## Thomson's Lamp Solution

What is the basis for reason? And mathematics?

Moderators: AMod, iMod

Eodnhoj7
Posts: 1004
Joined: Mon Mar 13, 2017 3:18 am

### Thomson's Lamp Solution

"Consider a lamp with a toggle switch. Flicking the switch once turns the lamp on. Another flick will turn the lamp off. Now suppose that there is a being able to perform the following task: starting a timer, he turns the lamp on. At the end of one minute, he turns it off. At the end of another half minute, he turns it on again. At the end of another quarter of a minute, he turns it off. At the next eighth of a minute, he turns it on again, and he continues thus, flicking the switch each time after waiting exactly one-half the time he waited before flicking it previously.[1] The sum of this infinite series of time intervals is exactly two minutes.[2]

The following question is then considered: Is the lamp on or off at two minutes?[1] Thomson reasoned that this supertask creates a contradiction:

It seems impossible to answer this question. It cannot be on, because I did not ever turn it on without at once turning it off. It cannot be off, because I did in the first place turn it on, and thereafter I never turned it off without at once turning it on. But the lamp must be either on or off. This is a contradiction.[1]"

https://en.m.wikipedia.org/wiki/Thomson%27s_lamp

+1- -1/2+ +1/4- -1/8+ +1/16- -1/32+ +1/64- -1/128+ +1/256
60 30 15 7.5 3.75 1.875 .9375 .46875 .234375
60 90 105 112.5 116.25 118.125 119.0625 119.53125 119.765625 .....ad infinitum

At the rate presented the lamp never reaches two minutes, it is a faulty question as the infinite supertask overrides time itself by forming its own seperate time zone.

Considering time is composed strictly of a relation of movements and the relation of the movements of x person expands infinitely in relation to the movements of timer y.

Timer y rings if and only if it reaches two minutes:

∃y ↔ 120

X is a series of movements greater than zero and less than 120 which is equivalent to infinity
x = [0 < a....b < 120] = ∞

X is equivalent to infinite movement, and considering time is movement, x creates a seperate temporal cycle outside of Y.

In one respect: Y never rings, as x is relative to itself as perpetual movement and exists within its own time cycle.

In a seperate respect Y ringing occurs at the lamp being turned on, off, and midway as the "ringing" embodies multiple different respects at the same time.

A dualism occurs, where:

from X, Y never rings, as x exists outside of Y's time zone considering time for x is measured according to its own movements.

from Y, X manifests all possible degrees of movement at one time in seperate respects. This implies, relative to Y, X is propagating multiple time dimensions and a form of "modal realism" can be observed in which the ringing of the clock observes multiple dimensions relative to each other at one time.

A solution to this dualism, would be Y both ringing and non-ringing as an extension of X and Y exists if and only if X. In these respects, Y is merely a gradation of X as: X/Y with X being the potential of Y.

Summary:
Y can be observed as a deficiency in X and not a thing in itself hence it only rings if and only if X manifests all possible dimensions at one moment.

In order for X to manifest all dimensions at one moment, it must manifest further temporal cycles which relate to eachother through X.

In these respects, multiple time cycles exist relative to Y both ringing and non-ringing.

Impenitent
Posts: 1665
Joined: Wed Feb 10, 2010 2:04 pm

### Re: Thomson's Lamp Solution

there is light but it cannot move ... at least that's what Schrodinger's cat says

-Imp

Eodnhoj7
Posts: 1004
Joined: Mon Mar 13, 2017 3:18 am

### Re: Thomson's Lamp Solution

Impenitent wrote:
Wed Nov 22, 2017 12:38 am
there is light but it cannot move ... at least that's what Schrodinger's cat says

-Imp
Or the center of a movement is its own time cycle. Theoretically it has to happen, various temporal micro-cycles colliding to form other micro cycles. Maybe gravity is temporality?

wtf
Posts: 387
Joined: Tue Sep 08, 2015 11:36 pm

### Re: Thomson's Lamp Solution

The answer to the Thompson lamp problem is that the state of the lamp is undefined at the end of the process. It's undefined because the problem doesn't define it.

For simplicity I prefer to start at time t = 0 and end at t = 1. In the OP's formulation it goes from 1 to 2 but that makes the formula a little more complicated.

So we start at time t = 0 with the lights off.

At t = 1/2 we turn it on.

At t = 3/4 we turn it off.

At t = 7/8 we turn it on,

and so forth.

