#portraitchallenge
I always liked pencil, but maybe charcoal is better 🤔
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Fish Face
@FishFace@ioc.exchange
mastodon 4.8.0-alpha.3+glitchNever used twitter but I am still a twit
One time mathematician
Full time pedant
41 Followers
65 Following
50 Posts
Joined February 07, 2026
#AuGhost 9 - Magic Hat
Did the ghosts haunt the hat, or did the hat enchant the ghosts? Or both?
#Aughost2026 #Ghostsoffedi #mastoart #kleinekunstklasse #monatsmalerei #watercolour
Replying to
@Vinni@troet.cafe doch! Sie sieht zwar nicht genau ähnlich aus aber du hast trotzdem etwas wichtiges eingefangen
Jo, das #portraitchallenge dieser Woche hat Spaß gemacht :) Als ich den Stuhl gezeichnet habe, habe ich nicht verstanden, was ich da drauf gesehen habe. Deswegen sieht man hier einen bloßen Stuhl; nachdem ich den gezeichnet hatte, erkannte ich, dass das ein Hut war :) Hoffentlich bleibt sein Kopf trocken!
#kleinekunstklasse #mastoart #rebelle #digitalart #watercolour
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@glynwolf@tiggi.es @IceWolf@masto.brightfur.net but left associativity is itself a notational convention. It's not a fundamental property of division: you can't prove that the division operation has this property, you have to decide you're going to follow the convention, and could choose not to.
Furthermore, left associativity does not help you in a mixed expression like 12÷3×4. The author is using a nonstandard definition of left associativity and if you look it up on Wikipedia or in a textbook you will see it gives you that a÷b÷c = (a÷b)÷c, but doesn't say what to do when you have a multiplication instead of a second division.
In our schooling, left associativity of division is a consequence of our order of operations conventions which say directly to do multiplication and division in order from left to right. If you do this with a÷b÷c you can see you immediately get (a÷b)÷c!
Examples where this order is not chosen include:
- Reverse polish notation
- Calculators which evaluate strictly left to right (used to be the only way calculators worked)
- Strange programming languages like APL
- Dutch classrooms until they agreed to use the more common order (they used to do multiplication before division)
If left associativity were an inherent property of division, none of these would actually be capable of doing division, yet somehow they are.
Replying to
@bemmesr@mathstodon.xyz yeah in that textbook there is no explicit rule that I was able to find. Lennes wrote a letter in some journal, IIRC, which clarified his position on this.
In some of his other textbooks it's made explicit, e.g. here https://archive.org/details/elementaryalgebr0000unse_l2r5/page/20/mode/2up
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@bemmesr@mathstodon.xyz @SmartmanApps@dotnet.social
In his eyes, the only sources that are relevant are high school textbooks, and only when they agree with him (Lennes' textbook from long ago did not, but nevertheless exists; if you look into his even whackier ideas like that 0.999... ≠ 1, it's very easy to find textbooks that contradict him. Somehow he manages to continue believing.)
I mean for goodness sake, this is the guy who makes a poll which proves that an expression is ambiguous (16% of people selected the variant) and still insists it's unambiguous. For him, ambiguity is purely a theoretical concept, not a practical one.
He has written that there is no ambiguity between the meaning of "f(x)" (whether it means f×x or the application of the function f to x) because you just need the additional information of whether f is a function. Well, if we have the additional information of how the writer of an expression with mixed multiplication and division intended it to be grouped, sure, that's unambiguous too.
BTW on calculators, one thing I never got him to cough to is that for decades most calculators didn't understand order of operations at all. The Casio fx-110 from 1977 is a good example because it was popular and has an example in its manual.
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@bemmesr@mathstodon.xyz Ages ago I tried to insist on some basics before moving on, but it was no use (and I was shown to be a paper tiger because I got dragged back in) because even for what I considered to be extremely basic facts he wouldn't agree... in that scenario the problem I faced was that discovering more of the contents of his mind was worth more to me than sticking to such principles.
In an ordinary debate, the other person would usually have an interest in keeping you engaged, so you can exercise some leverage.
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@Peejmaybe@mastodon.art caricature or play it straight, that's the question! @schnagi@mastoart.social
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@glynwolf@tiggi.es @IceWolf@masto.brightfur.net
a ÷ b ÷ c = a ÷ (b ÷ c) = a ÷ b x c
Can you justify the final equality?
I would write:
a ÷ b ÷ c = a ÷ (b ÷ c) = (a ÷ b) × c = (a × c) ÷ b
and if you like I'll justify those latter equalities using basic properties of arithmetical operations.
