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/sci/ - Science & Math

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5891788 No.5891788 [Reply] [Original]

Is infinity symmetrical? It seems to me that it would have an infinite number of axes of symmetry, but I'm not sure if the question itself is valid in the first place.

>> No.5891809

>>5891788
What? I don't even really know where to begin with this question.

For one thing, how are you defining "infinity"? If it's just a number, well, what do you mean by "symmetrical"? If it's a geometric shape, say, an infinite 2d plane, then yes, any line you draw through that plane equally divides it in two.

>> No.5891813

>>5891788
not really. thinking of set theory for example, and subtracting infinity from infinity gives you .. well.. we don't really know whata it should give you. it's not really logical to say it's 0, and as mcuh as it's 0, it';s also 7, and 10 million. so, i would say, no it does not have any symmetric properties.

>> No.5891815

>>5891809

The main reason I'm asking is because I was wondering if we can say that our universe has an infinite number of axes, assuming it is flat and obviously, infinite.

So basically the question was, does an infinite 3D volume have an infinite number of symmetries, but you pretty much answered it, thanks.

>> No.5891820

>>5891813

But addition is not the same operation as geometrical rotation, is it?

>> No.5891826

depends on the infinite object

>> No.5891829

>>5891815
the universe is not infinite, at least in the 3 spatial dimensions

>> No.5891834

>>5891829

how do you know this?

>> No.5891837

>>5891834
big bang theory?

>> No.5891842

>>5891829

Are you referring to the Hubble volume? I've been taught in my cosmology course that according to current observations the curvature of space is so close to 1 we might as well take it to be 1.

>> No.5891844

>>5891837

dark energy is what?

>> No.5891848

>>5891837

According to BBT distances used to be smaller, but the universe has always been infinite. Look up the distinction between proper distance and comoving distance.

>> No.5891849

>>5891837

I'm betting it was a relatively local event.

>> No.5891850

>>5891848
explain to me how the universe went from 0 volume to infinite volume
the universe was thought to be infinite before the big bang theory

>> No.5891854

>>5891850

>explain to me how the universe went from 0 volume to infinite volume

It never had 0 volume to begin with.

>> No.5891858

>>5891854
well, we dont know that, but I like to think of the primordial universe as a point. Eventough I have never studied cosmology seriously so I might be wrong

>> No.5891867

>>5891788
Infinity is the measure of the size of certain sets, such as N, R, C, etc.

When you ask "is infinity symmetrical," it's impossible to answer such a question, as it is asking, in laymen's terms, if a measurement of distance is symmetrical. A more pertinent question would be to ask what types of infinite sets possess symmetry.
The Real Number Line is reflective around each point in it, so that possesses some element of symmetry. Another for instance: y = tan(x) is rotational symmetric.

It is of course possible to consider rotations of a circle -- it is technically infinitely symmetric by rotation.

>> No.5891868

>>5891858

>well, we dont know that, but I like to think of the primordial universe as a point

'A point' is a mathematical object, not a physical one, and has rather problematic properties (no size, no dimension - you can't just arbitrarily change the dimensionality of the universe when it's 'small enough'). It also runs contrary to the current theory - at Planck time (10^-44 s I think), corresponding to Planck volume, quantum gravity kicks in - and since we don't have a theory of quantum gravity it fucks up our predictions. But the universe still has a non-0 dimensionality at this point.

>> No.5891870

>>5891858
All real "points" are only approximately pointlike.

>> No.5891871

>>5891858
>but I like to think of the primordial universe as a point.

Well, you probably shouldn't.

If the universe is infinite (and it might well be), it doesn't make sense to talk about the "size" at all, obviously. But you can still talk about the density. And as t approaches 0, density approaches infinity.

>> No.5891872

>>5891867

>The Real Number Line is reflective around each point in it, so that possesses some element of symmetry.

Thanks. Can this be extended to a 3D volume? And do you know what type of symmetry it might have?

Sorry if I'm not making much sense, I've never had good intuition for mathematical infinity.

>> No.5891895

>>5891872
There sure is -- in an intuitive sense, think of a ball. You can rotate it horizontally, vertically, and also reflect the sphere about its axes. Since the operation is "closed" -- that is, rotating a ball will never make it not a ball -- you can define a transformation of the space which does preserves its original shape, and thus maintain its self-similarity. This naturally can be applied to n-dimensional sphere rotations.

There are other symmetry groups as well, some far more interesting than infinite examples. Frieze groups, for instance, are 2-dimensional sets which are only symmetric in one way -- by a glide (think of it as wallpaper that is symmetric in only one direction)

Some groups have several degrees of symmetry, depending on the constraints allowed. I haven't gotten to that in Algebra yet, so I'm not really one to talk about how they work

>> No.5891899

>>5891895
>>5891872

I should note -- these are the operations available to a sphere. A cube for instance will possess very different symmetric properties, as will all regular solids.

>> No.5891910

>>5891895

bahaha, I also meant that frieze groups are symmetrical in one dimension, not in "one way."

Summer has killed my math OTL

>> No.5891937

>>5891895

That makes more sense, thanks.

>> No.5891951
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5891951

Congratulations OP you're the 100th thread on this board today.

Everyone on /sci/ pitched in and got you a present, we hope you like it.
Go on, try it out

>> No.5892013

>>5891951

Why don't you just tell me what upset you so much, it might make you feel better.

>> No.5892125

>>5891815
Not necessarily. For example: every prime number after 1. Despite the fact that something is infinite doesn't mean it's infinite in every direction, nor does it mean that it resolves itself into a shape that could be considered symmetrical. It can, but it doesn't have to form that way.

>> No.5892610

Think of a line. Think of a circle.
Yes, infinity is symmetrical.

>> No.5893151

The infinity symbol is symmetrical

>> No.5893878

>>5892610
Lines are circles are not related to infinity.

>> No.5894756

>>5893878
Do you even geometry?