It's grayish. Will it rain soon? In an hour or so I will walk about two miles, and I would prefer not to get wet.
Recently I play chess on Internet again, on Polish server "Kurnik". I got to the yellow ranking for a short while. First I got exactly 1500, then I won one game more and climbed to 1510, then I won another game, and climbed to... I don't know, than I lost 4 games in a row, in two sittings before I won one game. Oops, I still played more. Anyway, I am now only a miserable (:-) 1459. I won 44, drew 3, and lost 28 games. This positive proportion means only that my opponents had on average lower rating than me. The correlation between the won/lost ratio and ranking is weak. I'd rather have a negative won-lost score but play stronger opposition. Ironically, I had a clean score against my three top opponents, and even now I have a very positive score against my five top rated opponents:
opp r | won-drew-lost
1720 | 1 0 0
1699 | 1 0 0
1668 | 2 3 0
1651 | 1 0 0
1615 | 2 1 0
Against the next one I played three blitz games. The first two were 5m, and I had no chance. In the third one, played at the 7m control, I had a good game but I was not good enough to carry it to success. I wish, we played more 7m games but it was already nice for a strong player to play me 3 games. Thus the next two entries, sorted by the rating of my opponents, look like this:
1612 | 0 0 3
1600 | 1 0 1
Next, my score is mixed until the tail of the list, occupied by weak players. Against the last 19 players I won 20 games, drew 2, and lost 5. I have a minimal, negative score against just two of them, 0-0-1.
I should stop lurking on poetic Internet places. On the Polish ones I even post occasionally. That's not a good way to get away, but, say, do I want to all the way to the end.
Knol trivia. I'll restrict my table tnow to 3+ votes (the ones rated only once or twice make a better impression :-).
knol title | rat | #vt | views | description
==================================================================
Mathematics -- index | 5 | 6 | 608 | my mthKnolsIndex
M sp univ for 2pt sp | 4 | 5 | 143 | metric spaces
Euclid-Heron | 4 | 4 | 87 | triangle area, geom
Math -- two def-s | 4 | 3 | 106 | mth, general
Top sp & cnt maps | 4 | 3 | 66 | set topology, intro
Top.--the int. oper. | 5 | 3 | 43 | set topology
Ooooph, that's all. Time to go (and get soaked in the rain--I hope not).
Tuesday, December 30, 2008
Saturday, December 20, 2008
my knol stats and trivia update
By now too many of my knols were rated to waste time on a complete table of all rated knols. Most of them were rated only once though. Perhaps I'll waste time :-) on a table of those which were rated at least twice. Surprisingly, most of the scores are 5.0 (the top), With mostly one vote per knol it is a very fragile and not too meaningful statistics. They rarely are. I was pleased that some my non-mathematical knols got a positive response, even if minimal. It's a bit ironic that my most rated knols are mostly the ones which are not meritorious but logistic. My most popular and most rated knol is the index of my mathematical knols. It was rated 5 times (top rating each time, I think--Google irritates me by not providing the score explicitly and perfectly; instead, I see five gold stars; they look like solid gold, but are they?). I need to run now, more later (perhaps).
I'm back. I have three knols rated 1 (the lowest score), each time by one reader. One knol is about patents. Why would anyone react so strongly to such an innocent topic. Is this person somehow in the patenting business? Perhaps a patent office employee? Who knows. My another bottom rated knol is about the separation of the marriage notion and law+government. I advocate for years that it is not any business of the governmental and law agencies. A total blindness of law and government w.r. to the notion of marriage would empty many unnecessary problems and complications. And recently I "published" a list WhoWheWha (in progress) of people who had significant contributions to the human life quality. I wrote in a huge font that this knol is IN PROGRESS, that I have covered more or less only a few initial letters, for mathematicians only, plus a few musicians, plus two pure philosophers. Very soon I got rating 1. Most likely because I value philosophers and philosophy very little. I don't know. This is just a table with names, birth and death dates, and speciality--like mathematics, physics, music, biology... I want to add writers, movie directors, painters... Even politicians, including the pathological ones. This table takes awfully lot of time and effort though. At this moment it features 154 entries, 11 of them musical, 2 in philosophy, some in physics, astronomy. Only one in biology, Darwin, but I want to add Mendel.
Someone's knol gets in one week more pageviews than all 60++ of my knols over months.
Recently my knols are sprinkled with mostly single ratings, mostly the top one. One knol got rating while it has still only 3 pageviews. Another within hours since being "published"--Total logarithmic series, it has so far zero recorded pageviews, hey!
OK, time for the trivia table:
=============================================================
abbr. title - - - - - - |views#|rating|r-#|domain
========================|======|======|===|==================
Mth. -- index - - - - - | -608 |- 5 - | 5 |mth, general
Topology--sh-sh intro - | - 75 |- 4 - | 5 |mth topology
Met sp univ for 2-pt sp | -143 |- 4 - | 4 |mth metric sp
Euclid-Heron tr area - -| - 87 |- 4 - | 4 |mth geometry
Topological spaces ... -| - 66 |- 4 - | 3 |mth topology
The interior operation -| - 43 |- 5 - | 3 |mth topology
knolog - - - - - - - - -| -383 |- 5 - | 2 |general
Mathematical notation - | -263 |- 4.5 | 2 |mth, general
Right triangles - - - - | -160 |- 2.5 | 2 |mth geometry
ideals in Z, and gcd - -| -159 |- 2.5 | 2 |mth num th
Money--economy (part 1) | -147 |- 5 - | 2 |Art of Agr economy
Connected spaces - - - -| -122 |- 5 - | 2 |mth topologia
Mathematics -- two def -| -106 |- 5 - | 2 |mth, general
Top. subbases and bases | - 84 |- 5 - | 2 |mth topology
Kuratowski pairs & real.| - 76 |- 5 - | 2 |mth set theory
Met univ of (R^n d_m)--1| - 64 |- 5 - | 2 |mth Met sp
x^2 = -1 mod p(Euler)+W | - 34 |- 5 - | 2 |mth num th
Aleksandrov 2-pt sp - - | - 29 |- 5 - | 2 |mth topology
Cuts and miscuts - - - -| - 24 |- 5 - | 2 |mth topology
∞-Metrics - - - - - - - | - 22 |- 5 - | 2 |mth Met sp
Topological weight - - -| - 20 |- 5 - | 2 |mth topology
Fermat sequence base b -| - 13 |- 5 - | 2 |mth num th
I'm tired, it's well after midnight, I need to stop this now.
I'm back. I have three knols rated 1 (the lowest score), each time by one reader. One knol is about patents. Why would anyone react so strongly to such an innocent topic. Is this person somehow in the patenting business? Perhaps a patent office employee? Who knows. My another bottom rated knol is about the separation of the marriage notion and law+government. I advocate for years that it is not any business of the governmental and law agencies. A total blindness of law and government w.r. to the notion of marriage would empty many unnecessary problems and complications. And recently I "published" a list WhoWheWha (in progress) of people who had significant contributions to the human life quality. I wrote in a huge font that this knol is IN PROGRESS, that I have covered more or less only a few initial letters, for mathematicians only, plus a few musicians, plus two pure philosophers. Very soon I got rating 1. Most likely because I value philosophers and philosophy very little. I don't know. This is just a table with names, birth and death dates, and speciality--like mathematics, physics, music, biology... I want to add writers, movie directors, painters... Even politicians, including the pathological ones. This table takes awfully lot of time and effort though. At this moment it features 154 entries, 11 of them musical, 2 in philosophy, some in physics, astronomy. Only one in biology, Darwin, but I want to add Mendel.
Someone's knol gets in one week more pageviews than all 60++ of my knols over months.
Recently my knols are sprinkled with mostly single ratings, mostly the top one. One knol got rating while it has still only 3 pageviews. Another within hours since being "published"--Total logarithmic series, it has so far zero recorded pageviews, hey!
