Measuring infinity

[beero1000]

As far as I can tell, there's no way we could measure a property as infinite. Any gauge made by humans will have a finite size, and thus should only be able to encode a finite amount of information.

But that doesn't necessarily preclude infinity as a scientific possibility.

Let's suppose there is a location in the universe where some property actually is infinite. Nearby, the measurement is high and as you get closer to the singularity, it gets higher and higher. Until your gauge overloads and breaks.

We'll never be able to actually measure 'infinity' on a tool, but that doesn't preclude us from concluding that that an infinite measurement exists. It's a straightforward, falsifiable, scientific statement. In order to falsify it, an experimenter just needs make a tool that can withstand and measure the property at a finite value. If it overloads every tool we can make, is it reasonable to hypothesize that the value is infinite?

 

[Speakpigeon]

As I see it, it is always reasonable to hypothesise any logical possibility. Not doing this, we might just as well choose to die here and now.

Still, we can't in practice look into all logical possibilities, anyway, because there has to be an infinity of them, so we have to choose on a pragmatic basis rather than simply on a logical one.

In the case you describe, it would be more reasonable to hypothesise that the property has an infinite value than it would be to decide that it has some arbitrarily great value. Presumably, we should be able to find a wide range of mathematical curves fitting well enough the set of all the measures already done. I suspect that we would reason by limiting our choice to "reasonably" simple curves so that maybe an infinite curve would stand out as the best fit. Yet, even then, a finite solution wouldn't be excluded.

I guess it's just that opting for an infinite curve may be the more simple solution. We may choose an infinite solution and later get new measures contradicting this solution. But it may be the pragmatic thing to do to go for the infinite, and risk being contradicted. I think this is basically what happened to Max Planck, who had to realise, against his initial belief, that apparently energy interactions couldn't get infinitely small.

It may also be a good idea to assume a finite solution. Assuming an infinite solution may be like driving at full speed on a straight road you don't know, in the dark, without headlights, on the assumption that the road is infinite. Not exactly safe.


There's also a distinction to make. There's a difference between a curve with an infinite limit and a curve with a point at the infinite. An infinite limit doesn't necessarily belong to the curve itself. If electrons have no size, and assuming QM wrong, we could have the intensity of the electric field getting larger and larger nearer and nearer to the electron, effectively without limit, therefore infinite. Yet, at the location of the electron, the field would be undetermined, not anything like an actual infinite value.
EB

 

[untermensche]

As far as I can tell, there's no way we could measure a property as infinite. Any gauge made by humans will have a finite size, and thus should only be able to encode a finite amount of information.

But that doesn't necessarily preclude infinity as a scientific possibility.

Let's suppose there is a location in the universe where some property actually is infinite. Nearby, the measurement is high and as you get closer to the singularity, it gets higher and higher. Until your gauge overloads and breaks.

We'll never be able to actually measure 'infinity' on a tool, but that doesn't preclude us from concluding that that an infinite measurement exists. It's a straightforward, falsifiable, scientific statement. In order to falsify it, an experimenter just needs make a tool that can withstand and measure the property at a finite value. If it overloads every tool we can make, is it reasonable to hypothesize that the value is infinite?

Yes. Lets just imagine something can be infinite. Let's pretend some place in the universe could somehow be infinite.

What a worthwhile exercise.

Next let's pretend the concept of infinite wisdom is real too and look for that.

 

[ryan]

Here's a good experiment; I remember reading this article way back when it first came out, https://www.space.com/19202-einstein-space-time-smooth.html . It doesn't give us certainty of course, but it leaves us with the possibility of a continuous spacetime. And I would think that an infinitesimally smooth spacetime is a default position based on the evidence and theory that points that way.

 

[no-one-particular]

As far as I can tell, there's no way we could measure a property as infinite. Any gauge made by humans will have a finite size, and thus should only be able to encode a finite amount of information.

But that doesn't necessarily preclude infinity as a scientific possibility.

Let's suppose there is a location in the universe where some property actually is infinite. Nearby, the measurement is high and as you get closer to the singularity, it gets higher and higher. Until your gauge overloads and breaks.

We'll never be able to actually measure 'infinity' on a tool, but that doesn't preclude us from concluding that that an infinite measurement exists. It's a straightforward, falsifiable, scientific statement. In order to falsify it, an experimenter just needs make a tool that can withstand and measure the property at a finite value. If it overloads every tool we can make, is it reasonable to hypothesize that the value is infinite?

infinity = 1/insignificance

 

[beero1000]

As far as I can tell, there's no way we could measure a property as infinite. Any gauge made by humans will have a finite size, and thus should only be able to encode a finite amount of information.

