Language is so important to our internal experience, and we understand ourselves and others through interrogating our thoughts and our inter-relationships using language. As a result, our lives are bound up with those of other people in ways that are complex, tangled, and inseparable. That’s why we often remember and understand facts about things that happen to other people better that those that happened to us ourselves. You’ll see, I’m sure, why we come to love tales and gossip; remember information in the form of stories better than just in the form of facts and figures; and are more likely to buy or believe in something if it has a story attached. One could say that these linguistic relations are “chaotic,” but not completely inexplicable by a long way, although it’s difficult to find the appropriate words to describe them easily most of the time! Let me suggest the following, then. Rather than being a character in a story told by someone else, what about taking responsibility and beginning the journey that is truly difficult but so worthwhile of becoming a story-teller and master of your own fate? That’s what I did – escaping from the chains of a toxic existence – and if I can, you can too, in your own way, when you’re ready!

“Waking the Slumbering Giant”

Ms Sesiline Arian

Warmest greetings my lifelong buddies! Fred 'ere again! It is so gratifying to have the pleasure of your edifying and enthralling (I assume and hope!) company once again –especially in the face of the desolation, despair and dismay deluging this Downtrodden Dust-ball these distressing days. Today I wish to enlighten you regarding the burning topic of international cuisine. “The While Elephant” is my favourite restaurant without a shadow of a doubt. It is a most colourful place, which reeks of forbidden fruit from the Sintu Valley. Imagine scenes on the walls! Those two old scoundrels, Dvaldí and Hlevné, stark-naked in the Garden of Eyrthly Delights (there was no need for fig-leaves at that time) where sits, under the boughs of a pomegranate tree, a fat god who’s laughing heartily, with a long sinuous trunk, humungous flappable ears, and lots of arms like the Teasing Tickle Troll. And there the cheeky creature tempts the two who hunger after the knowledge of secret recipes with myriad dishes of delicious, steaming curry. (How mistaken that depiction is in its details, as far as I know, although not its sentiments. Everyone with even the slightest sophophilic bent should know that it was Davuth and Elena who were released from their servitude by Xlotlringku Vlaltanlu-tnalzse in the Grove of Xatlaltvazsu.)

Ooh, the officers of the new Military Branch of EGO are not too fond at all of such iniquitous dens where the food, the drinks, the stunning spices, the music and other entertainment, and the atmosphere, send one into paroxysms of delight. Indeed, the armed vicars could raid the place any time. Then again, I am but a humble and unimportant apothecary, of course, who tinkers with magic in his spare time, and it’s not as if there is a long line of Magicians in the family. The authorities do not pay too much attention to me, especially when I have been busy working so secretly in the laboratory of the Clinic in Aberdydd. Despite all my worries, therefore, regarding the terrible things that are occurring in every corner of the World, I cannot restrain myself from frequenting hidden food-outlets, underground picture-houses, illegal exhibitions, and abstruse courses.

I am not a brave man, but the fear makes the creative juices flow. All the gnawing uncertainty, indescribable terror, and abyssal fear’s certainly great for the tall tales I’m making up in me head all the time (when I can think straight!). Then I steep myself in the strange ideas that always arise to fill my fruitful imagination and inspire me. On occasion, I even feel like the Eyrth’s Unstoppable Force is pouring through me, calling me on towards some Other World, no mistake! Sometimes, when I meet  the other Demented Declaimers by the Mingin’ Midden, I feel like a real tub-thumping rhymer {Vexatious Versification}! Anyhow, I just sort of dream that if I fight back as often as I can in my own way, then that’ll be one in the eye for the oppressive authorities. This is a report based on my own experience, then, I hope you’ll enjoy it, or at least benefit somewhat from it.

I love spicy food, and indeed, what a culinary roller-coaster journey was to come. I would like to convey to you a little of the atmosphere I experienced the first time I darkened its door as a stripling lad, ages ago, but then again, an old dog has a long memory, doesn’t it? Perhaps I shall return for a second time before long, and I hope they will remember the old proverb – Sing sweet songs to your fake Great-gran; she's sure to be your biggest fan – when I do so. [*]

It was as quiet as the grave there at midday one wet Sadderday in the middle of Summertide (it was quieter to be honest, despite the presence of the "mother-wolf" and her litter of "cubs" who were busy polishing the grave-stones and planting hardy perennials in the verges of the cemetery next door). Sweet Hebé, they were having all manner of fun and enjoyment and diversion amongst the dead of the ages, despite the foul weather. In the period in which we live, everyone should celebrate more often the gift of a peaceful death and everlasting oblivion following it, because this is what makes living worthwhile, I believe. Oh, the things I’ve seen during my life, all the memories which remain with me. But one day everything will be gone like tears in the rain, when the time comes for me to sleep forever. Well, what a lot of over-indulgent tosh! Enough is enough with all the sophophilic musing, you old chatter-box.

1. OUR CONFUSING WORLD? Have you ever looked out through the window, thinking, I wonder what the weather will be like today? The weather forecast declared with conviction the night before that it would be as stifling as Summertide in Faraqand’s Largest Desert. But by now, it’s raining, and looking as if a hurricane from the Black Mountains of Kharsag is heading for your homestead. Of course, this is a bit of an exaggeration, but despite that the question arises: what’s up with all our efforts to describe and understand this kind of physical phenomenon? Unfortunately, the difficulty is an inseparable part of the thing that’s being investigated. It arises naturally when any system contains parts that can interact with each other so changing the system itself. Even if someone were to try and measure something, and were to know all the appropriate equations as well, she could not say exactly what would come to pass in the future. The reason for this is that in the real world, it’s impossible to keep track of everything that’s happening at the same time. Also, it’s never possible to measure anything totally accurately. And then again, the smallest differences one second can cause sweeping changes later. This is the phenomenon called “chaos” [**]. Chaos is everywhere, all the time – in traffic, economics, machines, codes, and biology. Perhaps it would appear that the entire world is basically totally unpredictable, then. But, having said that, all is not lost, because, on the other hand, the same kind of general patterns are to be seen all the time, despite how the details differ in each case. In other words, it’s impossible to predict all the details every time, but very often it will be possible to see a general sketch of what is to come in the future. So, in truth, the effects that arise from chaos are not examples of total disorder. Rather, they are collections of complex information, which we can understand, if we look at them correctly. Let’s investigate further.

So, let us proceed with the tale of the epiphany concerning my taste-buds. I was feeling so hungry I could eat my own pillow, after the tribulations of that week. Suddenly, however, it struck me that a step across the threshold is half the journey, and I hovered between two courses for an instant, cogitating and debating internally {Thinking}. Having said that, the manager was as pleased as the Burlesque Clown from the Absurd Circus, and all ears, when I asked for the menu. He had stridden towards me from within his premises while I was lurking outside it. He was a dignified, substantial fellow, wearing sea-green silken livery, with epaulettes and gold buttons, and on his head was a scarlet turban adorned with a phoenix feather. Like some servant to the Nuhwāb in the Albertan Age he was. Or perhaps he was a handsome but terrifying demon in one of the tales from the Great, Red Desert such as the Thousand-and-One Nights, how was I to know, in my distress? But whatever he was, I was mesmerized by his beard, which was as ginger as the consuming flames of the Bottomless Pit. Truly, it was to be an exceptionally special occasion.

