The Pitanga Club

I have wonderful friends here, kids just like me, couldn't choose better ones. We are of various ages. Timmy, the youngest, is less than seven months old and June, the oldest, is slightly more than eight. It may appear odd for such a big girl to reach this place, but when June arrived, she was "different". She couldn't talk and was totally apathetic and helpless. She had been that way all her life up to then. However, soon after she joined us, June blossomed and became talkative, active and friendly. Now all of us chat and laugh. Even little Timmy talks and laughs, just like the rest of us. Merriment is very meaningful to us. It distracts us from the anguish that we feel when we think of our parents, our sisters and brothers and all our friends whom we left behind.

All of us have a similar story. That's why we decided to establish a club. We called it the Pitanga Club in honor of … Oh, I haven't yet told you that the favorite member of our club is a sweet puppy whom we all adore, and therefore we decided to call our club in her name, Pitanga. What brought Pitanga here? Usually it doesn't happen to dogs. They are generally alert and the first to jump out when the door opens, but it seems that Pitanga had been sleeping and when she woke up it was too late.

Time doesn't pass here in the way it does down there. It has a different course, which I cannot explain. That's why I remained and shall forever remain four years old, yet ever since I arrived here I learned a lot about the nature of people and of everything in general. That's why Timmy will always be less than seven years old and June will always be slightly more than eight, and all the rest of us will forever stay at our permanent ages. Yet, just like me, all have learned a whole lot about everything, even Pitanga has.

What brought us here? Although each of us came from a different background, the occasions of our arrival here are very similar, even that of Pitanga our adorable puppy. So, let me tell my personal story, which is much alike to those of my friends in the Pitanga Club. But first it is important for me to emphasize that I don't bear a grudge against Dad. When the incident happened, I suppose I was furious, actually I can't say for sure how I felt. It was so intolerable that whenever I try to remember it my thoughts stray away in another direction. All I know is that my agony was indescribable, so horrid was it. What I do remember was that at first I couldn't understand how it happened that Dad forgot me in the back seat of the car. Dad, who had loved me so much, who always used to spoil me, who had rejoiced when he saw me every late afternoon on his return from work. Did he suddenly stop loving me? Had I done something so naughty that he didn't want me anymore?

Now, when I see – yes, we can all see everything that occurs down there, not through our eyes but in another way that I cannot explain – when I see how, every night, both Dad and Mom weep, Dad the big, strong, brave man crying like a little boy … When I see how both my parents hardly sleep at night and say again and again how much they miss me, I know that Dad never stopped loving me and Mom as well, of course. I see their grief and all I wish for them is happiness, laughter and joy as had been in our home before the incident happened.

Mom and Dad keep going to work every morning. They have no choice, needing to provide not only for themselves but also for my little sister and my two bigger brothers. Actually my little sister is by now bigger than I am, since she is nearing her fifth birthday while I am still and shall always remain four. 

As I stated above, I am not mad at my father. On the contrary, I love both Mom and Dad and am deeply sorry that they suffer so much, both of them. I miss them so much and it grieves me to know that we shall never meet again. I do deeply resent that wicked woman who shrieked at my father, when he was standing on the sidewalk shaking like a leaf, completely broken at the sight of my lifeless body being drawn out of the car. She cursed him, called him a murderer and wished him a life sentence in the worst possible prison. Also, I am furious at all those opinionated fools who, without understanding the harm that they are doing, posted on the Web such  venomous things about both my parents (yes, about my Mom too!), as though the horrible torment that they endure is not enough. It seems that most people think that it couldn't happen to them. My parents too used to believe that it couldn't happen to them. In the days that I was still with them body and soul, when similar tragedies were reported in the media, Mom and Dad were both shocked and appalled, unable to understand how parents can forget a child in the family car. They thought such negligence is criminal and were certain that it couldn't happen to loving, responsible parents such as they considered themselves rightfully to be. So they thought, until it happened to Dad.

