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I went to scientific american and stumbled unto this short but intriguing question: what is the origin of zero? Yeah. Stephen Hawkings has the "brief history of time", so what is the "brief history of zero"? (answer below)
"What is the Origin of Zero?"
http://www.scientificamerican.com/askexpert/math/math12/
Robert Kaplan, author of The Nothing That Is: A Natural History of Zero, provides this answer:
The first evidence we have of zero is from the Sumerian culture in Mesopotamia, some 5,000 years ago. There a slanted double wedge was inserted between cuneiform symbols for numbers, written positionally, to indicate the absence of a number in a place (as we would write 102, the '0' indicating no digit in the tens column).
The symbol changed over time as positional notation, for which zero was crucial, made its way to the Babylonian empire and from there to India, via the Greeks (in whose own culture zero made a late and only occasional appearance; the Romans had no trace of it at all). Arab merchants brought the zero they found in India to the West, and after many adventures and much opposition, the symbol we use took hold and the concept flourished, as zero took on much more than a positional meaning and has played a crucial role in our mathematizing of the world.
The mathematical zero and the philosophical notion of nothingness are related but aren't the same. Nothingness plays a central role very early on in Indian thought (there called "sunya"), and we find speculation in virtually all cosmogonical myths about what must have preceded the world's creation. So in the Bible's book of Genesis (1:2): "And the earth was without form, and void."
But our inability to conceive of such a void is well caught in the book of Job, who cannot reply when God asks of him (Job 38:4): "Where wast thou when I laid the foundations of the earth? Declare, if thou hast understanding." Our own era's physical theories about the Big Bang cannot quite reach back to an ultimate beginning from nothing-although in mathematics we can generate all numbers from the empty set. Nothingness as the state out of which alone we can freely make our own natures lies at the heart of existentialism, which flourished in the mid-20th century.
Answer posted October 04, 2001
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Now that you got an explanation, may I ask this question:
"What the origin of zero government?"
"State of nature", according to social contract theoreticians Hobbes, Locke and Rousseau.
"Primitive communal" mode of production, according to Karl Marx.
"Invisible hand/perfectly competitive market", according to classical economists like Adam Smith.
"Invisible nature", according to Nonoy Oplas. he he he.
-- Nonoy Oplas
But apparently something came out of nothing. This may seem strange, but is in accord with current physics. The "nothingness" (even between isolated hydrogen atoms in intergalactic space) is actually a seething, foamy soup where some things (photons, electrons, etc.) come into being for very, very short periods of time. This is not a violation of the laws of conservation of mass/energy. There is a loophole in those conservation laws related to the Heisenberg uncertainty principle, where for such short periods of time (Planck's constant in the uncertainty formula) some "things" will spontaneously "be" out of "nothing". An analogy --- if you're filching centavos from a multi-billion dollar trans-national, and you make sure to return those centavos very quickly, then the (conservation) accountant won't notice.
A practical example --- you would think that photons generated in the computer monitor travel across space and impact your retinas, thus generating the image you see. Well, not quite. There are "virtual" photons that spontaneously come into existence in the space between the monitor and your eyes. The reason these photons are "virtual" is because they lack the energy to become real. Thus, virtual photons dissappear as quickly as they appear.
But now a "real" photon from the monitor collides with one of these virtual photons (during its momentary, "magical" existence); the impact destroys the original "real" photon, while all its energy (momentum, spin, frequency, etc.) gets transferred to the virtual photon, which now (because of the energy input) becomes a "real" photon and continues the journey to your eyes. Along the way, this newbie photon collides with another virtual photon, etc. You get the photon ... errrr ... picture, so far?
So, am I saying that this foaming bubble bath where "particles" spontaneously come into being out of nothingness, is what there was before the big bang? Ahhh ... NO (don't hit me! promise, 3 paragraphs na lang, and all will be made clear, i hope :) You see, before space and time, there was no space-time within which the "foam" could exist (be).