In other words for each natural number n = 0, 1, 2, 3, ..., then

* At t = (2^n-1)/2^n we turn the light off if n is even, and on if n is odd.

For example:

n = 0, t = 0 and the light is off,

n = 1, t = 1/2 and the light is on,

n = 2, t = 3/4 and the light is off,

n = 3, t = 7/8 and the light is on,

and so forth.

Now we see the problem more clearly. If n is even the light is off. If n is odd the light is on.

So another way to express this problem is to ask whether the number after 0, 1, 2, 3, ... is even or odd. And when you put it that way, the question is seen to be nonsense.

If you wanted to, you could make up a magic number, let's call it ω, the Greek lower case omega, and notate our new number system: 0, 1, 2, 3, ..., ω. So ω comes after all the natural numbers.

Believe it or not, mathematicians are perfectly fine with this. ω is the first transfinite ordinal number. It's also the definition of the cardinal number Aleph-null, which is its more familiar name.

Now in the Thompson's lamp problem, you have told me what is the state of the light for n = 0, 1, 2, 3, ... and in fact any finite natural number.

But you didn't tell me what is its state at n = ω. Maybe the light turns into a banana. Or flies off into space. Both of those are perfectly consistent with the rest of the problem as stated.

So we see that the state of Thompson's lamp at n = ω, or t = 1, is simply undefined. It's as simple as that.

Now that I think about it, the confusion around this problem is caused by an unspoken assumption that there is some kind of convergence at the limit. But there isn't. The sequence 0, 1, 0, 1, ... doesn't converge. You can't assign a value for n = ω that makes the sequence converge. Which is what people are intuitively trying to do. The inputs (2^n-1)/2^n converge to 1 as n goes to infinity; but the output values do not converge.

Eodnhoj7 wrote:
Mon Nov 27, 2017 1:13 am
Or the center of a movement is its own time cycle. Theoretically it has to happen, various temporal micro-cycles colliding to form other micro cycles. Maybe gravity is temporality?
Well you've got me there.

Eodnhoj7
Posts: 1004
Joined: Mon Mar 13, 2017 3:18 am

### Re: Thomson's Lamp Solution

wtf wrote:
Mon Nov 27, 2017 4:37 am
The answer to the Thompson lamp problem is that the state of the lamp is undefined at the end of the process. It's undefined because the problem doesn't define it.

I pointed to a somewhat similiar answer above where:

The question is faulty and theoretically, if the clock rang, all possible dimensions of the lamp being "turned" on and "turned" off would happen simultaneously as multiple different times zones would exist at the same time in different respects. In simpler terms the answer would be "ad-infinitum" as the perpertual movement of the switch continually dividing upon itself would create its own time zone irrespective of the alarm clock.

Theoretically the alarm clock would not ring at all if the lamp was destined to reach its end at the two minute mark.

For simplicity I prefer to start at time t = 0 and end at t = 1. In the OP's formulation it goes from 1 to 2 but that makes the formula a little more complicated.

So we start at time t = 0 with the lights off.

At t = 1/2 we turn it on.

At t = 3/4 we turn it off.

At t = 7/8 we turn it on,

and so forth.

In other words for each natural number n = 0, 1, 2, 3, ..., then

* At t = (2^n-1)/2^n we turn the light off if n is even, and on if n is odd.

For example:

n = 0, t = 0 and the light is off,

n = 1, t = 1/2 and the light is on,

n = 2, t = 3/4 and the light is off,

n = 3, t = 7/8 and the light is on,

and so forth.

Now we see the problem more clearly. If n is even the light is off. If n is odd the light is on.

So another way to express this problem is to ask whether the number after 0, 1, 2, 3, ... is even or odd. And when you put it that way, the question is seen to be nonsense.

Interesting methodology with the even and odd, I like it.

If you wanted to, you could make up a magic number, let's call it ω, the Greek lower case omega, and notate our new number system: 0, 1, 2, 3, ..., ω. So ω comes after all the natural numbers.

Believe it or not, mathematicians are perfectly fine with this. ω is the first transfinite ordinal number. It's also the definition of the cardinal number Aleph-null, which is its more familiar name.

Now in the Thompson's lamp problem, you have told me what is the state of the light for n = 0, 1, 2, 3, ... and in fact any finite natural number.

But you didn't tell me what is its state at n = ω. Maybe the light turns into a banana. Or flies off into space. Both of those are perfectly consistent with the rest of the problem as stated.

