ENTERTAINING PARADOXES OF TIME
Nihil and Totus are
two persons fascinated by the paradoxes of time. They are moreover in the
centre of a work dedicated to this fascinating notion and entitled
" The paradoxes of time ".
-Dear Nihil, I am going to put your ingenuity
in hard test. I am going finally to know if you are endowed for the other
thing(matter) than the criticism.-J have the gift(donation) of the
gift(donation)! Speak so.
-I am going to present you
some problems of very simple appearance. To you to inform of the intuition and
the reasoning.
1) - Imagine that I go(surrender) of the city A to the city B at the
speed of 60km / hour and that I return then from the city B in the city A at
the speed of 120km / hour. Which is the average speed of my route going there
and back?
2) - Imagine that I go(surrender) of the city A to the city B at the
speed of 60km / hour. In which speed should I cross(go through) route return of
B in A to reach(affect) an average speed of 120km / hour on the set(group) of
the route going there and back?
3) - Imagine that we want to compare the performances of our cars on the
distance of 1km, settled(fixed) departure. Knowing that I cross(go through) the
last 200 metres in 4 " and that you cross(go through) the last 250 metres
in 5 ", what of our vehicles is the most successful?
4) - Imagine that I leave the city A at 12 hr and that I roll in an
average speed of 60km / hour towards the city B situated in 120km. For your
part, you leave the city B at 13 hr to run(drive) in an average speed of 120km
/ hour towards the city A. As we cross, what of us is closer of the city A?
At what time shall we
cross?
5) - Can you explain to me how I can go(surrender) of A in B in 1.
30 ' and of B in A in 90 ' while I run(drive) in the same average speed on the
way out and on the way back?
6) - Imagine that we leave at the same moment, respectively, you the
point B and I the point A distant of 100km. We roll both at the speed of 50km /
hour. At the time of the departure, a fly left the point B and goes to me at
the speed of 75km / hour. As she(it) gets(touches) my windscreen, she(it) turns
back immediately and flies towards you et cetera until we cross. At the moment
when we shall cross, what distance this fly will she have crossed(gone
through)?
7) - Imagine the previous situation. As we shall cross, will the fly
fly towards me or towards you?
8) - Let us invert time in the previous situation and imagine that
we go away one of the other one from our meeting place. The fly resumes its
flight(theft) from one to another of our vehicles. As we shall have
respectively reached(affected) you the point B and I the point A, where has to
be the fly?
9) - Imagine that your universe amounts to an elastic(rubber band)
of a length of 1km. Your speed of progress is of 1m / @. After every second,
the elastic(rubber band) lengthens(stretches out) of 1km. How long will it be
necessary for you to reach(affect) the end of it, if it is possible?
10) - Imagine two clocks. The one loses 1 ' every day. The other one
does not work at all. What of these two clocks gives mostly exact hour with
regard to a third clock which works she(it) completely correctly?
11) - Is it possible that the summit of the wheel of my vehicle
runs(drives) more fast than the base?
12) - Imagine that I announce you your death a day of the next week.
You know that I you étriperai a day of the week, but you are incapable to
know which(who). I add a stalk of cruelty to the punishment that you deserve to
have mocked at me in the course of the pages of this manuscript. Why do you
smile?
13) - Imagine that I made a surprising meeting. Two childhood friends.
They were born the same year. Nevertheless, the one is 32 years old and the
other one has it only 8. Would a it(he) have taken advantage of a relativist
rejuvenation treatment? No, they have the same physical appearance. Then, how
to explain this mystery?
14) - Imagine that your clock is settled(fixed). You have only a
resource. To come home and to verify hour on my clock, by hoping that I did not
forget to go back up(raise) her(it). You know that you make route going there
and back of your place of residence in mine in the same speed. How will you be
able to put back(hand) your clock at the hour?
15) - Imagine that your watch is settled(fixed). It is terrible for
you. You have indeed to take stamps at fixed hours and in the second near. It
is for you a question of life or death. You meet two twins. Their watches are désynchronisées, but the one indicates exact hour.
That of the twins the watch of which indicates good hour always says the truth.
His(her) brother, whose watch is not right, always lies. You have not any more
a lot of time before taking your next stamp, you know him(it) intuitively. You
have the right to put that a single question. This question, you put her(it) to
the two brothers. The answer that they will give you will indicate you exact
hour. Which is this vital question?
Let us clarify that you
have under eyes the watches of the enemy brothers.
16) - If a clock sounds the 6 knocks of 6 hours(o'clock) in 6 ", in
how long will she(it) sound the 12 knocks of midnight?
17) - Another problem of hour. You are locked into your prison
awaiting for your execution. Your obsession is time. You always wish to know
which hour it(he) is. You would not there sleep any more. You would force to
hold aroused to take advantage of every second. But fatigue brings down you.
You sleep profoundly. You wake up in start. A horrible nightmare in which you
did not know any more the hour than it is. But reality is cruel she(it) also.
You have no watch. Hour, you know her(it) due to the noise of a distant
carillon. This carillon sounds once all quarters of an hour and sounds complete
hours. How long is going to last your Calvary, in the worst of cases, before
you not silks sure of the hour when it is?
18) - I can not refrain from putting the enigma which the Sphinx
subjected in: which is the animal which progresses in 4 paws in the morning, on
2 paws at midday and on 3 paws in the evening?
19) - Which is the figure of the infinity?
20) - Are you capable of imagining a question which pulls(entails) us
in a perpetual motion?
21) - If I say to you that three hours ago by, it(he) had to pass by
till 8 hours. Twice no more time than it should pass by it in one hour, can you
say to me, without verifying your watch, which hour it is now?
22) - Prisoner of time. Nihil, I imprison you into an
indestructible cube, without the least hole which allows to pass the finest ray
of light. In brief, it(he) is hermetic. You have a machine to travel in the
time. How will you be able to escape from your prison, knowing that you have
the right only to a going there and back in the time, and that you can not
avoid returning at the precise moment when you left in the time?
23) The age of the captain
The last day of a
certain month of first world war, a grenade bursts and brings to light the
skeleton of a captain. By multiplying the age of the captain at the time of its
death by the quarter of the number of past years between its death and the date
of explosion of the grenade, by the remarkable day of the month of explosion of
the grenade, by the length the pertuisane halberd found next to the skeleton, one finds:
471569. Last indication: decompose this enormous number into first factors.
Which is the age of the captain 0et in which year he died
24) The flight(theft) of the Dove
At the same moment i, Nihil starts of the city A and Totus of the city B distant one of the
other one of 100 km, and go the one to the other one on a road perfectly
straight(right) in the constant speed of 100 kph. Of the city A leaves at the
same time as Nihil a Dove which goes in a straight line to Totus at the speed of 120 kph. When
she(it) meets Totus's vehicle, she(it) turns back immediately and goes to Nihil's vehicle; when she(it) meets this
one, she(it) turns back again immediately et cetera until Nihil and Totus's vehicles cross. At this precise moment,
what distance the Dove will it have crossed(gone through)?
25) How old are you?
When Totus asks him(her) for his(her) age, Nihil answers him(her): " Take three
times my age in three years, and deduct three times my age three years ago, and
you will know(can) my current age ".
26) Interglobal cruise
Every day at the same
moment, a vessel leaves the Earth in the direction of March, whereas the other
one leaves in March by making road towards the Earth. How much one of the
vessels will it(he) meet in the space of vessels making road in opposite
sense(direction), knowing that journey lasts exactly 7 days in a
sense(direction) as in the other one "?
27) Date of anniversary(birthday)
Day before yesterday, Totus was 32 years old, the next year, he
will have 35. Which of it is the date of Totus's anniversary(birthday)?
28) Past, present, future
Last year, Nihil was 32 years old, the next year, he
will have 32. Which age of it had Nihil here is two years, which age will
have Nihil in two
years and when will it(he) celebrate the next anniversary(birthday)?
29) Particles and time of half-life
One found rests of
bodies establishing(constituting) 25 % of the rate of carbon 14 present in
current bodies. Knowing that the half-life of this radioactive carbon is of
5700 years, which is the age of the rests?
30) Journey in the time
What happens if I go
back up(raise) in the time and if I kill my mother before she put me in the
world?
31) The enigma of Poincaré
How to measure a
drainage twice as fast of time? Imagine, as the mathematician Poincaré at the
beginning of century, as during your sleep, time passes twice as fast by
suddenly. Is there a means to realize it, if yes, who?
32) Lucky Luke's shadow
Can Lucky Luke more fast fire than the
shadow?
33) Millenarianism
When begins third
millennium?
34) Changes of hour
This night, one crossed(spent)
of daylight saving time at a time of winter, is to put off the needles of one
hours(o'clock). I have meeting at 13 o'clock. Golden, absent-minded, I
advanced(moved) the needles of one hour(o'clock) instead of putting off them?
