Physics of spacetime part I, distance as spacetime
I.1. Distance as space and time in one
In daily life we make a distinction between the spacedimensions and the
dimension of time. The 3 space dimensions we then experience as a unity. For
when you put 1 liter of water into a plastic bag and flatten the bag, making
the height dimension smaller, then the surface of the bag, so the length and/or
the width dimension, grows bigger. In this sense the 3 space dimensions form a
unity, the contents of space.
According to the relativity theories, space also forms a unity with time,
making it a 4dimensional spacetime unity. You then must imagine a 4th
dimension around the plastic bag, while changing this time dimension
influences the space dimensions. So a part of the contents of space can
dissolve into time and the other way around (mass can change into energy and
the other way around according to the special relativity theory).
At first sight, this unity of space and time seems incomprehensible. However,
in daily life we often experience space and time as a unity and we even have a
word to express this spacetime unity, the word distance.
Many of us think that the word distance is just an other word for the length of
a road. Physicists too use both concepts as if they are just different words to
express the same, even Albert Einstein is doing that .
However, that length and distance are different concepts becomes perfectly
clear when we think of an emotional distance. You can not replace distance by
length then, because an emotional length and even an emotional length to
bridge, is nonsense.
It is not a number of meters you think of when feeling distance. You even can
be very close together while feeling great distance. And the other way around,
a far away friend can be felt at short distance.
The concept distance contains something more than space alone, and this extra
element is the dimension of time. That becomes even more clear when we think of
being in a hurry or being very tired. Only 1 kilometer then can be a very long
distance, because you are experiencing it as long lasting.
It particularly is the speed that defines the distance of a
length. The faster you can go, the shorter the distance of a length is.
Walking from Amsterdam to Paris, or going by bike or by car or even by plane,
that makes a lot of difference.
The length of the road of course stays the same, but the distance of that
length is relative, depending on all kinds of circumstances. The wind or the
weather in general also plays a role like the condition of the roads, up or
down hill for example, the condition of your vehicle, your own condition and
even your mood.
And all these circumstances and conditions influence the time you need, your
speed. Or they define the time you have, like in the case of being in a hurry,
and then you are experiencing your speed as too slow.
Distance contains an element of time. But distance is not time alone. A 1 hour
distance can be 5 kilometers when walking, 25 kilometers when cycling, 100
kilometers by car and 1000 by plane. Distance is depending on speed.
Thus with distance we clearly mean space and time in one and the unity of space
and time therefore is not incomprehensible at all. We all know what distance is
and we always experience distance as a unity then, as space taking time. We all
know that the time you need at least influences the significance of the
space you have to bridge.
Although we experience distance as a unity, we need more than 1 figure to
express the distance. We need to know the time and the speed, or the speed and
the length, or the length and the time.
In the area we experience distance as a unity, however on the map we have to
split up distance in space separated from (points of) time. When reading the
map we therefore must realize that the map only is an abstraction.
It actually is time it self we can not map. We can map points of time, but not
time it self. Time always plays between these points of time.
What is the purpose of this chapter? I not only want to point at a difference
in the significance of two words, because that would not be really
important.
I want to show that in reality we always experience space and time as a
unity, as distance. Space only has a meaning for us if it takes time to bridge
the space, and that always is the case. Even when we draw the map, our pencil
needs time to bridge space. Even the fastest computer in future will take time,
since light, so electromagnetism, takes time to bridge space.
Would not we need time, so be able to go with an infinitely high speed, or
would the speed of light be infinitely high (also see the Relational
philosophy), then we would not experience space as distance and space then
would not exist at all. Space, thus matter as well, then dissolves into
nothing.
Seeing that space always is distance, spacetime in one, can make the theories
of relativity more understandable, less strange, and the same is true for
quantumphysics.
The spacetime measure of things and events, of fundamental particles as well,
always is relative, is distance, so defined by circumstances. There does not
exist objective length, not even on the map. There does not exist an objective
reality.
And that also is exactly what physicists discover when they observe the
processes that play in a very short interval of space and time, and then are
confronted with the quantumcharacter of reality.
Everything is distance thus relative and, if you can see light as awareness,
even subjective.
I.2. The field of light as the spacetime field
Light is a strange phenomenon, like time. We all feel familiar with time and
light. However, when we try to map these phenomena, then they are slipping
away. We for example say that light has a speed, and thinking of speed we think
of things traveling through space. But light does not behave that way. What is
this speed of light?
