Ya and I wasn't talking about a precise definition of the branch of mathematics called topology, I was using the definition analogously by applying it to the universe. We do stuff like this all the time, even with mathematical models, so again I don't see what your problem with it.



Like I said before, mathematical definitions of words aren't restricted to mathematics, for two reasons. The first is that mathematics corresponds to our real universe in a very real way. The second is that mathematics is a part of that universe. There is nothing wrong with me taking definitions from math that have a specific meaning and applying is analogously to other things. We do it all the time when we make mathematical models.

So for example when I'm figuring out how much interest I'm going to pay on a loan and using a specific function from mathematics, you'd be hard pressed to convince anyone that the loan-interest calculation is only defined within math. Stuff from math applies to the real world, including topological definitions.



And I gave that context clearly, so you shouldn't have a problem with it.

The universe does have a topology. In terms of its shape, it's a flat curved, intrinsically expanding manifold. It also has an underlying structure that gives rise to everything in it. It's analogously topological in manifold ways.


You have a very strange point of view on things. Language from mathematics is used analogously all the time, it doesn't mean the person doing it is a liar. It means you have seemingly very little ability to infer the meaning behind creative use of language.




That's an interesting point of view, considering both relativity and quantum mechanics were derived mathematically before any observations were made.

Math has traditionally led science. The mathematics for relativity, for example, were around for a couple decades before Einstein. So what? The fact remains that there is correspondence between mathematics and reality itself. This is not debatable. Insofar that there exists that correspondence, the universe and mathematics share an intersection at a fundamental level. In this sense, it's no different from consciousness. Consciousness intersects with reality. They inhere in each other. How far they inhere in each other is irrelevant. The only thing that matters is that they do.



So we can't stretch, deform, and manipulate a donut, so it's not a topological shape? That's ridiculous. This has more to do with the properties of the matter within a donut than it does to the donut not corresponding to the torus. If the torus was made out of playdough, you bet your ass I'd be able to change it into a coffee cup without making cuts in it.

I think at this point it's been proven beyond reasonable doubt that you're just here to argue, and being unreasonably contentious in order to do so. I have no problem with this, because if anyone's looking idiotic it's you.

Right.... so when you talk about definitions and quote definitions, you're not actually meaning the fancy technical word you used, but rather the idea of the technical word. I would call this highly deceptive and the sort of thing people do when they're trying to sound more competent than they really are.

But unfortunately for you, "topology" isn't a mathematical model for the universe at all. As I've pointed out, we do things in topology that make very little sense in the real world.

The problem with this isn't that it happened in isolation, but that this was about the fourth or fifth time in the conversation that you've thrown out a mathematical term and claimed that mathematics supported your logic and position, while completely undermining the entire mathematicalness of the thing you were using.

See? You've done it again. "Well, I'm going to make a mathematical analogy that doesn't actually use mathematics, but then use the true mathematical knowledge to justify whatever nonsense I'm about to say."

You literally have no clue what you're talking about.

As soon as you're able to physically manifest the Banach-Tarski paradox, I'll concede that all math applies to the real world.

No. You literally stripped away the context to suit your intellectually disingenuous ends. Here is you:

https://forumserver.twoplustwo.com/s...0&postcount=54

And here is reality:

https://forumserver.twoplustwo.com/s...1&postcount=72

There you go again, throwing around math terms to make yourself sound smart. Do you really know what a "manifold" is? Do you think that topology "gives rise to everything" in the space? (PS - Also, LOL at the universe is "flat curved." Those words are contradictory in the colloquial AND technical sense, but you said it anyway because you don't know what you're talking about. What? You meant "locally flat"? I bet you don't even know what that means.)

Do you actually know what we mean when we say something "has a topology"? For example, if I say, "The set of natural numbers has a topology" do you understand what I'm claiming about the set of natural numbers? I'll be the answer is that you don't. (And it may blow your mind that there are infinitely many different topologies we can put on the real numbers, giving rise to different types of structures.)

