Fractals Everywhere

I start off with a solemn apology, for having abstained from posting for so long. But nonetheless here's an interesting find. Fractals Everywhere.

It is common knowledge, that natural phenomenon like cloud formations, ocean currents and smoke follow fractal patterns. Taking a leaf off my interest in photography, I found fractal patterns using photographs I had clicked. The technique is simple, and I will add the explanation to this post in a little while. Till then, have a look at the patterns themselves.

The Buddhabrot (lookalike, so to say) : Receding waves at the beach

The Mandelbrot Set

Mandelbrot Set extension

More to come...

Warning labels suggested by physicists

Physicists have embarked on their own product safety campaign, recommending that manufacturers provide consumers with all of the following labels...

WARNING: Due to its heavy mass, this product warps the space surrounding it. No health hazards are yet known to be associated with effect.

NOTE: This product may actually be nine-dimensional but, if this is the case, functionality is not affected by the extra six dimensions.

HEALTH WARNING: This product (and every product of the Manufacturer) emits low-level nuclear radiation.

NOTE: A subatomic "glue" holds the fundamental constituents of this product together. Since the exact nature of this glue is not yet fully understood, its adhesive power cannot be guaranteed. To date, no known malfunction of the product has resulted from glue failure.

DISCLAIMER: Manufacturer is not responsible for loss should this product disappear into a wormhole.

LIMITED WARRANTY: Despite the efforts of the Manufacturer, the chaos in this package has increased since being shipped. If such chaos has rendered the product defective, Buyer shall not hold Manufacturer responsible. Claims in this regard should be aimed directly at the Shipper.

NOTE: Despite its appearance, this product is more than 99.99% empty space.

READ THIS BEFORE OPENING: According to quantum theory, this product may collapse into another state if directly observed.

HANDLE WITH CARE: This product contains countless, minute, electrically charged particles moving at extremely high speeds.

EXTREME CAUTION: This product has an energy-equivalent that, if exploded, could destroy a small town. Under no circumstance shall a User perform a mass-energy transformation on any of the contents in this package. In case of misuse, liability shall rest entirely with the User.

GUARANTEED RETURN CLAUSE: Because of the uncertainty principle, we have shipped this product with a limited speed notice. However, if shippers have disregarded our notice, we cannot guarantee that all the contents are in the box. If you discover missing components, please call the 1-800 number on the instruction sheet.

IMPORTANT: This product is composed of 100% matter: It is the responsibility of the User to make sure that it does not come in contact with antimatter. Under no circumstances will the Manufacturer be liable for User mishandling in this regard.

QUALITY STANDARD: The electrons, protons and neutrons are guaranteed to be of same quality as those used in other products of the Manufacturer.

DISAPPEARANCE EXCLUSION: Due to quantum tunneling, there is an extremely tiny chance that this product may suddenly disappear at any time (and reappear elsewhere). The Manufacturer will not be responsible for such mysterious disappearances.

AS REQUIRED BY LAW, we must inform you that any use of this product increases the amount of disorder in the universe. As of the date shipped, Congress has not passed any bills assigning a tax on disorder pollution.

USE LIMITATION: This product cannot be guaranteed to function normally near a black hole.

WARNING: According to the Copenhagen interpretation, this product may be used already. On a consolatory note, you shall have the unused product in a parallel universe.

more to come soon...

Source : Internet, and some contributed by me...

The butterfly, frayed jeans and sporadic behaviour

One of the most elegant, but mathematically and explicably complex phenomenon in nature, which alters the course of our lives starting at the most naive aspects, and finding roots in the most substantial happenings, is the essence of what science now calls "Chaos". It is responsible for the unexplained changes brought into our perception ranging from our observing the complex geometry of nature, topography or snowflakes to more intangible equivalents like

public behaviour, emotions and changes in personality itself.

Chaos theory is a relatively new science which deals with the chaotic changes brought to a system by minor factors which prevelant scientific methods usually neglected in their inconceivable potency. It started off as an explanation to the failure of accurate weather prediction even when aided by the most powerful computational facilites. The famous butterfly effect, which in popular culture has found tremendous fame owing to movies, sitcoms and books citing its nuances, and often using the same as the main plot, was the basis of the "Chaotic" interference in weather, which stated that a butterflies flapping of wings can trigger changes in weather which magnify over time (not neccessarily long though) to completely change its initial course. Now you possibly cannot know the exact pattern of flapping of wings of all butterflies over the face of earth, and hence, cannot know how the weather will exactly turn out to be. All we can do, is approximate.

