Yet another Math joke
br...@ssl.msfc.nasa.gov
>
>Suppose, there is a machine, that has 2 states (A and B)
>and can switch _instantaneously_ from one to another.
>
>Suppose, that machine started to work in state A at 1pm.
>Then, at 1:30 it switched to B, then at 1:45 -- to A,
>then at 1:52.5 to B again, and so forth.
>
>So, at 2pm the machine ended its work.
>
>What was (and is) its state ?
>
>-------------------------------------------------------------------
> Pavel V. Gusak
> Topaz - Inform
> pa...@topaz.kiev.ua
exhaustion
Pavel V. Gusak
Paul Giaccone
: In article <3sup1l$d...@castle.topaz.kiev.ua>, pa...@topaz.kiev.ua (Pavel V. Gusak) writes:
: >
: >Suppose, there is a machine, that has 2 states (A and B)
: >and can switch _instantaneously_ from one to another.
: >
: >Suppose, that machine started to work in state A at 1pm.
: >Then, at 1:30 it switched to B, then at 1:45 -- to A,
: >then at 1:52.5 to B again, and so forth.
: >
: >So, at 2pm the machine ended its work.
: >
: >What was (and is) its state ?
This is not a joke - it is a description of the Thomson lamp. The lamp
does not exist but is only part of a thought experiment.
The problem is equivalent to this one:
+infinity
--
Let l = \ 1/k. What is the last term in the sequence of addends?
/
--
k = 1
As "last" is ill-defined here, the problem has no solution.
--
Paul Giaccone | "In Brussels, anything is possible if you believe
k94...@kingston.ac.uk | carrots are a fruit and bananas should be
| straight." - The Rt Hon Michael Portillo MP (PM2B?)
H:WINSOCKKA9QSPOOLMAIL
> Suppose, there is a machine, that has 2 states (A and B)
> and can switch _instantaneously_ from one to another.
>
> Suppose, that machine started to work in state A at 1pm.
> Then, at 1:30 it switched to B, then at 1:45 -- to A,
> then at 1:52.5 to B again, and so forth.
>
> So, at 2pm the machine ended its work.
>
> What was (and is) its state ?
>
Since it can switch _instantaneously_, is there anything to prevent
it being in _both_ states...?
--
Pat McGibbon p...@megadata.demon.co.uk
Kim Hvarre
>In article <3sup1l$d...@castle.topaz.kiev.ua>, pa...@topaz.kiev.ua (Pavel V. Gusak) writes:
>>
>>Suppose, there is a machine, that has 2 states (A and B)
>>and can switch _instantaneously_ from one to another.
>>
>>Suppose, that machine started to work in state A at 1pm.
>>Then, at 1:30 it switched to B, then at 1:45 -- to A,
>>then at 1:52.5 to B again, and so forth.
>>
>>So, at 2pm the machine ended its work.
>>
>>What was (and is) its state ?
>>
>> Pavel V. Gusak
>> Topaz - Inform
>> pa...@topaz.kiev.ua
>exhaustion
Very, very heavy...
--
!?
I wonder why
Kim Hvarre
Email: ki...@crash.ping.dk
Kim_H...@online.pol.dk
Nancy J. Hoorn
both states simultaneously?
Nancy
-----------------------------------------------------------------------------
Nancy J Hoorn / E-mail is sort of like prayer--
Senior Secondary Education Student / but e-mail is slower and cheaper!
Math Major/Physics minor / Sometimes, prayer is answered
Mother of five, grandmother of two / BEFORE we ask and it cost God the
Grand Valley State University / life of His son.
Allendale Michigan /
e-mail hoo...@river.it.gvsu.edu /
==============================================================================
Sean Drake
> Suppose we have a computer that is initially running at a speed of 1
> instruction/second. Furthermore, this computer has an instruction to
double its
> speed with (that is: executing that instruction the first time has the effect
> that from then on the computer executes 2 instr./sec; executing it once more
> changes the speed to 4 instr./sec. etc.
>
> Suppose we have the following program:
>
> 1. double speed
> 2. go to 1.
>
> Does this program terminate ? If it does, when ? If not, after how many
> instructions do we exceed the running time of 1 minute ?
My prediction? With the computer speed increasing so rapidly, I would
guess that it would achieve self-awareness. Shortly afterward, it would
decide to terminate the human infestation on the planet. It would create
an army of robots to wipe out humans. The humans would form an
underground, and the computer would design some human-looking terminator
robots to infiltrate the resistance. However, the computer wouldn't
figure out how to make these robots undectable to ordinary dogs.
Faced with this losing battle, the computer would formulate a plan to
assassinate the leader of the resistance by killing the leader's mother in
the past. The computer would send a single robot back in time to
accomplish this.
I figure that the whole thing would take about 3 seconds. (I'm assuming
that the double-speed operation takes a full cycle BEFORE it finishes.
Speed is doubled at the end of the cycle. Also, I'm assuming that it
takes on cycle to execute a GOTO.)
--Sean
PS- If you didn't get the obvious movie reference here, then you're
spending too much time on your computer! Why, when I was a kid, we had
other things to do! Turn off your computer! Rent a movie and watch TV!
Nils Bruin
Gusak) writes:
>
>> Suppose, there is a machine, that has 2 states (A and B)
>> and can switch _instantaneously_ from one to another.
>>
>> Suppose, that machine started to work in state A at 1pm.
>> Then, at 1:30 it switched to B, then at 1:45 -- to A,
>> then at 1:52.5 to B again, and so forth.
>>
>> So, at 2pm the machine ended its work.
>>
>> What was (and is) its state ?
>>
Suppose we have a computer that is initially running at a speed of 1
instruction/second. Furthermore, this computer has an instruction to double its
speed with (that is: executing that instruction the first time has the effect
that from then on the computer executes 2 instr./sec; executing it once more
changes the speed to 4 instr./sec. etc.
Suppose we have the following program:
1. double speed
2. go to 1.
Does this program terminate ? If it does, when ? If not, after how many
instructions do we exceed the running time of 1 minute ?
(this formulation is loosely modelled on the meta-wish/djinn story in
Goedel/Escher/Bach by Hofstaedter)
Greetings,
Nils
Josep M. Lopez Besora
>> instruction/second. Furthermore, this computer has an instruction to
>double its
>> speed with (that is: executing that instruction the first time has the effect
>> that from then on the computer executes 2 instr./sec; executing it once more
>> changes the speed to 4 instr./sec. etc.
>>
>> Suppose we have the following program:
>>
>> 1. double speed
>> 2. go to 1.
>>
>> Does this program terminate ? If it does, when ? If not, after how many
>> instructions do we exceed the running time of 1 minute ?
Instructions time (s) total time
1 1 1
2,1 1 2
2,1 .5 2.5
2,1 .25 2.75
..
one is tempted to say that time can't exceed 3 s, until one realizes that speed can be doubling only for a finite number of steps, f=
or nothing's faster than light, and hence, after a while speed becomes constant as well as the time needed for a single cycle; the t=
otal time, then, can reach any value after a suitable number of steps.
______________________________________
Josep M. Lopez Besora=======jlo...@etse.urv.es
Universitat Rovira i Virgili===================
TARRAGONA.Catalonia.Spain===================