I have often been challenged by BT members and others to show some evidence to justify a belief in God, or, failing that, to explain why God does not manifest Himself in some tangible way, to us (or should it be we) humans?
Toward that end, The Group began a process a year or so ago to confront this challenge from a perspective which I believed at the time was a new approach. The Group sought to bring together a multi-disciplinary set of experts and to discuss issues, to present points to atheists for their comment and to publish the results in a book. The effort proved disastrous but not for the expected reasons and efforts to salvage A book have fallen through. But, as often happens with such disasters, an unexpected possible series of books may result from what we accomplished, at least some of the discussions we have boiled down and it is one of those ideas which I present here, in raw form.
I have hinted at it in another post Does P=NP? which so far has generated little interest.
In mathematics, the most basic concept is natural numbers (1, 2, 3, 4, 5, ...), and the most basic operation of mathematics is addition; 1+1=2, 2+4=6, 9+2=11, etc.
Adding single digit numbers is one of the first things children are taught in school and they learn it very early and very quickly. This is followed by adding two digit numbers which is also very easy and learned quickly.
A fun story is that when Gauss was a youngster he had a lazy math teacher who wished to occupy the students for some time by having them add the natural numbers 1 to 100. The teacher had hardly sat down when Gauss handed his paper in. The teacher, who had not previously worked out the answer could see that Carl was correct. What Carl did was to realize that there was a shortcut method of doing the task:
A + B = C
1 100 101
2 99 101
3 98 101
4 97 101
5 96 101
6 95 101
7 94 101
8 93 101
9 92 101
10 91 101
11 90 101
12 89 101
13 88 101
14 87 101
15 86 101
16 85 101
17 84 101
18 83 101
19 82 101
20 81 101
21 80 101
22 79 101
23 78 101
24 77 101
25 76 101
26 75 101
27 74 101
28 73 101
29 72 101
30 71 101
31 70 101
32 69 101
33 68 101
34 67 101
35 66 101
36 65 101
37 64 101
38 63 101
39 62 101
40 61 101
41 60 101
42 59 101
43 58 101
44 57 101
45 56 101
46 55 101
47 54 101
48 53 101
49 52 101
50 51 101
5050
Once the teacher saw that each sum was 100 and that there were 49 sums, it was obvious they added up to 5050
The point of this story is that math is highly logical.
So, suppose you had to sum the first 1000 natural numbers. You could do it the same way but the method reduces to a formula;
The Sum from 1 to n = n(n+1)/2
Which is written mathematically as
n
S n = n(n+1)/2
n=1
Try it for 10,000, or 567, or as large a number as your computer can handle and what do you get?
You get a POSITIVE natural number greater than one. What else could you possibly get since your inputs are all positive natural numbers starting with 1.
It even works for a google.
Let google = g
g(g+1)/2 =(g^2 + g)/2
Fantastic tool. Very mathematical. Very logical. Very comfortable.
EXCEPT, what happens if we go to infinity with the summation?
It turns out that :
infinity
S n = -1/12=-0.08333333333333000000*
n=1
*I am not sure if the value actually becomes zero or if Excel just stops computing at 14 decimal places.
So, how do we get a negative irrational number by adding an infinite number of positive natural numbers.
Is there a failure of logic?
Is there a failure of mathematics?
Or is there something about infinity which is inscrutable?
And, if infinity is inscrutable, and God is infinite, is it logical to assume that we can understand God?
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The Failure of Logic an Argument in Support of God
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- Dexter
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Re: The Failure of Logic an Argument in Support of God
There are definitely weird things that happen when you deal with infinity, but it's misleading to say the sum of that series is -1/12. I remember the video that this refers to:
https://plus.maths.org/content/infinity-or-just-112
Basically the "trick" is that for part of the "proof" they make the assumption that the series 1-1+1-1+1-1... = 1/2.
It is interesting that there are actually uses for this assumption, which is way over my head
https://plus.maths.org/content/infinity-or-just-112
Basically the "trick" is that for part of the "proof" they make the assumption that the series 1-1+1-1+1-1... = 1/2.
It is interesting that there are actually uses for this assumption, which is way over my head
- Interbane
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Re: The Failure of Logic an Argument in Support of God
All the math we deal with are the abstractions of real things. There are instances of the number 2, then there are the abstractions of those instances. We work with the abstractions. There is a structure to the abstractions just as there is a structure to the universe. But this doesn't mean the continuation of an abstract construct has a comparative instance. Are there infinite photons in the universe? Perhaps, but we can't know this. Does the universe extend infinitely in all directions? Perhaps, but we can't know this either. Is there an entity with infinite characteristics?Stahrwe wrote:And, if infinity is inscrutable, and God is infinite, is it logical to assume that we can understand God?