Having only read and thought about chaos theory a lot, I indulged myself in a self proposed experiment, in my first year of engineering. The pair of jeans I used to wear the most, I also had to fold the bottom of. So I carefully measured the length of the folds, increasing that of the left leg a centimeter more than the right's. (This was my slight change in the initial conditions, often the premise of chaotic events) My logic was that since the way both ends of the jeans would be moving will be approximately the same, also both going over the same terrain at the same velocity, to name a few, the initial change I made would be the pivotal factor governing the changes (if any) brought to the jeans. After a span of 2 months, the result was glaring at me in a stark realisation of the theories authenticity, and immense pleasure at having carrying out an explanatory experiment firsthand. The left leg of my (favorite) pair of jeans lay in a furiously frayed sartorial equivalent of a car crash. The right, although, was only slightly torn. The slight variation in parameters had rendered my jeans totally unwearable, atleast, a half of it. There were indeed a lot of other disturbances too, but notwithstanding, I was hooked into the

essence of chaos itself.

Coming to Chaos in our lives, it is an insurmountable adversary when it comes to predicting the course of events. And talking about the most intangible of its manifests, behaviour, and how a certain aspect of a relation may end up being, is totally unpredictable. These are also entities we cannot quantify using the arsenal of scientific procedures we currently have. So, how a person will behave regarding certain things is not only their personal choice, which may be discernible after a prolonged analysis of his behaviour, but is also effected by chaos. Slight changes in the course of action end up altering things to an extent of randomness. Like your saying "Im sure my relation with (Say) Alpha (Using the letter X for a person is not exactly my idea of exemplifying. Alpha sounds more of a name anyday, and yeah, its ALSO a letter * winks * ) will turn out to be exactly like * whatever it is you feel *." Now the very minute changes in your individual behaviours inevitably ends up changing the initial assumption to an extent where it is embarassingly different than what you thought it would be. The safest bet is hence not to be too sure of things. On a slightly unrelated topic, even G.F.B Reimann, the man behind the proposition of the dead famous Reimann Hypothesis actually said "Sehr warscheinlich" (meaning "most likely") regarding the occurence of the roots of the Reimann zeta function on the critical line, when it may actually be true, and hence awaited impatiently. This may not have to deal with chaos in any percievable manner (see this statement too keeps in mind any unlikely possibility), but it is just an example that surity is not as complacent amidst a vortex of uncertainity.

From the unpredictable motion of a simple double pendulum, to mapping random walks of people leading to fractals, to the abrupt change in behaviour of a person whom you thought you knew like the back of your hand, to stellar clusters of irregular pattern at first sight, chaos is an underlying initiator. What I do is to keep a blurred but definite objective for everyday activities in life, rather than a vividly detailed image of how to proceed to that objective, for the minor variations happening around me are totally beyond my involuntarily obtuse perception, let alone control, so how they'l effect the details of my initial plan, I cannot predict. The objective may be as simple as buying a few items from the store, visiting the ATM, collecting a reciept and recieving the clothes from the laundry. Now if I formulate a specific order in which I complete those tasks, in a normal day, I may be able to do it, but it will invariably lead to a day when everything goes wrong and I ask deaf heavens above "Why me?". The ATM may be crowded when I chose to reach, the bank official on a callously prolonged lunch break, the laundry still not done and the store out of stock. This would also effect my other nested plans to the initial one,

hence spoiling a later big picture. My ethereal surity that a close friend will always behave the same way, is bound to a mortal wound over time because there may be seemingly indifferent changes in the way we express to each other, our being possessive in some minor way, disliking and objecting to the most mundane traits, habits or likings, can eventually accumulate to so immense a difference in the outcome of the relation that we succumb to emotionally conjured pillars of disloyalty, mistrust, betrayal or mood swings of an obtuse order. Chaos is an undeniable aspect of governing offices, regardless of what you chose to observe. It would only be foolish, therefore, to ignore its effects.

