a veritable holocaust of opportunities, missed to death
each piece of writing isn't how I really feel
its only the times that I choose to capture my mind into ink and quill
several moods have to align in order for word to solidify out
almost like a rain drop condensing in a cloud, forming rain words
the proper conditions have to be right for the storm
those are:
a care for introspection
whatever shape or form the analysis carves into me
a belief that I am thinking of something profound enough to tolerate the pinching linear 1 dimensional process known as writing
and how well I can grasp and capture that analysis into words, they don't capture well...
but my mind does reek with ideas
a fountain of thoughts, sometimes a fire hose, some times a trickle
some amazing, some pathetic
some inspiring, some toxic
never the less, my writing doesn't represent my mind well
it is only in those conditions and hence those filters that anything is even written at all
and everyday I think of something worth writing, every hour I do so
and they are lost
a veritable holocaust of opportunities, missed to death
Wednesday, March 23, 2011
Saturday, January 8, 2011
Variable Bases
So I was thinking about what it would take to change a large integer, say:
But, I don't think such a thing is possible. But it is a conjecture of mine that it IS possible given variable bases for each decimal space.
so for instance, the way we think of number would have a base 10 at each decimal space. so for the number 547913765
5 4 7 9 1 3 7 6 5
[ 10 , 10 , 10 , 10 , 10 , 10 , 10 , 10 , 10 ]
Well, I think and believe there is a possible configuration of these bases that can turn any number into almost any other number. so if we were to plug a base 10 number into another base system say:
[ 7 , 7 , 7 , 3 , 10 , 4 , 7 , 11 , 32 ]
It would come out radically different. You run into problems with representing number over base 10 of course, and can only really sanely represent up to base 36 which would be 0123456789abcdefghijklmnopqrstuvwxyz.
My general question and belief is that any number can be represented as any other number of the same lexiconographical length. so my question is, using what variable bases of
[ I , H , G , F , E , D , C , B , A ]
can
897123564981762397869565
and subject it to a different base so as to turn said number into say444444444444444444444444
But, I don't think such a thing is possible. But it is a conjecture of mine that it IS possible given variable bases for each decimal space.
so for instance, the way we think of number would have a base 10 at each decimal space. so for the number 547913765
5 4 7 9 1 3 7 6 5
[ 10 , 10 , 10 , 10 , 10 , 10 , 10 , 10 , 10 ]
Well, I think and believe there is a possible configuration of these bases that can turn any number into almost any other number. so if we were to plug a base 10 number into another base system say:
[ 7 , 7 , 7 , 3 , 10 , 4 , 7 , 11 , 32 ]
It would come out radically different. You run into problems with representing number over base 10 of course, and can only really sanely represent up to base 36 which would be 0123456789abcdefghijklmnopqrstuvwxyz.
My general question and belief is that any number can be represented as any other number of the same lexiconographical length. so my question is, using what variable bases of
[ I , H , G , F , E , D , C , B , A ]
can
547913765
be represented as98723459
????????????????
The problem is I don't know of a fast way to code this into python YET. I'll keep you posted.
There might be some numbers that can not, given any variable bases, reach another number. Those would be the 'primes' of such a system.
man I got a wonky view of prime numbers
Wednesday, December 1, 2010
Mot Nath
Why allies are closer to war than enemies.
Its an interesting phenomenon I've witnessed and thought about recently. Why in fighting can occur amongst those who are ideologically closer to each other, rather than focussing the energy against those most distant from a point of view.
I hypothosis that this tactic of causing 'family feuds' has been used time and time again to weaken an enemy.
On the surface I recognise quarls can start from the less wise in the group.
Well, here is the hypothesis in a nutshell. It is easier to understand and judge a person who is closer to your way of thinking than it is an outsider. I can harness and carry more disdain and disgust over someone closer to my lifestyle than I can against someone who's way of life is utterly foreign to me. This has lead to some of the stupid quarls of our life time. It is why Pakistan and India point warheads at each other instead of at the country that ruled them both for so long. It is why black men are killing black men in LA instead of focusing on the racism that sewed the fields of hatred.
I can feel a closer level of disgust for my brother than I can for my enemy. Two countrymen who speak the same language can get caught up in the verbal meconium where as a foreigners tongue stings not as the hurtful words are meaningless. Only those who really know me can insult me and hurt me.
