Big Weird Numbers (from Small Things) That Amuse Me

One of my random new year resolutions I will disclose is that I'm trying to smarten up mathematically again, and to regain some comfort with doing hard core ciphers: learning and getting reacquainted with stuff like calculus, matrices, statistics, and the like; plus trying to find some practical use and application for such arithmetical methods in my own life. Right now though, it is all impractical, yet interesting and impressive (to me anyway). I thought about simple objects and puzzles around my home; they didn't involve high tech things either. I did some recreational computations (with the help of the Wolfram Alpha app) and found research results to get some of these wild figures . . .

1. 6,670,903,752,021,072,936,960 ( ≈ 6.67 x10²¹) : The number of possible valid complete solutions there are for a 9 x 9 Sudoku grid. That's about 16.67 billion times the highest estimate of the number
   of stars in our Milky Way galaxy. Some lucky bastard mathematician out there also got some grant money to prove that the absolute minimum number of clue digits needed to solve one is 17.
   
2. 20,822,964,865,671,167 ( ≈ 2.08 x 10¹⁶) : The total number of  all unique sets of counter bead position configurations on my 2 bead upper deck/5 bead lower deck/13 column standard Chinese suan pan (abacus). That's 18 possible bead configurations (a base of 18, represented from numbers 0 to 17) for each of the 13 columns, representing the exponential powers from 0  to 12. That then is {(17 x 18⁰) + (17 x 18¹) + (17 x 18²) . . .  + (17 x 18¹²)}, leading to a maximum total up to the aforementioned number in the heading converted to decimal/base 10 scientific notation form. Meaning, if I flicked a bead (or beads) at one interval per second to tally all possible counter bead configurations on this abacus, it would take approximately 660.7 million years to do it. It seems crazy on such a little frame with only a total of 91 counting beads, but that's the math talking. If the figure for the placements on an 81 spot Sudoku grid is as high as it is, why not this lesser figure for the 91 counter abacus? If I'm wrong about this calculation, I won't mind being corrected. It seems too strange and mind-blowing to be right.

   

   It reads 2017 in base 10. Happy New Year!

3.  43,252,003,274,489,856,000 ( ≈  4.33 x 10¹⁹): The number of possible of configurations a Rubik's Cube can have. Amazingly, it has been calculated (by supercomputers) that the cube can be solved, with the proper programmed algorithms, from any one of these configurations in 20 moves or less. The last time I tried, it took me about 32 minutes to solve it . . . most definitely not in the same league as a Cray supercomputer.
4. 1 in 6,227,020,800 (or 13!): the chance of taking a full suit of 13 playing cards, shuffling them, and then turning them over, one by one, and having them turn up in exact ranking order from ace to king (A,2,3,4,5,6,7,8,9,10,J,Q,K). In contrast, I learned that the chance of winning the jackpot for Lotto 6/49 is roughly 1 in 14 million, and 1 in 28.6 million for the Lotto Max*.
5. 6.53 x 10⁹⁰⁹⁰⁵²: The number of 9 word sentences (a fairly average length of sentence) that can be composed out of randomly selected words from the language with the largest vocabulary in the world: English. From the sentences, "A, a, a, a, a, a, a, a, a, a." to "We will never run out of things to say!", to "Big Weird Numbers (from Small Things) that Amuse Me.", to written onomatopoeia to denote sleeping,  "Zzz, zzz, zzz, zzz, zzz, zzz, zzz, zzz, zzz"**. _, inclusive. There's nothing around materially or temporally as an example to bring that number into comparison for adequate comprehension for the mind, since there are only an estimated 1 x 10⁸⁰ atoms in the entire universe, and its age is only about 4.3 x 10³⁵ in attoseconds***(super small time increments) since the Big Bang. Sure, a grand majority of them would be nonsensical, like "Shiver melon herring quickly kind zipper handy aardvark nipple". Like the random shit in English scrawled on teenagers' T-shirts in the Harajuku fashion district in Tokyo. If a password of nine random words like that were used, I would think that the world would be long vanished into oblivion before it could be hacked. Thankfully, we have few rules of grammar, syntax, context, articles, pronouns, prepositions, verbal tenses and conjugations, gerunds, participles, etc., to set limits and boundaries to things that would statistically and numerically whittle down that figure a lot. Even so, what is left is still more than what would have been, or will be, ever said by humans, past, present, and presumably the future. There's still lots of nonsense that comes from it, but we manage pull a few out that are real gems, and not from the cold dry probabilities of it, but from what's in the spirit of us as human beings. This fact brings to light a quote from Einstein: "Imagination is more powerful than knowledge". He think he got it bang on right . . . and with only seven words too.