So we see that the state of Thompson's lamp at n = ω, or t = 1, is simply undefined. It's as simple as that.

Now that I think about it, the confusion around this problem is caused by an unspoken assumption that there is some kind of convergence at the limit. But there isn't. The sequence 0, 1, 0, 1, ... doesn't converge. You can't assign a value for n = ω that makes the sequence converge. Which is what people are intuitively trying to do. The inputs (2^n-1)/2^n converge to 1 as n goes to infinity; but the output values do not converge.

I agree about your point in regards to convergence, however the measurement systems continually seem to be diverging ad - infinitum through a continual process of "halving" as "ever approaching zero". It appears one possibility, which would not contradict your answer of "no-definition", would be that multiple time zones erupt at ad-infinitum leading to all possibilities at one moment. This would correspond with ω (as aleph-null) however would result in ω → aω → bω→ cω → x simultaneously as each set of infinite numbers is still 1 set in itself.

Considering all possibilities happening simultaneously in different respect is conducive to no-definition through infinity, I am not sure if we really disagree.

Eodnhoj7 wrote:
Mon Nov 27, 2017 1:13 am
Or the center of a movement is its own time cycle. Theoretically it has to happen, various temporal micro-cycles colliding to form other micro cycles. Maybe gravity is temporality?
Well you've got me there.
The perpetual increase in acceleration of the lamp being turn on and off would, along with creating its own time zone, theoretically cause the lamp to develop its own gravitational field and possibly slow the clock at the same time in a different respect.

The infinite acceleration of the lamp, combined with the clock slowing down as an extension of the lamps gravitation field, might in theory actually warp the "light" when the lamp is turned on as the perpetual movement would result in a mini black hole.

wtf
Posts: 387
Joined: Tue Sep 08, 2015 11:36 pm

### Re: Thomson's Lamp Solution

Eodnhoj7 wrote:
Mon Nov 27, 2017 12:28 pm
The infinite acceleration of the lamp, combined with the clock slowing down as an extension of the lamps gravitation field, might in theory actually warp the "light" when the lamp is turned on as the perpetual movement would result in a mini black hole.[/color]
It's not a physical experiment. It's only an abstract mathematical story.

Eodnhoj7
Posts: 1004
Joined: Mon Mar 13, 2017 3:18 am

### Re: Thomson's Lamp Solution

wtf wrote:
Mon Nov 27, 2017 7:21 pm
Eodnhoj7 wrote:
Mon Nov 27, 2017 12:28 pm
The infinite acceleration of the lamp, combined with the clock slowing down as an extension of the lamps gravitation field, might in theory actually warp the "light" when the lamp is turned on as the perpetual movement would result in a mini black hole.[/color]
It's not a physical experiment. It's only an abstract mathematical story.
In that respect, movement towards zero should equate.

wtf
Posts: 387
Joined: Tue Sep 08, 2015 11:36 pm

### Re: Thomson's Lamp Solution

Eodnhoj7 wrote:
Mon Nov 27, 2017 7:23 pm
wtf wrote:
Mon Nov 27, 2017 7:21 pm
Eodnhoj7 wrote:
Mon Nov 27, 2017 12:28 pm
The infinite acceleration of the lamp, combined with the clock slowing down as an extension of the lamps gravitation field, might in theory actually warp the "light" when the lamp is turned on as the perpetual movement would result in a mini black hole.[/color]
It's not a physical experiment. It's only an abstract mathematical story.
In that respect, movement towards zero should equate.
Why? The sequence 0, 1, 0, 1, 0, 1, ,,, doesn't converge.

Eodnhoj7
Posts: 1004
Joined: Mon Mar 13, 2017 3:18 am

### Re: Thomson's Lamp Solution

wtf wrote:
Mon Nov 27, 2017 7:44 pm
Eodnhoj7 wrote:
Mon Nov 27, 2017 7:23 pm
wtf wrote:
Mon Nov 27, 2017 7:21 pm

It's not a physical experiment. It's only an abstract mathematical story.
In that respect, movement towards zero should equate.
Why? The sequence 0, 1, 0, 1, 0, 1, ,,, doesn't converge.
The rate the clock is turned on and off, through continual halving, is ever-approaching zero:
+1- -1/2+ +1/4- -1/8+ +1/16- -1/32+ +1/64- -1/128+ +1/256....ad-infinitum

You are right that 0,1 and one will never converge, at the same time in different respects, however in different times in the same respect they will have the lamp will create its own time zone at the lamp manifests its own time zone as its own measurement system. The rate at which the lamp flickers on and off will eventually move faster than that of an atomic clock.