OK, time for the trivia table:
=============================================================
abbr. title - - - - - - |views#|rating|r-#|domain
========================|======|======|===|==================
Mth. -- index - - - - - | -608 |- 5 - | 5 |mth, general
Topology--sh-sh intro - | - 75 |- 4 - | 5 |mth topology
Met sp univ for 2-pt sp | -143 |- 4 - | 4 |mth metric sp
Euclid-Heron tr area - -| - 87 |- 4 - | 4 |mth geometry
Topological spaces ... -| - 66 |- 4 - | 3 |mth topology
The interior operation -| - 43 |- 5 - | 3 |mth topology
knolog - - - - - - - - -| -383 |- 5 - | 2 |general
Mathematical notation - | -263 |- 4.5 | 2 |mth, general
Right triangles - - - - | -160 |- 2.5 | 2 |mth geometry
ideals in Z, and gcd - -| -159 |- 2.5 | 2 |mth num th
Money--economy (part 1) | -147 |- 5 - | 2 |Art of Agr economy
Connected spaces - - - -| -122 |- 5 - | 2 |mth topologia
Mathematics -- two def -| -106 |- 5 - | 2 |mth, general
Top. subbases and bases | - 84 |- 5 - | 2 |mth topology
Kuratowski pairs & real.| - 76 |- 5 - | 2 |mth set theory
Met univ of (R^n d_m)--1| - 64 |- 5 - | 2 |mth Met sp
Factor. in semigroups - | - 56 |- 5 - | 2 |mth algebra
Birkhoff lattice of top | - 54 |- 5 - | 2 |mth topology
Infinitude of primes - 2| - 37 |- 5 - | 2 |mth num thBirkhoff lattice of top | - 54 |- 5 - | 2 |mth topology
x^2 = -1 mod p(Euler)+W | - 34 |- 5 - | 2 |mth num th
Aleksandrov 2-pt sp - - | - 29 |- 5 - | 2 |mth topology
Cuts and miscuts - - - -| - 24 |- 5 - | 2 |mth topology
∞-Metrics - - - - - - - | - 22 |- 5 - | 2 |mth Met sp
Topological weight - - -| - 20 |- 5 - | 2 |mth topology
Fermat sequence base b -| - 13 |- 5 - | 2 |mth num th
I'm tired, it's well after midnight, I need to stop this now.
Tuesday, December 2, 2008
flu
" Will I or will I not get flu?" was not a question--I already had a flu, and the actual question is "how long?" will it keep me in its paws.
Google reformated knol environment, perhaps for the better. But it lost views! Now some of my knols have fewer views listed by google than I have recorded in the table. I wonder if they also lost some of the ratings? Perhaps not, because ratings are not anonymous to Google but attached to the readers. My quibbling is about trivia but I like trivia to be sharp, clean.
Google reformated knol environment, perhaps for the better. But it lost views! Now some of my knols have fewer views listed by google than I have recorded in the table. I wonder if they also lost some of the ratings? Perhaps not, because ratings are not anonymous to Google but attached to the readers. My quibbling is about trivia but I like trivia to be sharp, clean.
Sunday, November 30, 2008
emails and mathematical topics
Will I or will I not get flu?
Suddenly I got emails about mathematical topics from two of my friends. I have induced AP to program baroque numbers, which he was doing on and off, now on again. He uses the so-called genetic approach which is like simulated annealing + one additional kind of moves, where from two vertices one gets a new one (it simulates sexual reproduction). He has a better software, better computer, everything better than me but the results. Somehow it's not easy to communicate on long distance, in an irregular way, and it's hard for me to pass to him my experience. Actually, I am rusty these days myself, and will have to start almost from scratch (almost) if at all.
As the luck has it, around the same time I get an email from JBrz, who is excited about abc again. He and JBro have published a nice paper anbout abc years ago, about the integer and polynomial versions. So, they are serious, while I had only an amatourish interest in the topic, and only in the classical, integer version. But JBrz is all about the polynomial version these days. I am a social being, so I will try to join him.
I have a thousand of topics for knols (instead of working on one topic only), and now I have a thousand and two. And so it goes.
Recently I have finished ("published") my first knol about logarithmic and exponential functions, log and exp--a constructive and an axiomatic approaches . It has scored its first six views. The logarithmic knol is partially based on two knols about Integration of monotone functions and The ground level properties of integral.
Suddenly I got emails about mathematical topics from two of my friends. I have induced AP to program baroque numbers, which he was doing on and off, now on again. He uses the so-called genetic approach which is like simulated annealing + one additional kind of moves, where from two vertices one gets a new one (it simulates sexual reproduction). He has a better software, better computer, everything better than me but the results. Somehow it's not easy to communicate on long distance, in an irregular way, and it's hard for me to pass to him my experience. Actually, I am rusty these days myself, and will have to start almost from scratch (almost) if at all.
As the luck has it, around the same time I get an email from JBrz, who is excited about abc again. He and JBro have published a nice paper anbout abc years ago, about the integer and polynomial versions. So, they are serious, while I had only an amatourish interest in the topic, and only in the classical, integer version. But JBrz is all about the polynomial version these days. I am a social being, so I will try to join him.
I have a thousand of topics for knols (instead of working on one topic only), and now I have a thousand and two. And so it goes.
Recently I have finished ("published") my first knol about logarithmic and exponential functions, log and exp--a constructi
Friday, November 28, 2008
A table of my rated knols
It looks like two people who know me (? or only one of them knows me?) have sprinkled my mathematical knols with one or two 5s (top score) recently. One of them likes topology. Another number theory. A third one metric spaces? Let me waste some time to make another table:
==========================================================
abbr. title - - - - - - |views#|rating|r-#|domain
========================|======|======|===|===============
∞-Metrics - - - - - - - | - 15 |- 5 - | 1 |mth met sp
Aleksandrov 2-pt space -| - 26 |- 5 - | 1 |mth topology
Birkhoff lattice of t sp| - 49 |- 5 - | 1 |mth topology
Closure operation - - - | - 13 |- 5 - | 1 |mth topology
Congruences - - - - - - | - 14 |- 5 - | 1 |mth num th
Connected spaces - - - -| -108 |- 5 - | 1 |mth topology
Euclid-Heron area of tr.| - 77 |- 3++ | 3 |mth geometry
Factorization in semigps | - 39 |- 5 - | 1 |mth algebra
Fermat sequence base b -| -- 7 |- 5 - | 1 |mth num th
Ideals in Z, & gcd - - -| -124 |- 2.5 | 2 |mth num th
Infnitude of primes - 2 | - 30 |- 5 - | 1 |mth num th
Interior operation - - -| - 39 |- 5 - | 2 |mth topology
Iso-graphs of m m into R| - 27 |- 5 - | 1 |mth met sp
Knolog - - - - - - - - -| -322 |- 5 - | 2 |general
Kolmogorov axiom - - - -| - 37 |- 5 - | 1 |mth topology
Kuratowski pairs & real.| - 60 |- 5 - | 1 |mth set th
Linear orders in top sps| - 72 |- 5 - | 1 |mth topology
Marriage v. law & govern| - 33 |- 1 - | 1 |Art of Agr
Math -- two definitions | - 97 |- 5 - | 1 |mth, general
Mathematical notation - | -239 |- 4.5 | 2 |mth, general
Mathematics -- index - -| -549 |- 5 - | 4 |mth, general
Met sp univ for 2pt sp -| -139 |- 3++ | 3 |mth met sp
Met sp univ for 3 & 4 pt| - 62 |- 5 - | 1 |mth met sp
Met univ of (R^n d_m)-p1| - 49 |- 5 - | 1 |mth met sp
Money--economy (part 1) | -128 |- 5 - | 2 |Art of Agr
Patent Law - - - - - - -| - 26 |- 1 - | 1 |Art of Agr
Piecewise cont functions| - 17 |- 5 - | 1 |mth topology
Prods of bounded primes | - 13 |- 5 - | 1 |mth num th
Seq of coprime integers | - 10 |- 5 - | 1 |mth num th
Topological product of 2| - 20 |- 5 - | 1 |mth topology
Topological subb & bases| - 67 |- 5 - | 1 |mth topology
Topological subspaces - | - 28 |- 5 - | 1 |mth topology
Topological cuts & miscs| - 21 |- 5 - | 1 |mth topology
Topological weight - - -| - 17 |- 5 - | 1 |mth topology
Topology -- sh-sh intro | - 63 |- 4.6 | 3 |mth topology
Top. spaces & cont. maps| - 58 |- 4 - | 3 |mth topology
Triangles - - - - - - - | - 72 |- 5 - | 1 |mth geometry
x^2 = -1 mod p - - - - -| - 25 |- 5 - | 1 |mth num th
==========================================================
abbr. title - - - - - - |views#|rating|r-#|domain
========================|======|======|===|===============
∞-Metrics - - - - - - - | - 15 |- 5 - | 1 |mth met sp
Aleksandrov 2-pt space -| - 26 |- 5 - | 1 |mth topology
Birkhoff lattice of t sp| - 49 |- 5 - | 1 |mth topology
Closure operation - - - | - 13 |- 5 - | 1 |mth topology
Congruence
Connected spaces - - - -| -108 |- 5 - | 1 |mth topology
Euclid-Heron area of tr.| - 77 |- 3++ | 3 |mth geometry
Factorizat
Fermat sequence base b -| -- 7 |- 5 - | 1 |mth num th
Ideals in Z, & gcd - - -| -124 |- 2.5 | 2 |mth num th
Infnitude of primes - 2 | - 30 |- 5 - | 1 |mth num th
Interior operation - - -| - 39 |- 5 - | 2 |mth topology
Iso-graphs of m m into R| - 27 |- 5 - | 1 |mth met sp
Knolog - - - - - - - - -| -322 |- 5 - | 2 |general
Kolmogorov axiom - - - -| - 37 |- 5 - | 1 |mth topology
Kuratowski pairs & real.| - 60 |- 5 - | 1 |mth set th
Linear orders in top sps| - 72 |- 5 - | 1 |mth topology
Marriage v. law & govern| - 33 |- 1 - | 1 |Art of Agr
Math -- two definition
Mathematic
Mathematic
Met sp univ for 2pt sp -| -139 |- 3++ | 3 |mth met sp
Met sp univ for 3 & 4 pt| - 62 |- 5 - | 1 |mth met sp
Met univ of (R^n d_m)-p1| - 49 |- 5 - | 1 |mth met sp
Money--economy (part 1) | -128 |- 5 - | 2 |Art of Agr
Patent Law - - - - - - -| - 26 |- 1 - | 1 |Art of Agr
Piecewise cont functions| - 17 |- 5 - | 1 |mth topology
Prods of bounded primes | - 13 |- 5 - | 1 |mth num th
Seq of coprime integers | - 10 |- 5 - | 1 |mth num th
Topological product of 2| - 20 |- 5 - | 1 |mth topology
Topological subb & bases| - 67 |- 5 - | 1 |mth topology
Topological subspaces - | - 28 |- 5 - | 1 |mth topology
Topological cuts & miscs| - 21 |- 5 - | 1 |mth topology
Topological weight - - -| - 17 |- 5 - | 1 |mth topology
Topology -- sh-sh intro | - 63 |- 4.6 | 3 |mth topology
Top. spaces & cont. maps| - 58 |- 4 - | 3 |mth topology
Triangles - - - - - - - | - 72 |- 5 - | 1 |mth geometry
x^2 = -1 mod p - - - - -| - 25 |- 5 - | 1 |mth num th
Tuesday, October 28, 2008
Taxes
Can't people understand a simple principle? It's NOT the goal of taxes to reduce the material inequality between people. For this, taxes are a very wrong tool. Taxes are for one and only one reason: to provide government with money, so that it can operate and carry certain projects.
