Argument For God From Differential Equations

No serious mathematical understanding, aptitude, or even interest is required to enjoy this post. There’s this cool thing that I think you’ll find interesting, but there is just a bit of mathematical throat clearing we need to get through up front.

Here’s an example of a differential equation (seriously, this isn’t on the test):

This differential equation describes a damped oscillator. Imagine a weight on a spring. Drop the weight, and it bounces up and down, but less each time until it comes to a stop. That motion is described by this equation.

Equation 2 is a simplified representation (the dots represent a derivative with respect to time):

Move some terms around for one last simplification:

Analog computers

Okay, now it gets interesting. Decades before the early room-sized electronic digital computers like ENIAC, there were analog computers. They solve differential equations like this one.

Analog computers are made from elements like integrators, multipliers, and adders (I leave as an exercise for the reader why integrators make much more sense than differentiators).

To solve the equation above, we first assume that we have ẍ.

Crazy, right? We just proceed blithely along after first assuming that we already have the second derivative of the thing we’re trying to find.

Stick with me and see how this turns out. First, integrate it twice (each integration removes a dot—that is, one derivative of time). The signal moves from left to right through two integrators:

Okay, we’re almost there. We use the analog computer to create the right side of equation 3:

Magic time!

And here’s the fun part. We’ve now computed the right side of equation 3. But wait a minute—that’s equal to ẍ ! So that bizarre, unfounded assumption—we just assume that we have what we don’t have—was actually justified. We feed that output back in as and we’re done. Here’s the final layout:

Augustine’s contribution to differential equations

Augustine (354–430CE) didn’t have much to say on this subject, but see if this sounds like our analog computer project: “Seek not to understand that you may believe, but believe that you may understand.”

Just believe. Don’t worry about it making any sense—understanding will come with time. It’s like solving a differential equation with an analog computer: assume the result, and you will be rewarded.

The problem, of course, is that it actually works with an analog computer. Every time. By contrast, “just believe” is terrible advice when evaluating a claim with poor evidence—Oz, fairies, leprechauns, the Force, and so on.

Begging the question, Christian style

We see a similar assumption of the conclusion with many responses to challenges against Christianity. For example, we see in the gospels just what we’d expect to see if the resurrection were true. Therefore, the Christian apologist says, the gospels are important evidence for the resurrection being true.

Or, take the order and beauty we see in the world. The apologist tells us that this is just what we’d expect if there were a god.

Take an analogous argument:

1. If space aliens caused car accidents, we’d see car accidents.

2. We do see car accidents.

3. Conclusion: we now have more evidence that space aliens cause car accidents.

Or (for a different kind of rationalization) take the Problem of Evil, the puzzle of why an all-good god allows so much bad in the world. An all-knowing god could have his reasons, couldn’t he? That you skeptics don’t understand is hardly surprising—your finite mind may just be incapable of understanding it from that god’s perspective.

In other words, assume the Christian position and rearrange evidence to support it rather than start with the evidence and then reach a conclusion.

Assuming the conclusion works great when solving differential equations, since we have evidence that it works. The opposite is true for supernatural claims.

 In a universe of electrons and selfish genes,
blind physical forces and genetic replication,
some people are going to get hurt,
other people are going to get lucky,
and you won’t find any rhyme or reason in it, nor any justice.
— Richard Dawkins

Photo credit: Ryan Rahn

About Bob Seidensticker
  • RichardSRussell

    It’s usually cited as part of the scientific method to posit (assume) that a proposition is true, then predict what its consequences should be, then test to see if those consequences do in fact occur.

    Omitted from this simplistic explanation is something that turns out to be very important in medicine, namely ruling out other possible causes of whatever you have observed.

    A good experiment should be constructed to test for only the variable you are interested in.

    • GubbaBumpkin

      To paraphrase one of my undergraduate instructors: Given a poorly understood phenomenon, a physicist would reduce the number of variables, a biologist would collect more data.

      This was intended as a joke, but the point is that a good experiment is bound by what is possible.

