Math Proofs : Need Help

Every day I walk the dog a couple of miles to get her and me some fresh air and exercise.. it is usually the same route, meeting the same people, etc etc.. so I come up with things to keep my head busy. Sometimes its remembering as many elements and their isotopes, other times working out factors of numbers. Last week I started on the series (n^2+1) to see what their factors were. The first thing I realized was that while half of the numbers would be divisible by 2, around 40% would be divisible by 5 (because any number ending in 2,3,7,8 would square to a number that adding 1 would make it divisible by 5 (eg 13^2+1 = 169+1 = 170). Then after a lot of ticking off things I also realized that none of the numbers I could do (which isn't a lot .. I do this because math and me have a long bad history) were not divisible by 3.

Coming home I whipped up a python scriplet that basically did that for the first million digits and found that none of them were divisible by 3 (they weren't divisible by 7 either but I figured I would stick with 3 first). Now we know that n^2 is sometimes divisible by 3 (9, 36, 81 all being examples) and we know that a series that is always divisible by 3 is 3m (two series never divisible by three are 3m+1 and 3m+2). So from this I infer that the series n^2+1 only falls inside of the series 3m+1 and 3m+2 and never on 3m... and n^2 falls on 3m or 3m+1 (since if it fell on 3m+2 then n^2+1 would push those values to 3m). Ok but why?

Looking over the series I came up with the following:

n            1   2   3   4   5   6   7   8   9  10
n^2          1   4   9  16  25  36  49  64  81 100
m{3m+1/3m}   0   1   3   5   8  12  16  21  27  33
diff between m  1   2   2   3   4   4   5   6   6

Ok now I just have more silly numbers and probably a wild goose chase but it is interesting that the series of 3m/3m+1 growth grows in a regular pattern. Anyway, just an odd thing non-fedora related (i hope).

Ada Lovelace Day

March 24th 2010 is Ada Lovelace Day. Augusta Ada Byron-King, Countess of Lovelace is one of my heroines (next to Jane Austen). She was one of the first programmers and was able to see potential in one of the geekiest people of the 18th century, Charles Babbage. She was also a strong willed lady who pushed way beyond the limited boundaries women had then. Sadly cancer took her life at the age of 36 or we would have probably had a finished Analytical machine (pooie to anyone who thinks it wasn't physically possible.. nothing can stop Steam).

For some historical truth (and a golly fun steam punk fantasy) please read about Charles Babbage and Ada Byron at 2D goggles. Here is a 'history' of Countess Lovelace

Ada was also a pretty cool language that I learned after Pascal (the progress being Heathkit assembly, Apple Basic, Apple Assembly, Apple Pascal, then Ada).

[edited: 2010-03-24 15:14:22 UTC] corrected spelling of names. sorry about that

Mailing Lists, Parties and Fear

This blog post is more about my reactions to some posts, and maybe explain why some other people may not feel too happy about the analogy. In the end however, I do think making mailing lists into a more social medium is desired for certain areas.. especially ones designed for collaboration.

When I read through Mairin's post and then Luis's post via LWN, my first gut reaction was the same feeling I had at my High School Prom. The part where a girl asked me to dance, and the next thing I knew it was 10 minutes later and I was driving up the Interstate at 90 mph.

Parties are things I dread. I am socially awkward if not blind.. and never know if I am talking too long or what social gaffe I have enacted this time (that 40 minute monologue on Social Growth of Organizations at FUDcon.. probably way too long.... and the conversation on the bus about why some pictures are art and others demeaning, awkward.)

I have also never understood how do people shut off all the conversations going on? My brain is constantly trying to figure out if people over at the pool really should be talking with the people in the kitchen since they seem to be talking the same things. And how am I supposed to know that even though they agree with each other, they hate each others guts.