"Physicists like to think that all you have to do is say, these are the conditions, now what happens next?"

- Richard P. Feynman

Syllogistic Fallacy - When logic fails...

Logical analysis of situations is a human approach to life, in general. And logic, is not always universally justified, and has multiple implications and associations, for perceptions vary. Fallacies frequently mark the process of logical dissection of any situation.

Of the various "wrong" logical approaches, the Syllogistic fallacy is one which I extrapolate to in a vast number of situations. It falls under the category of reasoning which goes by the name "Syllogysms".

Syllogisms are arguments which consist of 2 statements, which include a "major premise" which is a general statement, and a "minor premise", which is a specific statement. There is a conclusion based on the two premises. Syllogisms can be tactfully used to persuade people regarding something wrong, which directly said would be rejected, but presented as a Syllogism, would lead to its acceptance.

A general representation for Syllogisms can be approximated to the following:

If A, then B. If B then C.

Since A, therefore C.

And a simpe example would go something like:

"If I get up late, I miss classes. If I miss classes, I run short of attendance. Hence if I wake up late, I lose attendance."

A Syllogistic fallacy, au contraire, is a widely misinterpreted form of the same, often seen in the intellectual iconoclasts who prefer to apply a partially understood logical musing than to grapple its nuances completely prior to experimentation. The various kinds of Syllogistic fallcaies can be enumerated as "Affirming the consequent", "Denying the antecedent", "Illicit Minor/Major" to name a few.

Here's a veritable digression from an acceptable approach.

"If I was Isaac Newton, I could solve this piece of calculus." Now I go ahead and actually solve the problem and then say, "I just proved I'm Isaac Newton", while I did no such miraculous feat...

The problem is evident now.

If A, then B : is true. But : since B, therefore A; is wrong to its very core.

It is a logically inappropriate approach, which people tend to follow with an ease of familiarity.

Teacher's, often tend to bask in Syllogistic fallacies, and use them as means, although inappropriate, to prove their students' subordination. How often does a teacher call upon a student to the board, when he is caught off guard sleeping, talking or not paying attention in his infinite appetite for distractions, and asks him to solve a seemingly obscene problem. Their approach is, approximately, this: "If you are a fool, you cannot solve it. Now you couldn't solve it, therefore, you are a fool." I would strongly disagree as to WHO the fool is, here, yes offence...

Other day to day encounters (from my perspective, needless to mention) include:

"We won the match, the people watching it are shouting." I cannot extrapolate, confined in my room, to the fact that "Since the people watching the match are shouting, we won". (This is a firsthand recollection. And I am not proud of it.)

"If you proxy for someone, there would be 2 similar handwritings on the paper. Now since there are 2 similar handwritings here, you have proxied". (A habitual fallacy my Strength of Materials teacher literally lives in.)

"Its thursday, the mess food is inedible. Now the mess food being inedible could lead you back to ANYDAY and ANYTIME" (Which is a universal truth)

If you liked this article, you probably read it to the end.

Now since you read it to this point, I'm sure you liked it.

Syllogistic fallacy.

- Vitruvius.

Schrodinger's Cat : Wanted Dead AND Alive

Theories, thought experiments, propositions and their likes are misinterpreted by many (A subtle Syllogistic Fallacy) to be looked upon as textbook tools, which not only incarcerates their own thinking, but also the true potential these theories hold, in simplifying life and in answering many questions. From dilemmas you cannot come out of to public behaviour, they can be answered using simple extrapolation of these laws into the situation you are in.

A dog is a man's best friend (or so they say), but the Cat, is surely his best guide...

Schrodinger's Cat, the classical thought experiment suggested by the great Austrian physicist Erwin Schrodinger. The paradox goes like this. A cat is confined in a closed box (Not interacting quantum mechanically with the surroundings), and the box has a flask of hydrocyanic acid, which is broken as a result of a random quantum mechanical event like disintegration of a radioactive element. Now, the question is, whether the cat is dead or alive, inside the box. The answer is, there is a finite probability of the cat being BOTH dead and alive at the same time, which cannot be told until the box is opened and looked into. This experiment has a Copenhagen interpretation which says that the system stops being a superposition of states (dead AND alive paradox) when it is subjected to observation. This is a Quantum decoherence of sorts, which prevents the independant states to interact with each other. This de-coherence means that when the observer is about to view the cat (which is initially split), the system splits into 2 paths, the observer facing a dead cat and another with an observer facing a living cat. This is in accordance to a multiworld theory.