Scientists who specialize in brain research offer  an explanation to the phenomenon. According to them, normative, responsible parents who love their children, care for them and take all measures to ensure their safety might, under stressing circumstances or unexpected distractions, forget a beloved child in the car on a hot day, remembering him or her only after Death has taken its toll. That's how our brain works, shoving to the background crucial information when preoccupied by new concerns. Yes, it can happen to anyone, no exceptions. So they say and I know how right they are. I know that the parents of all my Pitanga Club friends, even the couple who had adopted Pitanga our sweet puppy, were good folk, loving, caring, responsible and convinced that it could not happen to them. Alas, to their dismay and to ours, the truth proved in the cruelest way how delusive their confidence had been.

To claim that the parents are not guilty is not entirely correct, because they had disregarded all recommendations intended to prevent the occurrence of such tragedies, which appear from time to time on the Web, TV, radio and printed media. Whenever the media reported about a child who had died after being inadvertently left in a car, people like my parents expressed their disgust but rejected expert  evidence based on the fact that every driver, parent or not, who takes an infant in a car is vulnerable to such forgetfulness because of some distraction. They refused to believe it and shirked the trouble of learning and following expert advice and safety tips that are available on the Web (links are provided toward the end of this essay). Sure enough, they always fasten their seatbelts before driving off, mainly because if they fail to obey the law that demands it they are susceptible to a significant fine. However, there is at present no law that requires parents to take heed of tips intended to prevent boiling their beloved child to death, so why bother?

We, members of Pitanga Club, a cheerful bunch of kids who love company, are strongly opposed to receive newbies (kids, puppies or any other pets) because we realize how much endless pain is involved with each new arrival. It can and must be prevented.

Now, to be realistic, a dead child does not suffer. The dead do not suffer because they don't feel anything. The agony is first of all that of the beloved child who is cooked to death in the back seat of the sweltering car, then of his parents who are tormented for the rest of their lives. If you don't want to join those parents, if you don't want your children to join Pitanga Club, if you wish to continue leading a normal life that allows you to smile and laugh from time to time, do the right thing, pay full attention to expert advice, adopt the tips and make it a habit to use them. Do your utmost to safeguard your children from falling prey to a catastrophic diversion of mind. Click now on http://www.kidsandcars.org/heatstroke.html  to get to a site that provides valuable safety tips and detailed information about the issue. 

You may also consider buying and installing proper safety devices that are marketed on the Web, and/or downloading a suitable application to your smartphone. If you decide on that, make sure that you investigate the reliability of the device that you choose. However, don't rely blindly on any product, guarantied or not. It would be a good idea to regard such a device as an additional precaution to the safety habits that you have adopted. Remember, nothing is foolproof. The responsibility of your child's safety is first and foremost yours.

You can find links to safety device vendors as well as comprehensive information on the subject in the following site:

http://carseatblog.com/38247/babies-in-hot-cars-it-can-happen-to-you/

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What can be said about Space?

Did it start with the "Big Bang"?

 

Personally, I'm skeptical about the so-called Big Bang theory and prefer to call it a conjecture (educated guess at most). I realize of course that there is evidence that such a phenomenon occurred (cosmic background radiation, expansion of the universe, etc.) yet all this evidence is circumstantial. The Big Bang has never been actually observed in any scientific experiment.

Yet, by linear extrapolation of the expansion of the universe as measured by modern astrophysical methods there is common consent in the scientific community that approximately 13.8 billion years ago the entire physical universe started its existence as a tiny spot in space that violently exploded. All physical laws, including causality which is the very basis of these laws, came into being precisely at the moment that this enormous event occurred. Thus, the idea that the creation of the universe was spontaneous, without any prior cause, is not contradictory to logic. Total absence of physical rules means total absence of impossibilities. In other words, where there are no laws, nothing is unreasonable. Therefore the presumed spontaneous occurrence of the Big Bang did not logically require a cause.