At what time shall I appear at my meeting?
35) The time of holidays
Why are we all older
than we him(it,her) think?
36) Asymmetry
A plane flies at 400km /
hour with regard to the air(sight) with on the way out a head wind of 40 kph
and on the way back a favorable wind of 40km / hour. Which is the average speed
on the set(group) of the route?
37) To count days
On January 1-st of one
year not bissextile
falls Wednesday. Which day will be on December 31 of the same year?
And if it is about a
leap year?
38) Speed of light
How long would it be
necessary for an object in constant acceleration to reach(affect) speed of
light?
39) The girls of Totus
Totus puts Nihil in the challenge to discover the
age of his(her) three daughters.
The product of their
ages is equal 36.
The sum their ages is
equal to the number of its house.
Nihil reflects a good moment and
eventually said that he is short of an indication.
Totus clarify to him(her) while his(her)
elder daughter is fair.
Immediately Nihil gives the age of the three girls.
Which are so these ages?
( 10 points)
40) Diophante's age
Here is the epitaph of
Diophante's grave.
Days of Diophante, the sixth marked its childhood,
the twelfth the adolescence, then passed still by the seventh before its
marriage. Five years later, it(he) had a son who of the fate received twice
less than days when his(her) father. After the death of his(her) son, Diophante crossed(spent) another four years
in tears then he died. At which age died Diophante?
41) How much second per minute?
42) Which is the peculiarity of the time switch with regard to most
of the other objects of measure of time?
43) And of the calendar with regard to quite other object of measure
of time?
44) 86400 1440 24?
45) You arrange two egg timers, a which(who)
measures a time of drainage of 7 minutes, other one of the 5 minutes. How will you
measure the passage of 13 minutes?
46) Cloc, the small traveler of time, is lost in the labyrinth of the past and
future times. It(he) arrives at a temporal crossing. It(he) has absolutely to
join the time. A single branch of the crossing leads to it. On the edge of
time, a machine to investigate time occupied by the twins Nihil and Totus. Totus always lies, Nihil always says the truth. But nothing
allows Cloc to
distinguish who is Nihil and who is Totus. Cloc has
the right to put that a single question, but he can put her(it) to Nihil AND to Totus. Which question Cloc does it(he) have to put them to can
with certainty the way borrow(take) to join the time?
47) Inge suggests to Julien the age of his(her) sister Sandra through a devilish
statement: " I have twice the age which she(it) had when I had the age
which she(it) has. The sum our ages is of 49 years "!
48) A double water lily of volume every day. It(he) covers exactly
the surface of a lake at the end of 21 days. After how many days does it(he)
cover half of the lake?
SOLUTIONS
OF ENIGMAE
01) You did not
all the same hope that I was going to answer you 90 kph? It would be hang in
the trap of a too simple average, which does not take into account the reality:
to add two speeds and to divide them silly by two. One is not here in front of
an abstract mathematical problem, but a concrete physical situation which asks
for a "mobility" of the spirit.
Two speeds have the same
value. Being distance AB of 60km, him(her,it) to go at the speed of 60km / hour
makes in one hour, whereas return at the speed of 120km / hour makes only in 30
'. We have so a total distance of 120km made in 1. 30 '. To know average speed,
that is distance crossed(gone through) in one hour, it is necessary to divide
120 by 3. Cà average
speed in 30 gives us ': a 40km / hour. One multiplies by 2 and one obtains
average speed in one hour: a 80km / hour.
02) Second problem is
more subtle, but it can be easily resolved on the basis of the previous
reasoning. Spontaneous, mindless answer, which you expect to hear taking out of
my mouth, is a 180km / hour. Indeed, 180 + 60 = 240, and 240:2 = 120. No!
In the statement of the
problem, distance between cities A and B is not specified, because it has no
importance theoretically. But to make clearer the resolution of the problem,
let us take the conditions of the previous problem. One knows the speed on the
way out, distance enters A and B and global average speed. We are short of the
average speed of the return.
Let us make an attempt
with 180km / hour. It means that time to go is 1 hr or 60 ' and return 20 '.
According to our formula, it is necessary to divide 120 by 4 = 30 and to
multiply the whole by 3 to obtain global average speed: a 90km / hour. (80
':4=20'x3=60 ')
Let us multiply the
speed return by 1000: a 1800km / hour. One will not put so any more 20 ' but 2
' to make the route of return. On the whole, 120km is crossed(gone through) in
60 ' + 2 ' = 62 '. Not need to make the calculation of the average to realize
that she(it) is even lower at 120km / hour. And it is inevitable because the
time of route(course) of B in A sets of time. Now, one has already exhausted on
the way out the 60 ' of the global average. So global average will be always
lower at 120km / hour.
Only solution consists in
returning "immediately", that is in infinite speed, of B towards In.
Then only one does not add of time return while going him(her,it). And one well
obtains on the whole an average speed of 120km / hour.
03) To cross(go through)
200m in 4 ", one runs(drives) in an average speed of 50m / @. This average
speed is reached(affected) " half " of the time of route(course),
that is at the end of 2 ". It remains so 2 " to carry out the 150m
which remain to cross(go through). We are enough to divide 150 by 2 to obtain
average speed during the last 150 metres: 75m / @.
To cross(go through)
250m in 5 ", one runs(drives) in an average speed of 50m / @. This average
speed is reached(affected) " half " of the time of route(course),
that is at the end of 2 " and half. It remains so 2 " and half to
carry out the 200m which remain to cross(go through). We are enough to divide
200 by 2 and a half to obtain average speed in 1 " for the last 200
metres: 80m / @.
Conclusion is clear: the
vehicle b is more successful than has him(it,her).
04) Beautiful
affair(business). Do you take me so for an ass? As we shall cross, we shall be
naturally as near or as far(far), it is according to, of the city A or of the
city B the one that the other one.
We shall cross us at 13.
20 '. Indeed, at the moment when I start, at 13 hr, you have already
crossed(gone through) 60km. We are so separated one of the other one of 60km.
In one quarter of an hour, I shall have crossed(gone through) 30km and you
15km. On the whole 45km. A distance of 15km will still separate us so. If we
needed one quarter of an hour to cross(go through) together 45km , 5 ' will be
enough for us to cover together 15km. We add these 5 ' to the 15 ' the previous
ones and we obtain 20 '.
05) I would have been
unforgivable to fall in a trap so unrefined. Naturally 1. 30 ' and 90 ' is
equivalent.
06) Once again, I shall
avoid falling in the trap that you tighten(stretch out) me, even though it(he)
is less dangerous, less sneaky than the precedents. Because here, not to make a
mistake, but to run out in an infinite series of additions of fractions of
distances. Indeed, you expected that I add time and distances crossed(gone
through) by the fly during sound comings and goings between two trains. So, at
the end of one hour, the fly crossed(went through) 75km and the train A 50km.
But it is not at this moment that they meet. It is necessary that they
crossed(went through) to them two 200km before meeting first time. It is at the
end of ' 1. 36 ' that the fly and the train A will have crossed(gone through)
this distance. The fly will have then crossed(gone through) 120km whereas the
train will have covered with it 80. Naturally, at the same time, the train B so
crossed(went through) he 80km. So as the fly turns back, trains A and B are not
distant any more one of what of 40km. This 40km represents 1 / 5è some distance
initale, 200km. It is at the end of time 5
times as short that the fly and the train B will meet, or after 19,2 ' (1. 36
': 5). Because trains had crossed(gone through) 80km in 1. 36 ', they will
cover only 16km, or 5 times less in 19,2 '. Because trains A and B crossed(went
through) the same distance, they made to them two 32km and they are not distant
any more one of what of 8km. The fly turned back naturally when she met the
train B. She(it) will meet the train A for second time after 3,84 ', or 19,2:
5. Trains will have crossed(gone through) each in this time 3,2km, or 16: 5.
They are so separated only of 1,6km. Et cetera in the infinity.
Here is the answer which
you expected of my part. But I gave her(it) to you only to deceive you better.
Problem can be resolved in a much more simple way. Because trains A and B are
distant one of the other one of 200km and than they run(drive) in a constant
speed of 50km / hour, they will meet at the end of two hours. Because the fly
flies from one to another from a constant speed of 75km / hour, she(it) will
have crossed(gone through) 150km. It is as simple as it.
07) Nevertheless, the
resolution of the problem by the addition of an infinite series of fractions of
distances, allows to realize that question 7 has no solution. It is indeed
impossible to determine in which direction(management) flies the fly as trains
meet, because one can not assign a last term to the series.
08) Also one can not say
where will be the fly if one inverts phenomenon after trains met.
NB. CAN ART be useful
here?
09) If the length the
elastic(rubber band) did not vary, I would need simply 1000 " to go
throughout this one, or 16 ' 40 ".