  • wtfwjtd

    I blindly assumed that Christianity was true for most of my adult life. And yet, like author Paul Beaumont discussed in this blog post, I never saw, in all that time, one thing that could even remotely be considered only of God:

    http://www.patheos.com/blogs/creativeatheist/2013/12/the-downsides-of-paradise-with-a-wink/

    We’re not alone in this–2,000 years of history by billions of people haven’t been able to come up with anything convincing, either. For a religion that depends on the supernatural as its founding principal, you’d think there would be SOMETHING that could be only attributed to a divine being in all that time (i.e., a verifiable miracle). I finally came to the only possible logical conclusion: No supernatural, NO Christianity. Since neither I, nor anyone I know, nor anyone from any time in history that I know of can demonstrate a verifiable, repeatable supernatural act, Christianity must be false. It’s a self-defeating religion, simply by being unable demonstrate its own claims in any meaningful or verifiable way.

    • http://www.patheos.com/blogs/crossexamined Bob Seidensticker

      Christianity must be false.

      My approach is a little different but reaches the same conclusion: the evidence doesn’t support the remarkable claims of Christianity, so we are obliged to act as if they aren’t true. If future evidence changes things, great, but at the moment, we have no warrant for believing Christianity.

      • wtfwjtd

        I’d say that you were approaching the question of Christianity’s veracity as one from the outside, whereas for me, being raised in a zealous Christian household, approached the question more from the inside. I never believed or accepted supernatural claims of other sources–ghosts, witches, spirits, or what have you–simply for lack of verifiable evidence. In fact, I was encouraged to be skeptical of these other-source supernatural claims, but was not permitted to apply the same skepticism to the Christian supernatural claims. Once I finally did, the last shred of belief that I held unraveled completely. I realized that, for Christianity to really be true, not only did the original supernatural story need to be verifiable–the whole Jesus story–but even more, Christianity’s claim that its followers, both past and present, are capable of producing “even greater” supernatural events at will, needed to be true and verifiable as well. What we see in reality isn’t even remotely close to this.

        • Pofarmer

          Hold on, hold on, are you saying that Catholic priests don’t really perform the miracle of transubstantiation every day?

        • wtfwjtd

          Ha ha, you got me, I’m convinced! No, wait a minute….

        • http://www.patheos.com/blogs/crossexamined Bob Seidensticker

          The problem I have is the definitive claim, Christianity is false. Hey, make it if you want to. I could certainly defend that claim myself. I’m only thinking that you make it harder than necessary, debate-wise.

          I’d prefer to force the Christian to shoulder his burden of proof.

        • wtfwjtd

          As a matter of a debating point, I can agree with your approach Bob. “Christianity is false” is more a statement of how I view the matter privately; when discussing the topic, especially with the religious, I prefer to state my position as “Christianity is just another man-made religion.” In my experience this has had a more unsettling effect, and takes a lot less effort for me to pin down.

        • MNb

          “I was encouraged to be skeptical of these other-source supernatural claims, but was not permitted to apply the same skepticism to the Christian supernatural claims.”
          Ah, that’s much better. Consistency is a virtue.

    • Pofarmer

      What about the blood of St. Januarius in Italy? the hand growing back of St. John Democene, What about the Eucharistic miracle of Lanciano. Believers are convinced that all these and others are real.

      • wtfwjtd

        Of course they are Pofarmer, they realize that without the supernatural in the form of miracles, their faith is useless. I mean, who wants to serve an ordinary god who does ordinary things in ordinary ways? Don’t expect folks to be beating down the door of the establishment that tries to sell that shtick…

        • http://www.patheos.com/blogs/crossexamined Bob Seidensticker

          “Brethren, I want to celebrate today the non-miracle of a rock rolling down hill.”

          I dunno–I kinda like the sound of that.

        • MNb

          Frankly I think it quite a miracle that that rock up to now always has been rolling downhill and never uphill. It’s not a miracle in the religious meaning of the word though.
          But you already know I think science awesome.

        • Pofarmer

          Ah, geez. Today they were pushing the “Lady of Guadalupe” myth at the boys Church. They had allready concluded it was bullshit, and the fact that they built the Church on top of an allready existing Aztec shrine pretty much sealed the opinion, plus some other little historical facts we’d gleaned from the intertubes. Damned information. I really can’t believe the Catholic Church is back to pushing this miracles nonsense.

        • smrnda

          This reminds me, in a way, of a teacher I had who was a huge conspiracy theorist and UFO enthusiast, except that his nutty ideas weren’t endorsed by the administration.