2. A SIMPLE SITUATION: Imagine some beetles growing in some habitat of a fixed size, which contains an endless supply of food (yes, arithmosophists do imagine such strange things!). Of course, as they feed and grow, they produce poisons which tend to kill them, and slow down their growth. To start, there is a fixed number of beetles in the habitat. How will the number of beetles change over time? We can use a simple numerological model here. Its name is “The Nonlinear Intertwining Map,” but don’t worry, it’s not as frightening as it sounds! To be honest, it’s easier to talk about the fraction of the habitat covered by beetles (rather than the number of beetles), and that’s what we’ll do. A fraction equal to zero would mean no beetles. If the fraction is equal to one, it shows that the whole habitat is covered with them. The initial fraction of beetles in the habitat at the start is the first essential characteristic of the model. The equation contains “feedback” because the new fraction of beetles depends on the old fraction of beetles, and so the process goes on, creating generation after generation. The “constant,” that is a number which can be between 0 and 4, is critical. It represents how quickly the beetles grow, by using the food and the space which is available in the habitat. This constant is the second essential characteristic of the model.

Inside, the place was so tasteful. There were alien pieces of hand-craft everywhere; even the walls were decorated with pictures of blue divinities, and their huge coconuts and enormous spears. My eyes almost popped out of my head. It was nothing like a foul stereotype, then. Furthermore, it was neither too hot nor too noisy, apart from the ceaseless chanting that flowed from the loudspeakers like the screeching of some cat at death’s door (and I already knew too much about that, but I had better keep to the story). Despite that, there was not a glut of patrons (not a single living soul apart from me) and there was enough space to swing a cat (as it were), thank goodness, because I detest enclosed spaces. If I feel uneasy, there is a tendency for me to behave like an uncivilized imp, who shouts and wails, and tries to run off like the wind.

3. CALCULATING CHAOS: The Nonlinear Intertwining Map works like this. The constant is represented by k and the starting fraction of beetles by x₀: The calculations aren’t hard to do on a handheld reckoning-engine. Consider, for example, k = 0.95 and x₀ = 0.25.

It looks as if the fraction is decreasing every time. The graph of the results is shown in Figure 2(a) below. Next, we can investigate five additional situations where x₀ = 0.25, considering one different value of k in each one. Graphs of the results are shown in Figures 2(b) – 2(f) below.

In accordance with the imposing vizier’s advice, I had the house special, namely “Emperor’s Revenge” for thirty pounds including three courses and a pint. I am not made of money right now, not by a long chalk, nor was I was then either. I had lost my job in the chemical works some time before, and then had had to do community service. And Oh, what trials and tribulations ensued as a result of that, I'll never be the same again, but that’s a totally different story. Anyway, He who is born to fourpence will never achieve fivepence, as they say. But there was a lot of loose change in my pocket after I had spent that morning selling beauty cream containing cat fur and loopy-lichen tshay (that is, an infusion made from mashed-up Dimentiseybin wawrani) outside the the lovely local convenience store called Tesbyro.

4. TRAVELLING from ORDER to DISORDER: Let’s consider a series of conditions now. Figure 2(a) below (k = 0.95): The beetles don’t grow, and the fraction of them decreases towards zero, that is they die off completely. This is extinction. Figure 2(b) below (k = 1.2; k = 1.5): The beetles can use the food to some degree. They don’t die out, and the fraction reaches a constant value. This is stability.

I started with a first course of Glywysing-shire sausages with ginger, garlic, and cumin, a dish of cockle and seaweed soup, together with speckled naan bread containing Kaergenydd cheese and currants, for gobbling down the last drops. The combination of strange odours was like a symphony on my palate. All the time, I kept on thinking that too much pudding chokes a dog, but I could not restrain my appetite. Then, I forewent the usual snail curry, and in its place I enjoyed beef curry with extra crinkly chillis, and devilish hot it was, too, as it contained the world’s hottest peppers, namely “Rockyhill Reapers.” How do I know? Well, they are sold in Tesbyro, which is the least bad place to go shopping, in my humble opinion.

Figure 2(c) below (k = 2.9): The beetles can use the food well. They grow, but when there are too many of them, they begin to die. After that, they can grow once again. In the end, after oscillating back and forth, the fraction of beetles will reach a constant value. This is oscillation towards stability. Figure 2(d) below (k = 3.228): The oscillations are more obvious. The fraction of beetles never reaches a constant value. They survive, oscillating between two stable populations.

After all this, I was on the verge of dying of thirst, and I had to have a pint (or two) of lager, called “Sheep-dip,” to extinguish the scorching fire in my mouth. Remember now that I drink as a rule nothing but small bottles of bitter beer like “Boiled Owl.” Enwen my lodger won’t let me tipple on anything more intoxicating if she can stop me. But in days past, and in particular in that cave of delights that was so dark and enchanting, I could not resist. Great Heavens, that iniquitous brew was as strong as the black widow’s poison! In ecstasy, I finished the meal with spikni ice-cream and cinnamon and clove sauce.

Figure 2(e) below (k = 3.506): The beetles survive, oscillating between four stable populations. Figure 2(f) below (k = 3.948) (blue line): The beetles survive, but oscillating wildly. It appears that there is no order to the fractions. What will happen to the beetles later on? You can’t say, without calculating. Furthermore, even if the fraction of beetles starts from two different values that are very close to each other, the behaviour will be totally different in later generations. 

The example above in Figure 2(f) also considers x₀ = 0.251 (red line). Look at the two lines in the picture. They are similar to each other first of all, but they become totally different very quickly. So, small changes in the starting value (for example) can cause extraordinary changes sooner or later. What will happen to the beetles in one case or the other? You can’t tell, without calculating. However, note that we can make the following very important observations without the slightest ambiguity: they do not die out; they do not grow without restraint; and their number always stay within fixed limits. The “Bewitchment of the Beetle’s Breath” is the name for this behaviour. It reminds us how something as small as a beetle breathing hard in Kharsag can change the weather in Kimbria!

I was as happy as a sand-boy, although my insides were almost exploding. But, while I remember this, I must give you a word of warning: be careful whilst using the conveniences there. When my large intestine began to growl like a dog sucking the marrow from a juicy bone, I rushed to the latrine, which is bijou but most agreeable, where the door slammed shut behind me. Unfortunately, the lock got stuck, and after half an hour’s effort on the porcelain seat, followed by an hour of shouting through the keyhole, I was saved by a waiter in his splendid uniform. Moreover, because of my disconcerting experience, it was of the greatest importance for me to calm my tattered nerves. At once, therefore, I despatched a cup of Kimbric khawví (this contains much more whiskey than the common-or-garden Eyrwian sort) and then straightaway, another.

5. “CHAOTIC” ORDER: This is the phenomenon called chaos. It is not to do with just beetles, either: it is involved with the flow of traffic in cities, with the health of financial markets, with the interaction between robots and their environments, with creating encryption algorithms, and with the relationships between predators and prey. When parts of any system interact with each other, there are many different patterns that can occur. Which one happens will depend on values that describe characteristics of the system, like temperature, pressure, birth rates, and so on. In our simple example, there are only two things which control the system’s behaviour: the value of the constant, and the initial fraction of beetles. The behaviour of the system can cease completely, reach stability, oscillate between several values, or change without any obvious pattern at all (a summary is given in the Table below) [***].