Another "parable" to underline the statistical nature of our physical reality ---
Say you fill a kettle with water, put it on the stove and turn on the heat. You would expect that kettle to come to a boil in 15 minutes or so; which is what *usually* happens. However, it is possible (albeit very, very improbable) that all the water molecules in that kettle will by chance slow down to the point that the water freezes. It is also possible that a large number of those water molecules will simultaneously jiggle in an "up" direction. Voila! You have the highly unlikely (but possible, and possibly entertaining) scenario of your "takure" freezing over *and* dancing a jig on the stove.
Getting back to the "time" before space-time when there was no nothing ... think of "eons" as equally meaningless as "blink of an eye", there was no time in no-space. Then, out of nowhere --- a completely specious and capricious "Fiat Lux" - the Big Bang. Because of "it", space was suddenly defined and existed. Because "it" exploded (developed over time), then time also came into being (a very detailed account by Steven Weinberger describes the composition and time-table of the Big Bang, starting from billionths of a second after its eventuation).
Ah-whew! ... pant, pant, pant ... ang hirap no'on ah ...
Now, regarding the "zero" of existentialist nothingness :) ...
The logical framework of Existentialism developed using Kantian dialectic, through Hegel (and this is where it diverges from Marx) to Husserl's Phenomenology. The "nothingness" is described as existential (being) angst, the helplessness and despair one feels upon being "thrown" into an uncaring, amoral existence. Best exemplars of this thread of existential thought are the French leftist Jean Paul Sarte (Being & Nothingness) and the Nazi Jesuit Martin Heidegger (Being & Time).
There is a seperate thread in Existentialism (the one that I personally subscribe to) inititated by the Danish son of a child-beating Protestant minister - Soren Kierkegaard (a.k.a. Horatio Bogbinder), which, while acknowledging the dark and despairing situation into which we're thrown, seeks "authenticity" in an explicit admission that we are so helpless (try though we might to rise above the "herd"), that at the very edge of the reality of this dark precipice, we must take a "leap of faith" (yes, Kierkegaard originated that phrase, in the same way that Sarte originally stated: "hell is the other"). (BTW, both Kierkegaard and his dad were also suicides.)
Both Christian and atheist branches of Existentialism acknowledge the cold, barren "nothingness" (zero) of the reality of existence into which we are thrown.
- WYn Yu
In the "Brief History of Time," blackholes are described as super dense holes of nothingness. It is so dense that nothing can exist within its borders including time. Being super dense it sucks all matters near and turn them into nothing. Imagine the earth going deep into the core. Several kilometers down it is said that after the solid rocks, there is liquid (for how can a solid exist under pressure from the largeness of the crust and the rocks). Down to the very core, I forgot, but I can theorize that it should be a mixture of gas and liquid if not gas. Imagine an infinite pressure that acts on a matter, say a photon, then that infinite force will turn it into nothing. That is the blackhole, the origin and existence of nothingness if we set our time today (since we are way zillions from the big bang). A blackhole exist at the center of our galaxy, the Milky Way. All the galaxy stars revolve around the blackhole. If the big bang (before) is the original nothing of the universe, then it seems that the expanding universe has also created several centers of nothingness where all matters revolve. You see, everything therefore revolves around nothing and everything were created from nothing. How was that?
You see, if we ever want to travel the universe fast, human beings has to evolve into near nothingness. Because our physical being can't travel fast, i.e. at the speed of light. We have to turned into matters of energy to travel at the speed of light and then regroup :-) into its original upon reaching the destination in another galaxy. Wonder if it is possible that a beam of light as it travel bends like a curve? Because the matter where it is passing through is moving at a speed much faster than the speed of light. Just like if we are in a spaceship that travels faster than the speed of light, a light entering through a hole in one side of the spaceship will bend as it hits the other side of the spaceship. The universe is tricky because everything is infinite. And the irony of it all is that after infinity there is nothing. Notice the two mirrors facing each other in the barbershop. The orginal mirrors reflect each other, the second one has a second reflection of the other.. and so on until infinity where there is nothing.
