Mother’s Day was just a few weeks ago here in the US, and I’d like to focus on the process that results in biological motherhood: pregnancy. Stephanie Grey talked on Biola’s Think Biblically podcast back in January and mentioned the pro-abortion objection that since a mother isn’t legally obligated to give a sick child one of her kidneys, a mother shouldn’t be obligated to give the unborn child her uterus. Stephanie’s response was extremely insightful and one that I think will resonate with technical-minded people in particular. Let’s work through that today.
It was the trip of a lifetime.
We had enjoyed a gorgeous yet brutally hot day in Jerusalem and were now in the City of David located to the south of what is known as the Old City and the Temple Mount. Just to my right were the Kidron Valley and the Mount of Olives which sits to the east of the city. The Upper Room where Jesus and the disciples ate the Last Supper was a few hundred yards away up the hill to my left.
After leaving supper, Jesus’s group would have traveled from there to the Garden of Gethsemane, which is located somewhere on the Mount of Olives. Therefore, the most direct route would have taken them down the steep and rocky slope into the Kidron Valley just across from where I was standing. Only a hundred or so feet away, I saw some old stairs uncovered during the excavation of the City of David. These stairs were roughly dated to around the time of Christ and could have been used by the group to travel from the Upper Room to the garden on the night Jesus was betrayed.
The intersection of archeology and the Bible was the most fascinating and encouraging aspect of my trip to Israel – the land where the Bible comes alive. Our group visited many amazing sites while we were there. This site was underwhelming compared to many other locations; however, I was overwhelmed by the knowledge that Jesus may have walked those well-worn stairs. While there was nothing special about the ground or those stone steps, this place is where God and man came together—the natural and mundane met the supernatural.
Regrettably, after 4 1/2 years of new posts each week, circumstances have arisen that have made it more and more difficult to maintain that schedule. The rest of 2019 will likely be sporadic. I will continue trying to post when I can, and hope to bring some guest engineers on here, but the weekly writing by myself is not sustainable right now. This labor of love has been a 2nd half-time job for me on top of a very full-time engineering career. If you, dear reader, have been edified by anything I’ve written here, I thank God for that. If anything I’ve said has been in error, I take full responsibility, and ask your forgiveness. Since the posting schedule will most likely not be regular for the foreseeable future, if you would like to be notified when a new article is posted, you may subscribe by email on the website, like this page on Facebook, or follow it on Twitter. All accounts will remain active. In the absence of new content, there are still, at this point, 244 previous posts that may be of interest. The list of tags and the search box on the site are probably the best way to find particular content. If there is a topic you’d like to see addressed that hasn’t been yet, please contact me and let me know your thoughts. I will try to address any requests.
Take care, people, and don’t be afraid to work through tough questions about Christianity. I assure you, the toughest question you have, the most worrisome doubt you have, the most devastating objection you have – God can handle them all.
Yours in Christ,
On April 19, 1995, a truck bomb was detonated in front of the Alfred P Murrah federal building in Oklahoma City, Oklahoma. While it was an incredibly powerful bomb that did extensive damage to hundreds of buildings in a 16-block radius, there is one primary reason for the devastating partial collapse of the Murrah building. The front of the building, where the bomb was detonated, used what’s called transfer girders on the 3rd floor to support the columns for the upper six floors. They worked great for creating a more open entrance with ground-floor columns spaced at twice the distance of the columns on the 8 stories above, but they also decreased the number of load paths available for supporting the weight of the floors above. Therefore, when the truck bomb was detonated right next to a ground-floor column, shattering it and shearing through the columns on each side of it, 8 of the 10 bays of the building’s north facade were now unsupported. From the 3rd floor up, taking away that much support would’ve required eliminating 7 columns, but at the first 2 levels, it only took the destruction of 3 columns. This was a painful reminder that part of making a resilient building that can survive disasters is having redundancy, the ability to safely redistribute loads through alternate paths in the event of the loss of one load path. It’s what a lot of us engineers like to call a “belt and suspenders” design. As a Christian engineer, I have to ask, is my belief in God such that one crisis of doubt will destroy it, or is it more robust than that? I think you know the answer, but let’s work through that today.