So anyway, you are absolutely free to continue to embarrass yourself by asserting that you know things you know nothing about. But it's absolutely clear that you have no idea what any of these mathematical terms mean or how they're used.

When the language from mathematics is used in an analogous way, they no longer lay claim to being mathematical authoritative. And that's where you're running into problems. You can use language as creatively as you would like. You can try to form meaning out of words that mean other things all day long. But when you are being creative with language, you cannot also pretend that you're using language in the "normal" way.

My best analogy to this is the high school student that uses a thesaurus to try to replace some of their words to sound smarter. Yes, the thesaurus will give you words that have a similar meaning to the word you're actually using, and yes it's possible that creative license can be taken and the meanings stretched to be the same thing. But most of the time, it just makes you sound like you used a thesaurus because there's no useful meaning that way actually conveyed.


Do you know how many mathematical models people have come up with in an attempt to model the universe? Do you know how many of them failed? Just because we do something mathematically doesn't mean that we have *ANY* reason to believe it's actually a reflection of the universe.

Also, you're historically wrong:
* The origins of quantum mechanics date back to the very early 1900s when people started observing that things they thought were waves had particle-like properties. It was another couple decades before the Schrodinger equation was proposed.
* The derivation of special relativity (formally by Einstein in 1905) came at least in part as a result of the observations of the failure of aether drift, which came at the end of an approximately 100 year search for the explanation of the propagation of light through space.
* The derivation of general relativity came as an attempt to explain gravity in a new way. He wasn't trying to find an explanation of some new random observation, but rather construct a framework to understand ALL of the observations that have already been made.

So it makes no sense at all to say that they were mathematically derived without any observations. We've certainly made observations AFTER the mathematical model has been constructed which confirm the models, but that's an entirely different thing that what you've claimed.

What is the difference between a "topological shape" and a "shape"? I'm fine with the idea that a doughnut is an approximation or representation of a torus. But is it *actually* a torus? No. Believe it or not, there is more than one hole in your doughnut. How do I know? There's space between the molecules of the doughnut. There are gaps between the nucleus and the electrons (wherever they actually are). There are lots of ways to pass through a doughnut besides just the big hole.

In other words, a doughnut it NOT actually a torus. In fact, it's not a mathematical object at all.

Nope. You'd have a sloppy mess of playdough. And most likely, there would be some literal tearing (not allowed when applying a diffeomorphism) as you attempted to make it.

No, as I said before, I'm here to mock. This actually isn't an argument. What I'm doing is much more like an exposition. It's an annotation of your words that shows the gap between someone ignorantly throwing mathematical terms around and pretending to know something about physics, and someone who is actually a mathematician (with a strong physics background) who can elaborate on the ideas and concepts competently.

But please feel free to continue telling me mathematics and the history of physics. You *clearly* know so much about it.

no we dont.

The point of contention here is not what terms I'm using, but whether the universe corresponds to topology. You are essentially arguing that it doesn't, but you're wrong.

Wrong.

https://en.wikipedia.org/wiki/Connected_space

https://en.wikipedia.org/wiki/Topological_property

Wrong again. This is the fourth or fifth time you've pointed out what you consider to be semantic difficulties with the words I'm using, but that doesn't mean I can't use them. It simply means you don't like the fact I'm using them. Tough luck.



It does make sense though. The universe has topological properties.

You have a real problem with reading comprehension. The totality of math doesn't need to apply to the real world. If you want to call into question that it does at all, it would be simpler to use the problem of induction than Banach-Tarski. With that said, it's possible that your intuitions about mass, space and volume are simply wrong which is why you think BT is a paradox. If the universe is fundamentally mental like I'm claiming, the BT paradox isn't a paradox at all.



The doughnut and the picture frame are in fact reducibly the same thing. In much the same way, science assumes that everything that exists in the universe is reducibly the same as well, and we think we know that it is (matter/energy/information(?))





