Jonathan Bartlett replies to Jeffrey Shallit’s “pedantry”

JB, You have implied a really, really important question/raised a truly pivotal issue in an age dominated by computing (an application of Mathematics and broader mathematical thinking):

I would love to have a conversation about what is important in math

Why not, let's just do that, follow it up and see where it goes? For instance, I think a key insight is to find a useful, powerful definition of what mathematics is. If we understand what it is we are exploring, it may give us a deeper, richer view on how we may understand and apply it. And for this, I have come to the view that an adaptation of a view I was taught by my very first uni prof is key: Math is [the study of] the logic of structure and quantity. That, is, there are two aspects, first, the substance of a certain field of reality: it forms a coherent framework of largely abstract structures and quantities. Coherence, being the gateway to the logic that guides our reasoning, and turns on the premise that realities are so together, thus accurate descriptions of said realities -- truths -- must equally fit with one another as they must also fit with realities. This means, rational thought is a main tool (and increasing our power of rational thought is a key motive and end) of Mathematics. Further to this, I see a key application of the logic of being. For, key Mathematical entities, while abstract, are necessary, framework components of any possible world. Which immediately gives them enormous power and depth, as well as being a source of the aesthetic pleasure excited by well done Mathematics -- its beauty. Order, intricacy, organising principles reflecting verisimilitude. So, Mathematics can be enriching, enjoyable and en-nobelling. All of which are highly relevant to education and praxis. Also, the involvement of the appearance and substance of truth (with logical accountability and duties of prudence) brings out an ethical dimension, the other side of axiology. Mathematics is a value-rich environment. For example, ponder the compact, powerfully integrative insights locked in Euler's expression: 0 = 1 + e^i * π Going beyond, I find that a survey of key structures such as von Neumann's exploration of the natural counting numbers, N, will help flesh this out, also teaching us the style of creative, insightful exploration that draws out the insightful creativity you are seeking to promote: {} --> 0 {0} --> 1 {0,1} --> 2 . . . [HUGE!] {0,1,2, . . . } --> ω From this we may rapidly access the "mirror-image" additive inverses, thus the Integers Z. Ratios bring us to the rationals, Q. Infinite continued convergent sums of rationals give us the reals, R. Complex numbers C come in as rotating vectors (which then extend to basis vectors, the ijk system, general vectors, quaternions, matrices, tensors thus also groups, rings, fields and algebras). The transfinite ordinals, transfinite hyperreals and the catapult through 1/x gets us to infinitesimals. The Surreals come knocking at the door. Valid infinitesimals give us an insight into Calculus. With this in hand as a structured survey, all sorts of gateways for exploration are open, including a sound appreciation of sets, mathematical foundations, topology and more. Worthwhile in itself but also obviously relevant to the Calculus you wish to explore. Also, pointing to the world of computing. We then gain an insight on axiomatisation and how it is subtly shaped by exploration and discovery of key mathematical facts (especially, necessary entities present in the framework of any world). So, we see how axioms may need to be plausible and if well phrased allow us to spin out abstract logic-model worlds that may speak to this and other possible worlds. Where, computing allows us to use machines in that exploration. More broadly, modelling is seen as a powerful but potentially misleading approach. Thus, issues of validation and testing lurk. We could go on, but I think we see a vision. While I am at it, Mr Shallit's sneer falls to the ground, once we see the reality of necessary entities in world frameworks, the relevance of truth, beauty, prudence and more as well as the power of mind to have insight, to intuit, to perceive and to draw insights that transcend the capabilities of inherently blind, dynamic-stochastic, GIGO-limited computational substrates. Reppert, again, draws out the point decisively:

. . . let us suppose that brain state A [--> notice, state of a wetware, electrochemically operated computational substrate], which is token identical to the thought that all men are mortal, and brain state B, which is token identical to the thought that Socrates is a man, together cause the belief [--> concious, perceptual state or disposition] that Socrates is mortal. It isn’t enough for rational inference that these events be those beliefs, it is also necessary that the causal transaction be in virtue of the content of those thoughts . . . [But] if naturalism is true, then the propositional content is irrelevant to the causal transaction that produces the conclusion, and [so] we do not have a case of rational inference. In rational inference, as Lewis puts it, one thought causes another thought not by being, but by being seen to be, the ground for it. But causal transactions in the brain occur in virtue of the brain’s being in a particular type of state that is relevant to physical causal transactions.

Mathematics is an exercise of the human spirit, which points to that Spirit who is the greatest Mathematician of all. Manifest, in the Mathematical frameworks of our world. A point long since articulated by founders of modern science who saw themselves as seeking to think God's creative and world-sustaining thoughts after him. The prejudice that "Creationists" are inherently irrational and so cannot do Math -- ironic, given the many radical, self-falsifying incoherences of evolutionary materialistic scientism -- falls of its own weight. KF kairosfocus

Nope. In fact, I still believe it to be true. I’m just not claiming a mind-reading ability, only an action-reading.

Hm, it might be good to avoid making statements about states of mind, then. It's easy for these discussions to devolve into slanging matches without providing the other side easy meat. Bob O'H

So are you saying that when you write “For academics like Shallit, none of that is important”, you knew the statement to be false?