So because of this possibly volatile combustion due to close proximity of ideals, it would be easy to start infighting and to continue to fan the flames of self imposing degradation. No one knows your enemies weakness like your enemy, and if you can get them to go to war with themselves, you can control them better.
more of a mental notepad than anything - will work on this
Its an interesting phenomenon I've witnessed and thought about recently. Why in fighting can occur amongst those who are ideologically closer to each other, rather than focussing the energy against those most distant from a point of view.
I hypothosis that this tactic of causing 'family feuds' has been used time and time again to weaken an enemy.
On the surface I recognise quarls can start from the less wise in the group.
Well, here is the hypothesis in a nutshell. It is easier to understand and judge a person who is closer to your way of thinking than it is an outsider. I can harness and carry more disdain and disgust over someone closer to my lifestyle than I can against someone who's way of life is utterly foreign to me. This has lead to some of the stupid quarls of our life time. It is why Pakistan and India point warheads at each other instead of at the country that ruled them both for so long. It is why black men are killing black men in LA instead of focusing on the racism that sewed the fields of hatred.
I can feel a closer level of disgust for my brother than I can for my enemy. Two countrymen who speak the same language can get caught up in the verbal meconium where as a foreigners tongue stings not as the hurtful words are meaningless. Only those who really know me can insult me and hurt me.
So because of this possibly volatile combustion due to close proximity of ideals, it would be easy to start infighting and to continue to fan the flames of self imposing degradation. No one knows your enemies weakness like your enemy, and if you can get them to go to war with themselves, you can control them better.
more of a mental notepad than anything - will work on this
Friday, November 12, 2010
Factor Forward
So I decided to factor 420 for NO REASON WHATSOEVER.
And I came to 2 2 3 5 7
and due to my escapades in project euler, I looked at those numbers and said "Huh, what if they were concatenated to form a new number? and the factor of THOSE???"
well, as it turns out - 22357 has the factors 79 and 283
and 79283 is - itself - a PRIME
OOOoooohhhh goody. I due hope that all numbers can reduce to the concatenated form of their divisors. I'll keep you posted on the result after I create the program and run the first 1000 or so numbers.
++++++++++++++++++++++++++++++++++++++++++++++
SO - this is how it goes my little mathletes:
Unfortunately some of the numbers continue to blow up beyond a limit.
The fastest way to run this test was to first create a nice little list of prime numbers below N. easy peasy according to THE sieve.
My first list was only up to 1 billion (I use only here in jest)
AND I tested 1 - 1000
well, up to 1 billion pre-created prime tests: (DRUM ROLL please)
592 reached a prime -- 406 of them grew beyond 1 billion
thats - a yes for an election atleast . . . . :O(
BUT - if I bump my precreated list to 5 billion
WELL, from 1 to 1000 had THIS outcome
ahem
641 reached a prime - 357 grew beyond 5 billion! ! ! ! ! ! ! ! ! ! - OH HAPPY DAY
WELL, while I was typing this update - I was rendering another outcome
Survey SAYS:
from 1 to 10,000 under 1 billion
4071 reached a prime - 5927 blew beyond 1 billion
>:O[
damn
ok, well, as i type this - MrCool is cranking out 1 - 10,000 under 5 billion
we shall see. . . . . . . . .
And I came to 2 2 3 5 7
and due to my escapades in project euler, I looked at those numbers and said "Huh, what if they were concatenated to form a new number? and the factor of THOSE???"
well, as it turns out - 22357 has the factors 79 and 283
and 79283 is - itself - a PRIME
OOOoooohhhh goody. I due hope that all numbers can reduce to the concatenated form of their divisors. I'll keep you posted on the result after I create the program and run the first 1000 or so numbers.
++++++++++++++++++++++++++++++++++++++++++++++
SO - this is how it goes my little mathletes:
Unfortunately some of the numbers continue to blow up beyond a limit.
The fastest way to run this test was to first create a nice little list of prime numbers below N. easy peasy according to THE sieve.