Light is very fast, can bridge 300,000 kilometer empty space in 1 second, thus
3×10^{8} m/sec, nearly 8 times around the earth in 1 second.
But the speed of light is not infinitely high but only finitely high.
Light needs time to bridge space, though it is little time. And seen from an
objective point of view we can not even call our light fast, for compared with
for example 10^{100} m/sec our light is very slow.
In the same way we may not call an atom really being small. Because for a light
with speed 10^{100} m/sec our atom is like a whole cosmos. Our
specific light makes the ocean of space inside an atom to a small piece of
space and we experience this concentrating as mass.
Suppose our light would become faster and faster and infinitely fast in the
end? What will be the implications then? It will make all the difference.
If a spark of light would come to existence then, wherever in the cosmos, we
would see that light immediately here on earth and everywhere else in the
cosmos. We then no longer could say that a certain star is far away while the
sun is nearby, because there is no difference between far away and nearby for
infinitely fast light. Every distance then is zero, also for us as observers,
because we always use light to observe things.
And since light as electromagnetism also plays inside the things, inside our
body as well, the distances between and inside atoms would become infinitely
short as well if light would go infinitely fast. Things then no longer would
have a size, a measure, and therefore would not be things.
Physics too makes clear that there can not be space and therefore no reality if
the speed of light would be infinitely high, so if light no longer would need
time to bridge space. Because the speed of light c is like a
spider in the web of physics. Would you fill in infinite () for c, or zero (0), then zeros and infinities appear everywhere in the equations of physics, with the result that physics dissolves into nothing, like reality does.
The constant for
example (also see part II about the superfluity of the gram and the
coulomb) in Coulomb's law describing the strength of the electromagnetic
connection between and inside atoms and molecules, totally depends on the speed
of light c according to Maxwell's equation.
Would c become infinitely high or zero, would do the same, with the result that the electromagnetic force would become infinitely strong or zero as well. And atoms and all other things then would be concentrated in an infinitely small piece of space or would fall apart. All relations would disappear then, and a reality without relations, is nothing .
The equation E = mc^{2} of Einstein too makes clear
that m (= mass) would have an infinite value if the speed of light c would have an infinite value. And an infinite mass is no mass, like
an infinite size or measure is no measure.
And in the equation of Max Planck E = hf, the amount of
energy E would become infinitely big if c and therefore f
(the frequency of light) would become infinitely high, and that infinite light
then would annihilate everything.
If the speed of light would be infinitely high or zero, then there would be
nothing, no time for that light and therefore no space.
Our light needs time, that is why time exists. Our light needs time to bridge
space, and that is why space has a meaning for us, as distance. And that is
also why there is a reality, the world we are living in.
This analysis of the significance of the speed of
light again makes clear that space and time always form a unity. An
infinitely fast light does not need time and that is why space then does not
exist either. Our finitely fast light however needs time and that is why space
exists for us. Space and time therefore always form a unity, space only is
space if it takes time to bridge it.
Time creates space, duration creates space. Slowness (of light) creates
everything. Our reality is slowness; being real is being slow, being inert.
This unity of space and time, we all daily experience when we speak of
distance. The speed of the vehicle then particularly is important, or the speed
of the device you use to communicate. This speed, so the time it takes, at
least influences the significance of space, that is what I wrote.
And is space more than its significance?
If you can go infinitely fast, then every length has the same meaning for you,
a meaning of nothing. Does space then nevertheless still exist? Is there space
separated from the significance of it? Is there space without size or
measure?
Does there exist objective space?
No, I think, space always is distance, just significance. If space does not
have a meaning, then space does not exist.
Our light is finitely fast, so that the particles experience distance, space
taking time, relations taking time. And exactly this finite speed makes the
particles exist. Would the particles suddenly be able to throw an infinitely
fast light on each other, then everything would cease to exist, not just the
significance of space but also space and things themselves. Particles then no
longer would have a size, no border, no single measure, so would not be
particles.
We therefore can not truly speak of an objective space existing independently
from the light we shine on it. Would for example the speed of light not be
300,000 km/sec but 300 or 300,000,000 km/sec, then space would have a different
meaning for us. Then space would be different for us, more spacious or less
spacious; 1 kilometer then would be a 1000 times longer or a 1000 times shorter
distance. And this significance we attach to space then also is
space.
