Print

Please login or register.
1 Hour 1 Day 1 Week 1 Month Forever
Login with username, password and session length

[Draco18s]

The inner angles of a triangle must always add up to 180 by definition, for example

That is only because it is a requirement to even be a triangle.

A three sided shape that adds up to 180 degrees (because a line is being folded twice and connected) is a triangle.

You didn't understand my point. Allow me to reiterate.

...

NightWatchman suggested that it is possible for Pi to be equal to something other than Pi.

My point is that by definition a circle has one, and only one, relationship between the radius and circumference (Pi) of that circle. If you say that relationship is something else (Pi, as we know it, is something other than Pi), then it's not really a circle.

Like I wrote earlier, the same thing can be said of a triangle and the sum of the 3 inner angles.

So, while there are some constants which, in some other parallel universe,in theory, might have some other value..  I am suggesting that examples like those above can't change.

How can Pi be equal to anything other than Pi?  Curved space:
Here's an example of a triangle who's angles add to an impossible 270 degrees:

Start at Lat0, Long0.  Travel North until you're at Lat90, Long0.  Turn left 90 degrees.  Travel South until you're at Lat0, Long90.  Turn left 90 degrees.  Travel East until you return to your starting position, and turning left 90 degrees, complete the triangle.

90 + 90 + 90 = 270

You also traveled "perfectly strait" as far as you are aware from your reference frame.

Now, if all of space was curved such that it is not flat, you can get the same effect.

Now, a not-perfectly-flat universe has an absolute maximum size (as determined by the sphere it creates, though it is possible to have curves that do result in infinite size (eg negative curvature)).

[Deon]

Do you really enjoy trying to prove something using half-assed chat with a lot of flaws in your logic? I mean not the previous poster, but the whole crowd talking about "infinite space", parallel worlds et cetera.

[Devast]

Dudes.  Seriously.  Go read some Lovecraft and stop harshing our sci-fi mellow.  Like half of every Lovecraft story ever involved angles that JUST. WEREN'T. RIGHT.  Because it's, you know, scary.

Read The House of Leaves.Think a 1 room house with a door which leads down a 6m long hallway to the North and 2 windows on the east and west (.
Now imagine climbing out of the window and walking around the house, you'd expect to see the hallway right?.
Nope. and that is only the beginning. 

[Deon]

OF LEAVES? ELVEN HOUSE! Burn it with magma! We will not tolerate elven treachery!

[Innominate]

The universe is in all likelihood not infinite. Assuming the big bang theory is mostly correct, then we have a finite span of time and a finite (though variable) rate of expansion. Hence, at any point in time t < ∞ the volume must be finite. Sure, it will keep getting bigger faster than we'll be able to explore it (unless we somehow manage to exceed the speed of light reliably, which is unlikely), but it won't create new planets or anything as it goes along. Planets will continue to form and break apart from matter which already exists, and it will be very much finite. Now, big, yes, the universe will be very big. But very big is a different manner of beast from infinite.

But, moving away from big bang theory, we don't yet know the shape of the universe. It is possible that the universe is finite, infinite, bounded or unbounded in any of the four combinations thereof. Cosmologically, we're just getting started. We know the universe is expanding (at least from the light we've observed), that most - if not all - of the fundamental constants are the same (emissions spectra from stars billions of light years away are identical to those nearby) everywhere and that our local region appears isotropic and homogeneous. Beyond that... well, we're working on it.

[sir monko]

there is a theory i find way more interesting than possible dwarf fortress instance-planets in an infinite universe.

namely: lets assume there is only one real universe. sooner or later intelligence comes around, and gets intelligent enough to create simulations. the chance of "our reality" being that one real universe is pretty slim. the probability of us being nothing but an instance of a DF-like game, played by some bored teenage alien, is infinitley higher.

therefore, DF is exaclty as real as our own reality. QED.

[Sizik]

The inner angles of a triangle must always add up to 180 by definition, for example

That is only because it is a requirement to even be a triangle.

A three sided shape that adds up to 180 degrees (because a line is being folded twice and connected) is a triangle.

You didn't understand my point. Allow me to reiterate.

...

NightWatchman suggested that it is possible for Pi to be equal to something other than Pi.

My point is that by definition a circle has one, and only one, relationship between the radius and circumference (Pi) of that circle. If you say that relationship is something else (Pi, as we know it, is something other than Pi), then it's not really a circle.

Like I wrote earlier, the same thing can be said of a triangle and the sum of the 3 inner angles.

So, while there are some constants which, in some other parallel universe,in theory, might have some other value..  I am suggesting that examples like those above can't change.

How can Pi be equal to anything other than Pi?  Curved space:
Here's an example of a triangle who's angles add to an impossible 270 degrees:

Start at Lat0, Long0.  Travel North until you're at Lat90, Long0.  Turn left 90 degrees.  Travel South until you're at Lat0, Long90.  Turn left 90 degrees.  Travel East until you return to your starting position, and turning left 90 degrees, complete the triangle.