Having declared that division is right-associative, but not declared how we will handle expressions with mixed multiplication and division, we still have two choices of how to interpret a ÷ b × c: is it (a ÷ b) × c or a ÷ (b × c)? This is why I don't think you can justify your final equality without making a further notational convention.
If you adopt either of the conventions, "do division before multiplication" or "do mixed multiplication and division left-to-right" you will get your equality but no inconsistency. If you adopt either of the conventions "do multiplication before division" or "do mixed multiplication and division right-to-left" you will get the other equality, and again no inconsistency.
Note that, there IS an inconsistent option here: you cannot both have right-associative division AND do all divisions and multiplications from left to right, for the former necessitates that expressions consisting of multiple division operations be evaluated right-to-left.
What I should have said is that once you adopt the notation "numerator ÷ denominator" to express division, the rest follows as a logical consequence.
I still don't agree with this statement.
A different way of looking at this is that that notation tells us what to do with expressions involving two quantities only. You still need to adopt a notational convention on what to do with successive operations, unless you make it explicit with brackets.
I do think those examples are relevant, because for example, if any inconsistency flowed directly from adopting right-associativity for division written as "a ÷ b", there would be an inconsistency in APL, which use that notation (yes, with an obelus, not a slash) and right-associativity.
Replying to
@rascally12345.eurosky.social ich schweige ich schweige! Ich schwörs!
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@daviddoes@mastodon.social @ApostateEnglishman@mastodon.world @simon@bne.social @SmartmanApps@dotnet.social@Etch9@tech.lgbt
I highly recommend reading some of this guy's threads before deciding whether to further engage him on this. This list contains the clearest examples of his behaviour: https://dotnet.social/@SmartmanApps/115207044364101854 (In thread #3, you'll see me stick my oar in).
This user has a quite-likely-diagnosable obsession with the topic of order-of-operations (and a few others to a lesser degree) and is absolutely incapable of admitting a mistake. I recently observed him screw up an inductive argument - no great crime, but when someone else stepped in with a hint about his slip-up, he was having NONE of it.
Lots of people, including me, have tried to explain to him the difference between maths itself and the symbols and conventions used to write it, but to no avail. His response to my attempt is here: https://programming.dev/post/42555552/21442667 (warning: long post and thread).
#AuGhost 8 - Watering Can
Some ghosts can pass through walls, but less fortunate lost souls have difficulty squeezing through narrow gaps... Perhaps in life he ate one cheesecake too many 🥲
#Aughost2026 #Ghostsoffedi #mastoart #kleinekunstklasse #rebelle #digitalart
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@x_hace@mastodon.green
But there are software differences in how calculations are done: some software evaluates x/y/z as (x/y)/z while other software as x/(y/z). With mixed decorations, basic calculators evaluate left to right while more advanced ones use operator precedence. This can be a cause of real confusion, but you can always get what you want by placing brackets.
In higher maths it continues, by the way: if you order the nodes in a tree, and a is a descendant of b, is a < b or b < a in the ordering? Both conventions are used.
@beeoproblem@mastodon.gamedev.place
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@bemmesr@mathstodon.xyz
When you ask him for the proof I will be waiting with the greatest anticipation.
I'm still not clear on what he thinks an axiomatic system is, nor what a proof is, but you should beware the "proof by example" approach...
His latest is an example of a perplexing pattern. If he truly thinks he has a proof, why does he talk about textbooks instead of the proof?
Replying to
@chemoelectric@masto.ai what have I done or said that resembles bullying in your view? Told you you're wrong? I don't want to make you feel bad, I want to make you understand the world better.
You have enough information from me about emission theory if you wanted to use it.
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@chemoelectric@masto.ai I've always had an interest in science, which is why I bothered to investigate the science behind your interesting claims about Bell tests sufficiently to understand why you were wrong, and then investigate your number system sufficiently to understand that it was nothing more than fluff on top of standard mathematics, and then investigate your work on relativity to understand not only that your writeup was extremely wrong but how to derive the correct, falsified prediction of the scenario you claimed.
Along the way I've asked you simple questions you could use to further your own understanding or convince me (or anyone else - you constantly moan that the Establishment doesn't believe you), but can't answer.
This week for a last bit of fun, I looked at the so-called proofs in your huge document. You (or I guess the "inference engine") have written a "proof" of the Collatz conjecture which is merely the probabilistic argument everyone knows for why it "ought" to be true. Barry, you cannot prove a statement about *all numbers* by an argument that relies on behaviour *on average*. Because, and I'm afraid I have to point this out, it only takes a single counterexample for the conjecture to be false, and a single counterexample does not change the average.