There is, also, however, one hugely important thing that is not obvious from a graph like Figure 2(f). Despite the apparent disorder, there can exist a certain “hidden order” in such behaviour – and there are numerological ways to describe, understand, and use this “secret regularity.” For example, on any given morning the temperature might fluctuate unpredictably to all intents and purposes. Nevertheless, it definitely stays between well-defined limits, and we describe the morning as “warm” without a problem, and can clearly qualitatively distinguish it from a “cold” morning. The general pattern reveals itself by means of the complex details, despite their ever-changing nature. We must ask: are we so different from beetles or the weather from the viewpoint of this Cruel Planet, in truth?

In the end, I was singing along at the top of my lungs with the enchanting music while belching loudly. I was praised to the heavens in the most refined Ancient Sintic, full of references to Kaushala (the Cosmic Power), for being so brave, probably (there’s a colourful and expressive language for you). I have been really busy learning about things like alphabets and pictograms, and dead languages like Mesmes from Kushnubia, and Nyawaygi from Streylya, and Pataxó Hã-Ha-Hãe from Brasa-land. I dream of translating something interesting and entertaining into Kimbric in the future (‘The Shameful Tale of the Boisterous Red Monkeys,’ for instance), and I’m close to succeeding! That’s life-long learning for you, isn’t it? But enough about my hobbies.

6. CONCLUSION: All these behaviours are faces of chaos: the complete disorder, the obvious order, and the hidden patterns. Under many circumstances a definite system will behave very regularly. But there is a smooth path from order to disorder, which is controlled by the system’s parameters. Since you can never measure the system’s characteristics totally accurately, the numerical values that you predict can appear different from the values observed in reality, under chaotic conditions. In a chaotic system, the smallest change at one time can cause qualitative differences later on: it’s not the calculations which are at fault. However, the enormous paradox is that even then, you can usually understand very well how the system will behave in general. We cannot always predict exact behaviour, but we can often discern qualitative patterns, and that is what’s important and useful. The earliest sophophilists understood these ideas instinctively. And even though they did not have the ability to analyse them numerologically, they expressed the constant interplay between inside and outside, between light and darkness, between fullness and emptiness, by means of images like the following:

So, when you look through the window, and worry about the tempest or heatwave round the corner, don’t blame the weather-prophets. Rather, you should smile (or weep), remembering that blasted beetle in Kharsag. After all, our Cruel Eyrth is one giant interconnected system, and it is beetles (or other insects, in a manner of speaking) that control the fate of everything here. And, remembering the proverb “as below, so above,” you’ll be able to see that it is the smallest things that steer the fate of the All-World itself too.

I was shown to the door in no time by the manager who had kept and eagle eye on me throughout the magical performance (well, better a nod from the Nuhwāb than rejection by the Rādzhā, so they say!). And of course I was very polite when the chef showed me his sharpest knife on my exit, too. Kali god of destruction knows what would have happened were I to have drunk “Snow-leopard” or “Serpent's Breath”! I prefer cats to birds, but I’m frightened of large ones like lions and so on, not to mention legless reptiles! Wallabies (which are also known as dwarf-kangaroos) are great too, but they tend to be impudent if they get the chance (like in the story 'The History of the Eight Wicked Wallabies who Wanted to Take Over the Whole World')!

I would encourage you all to go to "The White Elephant" too in order to imbibe the indescribable spicy atmosphere (to say the very least!). The place is on the outskirts of the town down a back alley between the small graveyard of the Temple of the Hidden Glory (and there under the gravel lies the champion darts-player from a former age named Trey) and Tesbyro. There’s no sign outside it (to help keep it secret and safe from the EGO's Purity Police of course, and 'cos they're too lazy to put one up or paint one), so you’ll have to use your nose. There’s something there to everyone’s taste, if you like a red-hot meal which is based on Kimbric foodstuffs with a bucketful of herbs. You’ll get your money’s worth, and have fun, at the same time, without a doubt. A word to the wise (I’m a pacifist, so there’s no stick for the unwise) – drink only glasses of water with slices of lemon in (beer in the belly, tumult in the head, after all!); don’t sing whilst quaffing your curry; and, by Kartikeya, avoid the wrinkled chillis like the plague! 

*             *             *             *             *             *             *             *

[*] I have to confess something to you that seems important before we fly off on our magic bed to the shores of the River Kunguh, Mother of the Three Paths. The old scoundrel Dai Procter had been trying to tempt me from time to time to commit myself to his strange ideas regarding mentalism expressed in terms of the numerological models codifying on-Mansha’s “Principle of Organic Pleroma” which says that everything contains everything else. As I’ve been explaining, I’m not an expert in anything important, just some kind of journeyman who’s got to earn his crust from day to day and live from hand to mouth, by existing on a knife-edge, eating honey from the hive, and catching the mouse and swallowing it (as it were – I love very living creature apart from beetles, of course!). But (to shut him up – if I let the cat out of the bag – although there wasn’t a single feline to be seen anywhere in truth), I’d been labouring to understand the article he’d thrust into my sweaty hands a couple of weeks before. I didn’t succeed – stop joking – but it felt very important, somehow. Dai was hoping to find the “magic equations” containing the “critical parameters” to reach the “strange attractor” or something. He kept on moithering about “hey-grammatikéy prīma” and the “secret language of nature” all the time. So, I’m presenting the piece word for word below (I had a paper-copy at the time, and I was trying to read it that day, which is maybe why I was so vexed). It’s “From Disorder, Let Order Come: The Bewitchment of the Beetle’s Breath” by the famed Madame Hupatíā Síykōsis. Maybe I’ll be able to learn a little from it even now! — F.Ll.

[**] Note that the author uses the words “akosmos” and “akosmic” (implying “disorder”) throughout the original article. I have changed these to the currently more commonly used "positive" terms which were introduced by D B Procter (maybe to throw people off his scent). — P.M. [I know not about what the honourable co-Wizard is speaking. He is barking up the wrong tree and backing the wrong horse for sure. I would never willingly deceive (despite the old adage, “needs must” – at times at least). For more information regarding “connotative chains,” see “What the Thorlin Have Wrought: A Report on Unknowing” by T Hrohri and E Fasivne — D.B.P.]

[***] I have the greatest respect towards the members of the strictest sacred orders (one need hardly say that!). (Although I could not live such a life: My mind is willing indeed, but my feeble body is too weak.) However, I have become very frustrated trying to understand this work on my journey to master topics like dynamical systems, systems dynamics, difference equations, phase transitions, critical parameters, bifurcations, period doubling, and catastrophe theory. For one thing, there was a small error in one of the graphs (2b), and I contacted the author to let her know about it. As well as that, the rather sloppy notation in the Table is not of the greatest help to an amateur sweating blood to get to grips with these intricate issues so that he might galvanize the Pallid Planet to heal itself. Well, doubt is the beginning of wisdom, I suppose. — D.B.P.