Just because we can imagine a thing through abstraction does not make a thing real. Even if the format in which you imagine it makes it inscrutable. In that case, you're simply removing the goalposts altogether, claiming that this thing exists, but it is inscrutable therefore we can't be expected to provide any support for its existence.
Is it possible? Sure, of course. But this line of reasoning gets us nowhere.
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- stahrwe
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Re: The Failure of Logic an Argument in Support of God
n=Infinity
Sum n = -1/12
n=1
where n are natural numbers.
Sum n = -1/12
n=1
where n are natural numbers.
- stahrwe
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Re: The Failure of Logic an Argument in Support of God
Interbane, in fact the line of reasoning demonstrates a clear problem dealing with infinite things, it can be extrapolated to God as I have postulated
n=Infinity
Sum n = -1/12
n=1
where n are natural numbers.
Sum n = -1/12
n=1
where n are natural numbers.
- ant
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Re: The Failure of Logic an Argument in Support of God
Provide evidence for string theory and 11 dimensions of space.All the math we deal with are the abstractions of real things
Make it real for us to see and interact with.
- Dexter
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Re: The Failure of Logic an Argument in Support of God
You best have "The Group" look into this if you're going to use it as an example. There was a lot of discussion about this among mathematicians after that Numberphile video got a lot of attention.
Here's a brief note about its use in physics:
http://www.sunclipse.org/?p=1352
I'm sure you can find lots of counterintuitive results involving infinity (I always liked Gabriel's Horn, which apparently is only an apparent paradox.) I'm not sure what it has to do with God though, just because you used the word "infinite" with God.
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Re: The Failure of Logic an Argument in Support of God
Looking at Gauss' method, seems like you need to know the exact end number to add up to for it to work. He knew he was adding from 1 to 100. As you say it even works with google, but an equation using that method would not work without a specific end number. Infinity is not a specific number so the equation breaks down. (What is infinity -1? What do you get when you divide infinity by 2? Infinity I s'pose.)
Try running your example below when you don't know what the specific value of B is. You can't.
A + B = C
1 100 101
2 99 101
etc.....
Try running your example below when you don't know what the specific value of B is. You can't.
A + B = C
1 100 101
2 99 101
etc.....
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Re: The Failure of Logic an Argument in Support of God
I don't see any argument which disproves the mathematics, or that addresses the implication that it is illogical to claim there is no evidence for God when it can he shown that it is highly probable the human mind would not understand the evidence of an infinite God.
As for the website's sparse jibes directed at the math
Second, the website formula quoted in the above box is not correct. It leaves out infinity. Even later in the article when the author in des the term forever, it is still wrong. The term 'forever' is not the same as 'infinite.'
Finally, there is only one thing which can be infinite and that would be God. The fact that a math series extended to infinity yields weird result may not prove that God exists but it certainly shows that many of the demands atheists make demonstrate a lack of understanding of the nature of God, which is not a surprise to me.
As for the website's sparse jibes directed at the math
First, it is not a glib assertion. It is based on fairly standard algebra but also has been proved many times using sophisticated methodology most of which is way outside the YouTube videos.
Today’s instalment (noticed by my friend Dr. SkySkull): the glib assertion going around that
1+2+3+4+5+⋯=−1/12.
Second, the website formula quoted in the above box is not correct. It leaves out infinity. Even later in the article when the author in des the term forever, it is still wrong. The term 'forever' is not the same as 'infinite.'
Finally, there is only one thing which can be infinite and that would be God. The fact that a math series extended to infinity yields weird result may not prove that God exists but it certainly shows that many of the demands atheists make demonstrate a lack of understanding of the nature of God, which is not a surprise to me.
n=Infinity
Sum n = -1/12
n=1
where n are natural numbers.
Sum n = -1/12
n=1
where n are natural numbers.
- Interbane
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Re: The Failure of Logic an Argument in Support of God
I was trying to clarify that there are two types of infinite things. There are abstractions of infinite things, then there are instances of infinite things. You're conflating the two it seems. Dealing with abstractions of infinity does not mean there are correlating instances of infinity.Stahrwe wrote:Interbane, in fact the line of reasoning demonstrates a clear problem dealing with infinite things, it can be extrapolated to God as I have postulated
For instance, we can play around with the concept of infinite time mathematically. But that doesn't necessarily mean time is infinite.
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