But the elastic(rubber
band) lengthens(stretches out) of 1km by second. You expect that I say to you
that I shall never be able to reach(affect) the point B, because every second,
it goes away from me of 999m. Once again I avoid falling in the trap. Indeed, I
am a part of the elastic(rubber band). When it(he) lengthens(stretches out), I
advance(move) at the same time as he.
During the first second,
I crossed(went through) 1m, that is 1 / 1000è of the total distance. During the
second 2è, the elastic(rubber band) lengthened(stretched out) of 1000 metres.
It(he) measures so 2000m. As my speed is constant, I have still progressed of
1m. But this metre represents now 1 / 2000è left and neither 1 / 1000è left for
the total distance. Et cetera. One obtains so the following harmonious series:
Now we saw that this series is a divergent
series (to see the Paradox of Zénon's arrow). In other words, the more one adds
to him(her) of terms, the more the number x towards which she(it) aims is big. So
more she(it) goes away from the number of departure. It means that I shall
reach(affect) with certainty the end of the elastic(rubber band). The
denominator of the last fraction, x, indicates the number of seconds what it
will have been necessary for me to reach(affect) the end of the elastic(rubber
band), and he indicates me naturally also the number of kilometres of the
elastic(rubber band) at this moment. This time and this distance are immense,
older and bigger than the universe. But for me, it does not represent anything.
Let us see now the
variant which you propose to me. If the elastic(rubber band)
lengthened(stretched out) in an either arithmetical and geometrical progress,
that is if its length doubled every second, I would never reach(affect) it
extremity. Why? Because I would then have to deal with an either divergent and
convergent series. This series would converge 2/1000,
010) It is a
problem imagined by Lewis Caroll. In reason of one minute of delay a day, it will be necessary to
wait 720 days, because 12 hours count 720 minutes, to find exact hour. The
settled(fixed) clock gives exact hour twice a day. If one considers that hour
given with the most precise clock of the world stays entâchée of a tiny indistinctness, one can
even consider that the settled(fixed) clock gives twice by days absolutely
exact one hour, and to this occasion is more reliable than the most precise
clock which works. Reamrquable, isn't it?
011) Strange phenomenon
which puts in evidence the importance from the point of view for which one
takes place. I know in which point you were disturbed, dear Totus, by the paradoxes of the disc in
movement. The problem that you subject me is a variant of it. Maybe the
solution will clear up you ideas.
Observe the 4 positions
of the wheel on the figure. I indicated above two points: In in the summit, B
in the base. The speed of the wheel, or rather the speed of each of the points
is reckoned with regard to the ground. It is there the important point. Because
the speed is the report of the distance of the point to the ground by time, and
because time is the same for two points, the point B has a speed nobody, v = 0,
while the point A has a maximum speed, v = e/t, on the first drawing. E represent
the distance of the point to the ground. In the case of A, this distance is the
biggest possible. Because t constant rest, result is big.
But as it(he) comes
down(falls), the speed of the point A decreases, whereas the speed of the point
B increases as it(he) rises. Normal, the value of e decreases in the case of A
and increases in the case of B.
If one considered now
the case of the part of the wheel of a train which comes down(falls) under the
rail, the speed v =-e / t is negative, because it passes under the reference
line which establishes(constitutes) the height of the rail.
So the same wheel can
have different speeds at the same moment and even positive and negative speeds
at the same moment. Naturally all this explain himself by the adopted point of
view: the ground or the rail. Paradoxes fly away as soon as one takes the most
logical point of view, the one that puts all the points on the same foot: the
centre of the wheel. With regard to him, all the points always have the same
speed. This speed is an angular speed
012)
It seems that you love me too much or that you are too stupid to want really my
death. Indeed your devilish plan guarantees my survival. Because I must be
surprised that one comes to look me for the morning of my execution, I can not
die Sunday of the next week, who consitute the last day of the week. Because
if I was not yet éxécuté to there, Saturday at the end of morning, I
shall know with certainty that I shall be executed the following morning. Here
were which(who) kills the effect of surprise and leaves me safe life, because
the effect of surprise was a condition necessary for the éxécution of the punishment (of my
execution).
Naturally the same
reasoning can apply to Saturday. Because I can not die on Sunday, Saturday
becomes the last day when I can be executed. If I am not extracted from my cell
and from my existence on Friday at dawn, I shall know that the executioner will
come to look for me the following morning.
-?
-you have me surprised
air(sight). Would I have taken you in your own game? Let us conclude this
beautiful reasoning. If I can not be executed on Saturday, Friday becomes the
last day when I can be executed. For the reasons which you know, it is not
possible if I survived in the morning of the day before, on Thursday. I
save(spare) you the torture of the rehearsal of the explanation. Exit on Thursday, on Wednesday, on
Tuesday. We here is on Monday, that is tomorrow. I can be executed only this
Monday. But where is the effect of surprise? I leave you, I have so many things
to be lived still .
Hardly of the merciless
logic of the reasoning, Nihil executes some dance steps and some pieces of music. On Wednesday
morning, Totus
knocks at the door of Nihil's room(chamber). He enters at invitation of his enemy. With a
triumphant air(sight), it(he) takes out a gum of the pocket and complies
immediately at feet of Nihil's bed. This one, stunned, smiles of resentment to the sight of the
instrument of its torture. It is this smile which tries to give exchange, which
Totus erases. A tear pours on the cheek.
It is a tear of joy and sadness.
... In an another
time... Nihil, antiphénix, disappears ceaselessly of the
literary landscape, the thought which almost managed to realize nothingness.
Nihil admits, dear, that I left you stunned.
I was able to execute my judgment, contrary to what your subtle reasoning let
with you believe. This reasoning contained a fault. This fault widened with the
progressive execution of the days of the week when you thought of not being
able to be executed. Indeed, if you were convinced not to be able to be
executed any day of the week, your execution during some morning had fatally to
surprise you. You so gave me the possibility yourself of holding word. Admit
that your lot(fate) is ironic.
-continuous.
-I am going to give you
a logical explanation of the paradox of the impossibility of the surprised
execution.
The deductive reasoning
by which you tried to convince of the impossibility of your execution, proceeds
SRUOBER Has,
Against the normal
class(course) of the reality, the sense(direction) of time. Your knowledge of
the class(course) of events is retrospective, while the real knowledge of a
future event can not be that anticipative, forward-looking. You argue about events which
have not still taken place while you can only suppose their realization. Where
from paradox. Your logic does not take into account the reality. Now it is a
lot of reality that it is a question, your execution - surprise proves him(it).
It is so normal that logic and reality contradict themselves. Logic or reality?
Two terms can be subject and\or object.
Your reasoning
rests(bases) on one "if", hypotheses: " If I was not executed
the day before ". Here is the fault of your reasoning.
-but if one reduces the
choice of execution in two days? According to Poundstone, an intelligent being will know
that this(they) can not be the second day. So it is the first and more effect
of surprise. Indeed, if it is not the first, it is the second. No effect of
surprise. So çà can be only the second.
-forgery! One can not
compare certainty bound(connected) in the second day to the conviction
bound(connected) to the first. Logic would want that execution makes the first
day. But Totus, by
stupidity or by subtlety, can schedule(program) her(it) the second day. In any
rigour, Nihil can
be "certain" only it will be the first day. It(he) can be only
convinced of it. Important nuance. Reality is more subtle than logic.
-we have here an example
of the importance of the imagination in the time, the anticipation of time. By
her(it), one tries to eliminate time, to make quite realized, present. But
time, its class(course), exists.
013) Old problem of
calendar. It is clear that your stripling must have been born on @ February 29.
As this date falls only leap years, that is once every 4 years, the young man
has the occasion to celebrate his anniversary(birthday) no that every 4 years,
is 4 times less often than his friend. Where from a four times lesser age for
the same appearance.
014) I go back
up(raise) my clock and I hold(retain) the hour of my departure. I go(surrender)
at home. I note the hour of my arrival. I note the hour of my departure of to
you and the time stayed to you. I go(surrender) at home. I note the hour of my
arrival. I shield(subtract) her(it) from my hour of departure. I
shield(subtract) from this total the time when I stayed at home. The rest gives
me the time which I put to make route going there and back with constant speed.
I divide this time by two to know time put to return at home. I have to add
this time at the hour that I read on your clock at the time of my departure of
to you. And I know the exact hour which I have to indicate on my clock. Thank
you!
015) This problem is the
most beautiful that you put me. The solution requires(demands) a subtlety which
really put my neurones in hard contribution. It is a question of realizing that
the question which I have to put to the twins does not have to receive two
different answers. Indeed, because I ignore who of the accomplices lies, I can
not distinguish two different answers. I could make him(it) only if my question
contained an element of which I am sure of the truthfulness or the hypocrisy.