*- This is someone else's findings, not mine. Actually, for Lotto Max, the chance of winning on a single line of 7 numbers is roughly in the neighbourhood of 1 in 85.8 million, but you are given three lines, so divide those chances by 3, so 28.6 million. That's a little more optimistic!
**-An edit. Initially I thought that Zyzygy was the alphabetically last defined word that I could think of, but it was a misspelling of the word syzygy: an alignment of celestial bodies in a gravitational system.
***- 1x 10¹⁸ attoseconds = 1 second. Very few things or motions in the physical universe exist that can be timed within ten attoseconds, but who knows what will happen in the future as using measurements such as these become realities as advances in research and development of nanotechnology and quantum computing come about. 

Last Entry's solution, Reaching the Equinox

Down the page is the solution to last entry's logic problem, but if you are still doing it, don't give up yet. I included the following hints to  help you sort through the challenge before you scroll to the answer table.

Hints

From Clue 1., as well as there being no such leprechaun as Smiley O'Riley, one should reason that there are also no such leprechauns as Bleary O'Leary, Greeny McSweeny, Tally McNally, Whirly O'Hearly, or Greeny Mc'Nally. Greeny then wasn't the one with the pocket watch who hid his gold in a tree (Clue 2). McSweeny didn't use the well nor clay pipe nor the hayloft in Limerick, therefore no gold watch nor well in Limerick (Clues 3 and 4). From Clue 3., there is no leprechaun named Tally O'Riley, neither Tally or O'Riley then used the clay pipe. The well was either in Cork or Galway. There is no such leprechaun is Bleary O'Hearly (clue 4). From clues 1 and 5, we see that O'Riley didn't possess the pewter flask; there is also no Whirley McNally, so from the previous clues McNally's first name is either Smiley or Bleary. In clue 6, it can be deduced that the fifth leprechaun not included in the list is the one from Limerick, thus Smiley wasn't in Limerick. If the flask belongs to the bog leprechaun, the pipe belongs to the well leprechaun, and the walking stick belongs the manure pile leprechaun from Meath (not Limerick, Galway, Cork or Kildare) (clue 7), and the watch with the hollow tree leprauchaun, the tin whistle thus belongs to the hayloft trickster in Limerick. Thus O'Riley, not Smiley (from clues 1 and 6) owned the tin whistle, and from clue 5, we determine that his first name was Whirly. Using Clues 6 and 1, we eliminate McNally as the walking stick owner/manure pile leprechaun from Meath county. I could go on, but the rest of the puzzle should logically solved from here on in.

First Name	Last Name	County	Lucky Charm	Hiding Spot
Smiley	McSweeny	Cork	Pocket Watch	Hollow Tree
Bleary	McNally	Galway	Clay Pipe	Brackish Well
Greeny	O’Leary	Kildare	Pewter Flask	Peat Bog
Whirly	O’Riley	Limerick	Tin Whistle	Hayloft
Tally	O’Hearly	Meath	Walking Stick	Manure Pile

I wish I were able to add something else cheerful and positive to this entry, but today greeted me with some grief: my own challenge is to tear it apart with some focus, common sense, and logic. I'm faced with using my day to do my best to muddle through it. I'll just say that I'm at least glad that we've reached the point where the days are getting longer than the hours of darkness.

Blockages and Drainages, Logic and Leprechauns

I'm glad to say that the spring thaw has been coming aggressively throughout the past week here. It's still not quite warm enough to allow me to roost out on the deck to enjoy morning coffee/tea and my post-breakfast reading in the fresh air though. I'm hoping that will be possible within the next couple of weeks if the melting continues at this rate. I hope to be cycling then too as the streets get drier. For now, it still gets cold enough overnight to freeze things hard and thick enough to restrict all the run off from flowing away and draining properly. This part of the season seems to be a direct reflection of the way my own mind is working now*.
   
There has been a lapse between now and my last entry. It's because since I began la vie sans TV, I've been taking advantage of the extra silence and liberation from one less distraction, and I have been shifting my attention and focus to another writing project. I think the overall concepts of it are sound, but I'm still having problems with transposing the things from my notes, tables and spreadsheets into a workably progressive, and manageable flow of content. There doesn't seem to be enough time in the world to allow me to fix this stuff up right; especially not while working full-time hours, plus doing my unit chair position duties. The lightning bolts of originality and creativity just don't seem to be striking me as frequently anymore. The week off I had at the beginning of the month, although I welcomed it, didn't do as much to help me sort out things as I had hoped.