Nope. In fact, I still believe it to be true. I'm just not claiming a mind-reading ability, only an action-reading. In fact, the whole point of my post above (#4) was to show that Shallit's objections seem to imply a complete lack of understanding of what the question even is we are discussing. johnnyb

johnnyb -

I believe that the “lie” he is accusing me of is the rhetorical statement “For academics like Shallit, none of that is important”. Of course, this is a manner of speaking. I am obviously not claiming to be able to read Shallit’s mind, I’m just pointing out the natural implications of the nature of Shallit’s attacks.

So are you saying that when you write “For academics like Shallit, none of that is important”, you knew the statement to be false? Bob O'H

. Shallit begins his tirade...

I suppose it's not so remarkable that creationists can't do mathematics. After all, almost by definition, they don't understand evolution, so that alone should suggest some sort of cognitive deficit.

Good grief. Two demonstrably false statements combined in a non-sequitur - with emphasis. This is not a serious person. Upright BiPed

AaronS1978 - Thanks for your comments. Yes, I was confused at first as well. I believe that the "lie" he is accusing me of is the rhetorical statement "For academics like Shallit, none of that is important". Of course, this is a manner of speaking. I am obviously not claiming to be able to read Shallit's mind, I'm just pointing out the natural implications of the nature of Shallit's attacks. Shallit missed the main purpose of the paper and instead just found fault with trivialities. Thus, it is obvious from his actions that he is more concerned with the trivialities and pedantries than he is with the bigger project of helping students learn to have deeper thoughts. If Shallit actually thinks that deep thinking is important, I wouldn't know that from his criticism. Nonetheless, Shallit thinks that me saying "For academics like Shallit, none of that is important" is a lie. What's really ridiculous is that he doubles down on this, saying that the fact that he has won an award for teaching somehow proves that my characterization of him was false. As I pointed out in my tweet, I'm not doubting that he is successful at teaching what he attempts to teach. I'm skeptical of what he considers important in teaching. I found it quite odd that he doesn't seem to be able to distinguish between these two different things. Perhaps that's the root of the problem - perhaps too many academics don't even realize that there is some other way of teaching! I asked Shallit to clarify what he thought was important. He said - "Truth is important, math is important, and good education is important." Again, this points to the fact that as long as it is true and about math, that's all he cares about. Nothing deeper is needed (or perhaps even wanted). Shallit's final (so far) tweet showed that his main goal was one-upmanship. He didn't want to have a conversation about *whether* I was wrong, only my obeisance to his genius is sufficient. That's why I pushed my "gold star" business. He seems to require the validation. I would love to have a conversation about what is important in math. Perhaps if Shallit were to say why being precise (and modern) in the definition is more important than teaching students specific skills for thinking outside of the box, perhaps I would wind up agreeing with him, and changing my approach. But the "you're wrong! admit it! liar liar!" approach doesn't really work with me. johnnyb

Like what do you mean by you can read his mind he spends most of his time being angry at you anyways Second of all you seem incredibly confident when it comes to math and telling the truth but he seems to insinuate that you do not is that just him pointing fingers and being a jerk AaronS1978

Jeffrey Shallit @shallit43 · 8h Replying to @jb_61820 Do you enjoy making up entirely false claims about people, such as "For academics like Shallit, none of that is important"? This is disgraceful, but par for the course. 1 Jonathan Bartlett @jb_61820 · 7h Responding based on your actions - what you actually seem to consider important based on what you respond to. It is true that I cannot read your mind. I can only read your actions. I don't think anyone took me as physically reading your mind on the subject. 1 Jeffrey Shallit @shallit43 · 7h I consider it important to not confuse people by telling them false things. And to admit error gracefully when it is pointed out to me. You apparently don't. I guess that's why you're associated with the intelligent design movement. 1 Jonathan Bartlett @jb_61820 · 5h Then tell me - what do you find important, and how is that demonstrated by your public actions? 1 Jeffrey Shallit @shallit43 · 5h Truth is important, math is important, and good education is important. This is why I took issue with your arrogant and misleading piece. I have won an award for my teaching, which you could have easily found out with a minimum of effort. 1 Jonathan Bartlett @jb_61820 · 5h I have no doubt of your ability to communicate facts to students in a memorable way, and in fact did not question such. But I apologize for not also mentioning that the university gave you a gold star. I didn't mean to imply that my gold star was your only one. 1 Jeffrey Shallit @shallit43 · 4h You're not interested in why you were wrong, not interested in what's correct in math, and certainly not interested in thinking about why you're so quick to invent false stories about others. Good sir I am confused at what I am reading here it feels like I am missing some part of the conversation he is obviously constantly attacking you which to be honest with you is very irritating to me, But what is he talking about apparently that you’re just inventing things and telling false stories he just sits there and he belittles you, what false stories is he talking about, AaronS1978

Additionally, Shallit and I had some interaction on Twitter if anyone is interested: https://twitter.com/jb_61820/status/1164217944307589121?s=21 johnnyb