So why am I skeptical? Simply because the Big Bang conjecture contradicts common sense that is based on scientific experiments and discoveries. Why should we embrace a conjecture that our common sense rejects, rather than pursue a more sensible explanation that complies with astrophysical phenomena?

So, having failed to answer the first question, let me proceed to the next.

What is this thing called Space?

 

Before I begin to attempt a clear comprehensive answer I want to emphasize that by the word Space (capital S) I refer to the metric three-dimensional space that contains the entire universe, not just to a part of it.

We know how to measure distances and direction in Space, to specify locations and to mathematically express all aspects of motion in it. However, it is very difficult (I believe even impossible, at least for me) to envision Space without any material object or at least some sort of energetic radiation somewhere within it. That is because our vision of space is inherently coupled with metric dimensions and angular directions in term of measurements. Measurements are by nature comparative. Whenever a dimension or angle of anything is measured, it is compared to the corresponding known property of a material object or a wavelength (that is also true of other properties such as temperature, optical, electromagnetic or chemical values, etc.). If only our minds existed in an otherwise entirely empty Space, we couldn't perceive any dimension or direction because we couldn't compare them to anything (just for orientation we need the position of some object for reference, such as  our nose, the three-dimensional features of which can used to determine which direction points "forward",  which points "up" and which points "right" or whatever names we choose to call the axes of our frame of reference. By the way, when two orthogonal directions are specified by common nomenclature, the third is unambiguously determined, e.g. once we assert the directions of north and up we know exactly where east is). In fact, in such a ubiquitous void such properties would not exist, being comparative by nature. The concept of geometric forms such as straight line, circle, cone or sphere would also be meaningless (because the properties of any geometric form are inherently defined in terms of distance and direction – not just formally but by their nature).

Thus, the concept of Space requires the existence of matter or at least energetic radiation in it (not just because a living observer made up of these constituents is required, but because the absence of matter and energy divest Space of its inherent properties). In short, Space needs matter and/or energy in order to exist. Obviously, matter and energy need Space just as crucially, but that is not part of this essay.

Space also requires Time for its existence (and vice versa). In a former essay (Time, Causality and the Relation between them) I showed the interdependence of Time and causality for their mutual existence and experimented mentally with the imaginary concept of a universe devoid of causality. I explained (convincingly I hope) that the universe could not persist for any period of time, no matter how infinitesimal, without causality. Non-persistence for even the most infinitesimal period of time means nonexistence. Thus, Space depends on Time for its existence.

So, now that we are convinced (at least I am) that Space needs Time and matter in order to exist, how do we define it?

At last, a definition!

 

A definition is a proper answer to the question "What is …?". By proper I mean that it conveys the meaning of the concept defined as clearly and comprehensively as possible. I'll try to do it for Space as best I can, within the limits of my personal understanding of the term. You will notice that I shall admit that there are properties of Space that I don't know to their fullest extent (I believe that nobody does).

First of all, Space is the container of the entire universe. It is three dimensional, in the sense that we can use a three-dimensional orthogonal axes-system (known as a Cartesian system) or, if we prefer, a triplet of  polar axes or any other suitable system of three independent mathematical entities to pinpoint locations or determine directions in Space. It is isotropic, meaning that neither the lateral nor the angular position of a body in Space has effect on its dimensions and form. If a stiff rod, straight or crooked, is moved or rotated, all its geometric properties (length, thickness, curvature, roundness etc.) are maintained – assuming of course that they are not affected by external forces. Isotropy of Space also means that, without an external physical entity for reference (such as a viewable object, a source of sound, a gravitational or magnetic field, etc.) we cannot have the slightest idea about our location and orientation. That is because all physical laws that act on any object in Space do not depend on our position in Space.

We also know that there are some properties erroneously attributed by some people to Space, such as angular orientation, linear and angular motion (these properties are relative by nature, and cannot be attributed to Space because there is no reference to which they can be compared) or physical properties that material objects have. 