I took a break before I began this paragraph; a spell of creativity did manage to seize me. I directed it to fashioning something through writing that I enjoy doing: a logic problem. I do them once in a while. They are made for more esoteric and quirky personalities and are the less popular of the pen and paper puzzles, much less so than puzzles like Sudoku or crosswords, and sadly they seem to be a dying art form. They are to the puzzle magazine world like what polka is in the music world. I know the magazines dedicated to them are becoming harder to find. It's a shame too, because logical thinking is something that the world needs more of. I guess I like to retreat to them, and create them, because working with this kind of hard pure logic is compensation for feeling too often deprived of just being able to just verbally bash some common sense into some people I'm forced to interact with when I've exhausted all my tact and patience. Given that St. Patrick's Day is winding up quickly, I used an hour and a half of time to burn away some insomnia to compose this puzzle. The inspiration came to me from reading one of my cousin's posts on Facebook. I tested it, and the solution works. I'm still trying to figure out where to get these things published for a little extra cash. I risk showing everyone the weird way my mind works. I should have stashed it away in my portfolio of other such problems I made, but I thought I would share and sacrifice this one to the public, for anyone else who is up for the challenge. I crafted and pasted a logic grid for your convenience, to be found on the bottom of this entry. I'll post the solution in my next entry. St. Patrick's Day may have passed by the time you read this, but I hope you get a kick out of doing it anyway. All names used in this puzzle are completely fictitious.

The Leprechauns

The leprechauns of Ireland come out of seclusion once in a while to roam the land and collect treasure; and at the end of the day, the miserly little fellows make it a habit of returning to, and adding to, their hidden pots of hoarded gold; which in truth are found in far less enchanted places than at the ends of rainbows. If you’re lucky enough to find one and stealthily follow him, he may lead you to his preferred treasure hiding place. Leprechauns pretty much all look and dress alike; they usually can only be told apart from each other by whatever single prized possession they carry on their person. This ordinary looking possession they carry is actually their characteristic magical “lucky charm”. There are five such leprechauns in this problem, each one of them lives in a different Irish county. From the seven clues below, can you correctly sort out: the first and last name of each leprechaun, which county each one lives in (and keeps his treasure), which distinguishing lucky charm each one carries with himself (like a pocket watch that can detect where gold can be found), and which strange location each one stashes his pot o’ gold?

1. Smiley O’Riley has lovely lyrical ring to it; but this is not the full name of any of the leprechauns. In fact, none of the leprechauns’ proper first and last names rhyme together at all. However, the bearer of the magical tin whistle has either the first name Smiley, or the last name of O’Riley (who never goes near any peat bogs). When the tin whistle was played, it stunned the senses of whoever heard it, so that the leprechaun could have ample time to make a hasty escape from greedy people who found him or his gold. Greeny never possessed this enchanted object, neither did McNally (whose pot of gold isn’t in Meath county).
2. A pocket watch that magically signaled an alert to its keeper for the presence of gold was a mighty useful thing to have for indicating which unsuspecting strangers to pick-pocket. McSweeny, a very absent-minded leprechaun, also often used it to locate the right hollow tree when he lost his way in the thickly wooded forest (not in Kildare county) where he kept his hoarded stash. 
3. While walking home one evening, Mrs. O’Hara was scared half to death when she spotted an impish little figure crawling out from a derelict roadside well.  The locals never used it anymore because the water in it had long ago turned brackish and undrinkable, and some claimed that it was haunted by spirits. The clever little leprechaun she encountered took advantage of the well’s reputation and neglect, and had used his long stemmed clay pipe as a snorkel while he secretly dived in there to stash his gold coins in the submerged pot. This well wasn’t in either Meath or in county Kildare; nor did Tally or O’Riley use this place to hide their treasure.
4. It was near dusk when Mr. O’Toole, a farmer in Limerick, thought he heard a strange sound coming from the hayloft of his barn. When he went to inspect the place, he could have swore that he caught a glimpse of a shadow of an odd-looking little fellow, but he felt a bit dazed and thought it was just his weary eyes playing tricks on him. Neither Bleary nor O’Hearly was responsible for this commotion. Greeny didn’t do it either.
5. The constantly tipsy leprechaun with the pewter flask was also the one that always stank like the vile peat bog where he frequently visited to cache his gold. Very few curious people wanted to follow him. His first name wasn’t Whirly, his last name wasn’t McNally, and he never lived or roamed around Cork County. Whirly and McNally actually weren’t from that county either; one of these two did have a tin whistle, while the other one kept his gold in Galway County.
6. Four of the five leprechauns were: the one who drank from a pewter flask that turned bog water into whisky, Tally (who wasn’t in Limerick), the mischievous trickster from the county of Galway, and Smiley (who hid his gold in either a hollow tree or the brackish well).
7. A sneaky young vagrant, named Rowan McManus, secretly followed a tiny stranger who headed towards a great mound of rotting horse manure by a potato field. The little fellow poked his walking stick in the pile three times, and all of a sudden a pot of shimmering gold coins magically rose out of the dung heap. The leprechaun then tossed a few more coins into the pot, which then sank back into the compost pile and was once again concealed from view. The leprechaun suddenly caught sight of the astonished McManus, who witnessed it all while hiding behind a hedgerow. With an elfish grin and a wink, the leprechaun then said, “Well ya didn’t seriously think I was going to dig through all that mess, did ya?” Rowan left there and quickly returned after finding a shovel, and then he dug around and rummaged madly all day through that manure pile like the greedy fool he was, but he never did find any of the gold, and he never saw this rascally leprechaun (who wasn’t O’Riley) ever again. This incident never happened in the counties of Cork, Kildare or Galway.

