I am so sorry, JohnDoe, but I won't take your advice on learning logic. I took several logic courses at post-secondary institutions and I passed each course with flying colours. With over 90% in final marks in each. If there is one thing I know and understand then it is logic. I think your advice is wasted on me.

And I shan't take a learning advice on reading from someone who insists that a sentence can have more than one verb. Sorry.

But I do admit that I over-quoted the original post. I was tired. Much like you were writing a sentence that made no sense (because of a typo you hadn't caught, typing "is" instead of "if") --- not an inaptitude, but a sign of being tired --- I was also tired.

As far as I'm concerned, I close this thread. I gave the answer to it, and if you guys can't comprehend that, then please don't blame me and my alleged lack of logic.

What you guys need to learn is to appreciate the starting premises. The most startling premise was that the interval between switches of the switch was halved each time, without limit. This is not a realistic demand to uphold, and it can only be conceptualized in a math model. But you guys insisted on getting or attaining a reality model. A reality model I gave based on the math model. Of course it is not realistic, because the basic premise was not realistic. But the math model and its subsequent realistic model did comply with the unrealistic premise. This is what happened, and you guys are still scratching your heads.

## Thomson's Lamp Solution

- Arising_uk
**Posts:**10936**Joined:**Wed Oct 17, 2007 2:31 am

### Re: Thomson's Lamp Solution

I know you're not, it's why I think Mathematics is not about 'what there is'.-1- wrote:...

What you need to conceptualize is the time interval what calculus calls a "moment". It is a lengthless time interval, much like a point is a lengthless extent of space or of line.

I am not making this up.

### Re: Thomson's Lamp Solution

Hi, I haven't reviewed all the intermediate posts since this one but I've been meaning to get back to you.Arising_uk wrote: ↑Mon Dec 04, 2017 5:53 pmI'm just puzzled, is this lamp going to reach the two minute mark or not? Personally I think there has to be two counting systems for this experiment to work and as such the two minutes will be hit and then I'd have thought it would depend upon the starting state?

No, the lamp does not "reach" the two minute mark. Consider first the sequence of positive integers 1, 2, 3, 4, 5, 6, 7, , ...

Does this sequence ever "reach" infinity? No, of course not. Given any number you can get to the next one, but the process doesn't reach its conceptual limit. You give me 47 I'll give you 48. You give me a million one and I'll give you back a million two. The process never "reaches" anything.

Now suppose we have a hypothetical lamp that turns on if the number is odd and off if it's even. So when we get to 47 it's on and at 48 it's off and so forth. Does it ever "reach" some end state? No of course not. Does anything depend on where it starts? No of course not. I hope this is clear.

Now consider the sequence of rational numbers 1/2, 3/4, 7/8, 15/16, ... From calculus we know this sequence has a limit of 1. But it does not ever "reach" one for the exact same reason that the sequence of positive integers do not reach infinity. If you give me some integer n I'll give you back (2^n - 1)/2^n. But there is no concept or meaning to the idea of "reaching the end." It's meaningless. A sequence does not "reach" its limit; it merely gets arbitrarily close to it.

Now if we have a conceptual lamp that turns on at 1/2, off at 3/4, on at 7/8, etc. It's clear now that it's meaningless to ask what's its value when it "reaches" 1 since it never reaches 1. But if you want to say that at 1 it's on, or at 1 it's off, or at 1 it turns into a fish, all of those outcomes are consistent with the on/off pattern for 1/2, 3/4, etc.

In other words the experiment does not define what happens in the limit. Intuition gets confused because the problem is a disguised form of going 1, 2, 3, 4, ... = odd, even, odd, even ... Is that sequence odd or even at infinity? Neither. First, the sequence doesn't "reach" infinity so the question's meaningless. But even if you wanted to define the value of the sequence at infinity, you could make up anything you wanted. At odd numbers the lamp is on, at even numbers the lamp is off, and at infinity the lamp turns into a sturgeon.

I hope this is clear but if not please ask more questions.

Diophantus was Greek and he was the first great number theorist. It's Diophantus's book that Fermat was reading when he claimed that the margin was too small for his "marvelous" proof of Fermat's last theorem. It's from Diophantus that we get the name Diophantine equations, meaning equations that are to be solved using integers.Arising_uk wrote:

I also thought the Greeks would have no truck with the thing we call 'number' nowadays(or the best I can understand of what we call 'number' nowadays that is)?

My only point earlier was that Euclid gave us the notion of abstract mathematical proof based on axioms. But even Euclid had a pretty good sense of number. His Euclidean algorithm for finding the greatest common divisor of two integers is still taught today to students of number theory.

### Re: Thomson's Lamp Solution

-1- wrote: ↑Tue Dec 05, 2017 10:43 amI am so sorry, JohnDoe, but I won't take your advice on learning logic. I took several logic courses at post-secondary institutions and I passed each course with flying colours. With over 90% in final marks in each. If there is one thing I know and understand then it is logic. I think your advice is wasted on me.

Same here, top of a few philosophy course without even studying.

And I shan't take a learning advice on reading from someone who insists that a sentence can have more than one verb. Sorry.

Don't shoot the messenger.

But I do admit that I over-quoted the original post. I was tired. Much like you were writing a sentence that made no sense (because of a typo you hadn't caught, typing "is" instead of "if") --- not an inaptitude, but a sign of being tired --- I was also tired.

As far as I'm concerned, I close this thread. I gave the answer to it, and if you guys can't comprehend that, then please don't blame me and my alleged lack of logic.

What you guys need to learn is to appreciate the starting premises. The most startling premise was that the interval between switches of the switch was halved each time, without limit. This is not a realistic demand to uphold, and it can only be conceptualized in a math model.

I agree in many respects to this, however I took the lamp example as an observation of "alternating" movement and while not "feasible" in real life the concept of alternating movement is feasible elsewhere (using the lamp as an example...or maybe metaphor?) The logistics do correlate with the question being about the nature of movement.

Math and reality can only be seperated so far before we observe basic geometry as the median point.

But you guys insisted on getting or attaining a reality model. A reality model I gave based on the math model. Of course it is not realistic, because the basic premise was not realistic. But the math model and its subsequent realistic model did comply with the unrealistic premise. This is what happened, and you guys are still scratching your heads.

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