Mae iaith mor bwysig i’n profiad personol mewnol, a dyn ni’n ein deall ein hun ac eraill trwy holi’n meddyliau a’n cydberthnasau gan ddefnyddio iaith. O ganlyniad i hyn, mae’n bywydau ni ynghlwm wrth fywydau pobl eraill mewn ffyrdd sy’n gymhleth, dyrys, ac anwahanadwy. Dyna pam, yn aml, byddwn ni’n cofio a deall ffeithiau am bethau sy wedi digwydd i bobl eraill yn well nag am y rhai sy wedi digwydd i ni’n hun. Fe welwch chi, rwy’n siŵr, pam ein bod ni’n dod i ddwlu ar hanesion a chlecs; yn cofio gwybodaeth ar ffurf straeon yn well o lawer nag ar ffurf ffeithiau a ffigurau yn unig; ac yn fwy tebygol o brynu neu gredu mewn rhywbeth os oes stori ynghlwm wrtho. Gallai dyn ddweud bod y perthnasau ieithyddol hyn yn “gaotic,” ond nad yn hollol anesboniadwy o bell ffordd, er y bydd yn anodd cael hyd i’r geiriau priodol i’w disgrifio nhw’n hawdd ran fwya’r amser! Gadewch i fi awgrymu’r canlynol, felly. Yn hytrach na bod yn gymeriad mewn stori a adroddir gan rywun arall, beth am gymryd cyfrifoldeb a dechrau’r siwrnai dra pheryglus ond mor werth ei gwneud o fod yn gyfarwydd a meistr ar eich ffawd eich hun? Dyna beth a wnes i – gan ddianc rhag cadwyni bodolaeth wenwynig – ac os gallaf fi, gallwch chithau hefyd, yn eich ffordd eich hun, pan fyddwch yn barod!

“Dihuno’r Cawr yn Cysgu”

Ms Sesiline Arian

Cyfarchion cynhesaf fy nghyfeillion bore oes! Ffred sy 'ma to! Mor ddymunol ydy cael pleser eich cwmni dyrchafol a chyfareddol (rwy'n tybio a gobeithio) unwaith yn rhagor – yn enwedig yn wyneb yr adfyd, yr anobaith a'r arswyd yn amlhau ledled y Belen Byglyd hon y dyddiau dirwasgol hyn. Heddiw mynnaf eich goleuo ynghylch y pwnc llosg o fwyd rhyngwladol. “Yr Eliffant Gwyn” yw fy hoff dŷ bwyta heb gysgod o amheuaeth. Lle lliwgar iawn ydy, sy’n drewi o ffrwyth gwaharddedig o Ddyffryn Sintu. Dychmygwch lluniau ar y waliau! Y ddau hen ddihiryn hwnnw, Dvaldí a Hlevné, yn noethlymun groen yng Ngardd y Pleserau Daearol (nid oedd angen dail ffigys bryd hynny) lle dan ganghennau coeden bomgranad yr eistedd duw tew a chwardd yn ei ddyblau, ac iddo drwnc hir sarffaidd, clustiau dirfawr sigladwy, a llawer o freichiau fel y Coblyn Cosi Cellweirus. Ac yno mae’r creadur hyf yn denu’r ddau sy’n newynu am wybodaeth ryseitiau dirgel â dysglau fyrdd o gyrri stemllyd, danteithiol. (Dyna gyfeiliornus yw'r portread hwnnw o ran y manylion, er nad o ran y teimladau. Dylai pob dyn ag asgwrn athronyddol yn ei gorff wybod taw Davuth ac Elena a ryddhawyd o'u caethwasanaeth gan Xlotlringku Vlaltanlu-tnalzse yn Llwyn Xatlaltvazsu.)

Ww, dyw swyddogion Cangen Filwrol newydd yr EFE ddim yn rhy hoff o gwbl o’r fath ffeuau drygioni ble bydd y bywyd, y diodydd, y sbeisys syfrdanol, y gerddoriaeth ac adloniant arall, a’r naws, yn peri i ddyn lawenychu’n ddirfawr. Yn wir fe allai’r ficeriaid arfog ddwyn cyrch ar y lle unrhyw bryd. Eto i gyd, dim ond apothecari gostyngedig a dibwys wyf fi, wrth gwrs, sy’n tincran gyda hud yn ei amser sbâr, a dyw hi ddim fel petai olyniaeth faith o Ddewiniaid yn y teulu. Dyw’r awdurdodau ddim yn talu fawr o sylw imi, yn enwedig pan wyf wedi bod yn prysur weithio mor ddirgel yn labordy’r Clinig yn Aberdydd. Er gwaethaf fy holl bryderon, felly, ynghylch y pethau ofnadwy sy’n digwydd ym mhob cwr o’r Byd, dw i ddim yn gallu peidio mynychu bwytai cudd, sinemâu tanddaearol, arddangosfeydd anghyfreithlon, a chyrsiau astrus.

Nid gŵr dewr mohonof fi, ond bydd yr ofn yn gwneud i’r suddion creadigol lifo. Mae’r holl ansicrwydd dwysbigol, dychryn annisgrifiadwy, ac ofn affwysol yn grêt ar gyfer yr hanesion hynod dw i’n dyfeisio yn fy mhen drwy’r amser (pan wy’n gallu meddwl yn glir!). Yna fe fyddaf yn ymdrwytho yn y syniadau rhyfedd fydd yn codi bob amser i lenwi fy nychymyg ffrwythlon a’m hysbrydoli. O bryd i’w gilydd fe deimlaf fel petai Grym Diatal y Ddaear yn arllwys trwof fi, hyd yn oed, gan fy ngalw yn fy mlaen tuag at ryw Fyd Arall. Rywbryd pan fyddaf yn cwrdd â’r Datgeiniaid Dryslyd eraill ger y Domen Afiach, byddaf yn teimlo fel ‘taswn i’n wir fardd pen pastwn! P’un bynnag am hynny, rwy’n rhyw hanner breuddwydio mai os byddaf yn ymladd yn ôl cyn amled ag y medraf yn fy ffordd fy hun, dyna fydd un i’r awdurdodau gormesol. Dyma adroddiad wedi’i seilio ar fy mhrofiad fy hun felly, gobeithio byddwch chi’n ei fwynhau, neu gael rhyw les ganddo o leiaf.

Rwy’n dwlu ar fwyd sbeisiog, ac yn wir, am daith ar ffigar-êt coginiol oedd i ddod. Licswn i gyfleu ichi ychydig o’r naws a brofais y tro cyntaf y gwnes i dywyllu’i ddrws yn laslanc gwirion, amser maith yn ôl, ond eto i gyd, mae hen gof gan hen gi, onid oes? Efallai y byddaf yn dychwelyd yno am yr eildro cyn hir, a gobeithiaf y cofiant yr hen ddihareb – Cân di bennill mwyn i’th nain, fe gân dy nain i tithau – pryd bynnag y gwnelwyf. [*]

Cyn ddistawed â'r bedd ydoedd yno am hanner dydd un Sobr-ddydd gwlyb yng nghanol yr haf (roedd yn dawelach a bod yn onest, hyd yn oed o wybod presenoldeb y "famfleiddes" a'i thorlhwyth o "fleiddianod" a oedd yn caboli’r cerrig beddi ac yn plannu blodau parhaol caled yn ymylon y fynwent y drws nesaf). Hebé gu, roeddent yn cael hwyl a sbort a sbri o bob math ymhlith meirwon yr oesau, er gwaethaf y tywydd gwael. Yn yr oes yr ydym yn byw ynddi, fe ddylai pawb ddathlu rhodd marwolaeth heddychlon ac ebargofiant tragwyddol yn ei dilyn yn fwy aml, gan fod hon a wna i fyw fod yn werth chwil, rwy’n credu. O, y pethau rwy wedi eu gweld yn ystod fy mywyd, y cofion i gyd sy’n aros gennyf. Ond un dydd fe fydd popeth wedi mynd fel dagrau yn y glaw, pan ddaw’r amser i fi gysgu am byth. Wel am lol botes maip! Digon yw digon ar yr holl synfyfyrio athroniaethol, yr hen glebrwr.

