Reading the Comics, May 31, 2017: Feast Week Edition

You know we’re getting near the end of the (United States) school year when Comic Strip Master Command orders everyone to clear out their mathematics jokes. I’m assuming that’s what happened here. Or else a lot of cartoonists had word problems on their minds eight weeks ago. Also eight weeks ago plus whenever they originally drew the comics, for those that are deep in reruns. It was busy enough to split this week’s load into two pieces and might have been worth splitting into three, if I thought I had publishing dates free for all that.

Larry Wright’s Motley Classics for the 28th of May, a rerun from 1989, is a joke about using algebra. Occasionally mathematicians try to use the the ability of people to catch things in midair as evidence of the sorts of differential equations solution that we all can do, if imperfectly, in our heads. But I’m not aware of evidence that anyone does anything that sophisticated. I would be stunned if we didn’t really work by a process of making a guess of where the thing should be and refining it as time allows, with experience helping us make better guesses. There’s good stuff to learn in modeling how to catch stuff, though.

Michael Jantze’s The Norm Classics rerun for the 28th opines about why in algebra you had to not just have an answer but explain why that was the answer. I suppose mathematicians get trained to stop thinking about individual problems and instead look to classes of problems. Is it possible to work out a scheme that works for many cases instead of one? If it isn’t, can we at least say something interesting about why it’s not? And perhaps that’s part of what makes algebra classes hard. To think about a collection of things is usually harder than to think about one, and maybe instructors aren’t always clear about how to turn the specific into the general.

Also I want to say some very good words about Jantze’s graphical design. The mock textbook cover for the title panel on the left is so spot-on for a particular era in mathematics textbooks it’s uncanny. The all-caps Helvetica, the use of two slightly different tans, the minimalist cover art … I know shelves stuffed full in the university mathematics library where every book looks like that. Plus, “[Mathematics Thing] And Their Applications” is one of the roughly four standard approved mathematics book titles. He paid good attention to his references.

Gary Wise and Lance Aldrich’s Real Life Adventures for the 28th deploys a big old whiteboard full of equations for the “secret” of the universe. This makes a neat change from finding the “meaning” of the universe, or of life. The equations themselves look mostly like gibberish to me, but Wise and Aldrich make good uses of their symbols. The symbol $\vec{B}$, a vector-valued quantity named B, turns up a lot. This symbol we often use to represent magnetic flux. The B without a little arrow above it would represent the intensity of the magnetic field. Similarly an $\vec{H}$ turns up. This we often use for magnetic field strength. While I didn’t spot a $\vec{E}$ — electric field — which would be the natural partner to all this, there are plenty of bare E symbols. Those would represent electric potential. And many of the other symbols are what would naturally turn up if you were trying to model how something is tossed around by a magnetic field. Q, for example, is often the electric charge. ω is a common symbol for how fast an electromagnetic wave oscillates. (It’s not the frequency, but it’s related to the frequency.) The uses of symbols is consistent enough, in fact, I wonder if Wise and Aldrich did use a legitimate sprawl of equations and I’m missing the referenced problem.

John Graziano’s Ripley’s Believe It Or Not for the 28th mentions how many symbols are needed to write out the numbers from 1 to 100. Is this properly mathematics? … Oh, who knows. It’s just neat to know.

Mark O’Hare’s Citizen Dog rerun for the 29th has the dog Fergus struggle against a word problem. Ordinary setup and everything, but I love the way O’Hare draws Fergus in that outfit and thinking hard.

The Eric the Circle rerun for the 29th by ACE10203040 is a mistimed Pi Day joke.

Bill Amend’s FoxTrot Classicfor the 31st, a rerun from the 7th of June, 2006, shows the conflation of “genius” and “good at mathematics” in everyday use. Amend has picked a quixotic but in-character thing for Jason Fox to try doing. Euclid’s Fifth Postulate is one of the classic obsessions of mathematicians throughout history. Euclid admitted the thing — a confusing-reading mess of propositions — as a postulate because … well, there’s interesting geometry you can’t do without it, and there doesn’t seem any way to prove it from the rest of his geometric postulates. So it must be assumed to be true.