Now numerous reflections did not allow me to discover this element. It was
necessary so to pull down(reduce) me on a question which would bring an
identical answer on behalf of the two accomplices.
This question, it is:
" Which hour is going to indicate me your brother "?
What is going to answer
me the one who says the truth? Because he knows that his brother lies, he is
going to give me the answer that will give me his brother, in other words bad
hour.
What is going to answer
me the one who lies? A lie, naturally, which it is going to place, supreme
cowardice, in the mouth of his(her) brother.
Both indicate me so bad
hour. By default, good hour can be only that indicated with the second clock.
But if the liar, very
subtle, took into account my confusion and indicated to me good hour?
016) In 13 " 2/10.
Indeed, the 6 " 6 knocks of 6 hours(hr). Divide up on 5 intervals, what
gives 1 " 1/5 between two intervals, is 6/5. First blow does not set of
time. For the 12 knocks of midnight, there will be 11 intervals. Or 11 x 6/5 =
13,2 ".
017) Let us imagine that
I wake up at 12. 00 ' 01 ".
It will be necessary for
me to wait for 1. 44 ' 59 " to know exact hour. It will be necessary that
I hear(understand) 7 times 1 blow to be sure that he is 13. 45 '. Indeed, let
us imagine that I wake up at 12. 00 ' 01 ". I hear(understand) 1 blow at
12. 15 ', 1 at 12. 30 ', 1 at 12. 45 ', 1 at 13 hr, 1 at 13. 15 ', 1 at 13. 30
' and 1 at 13. 45 '. At 14 hr, I hear(understand) naturally 2 knocks, but I do
not have to wait for them to be sure of hour. Indeed, the alarm clock at 12. 00
' 01 " is extreme situation. The first time when I hear(understand) 1
blow, this(they) could be one of 7 knocks of the enumerated series. The second
time, one of 6 remaining knocks of the series. The third time, one of 5
remaining knocks of the series, etc. There is only in the seventh blow that I
am sure not to hear(understand) eighth time 1 blow. It(he) can not be that 13.
45 '.
018) The man
naturally. Child in four paws in the morning, adult on the two legs at midday,
old man with a stick in the evening.
019) This figure is the
8. A knocked down infinity which well represents the age of the extensive
movement.
020) I thought at first
of the question: " Which words compose this question? ". But you
would have been able to point out me that answer: " Which words compose
this question " did not understand(include) the question mark. Answer
would not have so established(constituted) a rehearsal of the initial question
which it would be necessary for us to answer eternally. But I found parade. I
am enough to replace word "words" by the word "signs".
Indeed, a letter is a sign and the question mark also. In the question: "
Which signs compose this question? " One answers unlimited: " Which
signs compose this question? ". Subtle, isn't it?
-I bow!
021) It(he) is 3 hr.
022) I am enough to move
back until the moment which precedes the pose(installation) of the last stone
of my prison. I go out of my prison and I return as I left her(it), in my
machine to travel in the time. I shall be free as the air(sight), but again
prisoner of time.
023) At first, to
decompose 471569 into first factors. The remarkable day of the month of
explosion of the grenade has to be on @ February 29. The 31 has nothing of
remarkable because one meets him(it) 7 times over the year. 23?
024) Useless to
complicate life by calculating endless series. It is at the end of one half an
hour that Nihil and Totus will cross. At this moment, the Dove will have crossed(gone through)
60km.
The mathematician John von Neumann
025) 19 years
026) 13
027) December 31
028) 28 and 32, in three
years
029) 11400
030) I go back up(raise)
in the time,
I kill my mother,
So, I do not exist,
So, I do not go back
up(raise) in the time,
So, I do not kill my
mother,
So, I exist,
So, I go back up(raise)
in the time...
031) SORRY!!!
032) Yes!
Lucky Luke fires more fast even
necessarily than the shadow?
The movement can not
exceed, quite as that of the shadow, the speed of 300000km / @.
But as shadow is taken
away from him, even from a tiny distance, the light which surrounds him(it)
takes certain time before reaching(affecting) its objective. This time,
although tiny, is sufficient to create a gap between Lucky Luke's movement and that of its
shadow. As Lucky
Luke unsheathes sound six knocks, his(her) shadow still has arms ballants.
As for him, Lucky Tachyon would unsheathe, in a
absolute way, sound six knocks more fast than the shadow.
If shadow precedes
sometimes its model in movement in the space, she(it) always follows him(it) in
the movement of time. Lucky Luke's shadow is always younger than Lucky Luke.
Lucky Luke, the man who fires more fast
necessarily than the shadow!
033) Everybody, or
almost, answers: " on January 1-st of 2000 ". And there are many
individuals, organizations and even nations which already prepare event with
restlessness, believers(regular customers) for the spirit millenarian. Some,
naturally, predict the end of the world or the worst disasters.
Nevertheless, it seems
that all these persons make a technical error. Third millennium, indeed, should
begin only on January 1-st of 2001. 2000 will conclude 2-nd millennium, as 1000
concluded the first. Confusion comes from the assimilation of the birth of the
Christ in the year 0. Really, the day of the birth of the Christ
establishes(constitutes) the 1-st day of the first year of the first century of
the first millennium. There is not of day 0 or of year 0. One begins directly
with 1. Consequently, the first day of the 2-nd millennium is well on January
1-st of 1001. And the first day of the 3-rd millennium on January 1-st of 2001.
Nevertheless, it is
necessary to recognize that this calculation leaves one
Diffuse feeling
dissatisfaction. Logical rigour not
Joined not intuition,
which can not refrain from finding more suitable the allocation of the beginning
of the third millennium on January 1-st of 2000. A small reasoning is going to
confirm us it. Let us ask questions to the sceptic:
When begins 3-rd
millennium? In 2001.
When begins 21-th
century? In 2000.
Here were which(who)
already has to seem strange for our interlocutor. Third millennium and twenty
one - ème
century do not begin at the same time. But let us pursue our reasoning.
When begins 1-st
millennium? In year 1 in 1-st century.
So, first century and
first millennium begin at the same time.
When begins 1-st
century? In year 1.
When begins 2-nd
century? In year 100.
Logically, 2-nd century
should have begun in year 101. So, a mistake in calculation is committed from
the 2-nd century and successful candidate since by everybody, including by those
that assert that 3-rd millennium begins 1/01/2001. According to them, 21-th
century should also begin 1/01/2001.
Consequently, or the
sceptic is right, 3-rd millennium begins well 1/01/2001, but then it makes the
error to begin 21-th century in 2000; is we unconsciously settled from the
second century the calculation which considers that one year 0 ago.
Conclusion, our
intuition according to which 3-rd millennium begins 1/01/2000 is not faulted,
the initial mistake in calculation of time faded, was likened with time! It is
the exception which confirms the rule(ruler).
And it is indeed that
seems to teach us common sense.
Nevertheless, listen or
to read that 1999 is the last one réveillon before the 3-rd millennium leaves a
taste of unfinished. One would then like to integrate 2000 into the 2-nd
millennium. Maybe this feeling it is due to our system of decimal numeration
which wants that one includes 10 in the first ten, 20 in the second, 100 in the
tenth ten or first hundred. First millennium inclurait so 1000 and second millennium comencerait in 1001, the third in 2001.
On the other hand, the
birth of the Christ has no sense(direction) 1/01/1 because it would already be
then in his(its,her) second year. In fact, he would have been born well 1/01/0,
in the first second of the first millennium. And to confirm while millennium
begins well 1000 , 2000 or 3000, one can notice that decimal counting works
very well from dozens. So, there are ten well numbers from 10 to 19, of 20 in
29, etc.
The problem of the first
ten stays which understands(includes) while 9 numbers, the 0 not being a part
of the family. It(he) will be moreover invented with the Indian only well later
Arithmetic. But it is
not this invention of the 0 which
Will provoke confusion
between two decimal systems of counting, a which includes 10 in the first ten,
and the other one in the second ten?
At any rate, we are in
front of a difficult question that one will leave care with the reader to cut
to the suitability.
034) At 11 o'clock
035) Because we passed
more or less three months in the womb of our mother.
036) 396 kph and not 400
kph as one is tried to answer it spontaneously. Indeed, let us imagine that the
plane has to cross(go through) the distance of 360 km. It(he) will cross(go
through) her(it) on the way out and in 49 in 1 hour ' on the way back, or 720
km in 109 minutes.
037) Wednesday and
Thursday
038) Immediate
finished speed
Since Röemer in the 17è century, one knows that
speed of light is finished. One knows today the precise value of this speed.
She(it) is of 299 792 458 m/s.
Of what one dreams less,
it is that light stemming from the flame of a match has to reach(affect)
immediately this fabulous speed.