The belief of hindu incarnation where an existing life will incarnate into a higher form of after-life is a linear analogy of the process from creation (from original nothing) into several stages until perfection (back to original nothing). Child of the universe!
They say classical economics, from Adam Smith to Marx, is Newtonian. This is exemplified materially by the mass production of similar goods during their time. So is neoclassical economics of Marshall where conceptualize an equilbrium exist, e.g. supply and demand. As the economy of men advances, so are the economic theories that applies. The differentiation of demand and the consequent response of production where customers are served almost simultaneously with the design intended of their current individual tastes and preferences, changes production economics. The multi-equilibrias of individual demands and production supplies are similar to molecules of quantum mechanics rather than Newton's equilibrium of forces.
Consider government. Originally there were no governments (from nothing). As information technology advances more, as individualism of men flourished in production and in peace, as perfect information is achieve, the market becomes infinitely efficient and there is no need for government (back to nothing).
-- Joey Sescon
I had been much into devouring C.S. Lewis materials and i think i am one with him in the idea that there is no such thing as the philosophical nothingness. Reality is not limited to the natural and to say that nothing lies beyond the natural is not correct. Lewis espoused the notion of the supernatural, where God resides, or that probably the supernatural is God itself. Philosophically he had substantially argued that well in his book "Miracles".
Since i believe in God's all-encompassing wisdom and The Creation, it seems inconceivable that God would leave an unutilized portion in the universe (thinking as if God is a economist , yeba!) even if its just 1/zillionth of a speck of dust. The philosophical zero is therefore non-existent.
Now on the mathematical zero, it does not symbolize nothingness as well. Zero is a symbol of empty space but not nothingness. Empty space has use, unlike nothingness. For example:
1. Take the number 10, if zero is nothingness 10 should be smaller than 9. But if zero is just an empty space but is existent, it is more conceivable that 10 is greater than 9.
Eto pa.
1 X 1 = 1
but: 10 x 10 = 100
It seems that zero is expanding in terms of space, while empty.
Now, zero an an empty space only makes sense if you have a concept of something that is not empty, say a 1 beside it.
consider this:
10 X 2 = 20
but: 0 X 2= 0
Therefore, an empty space creates emptiness by itself. But coupled with an occupied space like a 1 to make 10, the empty space manifests a new meaning. Like the sides of the bowl in relation to the empty space of the bowl. or, like the walls of the house to the empty psace in the house.
2. if you have nothingness between your legs, kawawa ka naman. But if you have empty space between your legs, either you are a female, a transvie... or a japanese. Sakang po kasi. joke.
3. According to some famous Chinese philosophers, the empty space of the bowl is what defines its usefulness. The bigger the empty space, the bigger the capacity of the bowl.
4. Also, the wider the empty space between the walls of the house, the bigger the house. But the smaller will be the universe outside.
From this 4th example, its really worth the thought that this universe is a zero sum game in terms of space and time. The only reason why beyond space and time its no longer a zero sum game is because the mind is infinite, and the heart is capable of loving one person, and then another, without necessarily losing the love for the first one. Kaya kung marami kang gelpren, oki lang yun.
5. If you have nothingness beside you, twilight zone ang dating nun. While if you have an empty space, isa lang ibig sabihin nun, mag asawa ka na! ;)
-- Ozone Azanza
From Joey Sescon: “In the "Brief History of Time," blackholes are described as > super dense holes of nothingness. It is so dense that nothing can exist within its borders including time.”
Ahhh ... actually there's something in them darn blackholes, prob is we can't even "imagine" what it's like in them. Even the mathematical formalism cannot describe what's *inside* a black hole. Super crunch-time to the max, 'ika nga.