1. EIN BYD DYRYS? Dych chi wedi edrych allan trwy’r ffenest erioed, gan feddwl tybed sut bydd y tywydd heddiw? Datganai rhagolygon y tywydd gydag argyhoeddiad y noson gynt byddai hi mor braf â’r haf yn Anialdir Mwyaf Faraqand. Ond erbyn hyn, mae hi’n bwrw glaw, ac yn edrych fel petai corwynt o Fynyddoedd Duon Kharsag yn cyrchu tuag at eich cartref. Wrth gwrs, ychydig o orliwiad yw hyn, ond serch hynny mae’r cwestiwn yn codi: beth sy’n bod ar yr holl ymdrechion i ddisgrifio a deall y fath hon o ffenomen ffisegol? Yn anffodus, mae’r anhawster yn rhan anhepgorol o’r peth sy’n cael ei archwilio. Mae’n codi’n naturiol pan fydd unrhyw system yn cynnwys rhannau sy’n gallu rhyngweithio gyda'i gilydd gan newid y system ei hun. Hyd yn oed tasai rhywun yn ceisio mesur popeth, a gwyddai’r hafaliadau priodol i gyd, ni fedrai hi ddweud yn gymwys beth fyddai’n dod i fod yn y dyfodol. Y rheswm dros hyn ydy fod yn y byd go iawn, bydd yn amhosibl dilyn trywydd popeth sy’n digwydd ar yr un pryd. Hefyd, ni fydd yn bosibl mesur unrhyw beth â manwl cywirdeb. Ac eto i gyd, y gwahaniaethau lleiaf un eiliad all achosi newidiadau ysgubol yn ddiweddarach. Dyma’r ffenomen o’r enw “caos” [**]. Mae caos ym mhob man, drwy’r amser – mewn traffig, mewn economeg, mewn peiriannau, mewn codau, ac mewn bioleg. Efallai y byddai’n ymddangos mai hollol anrhagweladwy yn y bôn yw’r ddaear gron, felly. Ond, wedi dweud hynny, dyw popeth wedi’i golli, oherwydd, ar y llaw arall, fe fydd yr un fath o batrymau cyffredinol i’w weld drwy’r amser, er gwaethaf sut bydd y manylion yn wahanol mewn pob achos. Mewn geiriau eraill, bydd yn amhosibl rhagweld y manylion i gyd bob amser, ond yn aml iawn fe fydd yn bosibl gweld braslun cyffredinol o beth sydd i ddod yn y dyfodol. Felly mewn gwirionedd, nid enghreifftiau o anhrefn lwyr ydy’r effeithiau sy’n codi o gaos. Yn hytrach, maen nhw’n gasgliadau o wybodaeth gymhleth, rydym ni’n gallu eu deall, os edrychwn ni arnyn nhw’n gywir. Gadewch i ni archwilio ymhellach.

Felly awn ni yn ein blaen gyda hanes yr epiffani o ran fy mlasbwyntiau. Roeddwn yn teimlo fel petawn yn bwyta gwellt fy ngwely ar ôl trallodion yr wythnos honno. Yn sydyn, fodd bynnag, roedd yn fy nharo i taw cam dros y trothwy yw hanner y daith, a chloffi rhwng dau feddwl a wnes i am eiliad gan ystyried wrthyf fy hun. Wedi dweud hynny, roedd y rheolwr cyn falched â'r Clown Bwrlésg o'r Syrcas Absẃrd, ac yn glustiau i gyd pan ofynnais am y fwydlen. Brasgamasai fe tuag ataf oddi mewn i’w adeilad tra oeddwn yn llechi’r tu mas iddo. Gŵr urddasol, swmpus oedd e, yn gwisgo lifrai sidan, wyrddlas ac arni ysgwyddarnau a botymau o aur; ac am ei ben roedd twrban ysgarlad wedi’i addurno â phlu ffenics. Fel rhyw was i'r Nuhwāb yn yr Oes Albertaidd oedd e. Neu ddichon yr oedd yn ellyll golygus ond dychrynllyd mewn un o'r chwedlau o'r Anialdir Mawr, Coch megis y Mil Noswaith ac Un, sut y gwyddwn i yn fy nghyni? Ond beth bynnag oedd e, roeddwn wedi fy mesmereiddio gan ei farf, oedd mor gringoch â fflamau ysol y Pwll Diwaelod. Yn wir, yr oedd i fod yn achlysur arbennig dros ben.

2. SEFYLLFA SEML: Dychmygwch chwilod yn tyfu mewn rhyw gynefin â maint penodedig, sy’n cynnwys cyflenwad di-ben-draw o fwyd (dyna bethau rhyfedd y mae rhifyddsoffyddion yn eu dychmygu!). Wrth reswm, wrth iddynt fwydo a thyfu, maen nhw’n cynhyrchu gwenwynau sy’n tueddu i’w lladd nhw, ac arafu eu tyfiant. I ddechrau, nifer penodedig o chwilod sydd yn y cynefin. Sut bydd nifer y chwilod yn newid dros amser? Rydym ni’n gallu defnyddio model rhifolegol syml yma. Y “Map Ymblethu Aflinol” ydy’r enw arno, ond peidiwch â phoeni, nid ydy mor frawychus ag y mae’n swnio! A bod yn onest, haws ydy sôn am ffracsiwn y cynefin a orchuddiwyd gan chwilod (yn hytrach na nifer y chwilod), a dyna y byddwn ni’n ei wneud. Byddai ffracsiwn yn hafal i sero’n golygu dim chwilod. Os bydd y ffracsiwn yn hafal i un, bydd yn dangos bod yr holl gynefin wedi’i gorchuddio ganddynt. Nodwedd hanfodol gyntaf y model yw ffracsiwn gwreiddiol y chwilod yn y cynefin ar y dechrau. Mae’r hafaliad yn cynnwys “adborth” achos bydd ffracsiwn newydd y chwilod yn dibynnu ar hen ffracsiwn y chwilod, ac felly bydd y proses yn mynd ymlaen, gan greu cenhedlaeth ar ôl cenhedlaeth. Hollbwysig yw’r “cysonyn,” sef nifer sy’n gallu bod rhwng 0 a 4. Mae’n cynrychioli pa mor gyflym bydd y chwilod yn tyfu, trwy ddefnyddio’r bwyd a’r lle sydd ar gael yn y cynefin. Ail nodwedd hanfodol y model yw’r cysonyn hwn. 

Y tu mewn, yr oedd y lle mor chwaethus. Roedd darnau dieithr o waith llaw ym mhob man; roedd hyd yn oed y waliau wedi’u haddurno â lluniau o dduwdodau gleision, a’u cnau coco enfawr a’u gwaywffyn anferthol. Bu bron i’m llygaid sefyll allan o’m ben. Nid oedd ddim byd fel ystrydeb ffiaidd, felly. Ar ben hynny, doedd hi ddim yn rhy boeth na swnllyd, heblaw am y gorgan ddi-baid a lifai o’r cyrn sain fel oernad rhyw gath ar fin marw (ac roeddwn eisoes yn gwybod gormod am hynny, ond well imi gadw at y stori). Serch hynny, doedd dim gormod o fynychwyr (nid yr un enaid byw heblaw amdanaf fi) ac roedd digon o le i chwipio chwannen (fel petai), diolch byth, achos fy mod yn casáu mannau caeedig. Os bydda i’n teimlo’n anesmwyth, fe fydd tuedd i fi ymddwyn yn debyg i goblyn bach anwar, fydd yn bloeddio ac yn udo, a cheisio rhedeg i ffwrdd fel gwenci.

