A Possible Objection to the Absurdity of Actualizing an Infinite Number of Things?

The Kalam Cosmological Argument

1. Everything that begins to exist has a cause.
2. The universe began to exist.
∴  The universe has a cause.

The second premise is well supported by modern cosmology. The Second Law of Thermodynamics, (accelerated) expansion of the universe, and the consensus upon age from background microwave radiation in the universe (13.77 billion years give or take a few).

But the argument has been both valid and sound for many years, not just since thermodynamics of the 19th century of cosmology of the 20th century.

Everything that begins to exist has a cause.

The first premise is affirmed by all of our experience (both casual and rigorous scientific study), and it undergirds rational inquiry. It is a restatement of the law of cause and effect, to deny the first premise is to say that sometimes the answer to the question, “Why?” is “Cause.” And that isn’t just due to not yet knowing or laziness, but because there actually is no reason. Further, if things happen for no reason, then why give reasons for anything? And in that case, why build logical cases and reason together? As Dr. William Lane Craig says, to believe that something comes from nothing is worse than magic; at least there is a magician and hat when the bunny appears.

The universe began to exist.

As for the second premise, modern cosmology indeed adds to its strength and appeal, but there is metaphysical support that transcends the particulars of cosmological physics.

If the universe doesn’t have a beginning, then it has an infinite past (consisting of an infinite number of meaningful time events, e.g. seconds). While infinity is a useful number in mathematics and helps us explain real world phenomena, an infinite amount of things cannot actually exist. If you don’t believe me, consider Hilbert’s Hotel. Further, a finite number plus another finite number can never equal infinity. In other words, you cannot count to infinity. You could start counting today and continue forever, and you’d never actually reach infinity. Now, you would get closer…and you would count extremely high, but 10^10^10^10^10 might be a number larger than any of us can conceive, but it is still infinitely far away from infinity.

The Paradox

I tried to find an objection to this metaphysical case; I couldn’t. But it did remind me of Zeno’s Paradox. While this paradox doesn’t actually refute the idea of the impossibility of an infinite number of past time events, here’s what might happen: if someone is familiar with the paradox but doesn’t understand how to explain it, this may lead that person to consider arguments regarding infinite things with a bit of wariness. To demonstrate that this isn’t just a math trick, I would like to resolve the paradox and show not only that it has an explanation, but that if the explanation required an infinite number of meaningful time events, then Hercules really never would pass the tortoise!

A simplified version of the paradox: if you want to move two meters at a speed of one meter per second, will you ever reach the two meter goal?

You see, before you move two meters, you must move half of that distance, one meter. And before you traverse the remaining meter, you must move half a meter. Before the remaining half, one quarter of a meter, and so forth…if you keep dividing, approaching an infinite number of divisions, you would never reach two meters! But, of course, you do reach the two meters. How does this happen?

First, let’s consider the math showing that this infinite series of halfway points does take you to two meters.

S = 1 + 12 + 14 + 18 + ...
12S = 12 + 14 + 18 + ...

S is the series of steps (continually halving the remaining distance). If you find half of S by halving each term (1 becomes 12 and so forth), you find that aside from the initial term (1) in S, the right side of both those lines are identical series. So if you subtract 12S from S, the answer is 1.

S - 12S = 1

We can then find the value of S (all of our steps, continually halving the remaining distance) by adding 12 S to itself.

S = 12S + 12S = 1 + 1 = 2

We do traverse the whole two meters, but it requires traversing a potentially infinite number of halfway points. How does this work?

The Missing Piece: Time

This is quite the paradox; if there are an infinite number of halves to cross, how could anyone have enough time to traverse/count them!? Ah, time. You are traveling at a velocity of one meter per second, so as we halve the distances, we must also halve the time required for that distance too.

