God is real. Change my mind

[tribal flint]

Absolutely

Bro. Anyone who reads the last 4 hours of this thread and still believes in god is a fighter

[normal current]

Spheres are 3d. Change my mind

New title

[tribal flint]

Hhahahah

[normal current]

Any of you math nerds understand tensor product and want to help me

[cosmic valve]

Oh I think I remember arguing this very point long ago. The definition of a sphere is pretty much bunk when you catch professors using it however they like. They do not like to be called out on it.

[tribal flint]

Not now, it's almost 3am and I've been trying to shut down my laptop for hours

[tribal flint]

Most math professors are actually very chill when you point out mistakes. Anyone that isn't, is just a bad teacher

At least, where I studied

[spark marsh]

So only the surface of the sphere can be 2d, but the shape or object itself is still 3d. This can be applied to all 3d shapes. When you consider all points of the outside surface, they can only exist together in the original way in a 3d world.

[tribal flint]

The sphere is the surface

[cosmic valve]

The sphere is defined as the surface mathematically.

[cosmic valve]

You have to call the object a ball to pass.

Even though some people that argue with you about it don't do the same.

[spark marsh]

Imagine we have two points somewhere on this "sphere" 1 inch apart (on the 2d plane) If I ask you the distance between them, it can change depending on if it is a circle or if it is a sphere. This is the problem with your claims. If you consider it in 2d space, they are 1 inch apart. But if we imagine that object is "embedded in 3d" then one point may be on "the opposite side" of the sphere, and in actuality they might be a foot apart. This is why this cannot be a sphere. It is distorted so that we don't know where each point is. If I was holding this sphere in 3d space in my hands, I could tell you how far apart the points are. If we are referring to a "disk" I can tell you how far apart they are. But trying to represent a 3d sphere in 2d space does not lend enough information to know for sure. This is why you cannot fully and accurately graph a sphere in 2d without any form of distortion.

[tribal flint]

No, they may be on on the opposite sides of the sphere, which are defined as 1 inch apart, because it's a projection.

It's still 2d

[spark marsh]

Exactly, even if the points are meant to be on the other side, we don't know because it tries to accurately show a 3d object in 2d space.

[tribal flint]

No, it's a 2d object embedded in 3d space, projected onto another 2d object in 2d space

[spark marsh]

And based on if we represent it in 3d or 2d space, the distance changes significantly

[tribal flint]

The distance changing doesn't make it 3d

You can take a disk and stretch out the X axis

With a geometrical transformation

A flattened disk isn't suddenly 3d because it's different

But again, if you don't know enough about the subject, please learn.

[spark marsh]

Say I have 3 points, equally spread out on the sphere. The 3 points when the sphere is represented in 3d shows that when in 3d space the distance changing between the points on the sphere means the sphere covers 3 different axes.

[tribal flint]

It's only 2 axes

You can represent them with polar coordinates

Or latitude and longitude

If my location on earth were 3d, I would need 3 coordinates to know my location

[spark marsh]

you can, but just because you only need 2 numbers doesn't mean it's in 2d space

[tribal flint]

That is exactly what it means to be 2d

Because the numbers are in orthogonal directions from eachother

Latitude is 1 dimension, longitude is the other

[spark marsh]

you could use 2 number to represent 1 point on the surface of a 3d cube

[tribal flint]

On the surface, yes.

[spark marsh]

yeah, and a cube is 3d

[tribal flint]

And the surface of a cube is 2d

But as I said, this isn't the topic of the forum post.

So if you want to learn more, do that somewhere else

[normal current]

This is a better topic than the original

[timid loom]

So true

I just got here and am enjoying the discussion lol

[tribal flint]

If I didn't agree, I wouldn't get sucked into the vortex over and over xD

[spark marsh]

The actual surface of a cube can be expressed in the same way that a 2d plane can be expressed. But the representation of that surface will be distorted from the shape the surface itself forms. The same goes for spheres.

[cosmic valve]

The crux lies in bad definitions. They define sphere as the surface and ball as the object (even though they don't have to follow that themselves with just slight descriptive words to differentiate). They hold you accountable for calling a ball a sphere as a common description of a ball. All this while not doing it to any other object. So saying cube and square means the same thing while saying sphere and ball interchangeably is wrong (even though they don't have to follow that themselves with just slight descriptive words to differentiate).

[tribal flint]

In fact, there should be more words for these other distinctions.

