Infinity of a Different Size

[Polymath257]

All of it, every digit that is the number pi. Every single one of them to infinity

So one particular way to represent it? Why pick that way?

Of course its in my imagination, just like infinity

I don't know how many galaxies there are, thought the universe is thought to be finite, so is an infinite number of galaxies allowable in a finite volume?

It is unknown whether the universe is finite or not.

 

[Polymath257]

@Polymath257

Is it Possible to Imagine Infinity in Our Minds?

I think it explains my view far better than i can explain it myself...

For many of us, it’s easy to understand the concept of infinity, but we can’t comprehend how “big” or “never-ending” it is, because our perception of time always has a beginning and an end — minutes, days, years, lifespans.​

Meh. I don't see time as being a relevant factor here.

Yes, I find it easy to understand that there is no largest number. I find it easy to envision that the entire set of natural numbers is a completed whole. It is 'just there'. Some of its properties may not be entirely obvious at first glance (are there any odd perfect numbers? Is every even number more than 4 the sum of two primes?), but I don't think that is required to say I understand it.

And, like I said, I have far more difficulty imagining very large *finite* numbers and seeing how they differ from other very large finite numbers.

Numbers like Graham's number, or n(3) are so large that they overwhelm anything that represents anything in the observable universe. So, in that sense, they are at least as much a figment of our imaginations as aleph_0. And with aleph_0, I have the distinct advantage that it is clearly larger than any finite number and clearly smaller than the next larger cardinal.

Can I envision pi? Sure. it is a bit over 3. Just like the square root of 2 is a bit over 1.4. I can get better approximations if I want, or I can go to exact methods that describe pi or the square root of 2 exactly in terms of other operations.

Do I have to know what the 5 billionth decimal digit is for the expansion of pi to envision pi? I don't think so. I don't need to see all decimal digits in 1/3 to understand and envision 1/3. Decimals are just one possible way to represent numbers and are not always the best method.

 

[ChristineM]

So one particular way to represent it? Why pick that way?



It is unknown whether the universe is finite or not.

Because it goes on to infinity which i believe the brain is not equiped to handle.

Correct, which is why i phased my statement in that way

 

[ChristineM]

Meh. I don't see time as being a relevant factor here.

Yes, I find it easy to understand that there is no largest number. I find it easy to envision that the entire set of natural numbers is a completed whole. It is 'just there'. Some of its properties may not be entirely obvious at first glance (are there any odd perfect numbers? Is every even number more than 4 the sum of two primes?), but I don't think that is required to say I understand it.

And, like I said, I have far more difficulty imagining very large *finite* numbers and seeing how they differ from other very large finite numbers.

Numbers like Graham's number, or n(3) are so large that they overwhelm anything that represents anything in the observable universe. So, in that sense, they are at least as much a figment of our imaginations as aleph_0. And with aleph_0, I have the distinct advantage that it is clearly larger than any finite number and clearly smaller than the next larger cardinal.

Can I envision pi? Sure. it is a bit over 3. Just like the square root of 2 is a bit over 1.4. I can get better approximations if I want, or I can go to exact methods that describe pi or the square root of 2 exactly in terms of other operations.

Do I have to know what the 5 billionth decimal digit is for the expansion of pi to envision pi? I don't think so. I don't need to see all decimal digits in 1/3 to understand and envision 1/3. Decimals are just one possible way to represent numbers and are not always the best method.

We are talking infinity not finity.

 

[Polymath257]

We are talking infinity not finity.

Yes, and infinity is easier to comprehend, in many ways, than certain finite amounts.

Because it goes on to infinity which i believe the brain is not equiped to handle.

I see it as better equipped for infinite amounts than for some finite amounts.

Correct, which is why i phased my statement in that way

If the universe is finite in volume, then there would be only finitely many galaxies. If it is infinite in volume, then there would be infinitely many.

 

[ChristineM]

Yes, and infinity is easier to comprehend, in many ways, than certain finite amounts

Only to maths, not in reality

I see it as better equipped for infinite amounts than for some finite amounts.

Again, only in maths

If the universe is finite in volume, then there would be only finitely many galaxies. If it is infinite in volume, then there would be infinitely many.

Yes, a flat universe indicates an infinite universe. Although measured to be flat to 5 decimal places you yourself have said that curvature may occur after those 5 places. I can agree with that... Though it's only supposition. Can we assume the universe is infinite?

Hubble, and the bb model have a beginning to the universe, and finite rates of inflation indicating a finite universe.

A quandary, to which i see only one answer. Our universe is finite with the potential of inflating to infinity sometime in an infinitely distant future.

If inflating from finite to infinite makes any sense at all

 

[Polymath257]

Only to maths, not in reality

Again, only in maths

In order to describe physics, you need some aspect of infinity in the math.