          Even when the Catholic church admits something is fake, they still seem to want to promote it, which is kind of a scary idea as it makes them look like a marketing firm with no concern for the truth. “If they think it’s real, sell it!”

        • Pofarmer

          My wife has gone to several “Marian Conferences” where they push the supernatural and miraculous HARD. When it comes to teh church, her bullshit detector is on full stop.

        • http://www.patheos.com/blogs/crossexamined Bob Seidensticker

          The earliest evidence we have of the Shroud of Turin is a letter within the church warning others that it was a fake and they knew the artist.

          That don’t mean that it’s not a money maker.

        • http://www.patheos.com/blogs/crossexamined Bob Seidensticker

          Yeah, but isn’t there a poncho that has her image magically transferred to it in a completely supernatural way? Answer that!

        • Pofarmer

          Yep, that’s the one.

        • JohnH2

          The Catholic church is notorious for re-appropriating the local religion and then building churches over their holy sites and laylines.

        • http://www.patheos.com/blogs/crossexamined Bob Seidensticker

          A friend of mine traveled extensively in Latin America and responded to all the “Virgins of ___” in various places that the importance of the virgin was that there’s supposed to be just one of her.

        • http://batman-news.com Anton

          As if the rural poor of Mexico don’t have a tragic enough existence, how ironic that the only symbols they have for any divine presence in their miserable lives are the ones the church of the conquistadores appropriated to deceive and exploit them. The condescension of the e-bourgeoisie is just icing on the cake.

          If nothing else, we should acknowledge the way this same sort of process plays out in the creation-evolution wars. It’s not about religious people constructing an alternative scientific theory, it’s about their fear that their jealous chieftain-god will make them pay for acknowledging the false god of the lab-coated clergy of Science.

        • http://www.patheos.com/blogs/crossexamined Bob Seidensticker

          Which reminds me of people who move away from Christianity. Often, the fear of hell is the last apron-string that holds them to the faith (“But what if I choose wrong and go to the Bad Place??”). But how is that possible when the reason they’re drifting away is because they now think that it’s not true?

          I guess that just shows the power of emotional arguments.

    • MNb

      *(No one) … can demonstrate a verifiable, repeatable supernatural act, Christianity must be false.”
      I am going to accept this challenge. Supernatural acts by definition aren’t verifiable and/or repeatable, so you’re presenting a non-sequitur.

      • wtfwjtd

        If supernatural acts by definition aren’t verifiable and/or repeatable, pinpointing a source would seem a rather more difficult exercise. According to Christian’s own holy book, Jesus told his followers that they would be capable of doing “greater works than these”. I had always assumed he was referring to his own bag of magic tricks. If they couldn’t duplicate and/or trump his stuff on demand, what would be the point of making the claim that they could?

        • MNb

          Perhaps your assumption was wrong?
          S**t, I can hardly believe I write this.
          Please don’t take me seriously.

        • wtfwjtd

          You mean my assumption that Christianity is false could be wrong? That is possible, but as a practical matter I don’t consider it very likely. If that turns out to be the case though, I’ll gladly go where the evidence leads. Heck, I could even be like the M&M in this commercial when he sees Santa for the
          first time:
          “Christianity IS for real! The Christian God as described in the Bible really does exist!” Ohhh…(thump)
          http://www.youtube.com/watch?v=IVRIaSunvyw

        • http://batman-news.com Anton

          I’ll gladly go where the evidence leads.

          Sure, as long as the evidence comes from empirical inquiry, which humans invented to understand natural phenomena in natural terms. What better place to look for evidence of something beyond human experience?

          All kidding aside, I don’t interpret “evidence” any less subjectively. A couple of years ago I got a last-minute ticket to Fenway Park and found myself sitting right next to an old family friend I hadn’t seen in years. I wouldn’t even know where to begin calculating the odds of such a coincidence, but I assume someone could make the case that such an occurrence is so unlikely it constitutes evidence of something or other. Not being a believer in “synchronicity” or “cosmic bonds,” I laughed and concluded that it’s evidence that vastly improbable things happen every day. I guess that shows how open-minded I’m not.

        • MNb

          “I wouldn’t even know where to begin calculating the odds of such a coincidence”
          Depends on how you look at it. The chance that specifically you and your old friend experience such a coincidence is very small indeed. The chance that two random people experience it given enough time is pretty large.
          Compare the lottery. Somebody winning it happens all the time. You winning it is extremely unlikely. You’re not going to conclude that it constitutes evidence of whatever if you happen to be the winner, are you?