Your commitment to science lasted just until the implications of the science got counterintuitive. You'd have been clamouring for Galileo's head, had you lived at that time.
This has been fun, and educational. (To clarify: I have educated myself, while you have avoided all questions) But I don't wish to waste my time on someone who trusts their own reasoning and the "reasoning" of language models so highly, when it produces such manifestly wrong claims, and who won't do even the basic courtesy of answering questions. My parting advice: keep your hobby private, and don't dump your trash all over the internet, if you don't actually want to engage with people over it.
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@bemmesr@mathstodon.xyz Yeah I guess that kind of questioning approach would be the way to go. Even if you don't find a contradition he accepts, you may find one *you* can see to be there, which may satisfy your curiosity.
One thing about Lennes: the reason, I believe, that Lennes adopted the rules he did is that he noticed that the actual mathematical practice was to interpret 1/2a as 1/(2a) rather than (1/2)a. His way of getting this result was to simply say, "do multiplications first" and indeed, that does achieve that result, and that result is desirable.
However, it seems plausible to me that in fact mathematical practice was then and is now more complex, at least in its most common form: I think most people interpret 1/2a as 1/(2a), but most people interpret 1÷2×a as (1/2)a.
This distinction is the one that gets the most exercise on social media, because most people have never been taught explicitly that the order of operations ought to be different in the two expressions.
But here we come up against another of his idiosyncracies: he does not believe there *is* multiplication involved in the expression 2a. So he fails to understand Lennes' position. This one *is* directly contradicted by textbooks, and he has been challenged with that on Lemmy, but he does not accept it
Replying to
@Vinni@troet.cafe passt schon! Ich finde die Vorlage schwierig heute, und deine Version gefällt mir.
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@Peejmaybe@mastodon.art the original eyes are so wonky! Nightmare!
Haven't decided how I'm going to do it.
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@bemmesr@mathstodon.xyz indeed. I don't think I've seen anyone confront him directly with it, or if I have I've forgotten, so it'd be interesting to see what he says. I think when I found these references originally I was also trying to find a second source, but didn't find anything good, and then he stopped replying in that thread before I thought to return to the search.
It's a constant balancing act what parts of his framework you challenge and what parts you accept for the sake of moving the discussion on...
Replying to
@chemoelectric@masto.ai I'm not going to read more from you after having investigated five or six claims of yours that go against the scientific consensus and finding them all to be either: provably wrong, based on wrong understanding, or contrary to experimental evidence that, while I cannot verify myself, have no reason to believe has been falsified. At this point I make a probabilistic argument: the next outrageous claim is most likely of the same variety as the last, and won't waste my time.
I haven't made any claims about you as a person and have only criticised your writing and arguments. Describing that as "ad hominem" is absurd. I'm the only person paying attention down here so I don't know whom you're writing that for, since we both know it's not true. Indeed, when you cast aspersions about my mindset, and literally call me "brain dead" instead of answering questions, methinks Barry doth protest too much. Describing asking such elementary questions - questions that any scientist or mathematician could easily answer about their systems and theories - as "sealioning" is another pathetic attempt to deflect from your inability to answer them.
Please don't bug me with any of your new guff. The reason I'm not muting you is to leave open the opportunity for you to answer outstanding questions, not to pester me with the latest essay from the slop cannon.
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@TimWardCam@c.im the context is a textbook for children recapping arithmetic. I think in that context it's fine.
But after age 15? Then we have better ways to express the same thing.
His central thesis (I refer to him in third person due to him having blocked me) is that there is no ambiguity in mathematics, including such expressions. He just ran a poll in which 16% of people interpreted such an expression "wrong"!
So to him "not ambiguous" doesn't mean "people might interpret it in two different ways" it means "I deem one interpretation correct and all others incorrect".
Users from the #Netherlands - do you remember, or have you heard of, the mnemonic "Meneer Van Dalen Wacht Op Antwoord"? I have been googling for information about this but am looking for more sources, preferably original textbooks from the 20th century. I can find quite a few references to it but only *after* it was already phased out. Let me know if you remember, are interested and/or can help!
I must confess up front I do not speak #dutch !
#nederland #wiskunde #math #maths #mathematics
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@chemoelectric@masto.ai you're not interested that you published something wrong? Not very scientifically minded of you. You should retract it.
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@beeoproblem@mastodon.gamedev.place
The point is that which you choose to do is merely a matter of convention, and conventions can differ. When you say "the priority IS the same" that's a true statement about the common conventions of today, but people could conceivably do maths differently just fine. They'd have trouble communicating maths with us folks, but not with each other.