The only institution which means to help poor people should be charity. Government should stay away from charity, it does more wrong than right, but if it has to be involved in helping the poor people then it should have a separate branch, called "Charity", while all other branches would be freed from such a consideration.
Actually, taxes should be lower, virtually non-existent, and charity should be done by people themselves, through a decentralized system.
I've described a way to tax, which would cause society the least harm, in Art of Agreeing, in Painless tax. (I stated this idea publicly a long time ago, and more than once, but never vigorously).
The only institution which means to help poor people should be charity. Government should stay away from charity, it does more wrong than right, but if it has to be involved in helping the poor people then it should have a separate branch, called "Charity", while all other branches would be freed from such a consideration.
Actually, taxes should be lower, virtually non-existent, and charity should be done by people themselves, through a decentralized system.
I've described a way to tax, which would cause society the least harm, in Art of Agreeing, in Painless tax. (I stated this idea publicly a long time ago, and more than once, but never vigorously).
Sunday, October 26, 2008
knol activity
Should I just edit another knol or should I take a step back, stop here, and write about my activity, as I was thinking about doing so for awhile?
my knol is here, it's the main entry. It has three main directions at this time:
I have not touched the first two in weeks. Now too, I feel like mentioning the latter one only, mathematics. Clicking on Mathematics leads to the index of my mathematical knols. Ironically, my index knol got the best rating so far (5 three times out of three). At the present the main parts are:
The general part consists of two knols:
I should extend both. Knol "Mathematical notation" helps its author, me, to write mathematical knols. I keep "Mth notation" in a window (or Firefox tab) next to the knol under editing, so that I can "borrow" mathematical symbols and similar from "Mth n.", and copy them into the knol window. The more symbols I store there, the easier it is to write m-knols.
I need to stop now, too bad.
my knol is here, it's the main entry. It has three main directions at this time:
I have not touched the first two in weeks. Now too, I feel like mentioning the latter one only, mathematics. Clicking on Mathematics leads to the index of my mathematical knols. Ironically, my index knol got the best rating so far (5 three times out of three). At the present the main parts are:
- General
- Algebra
- Euclidean geometry
- Metric theory of metric spaces
- Number theory, elementary
- Set Theory
- Topology, general
The general part consists of two knols:
I should extend both. Knol "Mathematical notation" helps its author, me, to write mathematical knols. I keep "Mth notation" in a window (or Firefox tab) next to the knol under editing, so that I can "borrow" mathematical symbols and similar from "Mth n.", and copy them into the knol window. The more symbols I store there, the easier it is to write m-knols.
I need to stop now, too bad.
Thursday, October 16, 2008
trivia update
knol --:early| Oct11 | Oct12 | oct16 | oct26 |
=============|=======|=======|=======|=======|
m ind -: 5*2 | ditto | ditto |- 5*3 -| ditto |
m nttn : --- |- 4*1 -| ditto | ditto | ditto |
t sp mp: 2*1 | 3.5*2 | ditto | ditto | ditto |
M un 2 : --- | ----- |- 1*1 -| ditto | ditto |
E_H ar : 5*1 | ditto |- 3*2 -| ditto | ditto |
AoA-mrg: 1*1 | ditto | ditto | ditto | ditto |
t s-s i: 3*1 |- 4*2 -| ditto | ditto | ditto |
MN-ec1 : --- |- 5*1 -| ditto | ditto |- 5*2 -|
t-i op : --- |- 5*1 -| ditto | ditto | ditto |
m tria : 5*1 | ditto | ditto | ditto | ditto |
AoA pat: 1*1 | ditto | ditto | ditto | ditto |
NTh gcd: --- | ----- | ----- |- 3*1 -| 2.5*2 |
I was in a hurry. I may double check it later.
(Oct 16)
Was ok. (Oct 26)
=============|=======|=======|=======|=======|
m ind -: 5*2 | ditto | ditto |- 5*3 -| ditto |
m nttn : --- |- 4*1 -| ditto | ditto | ditto |
t sp mp: 2*1 | 3.5*2 | ditto | ditto | ditto |
M un 2 : --- | ----- |- 1*1 -| ditto | ditto |
E_H ar : 5*1 | ditto |- 3*2 -| ditto | ditto |
AoA-mrg: 1*1 | ditto | ditto | ditto | ditto |
t s-s i: 3*1 |- 4*2 -| ditto | ditto | ditto |
MN-ec1 : --- |- 5*1 -| ditto | ditto |- 5*2 -|
t-i op : --- |- 5*1 -| ditto | ditto | ditto |
m tria : 5*1 | ditto | ditto | ditto | ditto |
AoA pat: 1*1 | ditto | ditto | ditto | ditto |
NTh gcd: --- | ----- | ----- |- 3*1 -| 2.5*2 |
I was in a hurry. I may double check it later.
(Oct 16)
Was ok. (Oct 26)
Monday, October 13, 2008
Pros and artsy types
I wish I were a pro, meaning the ability to work efficiently in adverse conditions. Unfortunately, I am of the artsy type--after a setback in my everyday life I stop the current project. When I get back into a better mood then I start life anew, meaning a new project. And so it goes. My present project is knol. It is like several projects. I have already started math-knol, Art of Agreeing knol, and dabanese knol. Each of the consists of subtopics, and, of course, mathematics is especially expansive. I am writing about general topology, a special flavor of Euclidean Geometry, and about metric spaces from the purely metric point of view (not topological). I also have, so far only one, short section about set theory--just to establish notions and terminology of the Cartesian product (diagonal product of functions). It's really a small fragment of the theory of categories, if I wrote it in full generality. In topology, at first I am aiming at the universal images. In metric spaces, I am trying fisrt of all to describe the isometric embeddings results. I would like to write on a bunch of topics while on the other hand the notion of giving up on writing, and on devoting myself to learning a new to me, reasonably deep mathematical item, is always present. I am just afraid to do it. I can quickly write a bit of this and of that. But learning good stuff requires my full concentration, piece of mind and better conditions, at least in my case. Write now I am writing this post because I am not able to write some more of my math-knol. Hm, it was supposed to relax me, not to depress :-) Ok, here's something which to me is mildly amusing. The only of my numerous knols which got rating 5 from 2 readers is the index to my math knols. Isn't it ironic to be appreciated for index? (well, it's just 2 guys). I guess, this is due to the fact that Google didn't provide authors with any special tool for hierarchy of their knols, while my index is a substitute for a true software solution.
Well, that was not entertaining, not funny, cannot help it. The sleepiness I feel is marginally relaxing. So, I'll lay down for a couple of minutes, to recharge myself.
Well, that was not entertaining, not funny, cannot help it. The sleepiness I feel is marginally relaxing. So, I'll lay down for a couple of minutes, to recharge myself.