I don't need to throw around math terms to sound smart, I just need to get involved in more debates with you.

There you go with semantic problems again. You strike me as the kind of guy who has reasonably high non-verbal intelligence but well below average verbal intelligence. We actually don't know what shape the universe is, because we can't calculate its total mass density which is required to do so. But we have good reason to think it's flat, with variations. Interesting, there's that word topology again.


I'm using language in the normal way. This is a problem with your level of understanding, not my use of language. This has been proven countless times by your inability to focus on the content of the language I'm using and instead focusing on petty definitional problems that I assure you are your problems only.

The best analogy I have for you is putting on a pair of coke-bottle glasses in an intense attempt to find problems, but ending up seeing worse than you did before.

"I don't understand the words you're using or why, so you must be wrong."

Semantics is, in fact, the domain where the vast majority of your problems with my posts reside. If I considered this to be resolvable for you, I would suggest focusing on being a little more flexible with language, but the more I interact with you the more it seems to be more a personality or intelligence flaw than anything else.






The mathematics of relativity largely pre-existed relativity. Riemannian and differential geometry, etc.



The same as the difference between the concept/theory/blueprint of an internal combustion engine and an internal combustion engine.

It is and it isn't. A torus is a conceptual object; a donut is an actual one.

Again, you're focusing on problems with the material of the donut, not the topological properties of it.



The donut isn't the formal definition of torus? You don't say! It does, however, correspond to a torus.

I laughed out loud: this is a self-refuting statement.

No its not. How do we experience consciousness? What does that even mean?

Also, again, circular reasoning.

You need to read up on what these terms mean.

Consciousness has a definition:

When you claim we are 'not conscious' you are relying on your consciousness to make the claim in all three aspects of the definition:
1. You are aware of your surroundings, including the computer you typed the post claiming 'we are not conscious' on
2. You both perceived my post and your post that you wrote in reply
3. You are necessarily aware of yourself conceptualizing, writing, and posting the reply

In other words, when you claim that 'we are not conscious,' you are making a self-refuting statement.

"Experiencing consciousness" is simply experiencing the attributes that define it, namely the experience of being aware of your surroundings, perceiving things, and being aware of yourself and 'the world.'

Circular Reasoning
I am making no argument that we are conscious. That we are conscious is true by definition. In this sense it is tautologous, which is different from 'circular reasoning':

Tautology
The definition of consciousness is as written above. Anything with those attributes is conscious, by definition. If you wish to redefine consciousness, you are free to do so, but please let us know what you have redefined it as, or it will be impossible to follow you.

"The universe corresponds to topology" isn't even a sensible sentence.

LOL -- This is just face-palmingly bad. Let's go back to the beginning. Here is how you used the term:

THIS IS LITERAL NONSENSE. Just as when you say "the universe corresponds to topology." The sentence is meaningless.

What you're trying to do (and have been trying to do) is assert mathematical authority (and scientific authority) when you use mathematical words and phrases to mean things beyond what they actually mean. You want to argue about making models, but your "analogies" don't actually correspond to those models. You're basically playing a bait-and-switch game with your words, which is why I've been repeatedly focusing on your use of language.

"The universe has a topology" -- This sentence is that the universe has some sort of "shape."
"The universe correspond to topology" -- This shows you don't know how to use the words.
"The property of self awareness is contained topologically by the universe." -- This is just stupid.

All you're doing is switching the meaning of the word around to mean whatever you want it to mean. Your statements, under some consistent understanding of your word usage, are devoid of meaning.

You can use them all you want. But as you change the meaning, you can no longer assert the authority of the original meanings. See the transition of your word usage above.

Is "consciousness" among those "topological properties"? If not, in what sense is consciousness contained topologically?

LOL -- There is no spoon. There is no Banach-Tarski paradox. Whatever you imagine is actually real. The universe is shorter than 7 feet in length, but contains a sun that is larger than that. Except the sun is just an idea in your head and not an actual sun, because why would you think there's an actual sun when you can't interact with it but only with the ideas in your head. Oh, and the universe is tautologously "flat curved" because that's definitely a thing.