[twilit shore]

The issue is trying to apply your everyday knowledge of English to a field where the definitions are already rigorously defined

[cosmic valve]

I agree. Lots would be gained by a single defining word such as surface. Like the surface of a ball or surface of a sphere or surface of a cube or surface of a cylinder.

[twilit shore]

No mathematician is ever confused by this

[cosmic valve]

No, the issue is that people were using the word sphere as common language and mathematical definition was imposed upon the conversation.

[tribal flint]

Definitely not, the conversation was about infinity in the context of abstract mathematics

[spark marsh]

So if you would like to define a sphere as "only the surface of a ball with no thickness or shape" then yes, a "sphere" is 2d. Congratulations. If you use the normal definition of a sphere, or even just the surface, a 3d object is formed.

[tribal flint]

That is the only reason why I added the footnotes for accuracy's sake

[tribal flint]

Well yeah, that's the mathematical definition

sort of

So you do understand, that's good

[spark marsh]

I understand that by redefining sphere into "a 2d object" that your new definition og sphere = a 2d object, yes.

[tribal flint]

It's been that for a while

But now at least we've moved from not understanding to being stubborn.

That's progress

[spark marsh]

At the same time, I understand that the common, accurate definition of sphere, makes it a 3d object.

[twilit shore]

Well no, you can have a drawing of a sphere that's 2d

[spark marsh]

The moral of the story is you can get anywhere with a false premise (sphere = 2d object)

[twilit shore]

You can have something "spherical" which isn't any physical shape cause it's an adjective which has no dimensions

[spark marsh]

I hope you're being ironic rn

[tribal flint]

Being stubborn again

Come on, that's unnecessary

[spark marsh]

Being stubborn about the truth is a positive quality

[twilit shore]

Could also be a verb which I just looked up. Maybe that's what a 1d time sphere is

[tribal flint]

Just stop embarrassing yourself

[spark marsh]

could be

What if, a sphere is actually a shoelace! Who knows? Maybe we're thinking about this the wrong way, fellas.

[normal current]

Does this make you feel smart?

[spark marsh]

It assures me I'm correct at least

[normal current]

https://en.wikipedia.org/wiki/N-sphere

[spark marsh]

We are talking about spheres not n-spheres
https://en.wikipedia.org/wiki/Sphere

[normal current]

ok

[spark marsh]

ok...

[quick nimbus]

So to summarise the last few days....spheres are 3-dimensional objects, but mathematicians prefer to think of them as being 2-dimensional.

[lean elbow]

It's only 3D because we need to a 3rd dimension to visualise it. Mathemetically it's perfectly described as a 2D object.

[spark marsh]

Almost; spheres are 3d objects, but hyperspheres (N-spheres) are 2d.

[tribal flint]

In the context of mathematics (like when arguing whether a theoretical circle contains an infinity) a sphere is a 2d object, embedded in 3d space, but outside of that context it doesn't really matter.

And the answer is yes, mathematically there's an (uncountably) infinite amount of points on a circle.

[cosmic valve]

Almost. A sphere is a technical mathematical definition as the mathematical surface of a completely round object, which itself is defined as a ball. This is a particular definition of a completely round object is separate from other objects.

If you say a cube is 2D because its is the surface of a block or a cylinder is 2D because its the surface of a rod, you would just be playing around.

[quick nimbus]

No. I'm not allowing mathematics to claim sole ownership of a commonly used word. That way madness lies.

[cosmic valve]

If you do, at least be consistent about it and stop playing around. 🤣

Although... take your ball and go home has a whole new meaning.

[quick nimbus]

That's not even true for all of mathematics. At best, it is a convention used by some mathematicians, but it is demonstrably ignored by many people in the field of mathematics.

What is 4/3 π r^3? It's the volume of a sphere. What is πr^2? It's the area of a circle.

I imagine that the mathematicians that try and claim that a sphere is 2d are the mathematicians that don't even get invited to mathematician's parties!

[cosmic valve]

https://www.youtube.com/watch?v=M5UXOwphsLk

[quick nimbus]

I mean, are we just going to collect examples of spheres being 3d? I feel like that game could go on for a while.

[cosmic valve]

A sphere that is HD is pretty wild.

[twilit shore]

1. God is infinite
2. Infinity doesn't exist
3. God doesn't exist

Rate my god disproof

[cosmic valve]

I looked up God is infinite (not an exhaustive search). I only found:

our Lord is vast in power and infinite in His understanding

God is able to accomplish infinitely more than we could ask

[lean elbow]

K, so updated Gostum God Disproof?...

