A Question Concerning Material Structure and the Speed of Light

originally posted by: PhotonEffect
1+1 = 2 is true, but is a concept.
I could argue, perhaps against widely held popular belief, that 1 + 1 = 1.
It really depends on what the underlying meaning is.

It isn't a concept, whatever you want to use as the symbols within math 1+1 cannot ever = 1, the math is the same where ever you are in the universe.

Hydrogen for example has one Electron and one Proton, this is as true at this place and time as it was 13 billion years ago and in all other places in the universe.

To deny the math is to deny reality and to deny reality is to deny math.

There is no distinction, you cannot have one without the other.

Korg.

a reply to: Korg Trinity

To deny the math is to deny reality and to deny reality is to deny math.

There is no distinction, you cannot have one without the other.

No one here is denying math, friend. Just that it's the "language of the universe". I don't see it that way.

But no reality without math? That's a bit of a stretch in my world.

Good talk though.

originally posted by: PhotonEffect
a reply to: Korg Trinity

To deny the math is to deny reality and to deny reality is to deny math.

There is no distinction, you cannot have one without the other.

No one here is denying math, friend. Just that it's the "language of the universe". I don't see it that way.

But no reality without math? That's a bit of a stretch in my world.

Good talk though.

Think of it this way.

How could there be a universe with no dimensions?

Korg.

a reply to: Korg Trinity

Not that it makes a difference to what you mean by dimension. Because dimensions are human concepts. Mere descriptors of physical space.

My guess is the universe existed before the idea of a dimension.

originally posted by: PhotonEffect
a reply to: Korg Trinity

No that it makes a difference to what you mean by dimension. Because dimensions are human concepts. Mere descriptors of physical space.

My guess is the universe existed before the idea of a dimension.

No Dimensions are not human concepts. They are fundamental properties of reality.

Korg.

a reply to: Korg Trinity

Says who?

originally posted by: PhotonEffect
a reply to: Korg Trinity

Says who?

I think you need to learn what it is your talking about.

It is true that water existed before humans could notice it as being wet.... but that does not mean that water did not exist until humans evolved.

This is true of all the properties of the universe, they existed before we were able to discover them..... So dimensions are a fundamental construct that defines reality and since dimensions are defined by numbers ergo math existed before us.

Korg.

a reply to: Korg Trinity

You've had to rely on circular reasoning to push your belief. You want so badly for the universe to be a mathematical structure.

Yes, Math has aided in the revealing of orderliness within in the universe. That's where it should stop though. The speed of light is not math. It is only defined by it. We use math and other languages to define the universe. This is more reasonable.

originally posted by: PhotonEffect
a reply to: Korg Trinity

You've had to rely on circular reasoning to push your belief. You want so badly for the universe to be a mathematical structure.

Yes, Math has aided in the revealing of orderliness within in the universe. That's where it should stop though. The speed of light is not math. It is only defined by it. We use math and other languages to define the universe. This is more reasonable.

No I had to resort to ultra simplifying the information because you appear unable to comprehend it.

Korg.

a reply to: PhotonEffect

And for aliens on the planet Quibble, dimensions would be Quibblian concepts.
On the planet Zarg, dimensions would be Zargonian concepts.

And so on and so forth.

This doesn't make them arbitrary or simple figments of the imagination, they are a reflection of reality as we have consistently observed it. You might as well say that gravity is a human concept and expect to float away.

a reply to: GetHyped

You might as well say that gravity is a human concept and expect to float away.

There's some truth in that jest. When people get into an idealist or dualist frame of mind, they actually start believing that mind is precedent to matter — believing, as Korg Trinity might put it, that water never existed until some ape with a mind showed up to notice that the stuff was wet. Short step from there to thinking you could abolish gravity by wishing hard enough.

After all, if the universe needs minds to manifest itself in, then the mind must surely be able to affect the manifestation to its taste? O Lord we pray, let there be a way — that beggars might ride, that tinkers might be made extinct, and that people who know no maths or physics might all win Nobel Prizes for their cogitations.

a reply to: GetHyped

And for aliens on the planet Quibble, dimensions would be Quibblian concepts.
On the planet Zarg, dimensions would be Zargonian concepts.

Sounds like a bold assumption on a number of levels. Perhaps relying on a little wishful thinking, or faith, so to speak.

This doesn't make them arbitrary or simple figments of the imagination, they are a reflection of reality as we have consistently observed it. You might as well say that gravity is a human concept and expect to float away.

This doesn't make them math either. Only part of an ordered system.

a reply to: Korg Trinity
Clearly you're a Platonist, and thus it renders your opinion a matter of philosophy, not science.