"Schrodinger's Cat" is a very good reply I find to most questions asked by people regarding life, situations and happenings. From trivial issues to contemplating whether the mess food is edible or not, the answer can be found out by "opening the box", i.e, to taste it firsthand, to people contemplating relationships, and whether they will work out or not. The latter is a more complex propositions and the number of variables involved is virually infinite.

Relationships are complex happenings (Occam's Razor CLEARLY suggests we must not include too many variables in our assumptions, like most people do while listing their "expectations" from their partners. It is a fallacy, and leads to states much more complex than contemplated due to chaotic changes brought in by minor disturbances in the details.) Coming back to the "Cat", it holds a lot of answers compensating for the questions it raises.

If you don't know what someone thinks of you (its now good AND bad), if you are undecisive as to whether the ATM is working or not (it is both functional AND being repaired), and EVERY similar dilemma is a superposition of states, which according to the Copenhagen interpretation will split into a state of existence which is unique. Although, the result may not always be in your favor. The food may still be bad, the ATM still non functional, the hostel bathroom geyser STILL * sigh * not switched on, but what I do in such cases is congratulate another Quantum Mechanical "me" which bifurcated into the desirable situation, and now happier than me, for I am pretty sure "he", or rather "they", must be doing the same whenever I am in a state of benefit and they are not. * I add a sympathetic look for every time "I" suffer for "my" benefit *

Before you read this post, there MUST have been a thought in your mind regarding whether or not it's worth reading. I do not know whether the cat was dead for you, or alive. But you approached the situation JUST as Schrodinger did. By opening the box.

We all think scientifically, only are a times too blind to notice it. I intend to draw parallels between theories and our applying them subconsciously in life.
Our world doesn't govern science, science govern's it. So enjoy its beauty and elegance, in EVERY walk of life. Like I do.

PS: Were I in Schrodinger's palce, my thought experiments would have a dog as a subject for sure. They scare me, no ends...

Vitruvius.

The Divine and the Diabolus

Irony marks the facets of life in so many instances, which are basically realisations of the initially overlooked. But then again, they are undeniable, and a close scrutiny of anything is bound to unearth underlying foibles and ironies.I had been playing with some trigonometry the other day, in Wolfram Alpha, that I uncovered this for myself.

Having been through the era of "Da Vinci Code", even the most mathematically disinclined minds are aware of the Golden ratio, Phi, equal to 1.618 approx. It is found to play a vital role in nature and its beauties. Often connected to proportions of the human body, proportions in plants, animal exoskeletons and around everything that seems beautiful in nature. Hence it was also named the "Divine Proportion".

Irony lies in the fact that this "Divine" proportion has more "Diabolic" origins, as the math reveals. The value of the "Divine Proportion" is exactly equal to "-2Sin(666)". Needless to mention, 666 being the "Number of the Beast". Satan's influence in the evolution of the world as we know it, has been speculated to being profound. Maybe he actually did sneak into the ratio too. Maybe just another instance of the intertwining of good and evil.

Symmetries, can also be disturbing.

Vitruvius.

Pilot

Alternate Datum, is my point of view of events, scientific or not, from mathematical and metaphysical grounds of interpretation. The posts must not be confused for scientific writeups. They are in all rhetorical reality interpretations in more scientific a manner than usually meets the eye. And this is what I had planned to blog about, when I learnt what blogging was somewhere astronomically down the timeline now. The thought stuck. But my introduction to blogging superseded the initial idea. So in a parallel venture, I have decided to revive the disintegrated thought before it goes beyond the event horizon of retrieval.

Alternate Datum :

Alternate : Unconventional, different, contradicting, and to some extent distant.

Datum : A reference line for measuring quantities relative to it.

I hope that explains the name.

With buoyant hopes.

Vitruvius.