1. God has some infinite capacities
2. Infinity doesn't exist
3. God's infinite capacities don't exist

[cosmic valve]

Do you mean the concept of infinity or infinity itself? Like there is no largest number?

[spark marsh]

Fixed:

1. God is infinite
2. Infinity doesn't exist in science or the natural world
3. God must be supernatural

[cosmic valve]

Infinity, by its very nature is unknown to exist or not. We cannot prove or disprove it. Counting infinitely, for example, cannot be tested with a temporary reality. We infer mathematical infinity by observing that numbers don't go away through division. That can't actually be proven infinitely with temporary reality as well. If temporary equipment can be maintained to divide infinity, we would still never be able to prove infinity unless it ended (disproving it). Thus proof of infinity is related to time.

[tribal flint]

It's just jargon, every field has that. So you have a problem with scientists using the word "theory" differently than most people?

[tribal flint]

That sounds like a phrase high school kids have to repeat, just like the quadratic equation.

[tribal flint]

I would even go further and say infinity hasn't been shown to exist in the natural world. The concept of a natural infinity seems unfalsifiable to me.

[quick nimbus]

I said they are not allowed "sole ownership" of words. I think academics can use words however they like when they are locked in rooms away from everyone else. They're just not allowed to force everyone else to change the way they use words just to suit them.

[fading mauve]

When religions fall so will the world

Or so most predicted ends of the world

Go

[lean elbow]

Shouldn’t we assume infinities don’t exist in the real world until we have proof that they do? (I’m not aware of any definitive proof beyond mathematics). Therefore premise 2 of the Gostum God Disproof is still valid?

[tribal flint]

Jargon isn't sole ownership.

[lofty kiln]

To summarise/my interpretation of what you are saying: 1) You want there to be something after you die, therefore you're happy to go along with something that tells you that is the case - that's an emotional reason to believe in something and in my experience, no amount of logic will disuade you from that position. Until you can accept that it's a possibility that there is nothing after death, then you won't be moved. 2) No scientific theory states the Big Bang came from 'nothing'. We have no way of knowing what came before, so we don't even address that question or pretend we have an answer. On the other end of the stick, you have no reason/evidence to believe that a God does or even can possibly exist. Again, it's just a nice happy thought that sits comfy with you, so you're happy to accept it.

[tribal flint]

Any claim has the burden of proof. Saying "Infinity doesn't exist" therefore has the burden of proof.

[lean elbow]

Yep, true.

[cosmic valve]

There is no definitive proof that mathematical infinity exists. Just like there is no definitive proof that we (through equipment) can count infinitely. To assume infinity doesn't exist is to assume time will stop in the real world. Infinity is tied to time, both for proof in mathematics and in the real world. Time is the real world factor that prevents infinity of being proven in mathematics. If time ever stops behaving like time, infinity doesn't exist. Theologically, that is a different question because our universe could end but time itself can have behavior as a macro question. The micro question posed by theology, in the natural world, is our own personal death. Assuming no infinity would assume that death is not not eternal. Which may or may not bring it back to the thread: Is paranormal research scientific?

[lean elbow]

Not sure why infinity is tied to time? Black holes may be infinitely dense points - that’s mass/volume - no time dimension.

[cosmic valve]

Because there is no proof of infinity without infinite time (even mathematically). Saying infinity doesn't exist is like saying death is not eternal. At that point, it becomes theology. Like asking "shouldn't we assume death isn't eternal in the real world until we have proof that it is?"

[quick nimbus]

I agree. I don't understand why you're trying to argue with me about something we apparently agree on 😄

[valid gate]

Ok that just confused me even more. How can the surface of a 3d object be 2d? FOr it to wrap around the entierty of the 3d object it'd have to be 3d correct? Or is it just cause it only has say length and width but no thickness, thus removing the 3rd axis?

And here I though math was just logical reasoning :( Maybe since its abstract thats why I struggle with higher level math but excelled at stuff like Algebra.

[cosmic valve]

Mathematically, a 3d surface can be unwrapped and then projected onto 2D. Like the surface of a cube forming a cross, when unwrapped and projected onto 2D.

[valid gate]

Yea, when it is unwrapped it can be projected into 2D, even then that piece of paper isn't 3d as it has a thickness, even if it is extremely thin.