I enjoyed making a small
calculation to know how long it would be necessary for a some object in
constant acceleration to reach(affect) speed of light?
We are in the habit of
formulating speeds in kilometres crossed(gone through) in one hour. Let us
convert
300000km / @ of the light
in kph: one obtains
10800000000 (ten
billions eight hundred million kilometres in one hour:
3600s x 300000km /).
The law of Galilee says
that the speed of an object in constant acceleration is a function of the
square of times. To know time put with the object to reach(affect) speed of
light, it is enough to remove the square root of
10800000000. One
obtains:
100004 hours. We have to
convert these
100004 hours in years to
obtain a more talking representation of this time. One year amounts in
8774,4 hours. Our
100004 hours amount in
11,397246 years. Here is
the time which it will be necessary for an object in constant acceleration to
reach(affect) speed of light.
039) " The product
of their ages is equal 36 ".
The first thing(matter)
to be made is to envisage all the possible combinations(overalls) of 3 figures
of which the product is 36
1. 1. 36
1. 2. 18
1. 3. 12
1. 4. 9
1. 6. 6
2. 2. 9
2. 3. 6
3. 3. 4
" The sum their
ages is equal to the number of the house of the neighbour of opposite ".
Second stage consists so
in adding each of the combinations(overalls)
1 + 1 + 36 = 38
1 + 2 + 18 = 21
1 + 3 + 12 = 16
1 + 4 + 9 = 14
1 + 6 + 6 = 13
2 + 2 + 9 = 13
2 + 3 + 6 = 11
3 + 3 + 4 = 10
It is here that that
becomes interesting. Without taking into account the Totus's third information, one says
himself that one can eliminate the number 13 because it repeats twice, but
having acquainted with this third information, one notices that she(it) does
not allow to distinguish between the other numbers the one that indicates the
number of the house of the neighbour, and that consequently, the supplementary
information which gives Totus concerns result 13. And suddenly, EUREKA, if Totus clarifies that his(her) elder
daughter is fair, it is that his(her) twin sisters are younger than her(it).
Consequently, ages to be held(be retained) are 2 , 2 and 9 years.
040) The sixth is not
the sixth day, but 1 / 6è days lived by Diophante. It is necessary so to find a
number which is divisible by 6, by 12 and by 7. The first of these numbers is
84. One is 14 years old for the youth, 7 years old for the adolescence and 12
years old still until Diophante's marriage, is in 33 years. He has his 5 year
old son later, or in 38 years. His(her) son lived twice less for a long time
that he, is 42 years. Diophante is so 80 years old when his(her) son dies.
It(he) laments 4 years and dies in 84 years.
041) A single
second second per minute.
042) The time of
the time switch is measured in rebours as the clock of failures(chess).
043) The calendar
measures an irreversible time against cyclic, reversible, repetitive movement
for the other means of measure of time.
044) 1 for day
045) It is an excellent
exercise of thought in movement, which distinguishes itself from the resolution
of problems static as geometrical problems. It is an intermediate stage between
the mathematical thought and the physical thought.
You turn(return) two egg
timers at the same time. When the sand of the egg timer of 5 minutes completely
passed by, you turn(return) him(it) immediately. When the sand of the egg timer
of 7 minutes completely passed by, you turn(return) him(it) immediately. When
the sand of the egg timer of 5 minutes completely passed by for second time, is
after 10 minutes, it(he) passed by three minutes for the egg timer of 7
minutes. You are enough so to turn(return) immediately this one to add 3
minutes to already sold 10 minutes.
046)
Which way is going to indicate me your brother?
The one that says the
truth, answering the place of his(her) brother, is going to give false answer
which that will give. As for the liar, he is going to cross(spend) his brother
for a liar and will indicate so anyway the bad way. Cloc obtains twice the same answer.
Indeed, not knowing who
is the liar and who says the truth, Cloc can not ask a question which brings
two different answers. It(he) has absolutely to ask a question which Nihil and Totus will answer the same thing(matter).
Because one is certain that one of the two lies, necessarily given answer is
false, so it is about the other way.
Directly to know the
good way, Cloc has
simply to ask: " Which way is not going to indicate me your brother?
"
047) The
peculiarity of this enigma is to require(demand) a big concentration to
understand(include) statement subtle of it.
7 years ago of distance
among Inge and Sandra. Inge is 28 years old, Sandra 21 years.
048) With a
beautiful enthusiasm, one answers " 10 days and a half "!
It is at the same moment
too simple and too much complicated.
It is necessary to
proceed, to count in rebours. One knows that at the end of 21 days, the
water lily covers all the surface and that it doubles of volume all days. It is
so that it(he) was twice as small in daytime and as it(he) covered then half of
the surface of the lake. It is at the end of 20 days that it(he) covers half of
the lake.
CURIOSITIES
__________
The enigma
of the mad cyclist
--------------------
Here is a reasoning
which shows the surprising consequences which one can pull(fire) of a
commonplace event of the daily life.
Let us imagine a
pedestrian walking(working) in the middle of a pavement and a child with cycle
which follows him(it) and exceeds him(it) by the left without having warned it
of it just like that of bell or a remark.
The pedestrian jumps,
surprised by the overtaking, and sends a sign of anger to the unconscious young
person.
But the quiet income
urges him(it) to wonder about the event.
And so it(he) realizes
that the warning of the child would have been useful only on condition that
this one rolls slowly (how to determine the maximal speed?). Indeed, the
warning could provoke an abnormality of the direction(management) of walking of
the pedestrian. As far as the pedestrian makes a movement of distance towards
the left, and far as the cyclist too fast rolls to anticipate him(it), here is
our pedestrian and our cyclist appalled.
On the other hand, if
the cyclist does not give any warning, he and the pedestrian will have any
interest that he runs(drives) very fast to avoid the collision. Indeed, the
absence of sound warning prevents from anticipating the possible distance from
the pedestrian. Better even, she(it) eases the risks of an abnormality of the
walking of the pedestrian. The best means to anticipate possible distance,
because an abnormality stays the best possible, means to take into account this
completely unpredictable distance, consists in settling a side of overtaking and
in crossing(going through) him(it,her) as fast as possible. The speed
guarantees all the more the success of the company of overtaking as it is more
high.
The danger of collision
diminishes according to the increase of the degree of the speed of overtaking.
The risk of collision is
inversément proportional in the degree of
increase of the speed of overtaking.
What it is funny to
observe in this reasoning, it is that two notions of "mastery",
control of the danger are outlined there in their additional opposition. In big
speed, it is by the reduced mastery of the vehicle that the cyclist
reaches(affects) a bigger control of the event (it is not the place here to
discuss the problem of the increase of the concentration, so the mastery of the
vehicle with big speed). The increase of the speed reduces the capacity of
mastery of the vehicle, but it is an indispensable condition to avoid the
collision, for all that naturally that the cyclist refrains from warning the
pedestrian of his operation of overtaking. So, in big speed, reduced mastery of
the vehicle, but big mastery of the event, the possibilities of accident.
In reduced, big speed
master of the vehicle and big mastery of the event. It is the ideal situation
which reflects the wisdom of the pilot. But we know that she(it) shows himself
rarely in the reality. We have so to take into account the most precarious
situations, which are also the most common(current).
So let us be careful
that there are two types of masteries: a mastery of the vehicle and a mastery
of the event, due to the anticipation of what can arrive. These two masteries
are excluded each other in the case of the operation of overtaking with big
speed, but they join in the case of the overtaking with reduced speed.
The paradox of the jet
lag
__________________________
To cross quickly time
zones, pass quickly from a time zone to the other one, that is to cross(go
through) the distance which separates two reels more fast than makes him(it)
the sun for the horizon, is doubtless means the surest and the most simple to
travel in the time.
Nihil journey westward, Totus eastward, in the same rhythm as the
sun.
Nihil always precedes the sunrise of one
hour(o'clock). It(he) is in the eternal night. Totus progresses in the same rhythm and
in the same direction(management) as the sun. The eternal day.
If Totus progresses eastward at the speed of
a reel by hour, it(he) progresses by slices(edges) of two hours(o'clock) with
regard to astronomical time. It(he) is 12 hr in the point of departure. It(he)
is 13 hr in the previous reel. If Totus moves in immediate speed, it(he)
will meet himself at 13 hr in the reel x-1 (x = reel of departure). But it(he)
puts one hour. It(he) will arrive there so at 14 hr. It is naturally the same
thing(matter) for the reel x-2. It(he) starts still at midday, but it(he) is at
the same moment 14 hours in the reel x-2. Totus travel during 2 hours. It(he) will
arrive so at the reel x-2 at 16 hr.
If one formalizes this
observation, the hour in which Totus arrives at a new reel is so:
Ha = Hd + tv.2 (hour of arrival = hour of
departure + time of journey x 2).
