tag:blogger.com,1999:blog-81013644965959326212014-10-04T23:31:14.187-07:00A Hike Through The Infinite ForestThe Hikerhttp://www.blogger.com/profile/16612988455097880734noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-8101364496595932621.post-680527562422008872011-03-23T04:56:00.001-07:002011-03-23T04:56:49.140-07:00writinga veritable holocaust of opportunities, missed to death<br /><br />each piece of writing isn't how I really feel<br />its only the times that I choose to capture my mind into ink and quill<br />several moods have to align in order for word to solidify out<br />almost like a rain drop condensing in a cloud, forming rain words<br />the proper conditions have to be right for the storm<br /><br />those are:<br /> a care for introspection<br />whatever shape or form the analysis carves into me<br />a belief that I am thinking of something profound enough to tolerate the pinching linear 1 dimensional process known as writing<br />and how well I can grasp and capture that analysis into words, they don't capture well...<br /><br /><br />but my mind does reek with ideas<br />a fountain of thoughts, sometimes a fire hose, some times a trickle<br />some amazing, some pathetic<br />some inspiring, some toxic<br /><br />never the less, my writing doesn't represent my mind well<br />it is only in those conditions and hence those filters that anything is even written at all<br /><br />and everyday I think of something worth writing, every hour I do so<br />and they are lost<br /><br />a veritable holocaust of opportunities, missed to deathThe Hikerhttp://www.blogger.com/profile/16612988455097880734noreply@blogger.com0tag:blogger.com,1999:blog-8101364496595932621.post-15640298893553054762011-01-08T09:05:00.000-08:002011-01-08T09:08:09.461-08:00Variable BasesSo I was thinking about what it would take to change a large integer, say:<br /><div style="color: #0b5394;">897123564981762397869565</div>and subject it to a different base so as to turn said number into say<br /><div style="color: #134f5c;">444444444444444444444444</div><br />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.<br /><br />so for instance, the way we think of number would have a base 10 at each decimal space. so for the number 547913765 <br /><br /> 5 4 7 9 1 3 7 6 5 <br />[ 10 , 10 , 10 , 10 , 10 , 10 , 10 , 10 , 10 ]<br /><br /><br />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:<br /><br />[ 7 , 7 , 7 , 3 , 10 , 4 , 7 , 11 , 32 ]<br /><br />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.<br /><br />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 <br /><br />[ I , H , G , F , E , D , C , B , A ]<br /><br />can<br /><div style="color: #134f5c;">547913765</div>be represented as<br /><div style="color: #38761d;">98723459</div><div style="color: #38761d;"><br /></div><div style="color: #cc0000;"><span style="font-size: large;">???????????????? </span></div><div style="color: #cc0000;"><br /></div><div style="color: #cc0000;"><span style="color: black; font-size: small;"> The problem is I don't know of a fast way to code this into python YET. I'll keep you posted.</span></div><div style="color: #cc0000;"><span style="color: black; font-size: small;"><br /></span></div><div style="color: #cc0000;"><span style="color: black; font-size: small;">There might be some numbers that can not, given any variable bases, reach another number. Those would be the 'primes' of such a system.</span></div><div style="color: #cc0000;"><span style="color: black; font-size: small;"><br /></span></div><div style="color: #cc0000;"><span style="color: black; font-size: small;">man I got a wonky view of prime numbers</span></div>The Hikerhttp://www.blogger.com/profile/16612988455097880734noreply@blogger.com0tag:blogger.com,1999:blog-8101364496595932621.post-37095317508620751322010-12-01T02:43:00.000-08:002010-12-01T02:43:11.082-08:00Mot NathWhy allies are closer to war than enemies.<br /><br />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.<br /><br />I hypothosis that this tactic of causing 'family feuds' has been used time and time again to weaken an enemy.<br /><br />On the surface I recognise quarls can start from the less wise in the group.<br /><br />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.<br /><br />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 <span class="imageTitle">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.</span><br /><span class="imageTitle"><br /></span><br /><span class="imageTitle">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.</span><br /><span class="imageTitle"><br /></span><br /><span class="imageTitle">more of a mental notepad than anything - will work on this</span>The Hikerhttp://www.blogger.com/profile/16612988455097880734noreply@blogger.com0tag:blogger.com,1999:blog-8101364496595932621.post-10913456590854405852010-11-12T01:38:00.000-08:002010-11-12T04:33:48.793-08:00Factor ForwardSo I decided to factor 420 for <a href="http://norml.org/">NO REASON WHATSOEVER</a>.