There isn’t a way to prove it from the rest of the geometric postulates, but it took mathematicians over two thousand years of work at that to be convinced of the fact. But I know I went through a time of wanting to try finding a proof myself. It was a mercifully short-lived time that ended in my humbly understanding that as smart as I figured I was, I wasn’t that smart. We can suppose Euclid’s Fifth Postulate to be false and get interesting geometries out of that, particularly the geometries of the surface of the sphere, and the geometry of general relativity. Jason will surely sometime learn.

• goldenoj 9:08 pm on Sunday, 4 June, 2017 Permalink | Reply

Just found these recently. I really enjoy them and catching up is fun. Thanks!

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• Joseph Nebus 1:05 am on Wednesday, 7 June, 2017 Permalink | Reply

Thanks for finding the pieces. I hope you enjoy; they’re probably my most reliable feature around here.

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Reading the Comics, April 15, 2017: Extended Week Edition

It turns out last Saturday only had the one comic strip that was even remotely on point for me. And it wasn’t very on point either, but since it’s one of the Creators.com strips I’ve got the strip to show. That’s enough for me.

Henry Scarpelli and Craig Boldman’s Archie for the 8th is just about how algebra hurts. Some days I agree.

Henry Scarpelli and Craig Boldman’s Archie for the 8th of April, 2017. Do you suppose Archie knew that Dilton was listening there, or was he just emoting his fatigue to himself?

Ruben Bolling’s Super-Fun-Pak Comix for the 8th is an installation of They Came From The Third Dimension. “Dimension” is one of those oft-used words that’s come loose of any technical definition. We use it in mathematics all the time, at least once we get into Introduction to Linear Algebra. That’s the course that talks about how blocks of space can be stretched and squashed and twisted into each other. You’d expect this to be a warmup act to geometry, and I guess it’s relevant. But where it really pays off is in studying differential equations and how systems of stuff changes over time. When you get introduced to dimensions in linear algebra they describe degrees of freedom, or how much information you need about a problem to pin down exactly one solution.

It does give mathematicians cause to talk about “dimensions of space”, though, and these are intuitively at least like the two- and three-dimensional spaces that, you know, stuff moves in. That there could be more dimensions of space, ordinarily inaccessible, is an old enough idea we don’t really notice it. Perhaps it’s hidden somewhere too.

Amanda El-Dweek’s Amanda the Great of the 9th started a story with the adult Becky needing to take a mathematics qualification exam. It seems to be prerequisite to enrolling in some new classes. It’s a typical set of mathematics anxiety jokes in the service of a story comic. One might tsk Becky for going through university without ever having a proper mathematics class, but then, I got through university without ever taking a philosophy class that really challenged me. Not that I didn’t take the classes seriously, but that I took stuff like Intro to Logic that I was already conversant in. We all cut corners. It’s a shame not to use chances like that, but there’s always so much to do.

Mark Anderson’s Andertoons for the 10th relieves the worry that Mark Anderson’s Andertoons might not have got in an appearance this week. It’s your common kid at the chalkboard sort of problem, this one a kid with no idea where to put the decimal. As always happens I’m sympathetic. The rules about where to move decimals in this kind of multiplication come out really weird if the last digit, or worse, digits in the product are zeroes.

Mel Henze’s Gentle Creatures is in reruns. The strip from the 10th is part of a story I’m so sure I’ve featured here before that I’m not even going to look up when it aired. But it uses your standard story problem to stand in for science-fiction gadget mathematics calculation.

Dave Blazek’s Loose Parts for the 12th is the natural extension of sleep numbers. Yes, I’m relieved to see Dave Blazek’s Loose Parts around here again too. Feels weird when it’s not.