In reading atheists’ stories of their deconversions from the Christian faith they had grown up espousing, I am struck by how precarious their trust (or faith) seems to have been. Atheists like Bart Ehrman, Dan Barker, and Matt Dillahunty have told of surprisingly small things making shipwreck of their souls. Whether it’s built on a particular emotional experience, or the teachings of a particular church or pastor, or some very shallow understanding of the Bible, they seem to often have a belief structure resembling a house of cards. Frustration with the hiddenness of God, a personal encounter with suffering, inability to fathom their omniscient Creator’s reasons – and the cards come tumbling down. Yet Christianity is anything but a house of cards. The basic belief in God is not built on one make-or-break proposition. Rather, we have a strong cumulative case based on multiple lines of reasoning. Most well-known among these are the Cosmological Argument, the Design Argument, the Moral Argument, and the Ontological Argument, although arguments from consciousness, miracles, religious experiences, beauty, and reason , just to name a few, have also been developed over the years in support of the existence of God. Different people often find particular lines of reasoning among these especially persuasive, and others not so much, hence my use of the term “argument” rather than “proof”. Proof can be very subjective, as anyone that’s ever had to sit through jury deliberations can confirm. But what’s fascinating is how many different supports there are for rational belief in God. Of course, like the many columns in a building, no single argument supports the entire “structure” of belief in God, but all of these different lines of reasoning, taken together, interlock well to provide a formidable framework highly resistant to collapse. While skeptics often seem to enjoy sniping at the views of others, the significant challenge for the skeptic is formulating a worldview of their own that explains so much of the world around us as well as Christianity does.
“But”, one might say, “you’re doing a bait-and-switch between the case for generic theism and the case for Christianity! Christianity has all its eggs in one basket – the Bible. So much for your redundancy!” Here’s the thing: while the Bible is conveniently bound in a single volume now, the writings contained therein were the result of multiple witnesses writing independently at different times and places. Though all inspired by God, they are separate historical records. And everything described in the Bible that has ever been able to be compared against archaeological findings has confirmed the truthfulness of the Bible. In particular, Luke, Paul’s companion and the author of the gospel according to Luke and the Acts of the Apostles, has been proven to be a historian accurate in even the most trivial details. So Christianity encompasses the general case for theism, which its strong philosophical support along several independent lines, as well as having strong historical attestation and archaeological support. In fact, I would say Christianity is the only system that answers so many questions coherently and is so well-grounded.
Now, for the Christian, our trust in Christ isn’t simply a matter of intellectual assent, but also a relationship with our living Creator. The Bible tells us that the Holy Spirit, the third person of the Trinity, dwells in each Christian, and testifies with our spirit that we are children of God [Ro 8:16]. This should be the single biggest contributor to an unshakeable faith, but we humans are often fickle creatures, prone to worry and doubt, falling far short of what God intends for us. To make matters worse, false religions have claimed similar certainty, such as the Mormon “burning in the bosom” that they genuinely believe to be authentic. Even though the existence of a counterfeit does nothing to refute the existence of the true original, it can still cause us to doubt the Spirit’s testimony in our own hearts. But this is where knowing that these different lines of reasoning all converge on the God of the Bible is helpful. While we typically use these apologetics tools to demonstrate to non-Christians the reasonableness of belief in God and trust in Christ alone, they can also help us to remember the truth ourselves in times of doubtful struggle (or encourage a struggling Christian brother or sister). That gives us multiple supports to lean on when we are weakened by attacks, whether from circumstances without or doubts within. Hence, apologetics helps us to build a resilient faith .