        • http://batman-news.com Anton

          Even at the time, my buddy (who’s sort of flaky, and his wife is a “Wicca”) pushed the coincidence as being a significant something or other. My own attitude (based on nothing but idle speculation) is that no matter who you sit down next to at the ball park, you’re bound to have some life experience in common, whether it’s people you know, places you’ve worked, etc. You just never end up finding out because you don’t delve into your neighbor’s life details. Or maybe you do, I don’t know.

          The point is, my beliefs shaped how I looked at this “evidence,” despite my self-image as an open-minded guy. Así es la vida.

        • smrnda

          There’s an interesting problem about how many people you need before there is a greater than 50% chance that 2 of them share the same birthday which tends to be a good example of something being not so improbable as it seems.

        • wtfwjtd

          I remember Kodie posted here somewhere that humans like to look for patterns and other repetitious occurrences,
          as a way to help them assign meaning to their lives. Organized religion offers a way for people to practice
          rigor and routine, and thus is attractive for some. I see no evidence that following these rigors and routines makes
          makes the outcomes of the complicated situations in their lives any less random or more in their control than the
          non-practicing, non-believers. As your personal experience demonstrates, random things happen to everyone from time to time;sometimes they are good, other times, not so good. The religious practitioner assigns all the random good to their god, while casually dismissing the random bad as “of the devil”or some such. As Bob has stated many times, because of this,Christianity (and a host of other religions) really are a non-falsifiable hypothesis, at least in the minds of the true believers. I guess that’s where the whole bit about assumptions and faith comes in: assume that your god exists,base your religion on faith, and then regardless of the evidence, you’ll always have a fall-back position.

        • http://batman-news.com Anton

          I see no evidence that following these rigors and routines makesmakes the outcomes of the complicated situations in their lives any less random or more in their control than the non-practicing, non-believers.

          I don’t think people in this day and age expect the rituals to literally affect the outcomes of events in their lives; they just give their lives structure and purpose. If that doesn’t work for you, by all means, don’t feel obliged to participate. I’m not much of a joiner myself. But the notion of a community of like-minded people is comforting to many.

          All I meant to say was that I think people have made up their minds and resist changing, even in the face of “evidence.” My belief that unlikely events can be expected to happen isn’t based on evidence or rigorous testing, it’s just one of those assumptions that are literally unfalsifiable. If unlikely events don’t happen, that’s to be expected. If they do, that’s expected too.

          Sorry to knock the über-rational positivism that is poised to save humankind.

        • http://www.patheos.com/blogs/crossexamined Bob Seidensticker

          My belief that unlikely events can be expected
          to happen isn’t based on evidence or rigorous testing, it’s just one of those
          assumptions that are literally unfalsifiable.

          An assumption? Sounds pretty obvious to me. Who would deny that unlikely events happen? To use the familiar example that’s been raised already, that Mr. Jones of 123 Main St. won a bazillion dollars in the lottery is insanely unlikely, but that someone did isn’t surprising.

        • http://batman-news.com Anton

          Who would deny that unlikely events happen?

          But but but where’s your evidence??

        • Pofarmer

          “I don’t think people in this day and age expect the rituals to literally affect the outcomes of events in their lives;”

          Yeah, you’d be wrong.

        • Little_Magpie

          that ad is kinda adorable…

    • smrnda

      I’ve heard accounts of supernatural events, but none of them sound particularly convincing. Some don’t even sound supernatural : ‘I applied to twenty jobs and I got hired!’ Well, great, plenty of people who weren’t praying had the same luck, and lots of people who did had no luck in the job search.

      The claims made about the supernatural are such that, even repeatedly unanswered prayers don’t prove the claims false, but certainly don’t prove it true.

  • Pofarmer

    This is just so frustrating. I hope it’s O.K. to vent here a little bit. So, my kids go to a Catholic school, I was a little more neutrally religious way back when, but, anyway. They were discussing cloning today in SCIENCE class, and they were taught that Human cloning was wrong because we are “Made in the image of God.” O.k. I get that this is a Catholic school, but this is a frickin SCIENCE class. If you want to discuss the theology of it, do it in religion class. This is just so frustrating.