3. CYFRIF CAOS: Mae’r Map Ymblethu Aflinol yn gweithio fel hyn. Cynrychiolir y cysonyn gan k a ffracsiwn y chwilod i gychwyn gan x₀: Dyw’r cyfrifiadau ddim yn anodd eu gwneud ar injan gyfrifo law. Ystyriwch, er enghraifft, k = 0.95 ac x₀ = 0.25.

Mae’n edrych fel petai’r ffracsiynau’n gostwng bob tro. Dangosir graff o’r canlyniadau yn y Ffigur 2(a) isod. Nesaf, gallwn ni archwilio pum sefyllfa ychwanegol lle mae x₀ = 0.25, gan ystyried un enrhif gwahanol o k ym mhob un. Dangosir graffiau o’r canlyniadau yn y Ffigurau 2(b) –  2(dd) isod. 

Yn unol â chyngor y fisir mawreddog, fe gefais i saig arbennig y tŷ sef “Dial yr Ymerawdwr” am ddecpunt ar hugain gan gynnwys tri chwrs a pheint. Nid craig o arian ydwyf erbyn hyn, nid o bell ffordd, ac nid oeddwn i y pryd hynny ychwaith. Roeddwn wedi colli fy swydd yn y gwaith cemeg beth amser cyn hynny, ac wedyn bu raid i fi wneud gwasanaeth cymunedol. Ac O, dyna helbul a helynt a ddigwyddodd fel cynlyniad, ni fyddaf fyth yr un peth eto, ond stori hollol wahanol ydy honno. Y mab a anwyd i rôt nid eiff byth i bum ceiniog, fel y meddant. Ond, roedd llawer o arian parod yn fy mhoced i ar ôl i fi dreulio’r bore ’na yn gwerthu hufen harddwch yn cynnwys ffwr cath a the cen crac, (hynny yw, trwyth a wneir o Dimentiseybin wawrani wedi'i fathru) y tu allan i’r siop hwylus leol hyfryd o’r enw Tesbyro.

4. TEITHIO o DREFN i GAOS: Ffigur 2(a) isod (k = 0.95): Dyw’r chwilod ddim yn tyfu, ac mae’r ffracsiwn ohonyn nhw’n gostwng tuag at ddim, hynny yw, maen nhw’n trengi’n llwyr. Dyma ddifodiant. Ffigur 2(b) isod (k = 1.2; k = 1.5): Mae’r chwilod yn gallu defnyddio’r bwyd i ryw fesur. Dydyn nhw ddim yn dod i ben, ac mae’r ffracsiwn ohonyn nhw’n cyrraedd enrhif cyson. Dyma sefydlogrwydd.

Fe wnes i ddechrau gyda chwrs cyntaf o selsig sir Lywysing â sinsir, garlleg, a chwmin, dysgl o gawl cocos a gwymon, ynghyd â bara naan brith a chaws Kaergenydd a chyrens ynddo, ar gyfer llyncu’r diferion olaf. Roedd y cyfuniad o sawrau estronol fel symffoni ar daflod fy ngenau. Drwy’r amser roeddwn i’n dal i feddwl taw gormod o bwdin a dagith gi, ond na allwn ffrwyno fy chwant bwyd. Wedyn, ymwrthodais y cyrri malwod arferol, ac yn ei le, mwynheais gyrri cig eidion â tsilis sybachog, ychwanegol, a chwilboeth ar y cythraul ydoedd hefyd, am ei fod yn cynnwys puprennod poethaf y byd, sef “Meddelwr Creigfryn.” Sut y gwn i? Wel, fe’u gwerthir yn Nhesbyro, sydd y lle llai drwg i fynd i siopa, yn fy marn ostyngedig i.

Ffigur 2(c) isod (k = 2.9): Mae’r chwilod yn gallu defnyddio’r bwyd yn dda. Maen nhw’n tyfu, ond pan fydd gormod ohonynt, byddant yn dechrau marw. Ar ôl hynny, byddan nhw’n gallu tyfu unwaith eto. Yn y pendraw, wedi osgiladu yn ôl ac ymlaen, bydd ffracsiwn y chwilod yn cyrraedd enrhif cyson. Dyma osgiladu tuag at sefydlogrwydd. Ffigur 2(ch) isod (k = 3.228): Mae’r osgiladu’n fwy amlwg. Dydy ffracsiwn y chwilod byth yn cyrraedd enrhif cyson. Maen nhw’n goroesi gan osgiladu rhwng dwy boblogaeth sefydlog.

Wedi hyn oll, bues o fewn y dim i drengi o syched, ac roeddwn i’n gorfod cael peint (neu ddau) o lagyr, o’r enw “Trochdrwyth Defaid,” i ddiffodd y tân eiriasboeth yn fy ngheg. Cofiwch chi yn awr na byddaf yn yfed fel rheol ddim ond poteli bach o gwrw chwerw gwan fel “Tylluan Ferw.” Ni bydd Enwen fy lojar yn gadael imi lymeitian ar unrhyw beth mwy meddwol os gall hi fy rhwystro. Ond ddyddiau a fu, ac yn enwedig yn yr ogof o londer honno, oedd mor dywyll ac mor swynol, ni allwn i ddim peidio. ‘Neno'r mawredd, roedd y lagyr hwnnw cyn gryfed â gwenwyn y weddw ddu! Mewn gwynfyd, cwplais i’r pryd o fwyd gyda hufen iâ spikni, a saws o ganel a chlof arno.

Ffigur 2(d) isod (k = 3.506): Mae’r chwilod yn goroesi gan osgiladu rhwng pedair poblogaeth sefydlog. Ffigur 2(dd) isod (k = 3.948) (llinell las): Mae’r chwilod yn goroesi gan osgiladu’n wyllt. Mae’n ymddangos nad yw unrhyw drefn i’r ffracsiynau. Beth fydd yn digwydd i’r chwilod yn nes ymlaen? Dych chi ddim yn gallu dweud, heb gyfrifo. Ymhellach, hyd yn oed os bydd ffracsiwn y chwilod yn dechrau o ddau enrhif sy’n agos iawn at ei gilydd, bydd yr ymddygiad yn hollol wahanol mewn cenedlaethau hwyrach. 

Mae’r enghraifft uchod yn y Ffigur 2(dd) hefyd yn ystyried x₀ = 0.251 (llinell goch). Edrychwch ar y ddwy linell yn y llun. Maen nhw’n debyg i’w gilydd yn gyntaf oll, ond maen nhw’n dod yn hollol wahanol yn gyflym iawn. Felly, newidiadau bychain yn yr enrhif cychwynnol (er enghraifft) sy’n gallu peri newidiadau aruthrol yn hwyr neu'n hwyrach. Beth fydd yn digwydd i’r chwilod yn y naill achos neu'r llall? Dych chi ddim yn gallu dweud, heb gyfrifo. Fodd bynnag, noder ei bod yn bosibl gwneud y sylwadau canlynol hyn sydd yn dra phwysig, heb yr un gronyn o amheuaeth: nid ydynt yn darfod â bod; nid ydynt yn tyfu heb lestair; ac mae eu nifer bob tro’n aros y tu mewn i derfannau penodol. “Cyfaredd Chwyth y Chwilen” yw’r enw ar yr ymddygiad hwn. Mae’n ein hatgoffa sut mae rhywbeth cyn lleied â chwilen yn chwythu’n galed yn Kharsag all newid y tywydd yng Nghimbria.

