Your account of things has "evolutionism" meaning (axiomatic) disbelief in (1) time-varying physical laws and (2) nondifferentiable natural phenomena. (I'll repeat that this is not in fact what "evolutionism" means, but we'll bracket that for now.)

You have, of course, not been precise about what you mean by those terms; if it turns out that what follows makes some wrong guess then I invite you to be more precise about your meaning rather than merely complaining that I guessed wrong about things you didn't deign to make explicit. But:

Consider the notion of "wavefunction collapse" in quantum physics. This may or may not be a real thing that happens (e.g., in the Everett "many worlds" interpretation it isn't), but many physicists have treated it as a real thing and there's no particular inconsistency in doing so. This is a nondifferentiable phenomenon. Discontinuous, even. The state of the world changes abruptly from one thing to another substantially different thing.

Do you need to believe in time-varying laws, in your sense (according to which such belief can rightly be termed "creationism"), in order to accept a version of quantum physics with instantaneous wavefunction collapse? It sure doesn't look like it to me.

More broadly: "nondifferentiable" and "time-varying" are just completely separate things; so far as I can tell, there is nothing that would make one of them enforce or prevent the other. Again, maybe you're using those terms in idiosyncratic senses that have little to do with what I think they mean; in that case, maybe it turns out that there is no "nondifferentiable constant case"; but in that case, you owe us an explanation of the meanings you're giving those terms.

I guess I need to address one specific thing you might be trying to do. (I hope you aren't, because it would be nonsense.) It is, of course, true that no mathematical function can be both (1) constant and (2) nondifferentiable. But that has nothing to do with the question here, despite your use of the phrase "nondifferentiable constant case"; you have made it clear elsewhere in the discussion that when you say things like "time-varying" or "constant" you are talking about the laws, not the specific functions they describe. (And of course literally no one believes that the functions by which we describe the physical world are all constant functions.)

I don’t have time to explain basic mathematics. Suffice to say, the concepts of changing over time and differentiating are very related. If you didn’t know that… that explains a lot I suppose.

I still don’t know what your point is, by the way. Maybe we should settle that.

(My current best-guess explanation for this conversation is that you don't understand basic mathematics and are just slinging words around in ways you hope will sound impressive. Maybe that's wrong and there's some actual mathematical/physical insight that you haven't successfully communicated to me, but if so then you ought to show us the details rather than simply waving your hands and trying to sound superior.)

I've made several points, almost all of which you have ignored in favour of (usually incorrect) nitpicking on side-issues. The other place where you complained of not knowing what my point was was a different bit of the discussion where we were talking about different things. I'm not going to try to re-explain every point I've attempted to make in this discussion, but very briefly:

In the other subthread, my point was that the only way for your statue-scenario to work (in the sense that an actual scientifically-minded person, as opposed to a stupid caricature-scientist out of the fantasies of creationists, would dismiss the possibility that some intelligent being created the statue) would be for someone or something with great power and cleverness to deliberately obfuscate all the evidence that there would be, in the ordinary actual world, that the statue was made by a person; and that if that's the sort of hypothesis you have to appeal to in order to claim that "creationism" and "evolutionism" are on some kind of equal footing, then you basically have to give up on the idea of ever having any real evidence for one thing over another.

(In the real world, of course that isn't the situation; what actually happened was that we looked at this thing-you're-analogizing-to-a-statue and sought to understand it more clearly, initially taking "intelligent design" as the default explanation, and the best explanations we could find surprisingly turned out not to involve any sort of designing intellect after all.)

In this one, my point is that (1) you originally tried to define evolutionism as "the worldview characterized by an axiomatic belief in the time invariance of physical laws" in contrast to "creationism, which posits non-differentiable physical behaviors", and (2) that is not in fact remotely what either of those words means, and (3) none of your mathematics-looking talk about this actually seems to make much mathematical sense. Specifically, (a) neither of those mathematical things either implies or is implied by the existence or nonexistence of God, or by the universe being or not being the creation of a God, or by God (if God there be) ever intervening in the universe; (b) the mathematical things you associate with "creationism" and "evolutionism" are pretty much completely independent of one another, as opposed to being some sort of opposites; (c) while you grudgingly admit the theoretical possibility of one of the other two possible combinations of them, the fourth is also possible so far as I can tell; (d) all of this looks to me as if you are slinging around words you do not understand deeply and hoping to make it sound as if there is something deeper to whatever variety of creationism you endorse than there actually is.

Exactly. We agree.