<br /><br />And I came to 2 2 3 5 7<br /><br />and due to my escapades in <a href="http://projecteuler.net/">project euler</a>, I looked at those numbers and said "Huh, what if they were concatenated to form a new number? and the factor of THOSE???"<br /><br />well, as it turns out - 22357 has the factors 79 and 283<br /><br />and 79283 is - itself - a <b style="color: red;">PRIME</b><br /><br />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.<br /><br />++++++++++++++++++++++++++++++++++++++++++++++<br /><br /><br />SO - this is how it goes my little mathletes:<br /><br />Unfortunately some of the numbers continue to blow up beyond a limit.<br /><br />The fastest way to run this test was to first create a nice little list of prime numbers below N. easy peasy according to <a href="http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes">THE sieve</a>.<br /><br />My first list was <i>only</i> up to 1 billion (I use only here in jest)<br /><br />AND I tested 1 - 1000<br /><br />well, up to 1 billion pre-created prime tests: <span style="color: #e69138;">(DRUM ROLL please)</span><br /><br />592 reached a prime -- 406 of them grew beyond 1 billion<br /><br />thats - a yes for an election atleast . . . . :O(<br /><br />BUT - if I bump my precreated list to <span style="font-size: large;">5</span> billion<br /><br />WELL, from 1 to 1000 had THIS outcome<br />ahem<br /><br />641 reached a prime - 357 grew beyond 5 billion! ! ! ! ! ! ! ! ! ! - <span style="background-color: #fff2cc; color: red;">OH HAPPY DAY</span><br /><br /><br /><br />WELL, while I was typing this update - I was rendering another outcome<br /><br />Survey SAYS:<br /><br />from 1 to 10,000 under 1 billion<br /><br />4071 reached a prime - 5927 blew beyond 1 billion<br /><br /><span style="font-size: x-large;">>:O[</span><br /><br />damn<br /><br />ok, well, as i type this - MrCool is cranking out 1 - 10,000 under 5 billion<br /><br />we shall see. . . . . . . . .The Hikerhttp://www.blogger.com/profile/16612988455097880734noreply@blogger.com2tag:blogger.com,1999:blog-8101364496595932621.post-26407321729725963292010-10-22T17:08:00.000-07:002010-10-22T17:08:08.274-07:00Pharaoh ShuffleI just learned the trick of Faro Shuffling.<br /><br />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 <span style="color: #cc0000;">8</span> times - you would get your original order back.<br /><br />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 <span style="color: #0b5394;">even</span> number of items. And so I have proven it to myself.<br /><br />Any even number of items in a certain order, when faro shuffled 8 times, will reproduce that order.<br /><br />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.The Hikerhttp://www.blogger.com/profile/16612988455097880734noreply@blogger.com0tag:blogger.com,1999:blog-8101364496595932621.post-56714466027819697902010-10-21T16:12:00.000-07:002010-10-24T16:58:01.434-07:00Perfect Number playSo 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 <a href="http://en.wikipedia.org/wiki/Perfect_number">wikipedia article</a> and the <a href="http://oeis.org/classic/table?a=396&fmt=4">OEIS list</a> for more info on them.<br /><br />Well, what if you continued to apply the "perfect number operation" onto a number and then its outcome over and over again? Random example:<br /><br /><br /><span style="color: #0b5394;">216</span> has the divisors <span style="color: #0b5394;">1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72</span> and <span style="color: #0b5394;">108</span>.<br />so<br /><span style="color: #0b5394;">1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 27 + 36 + 54 + 72 + 108 = 384</span><br /><br />so then we look at <span style="color: #274e13;">384</span><span style="background-color: #38761d; color: #274e13;"></span><span style="background-color: #0c343d; color: #274e13;"></span> who's divisors are<br /><div style="color: #274e13;">1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128 and 192</div>so<br /><span style="background-color: white; color: #274e13;">1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 32 + 48 + 64 + 96 + 128 + 192 = 636</span><br /><br />and so on with <span style="color: #274e13;">636</span> which turns into 876<br />876 -> 1196<br />1196 -> 1156<br />1156 -> 993<br />993 -> 335<br />335 -> 73<br />73 -> 1<br /><br />and bingo bango we have come to an end.<br /><br />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 <a href="http://oeis.org/classic/table?a=396&fmt=4">perfect numbers</a>, they are their own outcome and its futile to work on it further. Also <span style="color: #134f5c;">220</span>'s outcome is <span style="color: #0b5394;">284</span> - and <span style="color: #0b5394;">284</span>'s is <span style="color: #134f5c;">220</span>!! Also <span style="color: #cc0000;">1184</span>'s is <span style="color: #e69138;">1210</span> and <span style="color: #e69138;">1210</span> is <span style="color: #cc0000;">1184</span>!!! very interesting relations there. <br /><br />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?<br /><br /><div style="background-color: #999999; color: #ffe599;">(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?)