No Beginning? How Did We Ever Arrive Here Then?

[ERayR]

ERayR,

 

Just a little thought experiment.

 

Are there an infinite number of points in a circle?  Can you measure it's length?

 

Just to let you know, I am a professor of mathematics at BYU.  I've spent a good part of my life working with infinite sets.

 

We measure infinite sets all the time.  Some infinite sets have lengths (like circles) and some do not (a straight line in Euclidean space).  There are even ways to measure the difference between sizes of infinite sets (such as I linked to above).

 

Now you are correct that the formal mathematical definition of "infinite" (which just means "not finite", or in bijection with a natural number) is different than the philosophical concept of "infinity" given in the dictionary you quoted above.  However, mathematical tools are an excellent resource for trying to understand the universe, which is where the idea of the infinite originates in the first place.  It makes a lot more sense to try to model our understanding of infinity and the universe using mathematics, rather than an abstract philosophical definition of the infinite which is ipso facto the only understanding of infinity we can use.

 

Are BYU professors any different than the professors from other colleges and universities?   

 

When discussing a concept it always helps to have all participants working from the same definition.  

 

In your circle example you are not measuring infinity you are simply circumnavigating the same circle an infinite number of times.  The circle can be measured the circumnavigation of that circle is infinite.

[ERayR]

A lot of professional mathematicians (including myself) disagree.  But I guess you are more qualified to declare what makes "no...mathematical sense".  

 

Again an example of not working from the same definition.  This is always a danger when one redefines terms.

[Zeta-Flux]

ERayR,

 

I think we agree on more than you realize.

 

 

 

The circle can be measured the circumnavigation of that circle is infinite.

 

Thus, a thing which is infinite in one way (via circumnavigation) is finite in another way (via length).  The time to perform the infinite circumnavigation is also finite.  There are many other measures available for infinite things.

 

In other words, one *can* measure some aspects of infinite sets, just not all of them.  These sets can have boundaries in some ways, and be unbounded in others (they are infinite after all).

 

So, to sum up, if you read my posts above carefully, I'm not saying mathematicians measure infinity (per se); I'm saying they measure collections of infinite sets against each other.

[Zeta-Flux]

Rob,

 

Here is a question to start getting us on the same page (and please, if you want to have a conversation, drop the "stupids", etc...).

 

Is the decimal expansion of the number pi=3.1415926535... infinite?

 

Cheers,

Pace

[MormonFreeThinker]

Are BYU professors any different than the professors from other colleges and universities? 

 

But you disagree with all the BYU Biology professors, right? 

[MormonFreeThinker]

Rob,

 

Here is a question to start getting us on the same page (and please, if you want to have a conversation, drop the "stupids", etc...).

 

Is the decimal expansion of the number pi=3.1415926535... infinite?

 

Cheers,

Pace

 

I believe that Calculus was inspired by God, Calculus deals with infinities, therefore infinities are not useless. 

Edited July 22, 2014 by MormonFreeThinker

[thesometimesaint]

Rob,

 

Here is a question to start getting us on the same page (and please, if you want to have a conversation, drop the "stupids", etc...).

 

Is the decimal expansion of the number pi=3.1415926535... infinite?

 

Cheers,

Pace

 

We don't know for sure but at over 12.1 trillion decimal places it's a pretty good guess.

[MormonFreeThinker]

We don't know for sure but at over 12.1 trillion decimal places it's a pretty good guess.

 

There is a number called Graham's number, it is a finite number, but it is so big that we cannot comprehend it. 

Graham's number is the biggest useful number in Mathematics. 

Rayo's number is the biggest number ever expressed in Mathematics. 

 

So even finite numbers are hard to imagine. 

Edited July 22, 2014 by MormonFreeThinker

[Rob Osborn]

Rob,

 

Here is a question to start getting us on the same page (and please, if you want to have a conversation, drop the "stupids", etc...).

 

Is the decimal expansion of the number pi=3.1415926535... infinite?

 

Cheers,

Pace

As far as we know it goes on forever.

[Rob Osborn]

So, to sum up, if you read my posts above carefully, I'm not saying mathematicians measure infinity (per se); I'm saying they measure collections of infinite sets against each other.

This right here seems to me to be the point of no return. How exactly does one "measure" collections of infinite sets against each other? You simply cannot "measure" something which is made up of parts that are endless in measurement.

[MormonFreeThinker]

This right here seems to me to be the point of no return. How exactly does one "measure" collections of infinite sets against each other? You simply cannot "measure" something which is made up of parts that are endless in measurement.

 

Do you believe that Calculus was inspired by God? 

[Rob Osborn]

Do you believe that Calculus was inspired by God?

All man or God is capable of is math with finite values.

There are no workable math equations where an infinite number is comprehended and used. That is impossible.

Edited July 22, 2014 by Rob Osborn

[MormonFreeThinker]

All man or God is capable of is math with finite values.

There are no workable math equations where an infinite number is comprehended and used. That is impossible.

 

I agree we cannot reach infinity, but you can use infinities in Calculus. 

1/2 + 1/4 + 1 / 8 ... to infinity = 1 

[Rob Osborn]

I agree we cannot reach infinity, but you can use infinities in Calculus. 

1/2 + 1/4 + 1 / 8 ... to infinity = 1

Its not exact though. To get to "1" you have to cheat. The fact is you never will equal "1" by adding that way.