Just as another demonstration of how you're repeatedly flipping around your word usage...

The last two links are exactly the precise definitions of the branch of mathematics called topology.

The use of topology in the first is precisely the mathematical understanding of the term. Similarly with the other link that showed up later. This isn't about some "analogously defined" concept. When those scientific articles are talking about the "topology" of the universe, they are using the term in the sense of differential topology which is a particular area of mathematical study, and not some loosely defined idea that has vaguely to do with something like an analogous "shape" of an object.

I didnt claim we were not conscious. I disagreed with your claim that we experienced consciousness.


circular reasoning. You dont get to assume your conclusion in your premise.

I've never interacted with someone whose statements are nonsensical before, and I genuinely mean that. If you want this line of thinking to work, you have to accept the undermining of the validity of logic, which is a fine position to take. The only problem is you won't be able to argue for it.

DING DING DING

And then some spew about how your terminology is right and mine is wrong, because you don't get it. BORING

"I'm not using the language technically, but here's technical use of language to prove I'm right."

The sheer depths of delusion. SAD!

Care to address these uses of the word "topology" in an attempt to prove yourself right some more? Please do so!

I know multiple people who have in this thread, and I genuinely mean that.

Does the universe correspond to the topological definition of a connected space i.e.-is the universe a connected space? Does it have topological properties (including shape), or not?

If you answer yes to these questions, you admit that I am correct in my description of the universe as 'having correspondence to the definitions within the mathematical branch of topology.' If you answer no, there are a few hundred experts in cosmology who have a bone to pick with you.

It is not my problem that you don't understand the applications of the field of study you're supposedly involved in, and the more you talk, the more I doubt that you are involved in it. Either that or you're some kind of autist who is really bad at communicating.

Now beat it.

Unless you've been promoted to moderator, I don't believe you have the authority to say the bolded.

What is your conception of the universe? Is it the one you've been using throughout this thread, or is it something else? Is it ideas in your head or something outside of your head?

Assuming the concept that most normal people use (the one that contains an actual sun, for example), at the fundamental level the universe is not a connected space. That's merely an approximation. The reason for this is that according to quantum mechanics, we are unable to measure distances shorter than a Planck length, but connected spaces (and the concept of continuity) require us to be able to measure lengths that are arbitrarily small.

Now, whether or not this has anything at all to do with *your* usage of the words (in particular, claiming that you're not actually using the words in their mathematical meaning but rather making some sort of analogy), I have no idea because you've never really explained your actual usage of those words.

At the fundamental level, probably not. Quantum foam is kind of disintegration of the classical notions of geometry start to break down. Indeed, there's no real reason (based on what we know) that the universe is actually "smooth" in any real sense.

Similarly here, whether this corresponds at all to what *you* have been talking about (see the bolded below), I have no idea. Some rough idea of "shape" that really isn't the same concept used in topology? The universe corresponds to topology? Consciousness? Who knows?

Nope. I'm pretty sure they'd agree with my position and disagree with yours. The distinction is that they understand models and modeling. They understand the notion of an approximation being different from the actual thing. That, and they understand topology and you clearly don't. Being able to treat the universe at large scales as if it's continuous or connected is not the same as the universe *actually* being continuous or connected. Cosmologists *KNOW* that their models are fundamentally inconsistent with QM.

Your turn: Is consciousness contained topologically in the universe?

LOL -- Did you *really* just go down that path?

He can tell me to beat it. And I can also ignore his request. OrP is fairly generous in what he allows people to say, though he has limits.

If you and OrP are cool with it, then I'm cool with it.

I appreciate that you would come along to defend, but I give and take a lot of this sort of thing here, so I'm pretty unbothered by it.

Posting in a religion forum is definitely not for the thin-skinned.

You do a great job here in this forum, IMO. About the only time I think you're not doing a good job is when you disagree with me.