</div><br />One of the neat ones:<br /><br /><div style="color: #351c75;"><span style="font-size: xx-small;"><br /><span style="font-size: x-small;">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</span></span></div>The Hikerhttp://www.blogger.com/profile/16612988455097880734noreply@blogger.com1tag:blogger.com,1999:blog-8101364496595932621.post-22225934235035678662010-10-20T02:10:00.000-07:002010-10-20T02:10:14.866-07:00PalindroneSo about 6 months ago I made a list of numbers between 100000 and 999999 that are prime in both lexiconographical order.<br /><br />here's a sample:<br /><br /><span style="font-size: x-small;">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</span><br /><br />The full list can be found here:<br /><a href="http://ompldr.org/vNXZjbw">http://ompldr.org/vNXZjbw</a><br /><br />I don't recall how I isolated this list, but here it is none the less.<br />Yes I know that Palindrome isn't spelt with an "n"<br />And no I didn't know what lexiconographical even meant until someone on the net told me.<br /><br />Usefulness: <span style="color: #cc0000;">0.003</span><br />Fun: <span style="color: #bf9000;">2.3</span>The Hikerhttp://www.blogger.com/profile/16612988455097880734noreply@blogger.com0tag:blogger.com,1999:blog-8101364496595932621.post-32835619155191450482010-10-19T19:32:00.000-07:002010-10-20T02:24:32.690-07:00Look and saySo the local minimums and maximums for the polynomial of of the <a href="http://mathworld.wolfram.com/ConwaysConstant.html">Conway Constant</a> are APPROXIMATELY<br /><br />88.4609 <br />-36.3293<br />-2.3595<br />and<br />-917730.85932<br /><br />Whats the polynomial of the Conway Constant? Well, I'm glad you asked. Its<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://mathworld.wolfram.com/images/equations/ConwaysConstant/NumberedEquation2.gif" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="36" src="http://mathworld.wolfram.com/images/equations/ConwaysConstant/NumberedEquation2.gif" width="640" /></a></div><br />THIS bad boy.<br /><br /><br />As text thats:<br /><br />X^71-X^69-2*X^68-X^67+2*X^66+2*X^65+X^64-X^63-X^62-X^61-X^60-X^59+2*X^58+5*X^57+3*X^56-2*X^55-10*X^54-3*X^53-2*X^52+6*X^51+6*X^50+X^49+9*X^48-3*X^47-7*X^46-8*X^45-8*X^44+10*X^43+6*X^42+8*X^41-5*X^40-12*X^39+7*X^38-7*X^37+7*X^36+X^35-3*X^34+10*X^33+X^32-6*X^31-2*X^30-10*X^29-3*X^28+2*X^27+9*X^26-3*X^25+14*X^24-8*X^23-7*X^21+9*X^20+3*X^19-4*X^18-10*X^17-7*X^16+12*X^15+7*X^14+2*X^13-12*X^12-4*X^11-2*X^10+5*X^9+X^7-7*X^6+7*X^5-4*X^4+12*X^3-6*X^2+3*X-6<br /><br />But I really wouldn't recommend putting that into <a href="http://www.wolframalpha.com/">Wolfram Alpha</a> :OD<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/_5zw163Acdus/TL5Ust_BfBI/AAAAAAAAADY/2OuOBdkXvlY/s1600/conway.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="528" src="http://1.bp.blogspot.com/_5zw163Acdus/TL5Ust_BfBI/AAAAAAAAADY/2OuOBdkXvlY/s640/conway.jpg" width="640" /></a></div><br /><br />Usefulness Rating: <span style="color: #cc0000;">0.02</span><br />Fun Rating: <span style="font-size: small;"><span style="color: #38761d;">5.01</span></span><br /><br />I would like to thank Mathworld and KmPlotThe Hikerhttp://www.blogger.com/profile/16612988455097880734noreply@blogger.com0tag:blogger.com,1999:blog-8101364496595932621.post-87333157187457038172010-10-19T14:28:00.000-07:002010-10-19T14:51:43.410-07:00OptimusWhy are prime numbers so notoriously hard to write and find proofs for?<br /><br />Take the twin prime conjecture:<br /><span style="color: blue;">There are an infinite amount of consecutive primes.</span><br />ie 11&13 ; 41&43 ; 197&199<br /><br />This is an <a href="http://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics">open question</a> in math and hasn't been proved or disproved yet. There are however A LOT of open questions about prime numbers.<br /><br />I would like to see some solved and or proven conjectures using primes to see how easy / hard it is to write such proofs.The Hikerhttp://www.blogger.com/profile/16612988455097880734noreply@blogger.com0tag:blogger.com,1999:blog-8101364496595932621.post-54774087957991771652010-10-19T14:18:00.000-07:002010-10-19T14:18:49.106-07:00EmergenceSO! Here is it. The first post of my blog about math, science, philosophy and politics.<br /><br />The name I chose was based on my analogy regarding my explorations into math. A few months ago I started to explore into a certain direction of math. In essence I asked "Where does this path lead me?" and to my astonishment I found someone else's well worn path from a different direction with a sign post and notebook. I was hooked.<br /><br />I see mathematics as a truly infinite forest with paths criss crossing and diverging everywhere. I only hope that one day I can place a sign and flag with my name on it somewhere in that forest so that others may cross it in their own exploration. Or at the very least, chip away at the eternal and infinite mountain known as IGNORANCE and help do more research into the unknown.The Hikerhttp://www.blogger.com/profile/16612988455097880734noreply@blogger.com0