Sunday, October 12, 2008
The wonderful anonymous world :-)
My math knol rating honeymoon is over. Within 10 hours of my last blog entry someone (or would it be two independed readers) rated my two math knols as 1 (the lowest). Now the stats are:
knol --:early| Oct11 | Oct12 |
=============|=======|=======|
m ind -: 5*2 | ditto | ditto |
m nttn : --- |- 4*1 -| ditto |
t sp mp: 2*1 | 3.5*2 | ditto |
M un 2 : --- | ----- |- 1*1 -|
E_H ar : 5*1 | ditto |- 3*2 -|
AoA-mrg: 1*1 | ditto | ditto |
t s-s i: 3*1 |- 4*2 -| ditto |
MN-ec1 : --- |- 5*1 -| ditto |
t-i op : --- |- 5*1 -| ditto |
m tria : 5*1 | ditto | ditto |
AoA pat: 1*1 | ditto | ditto |
Let me compute the average:
(10+4+7+1+6+1+8+5+5+5+1) / (2+1+2+1+2+1+2+1+1+1+1)
= 53/15 = 3.5333...
Three single ratings were for Art of Agreement: (1+1+5)/3 = 2.333... It drags me down :-) Nobody rated dabanese. Thus for mathematics alone the average is: 46/12 = 3.8333... However, I got two 5s for the index of all things :-) Also one 4 for my math notation blog. This leaves 32/9 = 3.555... for actual, meritorious blogs. Ooooph, I got my stat trivia.
knol --:early| Oct11 | Oct12 |
=============|=======|=======|
m ind -: 5*2 | ditto | ditto |
m nttn : --- |- 4*1 -| ditto |
t sp mp: 2*1 | 3.5*2 | ditto |
M un 2 : --- | ----- |- 1*1 -|
E_H ar : 5*1 | ditto |- 3*2 -|
AoA-mrg: 1*1 | ditto | ditto |
t s-s i: 3*1 |- 4*2 -| ditto |
MN-ec1 : --- |- 5*1 -| ditto |
t-i op : --- |- 5*1 -| ditto |
m tria : 5*1 | ditto | ditto |
AoA pat: 1*1 | ditto | ditto |
Let me compute the average:
(10+4+7+1+6+1+8+5+5+5+1) / (2+1+2+1+2+1+2+1+1+1+1)
= 53/15 = 3.5333...
Three single ratings were for Art of Agreement: (1+1+5)/3 = 2.333... It drags me down :-) Nobody rated dabanese. Thus for mathematics alone the average is: 46/12 = 3.8333... However, I got two 5s for the index of all things :-) Also one 4 for my math notation blog. This leaves 32/9 = 3.555... for actual, meritorious blogs. Ooooph, I got my stat trivia.
Saturday, October 11, 2008
my knol stats
Stats are my silly fun, I like stats. Let me here start my knol stats, ratings (there is perhaps just one comment, it's from a young student from India, and it's just a social hello, email-like message rather than a comment). I am too tired right now to make an html table. A naive format will do for the time being.
knol - :early| Oct11 |
=============|=======|
m ind -: 5*2 | ditto |
m nttn : --- |- 4*1 -|
t sp mp: 2*1 | 3.5*2 |
E_H ar : 5*1 | ditto |
AoA-mrg: 1*1 | ditto |
t s-s i: 3*1 |- 4*2 -|
MN-ec1 : --- |- 5*1 -|
t-i op : --- |- 5*1 -|
m tri -: 5*1 | ditto |
AoA pat: 1*1 | ditto |
OK, enough of that. (That was in font Arial).
OK, enough of that. (That was in font Courier).
OK, enough of that. (That was in font Georgia).
OK, enough of that. (That was in font Lucida Grande).
OK, enough of that. (That was in font times).
OK, enough of that. (That was in font Trebuchet).
OK, enough of that. (That was in font Verdana).
OK, enough of that. (That was in font Webdings).
knol - :early| Oct11 |
=============|=======|
m ind -: 5*2 | ditto |
m nttn : --- |- 4*1 -|
t sp mp: 2*1 | 3.5*2 |
E_H ar : 5*1 | ditto |
AoA-mrg: 1*1 | ditto |
t s-s i: 3*1 |- 4*2 -|
MN-ec1 : --- |- 5*1 -|
t-i op : --- |- 5*1 -|
m tri -: 5*1 | ditto |
AoA pat: 1*1 | ditto |
OK, enough of that. (That was in font Arial).
OK, enough of that. (That was in font Courier).
OK, enough of that. (That was in font Georgia).
OK, enough of that. (That was in font Lucida Grande).
OK, enough of that. (That was in font times).
OK, enough of that. (That was in font Trebuchet).
OK, enough of that. (That was in font Verdana).
OK, enough of that. (That was in font Webdings).
Thursday, October 2, 2008
Just a blog entry
Any small mistake or negligence in the care of my father by care givers means a dramatic follow up for my father, and a lot of nerves and extra effort by me.
I sleep little these days, and I am often sleepy and unable to work on my projects. Thus I start or restart to work on a project then stop and switch to a new one. Unfortunately, I have stopped again my efforts on baroque numbers. I want to come back to the attractive for me goal of finding a bunch of new baroque numbers, but I already am writing knols on general topology, on euclidean geometry, on art of agreeing, on dabanese. And I'd like to write on many other topics, especially on more mathematical topics: elementary algebraic topology, elementary number theory, combinatorics, on translation lattices, ... Knols possibly will get a larger audience than a blog. Blog can be more of writing for myself mainly. After all, this very entry is sooooooo embarrassingly boring.
In topology, I'd like to present my theory of universal functions; also my cubical polyhedra approach to algebraic topology, and about the geometry of cubical polyhedrons as well. I have outlined the theory of cubical polyhedra back in Poland, in late sixties. Then in 1970, with J.B., when he was my Ph.D. student at UofM in A2, the one and only ever (I wish I had many) we published a series of papers in Italy, and J.B got his degree in a record fast time.
When it comes to number theory, I should stop playing on a kindergarten level, I should learn some advanced tools, analytic or combinatorial (sieves). Elementary games are fun but the advanced ones are so much more!
I got far away from poetry. I am still a bit active on one English language board, and on one Polish board (Poewiki) but it's only inertia, without contributing much of my energy. It's been ages since I've written any poem. I even feel that I am distancing myself from English! Objectively, I do have contact, like this blog, and in general mainly via Internet, a bit from tv, bits and pieces, when I visit my father. Hm, I have more contact with English than with Polish these days. But my contact with native speakers of (American) English is limited, despite one sharing my apt in the past three months or so.
Yes, it's early, only 21:24 but I definitely am sleepy. Let me lie down for a few minutes. Most of the time I am at the care house at this time, but today my father went to bed early. Later, I might to write about my (rather depressing) impressions from the presidential race.
I should check this entry for errors (typos, etc) but I'll stop now. I have this annoying feeling that I use word "but" way too often.
I sleep little these days, and I am often sleepy and unable to work on my projects. Thus I start or restart to work on a project then stop and switch to a new one. Unfortunately, I have stopped again my efforts on baroque numbers. I want to come back to the attractive for me goal of finding a bunch of new baroque numbers, but I already am writing knols on general topology, on euclidean geometry, on art of agreeing, on dabanese. And I'd like to write on many other topics, especially on more mathematical topics: elementary algebraic topology, elementary number theory, combinatorics, on translation lattices, ... Knols possibly will get a larger audience than a blog. Blog can be more of writing for myself mainly. After all, this very entry is sooooooo embarrassingly boring.
In topology, I'd like to present my theory of universal functions; also my cubical polyhedra approach to algebraic topology, and about the geometry of cubical polyhedrons as well. I have outlined the theory of cubical polyhedra back in Poland, in late sixties. Then in 1970, with J.B., when he was my Ph.D. student at UofM in A2, the one and only ever (I wish I had many) we published a series of papers in Italy, and J.B got his degree in a record fast time.
When it comes to number theory, I should stop playing on a kindergarten level, I should learn some advanced tools, analytic or combinatorial (sieves). Elementary games are fun but the advanced ones are so much more!
I got far away from poetry. I am still a bit active on one English language board, and on one Polish board (Poewiki) but it's only inertia, without contributing much of my energy. It's been ages since I've written any poem. I even feel that I am distancing myself from English! Objectively, I do have contact, like this blog, and in general mainly via Internet, a bit from tv, bits and pieces, when I visit my father. Hm, I have more contact with English than with Polish these days. But my contact with native speakers of (American) English is limited, despite one sharing my apt in the past three months or so.
Yes, it's early, only 21:24 but I definitely am sleepy. Let me lie down for a few minutes. Most of the time I am at the care house at this time, but today my father went to bed early. Later, I might to write about my (rather depressing) impressions from the presidential race.
I should check this entry for errors (typos, etc) but I'll stop now. I have this annoying feeling that I use word "but" way too often.