Replying to
@bemmesr@mathstodon.xyz I'm so sad he doesn't think I'm his friend :'(
I don't know if you want to go straight to the example, or see why exactly he interprets this in this way. @ColinTheMathmo@mathstodon.xyz had a poll up earlier in the week about interpretations of "do multiplication first". But I dunno if it's worth it when the example clarifies it.
It never worked for me, but you could try asking him a counterexample would look like.
Why not try an #AuGhost ?
Ghosts on vacation don't feel the heat (lucky them) but they still need to keep the sun out of their eyes while relaxing!
Featuring... #rebelle with thanks to @feff@comicscamp.club for inspiring me to try it! It works in Linux! Kinda! (I had a couple of crashes :( )
Nothing special but this kind of doodle is just what I wanted to be able to create digitally, so yay
#mastoart #aughost2026 #ghostsoffedi #kleinekunstklasse
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@Peejmaybe@mastodon.art I used to have to write on blackboards with chalk professionally, and the sensation of dust sucking all the moisture out of my hands was awful. I can't really remember using charcoal (I only ever did it at school) but I imagine it's the same.
I ended up buying plastic holders to prevent it! I still preferred chalk to whiteboard markers...
Thanks so much ^_^
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@chemoelectric@masto.ai
I want to criticise your presentation of Emission Theory, and so I did. You labelled distances with velocity measurements, so your "wave mechanics" are all wrong, and ignored the evidence and history that led to it being rejected, didn't you?
You talk a lot about having a scientific mindset. That means being able to accept when you are wrong about something - will you do that now, about Emission Theory, since it predicts that there is no transverse Doppler shift?
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@dpnash@c.im in fact it's weirder than that. He doesn't think that there is any operation going on in the expression 2x: he thinks that it is "already multiplied". It's not clear what this means; clearly for all x, 2x=2×x, and the fact it's written with two symbols means there is a step to turn them into a single number, which step is exactly the operation of multiplication.
He calls such a single symbol a "term". The normal meaning of which includes an expression like 2×x, and then invents some special rules for terms which are unsupported except by further tortured reading of a limited selection of sources.
Someone who merely hadn't seen advanced maths could be taught, but he's invented a whole special subject for himself!
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@Durcheinanderin@sueden.social schlaue Strategie, das Gesicht einfach senkrecht zu zeichnen!
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@bemmesr@mathstodon.xyz
I hadn't realised you were the same person as was asking about partial fractions :) That kind of thread truly makes me despair, as it's a high school topic that a high school teacher *should* be able to explain :/
There's a curiosity that he is very focused on linking the same topics again and again. Whether this is just to draw people to his own threads, or because those are just the topics he brings everything back to, I'm not sure. But in that case, your question *was not about* pronumerals so it's quite weird that that's what he brought up. In unrelated maths topics he relentlessly brings up order-of-operations as an example. My strong suspicion is that it's an unhealthy obsession that he can't let go of... and you know, I can't criticise him too heavily for that, can I?
The positive thing that came out of my past interactions with him is that I've been motivated to watch out for opportunities to explain maths.
Cajori is a source that SmartmanApps has read a lot (but not all of it - there's actually a fantastic section on factorials which points out several places where expressions like "n · n - 1 · n - 2 · ..." were interpreted as n! rather than n^2 - n - 2n - 3n etc. I love this because it's a situation where the intended interpretation is obvious even though it's not strictly in accordance with the rules as written.)
The sentence you quoted has a reference to Lennes' textbook. As far as I can work out, the textbook never makes this explicit, but it can be determined from examples. In Example 155 on p212 of the book (https://archive.org/details/highschoolalgeb01lenngoog/page/212/mode/2up?ref=ol&q=order) you can see that he is performing all multiplications before the divisions.
SmartmanApps is on the record as saying this textbook is just wrong, so it won't convince him. When I challenged him that he simultaneously thinks "all textbooks agree" and "Lennes' textbook is wrong" I believe this was the point where he said that, since his sentence was in the present tense, he had not meant to include Lennes. I never did work out exactly what timespan of publication he includes under "all textbooks agree." Perhaps it's a vacuous truth, unless at the very moment of utterance, a texbook on the subject is being written. Or printed?
I saw he brought up his "e-calcs" thing again. He needs to be reminded that they behave exactly the same as that Casio fx-110!
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@bemmesr@mathstodon.xyz It's easy if you don't know what a proof is ;) The real crime though will be the unproved assertion that the scenario he exemplifies with the teaching aids is written in the way he says...
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@laurazepam@mastodon.social I can confirm that a perfectly reasonable portion of time was spent.