As for "time", well that has to do with the "event horizon" which is the fringe *outside* the black hole where the pull of gravity (acceleration) matches the speed of light. We say that a photon will travel a "light-year" in a year; which is equating distance over time, and basing it on the massless speed-of-light particle - the photon. At the event horizon, the pull of gravity is so strong (or the curve of space-time is so great) that not even the ultra-light (massless) photon can escape. Since our physical measure of time is based on the photon, and since a photon will be effectively "frozen" at the event horizon, then we say that time stops at the event horizon (but time continues for an observer outside the event horizon).
On going into deep Earth, if you were to dig a hole straight through from Boracay to the Amazon jungle you would initially fall quickly through the hole. About halfway through to the core, your fall would slow down because "half" of the earth's mass would now be above you. You'd still have enough momentum to zoom you past the center of the earth and pop-out the other side with piranahs snipping at your heels. You'd hover over the jungle for a while, before plunging straight back down in our direction. You'd zoom back and forth through the earth in smaller oscillating arcs until you finally come to a wobbling rest in the middle of the Earth. NOT fun, methinks.
Also from Joey S: “You see, if we ever want to travel the universe fast, human beings has to evolve into near nothingness. Because our physical being can't travel fast, i.e. at the speed of light. We have to turned into matters of energy to travel at the speed of light and then regroup :-) into its original upon reaching the destination in another galaxy.”
There are 2 distinct issues in that paragraph. One is "encoding", the other is "transmission". The first part is to "read" you and transcribe you as a signal. The second part is to get that signal (info) from point A to point B, and then reconstitute/decode you at the destination.
I haven't the fuzziest notion of how to read/encode/transcribe a human being, warts and all. The "transmission" part is equally vague, but i have some ideas --- "speed of light" is actually a limiting factor. I'd go the whole hog and opt for *instantaneous* transfer of information across space-like intervals.
Current physics gives some hints at 2 options --- either 1.) trans-luminal propagation of information, or 2.) failure of local causality. The first implies instantaneous communications, the second imlpies that the butterfly fluttering at your window has something to do with a super-nova hundreds of light-years away. Weird, noh?
Possible that a beam of light as it travel bends like a curve? Yes, and this was experimentally proven during an eclipse after the First World War. You can imagine a beam of light bending under the powerful gravitational influence of a black hole, for example. However, strictly speaking, a "beam" of light (the path of a photon) is always straight. The beam will seem to bend because it is following a "straight" line in the vicinity (gravity) of curved space-time. The "beam" is straight, the "space" is curved.
More from Joey S: “Because the matter where it is passing through is moving at a speed much faster than the speed of light.”
While only photons can travel *at* the speed of light, there are ideas of a particle, called a "Tachyon" that can only travel faster than the speed of light. While photons are massless, the hypothetical Tachyon has a mass represented by an imaginary number (square root of negative 1, type thingy).
”... Just like if we are in a spaceship that travels faster than the speed of light, a light entering through a hole in one side of the spaceship will bend as it hits the other side of the spaceship.”
That is exactly the train of thought that lead Einstein to formulate the Special Theory of Relativity.
Notice two mirrors facing each other in a barbershop, the mirrors will invert left-right, but do not invert up-down. Don't you wonder at that?
From Ozone Azanza : “I am one with him in the idea that there is no such thing as the philosophical nothingness… Reality is not limited to the natural and to say that nothing lies beyond the natural is not correct. Lewis espoused the notion of the supernatural, where God resides, or that probably the superatural is God itself.”
Can we at least say that the "nothingness" referred to by Existentialist philosophers is a reference to a personal sense of despair and futility?
Lewis exactly posits the supernatural, therefore there can be no "nothingness" (in the beginning He hovered over the void). Kierkegaardian (Christian) Existentialism makes explicit the "dark chasm" of human experience, then presents the solution of the "leap of faith". Kay Lewis - faith muna, walang chasm; kay Kierkegaard - chasm talaga, then take the "leap of faith".