    • http://www.patheos.com/blogs/crossexamined Bob Seidensticker

      Sure, vent away. That’s a frustrating problem.

      Perhaps this is a holistic attitude–a little English in Math class, a little Ethics in Science class, and so on.

      Perhaps you can at least celebrate that they’re teaching the consensus view when it comes to the actual science stuff.

    • smrnda

      You can’t always count on teachers not to insert their own opinions when it isn’t appropriate. Plenty of teachers can’t even stay on topic.

    • wtfwjtd

      Why were they taught that cloning is wrong? I mean, isn’t more copies of God a good thing? Or is that maybe too much of a good thing?

      • Pofarmer

        Because we are “made in the image of God” so it’s wrong to clone humans. Apparently everything up to that is O.K.

        • Raymond

          I dont know that the statement “Human cloning is wrong because…” is a problem. If they are teaching science accurately, they can bring in the moral part if they want. It IS a Catholic school. But if they skipped a discussion of cloning where it pertained to the curriculum because of Catholic moral teaching, it would be a problem.

    • GubbaBumpkin

      Vent. I went to Catholic schools, but my HS science teacher was an atheist.

  • MNb

    As I understand some math I have the vain bias that I had a better laugh than those who lack that understanding.
    Ha! Who says that math is dry and dull?

    • Itarion

      Liberal arts majors.

    • GubbaBumpkin

      Most people.

  • Itarion

    But here is where the difference between christianity and mathematics pops out: in their axioms. The differential equation, and in fact all higher math, can be traced all the way back to addition. And everyone can agree that addition is fairly self evident. The power of mathematics, and by extension, logic, is in the extrapolation of very simple arguments into extraordinarily complex and powerful ones.

    Christianity proceeds from what it is trying to prove. This circular logic has no power, despite being “true” [in that it is non contradictory, Biblical contradictions aside], because there is no extrapolation. It goes nowhere, just spins in place, which is not useful. It’s a self contained system with no effect on its surroundings and no way to expand.

    • GubbaBumpkin

      Presuppositional apologetics compares poorly to the use of axioms in math and science.

      In mathematics, Euclidian geometry for example, you are not allowed to assume axioms that are redundant, or that could be proven within the system. And if an axiom leads to a contradiction, it has to be discarded.

      In science, the fewer assumptions the better, and even then your assumptions have to be open to question. My usual example is the Michelson-Morley experiment. This is usually help up as the first really solid evidence against the existence of The Ether. But that was not the intention of Michelson and Morley. They believed in the existence of The Ether, and were simply trying to establish its effects on the speed of light. Instead, their experiment put their presumption in question.

      • Itarion

        “In science, the fewer assumptions the better”

        And this is just freaking cool. The fewer assumptions you take into some problem, the more you can wring out of it. And when you can pull an assumption support out, and the whole thing stands up BETTER. I love it!

        Michelson-Morley being a good example. You remove the assumption that light needs a medium through which to propagate [which is odd, since it is technically a wave] and now you can describe so much more about the light, and the Universe as a whole.

        The fewer assumptions, the more stuff that pops out as a consequence of the assumptions, and the more powerful the predictive power.

  • Greg G.

    Whoa! You’re bringing Difficult Equations into Xtianity? I’m still trying to work out

    1 Cross + 3 Nails = 4 Given

    I get that my arithmetic teacher lied when she insisted the units MUST agree to do addition:

    11 yards + 24 inches = 35 feet

    I just don’t see any valid conversion factors in the Xtianity equation.

    • Machintelligence

      I remember getting in trouble with the teacher in math class when I insisted that you could add apples and oranges, as long as the answer was expressed in terms of fruit (least common denominator, and all of that.)

    • GubbaBumpkin

      Cross = 0
      Nails = feet
      And everything works out.
      Apparently Christianity is degenerate though, because the solution is not unique.

  • joey_in_NC

    In a universe of electrons and selfish genes,
    blind physical forces and genetic replication,
    some people are going to get hurt,
    other people are going to get lucky,
    and you won’t find any rhyme or reason in it, nor any justice.

    — Richard Dawkins

    This is a great quote that encapsulates materialist-atheism in a nutshell. If materialism is true, then there really is no such thing as reason. Ironic, isn’t it? Materialists place supreme importance to a thing that fundamentally is non-existent.