Thursday, September 4, 2008
Simulated annealing (sa) for baroque numbers--a warm up
The idea of applying the simulated annealing method to baroque numbers was with me for a long time. Finally I had invited others on pl.sci.matematyka (on 2007-05-19) to implement it in parallel with me (independently). I wanted to have some company, it'd be interesting. Somehow, after some positive (and negative) feedback, I ended up alone with a first version 2007-July. It was able to repeat the results obtained in 1990-ies. It couldn't do more because I used a 32-bit C++, and I have represented prime powers directly as actual integers, thus limiting them to the range pe <>32 (I even stayed lazily withing pe ≤ 231). Then I barely started to work on a more advanced version 2007-Aug before I already had to stop (for reasons not realated directly to the project). Now, (starting near the end of 2008-August but really this September, I hope) I am trying to psyche myself up for another round. This time I am going to remove the said limitation, and I'd like to actually discover new baroque numbers, not known before.
First let me present here a very naive approach, just for the illustration (I would never actually code it; you may program this way only if you enjoy programming for its own sake). Select a natural number topNum, say topNum := 10000 and an array of primes, say:
P := (2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79}
Your space of "vertices" V consists now of natural numbers n, 1 < 28 =" 22⋅7 is one of them. You want to find baroque numbers, which belong to V. For instance, 28 is one of them; indeed, the sum of divisors of 28 is:
sd(28) = 1+2+4+7+14+28 = 2⋅28
hence brq(28) = 2, which means that 28 is a perfect number.
Now define the penalty function pen(n) as the number of primes p ε P such that there exists natural exponent e for which pe is a divisor of n but not of sd(n). Observe thatg n is baroque if and only if pen(n) = 0. Thus now we may say that our goal is to find many (preferably all) n ε V for which pen(n) = 0.
The algorithm may start with vertex v(0) := 43 (or any other prime from P). Let's assume that the algorithm has already reached vertex v(n). Selecting the next vertex, v(n+1), involves two stages: we select a candidate, then the candidate is accepted with probability prob(n), or rejected. If it is rejected, then we select another candidate, which is going to be accepted as v(n+1), with the same probability prob(n), or rejected, etc., until certain v(n+1) gets finally accepted.
In order to select v(n+1), the algorithm selects randomly a prime p ε P. The product v(n)⋅p is the first candidate for v(n+1). Then it checks condition v(n)⋅p ≤ topNum. If it is satisfied, then it checks penalty: if pen(v(n)⋅p) < pen(n); then v(n+1) := v(n)⋅p is accepted as the next vertex. If the penalty didn't decrease then we still allow a prob(n) := 1/(1 + 10⋅log(1+n)) chance that v(n)⋅p is accepted. If it is rejected, for one reason or another, but p is a divisor of n then v(n+1) := v(n)/n is tried, i.e. the algorithm checks pen(v(n+1)). If v(n+1) := v(n)/n t is accepted then the task of finding the next vertex is accomplished (and algorithm will look for v(n+2)). Otherwise a new prime p ε P is randomly selected and the described candidate process is repeated, etc, until finally a new v(n+1) gets accepted.
The describes algorithm can be discussed, modified, refined but my goal was just to provide an idea how a simulated annealing might work for baroque numbers. Among the shortcomings of the described version is the necessity of representing v(n) actually and directly (naively) as an integer. This either limits the program to a small range of numbers or forces us to use a multi-precision software library--indeed, baroque numbers ten to be huge. In the next posts I'll describe a bit less naive approach.
Remark Above, I have proposed
prob(n) := 1/(1 + 10⋅log(1+n))
One may also try one of the many other possibilities, e.g.
prob(n) := 10/(10 + n1/4)
First let me present here a very naive approach, just for the illustration (I would never actually code it; you may program this way only if you enjoy programming for its own sake). Select a natural number topNum, say topNum := 10000 and an array of primes, say:
hence brq(28) = 2, which means that 28 is a perfect number.
Now define the penalty function pen(n) as the number of primes p ε P such that there exists natural exponent e for which pe is a divisor of n but not of sd(n). Observe thatg n is baroque if and only if pen(n) = 0. Thus now we may say that our goal is to find many (preferably all) n ε V for which pen(n) = 0.
The algorithm may start with vertex v(0) := 43 (or any other prime from P). Let's assume that the algorithm has already reached vertex v(n). Selecting the next vertex, v(n+1), involves two stages: we select a candidate, then the candidate is accepted with probability prob(n), or rejected. If it is rejected, then we select another candidate, which is going to be accepted as v(n+1), with the same probability prob(n), or rejected, etc., until certain v(n+1) gets finally accepted.
In order to select v(n+1), the algorithm selects randomly a prime p ε P. The product v(n)⋅p is the first candidate for v(n+1). Then it checks condition v(n)⋅p ≤ topNum. If it is satisfied, then it checks penalty: if pen(v(n)⋅p) < pen(n); then v(n+1) := v(n)⋅p is accepted as the next vertex. If the penalty didn't decrease then we still allow a prob(n) := 1/(1 + 10⋅log(1+n)) chance that v(n)⋅p is accepted. If it is rejected, for one reason or another, but p is a divisor of n then v(n+1) := v(n)/n is tried, i.e. the algorithm checks pen(v(n+1)). If v(n+1) := v(n)/n t is accepted then the task of finding the next vertex is accomplished (and algorithm will look for v(n+2)). Otherwise a new prime p ε P is randomly selected and the described candidate process is repeated, etc, until finally a new v(n+1) gets accepted.
The describes algorithm can be discussed, modified, refined but my goal was just to provide an idea how a simulated annealing might work for baroque numbers. Among the shortcomings of the described version is the necessity of representing v(n) actually and directly (naively) as an integer. This either limits the program to a small range of numbers or forces us to use a multi-precision software library--indeed, baroque numbers ten to be huge. In the next posts I'll describe a bit less naive approach.
Remark Above, I have proposed
One may also try one of the many other possibilities, e.g.
Simulated annealing algorithm
The goal is to obtain optimal or nearly optimal solutions for a given problem. Thus first of all we need to define a finite set V of vertices, which correspond to the solutions of the problem, and a non-negative real function, called penalty,
pen : V → R,
for which we would like to find a vertex v ε V such that the value pen(v) is minimal or nearly minimal, so that such optimal v will serve as a solution. This abstract statement sounds simple but in applications the vertices may represent complex configurations or situations.
Some pairs of the vertices are connected by directed edges, so that together, the vertices and the edges, they form a directed graf G := (V E), where E is the set of all edges. Edges are just one-way roads which allow us to travel directly from one vertex to another. An edge leading from vertex v to vertex w is also called (in simulated annealing) a move from v to w. Simulated annealing is applied only to connected graphs, meaning that one can reach any vertex from any other via a finite sequence of consecutive edges (moves).
It is up to the designer of the algorithm to define the graph G = (V E) and the penalty function pen : V → R. One may do it well or one may do it poorly. It's an art. The same goes for the selection of other elements of the algorithm.
In addition, we consider also a real parameter T ≥ 0, called temperature, or rather a decreasing sequence of temperatures T(0) ≥ T(1) ≥ ... ≥ 0, which approach (or even attains) the limit value 0.
The algorithm, i.e. the search for the optimal vertex, works as follows: we start a travel over graph G at a high initial temperature T(0) and in an initial vertex v(0). Let's assume that we are already in vertex v(n) at temperature T(n). Now algorithm selects randomly a candidate for a move from vertex v(n). Let v(n+1) be the destination of the candidate move. If the penalty has decreased, pen(v(n+1)) then v(n+1) is accepted. If not then it is accepted with the probability prob(n) which approaches zero together with the temperature. If the candidate is rejected then another candidate v(n+1) is selected, and the same acceptance procedure applies to it; and so on, until a candidate is accepted.
for which we would like to find a vertex v ε V such that the value pen(v) is minimal or nearly minimal, so that such optimal v will serve as a solution. This abstract statement sounds simple but in applications the vertices may represent complex configurations or situations.
Some pairs of the vertices are connected by directed edges, so that together, the vertices and the edges, they form a directed graf G := (V E), where E is the set of all edges. Edges are just one-way roads which allow us to travel directly from one vertex to another. An edge leading from vertex v to vertex w is also called (in simulated annealing) a move from v to w. Simulated annealing is applied only to connected graphs, meaning that one can reach any vertex from any other via a finite sequence of consecutive edges (moves).
It is up to the designer of the algorithm to define the graph G = (V E) and the penalty function pen : V → R. One may do it well or one may do it poorly. It's an art. The same goes for the selection of other elements of the algorithm.
In addition, we consider also a real parameter T ≥ 0, called temperature, or rather a decreasing sequence of temperatures T(0) ≥ T(1) ≥ ... ≥ 0, which approach (or even attains) the limit value 0.