To get to the fundamental theorem of calculus, which is fundamental in its applications to physics, you need the real numbers. And to get the real numbers, you need infinity.

Yes, a flat universe indicates an infinite universe. Although measured to be flat to 5 decimal places you yourself have said that curvature may occur after those 5 places. I can agree with that... Though it's only supposition. Can we assume the universe is infinite?

No. And neither can we assume it is finite.

Hubble, and the bb model have a beginning to the universe, and finite rates of inflation indicating a finite universe.

Not how it works. If it is currently infinite, it was infinite from the start. The finite rate of expansion also works in a spatially infinite universe.

A quandary, to which i see only one answer. Our universe is finite with the potential of inflating to infinity sometime in an infinitely distant future.

If inflating from finite to infinite makes any sense at all

And that isn't what would have happened. If space is infinite now, it was infinite for all times. It didn't expand from finite to infinite. It was simply always infinite and expanding.

 

[ChristineM]

In order to describe physics, you need some aspect of infinity in the math.

To get to the fundamental theorem of calculus, which is fundamental in its applications to physics, you need the real numbers. And to get the real numbers, you need infinity.



No. And neither can we assume it is finite.



Not how it works. If it is currently infinite, it was infinite from the start. The finite rate of expansion also works in a spatially infinite universe.



And that isn't what would have happened. If space is infinite now, it was infinite for all times. It didn't expand from finite to infinite. It was simply always infinite and expanding.

Correct, it is unknown.

Precisely how it is working.

You said universe, not space.

 

[Heyo]

Yes, a flat universe indicates an infinite universe. Although measured to be flat to 5 decimal places you yourself have said that curvature may occur after those 5 places. I can agree with that... Though it's only supposition. Can we assume the universe is infinite?

Thinking about a flat (=spacial infinite) universe gives me headaches. It would have so many implications. Either time would have to be separate from space or time would also have to be infinite. A local Big Bang in our neck of the woods would mean that there are possibly other Big Bangs beyond the horizon. Our universe could collide with another. The universe would have expanded into "empty" space (which we know isn't). We should have picked up spontaneously generated particle anti-particle pairs along the way. Could we measure that? So many aspects, so many questions.

 

[ChristineM]

Thinking about a flat (=spacial infinite) universe gives me headaches. It would have so many implications. Either time would have to be separate from space or time would also have to be infinite. A local Big Bang in our neck of the woods would mean that there are possibly other Big Bangs beyond the horizon. Our universe could collide with another. The universe would have expanded into "empty" space (which we know isn't). We should have picked up spontaneously generated particle anti-particle pairs along the way. Could we measure that? So many aspects, so many questions.

Andrei Linde et al have calculated 10^10^16 other universes out there that we could recognise as universes and close to twice that number that would be so strange we could no recognise them.

The hypothesis of how the BB occured that I favour is that of Laura Mersini-Houghton. There are 3 observations of oddities in our universe that indicate our universe is the result of a collision between other universe's that i find compelling. Her hypothesis is based on these phenomena

 

[Heyo]

Andrei Linde et al have calculated 10^10^16 other universes out there that we could recognise as universes and close to twice that number that would be so strange we could no recognise them.

In a multiverse model where the universes don't interact. This is different. We could collide with the universe next door any time.

The hypothesis of how the BB occured is that of Laura Mersini-Houghton. There are 3 observations of oddities in our universe that indicate our universe is the result of a collision between other universe's that i find compelling.

Again a multiverse model, but one with interaction.
And then there are the hyper(mem)brane models which propose that our local universe is the result of two branes colliding.
All very hypothetical and mathematical without measured (or sometimes measurable) phenomena.

 

[Revoltingest]

Picturing in the mind?
I can picture a cube. I can't picture a tesseract.

A possibility....
Consider extending a square (2 dimensional) into
a cube (3 dimensional space). Every infinitesimal
slice of the cube is a complete square.
Now, let's think of time as the 4th dimension.
The cube exists forward & backward in time.
Every infinitesimal slice of time has a complete cube.
We can't "see" backwards or forwards in time,
but we can imagine how it extends in time.

So I envision a tesseract as a really long cube,
wherein every slice is a complete cube.

 

[The Hammer]

Look up aphantasia.

Do you have aphantasia? That baffles my mind. I always see mental images. But I am also a very visual and auditory person.

 

[Polymath257]

Do you have aphantasia? That baffles my mind. I always see mental images. But I am also a very visual and auditory person.

I don't have a full blown case. But the most I ever get is vague outlines that fade almost immediately. Never color or texture. Most of my 'images' are more 'kinesthetic feel'.

The funny thing is that drawing helps me figure things out, but I can't do the picture 'in my mind'.