The only space that really can be called objective, is the space experienced by
an objective light, a light that does not know any limits or borders, thus an
infinitely fast light using infinite standards. And for such an unlimited point
of view there is nothing at all, no time, no space.
Only the absolute nothing therefore is really objective. This nothing then can
be called objective space, a space without measures, a spaceless space, the
eternal infinity of nothing.
So space, finite space, always is a relative thing, only space seen in a
certain finite light.
And when we see light as a kind of awareness, and we
often do that, then we can say that our reality is a finite awareness, a finite
light, a limited point of view. A limiting point of view actually,
limiting itself as well, existing by limiting. Would our awareness become
infinite, then everything would stop.
An atom then is to be seen as a point of view in the sense of awareness, a
limiting awareness that measures the surroundings with finite spacetime
standards, so that these surroundings have a significance as distance, so that
the point of view itself also has a significance, a size, a mass. Would the
point of view suddenly be able to measure the surroundings with infinite
standards, then at once it would experience nothing at all, not even it
self.
So only the absolute nothing is objective, while all finiteness is only
relative and even subjective if we can see 'throwing light' as awareness.
What is the purpose of this chapter?
We often make a distinction between at the one side
the spacetime field and at the other side the field of light. In that view,
light is some thing traveling through space, a message through space. There is
space and there is the message.
This distinction we make between space and light, resembles the distinction we
make between body and mind, or matter and idea. Our body exists in space, our
mind with his messages is separated from space in that dualistic view.
However, actually the spacetime field and the field of light are exactly the
same field. The motion of light then is not a speed through space but an
activity of giving significance to space, so actually some kind of
creation.
Light is measuring and that is why there are measures. Would not there be
measuring, then there was nothing at all. So the message is not a result but is
the cause.
I return to this subject in the next chapters. First something else, also as
a kind of introduction to part II of Physics of spacetime.
If our reality firstly is our specific finite light thrown on the infinity,
then there also must exist smallest spacetime measures in our reality. These
smallest measures, smallest wavelengths for example, múst exist since
the standards used by a finite light can never be infinitely small, because
that would involve an infinite light.
A finitely fast light will never be able to reach an absolute zero point of
nothing, nor will it be able to reach the infinity; only an infinitely fast
light can do that. A finite light therefore always is dwelling around such a
zero point, so on a kind of surface, a boundary between zero and infinite,
between nothing and all.
So given our finite speed of light, there must exist something like a smallest
space measure in our reality. This length or distance then must behave like a
constant in physics.
And that such smallest spacetime measures indeed exist, will be shown in part
II.
But first something about distance and the relativity theories.
I.3. Einstein and his changing rulers and clocks
Light is a strange phenomenon, like time. We say that light has a speed, and
thinking of speeds, we think of things traveling through space. But light does
not behave that way. What is this speed of light?
While speeds of cars, bullets and soundwaves are relative, the speed of
light has a kind of absolute character. When a car goes a 100 kilometer an hour
and you follow the car with 50 km/hr, then the speed of that car only is 50
km/hr for you. A bullet too is something you can escape from by going faster
than the bullet, like you also can go faster than the sound you make. These
kinds of speeds are relative, depending on your point of view.
Next fact also plays a role. The earth itself also has a speed around the sun.
And the sun moves as well, and our galaxy moves, et cetera. So what is the real
speed of that car? There is not such an objective speed, there does not exist
an objective point of view. Or you must think of an infinitely fast light as
objective point of view. But for such a light there is nothing at all, no
finiteness.
So speed is a relative phenomenon if it concerns cars, bullets and sound.
However, do you replace the car in the example by a beam of light or a photon,
then something strange is happening. No matter how fast you follow the beam of
light, light always will keep the same speed compared with you, 300,000
kilometer in 1 second in the empty space. So if you would follow, with a speed
of 150,000 km/sec, a beam of light, then you would not measure a speed of light
of 300,000 minus 150,000 = 150,000 km/sec. No, light then still travels 300,000
km/sec faster than you do, as if you are not following at all.
The speed of light is a constant. Whatever your point of view is, moving or
immobile, you will always measure a same speed of light, as if your point of
view is irrelevant. And that of course is incomprehensible if light is a thing
like a car or a soundwave. Light must be some other thing.