Bill Watterson’s Calvin and Hobbes rerun for the 13th is a resisting-the-story-problem joke. But Calvin resists so very well.

John Deering’s Strange Brew for the 13th is a “math club” joke featuring horses. Oh, it’s a big silly one, but who doesn’t like those too?

Dan Thompson’s Brevity for the 14th is one of the small set of punning jokes you can make using mathematician names. Good for the wall of a mathematics teacher’s classroom.

Shaenon K Garrity and Jefferey C Wells’s Skin Horse for the 14th is set inside a virtual reality game. (This is why there’s talk about duplicating objects.) Within the game, the characters are playing that game where you start with a set number (in this case 20) tokens and take turn removing a couple of them. The “rigged” part of it is that the house can, by perfect play, force a win every time. It’s a bit of game theory that creeps into recreational mathematics books and that I imagine is imprinted in the minds of people who grow up to design games.

Reading the Comics, March 10, 2015: Shapes Of Things Edition

If there’s a theme running through today’s collection of mathematics-themed comic strips it’s shapes: I have good reason to talk about a way of viewing circles and spheres and even squares and boxes; and then both Euclid and men’s ties get some attention.

Eric the Circle (March 5), this one by “regina342”, does a bit of shape-name-calling. I trust that it’s not controversial that a rectangle is also a parallelogram, but people might be a bit put off by describing a circle as a sphere, what with circles being two-dimensional figures and spheres three-dimensional ones. For ordinary purposes of geometry that’s a fair enough distinction. Let me now make this complicated.

• Kurt Struble 5:28 am on Wednesday, 11 March, 2015 Permalink | Reply

i have a question. if feeling impish describes how you would feel by proving that two points on a line can be shown to be a sphere … which i THINK you are implying you can do … then .,..

if by some formula or definition (i’m not sure which) D, you can describe a forest of trees by the density of trees within a certain area … AND … by another formula or definition B, you can, determine the number of board feet contained within the density of trees within a certain area …

… can it be said that, since you already know the number of board feet needed to build a two bedroom home, you can use the relationship between D and B to determine the number of two bedroom homes that could be built within any area populated by the same density of trees?

wull … assuming this is true then, is proving that two points on a line can be a sphere (you little devil) the same thing as not being able to see the forest for the number of two family homes that could be built?

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• Joseph Nebus 8:10 pm on Thursday, 12 March, 2015 Permalink | Reply

Well, now, indeed, I am putting forth that two points on a line can be, in the right context, interpreted as a sphere, or at least the way a sphere happens to exist in a one-dimensional space.

And, now, I agree with you almost all the way about describing the forest and the number of two-family homes it could be made into, if you have the density of trees and the number of board feet needed to build a home. But I think the setup falls a little short of what’s needed because it doesn’t make clear that the density of trees is really the density of usable board-feet in that area, and I’m not sure that we have a clear idea of how much area there is in the forest. If we take those as given, though, then yes: we’ve got missing forests for two-family homes.

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• Kurt Struble 11:04 pm on Thursday, 12 March, 2015 Permalink | Reply

well … first of all thanks for reading my earlier posts … the ones about rain, ice, the moon, universe, infinity, black holes, etc.

well … first of all my comment was attempt to draw a comic analogy between my interpretation of YOUR interpretation that two points on a straight line could be interpreted as a sphere, at least in one dimensional space.

the really humorous aspect of the statement for me being that, you could make the statement with a straight face knowing that most of the people who read your blog would accept and understand exactly what you meant by being impish (you little devil).

The mere thought that making this interpretation would be ‘’impish’’ is so far from my lexicon that, despite the fact that the people in your milieu probably completely understood your meaning … the statement took on a massive amount (like … the amount of energy it would take to completely fill up a black hole … which i realize is a really stupid thing to say but maybe funny?) of absurdist humor, to me!