Consider a similar series, but this time we won’t go quite to infinity:

S1 = 12 + 14 + 18 = 78

Now let’s rewrite this to be more generic by replacing the denominators with 2n:

S1 = 121 + 122 + 123 = 2n-12n = 78, n=3

Double check those numbers, because if this is true, it will continue for however long we keep running this sequence.

What we find is that no matter how many times we halve the distance (even for 10100100100 divisions), since we must also halve the time…and we will never reach two seconds. We get really close, but not quite there. As the number of divisions increase approaching infinity, the time required to traverse each becomes infinitesimally small (approaches zero) and thus it requires virtually zero time to cover a virtually infinite number of halves.1 In order to not cover the two meters, time would need to never reach two seconds, but time keeps rolling on; the two seconds pass, and the two meters along with them!

If we tried to actualize an infinite number of halves and go through and count them all at one second per half; that would be an actually infinite number of time events. We could never count all of them. But, this is impossible, so we need not worry about it.

Zeno’s Paradox (and this parallel example) doesn’t rebut the second premise, but a better understanding helps support it. This would indeed be a paradox if it tried to actualize an infinite number of time events…but instead we find that it is explainable because the infinite isn’t actualized, but if it were, one could never actually traverse the two meters. We do traverse the two meters, so an infinite isn’t actualized.

Conclusion

Given the impossibility of an infinite number of past time events, the second premise (he universe began to exist) enjoys firm support.


Footnotes:

1. Interesting…while considering this, I wondered how how much time or distance was meaningful in any way. You maybe be interested in planck time and planck length.

On Immigration Reform: Let’s Rise to the Challenge

Dear Republicans,

(Particularly those in federal office.)

Yesterday, President Obama signed two executive actions regarding how we treat illegal aliens. Here is the press release on the President’s Immigration Accountability Executive Actions; also, he outlined his plan in a public address Thursday night.

The uproar in response has been loud. Whether it’s Republican pundits (e.g. Limbaugh and Hannity) or elected officials (e.g. Rand Paul and John Boehner), the response by many is that Obama is “declaring war on the Constitution”, that he is “damaging the presidency itself”, and that he is bypassing Congress. While I don’t think Obama’s action is particularly out of line with historic actions, being a small government libertarian/conservative, I’m not a fan. But given our current context, his statements and actions are not very upsetting to me.

(Aside: I’m a registered Republican and a committee member in my town. I’ve directly volunteered for Republican candidates at both local and federal levels. But I’m not a party man. I often fantasize about seeing changes that would empower third parties and hopefully break up this two-party system, but that’s a pipe dream, so I do my best to work within this broken system. You see, I’m interested in politics for several reasons—mostly because I believe that liberty is important, that the citizenry must be challenged and responsible, and that government has serious responsibilities and the ability to effect change with stunning repercussions. This isn’t a game to me. In fact, I very much dislike, though I understand, the game aspect of politics; it physically sickens me. I hope that you, my party, will both take noble stands and embrace enough pragmatism to be helpful to the best principles and, ultimately, helpful to real people.)

Pardon my blunt statements, but I think efficiency and passion are needed: do you think I’m an idiot? While many of you blabber about Obama and his very possibly inappropriate (but needed) actions, you do nothing! Our immigration issues aren’t new. Do you think I’ll forget the past fifteen years? In fact, one of the first times I became genuinely upset with our system and President Bush particularly was when I realized he wasn’t genuinely interested in solving our immigration problems or defending America via our southern border. It’s not like we (Republicans) didn’t have the executive and both legislative chambers for six years at the beginning of this millennium. How could I forget this?

Yes, I’m upset about this immigration issue, quite upset. But not with President Obama (at the moment). I’m upset that we’ve had a massive immigration problem for well over a decade and nothing substantial has been done about it! There are many people to blame including our current president at times, but I lay the majority of the blame on my own party, the Republicans. Not only did we have a governing majority for the bulk of the Bush years, but more recently an opportunity came in the form of a bill passed in the Senate with Republican sponsors (including Graham and Rubio). Was it a perfect bill? No. I’m not even sure what a perfect bill would be. But it was a big step. Not only did the House Republicans not pass their own version, but they failed to even bring this vote up for a yes/no vote.