Westward, hour is always
the same: Ha = Hd.
T1 - T2 = 0. Time
stops(arrests) westward.
Totus seems to waste time to travel
eastward. Nihil on the
other hand seem to win it to travel westward. But earning is imaginary. In the
final discount, Nihil wastes time rather than he wins it because fatigue provoked by the
necessity of adapting itself to a new rhythm of life, requires(demands) a
spending(expense) of energy more high than of custom. Nihil will so waste time to let his(her)
body calm down. As for Totus, this physiological disturbance will add to its waste of time dûe in the jet lag.
The paradoxes of the
longevity
---------------------------
-Qu'entends-tu do you
listen by paradoxes of the longevity?
-this expression is the
fruit of a disturbing observation. I wondered which could be the explanation of
the longevity of a shape to be. It is then that I noticed that the forms to be
the most simple could have a life expectancy(cycle) extrèmement short or on the contrary extrèmement long. So the proton seems to have a
life expectancy(cycle) of several billion years. On the other hand, the virtual
particles stemming from the ocean of Dirac have a life expectancy(cycle) which
is reduced to a tiny fraction of second, of the order of the femtoseconde. Now the proton is not much more
complex than these virtual particles. Why so such a disproportion in the
longevity of these two types of particles?
-I ignore it. You know
doubtless that the association of a pit consisted of a proton and a neutron
with one or several electrons gives an atom. The most simple atom is the atom
of hydrogen. But the most stable atom is the iron atom. Nevertheless, it(he) is
neither the most simple nor the most complex.
Besides, one often hears
that " diamonds are eternal ". It calls it long on their longevity.
But how to explain this longevity?
In the vegetable world,
certain trees as the baobab or the locust tree are millenniums. They are very
impressive. But their majesty does not explain their longevity, it is it rather
a consequence.
Let us take another
example, in animal kingdom this time. The tortoise is the animal in the biggest
longevity, but it(he) is far from being the biggest and the most complex.
Einstein, Cléopâtre and the flint
-------------------------------
It is a question of
verifying the life expectancy(cycle) of the elementary particles and in the occurence the longest life expectancy(cycle).
But chances are not invalid that these lines are consisted of certain atoms of
the brain of Einstein, a tyrannosaur, a nose of Cléopâtre, of the first moments of the
universe or the crown of thorns of Jesus Christ.
The sorrow of Joconde
------------------------
On the contrary, any
eternal being particle, it is inevitable that the original representation of Joconde of Léonard de Vinci's hand, will
disappear sooner or later. Any shape to be, without exception, eventually
degraded. The enigmatic smile of Joconde can not challenge time. It will be
it all the more enigmatic.
Can
Lucky Luke more fast fire than the
shadow?
_________________________________________________
Yes!
The movement can not
exceed, quite as that of the shadow, the speed of 300000km / @.
But as shadow is taken
away from him, even from a tiny distance, the light which surrounds him(it)
takes certain time before reaching(affecting) its objective. This time,
although tiny, is sufficient to create a gap between Lucky Luke's movement and that of its
shadow. As Lucky
Luke unsheathes sound six knocks, his(her) shadow still has arms ballants.
As for him, Lucky Tachyon would unsheathe, in a
absolute way, sound six knocks more fast than the shadow.
If shadow precedes
sometimes its model in movement in the space, she(it) always follows him(it) in
the movement of time.
Lucky Luke, the man who fires more fast necessarily
than the shadow!
The paradox
of the illusion of the reality
_____________________________
Nihil is a comedian. It(he) can not
refrain from annoying Totus and from pulling(entailing) him in absurd adventures.
In the occurence it(he) decided to exploit(run) at
most the resources of the A.R.T.
It(he) imagined a small
experience(experiment) which has to leave without voice(vote)
Talkative Totus.
The way to be followed?
Nihil is going to present to Totus an interlocutor as high as his(her)
inspiration: Einstein. It(he) is going to throw(launch) a discussion
about Totus's
preference: " the utility of the art ". Warned musician, Einstein does not have to lack ideas on the
question.
Begun(affected)
conversation, Nihil will make off. He will not speak about the art. It(he) will put him(it)
in contribution. It(he) will put the A.R.T. in contribution. It(he) plans to
use the Accelerator and Speed bump of Time to slow down movements and thoughts
of the two interlocutors.
He(it,she) was advisable
with toward Totus
that it(he) would feign a faint and a fall during the conversation.
Because information
conveyed in the universe can not exceed the speed of propagation of the light,
maximum speed of 300000 km/s; because the transmission of the information of a broadcasting station
to a receiver is not "immediate", it(he) exists a gap enters the
moment when the broadcasting station sends its message and the moment when the
receiver registers(records) him(it).
So all the time of our
daily life, we perceive reality with a certain delay. Why do not we perceive
this delay? Because speed of light is so high as it seems to us immediate.
And sound?
It is true that the
phenomenon of echo indicates us a gap between the moment of
broadcast(emission,issue) of the sound and its reception.
Nihil plans a lot to slow down the speed
of propagation of brilliant and sound waves. It(he) is going to divide her(it)
by 100 millions.
Light progresses
normally at the speed of 300 million metres by second. So the new speed, due to
the A.R.T.
Will be of 3m / @. As for the sound, the normal speed is about a 1000km / hour,
is 300m / @. The new speed will be of 0,000003m / @, or 3 millionths of metre
by second.
Einstein and Totus is 9 metres one of the other one.
Totus sees Einstein such as he was there is 3 seconds.
As he says: " You look well, Albert. You inhale health ", Einstein collapses. Totus realizes it only 3 seconds later.
As for Totus's
remark, she(it) will reach the ears of Einstein's corpse only about 1157 years
later. Indeed, sound puts 100 million seconds to cross(go through) the distance
which crosses(goes through) light in 1 ".
The
paradox of the glance in past
______________________________
-the lovers of
celestial bodies well know this paradox. They know that they do not see the
star which they observe such as she(it) is today, at the moment when they
perceive her(it), but such as she(it) appeared when she(it) emitted(uttered)
the brilliant information.
If the star is situated at
a distance of 300000 km, the astronomer observes the star such as she was there
is one second.
The more distance
increases, the more embellishes with images him(her,it) whom(that) one
perceives of the star is old, or rather, the more the star of which one
perceives image is old, or rather more the light which reaches us from this
star is old.
If the star is situated
in 3000000 of km of the earth(ground), its light puts 10 seconds crossing(going
through) the distance which separates two celestial bodies.
In 30000000 of km,
she(it) will travel 100 seconds, that is when she(it) will put 1 ' 40 "
before to reach(affect) us.
If the star has just
exploded at the moment when you aim your telescope at her(it), you will not be
able to have the illusion to possess a weapon extraordinary, dear Totus.
Because during 1 ' 40
", the lens of your telescope will get the image of a radiant star of
health.
A fraction of a second
later, a fantastic fireworks will illuminate its retina.
If your telescope was a
powerful beam(shelf) lazer capable of reaching(affecting) the star in question, and of converting
it in a myriad of sparks, it would be necessary to count 3 ' 20 " between
the moment when you would send the destructive beam(shelf) and the moment when
you could notice his devastating effect: 1 ' 40 " to go him(her,it) and 1
' 40 " for the return.
It is disturbing to say
himself that one can "see" past. It is the direct consequence of the
fact that light is not immediate but moves with a limit speed: 300000km / @.
Until the calculation of
the Danish Römer in 1675, the men of science were convinced that light
propagated instantanémént. At the moment when one lit the candle, light reached(affected)
immediately any place around her(it), so remote it is.
-but why is not it so so
clear far as near the candle?
-because the intensity
of the light decreases with the distance. The intensity, not the speed.
The
telescope Hubble
-----------------
-what happens if one oberve the star with a more powerful
telescope?
-you think of the
telescope Hubble, this high-powered telescope which was sent to the space to
escape the pollution of the sky that establish(constitute) clouds and
electromagnetic waves?
-yes.
-what reveals us time
put by the light to reach of the star, it is the minimum age of the star. So
that light travels during 1 ', 15 years, 300 years, 6000 years, 8 billion
years, it is necessary that the star existed there is at least 1 ', 15 years,
300 years, 6000 years, 8 billion years. But it does not mean that the star was
at a distance of 1 ', 15 years, 300 years, 6000 years, 8 billion years - light
of the earth(ground) at the time of the sending of photons.
-not?
-to know the distance
which separates the star observed with the earth(ground), with the
earth(ground), it is necessary to take into account the experience(experiment)
of Michelson and Morley which showed that speed of light is independent from its source and
from the speed of its source; it is necessary also to take into account the
expansion of the universe.
If the universe is
static, and if the star is situated in 4 billion years - light of the
earth(ground), light will put 4 billion years to reach(affect) the
earth(ground).