I mean, i had never in my life heard … or indeed THOUGHT that i’d ever hear … such a statement made about such a subject. The absurdity of the statement … the sheer unexpected aspect of it … (please interpret ‘’absurdist’’ as an example of writing something good) caused me laugh last night, so hard that i woke my wife up who had been sleeping for at least an hour.

In fact, the statement was ALMOST as funny as a comment you made recently about pulling some really interesting artwork … the ‘medium’ being i believe, ice … ) out from beneath your swimming pool heater, which also sent me into paroxysms of laughter.

For me … humor … is the result of seeing or hearing something totally unexpected.

Both of your statements reached the highest level of humor since … how could i (a total and complete layman) EVER consider a person ‘impish’ because they could interpret two points on a straight line as a sphere but ONLY in one dimensional space? (hahahahahah

AND that you had found some interesting art work beneath your swimming pool heater?!!! (i’ve got a smile on my face as i write this … but hope i don’t start laughing because i want to finish this comment soon …

so anyway … as a result of my interpretation of your statement, about spheres while being impish, i decided to make up a situation that was absurd but, that i thought was fairly logical … except that, at the end i gave it an ‘absurd’ twist based on the statement … “you can’t see the forest for the trees” … which i thought was absurd enough to be pretty funny … wull … it made me laugh anyway …

i don’t think you got the joke … but that’s ok since … the fact that you proceeded to tell me the falsities of my ‘’suppositions’’ and why my conclusions were not necessarily valid … this caused even greater paroxysms of laughter.

as to your conclusion about the variation of the density of wood invalidating my conclusion … i would disagree with you completely since given a large enough sample, perhaps in a specific geographic area (which i KNOW i didn’t mention … ) the variations would even out so that the number of two bedroom homes COULD be determined.

so there … ! This is just another example of you NOT being able to see the forest for the trees … !! i enjoy your blog and will return … ks

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• Joseph Nebus 12:07 am on Monday, 16 March, 2015 Permalink | Reply

Aw, well, now, I did expect that you were being whimsical with writing about forests and trees, but I also didn’t want you to think I was just passing over your comment, and when I thought about it I could think of something interesting to say about it, and maybe useful in thinking about how to think about problems.

I like to think one of my good traits is being unafraid to look like I didn’t get the joke. It gives other people something amusing to respond to, if nothing else, and makes me look like a better sport than I worry I am.

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• Kurt Struble 1:16 pm on Friday, 13 March, 2015 Permalink | Reply

on jeeze … i didn’t see the forest for the trees!! ” … yes: we’ve got missing forest for two family homes.” ha ha ha ha … i guess if you assume that the ‘exercise’ applies to the real world (what is ‘real world’?) then there WOULD be missing forests … pardon my uppityness … .

Anyway, not being part of the mathematics/physics demographic, would you say that overall, this group is obsessed with definition? i wonder if i’d get along better with groups of “scientists” than people outside of this field … (i know there are other fields concerned with definitions … ) since i tend to zero in on words that people use, within statements, that i don’t think apply to the situation which eventually tends to piss people off if taken too far … .

i have learned to overlook the use of what i think could be a more specific word, but the word used, still bangs around inside my mind.

what happens is, my brain starts thinking of absurd usages for the word while i’m stifling myself from saying something.

this tendency to think of absurd uses for words is a great asset when it comes to writing. the result is, i love being a hermit (from time to time) when i want to do a lot of writing since i can focus in on word usage and not bug the shit out of people. i wonder if mathematicians think/feel the same way about numbers?

these kind of ridiculous”theories” that i pass on to people usually leave them scratching their heads wondering what the fuck i’m talking about. do mathematicians overall, tend to hang out in cliques of like minded people for the same reason?

i’m being serious and speaking the truth about such matters, from my own perspective … but i think it’s absurdly hilarious at the same time. please forgive me if it seems like i’m being patronizing because my intent is NOT to be patronizing.

my latest ‘obsession’ revolves around my thoughts on a much broader scope of POLARITY in the world around us.