But that doesn't necessarily preclude infinity as a scientific possibility.

Let's suppose there is a location in the universe where some property actually is infinite. Nearby, the measurement is high and as you get closer to the singularity, it gets higher and higher. Until your gauge overloads and breaks.

We'll never be able to actually measure 'infinity' on a tool, but that doesn't preclude us from concluding that that an infinite measurement exists. It's a straightforward, falsifiable, scientific statement. In order to falsify it, an experimenter just needs make a tool that can withstand and measure the property at a finite value. If it overloads every tool we can make, is it reasonable to hypothesize that the value is infinite?

infinity = 1/insignificance

Yeah, ... no.

 

[fromderinside]

function Convergence nonconvergence testing?

 

[untermensche]

As far as I can tell, there's no way we could measure a property as infinite. Any gauge made by humans will have a finite size, and thus should only be able to encode a finite amount of information.

But that doesn't necessarily preclude infinity as a scientific possibility.

Let's suppose there is a location in the universe where some property actually is infinite. Nearby, the measurement is high and as you get closer to the singularity, it gets higher and higher. Until your gauge overloads and breaks.

We'll never be able to actually measure 'infinity' on a tool, but that doesn't preclude us from concluding that that an infinite measurement exists. It's a straightforward, falsifiable, scientific statement. In order to falsify it, an experimenter just needs make a tool that can withstand and measure the property at a finite value. If it overloads every tool we can make, is it reasonable to hypothesize that the value is infinite?

infinity = 1/insignificance

Absolutely!

To think it real is to be a child.

 

[PyramidHead]

As far as I can tell, there's no way we could measure a property as infinite. Any gauge made by humans will have a finite size, and thus should only be able to encode a finite amount of information.

But that doesn't necessarily preclude infinity as a scientific possibility.

Let's suppose there is a location in the universe where some property actually is infinite. Nearby, the measurement is high and as you get closer to the singularity, it gets higher and higher. Until your gauge overloads and breaks.

We'll never be able to actually measure 'infinity' on a tool, but that doesn't preclude us from concluding that that an infinite measurement exists. It's a straightforward, falsifiable, scientific statement. In order to falsify it, an experimenter just needs make a tool that can withstand and measure the property at a finite value. If it overloads every tool we can make, is it reasonable to hypothesize that the value is infinite?

Not necessarily, because there is always the possibility that our measurement tools are thousands of orders of magnitude too crude. Depending on the phenomenon, of course. The fact that we don't have a definite measurement of something is only evidence that it's infinite inasmuch as having a definite measurement would prove that it's not infinite. But that's like saying the Pope's claim of infallibility is evidence that he is infallible, since if he said he wasn't infallible that would prove he wasn't. In other words, being too high to measure is merely consistent with being infinite, but it's also consistent with a great many other possibilities that can't really be discarded in favor of infinity in any principled way.

 

[Bomb#20]

Not necessarily, because there is always the possibility that our measurement tools are thousands of orders of magnitude too crude. Depending on the phenomenon, of course. The fact that we don't have a definite measurement of something is only evidence that it's infinite inasmuch as having a definite measurement would prove that it's not infinite. But that's like saying the Pope's claim of infallibility is evidence that he is infallible, since if he said he wasn't infallible that would prove he wasn't. In other words, being too high to measure is merely consistent with being infinite, but it's also consistent with a great many other possibilities that can't really be discarded in favor of infinity in any principled way.

But of course being measured at some specific finite level is also consistent with a great many other possibilities, including that the quantity is infinite. All measurements are theory-laden, instruments are often wrong, and we take a measurement seriously only because we believe the specific quantity in question matching what the particular instrument says is a better explanation for that instrument saying what it says than any competing explanation we've been able to come up with yet. It's not the instrument but rather the explanation that justifies the conclusion that the quantity is finite.

That works in reverse too. Consider the number of points in space between the front of a ruler and its one-centimeter mark. We don't know how to build a meter we think can count such things; but let's imagine we did. That would mean we'd have to have a theory of physics that implies "If such-and-such a meter says A then the number of points is about X; if it says B then the number of points is about Y; ...". Let's say we built one and the meter said B. We'd conclude that the number of points is about Y; but our evidence for that conclusion would only be as good as our evidence for the theory itself. So at that point we'd simply have a well-evidenced theory, the best explanation for phenomena in general, telling us a centimeter contains, for example, about 10³³ points in space.