If the universe is
expanding and if distance between the star and the earth(ground) at the time of
the explosion doubled as light reaches(affects) the earth(ground), the
earth(ground) and the star going away one of the other one in a constant speed,
how long will put light to reach(affect) its objective?
-light will put 8
billion years to reach(affect) the earth(ground) which goes away, because if
light is independent from the speed of the source, it doesn't much matter that
its star of origin is fixed or in movement, it is sensitive at the speed of the
objective, in the occurence the earth(ground).
T ... E BANG
T2------+ t1
C
T ....... E
T2----------------------+ t1
C
-forgery. You fell
in the panel. You gave the time during which would travel light if it covered the
total distance which separates the star of the earth(ground). But she(it)
crosses(goes through) only 3/4 of this distance. Indeed, she(it) crosses(goes
through) the distance of departure more half of the distance of estrangement of
the star and the earth(ground).
T1 BANG
T ....... E
T2------+----¦----¦----¦----¦
C
Result, light does not
travel during 8 but hanging 6 billion years, because with regard to the moment
of the departure of the light of the star, the earth(ground) went away once and
half of the light in its source.
-does it explain why one
can see a light older than the star which emitted(uttered) her(it), as suggest
him(it) the observations of the telescope Hubble? Once left for the star, light
does not more have anything to see with her(it). But is it enough to justify
this paradox?
-I do not believe. To
waste time, it would be necessary that light makes bends. Now she(it)
propagates in a straight line.
-yes, but she(it) can be
slowed down by the forces of gravitation.
-even in that case, time
put by the light to reach(affect) the earth(ground), stays a correct measure of
the age of the star which sent her(it). In the brains to stir!
The paradox of the
incompatible ages
-----------------------------
-that revealed the
analyses of the results of the first observations of the telescope Hubble?
-that the universe seems
to be younger than the stars which it contains. So the traditional fork from 10
to twenty 20 billion years which would allow to determine the age of the
universe would be returned to 8 in 12 billion years. But the oldest stars have
more or less 15 billion years. How so contents could it be older than the
packaging? Here is a paradox which instigates the reflection of the scientific
world. We visit that a solution of this problem passes by the exact
understanding of the expression " to see far, it is to see early ",
of which the previous chapters we shown how it could mislead us.
big clap and expansion
------------------
Einstein is doubtless the biggest physicist
of twentieth century; it is one of the pioneers of the quantum physics and he
elaborated theory of relativity. Through the theory of relativity, it(he)
showed that the space and the time were a part of a continuum in four
dimensions, that is that they were inextricable and that they were affected
together by the material(subject) which they contain and which they affect this
one in return: and so Einstein put in evidence the curvature of space-time.
But it is a point on which he made a mistake: the state of the universe. Einstein was so convinced of the static
character of the universe, that he introduced into his equations a "
constant cosmologique " who cancelled the effect of expansion of the universe which they
let foresee. In the light of the works of Friedmann and Lemaître, Einstein recognized that he had made a
mistake. The universe arose from the explosion of an initial peculiarity called
later Big Bang.
Since this Big Bang,
the universe pursues its expansion just like a pudding which would swell infinitely.
In 1929, the American astronomer Edwin Hubble gave a spectacular confirmation of
the theory of the expansion of the universe by noticing systematic gap towards
the red of galaxies. What it wants to say? Galaxies emit(utter) of the light.
The spectre of the light is consisted of several frequencies, the infrared for
the weakest frequency, in the ultraviolet ray for the strongest frequency. If
the light which reaches us from a body aims towards the red, it is that the
wavelength of this light increases, so that the object which emits(utters)
him(it) goes away from us. Hubble establishes as well as galaxies go away some
of the others in a proportional speed at their distance. If one succeeds in
determining this speed exactly, one will be able to know the age of the
universe. Indeed, it will be enough to invert the sense(direction) of time in
equations to know the date about which all the galaxies were concentrated in a
single place, and so the age of the initial peculiarity. It is here that we
find our telescope Hubble, the name naturally of the astronomer who confirmed the theory of the
expansion of the universe. The analysis of the first observations of this
telescope allows to determine a speed of expansion of galaxies much more
precise than that known until then. This speed of expansion gives to think that
the universe would be old from 8 to 12 billion years while its oldest stars,
according to the analysis of their constituents, have to have 15 billion years.
Sphere and
privileges
-----------------
Let us return to Einstein. The essential education of the
theory of relativity consists in the observation that there is no place
privileged to make an observation. There is no absolute place, that is a place
which would be fixed for any observer of the universe. If there is no
privileged place, one can not determine in a absolved way the simultaneity of
two events. Consequently, time, the measure of time is relative towards where
is made observation. Even acceleration, movement of which is considered as
absolute, can as indeed explain itself by the influence of intense forces of
gravitation as by the more and more fast movement in the space. The observer in
a repository in acceleration can not distinguish these two types of
explanation. This relativity of time and of the space must be connected with a
particular geometry. It is the geometry of curves and sphere. The sphere is the
only volume all the points of the surface of which are equivalent, that is that
there is no place privileged on the surface of a sphere. At the moment, let us
return in our problem of the observation of celestial bodies.
What has to see of the
universe another observer than the ground observer? Will it(he) observe the same
speed of expansion of the galaxies as us from the earth(ground)? Yes, on a
condition: that the universe is expanding uniform. If it is case, because there
is no point privileged in the universe, an observer very remote from us will
make the same observations as us. It is what explains the fact that we can hope
to determine the age of the universe while we are not in the centre of the
universe. In a way, any point of the universe can represent the centre of the
universe. To determine the age of the universe, it will be enough to know the
distance which separates us galaxies which are the most taken away from our
galaxy. One estimates this distance by the observation of the spectre of the
light emitted(uttered) by these galaxies. By calculating the time which it was
necessary for these galaxies to go away from ours in the point where they are
it today, one can determine their age and consequently the age of the initial
peculiarity. It is well in the sense that it is necessary to
understand(include) expression: " to see far, it is see early ".
The present past
--------------
We have to approach the
funniest chapter. We saw that there was no place privileged in the universe.
The situation of our galaxy and any more particularly the earth(ground) does not
differ from that of the other celestial bodies. Let us imagine an observer
situated in million years - light of the earth(ground). If it(he) can not
observe that the spot which form possibly our asylum in the sky of its planet,
he will know that this spot is that of a more or less old body. Are we the past
of the present of this extraterrestrial? If it(he) has a rather powerful
telescope to give him(her) the impression(printing) that the earth(ground) is
under its nose, will he see us we entretuer in real time? No! Because an image
does not walk only in the universe. Photons have no memory(report). If the sun
shines with its absence eight minutes after it exploded, it is because it is
the light. Besides, the extraterrestrial will notice that the earth(ground)
goes away from him in a proportional speed at its distance. Following a small
calculation, it(he) will estimate the moment when all the galaxies had to form
only a point, and so the age of the universe. Surprised! He notices that the
universe is younger than certain stars.
What is it(he) to it of
this paradox bound(connected) to the incompatibility of the longevity of stars
with that of the universe?
The first idea which
comes to the spirit is that of the desolation of the hypothesis of the
expansion of the universe. But then from the other questions appear. How to
explain gap towards the systematic red of the spectre of galaxies? How to
explain the uniformity of the fossil brilliance to 3 ° kelvin in all the directions(managements)
of the space?
One can think as well as
the speed of moderate expansion is not correct.
One can question the age
of the oldest stars.
One can resort to the
hypothesis of universes - islands and holes of towards.
Safety
-------
A fortuitous observation
revealed to Totus the
unexpected.
Totus circulated in an underground train.
Totus sat in an underground train which
circulated in little frequented places (what in itself already
establishes(constitutes) a paradox).
Totus sat on a footpath(banquette) of an
underground train which crossed(went through) little frequented districts (what
is always also paradoxical).
The oar
reached(affected) its cruising speed: hundred kilometres an hour.
Totus watches disentangling the vestiges
of the civilization. batîments in ruins, factories covered with the grime of
smokes spat with their fireplaces, piles of scraps... The dizziness of the
civilization.
In this petrified
decoration, a man.
A man whose only the
movement of the head gives evidence of the life.
At the moment when Totus passes at his(her) height, he
notices that the individual greets him(it). It(he) lowered(dimmed) the head as
to give evidence him(her) of a sign of friendship.
Totus remain perplexed. By politeness, it(he) returned the
safety to the individual, but it(he) does not remember the ever seen resources.
Why would it(he) have so made him(her) sign?
It is then that a
thought crosses him(her) spirit. Totus remembers that the individual was
not able to notice his safety because at the moment when Totus lowered(dimmed) the head in
his(her) tour(tower), the oar had crossed(gone through) a little less than
thirty metres.