Einstein explains the constancy of the speed of light in his
special theory of relativity, and he is doing that in two steps. Firstly,
he argues, it is a fact that when we speak of speed, we talk about a
measured speed. And measuring of speeds happens by means of a speedometer,
and that always is a combination of a ruler and a clock, the ruler to measure
the length of the road, the clock to measure the time it takes to bridge that
length, and length divided by time is speed.
Einstein's second step was the assumption that rulers might become shorter and
clocks slower when they have a speed themselves. And on such adapting
speedometers one then can always measure a same, so constant speed of light,
provided of course that the adaptations coincide with each other and the
Lorentz transformations take care of that.
But what becomes shorter then? The real length of the ruler or the distance,
the significance? Einstein uses the concepts distance and length as if they
mean the same and that anyhow can be called a careless use of language.
If things really become shorter and clocks slower, so your
size and your heartbeat as well, then it leads to strange paradoxes. If you
would be able to move your arm like a wing of a mill and very fast so that your
hand (with wristwatch) reaches the speed of light, then your hand will stay
young forever (and your watch will stop running), according to the special
theory of relativity, while the rest of your body will grow older and die. Your
hand and wristclock will also become infinitely small then.
Such velocity of your hand of course is impossible in practice. But it is
possible in theory, and a theory like the relativity theory also must be able
to explain such theoretical implications, I think.
In examples pointing at this paradox, there often are two different points
of view, a train and a railroad for example, or twin brothers. One of the twins
travels very fast through space, the other twin stays at home. Which of the two
brothers then has a speed and therefore becomes shorter and ages slower, is
depending on the point of view. The traveling twin does not experience his
speed. For him it is as if his brother on earth has a speed and stays
younger.
In the example I give, both points of view in a way coincide, making the
paradox better visible.
So what is really happening with rulers and clocks?
It is a fact of course that speed influences the distance
of space. Suppose you are in a train with a length of 100 meter. If the
train stands still on the railroad, then 100 meter of the rail is as long a
distance as the 100 meter of the train; it takes you 1 minute so 60 seconds by
feet for example. However, if the train starts moving, for example with a speed
of 10 m/sec, then the distance of the train still lasts 60 seconds for you,
while 100 meters of the railroad then only take 10 seconds, and even less if
you walk in the same direction.
The one length of 100 meter then is a longer distance than the second length of
100 meter. Thus speed indeed influences the distance of space. In this example
the distance of the rail becomes shorter, seen from the train.
In Einstein's theory however, it is the length of the train, the ruler that
measures the railroad of light, that becomes shorter.
So what is really happening?
It anyhow seems useful to me that physics pays attention to this difference
between length and distance. Also given the fact that the relativity theory
conflicts with quantumphysics, while quantumphysics is based on facts.
Distance contains a subjective or at least relative element, and I think it is
necessary that physics gives more room to this subjective or relative aspect of
reality, the relations in nature as the spirit of nature (also see the
Relational philosophy on this website). It especially is the activity of
measuring that deserves more attention, I think.
Next to that I wonder if we must continue to speak of light having a speed, as
if light is a thing traveling through space. As if the field of light and the
spacetime field are two independently existing phenomena.
I think the field of light is exactly the same as the spacetime field. If
light would go infinitely fast, then time and space would lose all
significance, that is a fact. The significance spacetime has for us now,
therefore is the result of the finiteness of our speed of light. And every
thinkable speed of light goes with an own significance of space and time. And
space is nothing more than this significance we attach to it.
In other words, light is not some thing with a speed through space, but is
dynamical space itself. Light is a giving significance to space, in terms of
time, in terms of distance. In our reality 300,000,000 meter is 1 second at
least.
And this minimal significance of space clearly stays the same for us, is a
constant. Whatever speed we have ourselves, we can not escape from space
itself.
But even then we are not yet ready with light and its character. Because this
dynamical significance of spacetime also must be expressed as a quantity in
physics, be expressed as a space/time relation. And such a space/time relation
resembles a speed very much.
Maybe it is better to speak of the slow or inertness of light. Our
light can not follow an infinitely fast light. Would we overtake this arrear,
we would have infinite dimensions ourselves and therefore disappear into
nothing. And that also is the final conclusion of the special
relativitytheory.
I.4. Light as moresided movement
According to me, the constancy of the speed of light means that the minimal
significance of space is a constant for us. Whatever we do, we can not escape
from space, not from reality. A finite being will always experience
distance.
