Do numbers exist in nature or are they human contructs?

[FBM]

I'm pretty sure things have been observed, but not so sure numbers themselves ever have.

Depends what you mean by ''exist'' then. Physical things exist. And they have properties.
Do properties ''exist'' ? I think they do. If they don't exist, they can't cause change.
We don't observe gravity. We observe it's effect. It's the same with numbers. We don't observe the numbers, we observe their effects.

Properties are dynamic phenomena. Not so sure about numbers. We can imagine unicorns and gods and whatnot, maybe numbers are just a very useful fiction. I'm not convinced one way or the other about the OP. I haven't seen anything conclusive here yet.

[pErvinalia]

I'm pretty sure things have been observed, but not so sure numbers themselves ever have.

Depends what you mean by ''exist'' then. Physical things exist. And they have properties.
Do properties ''exist'' ? I think they do. If they don't exist, they can't cause change.
We don't observe gravity. We observe it's effect. It's the same with numbers. We don't observe the numbers, we observe their effects.

Gravity is a physical phenomenon. Numbers aren't.

One one hand, I still think numbers are a manifestation of our propensity to pattern match and categorise. So in that regard they have no set physical value. But on the other hand, numbers in physics ARE representing something physical. So even though we could call our units metres or flugals, such that there are 4 x 10-13 metres, or 7.46 x 10-9 flugals, in between molecules in ice, they both represent the same thing. That sort of implies that there are such things as numbers. How else could we represent the physical world without numbers?

[JimC]

They can also be thought of as a property of how matter is organised in our particular Universe, into a series of discrete, separate entities, at many levels, that allow for a set theory containing discrete elements.

One could imagine a very different universe, perhaps only containing classical energy fields, with no quantum effects, where all aspects of physical reality change absolutely smoothly in magnitude and direction; no steps, no jumps, no discrete entities. If an intelligent alien form of life evolved in such conditions, it would have no concept of integers at all - it would be interesting to speculate on what aspects of mathematical theory we would have in common (calculus?), and what would be unique to each of us...

In that context, you say absolutely, but you mean ''infinitely''. Yes?
That's not actually as easy as it sounds, to imagine. An actual infinity is supposed to be impossible in the physical world. Which is why quantum jumps make sense.

Yes, it's certainly not how our Universe works, so I'm being speculative about the possibility that universes with any arbitrary physical laws are "possible", more to illustrate the point that discrete jumps and entities are built in to our Universe from the ground up...

[FBM]

Is a perceived object a singular entity with inherent "one-nature" to which the human mind responds? Not sure how it could be, because a rock or chair or whatever is divisible into component parts, so "one-ness" doesn't seem to be inherent in any compounded entity.

[JimC]

Is a perceived object a singular entity with inherent "one-nature" to which the human mind responds? Not sure how it could be, because a rock or chair or whatever is divisible into component parts, so "one-ness" doesn't seem to be inherent in any compounded entity.

Go down far enough, and "oneness" is inherent in the atomic nature of matter. There really are discrete entities in matter, at many levels. My earlier point was speculating that this doesn't have to be, in an alternative reality where existence is smoothly "smeared".

Not in this universe, however...

[FBM]

But we don't perceive subatomic particles. We perceive compounded objects and assign them discrete singularity...erroneously. That singularity is an illusion of limited perspective, no? Convenient and useful, but neither convenience nor utility is evidence for truth...

Edit:

http://arxiv.org/abs/1204.4616

There are no particles, there are only fields

Art Hobson
(Submitted on 19 Apr 2012 (v1), last revised 29 Nov 2012 (this version, v2))
Quantum foundations are still unsettled, with mixed effects on science and society. By now it should be possible to obtain consensus on at least one issue: Are the fundamental constituents fields or particles? As this paper shows, experiment and theory imply unbounded fields, not bounded particles, are fundamental. This is especially clear for relativistic systems, implying it's also true of non-relativistic systems. Particles are epiphenomena arising from fields. Thus the Schroedinger field is a space-filling physical field whose value at any spatial point is the probability amplitude for an interaction to occur at that point. The field for an electron is the electron; each electron extends over both slits in the 2-slit experiment and spreads over the entire pattern; and quantum physics is about interactions of microscopic systems with the macroscopic world rather than just about measurements. It's important to clarify this issue because textbooks still teach a particles- and measurement-oriented interpretation that contributes to bewilderment among students and pseudoscience among the public. This article reviews classical and quantum fields, the 2-slit experiment, rigorous theorems showing particles are inconsistent with relativistic quantum theory, and several phenomena showing particles are incompatible with quantum field theories.