> best explanations we could find

We have no tested explanation of abiogenesis, chiefly. Among many other questions. Lots of theories that say “and throw your hands up and wave them around and wait 8 million years and tada, probably, idk”

God intervening in the universe is a potential source of sudden changes in the laws of physics. For instance changes that allow a man to walk on water or split a sea. Those changes are stepwise, they do not impact space time gradually. Thus non-differentiable. If the change was gradual, evolutionists would come up with a formula for it and say it magically is that way, for “reasons”. They might look at how their laws of gravity work and see that they aren’t right for galaxies, and say the reasons are “dark matter”, for example. I might say they’re God working exerting a differentiable influence, but those two are interchangeable, at least on the surface. It’s only the stepwise that is Godly.

In any case, if your position leads you to this sort of cognitive nihilism, so much the worse for it.

We have plenty of plausible explanations for abiogenesis. We don't know whether any particular one of them is right -- good evidence about what happened billions of years ago can be scarce. (Not because of any general impossibility in getting evidence about the past. Sometimes it's there, sometimes not.) And we for sure don't know all the details. Maybe we never will.

That isn't any sort of advantage for creationism as a theory of the origins of life, because we also don't have any details of how God allegedly created life. "God said 'let there be X' and there was X" is no more detailed an explanation than even the handwaviest naturalistic theories of abiogenesis.

(We should ask: how detailed an explanation should we expect to be able to figure out, if either sort of theory is right? And I think the right answer is "probably not very detailed in either case, though the prospects are maybe better for the naturalistic theories".)

I understand that you're saying that divine intervention could produce non-differentiable changes. But I think you're completely wrong about the logical relationships between different kinds of change and possible divine intervention. (1) I'm pretty sure that as far as human observation can distinguish, anything that can be done by a non-differentiable divine intervention can also be done by a differentiable one. (If you restrict God to real-analytic interventions, that might be a different matter.) (2) I can't see any reason why non-differentiable changes should require any sort of god; I already gave several examples of (conjectural but) perfectly respectable naturalistic physics involving non-differentiable changes.

When you're faced with something that doesn't fit well with existing physical theories, you can postulate divine intervention, or postulate that some amended naturalistic theory might fix it up, and that's true whether or not something nondifferentiable seems to be involved. (Especially as, lacking the ability to look infinitely closely at things, we can never tell for sure whether something nondifferentiable is going on. E.g., one of my examples of possible nondifferentiable change in naturalistic physics was "wavefunction collapse", but you could have objective wavefunction collapsing that happens smoothly but very very quickly and no observation we're currently able to make could tell the difference.)

Historically, the track record of the "look for amended naturalistic theories" approach is pretty good; it seems like it leads to genuinely new and improved understanding more than the "give up on naturalistic explanations and say a god did it" approach does. And there's an obvious reason why: if you just say "God did it" then that doesn't make any progress in understanding, whereas if you make yourself look for better naturalistic theories that actually work then you're forced to come up with theories that do a better explanatory job. In principle, of course, it might happen that every time you postulate "God did it" you get new insights into the purposes and preferences of God, and that might e.g. help you make predictions just as well as new scientific theories do. In practice, that doesn't actually seem to happen. (One might ask why that is, and of course the atheist has an obvious answer to that question.)

So, e.g., let's take your example of gravity and the rotation of galaxies. We don't yet know what's going on. We have a rather vague candidate naturalistic explanation: there's a load of stuff in the universe that has mass but doesn't otherwise interact much with the things we can detect. That isn't a very satisfactory explanation because it's so unspecific (though e.g. it does let us make sense of some puzzling things besides the rotation of galaxies, such as the so-called "Bullet Cluster"). You suggest that maybe it's "God working exerting a differentiable influence". Could be.

So, what might be our state of understanding 50-100 years down the line? We might be just as confused as we are now. But it seems at least plausible that we might by then have a better naturalistic theory (more details, more concrete predictions, more things we can check), which may or may not still involve "dark matter". Do you think it's plausible that we will have a better divine-intervention theory? One where we can say "we now understand that the rotation of galaxies is the way it is, because God is doing X, which he wants because of Y"? So far as I know, the number of cases where this sort of intellectual progress has come out of saying "God did it" is zero.

That doesn't necessarily mean "God did it" is false. Maybe we're unlucky (at least in so far as we were hoping to understand the universe) and a lot of things are the result of divine activity that's simply beyond human comprehension. But every time we see something puzzling, go looking for naturalistic explanations, and find them, that becomes less plausible.