The algorithm, i.e. the search for the optimal vertex, works as follows: we start a travel over graph G at a high initial temperature T(0) and in an initial vertex v(0). Let's assume that we are already in vertex v(n) at temperature T(n). Now algorithm selects randomly a candidate for a move from vertex v(n). Let v(n+1) be the destination of the candidate move. If the penalty has decreased, pen(v(n+1)) then v(n+1) is accepted. If not then it is accepted with the probability prob(n) which approaches zero together with the temperature. If the candidate is rejected then another candidate v(n+1) is selected, and the same acceptance procedure applies to it; and so on, until a candidate is accepted.
Remark 1 In addition to simulated annealing algorithm there are also other optimizing algorithms which serve similar purpose. One of them is the so-called genetic algorithm, which is like simulated annealing but richer: besides moves it has also procreation, where one gets a new vertex out of a pair of two previous ones. This provides more possibilities (while it is harder now to provide a scientific foundation as solid as in the case of simulated annealing).
Remark 2 The algorithm may look just for one solution. Then after finding it, it may stop. Or it may look for many solutions. Then after finding a consecutive solution it restarts itself.
Sunday, August 31, 2008
Baroque conjectures
Let me address the views (guesses) on the four questions, about the perfect and baroque numbers, listed in the previous post:
- everybody believes that there are infinitely many (even) perfect numbers, because everybody believes that there are infinitely many Mersenne prime numbers p (i.e. prime numbers p such that 2p-1 is a prime too);
- it seems to me that some (many? most?) specialists believe that there are only finitely many baroque numbers which are not perfect; some even think that all baroque non-perfect numbers are already known (no way!). Myself, I believe that there are infinitely many of them but finitely many for each baroqueness coefficient;
- nobody believes that there is any odd perfect number;
- I think that nobody believes that there is any odd baroque number; I don't either but I am not so sure :-).
Saturday, August 30, 2008
Back to baroque numbers?
The classical, standard name for my term baroque numbers is pluperfect or polyperfect
numbers or similar. A natural number n (n = 1 2 ...) is called baroque when the sum sd(n) of all natural divisors of n is divisible by n; let's call
the baroqueness of n. When a baroqueness of a number is two, brq(n) = 2, then it is called perfect. The smallest perfect number, known since the ancient times, is n=6. Indeed, in this case
Questions about the baroque numbers are among the oldest, open (unresolved) problems of the whole mathematics. They are difficult and, today, somewhat isolated from the main developments, hence they are not as popular among the best mathematicians as they used to be in the past, when Euclid, Fermat, Decart, Euler and others were interested in them. Let me list the main open questions:
The Euclid-Euler tandem (:-) proved that an even natural number n is perfect if and only if there exists a (unique) natural number p such that the following two conditions hold:
Another old result (an ancient observation) is that brq(120) = 3, i.e. 120 is a baroque number, and its baroqueness is 3.
numbers or similar. A natural number n (n = 1 2 ...) is called baroque when the sum sd(n) of all natural divisors of n is divisible by n; let's call
brq(n) := sd(n)/n
the baroqueness of n. When a baroqueness of a number is two, brq(n) = 2, then it is called perfect. The smallest perfect number, known since the ancient times, is n=6. Indeed, in this case
sd(n) = 1+2+3+4+6 = 12 = 2*n
Questions about the baroque numbers are among the oldest, open (unresolved) problems of the whole mathematics. They are difficult and, today, somewhat isolated from the main developments, hence they are not as popular among the best mathematicians as they used to be in the past, when Euclid, Fermat, Decart, Euler and others were interested in them. Let me list the main open questions:
- are there infinitely many perfect numbers?
- are there infinitely many baroque numbers?
- does there exist an odd perfect number?
- does there exist an odd baroque number > 1?
The Euclid-Euler tandem (:-) proved that an even natural number n is perfect if and only if there exists a (unique) natural number p such that the following two conditions hold:
- 2p - 1 is prime;
- n = 2p-1*(2p-1)
Another old result (an ancient observation) is that brq(120) = 3, i.e. 120 is a baroque number, and its baroqueness is 3.
Sunday, July 20, 2008
Everyday language
The common goal of a conversation is to get to the point, without an unnecessary worrying about the precision in relation to the side issues, which are mentioned only casually. Possibly, the side items were mentioned without even meaning them as something to be dwelt upon anymore. We are humans and not robots, hence we add occasionally this or that.
The lack of precision of the everyday language is its strength, but strengths and weaknesses tend to walk together. The everyday language will be abused easily when there is no good will on one or more of the conversing parties. And one of the ways is to zero on the side issues, when the other party have not even dreamed about actually discussing them and having their each word scrutinized in a hostile way.
For example, in the everyday language we often don't make it clear whether we talk about the total set or about the existence of just one member of a set, as in the phrase "young people tend to be careless" - are ALL young people assumed to have a tendency to be careless or just SOME of them? The speaker most likely didn't care about it at the time of saying it. But the precision police would give that speaker hard time. The surprised and shocked and frustrated by the attack speaker would possibly defend its pronouncement, would get trapped into new situations, and would be doomed. If you attack someone who didn't mean any battle, then the person will say things ad hoc, and you will prevail, and the communication will lose. You will always find something, you will always generate some "faults" in the other person, and you will feel so righteous.
Add to this some relaxed phrases, some light jokes, an occasional not politically correct wording, and the person allowing itself of such a luxury will be doomed, there will be so much material against the unsuspecting soul. The winner prevails, but how intellectually and emotionally poorer is the winner's life! And how meager are such "victories"!
The lack of precision of the everyday language is its strength, but strengths and weaknesses tend to walk together. The everyday language will be abused easily when there is no good will on one or more of the conversing parties. And one of the ways is to zero on the side issues, when the other party have not even dreamed about actually discussing them and having their each word scrutinized in a hostile way.
For example, in the everyday language we often don't make it clear whether we talk about the total set or about the existence of just one member of a set, as in the phrase "young people tend to be careless" - are ALL young people assumed to have a tendency to be careless or just SOME of them? The speaker most likely didn't care about it at the time of saying it. But the precision police would give that speaker hard time. The surprised and shocked and frustrated by the attack speaker would possibly defend its pronouncement, would get trapped into new situations, and would be doomed. If you attack someone who didn't mean any battle, then the person will say things ad hoc, and you will prevail, and the communication will lose. You will always find something, you will always generate some "faults" in the other person, and you will feel so righteous.
Add to this some relaxed phrases, some light jokes, an occasional not politically correct wording, and the person allowing itself of such a luxury will be doomed, there will be so much material against the unsuspecting soul. The winner prevails, but how intellectually and emotionally poorer is the winner's life! And how meager are such "victories"!
Interpersonal (mis)communication, public and private
There is so much of miscommunication. A lot of it because people simply don't like one another, in which case the truth does not matter. There are also power games, ego games, psychological insecurities, etc., both in public and in personal exchanges. The difference of experience, of knowledge, of understanding, of class, between the participants also play a big role. Even when two people care about each other, the insecurities, the games, and similar, may still spoil the communication.
In adversary exchanges there is no point to even worry about such things. One should and often does address the public and not the adversary. Most of the time there is no chance to affect the adversary. For these reasons I have developed a flexible, neutral format for Internet discussion groups (it's an application of my Art of Agreement), but that is a topic for another thread.
Below, I'll provide an example of a (fictitious but realistic) conversation which went down the drain.
***
A. and D. talk about the treatment by different computer languages of the upper/lower case in the names of variables and similar. First languages had upper case only (e.g. Fortran). A. and D. remember that other old languages allowed for the either case; the lower and the upper case of any letter was treated as equivalent. Thus Mary mary MARY maRy mARy etc. would all stand for the same variable. This feature was widely used by programmers to enhance the readability of their programs. In particular A. was fond of the especially consistent and useful way this was done at the company for which A. had worked years ago.
Then D. mentions that a new option is offered by the wiki engine. According to this convenient in the wiki contest convention, wiki is sensitive to the case of all letters in the path except for the very first letter: you may write Albert_Einstein or albert_Einstein, and it will amount to the same link, but Albert_einstein and ALbert_Einstein will be different (and most likely each will be just a mistake).
D. knows A., hence he said carefully wiki engine. There are several wiki and wiki-like engines, while there is only one default wiki engine, the one that powers the English wikipedia (and several other wikipedias and similar portals, while there are also wiki portals which use different engines). All these things both A. and D. know well over the years of being somewhat interested in the topic (and D. being even active in some wiki portals; and each of them knows that the other one knows). D. was careful to say wiki engine, while it would be an exaggeration to spent more words on this precision. Nevertheless A. objects that not all wikis are alike, and asks: how do you know that all wikis are like this? D. answered that he knows only about three of them, including the English wikipedia. The conversation is ridiculously going along this line, with A. accusing D. of being a liar! According to A., the other person claimed in the beginning that ALL wikis are supporting the mixed convention. D. knows very well that it was not the case, of course not. So D., irritated, responds that it is A. who is the "liar". In a sense, D. even believes that this is the case – that A. is manipulating the conversation instead of allowing the pleasure of joint exchanges of knowledge and reminiscences.