Oops, haven't finished! Seems there is more to be said!

 

So far so good, but Space has other properties too, some of which are to this day an unsolved mystery or at most under scholarly debate. Does it somehow extend beyond the limits of the universe?  Is it really expanding or oscillating? Is it enveloped by a spherical or other-shaped boundary or is it infinite? Does it have a distinct center? Is it continuous or discrete? How is it affected by the laws of relativity (both special and general) and quantum physics? Is it unique or a subsystem of an esoteric hyperspace? Can it split into multiple spaces that cannot interact with each other? Why is metric Space three dimensional and not, for example, four-dimensional? I assume there might be other questions that have so far been left unanswered.

I don't have a definite answer to any of these questions and I doubt that anybody in the World does. However, prominent scientists do have their opinions on at least some of these issues, backed by experimental evidence, analysis, logic and common sense. I also have an opinion on these issues that is based on ideas that I have heard, read, learned or arrived at by thoughts that occupied my mind.

First of all, the relation between the boundaries of Space to those of the universe is a semantic issue. As far as I know, all serious scientists regard Space as the locus of the universe in its entirety. If the universe is finite, Space does not extend beyond it and there are no physical rules beyond it. That's unimaginable, but otherwise either the universe is infinite (hard to imagine) or closes upon itself in a three-dimensional analogy to a closed circle within a four-dimensional hyperspace (such an idea has been seriously proposed by scientists but at least for me it is totally beyond imagination). Most physicists and astrophysicists believe that the universe (and thus Space) is finite and expanding.

Some scientists toy with the idea that the universe is oscillating, at present in the phase of expansion in a periodic cycle which will eventually pass to a phase of contraction. That's a weird idea because it defies the rule of increasing entropy (if you don't know what entropy means, just take my word for it), which apparently means that causality is reversed. If that is not sheer nonsense, I don't know what sheer nonsense is.

Most scientists today believe that the boundaries of Space are continuously pushed out by the radial expansion of the presence of matter (and perhaps antimatter) and radiated energy. Physical laws are carried outward up to those boundaries in unison with this expansion. Nothing exists beyond those boundaries, not even empty space, and thus physical rules do not extend beyond those boundaries. Even the phrase "beyond those boundaries" is meaningless, unimaginably as it sounds. Are these boundaries spherical? My answer to this and to the question about whether Space has a distinct center is: "Who knows? Who cares?" Hopefully I'm not offending anybody. I can assure you that our planet is at a safe distance from the nearest point on the boundaries of  Space, if such exist, by at least thousands of light years (probably much more).

Is Space continuous or discrete? I mean Space, not the universe (which is not synonymous to Space). Well, from the point of view of classical physics, discreteness means that the points that constitute Space are separated by gaps. If that were the case, the metric dimensions of each Space point would each have a value that we may call "the elementary unit of length in nature" and nothing material, wavy or void could be smaller. Even if that were a valid possibility, we still have gaps of this model to consider. If they are microscopic regions of empty space (just gaps in the universe) then they are still included in the regions that constitute Space and therefore are not gaps as far as Space is concerned. If they are true gaps in Space then they are dimensionless, meaning that distance measurements that pass through them do not skip any metric lengths and are therefore continuous. So, in any case, classical physics rules out discreteness in Space.

Special relativity deals with differences in time durations, metric lengths, masses and all other material properties related to them as measured in frames of references that move relatively to each other. To my best knowledge, these differences do not affect the continuity or discreteness of Space, whichever is true. As far as I know, neither does general relativity, my knowledge of which is limited to popular scientific publications. What remains is quantum theory with its Heisenberg principle of uncertainty according to which the exact location of every elementary particle is inherently somewhat vague, with a precision that is inversely proportional to the precision we have of its momentum. Quantum theory also deals with discrete values of energy, spin and other properties of elementary particles when they interact with other particles inside atoms. I'm far from being an expert on the subject but I've never heard or read of any effect that quantum theory has on the properties of Space itself, so I conclude that as far as I know, Space must be continuous. 