My first list was only up to 1 billion (I use only here in jest)
AND I tested 1 - 1000
well, up to 1 billion pre-created prime tests: (DRUM ROLL please)
592 reached a prime -- 406 of them grew beyond 1 billion
thats - a yes for an election atleast . . . . :O(
BUT - if I bump my precreated list to 5 billion
WELL, from 1 to 1000 had THIS outcome
ahem
641 reached a prime - 357 grew beyond 5 billion! ! ! ! ! ! ! ! ! ! - OH HAPPY DAY
WELL, while I was typing this update - I was rendering another outcome
Survey SAYS:
from 1 to 10,000 under 1 billion
4071 reached a prime - 5927 blew beyond 1 billion
>:O[
damn
ok, well, as i type this - MrCool is cranking out 1 - 10,000 under 5 billion
we shall see. . . . . . . . .
Friday, October 22, 2010
Pharaoh Shuffle
I just learned the trick of Faro Shuffling.
Lets say you have a brand new deck of cards, each suit organized ace to king. A faro shuffle would be what you would consider a perfect shuffle. Split the deck into even halfs, then create a new deck using one card at a time from each half deck. Seems random enough, but if you were to do this 8 times - you would get your original order back.
I just tried this with 26 cards, with hearts and clubs. I laid them out on the table face up each time to witness the "randomness" of them. I thought I had made a mistake somewhere, but to my astonishment, they returned to their original order. I also doubted myself in the middle thinking "Maybe this only works with 52 cards." But my intuition told me that this would work with any even number of items. And so I have proven it to myself.
Any even number of items in a certain order, when faro shuffled 8 times, will reproduce that order.
I totally thought there would be a nice java applet somewhere on the net showing this amazing truth, but there is not. Google searches for faro shuffling produce card tricks and not math. I would write a program for this, but I'm not too good with arrays.
Lets say you have a brand new deck of cards, each suit organized ace to king. A faro shuffle would be what you would consider a perfect shuffle. Split the deck into even halfs, then create a new deck using one card at a time from each half deck. Seems random enough, but if you were to do this 8 times - you would get your original order back.
I just tried this with 26 cards, with hearts and clubs. I laid them out on the table face up each time to witness the "randomness" of them. I thought I had made a mistake somewhere, but to my astonishment, they returned to their original order. I also doubted myself in the middle thinking "Maybe this only works with 52 cards." But my intuition told me that this would work with any even number of items. And so I have proven it to myself.
Any even number of items in a certain order, when faro shuffled 8 times, will reproduce that order.
I totally thought there would be a nice java applet somewhere on the net showing this amazing truth, but there is not. Google searches for faro shuffling produce card tricks and not math. I would write a program for this, but I'm not too good with arrays.
Thursday, October 21, 2010
Perfect Number play
So there is this set of numbers out there that just happen to have their proper divisors add up to itself. For some reason, everyone wants to call them "Perfect numbers." I think thats a bit presumptuous, but whatever. I didn't make it up. So a perfect number, again, is defined as a number who's divisors add up to itself. See the wikipedia article and the OEIS list for more info on them.
Well, what if you continued to apply the "perfect number operation" onto a number and then its outcome over and over again? Random example:
216 has the divisors 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72 and 108.
so
1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 27 + 36 + 54 + 72 + 108 = 384
so then we look at 384 who's divisors are
1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 32 + 48 + 64 + 96 + 128 + 192 = 636
and so on with 636 which turns into 876
876 -> 1196
1196 -> 1156
1156 -> 993
993 -> 335
335 -> 73
73 -> 1
and bingo bango we have come to an end.
Not all numbers come to a small end like this though. Some of the numbers get HUGE (30 out of the first 1000 actually) I didn't calculate past 100,000,000 ( 100 million) - better things to do you see. Also, some of the numbers get caught into infinite loops. Once you come across one of the perfect numbers, they are their own outcome and its futile to work on it further. Also 220's outcome is 284 - and 284's is 220!! Also 1184's is 1210 and 1210 is 1184!!! very interesting relations there.
SO I present to you the list from 10 to 1000 of continued perfect number operations. I need to come up with better names for things....what should I call this?