Mathematics is a rule-based system of purely intellectual operations. In a technical sense, you could invent an arithmetic in whch 1+1=1, but it would be a very dull arithmetic, one in which no actual mathematical operations could be conducted. 1+1=3 arithmetic is a bit more accommodating, although the answers it produces would be wrong.

By 'wrong', I mean that 1+1=3 arithmetic is internally inconsistent and would fail to describe or explain anything in the real world, whereas the mathematical systems we do utilize are amazingly good at this.

They were not contrived thus. They work so well because they were abstracted, all unknowing, from quantitative relationships observed in the natural world. It is only in more recent times that mathematicians grew bolder and began inventing mathematical systems that digress from observed reality. Sometimes, their relevance is discovered later, as was the case when Einstein discovered that Riemann geometry worked beautifully for describing operations on spacetime.

People have been debating for centuries whether mathematics is a discovery or an invention. What is not in doubt, however is that

1. absolute quantities (that is, quantities that are the same no matter how, where and when they are measured), do exist in the universe. I have already mentioned two: the Planck length and the speed of light. There are others. Collectively, they are termed the fundamental constants.
   
   
2. These fundamental constants are related to one another in ways that do not vary, and which govern the behaviour of all objects and entities in the universe. These relationships are called the laws of nature. No philosopher, as far as I know, denies that they exist. Physicists take them for granted.
   
   
3. Mathematics is a language for describing the laws of nature. Yes, we invented the mathematical systems we use; but the relationships they describe were observed, not invented, or else they were theoretically derived from the laws and later validated by observation.
   
   
4. Because of this, any mathematical system that is consistent and can be used to produce reasonably accurate descriptions of reality can be translated into any other mathematical system of which the same may be said. This is true whether the system was invented by humans or by triffids. The fundamental constants and the laws of nature are used to effect the translation.

I trust this resolves the argument.

Is math invented or discovered?

what kinds of materials are we talking about here?

originally posted by: Astyanax
Is math invented or discovered?

From your article:

Sometimes scientists create methods specifically for quantifying real-world phenomena. For example, Isaac Newton formulated calculus for the purpose of capturing motion and change, breaking them up into infinitesimally small frame-by-frame sequences. Of course, such active inventions are effective; the tools are, after all, made to order. What is surprising, however, is their stupendous accuracy in some cases.

Key take away: Math is "made to order", but thankfully, also happens to be accurate (at describing nature), sometimes.

Even more astonishing, perhaps, mathematicians sometimes develop entire fields of study with no application in mind, and yet decades, even centuries, later physicists discover that these very branches make sense of their observations.

Key take away: Well that's a relief. So what were these "fields of study" for before it was discovered they actually had some applicable use?

A pattern emerges: humans invent mathematical concepts by way of abstracting elements from the world around them--shapes, lines, sets, groups, and so forth--either for some specific purpose or simply for fun. They then go on to discover the connections among those concepts. Because this process of inventing and discovering is man-made--unlike the kind of discovery to which the Platonists subscribe--our mathematics is ultimately based on our perceptions and the mental pictures we can conjure.

Key take away: I'll let this tidbit speak for itself. (Korg: this one's for you)

Not only do scientists cherry-pick solutions, they also tend to select problems that are amenable to mathematical treatment. There exists, however, a whole host of phenomena for which no accurate mathematical predictions are possible, sometimes not even in principle.

Key take away: You don't say... (Korg?)

mathematics itself is limited, as Austrian logician Gödel famously proved.

Key take away: Indeed he did, with this.

a reply to: PhotonEffect


Goedel proved that formal logical systems (first order logic) are limited.

Mathematics, as practiced by advanced humans, is not so limited, and Goedel believed in this power of mathematics.

users.ox.ac.uk...

O.k. Let's break down the obviously misunderstood document as you have done and answer your questions directed to me.

originally posted by: PhotonEffect

Even more astonishing, perhaps, mathematicians sometimes develop entire fields of study with no application in mind, and yet decades, even centuries, later physicists discover that these very branches make sense of their observations.

Key take away: Well that's a relief. So what were these "fields of study" for before it was discovered they actually had some applicable use?

To understand why that is the case you have to first acknowledge that the universe is ultimately and intrinsically connected to Math as I have already intimated..

You see exploration of space and time happens more on paper than out there in space. This has a lot to do with our limited abilities to actually travel the distances and experience reality in the fullest.

However we can explore the stars and in fact the whole universe using math. Math is very much like that proverbial jigsaw puzzle I talked about earlier... it can grow in all directions. Once piece of math may fit perfectly with another and like following a path one might follow the direction the math is taking us beyond our understanding of it's meaning. Only that it fits....

Then later when we understand more about the universe we often look back at what math has already been done and find that the calculations were discovered before the existential phenomena was discovered.