Republicans: if we don’t want Obama’s executive actions, let’s actually pass a bill! A bill would clearly override and make obsolete anything Obama’s stated thus far. Not only is this true, but Obama openly welcomes such action. Further, I think Obama genuinely craves such action. He has humbly but strongly requested such action. Just listen to his speech Thursday with an open mind. Here’s an excerpt:

And to those Members of Congress who question my authority to make our immigration system work better, or question the wisdom of me acting where Congress has failed, I have one answer: Pass a bill. I want to work with both parties to pass a more permanent legislative solution.

And to those who reply, “He’s just saying that for political points.” Three thoughts:

  1. Stop sounding like the little boy who just was scored upon in two-hand-touch football and is trying to overturn it via technicalities. Grow up and score on your opponent like adults!
  2. Further, last year he supported a bipartisan bill that passed in the senate. Meaning, he isn’t all talk, he has actually supported real congressional action.
  3. And lastly, maybe he is, but then let’s call his bluff. As of this January we will have majorities in both chambers of Congress. Let’s pass something meaningful and see what Obama does. If he’s bluffing, it will not play well for his party come 2016.

This is more than just a rant, I hope. This is a meaningful challenge to those in my party who’re stuck playing games, who talk loudly but do nothing (and for many years now). Please, let’s do something. I believe the vast majority of our elected officials (from both parties) are intelligent men and women who want to govern well. I know we have different ideologies (even within our party) which make passing effective legislation difficult at times, but this is a real problem that must be dealt with in a timely manner. America needs meaningful immigration reform (and we can’t sit back, the President’s actions don’t solve this issue in the long-term). Do something, please. Stop complaining about the fact that Obama wants to actually solve this problem and resolve to be helpful yourselves.

The next step is action, not anti-Obama action but meaningful immigration reform. Let’s rise to the challenge!

Feminism the Label

Dear feminists,

I’m not very clever and rarely anything other than straightforward, so let me begin by saying I don’t identify as a feminist and I never have. That said, some of you are good friends of mine. And I have purposed (and continue to do so) to better understand feminism both today and historically, and related issues that feminists care about. This is because feminism is a significant movement and because many of these issues are issues about which I also passionately care (e.g. sexual violence and objectification).

I’m writing today because I hope to shed some light on a question I’ve heard several times: why aren’t there more feminists in America? According to a recent poll, only 20% of of Americans identify as feminists, but over 80% affirm the statement that men and women should be social, political, and economic equals. Put another way, I’ve heard some define feminism as broadly as the idea that “women are people too.” I don’t have a number on this one, but I’d put money on well over 95% of Americans affirming that statement.

So what’s the catch? Why do most Americans support feminism as defined but reject the label itself?

Feminism has a complicated history of multiple iterations (waves) and continues to exist in a variety of forms and sub-movements. (In short, I realize you’re not an entirely homogeneous group.) This history includes some proud moments and important victories, and, while no group of people is ever perfect, I’m thankful for the opportunities women have today in the United States. And I support efforts to improve the condition of all people and especially women around the globe. But this century plus history isn’t all beautiful, I’d posit that feminism has had its share of conspicuous and negative moments. But I don’t need to go back in history for an example, I just saw a video that was posted yesterday that may help us understand the public’s distance from the term.

http://www.FCKH8.com (F#*k hate, in case the name initially confused you.)

This is a group that supports goals commonly purported by self-identified feminists (ending racism and sexism and LGBT inequality). Their approach is a bit crude, and they’re making a point by it, I realize…still, it doesn’t sit super well for me, but whatever…until they released a video about 24 hours ago: little girls dropping f-bombs (and not feminism but f#*k).