 See The Blackwell Companion to Natural Theology (Blackwell, 1st edition, 2012) for several of these. See C.S. Lewis, Miracles (Macmillan, 2nd edition, 1960), for his argument from miracles, as well as Craig Keener’s massive 2-volume work on the subject. Also see Chapter 4 of Lewis’ Miracles for his argument from reason, and Ch. 6 in Blackwell for Victor Reppert’s detailed defense of Lewis’ argument from reason and response to objections. Pascal’s “anthropological argument“, presented in chapter 10 of Christian Apologetics, by Doug Groothuis, is another contribution with significant explanatory power.
 Though not specifically quoted, much of this last paragraph is inspired by the ever-insightful William Lane Craig, and his excellent book Reasonable Faith, 3rd Ed. (Wheaton, IL: Crossway, 2008), pp. 43-51 .
As we just celebrated Mother’s Day, I saw an interesting response to a pro-life Twitter thread. The pro-life tweet had pointed out that the baby had separate DNA and was not part of the mother’s body, and therefore was a separate life that needed to be respected. An abortion supporter agreed that the baby was indeed a separate body, but then proceeded to say that abortion was still acceptable because the baby’s body was dependent on the mother’s body. Did she have a valid point? Let’s work through that today.
I was recently involved in a strange Twitter debate with an abortion supporter who argued that the fetus was a part of the mother. I suppose this was based on the silly “my body, my choice” mantra, but it surprised me that someone would actually consider that slogan a serious reason, particularly in this age of increasing medical knowledge. But despite all evidence to the contrary, she insisted on believing that abortion was a matter of “healthcare” for the mother because the mother was the only individual involved since the fetus was a part of her body. Abortion supporters have even tried saying that the baby was part of the mother’s body because of the umbilical cord (which only connects the two together to provide nourishment to the baby’s separate body). Sadly, this level of scientific ignorance is rampant in our culture, so let’s see what medical experts have to say. And, as always, don’t just take my word for it; do the research for yourself. Now, let’s get to work.
Does objective truth – and specifically objective moral truth – matter for Christians? In a survey of teenagers conducted by Barna Research on Feb 12, 2002, 83% of those teenagers said moral truth depends on the circumstances, and only 6% overall said moral truth is absolute. Of those who identified as born-again Christians, only 9% agreed that moral truth is unchanging and not relative to the situation. Those teenagers of 17 years ago are now the middle-aged backbone of our working society, as well as parents raising the next generation. But does that dim view of objective moral truth even matter in our time? Let’s work through that today.
The NY Times columnist Nicholas Kristof recently interviewed Serene Jones, President of Union Theological Seminary, in an op-ed entitled “Reverend, You Say the Virgin Birth Is ‘a Bizarre Claim’?” The responses, like the one referenced in his op-ed’s title, can only be described as bizarre to hear coming from someone claiming to be a Christian. But this is what is being held up as Christianity to a watching world in the pages of a major media outlet, so it warrants a response. I encourage you to click the link above to read the whole article for yourself. Then let’s work through some of the more glaring issues and see how this stacks up against actual Christianity.
As we have just celebrated Palm Sunday, and are looking forward to Easter next Sunday, I am reminded of the strong historical emphasis in the Bible. Why is that significant? Let’s work through that today.