The speed of light also plays in a different sphere, I think. When cars or
bullets have a speed, they act. But next to acting, all things also are
existing, and that existing too is a kind of movement. In that sphere of
existing, we must search for light and its speed, I think. I come back to this
subject.
Nevertheless it is useful to imagine the movement of light in a kind of
touchable way, and I think we can do that. Imagine a big balloon on which we
can walk and ride. A balloon that is expanding in a constant speed, so that the
surface of the balloon becomes larger in a constant speed as well. Also imagine
dots on the surface of the balloon. The distance between two dots then becomes
longer in a constant speed.
If you start walking or riding over the surface of the balloon, then you
will see that there are two different kinds of movement, your own speed and the
expansionspeed. Your own speed then does not influence the expansion speed. No
matter how fast you travel over the surface, the expansionspeed will always be
a constant for you, so comparable with the speed of light.
Actually, you do not even have a speed compared with the expansion speed. For
suppose you are standing on a dot, seeing the other dots move away from you,
with a minimum expansion speed of for example 10 m/sec. You decide to follow
your first neighbordot. Your speed then must be 10 m/sec. Or you decide to
follow your second neighbordot, and then your speed must be 20 m/sec. Et
cetera.
Whatever speed you have then, you will always find yourself hovering more or
less immobile above one of the dots, so that you can easily land on it. And
then you are again standing on a dot, seeing the other dots move away, as if
nothing has changed in your situation. Whatever your speed is, you will always
find yourself in the center of the expansion.
In this way we can imagine the movement of light in a kind of touchable way, as
an expansion of the space we are living in. And space and light are one and the
same field. Our finite light creates space, gives a finite significance to
space by taking time to bridge it. And creating something out of nothing also
resembles expansion.
The difference also is lain in the fact that an expansion speed is a moresided
movement, while an ordinary speed is a onesided movement. And all relations
are moresided. One can not split up a relation like playing between bolt and
nut or man and woman into two onesided half relations. A relation always is 1
movement, 1 screwing if it concerns bolt and nut. There of course are two
opposite points of view then, however at exactly the same movement.
Light is a relational phenomenon according to me, not a onesided speed.
That is why onesided speeds do not influence the speed of light.
In this way we can understand the movement of light in a kind of touchable way,
so as a moresided movement. And it only is a simile, because in the example of
the balloon we still observe the moresided movement from a distance, while in
real reality we never can take distance from the field of light. The field
of light also is playing inside our body, we are even formed by it.
Actually, our finite light is constantly creating our finite space. Our finite
light constantly creates everything, our own body as well. So actually the
constancy of the speed of light is the constancy of our size and of other
sizes, of space as well, compared with nothing and compared with the infinity.
Light is constantly giving everything a constant finite measure, that is the
motion of light, I think.
If it concerns cars or living beings there by the way also are these two
different kinds of movement. Next to the speed over the road, there also is an
inside movement holding the parts together. This relational activity also has
formed the car. The two movements then play in a different sphere, and do not
influence each other. By driving faster, the car is not built faster.
Light plays on a deeper level than ordinary relations do like breathing the
air, eating our food, walking over the roads and the like. All these things
like air, food, roads, shoes et cetera already are related on that deeper
level. They already are existing.
And superficial relations like eating and walking then of course do no
influence these deeper relations. Eating food does not change food being food.
Bridging distance does not change distance being distance.
These deeper relations then are not just accidents or results, but actually are
the fundament. Light first creates the things, and then afterwards these things
can have a speed, can eat or be eaten et cetera.
That is how we must understand the constancy of the speed of light, I
think.
I.5. Distance and the general relativity theory
Next to the special theory of relativity, there also is the general
relativity theory about the gravity force.
Newton was the man who first discovered the law followed by things that
experience gravity. He discovered that the force by which the apple falls down,
is exactly the same force that keeps the moon in its orbit around the
earth.
The mass of the earth causes a gravity force in its surroundings and this force
gets weaker according as (the square of) the distance to the earth grows
longer; that is Newton's gravitylaw.
But how is the earth transmitting the force to the moon? What is happening
there? Is there a contact between the earth and the moon? How fast is that
contact?
Einstein made gravity more understandable in his general theory of relativity.
In that theory a mass like the earth transforms space, and this transformation
is spreading out in space. The earth curves space according to the general
relativity theory, and the moon then just follows the curved space and does not
need to be in contact with the earth.