Mor llawen â’r gog ar y gainc oeddwn, er bu bron i’m perfeddion ffrwydro. Ond o gofio hyn, rhaid i fi roi gair o rybudd i chi: byddwch yn ofalus wrth ddefnyddio’r cyfleusterau yno. Pan ddechreuodd fy ngholuddyn mawr chwyrnu fel ci’n sugno’r mêr o asgwrn suddlon, rhuthrais i’r tŷ bach, sy’n dwt ond yn bêr iawn, lle caeodd y drws yn glep y tu ôl i fi. Yn anffodus, aeth y clo yn sownd, ac ar ôl hanner awr o ymdrechu ar y sedd borslen, wedi’i dilyn gan awr o weiddi drwy dwll y clo, fe’m hachubwyd gan weinydd yn ei lifrai odidog. Ar ben hynny, oherwydd fy mhrofiad anesmwythol, roedd o’r pwys mwyaf imi dawelu fy nerfau carpiog. Ar unwaith, felly, fe chwafftiais ddysglaid o goffi Kimbrig (mae hon yn cynnwys llawer mwy o wisgi, na choffi Eirwig cyffredin) ac wedyn, yn syth, un arall.

5. TREFN “GAOTIG”: Dyma’r ffenomen o’r enw caos. Nid ydy’n ymwneud â chwilod yn unig, ychwaith: mae a wnelo â llif traffig mewn dinasoedd, ag iechyd marchnadoedd cyllidol, ag y rhyngweithiad rhwng robotiaid a’u hamgylchfyd, â chreu algorithmau amgryptio, ac â’r perthnasau rhwng ysglyfaethwyr ac ysglyfaethau. Pan fydd rhannau unrhyw system yn rhyngweithio gyda’i gilydd, llawer o batrymau gwahanol a all digwydd. Pa un sy’n digwydd a fydd yn dibynnu ar enrhifau a ddisgrifia nodweddion y system, fel tymheredd, pwysau, cyfradd genedigaethau, ac ati. Yn  ein henghraifft seml, dim ond dau beth sy’n rheoli ymddygiad y system: enrhif y cysonyn, a ffracsiwn cychwynnol y chwilod. Gall ymddygiad y system ddod i ben yn llwyr, cyrraedd sefydlogrwydd, osgiladu rhwng sawl enrhif, neu newid heb unrhyw batrwm amlwg o gwbl (ceir crynodeb yn y Tabl isod) [***]. 

Fodd bynnag, mae hefyd un peth tra phwysig nad ydy’n amlwg mewn graff fel Ffigur 2(dd). Er gwaethaf yr anrhefn  ymddangosiadol, mae’n bosibl bod rhyw “drefn guddiedig” yn bodoli yn y fath ymddygiad – ac mae yna ddulliau rhifolegol i ddisgrifio, deall, a defnyddio’r “rheoleidd-dra cuddiedig” hwn. Er enghraifft, ystyried rhyw fore penodol, pan fydd y tymheredd yn newid yn anrhagweladwy i bob pwrpas. Serch hynny, mae’n aros rhwng terfannau penodol yn bendant, a byddwn ni’n disgrifio’r bore fel un “twym” heb yr un broblem, ac yn gallu gwahaniaethau’n glir o ran ansawdd rhyngddo a bore “oer.” Bydd y patrwm yn ei amlygu ei hun trwy gyfrwng yr holl fanylion cymhleth, er gwaethaf eu natur cyfnewidiol. Rhaid i ni ofyn: a ydym ninnau mor wahanol i chwilod neu’r tywydd o safbwynt y Blaned Greulon hon, mewn gwirionedd?

Yn y pendraw, roeddwn yn cydganu nerth esgyrn fy mhen gyda’r gerddoriaeth gyfareddol gan fytheirio’n uchel. Fe gefais fy nghanmol i’r cymylau mewn Hen Sinteg coethaf, yn llawn cyfeiriadau at Kaushala (y Pŵer Cosmig), am fod mor ddewr, siŵr o fod (dyna ichi iaith liwgar a mynegol). Rwy wedi bod wrthi hi’n dysgu am bethau fel gwyddorau ac arwyddluniau, ac ieithoedd marw fel Mesmes o Kwshnwbia, a Nyawaygi o Streilia, a Pataxó Hã-Ha-Hãe o Dir Brasa. Rwy’n breuddwydio am gyfieithu rhywbeth diddorol a diddanol i’r Gimbreg yn y dyfodol ('Hanes Gwarthus y Mwncïod Cochion Hwyliog,' er enghraifft), ac rwy o fewn ychydig i lwyddo! Dyna ddysgu gydol oes ichi, onid ife? Ond digon am fy hobïau i.

6. CASGLIAD: Mae’r ymddygiadau hyn i gyd yn wynebau caos: yr anhrefn lwyr, y drefn amlwg, a’r  patrymau cudd. Dan lawer o amgylchiadau bydd system benodol yn ymddwyn yn rheolaidd iawn. Ond llwybr gwastad sydd rhwng trefn ac anhrefn, a reolir gan baramedrau’r system. Am nad ydych byth yn gallu mesur nodweddion y system yn fanwl gywir, gall y gwerthoedd rhifiadol y byddwch chi’n eu darogan ymddangos yn wahanol i’r meintiau a fesurir mewn realiti, dan amodau caotig. Mewn system gaotig, y newidiad lleiaf ar un adeg sy’n gallu achosi gwahaniaethau ansoddol yn nes ymlaen: nid y cyfrifon sydd ar fai. Fodd bynnag, y paradocs caotig yw mai hyd yn oed wedyn y byddwch chi’n gallu deall yn dda iawn sut bydd y system yn ymddwyn yn gyffredinol. Ni allwn ddarogan ymddygiad manwl bob amser, ond fe allwn ni ganfod patrymau ansoddol yn aml, a dyna a fydd o bwys ac yn ddefnyddiol. Deallai'r athronwyr cynharaf y syniadau hyn yn reddfol. A hyd yn oed nad oedd ganddynt y gallu i'w dadansoddi'n rhifolegol, fe fynegent y cydadweithio cyson rhwng y tu fewn a'r tu fas, rhwng golau a chysgod, rhwng llawnder a gwacter, trwy gyfrwng delweddau fel y canlynol:

Pan fyddwch yn edrych trwy’r ffenestr, felly, ac yn poeni am y dymestl neu’r don wres ar ddyfod, peidiwch â rhoi bai ar y proffwydi tywydd. Yn hytrach, dylech chi wenu (neu wylo), gan gofio’r chwilen blagus honno yn Kharsag. Wedi’r cwbl, un system enfawr gydgysylltiol ydy ein Daear Greulon, a chwilod (neu drychfilod eraill, mewn ffordd o siarad) sydd yn rheoli ffawd popeth yma. Ac o gofio’r ddihareb “megis isod, felly uchod,” byddwch yn gallu gweld mai’r pethau lleiaf sydd yn llywio ffawd yr Holl Fyd ei hun hefyd.