my attempts to explain these thoughts to my wife the other day, resulted in her getting pissed off at me which lead me to try to use that circumstance as an example of how polarity can ratchet up in the real world which … made matters worse.

the last comment or question i would like to make is … is there any reason why the Great Salt Lake couldn’t be made into a ‘super dynamo’ since salt water is a necessary ingrediant for making electricity?

i figure that, since plus and minus are mathematic terms maybe you’d have an opinion.

or, you could table this discussion since i’m sure you have much more important issues to deal with. (another example of polarity)

in any case … don’t waste your time if you have limited amounts of it .,.. and thank you so much for reading my blog … ks

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• Joseph Nebus 12:17 am on Monday, 16 March, 2015 Permalink | Reply

I’ve been doing a fair bit of thinking about this because I think it’s an interesting question: are mathematicians (and people in related fields) obsessed with definitions? I think I’ve come to conclude that while mathematicians (and that demographic) tend to think more, and maybe more critically, about definitions than average folks do, it’s not exactly because they’re obsessed with definitions, but because they’re interested in what they can do with definitions.

The big interest that mathematicians have, I think, is in finding interesting things which are true to say about something. But what makes something interesting to say? It’s probably got to be something which is implied by the system you’ve set up, but which isn’t obvious from the original setup. But if it’s not obvious, then it’s got to be something that can be deduced from the setup, and it has to be something which can be judged against the rules of the setup and said to be either true or false.

And that’s where definitions come in: if you don’t have a fairly good idea of, say, what a Therblig Number is, you can’t really say whether “2,038” is a Therblig Number, or whether it isn’t. And if nobody knows what a Therblig Number is (certainly I don’t, and I made up the name), it’s not going to be interesting to say whether it is or isn’t. Your idea of what the definition is might not be precise, and it might need revision as you find it implies things you don’t want it to, but you have an idea there is this thing called a Therblig Number and that it has some traits you find interesting enough to label, and that’s why definitions — or, more generally, working out what the properties of a well-defined problem are — end up being of interest to mathematician types.

As for the Great Salt Lake, I’m afraid I don’t actually know that salt water is necessary for making electricity, or how using it for electricity would affect the lake’s other uses, so I don’t think I know enough about the problem to venture an opinion.

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• Kurt Struble 5:39 am on Monday, 16 March, 2015 Permalink | Reply

you bring up some really interesting points which i am going to LOVE to delve into with, having to do with art and science … (and i don’t mean art V.S. science) i don’t have time to delve at the moment though since it’s going on 1:00 a.m. here. but i WILL and i’m looking forward to it. i have reservations though, … you might say i am an over analytical person … so for every statement you make i’ll come up with a couple of conclusions which can branch off and soon i am lost in space … whoops .. i’m going off on a tangent right now … and i don’t want to … maybe one way to overcome this problem is to look at how i think … in terms of vectors … now …. i always think of vectors as straight lines … and i think if vectors are straight lines then they will intersect with other vectors … but, intersecting vectors are not ”tangents’ ‘ (which is the way i think … ) (jeeze, this gets complicated since i don’t know your lexicon so my use of ‘tangent’ and your usage is probably completely different than mine) … so while two vectors … after they intersect … even though they go off in two separate directions … this is not the same as a tangent … which ….. TO ME … a tangent would be a vector that suddenly splits … so that the vector goes off in two directions … … maybe this ‘species’ of vector has a definition i’m not aware of …. the point i was tying to make is … my mind … thinks in terms of split vectors … let’s call it a Therblig Vector, so discussions can get pretty tedious … i think the beauty of science is that you are looking for Truth … but by scientific definition, (i’m going out on a real long limb here … ) TRUTH is a single statement … E = mc2 …