God given Her omniscience and omnipotence may or may not have Her reasons for creating and maintaining a "null-zone" of nothingness. Who are we to gain-say that? After all, this God gave us free will, which is heroic/tragic from an human perspective, but strange (irrational?) from the POV of an omni-potent God ... until you factor in "caritas" - viz. I cannot love even the most perfect of androids, but i can and do love this crazy human being who goes completely bonkers every time she gets PMS.
Ozone: “Now on the mathematical zero, it does not symbolize nothingness as well. Zero is a symbol of empty space but not nothingness. Empty space has use, unlike nothingness.”
"Placeholder", I agree. Seeing your math examples though, I have one caveat --- the commutative principle (in arithmetic) does not apply to quantum physics. That is to say, at the sub-atomic level, "a * b" does NOT equal "b * a".
Meanwhile, there's this story about a professor who described correlations between a structure and such things as the distance from Sol to Sirius. Panay ang paliwanag, kuwenta at kuwento sa klase niya. The class was really "wowed" by the significance of these stunning correlations. At the end of the period, the prof pointed out the window to a newstand/kiosk. The students actually checked all the numbers (including the angle of the kiosk roof vis-a-vis the spring solistice), and all the figures checked.
-- Wyn Yu
One of the sites I visited yesterday (don't remember which one) had an article title, something like "Stephen Hawking says humans are doomed unless they colonize a planet". Weird; but then Hawking is a no-nonsense scientist.
Anyway, my initial calculation (I made it about 2 years ago, have to verify the data & assumptions):
If the age of the universe is around 14.6 billion years, age of earth around 4.5 billion years,
modern man (homo sapiens, excluding the neanderthal, java man) developed only over the last 30,000 years, then:
If the universe was formed by the big bang some 24 hours ago, then modern man came into being only over the last 0.4 seconds! Yep, not even 1 second over the last 24 hours.
And this has many implications in our understanding of present natural environment, even our concerns for the green environment. The greens, the environmentalists who say that global warming (is there a consensus already among scientists that it's already here?) is entirely due to human activities (the CO, particulates, SOx, CO2, lead, etc. emissions). Other scientists don't believe this, that some astronomical events could partly explain temperature change in this planet. Is the earth revolving closer to the sun but at a slower pace? Is the sun producing more nuclear fuels (& more heat) at certain periods - these decades for instance - but will later tame such nuclear production after sometime (the next few decades or the next century). hetsetera hetsetera possibilities.
Of course the volcanoes. When the earth was young, there were fireworks all over, of hundreds of volcanoes erupting all at the same time. But there were no human casualties then, only some trilobytes and early species of the dinosaurs. Now, only 1 volcano erupting violently, dozens, even hundreds, could die. The problem is not volcanoes, but people (he he he).
Stephen Hawking says time travel is possible - only if one is willing to enter a black hole and get out of it successfully. Get a rocket ship, have those ultra-efficient fuels, go to some place of Milky Way where some blackholes are taking some snacks (lights fadinnggg... then gone). You enter the hole as handsome as Monching, then come out a spaghetti, try to "regroup" your cells and atoms - some 90 years past. Wow, you can have the chance to ligate ex-pres. Marcos' mother so he wouldn't be born.
ahhh, the nothingness of such period where humans will not be bothered by any economic or political problems even for just 1 month. In the absence of such nothingness (hence, the presence of such existence, ekkhh!), we retreat, step back and wonder what life will be if there'll be no more governments in the future...
-- Nonoy Oplas
Noy, I think the universe will be doomed if humans will have the capability to colonize other planets. just think of what the early colonizers did to some indigenous people (e.g., aztecs, chibchas, american indians, etc.) and to the environment, in the name of science and some long-forgotten monarchs.
