An infinite network (XKCD) - is it not clear?

In summary, the comic's answer is that it is finite, with two parallel resistances that can only lower the resistance.
  • #1
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Hi, unless I'm missing something here, it seems to me that the answer is that it is infinite, and that that is pretty intuitive.

Is that not the case?

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I would think it could be simplified to view as two parallel and infinite resistances, giving ∞2/2∞, which simplifies to half infinity, which is of course really (in as much as it is) still infinite.
 
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  • #2
I have no solution, but the resistance cannot be larger than 1.5 Ohm, since there are two independent paths of 3 resistors between the points. The other parallel paths can only lower the resistance. So it's definitely finite.

The forum page of this comic will no doubt contain the correct answer.
 
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  • #3
I think it is intuitive that the resistance can not be infinite.

With some hand-waving: whenever you have a parallel circuit the equivalent resistance is lower than any of the branch resistance, so the resistance between any to adjacent nodes must be less than 1 Ohm. This means you have a path between the two marked nodes as a series of three networks that can be replaced with a resistor less than 1 Ohm, totaling less than 3 Ohm.

The exact solution, I seem to remember from years back, is a bit harder to obtain. Found a derivation [1] that may be of some use (haven't read it thoroughly enough to say if it is correct or not).

[1] http://mathpages.com/home/kmath668/kmath668.htm
 
  • #4
ZVdP said:
I have no solution, but the resistance cannot be larger than 1.5 Ohm, since there are two independent paths of 3 resistors between the points. The other parallel paths can only lower the resistance. So it's definitely finite.

Filip Larsen said:
I think it is intuitive that the resistance can not be infinite.

With some hand-waving: whenever you have a parallel circuit the equivalent resistance is lower than any of the branch resistance, so the resistance between any to adjacent nodes must be less than 1 Ohm.
[1] http://mathpages.com/home/kmath668/kmath668.htm


Right, that was stupid of me. Thank you both - and for the link.

I see why it was comic-worthy now, the answer is certainly not trivial!
 
  • #5


I would say that the concept of infinity is a complex and abstract one that can be difficult to fully comprehend. In the context of a network, an infinite network would mean that the number of nodes or connections is infinite, which is not something that we can easily visualize or understand. However, mathematically, it is possible to represent an infinite network using equations and models. In the example given, the approach of simplifying it to two parallel and infinite resistances is a valid way to conceptualize it, but it is important to note that this is just one way of looking at it and there may be other ways to model an infinite network. Ultimately, the answer to whether an infinite network is clear or not depends on the perspective and understanding of the individual.
 

1. What is an infinite network?

An infinite network is a hypothetical network that has an infinite number of nodes or connections. It is often used in mathematics and computer science to model complex systems that have a large number of components.

2. How does an infinite network work?

An infinite network works by connecting an infinite number of nodes or components together in a specific pattern or structure. This allows for the representation of complex systems and the study of their behavior.

3. What is the significance of the XKCD comic about an infinite network?

The XKCD comic about an infinite network is a humorous representation of the concept of an infinite network. It highlights the complexity and absurdity of trying to understand and navigate such a network.

4. Is an infinite network possible in real life?

An infinite network is a theoretical concept and cannot exist in reality. This is because it would require an infinite amount of resources and time to create and maintain, which is not possible.

5. What are some real-life examples of infinite networks?

While an infinite network cannot exist in reality, there are some systems and structures that can be approximated as infinite networks. Examples include the internet, transportation networks, and social networks, which have a large number of interconnected nodes and components.

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