*- I'm also pissed off about recently discovering that my dishwasher (something I deem as an essential time-saver) has also all of a sudden failed to drain properly. I stayed up until 2:00 AM last night trying to fix the damn thing to no avail. It represents yet another inconvenient blockage coming along my way, both reminding and frustrating me about how stuck I'm feeling about so many other things.

Using Graph Theory, Creepy Tent City

It was just too hot to sleep last night; I slept like crap, and I woke up too late this morning to take advantage of more tolerable conditions for running. It's climbing up to the mid-thirties today temperature-wise: even hotter than yesterday. So, I'm going to relax today and recover from the strain of the gym work and running around I did yesterday. I was a bit too ambitious and overworked my arms. I can barely straighten them now. If I did hit the trails later today, I'd be destined for heatstroke and cramping. I have to smarten up and start healing right.


My scribbled out algorithmic representations
 of this city's trails and bridges.

Since I did my hard work Friday and Saturday, I thought I should do my smart work today. It was one of those good moments when I got the chance to blow the dust off of some obscure knowledge of discrete mathematics and graph theory locked up in my memory somewhere, and making it somehow meaningful. Extreme insomnia is often the cause and reason for jolting me into these deviations into harmless, yet eccentric, numerical explorations. I thought I should apply myself to it before my already too-tired pulpy mush of brain softens up even more from today's heat. I played around with some Hamiltonian circuits and weighted digraphs. I used that stuff to figure out the optimal path between points along my running routes which would constitute the most effective and ideal half-marathon training course for the sake of my own safety and efficiency. I should have been using this analysis ages ago, which could have spared me some agony, but I've been procrastinating. It's stuff I think I'll be using more often in the future to avoid some other negative extremes in training and personal logistics.

Speaking of extremes, the other observation my half-cooked mind is noting is how weird the vibe has switched over in the neighbourhood with the presence of some glaringly conspicuous newly erected monument to piety. The Seventh Day Adventist school across the alley from my building has went through some considerable effort and expense to set up sort of temporary compound of plain white large tents and awnings, all surrounded and visually shielded by a two meter high white tarp-draped fence. The sign outside of it calls it a "tour of the history of the bible"* or some such thing. There is this structure with towering gold-painted columns that especially looks freaky: like fucking Caligula was camping there. It's the noise element that's creeping me out most, or rather the lack of the noise you would expect and associate with entertainment when you see such structures. If you didn't know that this was some attempt by these people to fashion some kind of  'Jesus Circus', you would think it was a refugee camp, or that an emergency battlefield hospital was set up there as if an outbreak of some kind of plague was happening. It's very unsettling. I won't dare enter that place, no matter how curious its presence is making me. The weird setup of the fence makes it look ultra-secretive. The only impression I gather of what religious activity might be going on in there is the kind where cult members have their finally stop to drink their cyanide laced Cool-Aid. It's a disturbingly ominous looking setup, and I'll be glad when this thing gets all knocked down by the end of the month.