The lamp will have its own time zone and the timer will have its own time zone.

Observing either 1 or 0 at the ring of the clock is a moot point if the rates they manifests are in a continual flux. Keep in mind that the observation of the "ring" in itself is movement so what we are observing are temporal cycles within temporal cycles.

The timer, in its measurement of seconds, observed through the ringing, observes a movement ranging between "A" and "C" degrees.

The lamp, at the rate it is going will eventual turn "on" between "A" and "B" degrees and "off" between "B" and "C" degrees so that the movement of "A" and "C" contains the light going "on" and "off". At "B" degree the lamp switch would be in a neutral position.

The problem occurs in that the movement of the lamp is exponential so that it could turn "on" between "A/A1" and "B/B1" and off at "A1/B" and "B1/C"....an the rate would continue.

However this rate if infinite, so when the clock rings through the movement of "A → C" the lamp will be "On", "Off" and "Neutral" through infinite movement at infinite times in infinite time zones as microcycles within themselves. The lamp, in certain respects, would form its own clock as perpetual movement manifesting simultaneous time zones as dimensions relative to eachother much in same manner we observe simultaneous linear movements fold upon themselves through a particle wave motion. Each time zone would be its own "wavelength" corresponding to linearism as potential curvature.

So yeah you are right in regards to the answer being indefinite through 1/3 of the movements being neutral, however 2/3's of the movements will be definite in regards to being "On" and "Off" and in this respect you are wrong as "approximation" it constructed of definite natures.

In summary, I agree and disagree with you in different respects.

wtf
Posts: 387
Joined: Tue Sep 08, 2015 11:36 pm

### Re: Thomson's Lamp Solution

Eodnhoj7 wrote:
Tue Nov 28, 2017 12:56 pm
You are right that 0,1 and one will never converge, at the same time in different respects, however in different times in the same respect they will have the lamp will create its own time zone at the lamp manifests its own time zone as its own measurement system.
What do you mean by time zone? I'm in the Pacific Standard time zone. Is that what you mean? No, of course not. So ... what do you mean by its own time zone?
Eodnhoj7 wrote:
Tue Nov 28, 2017 12:56 pm
In summary, I agree and disagree with you ...
That makes me happy ... and sad.

Eodnhoj7
Posts: 1004
Joined: Mon Mar 13, 2017 3:18 am

### Re: Thomson's Lamp Solution

wtf wrote:
Tue Nov 28, 2017 10:55 pm
Eodnhoj7 wrote:
Tue Nov 28, 2017 12:56 pm
You are right that 0,1 and one will never converge, at the same time in different respects, however in different times in the same respect they will have the lamp will create its own time zone at the lamp manifests its own time zone as its own measurement system.
What do you mean by time zone? I'm in the Pacific Standard time zone. Is that what you mean? No, of course not. So ... what do you mean by its own time zone?

A mini cycle, possibly not even observable to the naked eye, where realities move at speeds greater than light for a brief moment and then "flutter out".
Eodnhoj7 wrote:
Tue Nov 28, 2017 12:56 pm
In summary, I agree and disagree with you ...
That makes me happy ... and sad.

wtf
Posts: 387
Joined: Tue Sep 08, 2015 11:36 pm

### Re: Thomson's Lamp Solution

Eodnhoj7 wrote:
Thu Nov 30, 2017 1:06 am

A mini cycle, possibly not even observable to the naked eye, where realities move at speeds greater than light for a brief moment and then "flutter out".
Very poetic but not very scientific.

* What is a "reality?" If you tell me that a rock travelled at some speed, that's science. Physics. If you tell me a "reality" travelled at some speed, that's not science.

* Nothing can move faster than light. If "realities" are things that can move faster than light, that's a nice story, but it's not science.

* And a mini cycle, what is that? I googled mini-cycle and it's a small exercise device.

You have taken these vague and meaningless ideas and called them a "time zone." That does not communicate anything nor do your ideas make sense.

Like I say the image is poetic, and perhaps that's how you mean it. In which case I ask you, are you speaking poetically? Or are you trying to make a rational point that somehow ties in with known science?

Eodnhoj7
Posts: 1004
Joined: Mon Mar 13, 2017 3:18 am

### Re: Thomson's Lamp Solution

wtf wrote:
Thu Nov 30, 2017 2:30 am
Eodnhoj7 wrote:
Thu Nov 30, 2017 1:06 am

A mini cycle, possibly not even observable to the naked eye, where realities move at speeds greater than light for a brief moment and then "flutter out".
Very poetic but not very scientific.