One of the neat ones:
864 -> 1656 -> 3024 -> 6896 -> 6496 -> 8624 -> 12580 -> 16148 -> 14764 -> 11080 -> 13940 -> 17812 -> 14304 -> 23496 -> 41304 -> 62016 -> 120864 -> 196656 -> 343488 -> 565832 -> 495118 -> 316322 -> 158164 -> 118630 -> 94922 -> 52150 -> 59450 -> 57730 -> 51134 -> 27754 -> 13880 -> 17440 -> 24140 -> 30292 -> 22726 -> 14498 -> 9262 -> 5930 -> 4762 -> 2384 -> 2266 -> 1478 -> 742 -> 554 -> 280 -> 440 -> 640 -> 890 -> 730 -> 602 -> 454 -> 230 -> 202 -> 104 -> 106 -> 56 -> 64 -> 63 -> 41 -> 1
Well, what if you continued to apply the "perfect number operation" onto a number and then its outcome over and over again? Random example:
216 has the divisors 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72 and 108.
so
1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 27 + 36 + 54 + 72 + 108 = 384
so then we look at 384 who's divisors are
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128 and 192
so1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 32 + 48 + 64 + 96 + 128 + 192 = 636
and so on with 636 which turns into 876
876 -> 1196
1196 -> 1156
1156 -> 993
993 -> 335
335 -> 73
73 -> 1
and bingo bango we have come to an end.
Not all numbers come to a small end like this though. Some of the numbers get HUGE (30 out of the first 1000 actually) I didn't calculate past 100,000,000 ( 100 million) - better things to do you see. Also, some of the numbers get caught into infinite loops. Once you come across one of the perfect numbers, they are their own outcome and its futile to work on it further. Also 220's outcome is 284 - and 284's is 220!! Also 1184's is 1210 and 1210 is 1184!!! very interesting relations there.
SO I present to you the list from 10 to 1000 of continued perfect number operations. I need to come up with better names for things....what should I call this?
(seems the service I was using to link my large text files doesn't want me to. I need to find a different one. Anyone have any suggestions?)
One of the neat ones:
864 -> 1656 -> 3024 -> 6896 -> 6496 -> 8624 -> 12580 -> 16148 -> 14764 -> 11080 -> 13940 -> 17812 -> 14304 -> 23496 -> 41304 -> 62016 -> 120864 -> 196656 -> 343488 -> 565832 -> 495118 -> 316322 -> 158164 -> 118630 -> 94922 -> 52150 -> 59450 -> 57730 -> 51134 -> 27754 -> 13880 -> 17440 -> 24140 -> 30292 -> 22726 -> 14498 -> 9262 -> 5930 -> 4762 -> 2384 -> 2266 -> 1478 -> 742 -> 554 -> 280 -> 440 -> 640 -> 890 -> 730 -> 602 -> 454 -> 230 -> 202 -> 104 -> 106 -> 56 -> 64 -> 63 -> 41 -> 1
Wednesday, October 20, 2010
Palindrone
So about 6 months ago I made a list of numbers between 100000 and 999999 that are prime in both lexiconographical order.
here's a sample:
384187, 384203, 384253, 384257, 384301, 384359, 384383, 384473, 384497, 384581, 384589, 384611, 384673, 384737, 384751, 384821, 384841, 384889, 384913, 384961, 385039, 385079, 385087, 385159, 385171, 385223, 385249, 385267, 385291, 385321, 385331, 385393, 385471, 385621, 385709, 385741, 385811, 385837, 385843, 385901, 385991, 386017, 386041, 386119, 386149
The full list can be found here:
http://ompldr.org/vNXZjbw
I don't recall how I isolated this list, but here it is none the less.
Yes I know that Palindrome isn't spelt with an "n"
And no I didn't know what lexiconographical even meant until someone on the net told me.
Usefulness: 0.003
Fun: 2.3
here's a sample:
384187, 384203, 384253, 384257, 384301, 384359, 384383, 384473, 384497, 384581, 384589, 384611, 384673, 384737, 384751, 384821, 384841, 384889, 384913, 384961, 385039, 385079, 385087, 385159, 385171, 385223, 385249, 385267, 385291, 385321, 385331, 385393, 385471, 385621, 385709, 385741, 385811, 385837, 385843, 385901, 385991, 386017, 386041, 386119, 386149
The full list can be found here:
http://ompldr.org/vNXZjbw
I don't recall how I isolated this list, but here it is none the less.
Yes I know that Palindrome isn't spelt with an "n"
And no I didn't know what lexiconographical even meant until someone on the net told me.
Usefulness: 0.003
Fun: 2.3
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