Thankfully after walking the dog, I started to think about why I was afraid versus making some angry supposedly "witty" response. Why was I afraid? In the end it is because email and mailing lists make everyone else socially blind like me. Is Jack a jerk, or someone who only knows English from Quentin Tarantino films? On a mailing list, you can not tell and so have to lumber along. The only social ques you get are if people respond to you, and well even if its a long rant about everything you had wrong in your post.. it is a response.

But why should everyone be 'blind' because I am? Being socially 'blind' is rather unfair, but so is making everyone else be that way. Neuro-typical people are built to be social creatures wanting to build tribes, and without various ques will degrade into sociopathic forms as evidenced on Fedora about updates or Ubuntu about where your buttons are.

So the important question is, how can we make this better for people in general? I think that having some sort 'out-of-band' ques will help the majority of neuro-typical people. It might even help me if there is some way that it can give me feedback on how to do better.

Relationships

Just because it made me smile.


“I would say Fedora is the father to RHEL.” Paul Frields: “And the son has an incredibly lucrative job.”

It is a great way to look at things.

The 80's remembered through your kids

This blog about serious Fedora things (*cough*), and will go into the fact that I currently have the MacGyver and A-Team songs stuck in my head. We got parts of Season 1 of each to watch this week.. and the kid has been sucking through them like pixie sticks.

But other than the bad synthesizer music, and painful first season plots that every show goes through... the shows weren't too bad.. ok I lie, they were painful at first until I started watching it through my kids eyes. Over the top explosions were his first attraction, but then I noticed what he really thought cool was all the things the A-Team and MacGyver did with common things. And how often things broke down or plans blew up in their faces. It was like this sudden realization in both our perfectionist minds that its ok to fail. You learn from the failure, and you keep going.

Wait, I guess I did end up talking about Fedora after all :)

If you have nothing nice to say...

So going through various posts today, I came to the conclusion that the most wearing of body and soul are the ones where the writer has nothing but critiques of an idea, a position, the implied criticism that the person who wrote the letter has no worth as a human being, and the fact that no part of the idea should ever be implemented, reviewed, added onto or listened to.

It is really depressing... because it implies

• that unless you have a perfect plan, do nothing.
• that failure is never an option
• failure reflects upon the very character of the person who tried.
  
• that to speak is to open yourself up to being abused.

Personally I am tired of it. bone tired. I think the wise saying my parents told me seems to be missing:

If you have nothing nice to say, say nothing at all.

Reply to a Reminder

Seth Vidal reminds us:

fedora is not a government nor a government body.

I often wonder about that. Why do so many of us (I have been under this delusion several times) make this mistake. What trappings of Fedora make it so we think that we have 'rights'? Is it because we have elections? Is it because of the words we use in the Five Foundations: "Freedom, Friends, First, Features, Failure"?

But even deeper than that we need to answer questions like:

• What is a government?
  
• What are rights?
  
• What grants rights to us, and what takes them away from us?
  
• What is politics?
• What is bureaucracy? [And why can't I remember how to spell it correctly?]
  

The first definitions of government from good old Google comes from Princeton is:

• the organization that is the governing authority of a political unit;
• the act of governing; exercising authority;
  
• (government) the system or form by which a community or other political unit is governed;
• politics: the study of government of states and other political units
• political unit: a unit with political responsibilities [whee circular definitions]
  

These would seem to cover various units like FESCO and the Fedora Board in that they exercise authority over things like the Fedora brand, what packages are in Fedora, how packages are built, etc.

However this still does not fit into the larger definitions of Government. Fedora can not start a war with something. It can not jail dissidents, any Legal issues would require local courts where the individual is located. Rights that a 'Government' can recognize and allow (Freedom of Press, Freedom of Religion, Freedom of PiDay) are not the same that Fedora can actually allow. Even if it were an independant foundation located in Switzerland, it would be bound by the laws of Switzerland, and each member would be bound by the laws of their own country. Anyway, I have probably completely missed the point here.. so I am going back to downloading an Alpha.