[cosmic valve]

Yes (you mean it isn't 2d), 2D is a theoretical mathematical plane. Like a line is theoretical 1D. 2D doesn't exist but it can be mathematically calculated upon. Length times width is the side of a building but it never considers the grain of the structure (its theoretical area for paint, for example).

[valid gate]

Ok got it

[cosmic valve]

The hardest part of 2D in the real world is selling a mathematician a little extra paint before they come back.

[normal current]

Abstract reasoning is, as someone else pointed out, something everyone does all the time, and I bet that if you found the explanation that clicked for you or had a great teacher you could learn some higher level math and surprise yourself

Math is cool

[cosmic valve]

Realism is also something everyone does all the time, unless its neglected because they are too encased with abstract thought. Balance with realism is required.

[cosmic valve]

Taking abstract thought and applying it in the real world knowing there are other factors involved brings math to a forefront in human progression opening all fields of science (except health science, as far as I know).

[valid gate]

Abstract thought isn't something I'm very good with in general, I mean I just base everything in reality because that's just how I think, everything I experience is in reality so I just find it hard to comprehend some abstract thoughts.

[cosmic valve]

Just come up with as many real world comparisons that you can. Like when you study derivatives, think about the function as the road, the 1st derivative as the direction the car is pointing, and the 2nd derivative as the steering wheel simplified (center, left or right). It helps ground what your learning and to define it more concretely.

Having a teacher in high school that passes down old school simplified observations like all end behavior of polynomials is X^2 or X^3 or the negative is helpful. It brushes off complexity when unneeded. That type of grounding is not extremely common within the mathematics field itself but other fields heavy in math can have some grounding.

This means that, unfortunately, you have to come up with most comparisons/observations on your own. Like algebra is just mental gymnastics moving an item to the other side as long as your using the right parallel bars, flips and cartwheels, etc.

Going to simplified observations after coming to personal comparisons is like a "roll your eyes" moment. When you hit those, you know your extremely grounded. For, example E=IR (Ohm's law) can be expressed as E over I R and you just cover what you are calculating. Its extremely simplified compared to being able to mentally gym E=IR.

[fierce furnace]

abstract when it comes to math is more like doing math stuff that doesn't really seem relevant to the real world, or things that we have never encounterd. Say talking about spaces with more than 3 dimensions, which is pretty weird and seems imposible to us.
But it is still first off all based on logic, you can't just do whatever you want in math, you have to prove it. And often those things can be found to have real life usage (after some time though), in unexpected areas...

[valid gate]

Yea I took Calculus 1 last semester, 1st semester of college, got a D in it. Literally every test the professor would right that I did all the algebra correct, it was only remembering specific derivitives and rules for calculus that I wasn't getting correct.

[lean elbow]

It's still amazing to me the extraordinary correlation between maths and reality - loads of examples where we've discovered maths hundreds of years before we find a deep connection to a new physics theory. What Wigner dubbed "the unreasonable effectiveness of mathematics" has prompted some very clever people to suggest that maths is actually more fundamental that reality (Max Tegmark is prob the highest profile proponent of this view).

[normal current]

You use E as the symbol for voltage? I haven’t seen that before, where are you from?

[cosmic valve]

E is technically old school electromotive force (voltage as opposed to modern EMF). Its an old school way of never forgetting the roots. Modernization marks it as either E or V, those that use E usually do so in acknowledgement of the past and technicality omitted in the formula during some applications. Such as Delta V (change in potential measured between two points, known as voltage drop) and a nod to Current Intensity (where I comes from).

[normal current]

Ohh yeah I have seen e for electromotive force

Just like a script e or soemthing so as not to confuse with electric field

[cosmic valve]

Its a lower case epsilon (ε).

But enlarged

[barren cape]

I dont want to mix myself into this discussion again, but medicine makes full use of abstract mathematics to predict real world outcomes

[cosmic valve]

Yes. That is why math is at the forefront of human progression. Other factors in medicine would be side effects of varying degree depending upon individual biological reaction and alternatives, diagnosis of differing symptoms for the same illness for statistics, etc.

Or are you referring to something else entirely? Not sure what you mean.

[cosmic valve]

Oh, I see you mean health science. Ya, that was a google result. If you want to go into a field that has no math, you can google that. Health science seemed specific. I had to google it because I couldn't think of any so I checked. Apparently, google just called side jobs health science.