90 + 90 + 90 = 270

You also traveled "perfectly strait" as far as you are aware from your reference frame.

Now, if all of space was curved such that it is not flat, you can get the same effect.

Now, a not-perfectly-flat universe has an absolute maximum size (as determined by the sphere it creates, though it is possible to have curves that do result in infinite size (eg negative curvature)).

Space being curved still doesn't change the value of pi.

[Draco18s]

How can Pi be equal to anything other than Pi?  Curved space:
Here's an example of a triangle who's angles add to an impossible 270 degrees:

Start at Lat0, Long0.  Travel North until you're at Lat90, Long0.  Turn left 90 degrees.  Travel South until you're at Lat0, Long90.  Turn left 90 degrees.  Travel East until you return to your starting position, and turning left 90 degrees, complete the triangle.

90 + 90 + 90 = 270

You also traveled "perfectly strait" as far as you are aware from your reference frame.

Now, if all of space was curved such that it is not flat, you can get the same effect.

Now, a not-perfectly-flat universe has an absolute maximum size (as determined by the sphere it creates, though it is possible to have curves that do result in infinite size (eg negative curvature)).

Space being curved still doesn't change the value of pi.

From an observer in curved space, Pi would appear to have a value that is not 3.1415...
Proof:

Pi or π is a mathematical constant whose value is the ratio of any circle's circumference to its diameter in Euclidean space; this is the same value as the ratio of a circle's area to the square of its radius.

Note the bolded phrase.  Outside of Euclidean space (aka flat universe or flat space) Pi's value is not the same as it is in Euclidean space.  If a circle only has 270 degrees going all the way around (space highly curved such that in flat space, the arc is only 270 degrees) then Pi in that space is 3/4 the value of Pi in flat space.

Example:
Draw a circle along the surface of a cube, such that the center of the circle is on the very corner of the cube.  You will have 3 90 degree arcs that to a 2 dimensional observer would be a full circle.  Thus, I created a circle in non-Euclidean space that has a circumference:radius ratio which is not Pi, but is in fact 2.35619...

[Kishmond]

C'mon guys. I answered the thread in the second post.

[Sizik]

From an observer in curved space, Pi would appear to have a value that is not 3.1415...
Proof:

Pi or π is a mathematical constant whose value is the ratio of any circle's circumference to its diameter in Euclidean space; this is the same value as the ratio of a circle's area to the square of its radius.

Note the bolded phrase.  Outside of Euclidean space (aka flat universe or flat space) Pi's value is not the same as it is in Euclidean space.  If a circle only has 270 degrees going all the way around (space highly curved such that in flat space, the arc is only 270 degrees) then Pi in that space is 3/4 the value of Pi in flat space.

Example:
Draw a circle along the surface of a cube, such that the center of the circle is on the very corner of the cube.  You will have 3 90 degree arcs that to a 2 dimensional observer would be a full circle.  Thus, I created a circle in non-Euclidean space that has a circumference:radius ratio which is not Pi, but is in fact 2.35619...

A circle is a simple shape of Euclidean geometry consisting of those points in a plane which are equidistant from a given point called the centre.

If your circle is non-Euclidean, it's not a circle. Pi isn't defined by what we measure in the real world (anymore).

[dragnar]

there is a theory i find way more interesting than possible dwarf fortress instance-planets in an infinite universe.

namely: lets assume there is only one real universe. sooner or later intelligence comes around, and gets intelligent enough to create simulations. the chance of "our reality" being that one real universe is pretty slim. the probability of us being nothing but an instance of a DF-like game, played by some bored teenage alien, is infinitley higher.

therefore, DF is exaclty as real as our own reality. QED.

The only flaw in this theory is that it assumes that it is possible to simulate an entire universe using a computer smaller than the universe.
If this is possible, then a computer can have infinite processing power by simulating a computer more powerful than itself, which then simulates a computer larger than itself... until you have a computer powerful enough to solve anything instantly. You could produce infinite data in a finite period of time.

[Draco18s]

From an observer in curved space, Pi would appear to have a value that is not 3.1415...
Proof:

Pi or π is a mathematical constant whose value is the ratio of any circle's circumference to its diameter in Euclidean space; this is the same value as the ratio of a circle's area to the square of its radius.

Note the bolded phrase.  Outside of Euclidean space (aka flat universe or flat space) Pi's value is not the same as it is in Euclidean space.  If a circle only has 270 degrees going all the way around (space highly curved such that in flat space, the arc is only 270 degrees) then Pi in that space is 3/4 the value of Pi in flat space.

Example:
Draw a circle along the surface of a cube, such that the center of the circle is on the very corner of the cube.  You will have 3 90 degree arcs that to a 2 dimensional observer would be a full circle.  Thus, I created a circle in non-Euclidean space that has a circumference:radius ratio which is not Pi, but is in fact 2.35619...