My next two questions, whether Space is unique or part of an esoteric hyperspace and whether it can be split into multiple spaces, sound perhaps like referring to science fiction. However, renowned scientists regard these questions seriously. None has come up with an answer, not even a clue except some conjectures about black holes being portals to other universes (reminds me of Costigan's Needle, a science fiction book I read decades ago). I believe that it is absolutely impossible to either prove or refute these issues.

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The assumption that multiple spaces exist raises at least four possibilities:

1.     All spaces exist in mutually disjoint locations in a common three dimensional container - OR

2.     Each space has its exclusive set of  three dimensions, completely dissociated from those of its peers - OR

3.     All spaces exist along disjoint "time" axes - OR

4.     All spaces share the same time axis, their metric properties might coincide or overlap with different boundaries, but all the "material" and "energetic"  constituents as well as all natural rules in each space cannot interact in any way with those of the other spaces.

The first model seems to me least likely for the following two reasons.  First, it implies null-dimensional  gaps that in turn implies that the spaces are completely crammed together. That is plausible only for a limited set of polyhedra (assuming that all spaces are of the same form) or a weird collection of convex and concave forms. Second, it implies metric continuity at the boundaries unifying all spaces into one.

The second and third models seem to be abstract ideas. I think they are both beautiful, baffling, esoteric, a challenge to inquisitive minds. Abstract I said? I have examples that I'm sure that anyone who reads this can understand, because undoubtedly everyone has experienced them. One of them is fiction, the other is dreams (including daydreaming). In both examples, our mind is exposed to an imaginary ambiance with metric and temporal features same as those we have in "true life". (I admit that these examples are not perfect, because their features are affected by those of the "real world", however once they have been created there is no further interaction). OK, you may say, but they are imaginary. So what if they are just imaginary, whereas our Space is real? What does "real" mean? If multiple spaces exist, is our Space real and the others imaginary? Objectively, all spaces should be of equal standing, so that if the others are imaginary, so is ours. Furthermore, there are philosophers who propose that our existence is imaginary, a thought experiment of a mind somewhere out there in hyperspace.

  

The fourth model actually proposes multiple universes residing in one common space, except that they might perhaps have different boundaries (beyond which the physical laws of the corresponding spaces do not exist). Such a notion might challenge scientists to seek signs of the existence of so far unknown forms of pseudo-matter or pseudo-energy that would, under special laboratory conditions, emerge to the surface and hopefully not swallow us all.

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The last question I brought up was why does Space only have three dimensions. Before I continue I suggest that if you are not acquainted with vector analysis or have forgotten what you learned in college years ago, read a concise and very clearly written tutorial explaining Elementary Vector Analysis on the Web. It should suffice to understand the following answer to the question, but if you wish to obtain more information you can of course google for more advanced texts on the subject.

The shortest answer I can think of to the question above is that mathematically, a metric isotropic space cannot have more than three dimensions. That is because Space must have geometric properties that can be represented by an orthogonal coordinate system. According to the rules of vector analysis, the cross product of any two orthogonal unit vectors in a three dimensional system yields a unit vector normal to their common plane. There cannot be an analogous relationship between the constituents (unit vectors or unit planes or whatever) of a higher dimensional coordinate system. So, there go any prospects you may have for a four-dimensional metric space. Of course, Time is referred to as the fourth dimension in scientific parlance, but evidently it is not metric.

Just a few more words

 

That's all for now. The short account that I intended to write of my thoughts about Space blew up as in a Big Bang and if I don't stop now who knows how far its boundaries will be pushed out, so, to conclude I would like to beseech the Almighty if He (or She) is behind  the creation of the universe: "Please stop expanding our boundaries, at least for a while. We are very curious to know what lies beyond them but we just can't keep up with your pace!"