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I can sort of deal with it conceptually, and even work with it mathematically - but are there any examples of it as a property of something in the physical universe? (I'm probably missing something obvious..)
Math Is Hard said:I can sort of deal with it conceptually, and even work with it mathematically - but are there any examples of it as a property of something in the physical universe? (I'm probably missing something obvious..)
Thanks for your response. Now to the infinite cutting, I would say no. To cut a piece into infinitely small parts involves at some step cutting apart atoms, and as a member of PETA (People for the Ethical Treatment of Atoms) I am against this.kant said:Hmm... To me, your question is like asking if you can cut a piece of "stuff" down to infinite many parts. Is it possible? i don t know.
Math Is Hard said:Thanks for your response. Now to the infinite cutting, I would say no. To cut a piece into infinitely small parts involves at some step cutting apart atoms, and as a member of PETA (People for the Ethical Treatment of Atoms) I am against this.
What I was thinking of is this.. is the universe infinitely big or just really, really big? Are there things in nature that are infinitely small? This I don't know. Can something be infinitely complex - no probably not, because the universe will expire before it evolves to infinite complexity.
In what sense a singularity is infinite? Is it infinite because it is incountable? I do not think so. Is it infinite because there is an asymptotic function to some value in space but the function itself does not reach this point (e.g. 1/x and the y-axis)? Do you mean something like this by a qualitative change?saltydog said:Infinity is a metaphor for a singularity. Passing through such a singularity involves a qualitative change.
Why do you call this an infinity? It is a border for the application of a concept, but is it also an infinity?The Universe is infinitely big, complex, nested, small only to the extent that such regressions involve qualitative changes in concepts: we keep looking for bigger and bigger and smaller and smaller, more and more complex until we reach singularities which change the qualitative nature of our conceptions rendering them no longer applicable. For example, we can consider swimming in cold water until we reach the freezing point. When it turns to ice, swimming is no longer applicable.
I’m not so sure about that. Quantum physics has its name from the quantum that is the discrete smallest entity. In mathematics you always can detect a smaller number but the question of this thread is whether and in what degree this mathematical feature (and other mathematical procedures that lead to infinity) can be applied in physics. I think in concrete nature there is always a border. Hence there is no concrete infinity, nothing concrete is infinite big, infinite small, or moves with infinite velocity (although there may be a velocity higher then the speed of light c)nameta9 said:Infinity does exist. Physics and devices may some day be able to go down to the smallest dimension of 10^-40 mm (planck level). But 10^-10,000 mm exists as does any infinitely small dimension.
One small divergence: I’m not sure whether there can be a logical explanation for this. If you want to explore the connection of mathematical infinity and concreteness by logic you take another infinite discipline for exploration. But the main part of the first question is: How can an infinite system explore?Chronos said:No confirmed observations of an 'infinite' amount of anything has yet been observed, to my knowledge. My guess, it would probably take an infinite amount of time to confirm any such suspected observation. Mathematical infinites, of course, lurk behind every corner. And they are maddening. We have numerous examples of finite numbers that represent the sum of an infinite number of non-zero quantities - like pi [be warned, I'm just dying for someone to ask to see that formula]. How can that be explained logically?
Tychic said:In what sense a singularity is infinite?
nameta9 said:Size can't loose meaning at any point. It just keeps on getting smaller forever. If it did loose meaning then what would it become, larger than the previous "size" ? A possible solution is to think of the universe as circular. At 10^-1000 mm we have the universe all over again and as you get smaller you can see the Earth again and then ourselves and then atoms and then the cycle repeats forever. So we would in effect be made up of ourselves in this infinite loop. It would be like an infinite recursion where A is composed of B and B is composed of A etc.
Of course in between you could have all kinds of structures maybe at 10^-10000000000 mm you could have all kinds of oddball universe and matter, but the bottom line is that elementary particles would not really exist anymore and even size as a concept would no longer make much sense since all is made up of itself forever.
This reciprocal definition could also be implemented in some other places of the universe that do not have any connection to infinity (e.g. between receptive and effective properties in Gregg Rosenberg's causal theory) and I do not think that this will help us in talking about the infinity in nature.nameta9 said:In my recursive universe A is composed of B, and B is composed of A but it may also be that the loop ends there and the last A is equal to the first.
selfAdjoint said:saltydog, what you are calling a singularity is actually called a critical point. For exmple 200 degrees Fahrenheit is a critical point for water (at standard conditions), where it changes from liquid to gas form. The study of critical points and the attempt to calculate them from firstr principles is a hot area these days.
The same idea has been popularized in social systems as a "tipping point".
A singularity is a state in which some value increases without bound; "goes to infinity" in informal speech. The function [tex]\frac{1}{(x-5)}[/tex] has a singularity at x=5.
When we say that nature "abhors" infinity, it means that nature does not allow for infinite quantities or values. In other words, nature has limits and boundaries that prevent infinite quantities from existing.
Nature appears to have limits and boundaries because it is governed by physical laws and principles that determine how things function and interact. These laws often involve concepts like energy conservation and entropy, which restrict the possibility of infinite quantities.
While it is true that nature does not allow for infinite quantities, it does not mean that infinity does not exist at all. In mathematics, infinity is a concept that is used to describe unbounded or unlimited values. It can be a useful tool for understanding certain phenomena in nature, even if it does not physically exist.
There are some phenomena in nature that can be described using the concept of infinity. For example, the universe is often considered to be infinite in terms of its size and scope. Additionally, some scientists theorize that the concept of infinity can be applied to the concept of time, with the idea of an infinite past or future.
The concept of infinity can have a significant impact on scientific research and understanding. It allows scientists to think beyond the limitations of finite quantities and explore possibilities that may seem impossible. It also encourages new ways of thinking and problem-solving, leading to advancements in our understanding of the natural world.