[Rob Osborn]

A simple thought experiment if you will-

Suppose that you had an infinite set of real numbers on the right decimal side. and on the other side you had the natural numbers. Now, instead of looking at the numbers as their actual values we are just going to asign each one with the same eaxct black dot. So, now we have an infinite amount of dots on the right side of the decimal and we have an infinite amount of dots on the left side of the decimal. They all look like at this point just endless black dots that look exactly alike. On the one side you have an endless supply of them and on the other you also have an endless supply of them. Now we are going to pair them up. With logic we cannot ever show where we could ever pair all of them together because it would require and endless task of pairing them up. It could never be done- there is always just more of an endless supply of dots on either side. Even if it were possible to do it all at once you would still have the problem of noting that it is not comprehendable and untestable. What really are we measuring here then? When we try to take abstract numbers, on paper, by themselves, without applying it to real world scenerios it means nothing- it doesnt exist. Its only when we can apply it to tangible things that it makes sense and becomes real. The dots show that you can take abstract infinity symbols, turn them all into the same substance and show that two infinities of something cannot compete for overall size because there is no such thing as something endless having a value less than another thing which is also endless. Even with real numbers, no matter how many you ever came up with, no matter how many there were to ever exist, it is always possible to number all of them with a natural number.

[ERayR]

ERayR,

 

I think we agree on more than you realize.

 

 

Thus, a thing which is infinite in one way (via circumnavigation) is finite in another way (via length).  The time to perform the infinite circumnavigation is also finite.  There are many other measures available for infinite things.

 

In other words, one *can* measure some aspects of infinite sets, just not all of them.  These sets can have boundaries in some ways, and be unbounded in others (they are infinite after all).

 

So, to sum up, if you read my posts above carefully, I'm not saying mathematicians measure infinity (per se); I'm saying they measure collections of infinite sets against each other.

 

We measure the finite, that being the area of of the circle and the time to make one or a number of finite circumnavigations not the infinite number of circumnavigations.  What you are measuring is a finite set carved out of an infinite set.  You are conflating the part with the whole.  The part is not the whole.

 

You can circumscribe an area with a circle  You can then measure the area of the circle but you can not measure the line that circumscribes that area without assigning a beginning and ending point..  Measuring the area of the circle does not measure the line that circumscribes it.  You can measure that line by assigning a point on it to represent a beginning and an end but when you place a break on the line it is no longer infinite.  It has a beginning and an end which just happens to be the same point.  That brings up another problem, Is the length 0 or some other finite number.

[ERayR]

This right here seems to me to be the point of no return. How exactly does one "measure" collections of infinite sets against each other? You simply cannot "measure" something which is made up of parts that are endless in measurement.

 

See my post above #116.

[wenglund]

To LDS, their wedding and other rings may represent one eternal round (see HERE), though the size of their rings can yet be measured., 

 

Thanks, -Wade Englund-

Edited July 22, 2014 by wenglund

[ERayR]

To LDS, their wedding and other rings may represent one eternal round (see HERE), though the size of their rings can yet be measured., 

 

Thanks, -Wade Englund-

 

Only by changing the parameters and assigning finite characteristics to the object.

[Zeta-Flux]

We measure the finite, that being the area of of the circle and the time to make one or a number of finite circumnavigations not the infinite number of circumnavigations.  What you are measuring is a finite set carved out of an infinite set.  You are conflating the part with the whole.  The part is not the whole.

I'm going to try one more time.  (1) How many points are on the circle? (2) Am I measuring the number of points, or some other property that the specific configuration of points possesses?

[Zeta-Flux]

We don't know for sure but at over 12.1 trillion decimal places it's a pretty good guess.

 

As far as we know it goes on forever.

 

So, would it be correct to say that the finite number pi has properties which are infinite in nature?

 

(By the way, mathematicians have proven that pi will never stop, in case you were wondering.)

[Ahab]

I'm going to try one more time. (1) How many points are on the circle? (2) Am I measuring the number of points, or some other property that the specific configuration of points possesses?

You do understand that you can always make another point between any 2 points, don't you?

You could start measuring by counting the number of points but you'll never count all of them because there is an infinite number of them.

[ERayR]

You do understand that you can always make another point between any 2 points, don't you?

You could start measuring by counting the number of points but you'll never count all of them because there is an infinite number of them.

 

It appears to me that mathematicians cheat by changing the definitions.

[Zeta-Flux]

This right here seems to me to be the point of no return. How exactly does one "measure" collections of infinite sets against each other? You simply cannot "measure" something which is made up of parts that are endless in measurement.

 

Maybe it is the word "measure" which is throwing people off.  If I was given a ball, there are many things about it I could measure.  Its age, its weight, its volume, its electrical charge, the number of people who have touched it, the amount of hydrogen inside, etc...

 

Similarly, there are things which possess infinite properties but we can still measure other aspects of them.  For instance, the number pi possesses an infinite and unending decimal expansion, but the absolute value of the number is between 3 and 4, it is not rational (a fraction of integers), it satisfies some beautiful equations, etc...

 

Likewise, there is something called cardinality, which is an important measure given to infinite (and finite) sets.

[wenglund]

Only by changing the parameters and assigning finite characteristics to the object.

 

I see it as simply recognizing and accounting for the shared infinite and finite aspects of the same object--not unlike the infinitely divisible, yet finite space between where a philosopher is standing and the wall mentioned in the OP.

 

Thanks, -Wade Englund-