Palm Sunday is the day Jesus rode into Jerusalem on a donkey while people honored Him like a king by putting their cloaks and palm branches in the road before Him [Mt 21:8]. Good Friday commemorates the day later that week that Jesus was crucified and buried [Jn 19:41-42]. Easter, or Resurrection Sunday, is the day He rose from the dead, accomplishing the mission He came here for [Mk 16:1-8]. Notice that these are all public, rather than private, events. For instance, when Moses beheld the burning bush in the desert, and heard God speaking to him from it, that was a private event; Moses was the only human there to tell what happened. However, God later confirmed that He was working through Moses via some very public events in Egypt in the form of the plagues He brought on the Egyptians. And while the Bible records a variety of private events like dreams and visions, it is interesting how often God points us back to public events that could be confirmed by multiple witnesses as testimony of His trustworthiness in the present and future. For instance, the apostle Paul refers to the Resurrection as having provided proof to all men that Jesus is the one chosen by God to judge the world [Ac 17:31]. And as Paul told King Agrippa at his trial, these things weren’t “done in a corner” [Ac 26:26]. Indeed, Paul writes to the Corinthian church listing the various witnesses of Christ, and mentions the fact that over 500 people saw Him at one time after His resurrection, many of whom were still alive at that time [1Co 15:3-8]; his readers could fact-check him if they wanted. The apostle John consistently refers to the fact that he and the other disciples had been present during Jesus’ life, and had witnessed His message and His miracles [Jn 19:34-35, 21:13-14, 1Jn 1:1-3]. Luke wasn’t a direct witness, but sought to compile a more orderly account of all the initial eyewitness reports of what happened [Lk 1:2-3], and noted that the witnesses had seen, heard, and touched Jesus after the Resurrection (i.e. Jesus was alive in the flesh and not simply a ghost or vision) [Lk 24:37-43]. And God Himself repeatedly pointed the Israelites back to the historical fact that He had miraculously rescued them out of Egypt [Ex 20:2, Lv 11:45, De 7:8, Am 2:10, etc]. In fact, He established a yearly ritual (the Feast of Unleavened Bread) to remind them of this Passover event [Ex 12:14, 25-27]. Later, when Joshua led them across the parted Jordan River, he had a monument erected with stones from the bottom of the river specifically to remind their descendants of what God had done for them in the past [Jos 4:6-7].
Why is the distinction between private and public events important? Private events depend on the truthfulness of the one recounting the event, while their account of a public event can be refuted by other witnesses if it doesn’t correspond with reality. For instance, Islam hinges on Mohammad actually being visited by an angel while he was alone in a cave. Mormonism depends on Joseph Smith actually being visited by an angel. Appealing to the actual occurrence of historical events is problematic for scammers (such as Smith’s supposed “Reformed Egyptian” that he tried claiming he had translated), but not for those telling the truth.
So, as we Christians have just celebrated one historic event and prepare to celebrate the turning point of all human history, I am grateful that God has established a public record to remind us of His actions throughout history. While there is revelation given to certain individuals directly in the Bible, God also often provided public signs and miracles to attest to the authenticity of their prophecies. We memorialize things with monuments so that we “never forget”, and God has likewise set up a string of historical events to serve as markers of His faithfulness – monuments to remind us lest we forget what God has done.
I was recently watching a series of classroom videos on Finite Element Analysis (FEA), and the professor mentioned that FEA is not a classical closed-form solution, but rather an iterative, open-form solution. What on earth does that mean, and how could it possibly relate to looking at the case for God? Let’s work through that this week.