Super! :-) Now, what is the mechanism of such disasters? It seems that A. has the need of being right, and being the only one who is right. Thus others have to be wrong. The conversations for A. are trials where he is the prosecutor, the investigation officer, the judge and the jury. While D. naively treats the conversation like it were about the upper/lower case option, it turns out that the conversation is about D., that D. has to defend in true or imaginary detail each of D.'s casual pronouncements -- surprise, surprise! A. believes in being always right, that others are sloppy, illogical and stupid. A. is sane enough and has the necessary self knowledge about A. not being an Einstein, that A. has not won a Noble prize nor the wealth of Bill Gates. Thus to have its self-respect A. needs to put others down. A. will go so far (and with a strong conviction! -- ridiculous as it sounds) as to call others liars, where it is A.'s inability to listen and to stick to the topic. One may, like A., have difficulties to concentrate and catch all the fine points but then one should allow for the margin of not getting them, and of not understanding everything all the time. A good conversation requires patience and trust. And first of all, a conversation should not be a trial on which one puts the other person, who never got any court invoice. When a conversation is strictly about a computer language option of upper/lower case , with neither partner having any material interest in the topic (just intellectual curiosity), A. has no right to switch to an investigation of the D.'s personality qualities (say, to true or imagined D's inability of expressing things precisely) -- that's absolutely wrong.
The basis for such disasters is psychological, but there is also a tool (a method), which A. uses with a practiced agility to achieve such spectacular negative effects. The A.'s method is grounded in the common usage of the everyday language (as opposed to scientific language). See the next post.
In adversary exchanges there is no point to even worry about such things. One should and often does address the public and not the adversary. Most of the time there is no chance to affect the adversary. For these reasons I have developed a flexible, neutral format for Internet discussion groups (it's an application of my Art of Agreement), but that is a topic for another thread.
Below, I'll provide an example of a (fictitious but realistic) conversation which went down the drain.
***
A. and D. talk about the treatment by different computer languages of the upper/lower case in the names of variables and similar. First languages had upper case only (e.g. Fortran). A. and D. remember that other old languages allowed for the either case; the lower and the upper case of any letter was treated as equivalent. Thus Mary mary MARY maRy mARy etc. would all stand for the same variable. This feature was widely used by programmers to enhance the readability of their programs. In particular A. was fond of the especially consistent and useful way this was done at the company for which A. had worked years ago.
Then D. mentions that a new option is offered by the wiki engine. According to this convenient in the wiki contest convention, wiki is sensitive to the case of all letters in the path except for the very first letter: you may write Albert_Einstein or albert_Einstein, and it will amount to the same link, but Albert_einstein and ALbert_Einstein will be different (and most likely each will be just a mistake).
D. knows A., hence he said carefully wiki engine. There are several wiki and wiki-like engines, while there is only one default wiki engine, the one that powers the English wikipedia (and several other wikipedias and similar portals, while there are also wiki portals which use different engines). All these things both A. and D. know well over the years of being somewhat interested in the topic (and D. being even active in some wiki portals; and each of them knows that the other one knows). D. was careful to say wiki engine, while it would be an exaggeration to spent more words on this precision. Nevertheless A. objects that not all wikis are alike, and asks: how do you know that all wikis are like this? D. answered that he knows only about three of them, including the English wikipedia. The conversation is ridiculously going along this line, with A. accusing D. of being a liar! According to A., the other person claimed in the beginning that ALL wikis are supporting the mixed convention. D. knows very well that it was not the case, of course not. So D., irritated, responds that it is A. who is the "liar". In a sense, D. even believes that this is the case – that A. is manipulating the conversation instead of allowing the pleasure of joint exchanges of knowledge and reminiscences.
Super! :-) Now, what is the mechanism of such disasters? It seems that A. has the need of being right, and being the only one who is right. Thus others have to be wrong. The conversations for A. are trials where he is the prosecutor, the investigation officer, the judge and the jury. While D. naively treats the conversation like it were about the upper/lower case option, it turns out that the conversation is about D., that D. has to defend in true or imaginary detail each of D.'s casual pronouncements -- surprise, surprise! A. believes in being always right, that others are sloppy, illogical and stupid. A. is sane enough and has the necessary self knowledge about A. not being an Einstein, that A. has not won a Noble prize nor the wealth of Bill Gates. Thus to have its self-respect A. needs to put others down. A. will go so far (and with a strong conviction! -- ridiculous as it sounds) as to call others liars, where it is A.'s inability to listen and to stick to the topic. One may, like A., have difficulties to concentrate and catch all the fine points but then one should allow for the margin of not getting them, and of not understanding everything all the time. A good conversation requires patience and trust. And first of all, a conversation should not be a trial on which one puts the other person, who never got any court invoice. When a conversation is strictly about a computer language option of upper/lower case , with neither partner having any material interest in the topic (just intellectual curiosity), A. has no right to switch to an investigation of the D.'s personality qualities (say, to true or imagined D's inability of expressing things precisely) -- that's absolutely wrong.
The basis for such disasters is psychological, but there is also a tool (a method), which A. uses with a practiced agility to achieve such spectacular negative effects. The A.'s method is grounded in the common usage of the everyday language (as opposed to scientific language). See the next post.
Monday, June 2, 2008
Dabanese 2008. Syntax.
A dabanese reader/writer, dabaner for short, has to know only four notions and the simple syntax rules. The notions are:
Phrases { A B C } and { B C A } are in principle equivalent, they have the same meaning in dabanese, the difference is at the most artistic and similar. When you quote a daba text then you may change the order of subphrases in the unordered phrases (unless there is a claim of the completely exact quoting). In particular it is legal to change the order of subphrases in unordered phrases when quoting in legal situations. On the other hand you must preserve the order of subpphrases of the ordered daba phrase, when you quote them even in informal situations or otherwise it is not a quote. Any change of order in ordered phrase is likely to result in a drastic change of its meaning. Claiming to be quoting when changing on purpose the order in ordered phrases would be cheating, while an inadvertent change would be an irresponsible sloppiness.
Rules 2. and 3. applied to the empty sequence give us phrases { } and ( ), which stand for "nothing" or for emptiness, etc. There will be dabanese dictionaries but there always will be the room for the customary poetic interpretation of the text by the dabaners, depending on the context, just as in the natural languages. For instance, [ hmn ] phrase tells us that human is the subject (of the respective portion of a daba text), as in { ( ) [ hmn] }, which points perhaps to a human who does not represent anything, who is totally uninteresting. Now let's consider phrase [ [ hmn ] ], with a double accent. To me it means that the topic is the attention on human, while I am afraid that to many people it will mean an extra strong accent on human. Thus daba phrase { ( ) [ [ hmn ] ] } means to me something like "an empty (useless) attention on human", while to others it may mean that especially all or some or particular human is silly (more silly than non-humans or other humans), with the extra emphasis on the group which is meant. Possibly, the same phrases will mean different things to different people.
Dabanese cannot and does not attempt to define every reading of the dabanese text. For instance someone may talk about arithmetic calculations using the infix notation ( 2 + 5 ), and another may use the postfix ( 2 5 + ). it is up to dabaners to understand each other. In the given text they should use the ordered phrase in each case. But if they want to make sure to be understood they may add an extra description: let ideogram rPn stand for the reversed Polish notation. Then one may write { rPn ( 2 5 + ) }. Perhaps the best is to write it as follows: { 2 5 [ + ] }. Now it is pretty clear. The subject is sum, but it is a sum described by 2 and 5, so it is 7. Then phrases { 2 [ + ] 5 } and { [ + ] 5 2 } mean the same, i.e. 7. A different meaning would have a phrase like ( [2] + 5) – it would mean something like: 2, to which 5 was/is/will be added.
A daba phrase without any subject (i.e. when none of its subjects are accented; even when a subject of a subject may be accented) are called lists – there are ordered and unordered lists. A daba phrase may have more than one accent but it is not advised. A strict daba phrase should have at the most one accent. If you want to have more than one then do it for instance as follows: { A B [ { C D } ] } rather than by { A B [ C ] [ D] }, but it's up to you.
- ideogram
- unordered daba phrase
- ordered daba phrase
- accent (subject)
- ideogram is a daba phrase;
- a finite sequence of daba phrases enclosed between braces, {...}, is a daba phrase – it's called an unordered phrase;
- a finite sequence of daba phrases enclosed between parentheses, (...), is a daba phrase – it's called an ordered phrase;
- a daba phrase enclosed in brackets, [...], is a daba phrase – it's called an accented phrase or a subject;
- all daba phrases are obtained by a finite application of rules 1-4.