It’s disturbing and saddening. And very, very unattractive. One of the numbers they cite has to do with sexual assault, an issue that is very significant to me. I have close friends who’ve been abused, and I have friends who’ve been assaulted. I have friends who’ve been perpetrators. This issue is truly tragic and we need to come together to solve these problems. Justice needs to be served, compassion and help extended. But this video??? This is not a solution. Feeding little girls vulgar lines only causes a myriad of further problems!

Again, I know that there are sub-movements within feminism, so I’m not holding all feminists responsible for this video (some of you are my friends, and I know you wouldn’t approve). By why would I support or take on a label that when defined is embraced by 80-95% of Americans (and me) while the label itself is only embraced by a few, and has supporters that create media like this?

Here’s the video if you’d like to see it. The content itself isn’t anything you might not see in an R-rated movie, but the context of little girls and the manner in which they speak is somewhat disturbing.

jamie

p.s. While not nearly as offensive, the use of that classic 23% wage gap figure is continually and excessively troubling. It’s so obviously false if you just think about it for a moment, and it’s been demonstrated many times. Hopefully all seekers of truth (feminist or not) will clear up the usage of this terribly misleading statistic which is regularly cited by many including our current president, Obama. Here’s one piece that explains it, but just use Google if you want more!

For I Shall Yet Praise Him

Three weeks ago, I was jubilant and couldn’t help but share my news. For over two years I’d had vocal fatigue, and God had touched me. My voice was clear and strong…but now I’m somewhat confused. I wouldn’t ordinarily bring others into my confusion, but since I’ve put this story out there for the world to see, I feel integrity compels me to share this publicly.

For a couple days my voice was different and better, and then it began to fatigue again. By Friday, April 11, four days later, I’d recognized this fact. But I wasn’t ready to deal with it.

Yesterday, I began thinking about this present reality.

You might wonder, why am I just beginning to deal with this now? Dealing with suffering is difficult enough, but on that particular day, Friday, April 11, I had no time because I was organizing and leading a group of thirty-five persons going to a conference down in Rochester, NY. I didn’t have time, I didn’t have spare emotional energy…

One of the convenient (and sometimes terrible) things about my personality is that I can just shove my emotions into a corner. Not in an attempt to be fake…but in an effort to stay sane and capable. This is never a good long-term solution, hence why I’m dealing with this now.

But before I left for the weekend, I wrote some thoughts in a journal. Here are excerpts from my entry on Friday, April 11.

God, I thought April 7 was one of the biggest days of my life thus far . . . I thought You healed me. I could feel Your presence. My voice felt good, and it sounded strong and clear. I testified; I overcame doubts and trusted completely. I took a bold step of faith and declared Your goodness to the congregation of saints.

That night I was so excited. I could still feel Your presence. I couldn’t sleep. So I came down, journaled. Posted the good news on Facebook . . . Initially, every notification was a reminder of Your goodness and grace.

But then, my voice began to fatigue again.

On Thursday, I began to realize my voice hasn’t been healed. I haven’t told anyone this revelation. It’s crushing. The weight of this fatigue, I’d become accustomed to carrying. Monday night when God touched me, I cried in joy and relief. Now, that same weight is back, but I feel as if it has fallen from a great height. I am crushed.

Oh God, what has happened!? Why did you let me think I was well if I wasn’t?

Thursday night and Friday morning, my head spun with many different possible explanations: Maybe God was trying to send me a message? Maybe He’d never touched me? Maybe it was all in my head? Maybe it was a bit of a “men as trees” healing? Maybe…? Maybe…? I’m convinced God did do something, and I’m still praying for healing, but I definitely don’t have all the answers.

I wouldn’t be surprised if there is a possible explanation that would fit and confirm whatever you want to believe. But, to be honest, it’s hard for me to even care at this point…because what I’d really like is to not be dealing with this vocal fatigue any longer. What happened these past three weeks would quickly become an odd dream if tomorrow I woke up fully healed.