The math describing nature accurately even before we discovered the nature is a pretty obvious sign post that should read that Math is fundamental to the universe itself.

A pattern emerges: humans invent mathematical concepts by way of abstracting elements from the world around them--shapes, lines, sets, groups, and so forth--either for some specific purpose or simply for fun. They then go on to discover the connections among those concepts. Because this process of inventing and discovering is man-made--unlike the kind of discovery to which the Platonists subscribe--our mathematics is ultimately based on our perceptions and the mental pictures we can conjure.

Key take away: I'll let this tidbit speak for itself. (Korg: this one's for you)

It does speak for itself but your implied understanding of it is wrong.

What is the purpose of math, why did humans start to use math?

It isn't that we invented it and then nature conformed to our invention... it was a path of discovery. the most fundamental of these discoveries has to be that one more than one is two and one more than two is three and so on.... it doesn't matter what symbols were used to describe the discovery the fact that this is a universal aspect of reality is what is important.

you called me a platonist... you could not be more wrong, it is you who believe that Math is based upon our mental picture.... I am a Scientist... I believe Math is a fundamental aspect of reality, Discovered by humans because we have the intellect to understand complex ideas and relationships.

Not only do scientists cherry-pick solutions, they also tend to select problems that are amenable to mathematical treatment. There exists, however, a whole host of phenomena for which no accurate mathematical predictions are possible, sometimes not even in principle.

Key take away: You don't say... (Korg?)

Just because we cannot describe a phenomena with math does not mean there isn't a proof yet to be discovered. Often it has been the case that a whole arm of mathematical proof has been rebuilt due to a discovery that changed the starting values.

Math is like a light in a dark room... the more we understand the more math that connects the brighter the light and the more of the room you can see. Sometimes you know there is a problem when the math progresses but the room get's no brighter.... this doesn't mean that the math is necessarily wrong... just that there maybe something missing we have yet to describe.

There is only two phenomena to my knowledge that defy mathematical description... 1. A Singularity and 2. Quantum Foam

Everything else in the universe can be described mathematically 100% Including consciousness itself.

The fact that we do not have a proof yet for everything does not mean there isn't a proof!

Korg.

originally posted by: Korg Trinity

There is only two phenomena to my knowledge that defy mathematical description... 1. A Singularity and 2. Quantum Foam

Everything else in the universe can be described mathematically 100% Including consciousness itself.

Wait---a singularity can be handled just fine mathematically! Poles and other hairier objects in complex analysis have been known for a long time.

It's just that physicists experience with these in the mathematical theory is that they represent failures of the validity of the theory close to them and the results of the theory are not physically correct in that case.

Consciousness? Uh, there's a whole lot more work to go there, and consciousness may not be a singular unique phenomenon.

Not sure about 'quantum foam' but I bet it is a description of certain hypothesized field theory/string theory variants and the theories have a mathematical representation.

originally posted by: mbkennel

originally posted by: Korg Trinity

There is only two phenomena to my knowledge that defy mathematical description... 1. A Singularity and 2. Quantum Foam

Everything else in the universe can be described mathematically 100% Including consciousness itself.

Wait---a singularity can be handled just fine mathematically! Poles and other hairier objects in complex analysis have been known for a long time.

It's just that physicists experience with these in the mathematical theory is that they represent failures of the validity of the theory close to them and the results of the theory are not physically correct in that case.

Consciousness? Uh, there's a whole lot more work to go there, and consciousness may not be a singular unique phenomenon.

Not sure about 'quantum foam' but I bet it is a description of certain hypothesized field theory/string theory variants and the theories have a mathematical representation.

I'm afraid not.... I wish it were so as it would be the discovery of all time.... quite literally... No I'm afraid Singularities are not currently describable mathematically.

Oh we have math to describe the function but this only serves to isolate the issue from the equations. We can describe pretty much anything up to the point of the singularity... but beyond that it's just a big (∞)

Now I use infinities in my daily job all the time. In fact I wouldn't be able to do my job if not for the container ∞ for that is all there is to say about ∞ in math, it is a container by which you can do some interesting things.

Concerning Quantum foam... this is also a point our equations break down... there is no way to describe something that is pure chaos... and I don't mean chaos in the sense you might think... I mean true chaos of reality itself...

Further more, even if we were to discover a mathematical construct that did appear to describe such enigmatic aspects of nature, we would not have the ability to test it.

Therefore Singularities and Quantum Foam defy mathematical description.

Consciousness is not unique to you and I... animals also exhibit consciousness and as such it is easy to see that consciousness itself is an emergent property of a sufficiently organised network of information flow. Moreover, as information flow and network nodes are a finite quantity in this case, it can eventually be described mathematically, understood and replicated.

Do you follow?

Korg.