A circle is a simple shape of Euclidean geometry consisting of those points in a plane which are equidistant from a given point called the centre.

If your circle is non-Euclidean, it's not a circle. Pi isn't defined by what we measure in the real world (anymore).

If space is non-Euclidean, then the only way to figure anything out is to use Euclidean geometry and 3D representations of 2D surfaces.  If the universe itself is curved there's no reference point.  Assuming that space is curved, a circle is in fact a circle, because all the points on the line are equidistant from the center.  Finding a nearer center may in fact be impossible.

Example: put a stake into the ground.  Attach a very long rope.  Holding the end, walk in a circle.  Where's the center of the circle you just walked?

[AtomicPaperclip]

Imagine if Pi was exactly 3, or Sound travelled 12 miles faster?

Pi can't be three, as it is defined to be the ratio of the circumference to the diameter of a circle in a Euclidean (flat) plane.

The speed of sound is dependent on the medium in which it travels. For example,

[it travels] about 4.3 times faster in water than in air at 20 degrees Celsius.

it could if we used a base of pi

[Lord Dakoth]

The universe is in all likelihood not infinite. Assuming the big bang theory is mostly correct, then we have a finite span of time and a finite (though variable) rate of expansion. Hence, at any point in time t < ∞ the volume must be finite. Sure, it will keep getting bigger faster than we'll be able to explore it (unless we somehow manage to exceed the speed of light reliably, which is unlikely), but it won't create new planets or anything as it goes along. Planets will continue to form and break apart from matter which already exists, and it will be very much finite. Now, big, yes, the universe will be very big. But very big is a different manner of beast from infinite.

If you restrict the definition of "the universe" to the area that contains planets, then of course the volume is finite. There doesn't need to be matter present for there to be spacetime. There just needs to be an observer.

However, if we can't see it, it might as well be infinite. The lack of an observer removes the restriction on the possibilities. The cat is either alive or dead.

Let us consider an "open" universe. Perhaps it truly is infinite, in every sense of the word. In that case, we cannot reach the end of space-time, even if we travel at an infinite speed. The box is closed, and the cat is again either alive or dead.

But what if the universe is finite? Unless we travel faster than light, we will never catch up with the "edge" of the universe. We could go for an infinite amount of time in any one direction, as long as our speed is less than c. Thus, the universe is infinite in the sense that we will never reach its edge, and it makes no real difference whether it is truly infinite or not. The cat is both alive and dead.

Let us say that we can travel at faster-than-light speed, and catch up to the edge of the universe. Just say that we try to "pass" this point of expansion. What happens? Does our spacecraft refuse to maintain its speed? Do we pop out of existence as we transcend the limits of the universe? If we do, then there is no longer an observer, and the edge of the universe is unreachable, and therefore again infinite. The cat is dead, but is magically resurrected as soon as we peek in the box.

But what if we "pass" the edge of the universe, and do not pop out of existence? Where are we? Past the point of creation? No, rather we have created a new portion of the universe, simply by observing it. By being at that specific point, we have expanded the possibilities and created more universe. But what's that in front of us? If we speed up a little more, we can reach MORE universe! We could increase our speed without bound, and as long as we still are, the universe is infinite, unless we can somehow escape the confines of dimensionality. The cat is neither alive nor dead, and not both, but suspended in a sort of limbo.

However, if there is no observer, the restrictions on probability are removed. Adding a self-aware consciousness to the picture is essentially assigning bounds to an integral. If there is no observer, anything is possible. Thus, the only way that we can prove that there is a finite universe is if we are simultaneously aware of each and every point within it, which would require for us to be present everywhere.

Oh, by the way, I just looked in the box, and realized that you forgot to put the cat in.

[sir monko]

The only flaw in this theory is that it assumes that it is possible to simulate an entire universe using a computer smaller than the universe.

why make the computer smaller than the universe? make it bitter! after all, it's not our (simulated) universe, this computer is in, but the one one level higher.

okay, let me rephrase:

therefore, DF is exaclty as real as our own reality, just a bit less complex.[/quite]

the size and complexity of the simulation is bound by the capability of the computer it runs on. but does that matter?

is our universe infinite? no. it's just a damn good simulation that makes us think it is (at least in some aspects).

you, dear sir dragnar, are an object with some properties (e.g. position 3d-vector, including rounding errors, ask heisenberg) and methods, and you'll probably get garbage collected (sorry!) some time. you may experience the universe as infinite the same way a dwarf is unable to understand the borders and restrictions of his map: "what do you mean with: 'go over there'? of course you can't cross the inivisble map-border! it's just not possible. never was. never will be. fundamental law of physics!".
though obscure dwarven religions do have a concept of the space out there, called "7th hell of buffer overflow", when their prophet once glimpsed a BSOD for a splitsecond.