Ah, I feel pathetic, knowing that there are people who deal with much graver suffering. But that doesn’t make mine any less real. I understand this may seem trivial to an outside observer, “So you can’t talk for long without getting a sore throat and losing vocal quality?” Yeah…but when you’ve been called to teach, counsel, preach, and sing, when these are some of your most significant callings, vocal fatigue is trying.

I confess, initially I felt a little betrayed, and I wrote that in one of my journal entries. But now, a few weeks later, as I reflect, I certainly know that God doesn’t owe me anything, so I’m unoffended. However, I am somewhat confused and very bummed, to put it mildly. But I’m doing my best to trust Jesus.

Actually, in my journal entry from that original Monday night, I clearly articulated that my praise and worship don’t hinge upon whether or not I’m healed. And this is another opportunity to walk in that truth.

Tonight Jesus healed me.

Oh thank you Lord!

It’s difficult to express how huge this was for me…however, as I was thinking excitedly about how awesome this will be, now having my voice, I was challenged: Jesus is no different today than He was yesterday. With or without a voice, I can praise Him. With or without a voice I can do everything to which He’s called me. I need not doubt that He is able when I’m not.

That said, having a voice is mad convenient, and I’m grateful! Thank you Jesus!

It’s painful to even read that entry; this is a difficult season for sure. The enemy is at the door, waiting to bring in fear, frustration, discouragement, and depression. But I choose to turn to Jesus.

I’m not a very personal guy, and if it weren’t for the fact that I’d already made this a very public thing on Facebook, I doubt I’d say anything to almost anyone. But I try to be honest, and I must make sure that public accounts are clear and true. But the last thing I want to do is somehow allow that which could greatly discourage me discourage others. So, I’ll leave you with Psalm Forty-Two; I love how it ends, “For I shall yet praise Him.”

Do I have questions? Yes. Is this wicked difficult? Yes. Is Jesus worthy of our affection, devotion, praise, and worship? Yes.

1 As the deer pants for the water brooks,
So pants my soul for You, O God.
2 My soul thirsts for God, for the living God.
When shall I come and appear before God?
3 My tears have been my food day and night,
While they continually say to me,
“Where is your God?”

4 When I remember these things,
I pour out my soul within me.
For I used to go with the multitude;
I went with them to the house of God,
With the voice of joy and praise,
With a multitude that kept a pilgrim feast.

5 Why are you cast down, O my soul?
And why are you disquieted within me?
Hope in God, for I shall yet praise Him
For the help of His countenance.

6 O my God, my soul is cast down within me;
Therefore I will remember You from the land of the Jordan,
And from the heights of Hermon,
From the Hill Mizar.
7 Deep calls unto deep at the noise of Your waterfalls;
All Your waves and billows have gone over me.
8 The Lord will command His lovingkindness in the daytime,
And in the night His song shall be with me—
A prayer to the God of my life.

9 I will say to God my Rock,
“Why have You forgotten me?
Why do I go mourning because of the oppression of the enemy?”
10 As with a breaking of my bones,
My enemies reproach me,
While they say to me all day long,
“Where is your God?”

11 Why are you cast down, O my soul?
And why are you disquieted within me?
Hope in God;
For I shall yet praise Him,
The help of my countenance and my God.

p.s. I’ve loved this song by Tim Hughes for many years (one of the first worship songs I learned to play on guitar several years ago).

§117 · April 28, 2014 · Miscellaneous ·

Why Do You Entertain such Futile Thoughts?

Note: this is an *entirely* fictional. An explanation.

My father, to keep his cool, was looking away from me and out the window. His speech paused for a moment as he inhaled deeply of his Cohiba Esplendido cigar, a high-end Cuban of which he was particularly fond. Personally, I don’t enjoy smoke nor the negative effects upon one’s health, but seeing that it lightened his dyspeptic mood, at that moment I was very thankful for the wonderful class of things resulting from tobacco use. As he exhaled, the smoke lingered for a moment but slowly began to rise; he continued. [Read the full post.]

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