The individual had to
say himself that Totus lacked good manners. But, on second thought , in the deepening of the
reflection, Totus
understood(included) finally that he had been mistaken about the intentions of
the individual. Totus did not miss courtesy and the individual did not give evidence of an
excessive sociability.
The individual had not
greeted Totus.
Here is what had
occurred.
The underground train is
thrown(launched) to 100 km an hour. The watman, Nihil, perceives the individual on the
edge of the way. It(he) the reconnait and, some thirty metres before arriving at the
height, it(he) greets him(it). Civilian, the individual answers politely his
companion by lowering(dimming) the head in his tour(tower), but only as Nihil arrives at his(her) height. Now
time passed with the oar between these two events. Two seconds exactly passed
by between the moment when the watman lowers(dims) the head and that where the
individual complies. No injury time!
Second must be converted
in metres. Hundred kilometres an hour amount to 100000 metres an hour. To know
distance crossed(gone through) in one second, it is enough to divide 100000 by
3600 (60 minutes x 60 seconds). One obtains about 30 metres a second.
Now 30 metres separate
the watman of
the seat on which settled down Totus.
So at the moment when
the individual makes a movement of head, Totus arrived at his level and estimates(esteems)
that he is sent to him(her).
At the moment when Totus shakes he also the head, 30 new
metres were crossed(gone through) and a small old lady always wonders why Totus greeted her(it).
Unless she(it) possesses
some notions of physical appearance(physics), or simply the gift(donation) of
the observation and a little of common sense.
The paradox
of injury time or meanwhile
_____________________________________
-dear Nihil, I would wish that you make me a
service. Do you see this dove which beats wings above our heads? I would love
that you immortalize the flight(theft) on the film of your camera.
-nothing more easy.
-I am happy to see you
so cooperative. Here is finally come the moment when we get. Have a good laugh
insults. Do you believe that this dove urges us to make peace? Which symbôle.
-peace! I do not manage
to concentrate.
-?
-magnificent fowl
Symbôle of peace of the womb.
-monster.
-which idea. What to say
of the man if you already find one so small to be disgusting?
-respite to muddle up me
spirit. The monster, it is you, naturally.
-but I am not a man.
-Aaaarrrggh...
-but without wanting to
miss, looks your dove. She(it) beats of the wing.
-well then?
-here is which(who)
loses of the height. She(it) she(it) falls; she(it) buries the existence.
-continuous to film.
-but it is necessary to
try to save her(it).
-film! You obtained what
you wanted: I am cynical. It is in the air(sight) of time. If it was necessary
to begin to save the least earthworm which wriggles on the road having left his
wet earth(ground), time would be counted us.
-?
-she(it) has just
crashed. You can stop(arrest) filming and prepare the place setting. Such
feelings open the appetite.
-C should it anything be
understood. How were you able suddenly to become so cruel? In less unless you
found there the means to finish it with our sarcasms. If you are more cynical
than I, how could I prick you, how could you take offence at my cynicism?
-by the sweetness.
-it was not a question.
-it is not an answer.
-I know how how to
disturb you. Here is the film of the tragedy which has just deceived under our
eyes. I cross(spend) him(it) to you. The energy of this small ball of feathers
admires this flight(theft) grâcieux. Suddenly, here is which(who) begins to fall.
What happens? Would a hunter have pulled(fired) her(it)? A ruptured aneurysm?
Question is: is there an
image which shows the passage of the normal flight(theft) at the beginning of
the fall?
-logically yes. I filmed
the hanging scene 5 ' at the rate of 24 images by second, or 7200 images to
immortalize the death of the symbôle of the peace.
-two of these 7200
images have to represent the exact moment of the passage of the flight(theft)
normal for the fall.
-I stop(arrest) you!
These images are immediate taken on the movement. You would like to find this
precise moment when the dove begins to fall(flop). Now you need for it of two
images. But you forget that the speed of the film is arbitrary. 24 images by
second allow to feign real movement, but in theory, one can divide in the
infinity flight(theft) and fall of the dove. Indeed, as close in the time as
are the two images which will represent the passage of the flight(theft) in the
fall, it seems that one can, in theory, photograph an infinite number of moments
between two successive images. You will be able to find so never two images who
will indicate you the exact passage of the flight(theft) to the fall.
-D a logical point of
view, it is true that the passage of the flight(theft) in the fall seems impossible.
Ultimately the dove can not fall. She(it) can not die, even though mathematics
integrated the notion of passage into the limit. But from a practical point of
view, what you say is not completely exact. From a practical point of view,
from a point of view of the physics and neither only the mathematics, one can
not divide time below the limit of
Which(who) represent the time of Planck.
It means that the most
moved closer two images that one can obtain are in the report of
0,0000000000000000000000000000000000000000001
In
0,0000000000000000000000000000000000000000002. enters these two
Numbers, there is no
figure. It is the administration of the formless, so the not measurable.
Science is very far from being able to reach(affect) such limits. But anyway,
it seems paradoxical to want to realize 1 moment through 2 clichés. It is
doubtless there that hides contradiction. It is necessary to admit that "
everything costs more than the parts ", at least that the parts which we
impose on him(her). So, the time of the passage of the flight(theft) in the
fall costs more than two supposed images to represent him(it). Time, identified
with the movement, costs more than a sum moments.
-a moment is one time -
death! And indeed, as we saw him(it) throughout these chapters, the language of
the logic and more generally the mathematics allows us to cut reality, but it
does not allow us to recreate him(it). It(he) gives us an illusion of reality.
For a very good reason, there is a difference of dimension. Mathematical
representation makes in best in 2 dimensions while reality counts it 3! It is
an error to want to recreate reality through the language, to believe to be
able to so perfectly master him(it) or to reflect him(it).
-one can not better
illustrate what you say that through an interesting variant of the problem
which we have just studied: that of the "beginning" of time, this
paradox of paradoxes.
Let us imagine God with
his camera. It(he) would film this moment when time, that is space-time,
appears. Because it(he) had to well occur, this moment when time began to pass
by.
-but how can you speak
about moment without reference to anything? How this moment could it be a
moment comparable to the others? It is the peculiar moment which is not still a
part of time and which is not a part any more of the nothingness.
-C should to become mad.
Would it mean that time has never begun? If this moment which it one is not yet
contradicted the principle of non-contradiction and questions the law of duality...
-what so?
-the principles of the
logic are the following ones:
Identity: p = p said
that a thing(matter) is equal to herself(itself).
The third(third party) -
outcast: p or-p said that there is nothing except a thing(matter) or its
opposite.
Non-contradiction: - (p
and-p) said that one can not have at the same time a thing(matter) and its
opposite.
The law of duality: p
and-p said that a thing(matter) and its opposite can not have the same value at
the same time. It is a variant of the principle of non-contradiction.
-very well.
-let us return at our
initial moment. As moment outside the line of time, it(he) contradicts the
principle of the third(third party) - outcast. It(he) is one moment and it(he)
is not one moment. It means, is that logic is not adapted to the reality, or
that time always existed, so that world, being always existed, and that he is
vain, and even absurd, to want to find his origin. But it seems that we have
not enough humility to admit him(it).
-one finds here Zénon and Parménide's paradoxes. It is moreover the
same paradox, that of Zénon and that of Parménide. Zénon conceived his(her) paradoxes to
illustrate those of his(her) mister . Parménon and Zénide.
-L moment of the passage
would be reduced to time - death! Where from contradiction.
-it means that movement
exceeds us infinitely. In a way, movement is the realization of the infinity,
the space, the impossible.
-logic does not indeed
seem adapted to the reality. Paradox is all the more stunning as the discovery
that the universe has a history, because it would arise from Big Bang, and discovery of the
evolution of the material(subject) of the simple towards the complex, urge us
to believe that there was the beginning of time.
In summary, here is the
most fabulous paradox that one can conceive:
TO BE > NON-ETRE
TO BE > NON-ETRE
TO BE > NON-ETRE
TO BE > NON-ETRE
TO BE > NON-ETRE
TO BE > NON-ETRE
TO BE >...
The being, or the time,
results from the non-being or from the being. It seems impossible that
something comes from anything. The being him has so been. But this being has to
come to be him et cetera in the infinity.
One can pay(pour) a tear
of sadness and enjoyment in front of this stunning spectacle.
The Christian
calendar and the age of Jesus
-----------------------------------------------------------
Our calendar established
as origin, as not 0, the birth of the Christ. Now everybody knows that the
anniversary(birthday) of the birth of Jesus celebrates on December 25, is 6
days before the year 0 which this birth is supposed to place. But there is
better. For some years, the historians are convinced, on the basis of the
analysis of authenticated texts, that the Christ was born 6 years before year
0. One is certain besides that he died on the cross in 30 of the new era. Jesus
would have so died in 36 years and 6 days and not in 33 years.
INDEX
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