Phrases { A B C } and { B C A } are in principle equivalent, they have the same meaning in dabanese, the difference is at the most artistic and similar. When you quote a daba text then you may change the order of subphrases in the unordered phrases (unless there is a claim of the completely exact quoting). In particular it is legal to change the order of subphrases in unordered phrases when quoting in legal situations. On the other hand you must preserve the order of subpphrases of the ordered daba phrase, when you quote them even in informal situations or otherwise it is not a quote. Any change of order in ordered phrase is likely to result in a drastic change of its meaning. Claiming to be quoting when changing on purpose the order in ordered phrases would be cheating, while an inadvertent change would be an irresponsible sloppiness.
Rules 2. and 3. applied to the empty sequence give us phrases { } and ( ), which stand for "nothing" or for emptiness, etc. There will be dabanese dictionaries but there always will be the room for the customary poetic interpretation of the text by the dabaners, depending on the context, just as in the natural languages. For instance, [ hmn ] phrase tells us that human is the subject (of the respective portion of a daba text), as in { ( ) [ hmn] }, which points perhaps to a human who does not represent anything, who is totally uninteresting. Now let's consider phrase [ [ hmn ] ], with a double accent. To me it means that the topic is the attention on human, while I am afraid that to many people it will mean an extra strong accent on human. Thus daba phrase { ( ) [ [ hmn ] ] } means to me something like "an empty (useless) attention on human", while to others it may mean that especially all or some or particular human is silly (more silly than non-humans or other humans), with the extra emphasis on the group which is meant. Possibly, the same phrases will mean different things to different people.
Dabanese cannot and does not attempt to define every reading of the dabanese text. For instance someone may talk about arithmetic calculations using the infix notation ( 2 + 5 ), and another may use the postfix ( 2 5 + ). it is up to dabaners to understand each other. In the given text they should use the ordered phrase in each case. But if they want to make sure to be understood they may add an extra description: let ideogram rPn stand for the reversed Polish notation. Then one may write { rPn ( 2 5 + ) }. Perhaps the best is to write it as follows: { 2 5 [ + ] }. Now it is pretty clear. The subject is sum, but it is a sum described by 2 and 5, so it is 7. Then phrases { 2 [ + ] 5 } and { [ + ] 5 2 } mean the same, i.e. 7. A different meaning would have a phrase like ( [2] + 5) – it would mean something like: 2, to which 5 was/is/will be added.
A daba phrase without any subject (i.e. when none of its subjects are accented; even when a subject of a subject may be accented) are called lists – there are ordered and unordered lists. A daba phrase may have more than one accent but it is not advised. A strict daba phrase should have at the most one accent. If you want to have more than one then do it for instance as follows: { A B [ { C D } ] } rather than by { A B [ C ] [ D] }, but it's up to you.
Sunday, June 1, 2008
Dabanese 2008. Pigeon ideograms.
(I see the "New Post" user option, but not "Edit" user option - how frustrating since I want to correct typos spontaneously, when I see them).
I'll write about dabanese from scratch. Writing from scratch is my weakness. After a break I am incapable to just continue.
I'll start to create a dictionary of ideograms, still in their pigeon form. For the sake of convenience I'll consider all English and Polish nouns, in their main form, and noun like words, as pigeon ideograms. However, some ideograms will start to have a legal status. At least conceptually (not graphically). Here we go (ideograms in the same line are synonymous):
I'll write about dabanese from scratch. Writing from scratch is my weakness. After a break I am incapable to just continue.
I'll start to create a dictionary of ideograms, still in their pigeon form. For the sake of convenience I'll consider all English and Polish nouns, in their main form, and noun like words, as pigeon ideograms. However, some ideograms will start to have a legal status. At least conceptually (not graphically). Here we go (ideograms in the same line are synonymous):
- := – ideogram of definition.
- { {} := { } } – this dabanese definition tells us that ideogram {} stands for nothing or Polish nic. Actually, () and nic are synonymous ideograms for nothing, i.e. each of them is legally equivalent to ideogram {}:
() – synonym of {};
nic – synonym of {}; - daba – the ideogram for everything, as well as for the (universal) data base daba:
∀ – synonym for the ideogram daba. - self – ideogram of the reference of the source of the given dabanese phrase.
się – synonym of the ideogram self.
- :=
- {} () nic
- daba ∀
- self się
2008-June
I am slowly, a bit at the time, learning about the details of this blog's logistic (of the user interface). E.g. I just saw the "new post" menu option at the top of this blog window. Such small details can keep me back. I am hopeless.
I ran into (Artur P)'s blog. Somehow it had a very positive influence on me, made me come back here too, and to take another look at my present situation. Perhaps, with a bit of discipline, I can still squeeze from myself a bit of consistent, constructive effort. My main problem is, or I should mbeliwve that it is psychological. Since Biblical time people understand the necessity of Sabbath or Sunday, and of the holidays, while for years I have none of them. However, iof I somehow fool myself into pretending that I have some, then perhaps I will get going a bit instead of having excuses. Chess players are especially good in making excuses. In this respect I am by far a world champion (otherwise I am another poor, club level chess player).
As a first step let me write some of my present projects and activities (besides assisting my father):
Artur's blog is interesting. In particular, he has poetic photos of the Cracow's suburbs, Kazimierz & Pogórze.
I ran into (Artur P)'s blog. Somehow it had a very positive influence on me, made me come back here too, and to take another look at my present situation. Perhaps, with a bit of discipline, I can still squeeze from myself a bit of consistent, constructive effort. My main problem is, or I should mbeliwve that it is psychological. Since Biblical time people understand the necessity of Sabbath or Sunday, and of the holidays, while for years I have none of them. However, iof I somehow fool myself into pretending that I have some, then perhaps I will get going a bit instead of having excuses. Chess players are especially good in making excuses. In this respect I am by far a world champion (otherwise I am another poor, club level chess player).
As a first step let me write some of my present projects and activities (besides assisting my father):
- I participate in a private Internet forum for my school classmates. There are fewer and fewer of us left. The forum has strictly sentimental value. But so what? Isn't it about being humans (for better or worse), and not just about achievements etc? There were really only 7 of us active (on and off). Now it's 9. Others are lurking or not involved (while formally all classmates are automatically among participants, if their email is known).
- I have started to write, in TeX :-), a consecutive article for Delta. This time about the magic squares. I have go back to it.
- I should truly concentrate on my dabanese language, especially, that I got Artur interested (at least for the moment).
- I should go back to writing about my "The art of agreement". In particular, I have written recently 4 installments in Polish for an electronic zine, and I should continue. Somehow that zine is not making the writing process attractive. I should still continue.
- A reincarnation of a poetic Polish portal is in making. Somehow participants are passive. The main force of the project, PŁ, set up a deadline around June 20 something. I should finish writing the statue of that portwal without worrying about inactivity of others. If that portal did happen I would feel real good, hopefully I would write there my more complete view of poetry (it goes back to the old views on poetry). I wish such a nice portal existed in the past, not just for poetry but also in other domains - the quality of my life (and of others, I believe) would be higher.
Artur's blog is interesting. In particular, he has poetic photos of the Cracow's suburbs, Kazimierz & Pogórze.
Friday, January 11, 2008
Preschool mathematics
Outstretch two fingers of your left hand, and three of the right. Ask you child: which is greater?
Now, do not count. Just match the outstretched left fingers with the right ones. One right finger will be left unmatched. Thus there were more fingers on the right than on the left.
Repeat this exercise with different combinations of the outstretched fingers. Even when you ask about three and three fingers, you may still use different combinations of the three fingers.
Now show your child:
and ask, which is greater?
You may rearrange the patterns as follows
The answer is clear.
Conclusion: you don't need to count to compare.
Do the same for other squares and rectangles, e.g. for 5x5 versus 4x6, or for 4x5 versus 3x6, etc. Even small children can do these comparisons, since they do not need to count. What's more important, this way is not boring. It gives an insight into mathematics (set theory, geometry, algebra).
Now, do not count. Just match the outstretched left fingers with the right ones. One right finger will be left unmatched. Thus there were more fingers on the right than on the left.
Repeat this exercise with different combinations of the outstretched fingers. Even when you ask about three and three fingers, you may still use different combinations of the three fingers.
Now show your child:
versus
* * *
* * *
* * *
* * * *
* * * *
and ask, which is greater?
You may rearrange the patterns as follows
versus
* * *
* * *
* * *
* * * *
* * * *
The answer is clear.
Conclusion: you don't need to count to compare.
Do the same for other squares and rectangles, e.g. for 5x5 versus 4x6, or for 4x5 versus 3x6, etc. Even small children can do these comparisons, since they do not need to count. What's more important, this way is not boring. It gives an insight into mathematics (set theory, geometry, algebra).
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