I could just imagine earthlings visiting an alien world teeming with populace who may be gentle and peace loving. genocide may not be the order of the day but humans will just impart (through a period of association with these people) greed, avarice, and other derivatives of the deadly sins. and that's why we will not evolve into a higher form of being (like the starchild depicted by the greatest film director of all time –stanley kubrick in 2001: a space oddysey) .
And maybe, that's the reason why God, in His infinite wisdom, has not shaped our mortal minds to discern the intricacies of the clockwork universe. we have tried to posit some assumptions on the moments after the big bang. but there are still some phenomena which cannot be explained by mathematics and physics. a recent example is the unexplained slowing down of Pioneers 10 and 11 spacecrafts (which are hurtling out towards the stars in opposite directions) that defies the best minds of NASA up to this time.
In the end, our planet will just be an island in the stream of universal nothingness. the author of ecclesiastes summed it up when he wrote that there is nothing under heaven. what he was implying was that we should focus our attention to God who's above or in heaven.
Incidentally, the best layman explanation I got about black holes, stargates, and time warp was the episode in voltes v wherein a briefing was conducted for the crew of voltes v before the invasion of the boazanian planet.
-- Glenn de Guzman
But i have a theory that runs contrary to what Repang Glenn said
My theory is that God did shape our mortal minds to discern the intricacies of the universe. Eventually humans will understand the order in chaos. In the time line set by God for humans to live and evolve, we are perhaps at present just in the first stage of a thousand stages. Or we may visualize ourselves having only run the first ten meters of a destined one thousand kilometers run.
Why do i say this? At present we are said to be just using around 20% of our brain, and that is why comprehend only up to a certain extent the complexities of the universe. And we get so stoppled by the thought of having a philosophical and mathematical zero. But hey, as we get to learn to use more of our brain, with the help of technological innovations like the internet and who knows what else shall we come up with in the next few decades, humans will comprehend more and more.
I think the ultimate objective set by God for humans is the final understanding of life in the universe. And we will do so only when we reach that point where humans are able to use 100% of the brain. And this is what i'd like to think as the real Sapiens Universalis.
Therefore, every human being born to this time will be said to have worked towards God's purpose (and therefore will be saved and go to heaven) only if they would be able to say that they have contributed towards the evolution of humans to Sapiens Universalis.
Say you got married and had a kid, that's possibly your ticket to God because you may say that you have contributed to the propagation of humans so that they can evolve further. And Bill Gates can say that through his computers, evolution was hastened as knowledge exchange and absorption wwere greatly enhanced. And the PFers? Well, we seem to have doubled each others knowledge and ability through our debates here so we will all go to heaven too. See you there Bill!
However, my theory includes the devil as well. The devil continually tries to contradict our evolution through wars and conflicts because if do end up killing ourselves, then God's plan is botched and the devil wins. And the devil at times would make some people say that the internet is bad so that we would not want to benefit from it. And sometimes the devil makes some people say that globalization is bad so that we may not learn and develop as fast as we will if we embrace globalization. I wonder what Walden Bello has to say about this theory?
And what do we make of intergalactic travel? I say that as long as we will continually expand the use of our brain by interacting or even to the point that we colonize other planets, then so be it. Because for all we know, God created other being there like us and gave them the same challenge. And so it is either them or us who will end up undertanding the universe. Maybe this is all just a contest for his amusement. Or a huge market where different beings are supposed to compete for a vast (to our present minds) but limited resources to satisfy wants. By Golly. I really think God is an economist.
-- Ozone Azanza
From Glenn: “I think the universe will be doomed if humans will have the capability to colonize other planets. just think of what the early colonizers did to some indigenous people (e.g., aztecs, chibchas, american indians, etc.)...”
I am a Trekkie, Interplanetary Travel is still nascent to be a possibility. Hopefully, by the time we do travel through space and time, we would have evolved to a more logical and practical type of species that learns to work and adapt with other biological life forms (The Prime Directive versus Starship Troopers).