So how is that different from what we have now? We already have a well-evidenced theory, the best explanation for phenomena in general, that can already tell us how many points in space a centimeter contains. It's the Standard Model, and it says there are infinitely many points in a centimeter. How is it any less reasonable to believe that than it would be to believe a hypothetical meter backed up by a hypothetical competing theory? In effect, we already have a points-in-a-centimeter meter: it's the whole visible universe and the whole of modern physics. The Standard Model is the best explanation of what we observe, which is as much as any measuring instrument can ever aspire to be; and it measures points-in-a-centimeter to be infinite, because there currently exists no mathematical model of physics that assumes discrete space and is as good as the Standard Model at making predictions. Anybody who wants to argue that the number of points in a centimeter is probably finite has the burden of constructing a nonstandard model of physics that assumes it's finite, that can compete with the Standard Model at the prediction game, and that at least gets a tie.

Here's a good experiment; I remember reading this article way back when it first came out, https://www.space.com/19202-einstein-space-time-smooth.html . It doesn't give us certainty of course, but it leaves us with the possibility of a continuous spacetime. And I would think that an infinitesimally smooth spacetime is a default position based on the evidence and theory that points that way.

Bingo.

 

[beero1000]

As far as I can tell, there's no way we could measure a property as infinite. Any gauge made by humans will have a finite size, and thus should only be able to encode a finite amount of information.

But that doesn't necessarily preclude infinity as a scientific possibility.

Let's suppose there is a location in the universe where some property actually is infinite. Nearby, the measurement is high and as you get closer to the singularity, it gets higher and higher. Until your gauge overloads and breaks.

We'll never be able to actually measure 'infinity' on a tool, but that doesn't preclude us from concluding that that an infinite measurement exists. It's a straightforward, falsifiable, scientific statement. In order to falsify it, an experimenter just needs make a tool that can withstand and measure the property at a finite value. If it overloads every tool we can make, is it reasonable to hypothesize that the value is infinite?

Not necessarily, because there is always the possibility that our measurement tools are thousands of orders of magnitude too crude. Depending on the phenomenon, of course. The fact that we don't have a definite measurement of something is only evidence that it's infinite inasmuch as having a definite measurement would prove that it's not infinite. But that's like saying the Pope's claim of infallibility is evidence that he is infallible, since if he said he wasn't infallible that would prove he wasn't. In other words, being too high to measure is merely consistent with being infinite, but it's also consistent with a great many other possibilities that can't really be discarded in favor of infinity in any principled way.

There's always the possibility that I can fly. The fact that I don't have definite proof that I can't doesn't prove that I can.

Science isn't about considering every possibility - it's about falsifiably explaining the evidence. For any finite value there are higher finite values, so in this hypothetical, how high must we be able to measure before we can conclude the value is infinite? What if there's theoretical evidence supporting it, say like a singularity in a well-supported theory?

 

[cpollett]

A set is basically a data structure equipped with an elementOf algorithm that returns true or false depending on whether or not something belongs to it.

The axiom of infinity asserts that there is a set whose elementOf algorithm returns true when given the empty set as input, and that returns true on x cup {x} whenever it returns true on {x}. The other axioms of set theory assert there is a set whose elementOf always returns false (i.e., empty set exists), give various ways to create sets with elementOf algorithms based on existing sets' elementOf algorithms, and prevent (via the foundation axiom) having an elementOf which always returns true.

Typically we choose our physical models to try to minimize the size of both the model and the number of bits needed to specify how it disagrees with observation. Our physical models are specified in terms of mathematics which can in turn be formalized in set theory.

Specifying the elementOf algorithms sufficiently for the sets involved to do calculations can be done with a fixed finite number of bits. If the choice of elementOf algorithms for the best physical theory is more succinctly described if some of its sets' elementOf algorithms satisfy the axiom of infinity, then to me that would argue that reality is best described using infinite sets.

 

[Jobar]

The concept of finiteness seems to inescapably imply infinity; ending implies endlessness. But that isn't the same as measuring infinity.

Semantically, the concepts of measurement and infinity seem incommensurable; the definite cannot be infinite, nor vice versa.

 

[untermensche]

The concept of finiteness seems to inescapably imply infinity; ending implies endlessness. But that isn't the same as measuring infinity.

Semantically, the concepts of measurement and infinity seem incommensurable; the definite cannot be infinite, nor vice versa.

Finiteness does not imply infinity.

It implies finiteness.

Infinity is an imaginary concept we sometimes apply to finiteness.

We apply this imaginary concept of endlessness to finite things.

But there is no reality except the finiteness.

 

[steve_bank]

Conceptually infinite and quantifiable are mutually exclusive.

On a continuous probability distribution it is not possible to determine an exact probability.