three observations of the kinds of poor choices and values uncritically displayed:

1. The dad seems sensitive and reasonably smart, yet he brings people of awful quality (stepmother and two stepsisters) into his and his daughter’s life. That’s bad judgement. Strangely, Ella doesn’t seem to hold him responsible in any way.

2. Ella decides to stay in an abusive situation, rather than find another job and home. That’s not courage. She obviously has many skills and is hard-working. Yet when a former maid offers to help find a better place, Ella argues that she loves the house and her parents did too. Clearly, her parents did not communicate proper priorities (daughter’s well-being first, house distant second).

3. Ella ends up forgiving the stepmother. That is not kindness, but perpetuating the abuse. Excusing and showing empathy towards a sociopath means the sociopath wins and has power of you. The stepmother not only has caused a lot of harm, there was no indication that she recognized it or felt sorry. So, Ella’s forgiveness of persistent evil raises the question of whether she will remain alert and able to protect herself in the future.

It’s important to recognize when the two virtues promoted in the story (courage and kindness) are being manipulated and distorted to allow for abuse to continue. Such confusion is what allows abuse in the first place.

Enumerating Diophantine equations

I mentioned this problem in passing in my last post, but it’s really not trivial. Here’s the method exposed in Matiyasevich’s Hilbert’s Tenth Problem. The method originates from Julia Robinson, in Diophantine Decision Problems (in Studies in Number Theory).

Here are the rules she offers to generate all integer polynomials P_m and all positive integer polynomials T_n:

• T_4n = n
• T_4n+1 = x_n
• T_4n+2 = T_{CantorLeft(n)} + T_{CantorRight(n)}
• T_4n+3 = T_{CantorLeft(n)} * T_{CantorRight(n)}
• P_m = T_{CantorLeft(m)} - T_{CantorRight(m)}

As you can see, T_n will includes all possible constants and unknowns, as well as any sums or products of other T_n elements. Then P_m will be the difference of any two T_n elements.

An example: P_{7,297,614,550} = 2.x₀² - (1 + x₁²)

One thing to notice is that T_n will generate duplicates. For instance, T_4n+2 = T_4m+2 when CantorLeft(n) = CantorRight(m) and CantorRight(n) = CantorLeft(m). I don’t know if there is a numbering that avoids such duplication.