First, let me give some background so you can maybe see why a nerd like me would make that connection. A closed-form solution, in this context, is where you can simply solve an equation to find the unknown variable. For instance, in my practice of structural engineering, the deflection of a cantilever beam may be something I need to know as I’m sizing the beam. If the beam conforms to certain assumptions like a constant cross section, constant material stiffness, a uniform load, and so forth, I have a simple equation: . If it’s a concentrated load at the end, there’s a slightly different equation. These equations are each derived from beam deflection theory for a specific boundary condition, like a cantilever, or a simple span beam, and they provide exact answers. We engineers like exact answers. It’s nice to be able to say “this beam will only deflect 1.21 inches under that load, which is still acceptable.” I like closed form solutions because they are directly solvable for the variable I’m looking for, but sometimes, even with tables of equations for dozens of different conditions, there are no closed-form solutions, or they are too complex to use, or it would take a while to derive the equation from scratch. An open-form solution like the approximation methods used in FEA is iterative and relies on the results of previous attempts. FEA models a component like a beam with lots of little pieces that can each respond differently, so I’m not quite as limited by simplifying assumptions. Think of a beam made out of lots of LEGO® bricks. Each brick (a “finite element”) is connected to multiple other bricks, and the total strength of the beam depends on the behavior of all of those individual connections. In general, the smaller the bricks, the more accurately you can represent the beam. But as the number of LEGO® bricks increases, the time to calculate all of those interconnections increases exponentially. That type of solution gets complex pretty quickly, and requires a computer for any problem worth solving. But it also doesn’t produce an exact solution. It iterates, or repeats the calculations with different input values until the successive estimates begins to converge. In other words, it runs through the thousands of equations over and over until the results aren’t changing much with each pass, and are within a tolerance the user sets for what is “close enough”. And what is “close enough”? That’s going to vary with the user and the type of problem being solved. Also, another engineer could try solving the exact same problem with a different mesh size (i.e. bigger or smaller LEGOs) and arrive at different results since it’s not just the beam properties that determine the answer now, but the modeling choices like mesh sizes, convergence tolerances, and iteration method. So why would I want to use a complicated, inexact, and sometimes difficult to verify process like that? FEA lets me solve things I couldn’t otherwise. Some problems get far outside the simplifying assumptions of our various formulas, and FEA (done correctly), is the best option for finding a solution, even if it isn’t exact.
Now, what if our search for “proof” of the existence of God is like that open-form calculation? I often read forum comments from skeptics wanting “proof” of God’s existence: an end-all silver bullet that would provide a 100% certain, undeniable answer. And until they get that 100% certainty, they refuse to believe. But that’s like wanting that exact, closed-form solution to some complex engineering problem for which there is no formula. Also, even if I had a nice formula for something, those “exact” answers are often based on simplifying assumptions, such that the “approximate” solution from my finite element model of a complex design may actually match up better with reality. If I held out for an exact solution, I might never get my answer even though maybe a minute of my computer working through Newton’s Method will get me close enough to finish designing that component and move on to the next task. Moreover, we don’t normally expect anywhere near 100% certainty about anything else in life. Most decisions in life are made with far more uncertainty because, whether we know it or not, we use a process called “abductive reasoning”, or “reasoning to the best inference,” to arrive at a reasonable answer in the face of uncertainty or missing information. In the case of the existence of God, there isn’t one knockdown argument that yields certainty for everyone, but there are a host of different arguments that all converge on the same answer: the world we observe is the result of intentional, purposeful, goal-oriented interaction best explained by the God revealed in the Bible. It’s a cumulative case that becomes more and more certain as we see more lines of evidence and reasoning trending toward the same result. And at some point, which varies from person to person, the convergence of the objective evidence gets within our subjective tolerance where we finally have to either accept where the evidence is leading and bow the knee to our Lord, or deny reason itself to maintain our rejection of Him.
If you’ve been a skeptic toward God, I encourage you to look at your expectations. Have you set an unreasonable standard? Let me ask you, if Christianity were true, would you believe it? If not, that should concern you. If you’d answer “Of course, but it’s not true,” think about what evidence you would accept. Don’t be content with “I just need more”, but seriously contemplate what your “convergence tolerance” is. What kind of evidence will you accept? How much is enough? Why do you discount some types of evidence, and are those really good reasons to do so? Will you gamble with your eternal soul over a 10% uncertainty? How about 1%? Or 0.01%? Interestingly, in FEA, a sufficiently accurate result for most structural problems can be had in seconds to minutes, while asking for more accurate approximations can make the solution time increase exponentially, requiring hours to days, and often with only marginal differences that don’t change the final design and don’t justify the extra time. Tomorrow’s not guaranteed for any of us, so don’t waste your life demanding the nth degree of proof when the evidence you’ve already seen is sufficient to know the truth and decide accordingly. As the Bible warns, “Today if you hear His voice, do not harden your hearts.” [Heb 4:7]