Fe’m danfonwyd i’r drws cyn pen dim gan y rheolwr a gadwasai lygad barcut arnaf trwy gydol y perfformiad swynol (wel, gwell cydnabyddiaeth gan y Nuhwāb na gwrthodiad gan y Rādzhā, meddan nhw!). Ac wrth gwrs fe fues i’n foesgar iawn pan ddangosodd y sieff ei gyllyll fwyaf miniog imi ar fy ffordd allan, hefyd. Kali dduw dinistr a ŵyr beth fyddai wedi digwydd pe buaswn i wedi yfed “Llewpard Eira” neu “Anadl Sarff”! Mae’n well gennyf gathod nag adar, ond yr wyf yn ofni’r rhai mawr fel llewod ac yn y blaen, heb sôn am ymlusgiaid heb goesau! Mae walabïod (a adwaenir fel gor-gangarŵod) yn wych hefyd, ond tueddant i fod yn haerllug, os cânt y cyfle (fel yn y stori 'Hanes yr Wyth Walabi Drwg oedd Eisiau Cymryd yr Holl Fyd Drosodd')!

Fe fyddwn i’n eich annog chi i gyd i fynd i'r "Eliffant Gwyn” hefyd er mwyn drachtio’r awyrgylch anhraethadwy o sbeisiog (a dywed y lleiaf yn wir!). Mae’r lle ar gyrion y dref i lawr llwybr gefn rhwng mynwent fechan Teml y Gogoniant Cuddiedig (ac yno mae pencampwr dartiau o’r oes a fu o’r enw Trey yn gorwedd dan y gro) a maes parcio Tesbyro. Nid oes ddim arwydd y tu allan iddo (i helpu i'w guddio rhag Polîs Purdeb yr EFE wrth gwrs, ac am eu bod yn rhy ddiogel i hongian neu beintio un), felly bydd rhaid ichi ddilyn eich trwyn. Mae yna rywbeth at ddant pawb, os hoffwch bryd o fwyd gwynias sy’n seiliedig ar ymborth Kimbrig gyda llond bwced o berlysiau. Fe gewch chi werth eich arian, a hwyl, ar yr un pryd, heb os nac oni bai. Gair i gall (heddychwr ydwyf, felly ni bydd ffon i’r anghall) – yfwch wydreidiau o ddŵr a thafelli o lemon ynddynt yn unig (cwrw yn y bol, twrw yn y pen, wedi’r cwbl!); peidiwch â chanu wrth gwafftio’ch cyrri; a, myn Kartikeya, osgowch y tsilis crych fel y pla!

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[*] Rhaid i fi rannu rhywbeth wrthoch chi sy’n ymddangos yn bwysig cyn i ni hedfan bant ar ein gwely hud tuag at lannau Afon Kunguh, Mam y Tri Llwybr. Roedd yr hen ddihiryn Dai Procter wedi bod yn trio fy nhemtio i o bryd i’w gilydd i ymrwymo â’i syniadau rhyfedd ynghylch meddyliaeth fynegwyd yn nhermau modelau rhifolegol sy’n cyfundrefnu “Egwyddor Cyfanrwydd Organig” on-Mansha, a ddywed fod popeth yn cynnwys popeth arall. Fel dw i wedi bod yn esbonio, nid arbenigwr mewn dim byd o bwys mo fi, dim ond rhyw fath o jermon sy’n gorfod hel ei damaid o ddydd i ddydd a byw o'r llaw i'r genau, drwy fodoli wrth fin y gyllell, bwyta'r mêl o'r cwch, a dal y llygoden a'i bwyta (fel petai - dw i’n dwlu ar bob creadur byw ac eithrio chwilod, ac yn enwedig cathod gwyn a cheiliogod du, wrth gwrs!). Ond (er mwyn rhoi taw arno, a gadael y gath o’r cwd, er nad oedd yr un gath i’w gweld yn unman mewn gwirionedd), bues i’n llafurio uwchben deall yr erthygl a gwthiodd e i’m dwylo chwyslyd gwpl o wythnosau o’r blaen. Lwyddais i ddim - peidiwch jocan - ond bu’n teimlo’n bwysig iawn, rywsut. Roedd Dai’n gobeithio dod o hyd i’r “hafaliadau hud” yn cynnwys y “paramedrau critigol” er mwyn cyrraedd yr “atynwyr rhyfedd” neu rywbeth. Roedd yn dal i falu awyr am “hey-grammatikéy prīma” ac “iaith gyfrin natur” drwy’r amser. Felly dw i’n cyflwyno’r darn air am air isod (roedd copi ar bapur ‘da fi ar y pryd, ac roeddwn i’n ceisio’i ddarllen y dydd ‘na, a dyna pam mod i’n becso gymaint, siŵr o fod). “O Anhrefn, Deled Trefn: Cyfaredd Chwyth y Chwilen” yw hi, gan yr enwog Fadam Hupatíā Síykōsis. Falle bydda i’n medru dysgu ychydig ganddo fydd o gymorth i ni yn y dyddiau ‘ma, hyd yn oed yn awr! — Ff.Ll.

[**] Noder bod yr awdur yn defnyddio’r geiriau “acosmos” ac “acosmig” (yn awgrymu “anhrefn”) drwy gydol yr erthygl wreiddiol. Rwy wedi newid y rhain i’r termau "positif" a gyflwynwyd gan D B Procter (i daflu pobl oddi ar ei drywydd, falle), ac a ddefnyddir yn fwy aml bellach. — P.M. [Ni wn am beth y mae’r cyd-Ddewin anrhydeddus yn sôn. Mae’n mynd ar ôl ysgyfarnog ac yn cefnogi’r ceffyl anghywir i sicrwydd. Ni thwyllwn i fyth o’m bodd. (er gwaethaf yr hen ddywediad, “angen a yrr yr hen i redeg” – ar adegau o leiaf). Am fwy o wybodaeth ynghylch “cadwyni cynodiadol,” gweler “Yr Hyn a Wnaeth y Thorlin: Adroddiad ar Ddiwybod” gan T Hrohri ac E Fasivne — D.B.P.]

[***] Mae gennyf y parch mwyaf tuag at aeloda’r urddau cysegredig caethaf (prin bod angen dweud hynny!). (Er na fedrwn i fyw’r fath fywyd: Fy meddwl yn wir sydd yn barod, ond fy nghorff ffaeledig sydd ry wan.) Fodd bynnag, rwy wedi mynd yn rhwystredig iawn wrth geisio deall y gwaith hwn ar fy nhaith i feistroli pynciau megis systemau dynamig, dynameg systemau, hafaliadau gwahaniaeth, trawsnewidiad gwedd, paramedr critigol, deufforchiadau, dyblu cyfnodau, a theori catastroffeau. Yn un peth, roedd camgymeriad bach yn un o’r graffiau (2b), a gwnes i gysylltu â’r awdures i roi wybod iddi amdano. Ar ben hynny, nid ydy’r nodiant eithaf esgeulus yn y Tabl o’r help mwyaf i amatur yn llafurio uwchben cael gafael ar y materion dyrys hyn, er mwyn galfaneiddio’r Blaned Biglas i’w gwella ei hun. Wel, amau dechrau doethineb, mae’n debyg gennyf. — D.B.P.