When we think of a twodimensional flexible sheet with
a heavy bullet or ball on the center of it, we actually can see this curving of
space, caused by the ball. All things on the curved sheet then fall in the dale
or will circle around it, provided that their speed is high enough.
But how can we imagine curved space in three dimensions and without flexible
sheets? I think we can do that by making a distinction between length and
distance. The length of a thing is an objective measure, the length is fixed.
The distance of that length however is depending on all kinds of circumstances
and especially the speed then plays a role.
Now suppose that the speed of light is not exactly the same everywhere in the
empty space. Suppose there are spheres in the cosmos wherein the speed of light
gradually changes when one is nearing the center of the sphere. A minor change
of the speed of light then suffices, I think.
Thinking in terms of absolute lengths and relative distances, we now can say
that such a sphere is characterized by the fact that a certain length of for
example 1 meter, does not everywhere have the same significance in terms of
distance in that sphere. If the speed of light slows down in the sphere, then
the distance of a length of 1 meter lasts longer and therefore is longer in the
center of the field than on the edge of the field. In the center there is more
space, since there is more time. Empty space then can be more or less empty or
spacious.
Now suppose we make two maps of that sphere, one with the lengths on it, a
second map with the distances. The map with the lengths then shows only
straight parallel lines. On the distancemap of the field however, the distance
between two neighborlines gradually changes, resulting in curved lines.
In this way we can imagine curved space. Empty space then can be more or less
empty or spacious. Gravity then can be compared with the way a vacuum or low
pressure area works. Every thing that nears such an area with low pressure,
will search for the most spacious space, so where the pressure is lowest or the
distances are longest.
This change of the speed of light also exists and can even be measured. Light
moves slower in a gravity field. One even uses gravityfields as instrument in
physics, since such a field works as a kind of lens, like real lenses bend
light.
An important question still remains now. What is the real cause of gravity?
According to both Newton and Einstein, mass is the cause of gravity. Mass
curves space. Light then needs more time to bridge that curved space, and that
is why light is slower in a gravity field. The change of the speed of light
then is a result, caused by mass.
I however, can imagine a cosmos wherein it is exactly the other way around. In
that imaginary cosmos, light it self slows down its speed sometimes and here
and there, by some cause.
So in this imaginary cosmos there are minor irregularities in the for the rest
constant speed of light, with the result that there also is a variation in the
significance of space in terms of distance.
In that imaginary cosmos mass is not the cause of gravity. Light is the cause
of gravity there, light that slows down here and there, curving space by
gradually changing the distance of a certain length.
However, such a cosmos nevertheless can exactly look like our cosmos. Because
in that other cosmos too, mass will pile up in the centers of these gravity
fields, because there space is more spacious.
Also suppose these spheres move in space, circling and whirling around each
other, influencing each other, even absorbing each other. Then the piled up
masses will be forced to move along with the spheres. And the result is a
cosmos very much looking like our cosmos.
Seeing the difference between length and distance anyhow can help us to better
understand the general theory of relativity even if mass indeed is the cause of
gravity.
And whether or not mass is the cause of gravity, is not really important in
physics. For traveling in space for example, we only need to know the strength
of the gravity force, so the experienced acceleration at a certain distance
from a planet or moon. The cause of this acceleration then does not matter at
all.
And even if mass causes gravity, then mass is not the fundament of all. Because
mass itself only is an expression of the finiteness of our light. Light is the
cause of everything, and in this sense also of gravity.
This part I of physics of spacetime was about distance as space and time in
one. And in real reality we always experience distance, spacetime as a
unity. Space is space for us, since our light needs time to bridge space.
However, on the map we can not picture distance as a unity. A 1 hour distance
can be all different numbers of kilometers. And only 1 meter can have all kinds
of significances in terms of distance.
So on the map of physics we have to split up distance in meters separated from
seconds. When studying the map, we should always have in mind then that the map
only is an abstraction.
I think we never will be able to understand the essence of reality if we
only concentrate on the map. It is like with music. Feeding a computer with
only figures, can create the most beautiful music. But music is more than
figures of course.
Music plays between the figures, like time plays between the ticks. And time
only can be felt. Time can not be measured, not be mapped anyhow. Only points
of time can be mapped. Real understanding therefore is a feeling, a filling in
as well.
Jan Helderman
end 1999  beginning 2000
