January 26

My Day

Dear Diary! As I told you yesterday, I had blocked YouTube for today. This means, after I got up (with a delay – not at 9am) I immediately (+-) started to study. And I have to say, I did that really good. I Studied until about half past four, with only a few breaks.

Break 1: Lunch – understandable
Break 2: I had to cut my brothers hair again, since yesterday I apparently did a poor job haha.
Break 3: Yesterday, I told you, that my Achilles tendon is acting up. Well; today it was even worse. That meant, I couldn’t really walk. More precisely: I cant stretch my tendon, so I can walk, but only with an extended leg…
But what has that to do with my break? I initially wanted to go to the gym, but since I couldn’t walk, I didn’t go. Instead I had a small home work-out.
My mother and I did a short (about 45 min) shoulder workout together with elastic bands. I had to convince her, to participate, but after we were done, she meant, that it does feel good, working out.
So break 3 was a short home work out.

I was basically done studying for today at about 5pm. I even went over all my Algebra exercises. This is more than I had planned initially. So then, I didn’t want to start with my ODE’s. Because of that, I thought, it’s aight, if I use YouTube again. So there you have it. I did use YouTube today, but only I had a great studying session.

New Years resolution failed already?!

As you might know, one of my new years resolution was, to go to the gym at least twice a week. But, I did not do that this week. I went once on Tuesday, and had my short-ish home workout. Does that mean, I already failed my resolutions? You decide. I think, kinda yes. But my counter argument would be:
If I were sick and I wouldn’t go to the gym, this wouldn’t really constitute a fail of my resolutions. And now, since I have my Achilles-tendon injured (or at least in pain) I believe this is a good enough reason, to not go to the gym.
Even if it only counts as half a reason: I did half a work-out at home, so that’s fine either way.

With that being said: No – I don’t believe, that I failed my new year’s resolution.

Social Status Theories

As I told you on January 23, I’ve been thinking a little bit about the modeling of a social status with respect to humans and to the model presented there. I played around with that for a little bit, and I have some short results to present, and then a few more theories which I have to test.

Test 1 – Helping Others

My tests resulted with: If you only help others, but they don’t change:

1. You get a lower ranking
2. The person you help, gets a higher ranking
3. other people’s ranking can get up, or down

You can interpret yourself what that means…

Test 2 – Best Friend / Partner

If you get a “best friend” or a “partner”, and nothing else changes. (So you “help” this person more, and this person “helps” you more)

1. Both of your rankings improve
2. All the other rankings decrease

This means, a best friend, or partner helps you improve both of your rankings.

Question 1 – How to maximize overall rankings?

Assume every person has a maximal amount, with which they can help. (You may think of it as “potential” or “everybody has to sleep for some time – which is time, they don’t spend helping others”.) Now the question emerges: how should these persons help each other, so that the growth of social-status grows the fastest?

Or in a more math way: Given some potentials \(p_i\), we then have the “transformation-matrix” \(A\) with all entries \((A)_{ij}\geq0\) and the sum of column \(i\) is equal to \(p_i\). $$p_i=\sum_{j=1}^n(A)_{ji}$$

Then the question is: how to “build”/ what is the \(A\) with the greatest spectral radius.

Question 2 – Only symmetrical relations \(\rightarrow\) What changes?

Assume, if A is a friend of B, then also is B a friend of A. Does this change anything? If so, what? probably, it will improve your own ranking then, if you help others. This was seen in Test 1. But the question still remains, if this holds, if all relations are symmetrical. (Since in my “tests” they weren’t.)

And if your helping improves your ranking. What is the best way, to improve your own ranking? How can you maximize your ranking (maybe given a potential as in question 1).

Conclusion

Take all these experiments/tests with a grain of salt – or better a full spoon of salt. This all hardly means anything.

I think, I’ll do some more tests, after my exams. Until then, keep in mind, helping others has never hurt anyone. So do that! (very mathematical conclusion – mhm)

Good Bye’s

That’s all for today. I’ll see you tomorrow! Bye-Bye!