[Xamonas Chegwé]

Is a perceived object a singular entity with inherent "one-nature" to which the human mind responds? Not sure how it could be, because a rock or chair or whatever is divisible into component parts, so "one-ness" doesn't seem to be inherent in any compounded entity.

Go down far enough, and "oneness" is inherent in the atomic nature of matter. There really are discrete entities in matter, at many levels. My earlier point was speculating that this doesn't have to be, in an alternative reality where existence is smoothly "smeared".

Not in this universe, however...

There are also definite, quantum properties of fundamental properties that have specific, numerical values - spin is the most obvious. All bosons have integer spin. All fermions have integer +1/2 spin. Also, electromagnetic charge occurs in discrete values. Up-type quarks have charge +2/3, down-type quarks have charge -1/3, electrons (and their heavier cousins) have charge -1.

These numbers are not arbitrary - they are a very real part of how everything is made.

[Azathoth]

Dafuq? When did 1/2 become an integer. Stupid quantum weirdness

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[Xamonas Chegwé]

Dafuq? When did 1/2 become an integer. Stupid quantum weirdness

Where did I say it was?

Spin is either integer or integer+1/2, ie. {0, ±1, ±2, etc.} or {±1/2, ±3/2, ±5/2, etc.}

Charge is either 0, ±1, ±1/3 or ±2/3.

Other quantum quantities have similar sets of values.

[Azathoth]

Aah don't mind me. Little bit dunk and gone from late to early

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[JimC]

FBM wrote:

We perceive compounded objects and assign them discrete singularity...erroneously. That singularity is an illusion of limited perspective, no? Convenient and useful, but neither convenience nor utility is evidence for truth...

In many cases, I think our perceptions are straightforwardly correct. There are many clear-cut instances in the material world where things, often living things, come as single, clearly separate entities. One fish doesn't blur into another fish, nor does one pebble smear into another...

[pErvinalia]

That's just a matter of perspective, isn't it?

[FBM]

FBM wrote:

We perceive compounded objects and assign them discrete singularity...erroneously. That singularity is an illusion of limited perspective, no? Convenient and useful, but neither convenience nor utility is evidence for truth...

In many cases, I think our perceptions are straightforwardly correct. There are many clear-cut instances in the material world where things, often living things, come as single, clearly separate entities. One fish doesn't blur into another fish, nor does one pebble smear into another...

But fishies are made of millions of cells, which are made of etc, etc. At the smallest scale, you have fields, not little fundamental ball bearing-like things. According to them people wot I linked to above, anyway. I haven't looked.

[FBM]

That's just a matter of perspective, isn't it?

Maybe. That depends on how you look at it.

[JimC]

FBM wrote:

We perceive compounded objects and assign them discrete singularity...erroneously. That singularity is an illusion of limited perspective, no? Convenient and useful, but neither convenience nor utility is evidence for truth...

In many cases, I think our perceptions are straightforwardly correct. There are many clear-cut instances in the material world where things, often living things, come as single, clearly separate entities. One fish doesn't blur into another fish, nor does one pebble smear into another...

But fishies are made of millions of cells, which are made of etc, etc. At the smallest scale, you have fields, not little fundamental ball bearing-like things. According to them people wot I linked to above, anyway. I haven't looked.

Sure - objects are compound, complex, and when we apply reductionist techniques, aspects of their nature change according to the scale at which we wish to observe. Fascinating, interesting, scientifically important and sometimes confusing in terms of language used to describe the phenomena...

None of which changes the fact that I, a computer, or an alien can simply and easily count how many discrete fishes exist at any one time in a given aquarium...