BTW space warp travel was an idea used by Gene Roddenberry for Star Trek to explain real time travel by Capain Pike and Kirk. I think the original idea came from the Warp Drive came from Sturgeon. Isaac Asimov was later hired by Roddenberry during the making of Star Trek 1 the movie to come up with a plausible explanation for warp speed!
-- Ricky Sunico
From Glenn: “I could just imagine earthlings visiting an alien world teeming with populace who may be gentle and peace loving. genocide may not be the order of the day but humans will just impart (through a period of association with these people) greed, avarice, and other derivatives of the deadly sins….”
Enter the twilight zone...
A group of superior aliens surrounded earth with hundreds and thousands of fearsome looking spaceships and announced that they will destroy the whole planet within 48 hours unless us puny earthlings give them a reason not to do so.
Naturally, all the leaders met via teleconferencing (siyempre hi-tech) and agreed to draft a worldwide resolution for peace. they pulled together all renowned academicians, leading think tanks, economists (siyempre) and political leaders and miraculously came up, at the last hour, with several volumes of thick documents detailing the plans, resolutions and agreement for global peace, fair distribution of wealth and overall global economic prosperity. tired, sleeples and without even brushing their teeth for the last 2 days they proudly presented their accomplishment to the aliens.
The alien boss (think John Travolta in Battlefield Earth) browsed through it and laughed - "Fools!", he said. "We bred you hear to be warriors! And after all these thousands of years, all you turned out to be are peaceniks!"
Poof! he disappeared, and Earth returned to what it was before, "nothing".
-- Eric Tiongson
Yep, we're nowhere near utilizing our full potential. At this point in our evolution we seem to have this tendency to "self-destruct" through man-made calamities like war, disease--part natural and part man-made and what have you. Some days it seems like this devil is winning and all we do is thrive on chaos. But in understanding what evil is about and what it can do to destroy humankind, we learn what to avoid or guard against. And move forward marching to a single beat. Wow! Wouldn't that be the day!
....and then I remember what the minister tells me during Ash Wednesday...from dust you have come, to dust you shall return...back to nothingness....
-- Llana Domingo
The lengths and breadth by which this topic preoccupied some PFers thoughts had amused if not perplexed me. Ozone's theory on 0 equated to an empty space and not nothingness is very interesting and thought-provoking, although I do have a problem with him alluding to 0/empty space with the female species which following his line of thinking "only makes sense if you have a concept of something that is not empty, say a 1 beside it." It may be a joke, but somehow, it diminishes the value of the female species to be equated to what is not evident between her lower extremities (an empty space as he referred to). On the flip side, following his logic, I may give him credit though for the theory that zero can actually have an expansive effect that may give new meaning to a digit standing by itself. Hence, by reverse logic, one can only have a sense of the value of a digit (e.g. 1) in contraposition with a zero. Anyway, I am not mathematician nor philosopher nor scientist.
I am a romantic and a cynic all rolled into one. For the romantics out there, here is a prose that I got from Robert James Waller in his bestseller BRIDGES OF MADISON COUNTY. It might have tangential relation to this topic of "zero and nothingness redux"
"FALLING FROM DIMENSION Z" - Robert Kincaid
"There are old winds I still do not understand, though I have been riding, forever it seems, along the curl of their spines. I move in Dimension Z; the world goes by somewhere else in another slice of things, parallel to me. As if, hands in my pockets and bending a little forward, I see it through a department store window, looking inward….
Euclid is not always right. He assumed parallelness, in constancy, right to the end of things; but a non-Euclidean way of being is also possible, where the lines come together, far out there. A vanishing point. The illusion of convergence.
Yet I know it's more than illusion. Sometimes, a coming together is possible, a spilling of one reality into another. A kind of soft enlacing. Not prim intersections loomed in a world of precision, no sound of the shuttle. Just ... well... breathing. Yes, that's the sound of it, maybe the feel of it, too. Breathing….”
-- Elizabeth Cueva
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