    • http://batman-news.com Anton

      What is EQUIVOCATION?

      Thanks, Alex, I’ll stick with Message Board Logical Fallacies for $400.

    • Pofarmer

      Reason is a human function. What of it?

      • joey_in_NC

        Given the context of Dawkins’ quote, is there a fundamental difference between a human action that is ‘reasonable’ and an action that is ‘unreasonable’, considering both are the result of “electrons and selfish genes, blind physical forces and genetic replication”? The answer is…absolutely nothing.

        • http://www.patheos.com/blogs/crossexamined Bob Seidensticker

          Are you arguing that the atheist can’t point to an absolute or objective source for morality, meaning, or reason? I agree. If you’re saying that you can, show me.

        • joey_in_NC

          I’m posting a question to the materialist. What exactly is ‘reason’? When materialists say that they value ‘reason’, what exactly are they valuing? Does it even exist, or they valuing an illusion?

        • http://www.patheos.com/blogs/crossexamined Bob Seidensticker

          Are you looking for Arguing with Philosophers? That’s just down the hall.

        • Pofarmer

          Yep, Chris Hallquist would be your best bet.

        • joey_in_NC

          My bad, I thought philosophical debates on the existence/non-existence of God are encouraged in this forum.

        • JohnH2

          joey_in_NC,

          I think you need to read “Introduction to the Theory of Computation” by Sipser. Also, Russell/Norvig’s “Artificial Intelligence: A Modern Approach”. Then if you still want to go further on what specifically reason is you should probably read Kant’s “Critique of Pure Reason” and go from there.

          In the comments of a few posts back we actually cover the subject that you are asking about.

        • joey_in_NC

          In the comments of a few posts back we actually cover the subject that you are asking about.

          Thanks, can you provide a link? I’ll look into the sources that mentioned above.

        • Pofarmer

          I don’t who you are trying to label as materialists, but “reason” is what we humnas use to make sense of the world around. “Reason” is a function that most humans have, but no other species on Earth appears to. Reason, allows us to make predictions of what will happen in a given set of circumstances, given past history and knowledge. “Reason” is a method.

        • MNb

          Totally speaking for myself: reason means using deduction and/or induction. You may argue that they are illusions, but given the way the combination of those two has changed the world last 200 years or so I assume they aren’t.

        • joey_in_NC

          Totally speaking for myself: reason means using deduction and/or induction.

          I can agree with this. But does one actually freely choose to use deduction and/or induction? The problem essentially boils down to the issue of freedom, which many materialists view as an illusion.

          Does a spider use logic and mathematics to spin a web? Can it be argued that the spider has ‘reason’? Or is it simply ‘programmed’ to do so.

        • MNb

          “the issue of freedom, which many materialists view as an illusion.”
          I leave that to neurobiologists to find out. As far as I know they haven’t formulated a satisfactory of the human brain yet. So how can I know?

        • joey_in_NC

          I leave that to neurobiologists to find out.

          I don’t see how neurobiologists can say anything at all about freedom, other than it doesn’t exist.

        • MNb

          If physicists can, why not neurobiologists?

          http://en.wikipedia.org/wiki/Degree_of_freedom_(mechanics)

          Even weirder is

          http://en.wikipedia.org/wiki/Double-slit_experiment

          “detection of individual discrete impacts is observed to be inherently probabilistic, which is inexplicable using classical mechanics.”

          Maybe your definition of freedom is wrong. Maybe it must be redefined in probabilistic terms. We’ll won’t know before neurobiologists have settled on a model for the human brain.
          OK, one further important issue in this respect:

          http://ngm.nationalgeographic.com/2007/07/swarms/miller-text

  • DoctorDJ

    Thanks for this! I hadn’t thought of analog computers in many a decade.

    Didn’t Asimov’s protagonist in Foundation simulate the future using an analog laptop, predicting the fall of civilization? That was one powerful routine!

    • http://www.patheos.com/blogs/crossexamined Bob Seidensticker

      :-) There’s nothing that a good dose of analog computer logic can’t make a little better. (They originally had that in Mary Poppins’ song “A spoonful of sugar,” but it didn’t make the final cut.)

      This “assume what you want and your hope will be justified” trick also applies to an algorithm that uses continued fractions, but that would really be taking things far afield.


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