What little I know about the Seventh Day Adventists is this: they hold a more literalistic interpretation of the Bible, and more staunchly conservative (puritanical) than most other Protestant Baptist denominations. They abstain from alcohol and tobacco, they don't dance, and don't approve of immodest dress. Like the Jews, they observe Saturday as the Sabbath, and there is following the Kosher dietary laws (no pork, shellfish, etc.). I have no personal qualms with them. When it comes right down to it, I wish more of the dope dealing assholes would move out of the neighbourhood, and more Adventists would move in their stead. What does sicken me though about this setup of this Messiah Mansion, is that this too is proof of just how likely they are, as with any other religious group, to resort to using such a tawdry display as a meme-warfare tactic, despite appearing outwardly more conservative, to attract more followers . . .  of what amounts to be mythology. So many other things could have been done with that money and energy for real charitable work than wasting it on setting up this tacky showpiece; which I must add, has been largely vacant since it arrived here.

On Saturday, I was shamelessly sun tanning on my deck, less-than-modestly attired, in full view of the people running this show, drinking my beer, and snacking on some spare ribs and smoked oysters. In my own way, that's how I've been rebellious and defiant to the presence of this monstrosity.

*-  I highly doubt that this history includes a case for evolution. As kindly and civil as they may appear, when it comes to literalistic followers of scriptures in Abrahamic religions: be it Biblical or Koranic, I have no desire to waste my time with people stupid enough to actively refute the scientific evidence of evolution, and too sanctimonious to even bring it into question.

Amusements in Logic

Starting Monday, I have about 11 hours left of short shifts to do this week before I do some holiday time. In a way that's good. I do three or four hours within three days, and I'll hopefully have enough energy and momentum to clear stuff away at home for the remainder of those days before I dive into time that's to be devoted to mostly leisure. Perhaps weaning myself away from work gradually like this is the way to go, rather than having a more radical transition. 

I'm doing some more advanced programming exercises now. Messing around with the process of trial and error in correcting some missing details and other silly mistakes, is making me think that there was a time in the past when I would have been so much better able to retain the knowledge, hone my skills, and have a peak performance at doing such tasks.* Right now though, I feel as though my brain has to have a lot of rust, dust, and cobwebs brushed and knocked out of it before I can deal with anything that's purely logical. 

There was a time in my life, when I had less busy days and was better able to focus, when I was becoming a real enthusiast for doing the rather esoteric hobby of solving logic puzzles. The British ones were (still are) the best. It was a way to sort of play detective. I was correctly completing ones ranked five stars in difficulty; even the ones without a logic grid, on a regular basis. I became so interested in them that I wondered if I could even create any of my own that would ever be acceptable enough for publication in any one of the puzzle magazines one finds them in. I did start a small portfolio of some that I drafted up, working at composing and editing them piecemeal. I don't remember when it started happening, but I'd guess that it was something I did as an effort to endure the coldest, darkest, loneliest days of winters past.
 

I doubt if dreaming up and writing these things is something one could ever get rich at, or allow me to just quit my day job. Logic puzzles, at least non-digital ones, are a dying amusement these days, like most of the other pencil and paper puzzles; thus their creation is becoming a dying art as well. The jest and appeal of it for me though is that I’d be creating something that like-minded people want to approach for a bit of diversion and positive mental stimulation. Also, the thought of making even a little money from watching an idea grow and come to fruition, even if it's just a small and trivial one, is now becoming a hell of a lot more thrilling to me than that of earning comparatively more money from doing stuff that wears you down with boring routine, and constantly muddling through and dealing with others' ignorance and stupidity in the act (guise) of service.

Back when I taught English for my brief time overseas; being sent frequently without a prepared lesson plan, into a classroom full of kids often too incorrigible or indifferent to learning anything, making and presenting a logic problem was often my salvation. If the kids were disinterested in learning language directly, they were more often than not more willing to be involved with a game or puzzle based on a formula, which they had to force themselves to express in English. I wasn't any good at enforcing classroom management with structure and discipline, but I did alright with at least capturing the attention of those few students who enjoyed the challenge of doing more critical thinking.

The one thing I miss most is getting to be engaged with more people who regularly deploy logic and common sense; so that's the kind of company I should be seeking out during my holiday time. I suppose then that one of my ambitions during this vacation time will be to start probing through and editing these past works of mine, and find publishers to submit them to. If they get rejected, I'll post them here to share with other interested parties. Perhaps my followers who are logic puzzle enthusiasts, especially those from the UK** who read my blog, could help me with this project.

 *- I'm referring to a time when the computer languages and technology I'm messing around with now did not yet exist.

**- The stats from my reader numbers by nation indicate that readers from the UK are only 7th in the standings. As it is currently, the rankings of my numbers of followers before that placement, by nation, rank as such: 1. Canada, 2. Russia, 3. Latvia, 4. United States of America, 5. Germany, 6. Ukraine.