* What is a "reality?" If you tell me that a rock travelled at some speed, that's science. Physics. If you tell me a "reality" travelled at some speed, that's not science.
An existence.

* Nothing can move faster than light. If "realities" are things that can move faster than light, that's a nice story, but it's not science.

One possible argument would be for the ether, as speed is merely gravity from a center point.

viewtopic.php?f=5&t=21768&p=305127#p305127

* And a mini cycle, what is that? I googled mini-cycle and it's a small exercise device.

You have taken these vague and meaningless ideas and called them a "time zone." That does not communicate anything nor do your ideas make sense.

Time zones are merely the observation of movements, specifically those found in atoms, where a revolution (or cycle) determines the movement as time. Time is measured through cycles, whether at the micro scale through atoms, the macro scale through stars, or at the everyday through a clock.

Like I say the image is poetic, and perhaps that's how you mean it. In which case I ask you, are you speaking poetically? Or are you trying to make a rational point that somehow ties in with known science?

Time is merely movement, with the core of these movements stemming from cycles of various sorts.

wtf
Posts: 387
Joined: Tue Sep 08, 2015 11:36 pm

### Re: Thomson's Lamp Solution

Eodnhoj7 wrote:
Thu Nov 30, 2017 6:01 pm
An existence.
What does that mean? Can you give a definition and some examples?
Eodnhoj7 wrote:
Thu Nov 30, 2017 6:01 pm
One possible argument would be for the ether, as speed is merely gravity from a center point.
Eodnhoj7 wrote:
Thu Nov 30, 2017 6:01 pm
Time zones are merely the observation of movements, specifically those found in atoms,
But the lamp experiment is only a mathematical thought experiment. It has nothing to do with atoms. Nor does your explanation make sense even in the context of atoms. Time zones are observations? What does that mean?
Eodnhoj7 wrote:
Thu Nov 30, 2017 6:01 pm
where a revolution (or cycle) determines the movement as time. Time is measured through cycles, whether at the micro scale through atoms, the macro scale through stars, or at the everyday through a clock.[/color]
Where do you get all this stuff? Is this something you made up?
Eodnhoj7 wrote:
Thu Nov 30, 2017 6:01 pm
Time is merely movement, with the core of these movements stemming from cycles of various sorts.
Oh, well now that you've explained it ...

EchoesOfTheHorizon
Posts: 375
Joined: Mon Oct 23, 2017 6:08 am

### Re: Thomson's Lamp Solution

You got about a 3rd realized Eod, , and this thread WTF is more focused on a engineering issue with a classical cosmological system, that is more Pythagorean in it's physics. He is on the right track so far, but as I pointed out, another unexpected supertask barrier sits behind the supertask solution. It will hit you once you figure out the solution.

I do like how you are looking at it as a single circuit broken up into time zones, I didn't do that quite that way. I merely reversed engineered a hypothetical lamp that could abide by the parameters for Thompson's Lamp, and studied the limitations the network would have for size and complexity of a switch that branches, able to turn a light on and off at the same time. A exceptionally large Lamp can do this, but there is a network limit on the bifurcation of any signal sent that increases both geometrically as well as by arthimatic. Causes a lot of noise, but Thompson Lamp doesn't prohibit it. And the Lamp is presumed to exist, so it can be calculated. A overzealous mathematician later on decided the question had problems, but of course, most mathematics that test real problems at the start of a experiment don't have all the variables expressed or known, they become known over time, so merely posing a incomplete question isn't a prohibition to following it. It doesn't matter if the problem is fully defined or not, as it can still be pursued and solved in regards to the primary question regarding super tasks.

A few systems humans have in them, or have built (our neurology, plumbing) already have the physical conditions that if analyzed, would express the solution more adequately to Thompson's Lamp. It is a question that aims at figuring out super tasking, observation as well as tracking/knowing it is accomplished. That's all you need to know to grasp it. It is a geometric progression as much as a additive build. You are close. Think "bigger", think about efficiency factors. What stops a Lamp switch from being more efficient, what it the limitations physics puts on the most efficient Lamp switch possible, and what are the work arounds. I gave you the hint in the other thread. Plato had something written above the door to his academy.... you know....

### Who is online

Users browsing this forum: No registered users and 2 guests