there’s great beauty i n the language you use i order to find this ‘truth” because it’s so ‘precise’ … but based on the way i think … everything is ‘tangental” .. thoughts splitting and resplitting … to me, discoveries can be made by this constant re-splitting … re-splitting … going deeper and deeper into these splits …. so that there are many many discoveries made along the way as opposed to having an idea that there’s something then trying to find the language to confirm that the thing exists … vectors continually splitting gives an infinite places to go and i suppose an infinite amount of discoveries to make along the way … ………. i think there’s some truth to this since structurally, the brain is comprised of branching ‘vectors’ … as are … if you look .. at the structure of trees … their limbs … basically there are splits and splits and splits … reaching out collecting information … while at the same time the roots of the tree … as a reflection of the tree’s limbs .. are doing the same thing underground …

so i started out saying i had to go to bed and it’s now getting close to two o’clock and it’s all because i was being over analytical looking at the application of vectors and ”tangents” (by my definition) as they apply to how we think and whether it is best to journey through time seeking TRUTHS as opposed to seeking TRUTH … hey … please forgive me … i think i’m going off half cocked here … making all these statements … my final comment is …. that, maybe the definition of ART is … a random discovery made while searching for the right word or the right color … a search that’s almost random in nature waiting for something to ‘fall into place ” by following the right ‘split’ … or tangent …

it’s the idea that maybe this is the difference between pure art and pure science … DON’T GET ME WRONG … I’M NOT SAYING THAT WITHIN MATH. OR SCIENE IN GENERAL there isn’t creativity … i guess i’m writing more about the different languages and different approaches … even though i know there is plenty of overlap … i’m really sorry if i’ve confused you … i’m not going to proof read this … so i know it’s probably confusing but maybe there are a couple of grains of corn that we can harvest into a nicely organized corn cob that we both can look at and think is beautiful for the same reasons and for different reasons … jeeze … i had no idea where this whole thing was going … and didn’t even think i’d continue and … here i am … i hope you slept well … thanks … for even considering my words … ks

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• ivasallay 2:34 pm on Thursday, 12 March, 2015 Permalink | Reply

I liked that the equation on the blackboard EQUALED z, an often used variable. Dark Side of the Horse often seems to have good math comics, doesn’t it?
I can think of times when that Frank and Ernest strip would be quite good to show in a classroom.

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• Joseph Nebus 8:03 pm on Thursday, 12 March, 2015 Permalink | Reply

Yes, letting the variable be z is one of those little touches of craftsmanship that makes Dark Side of the Horse stand out in these mathematics roundups. I don’t know Samson’s biography. It’s easy to suppose she or he might have a mathematics-inclined background, although it’s just as easy to suppose she agrees with the notion that having the irrelevant details check out makes the overall joke stronger.

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A bit more about Thomas Hobbes

You might remember a post from last April, Thomas Hobbes and the Doing of Important Mathematics, timed to the renowned philosopher’s birthday. I talked about him because a good bit of his intellectual life was spent trying to achieve mathematical greatness, which he never did.

Recently I’ve had the chance to read Douglas M Jesseph’s Squaring The Circle: The War Between Hobbes And Wallis, about Hobbes’s attempts to re-build mathematics on an intellectual foundation he found more satisfying, and the conflict this put him in with mainstream mathematicians, particularly John Wallis (algebra and calculus pioneer, and popularizer of the ∞ symbol). The situation of Hobbes’s mathematical ambitions is more complicated than I realized, although the one thing history teaches us is that the situation is always more complicated than we realized, and I wanted to at least make my writings about Hobbes a bit less incomplete. Jesseph’s book can’t be fairly reduced to a blog post, of course, and I’d recommend it to people who want to really understand what the fuss was all about. It’s a very good idea to have some background in philosophy and in 17th century English history going in, though, because it turns out a lot of the struggle — and particularly the bitterness with which Hobbes and Wallis fought, for decades — ties into the religious and political struggles of England of the 1600s.

Hobbes’s project, I better understand now, was not merely the squaring of the circle or the solving of other ancient geometric problems like the doubling of the cube or the trisecting of an arbitrary angle, although he did claim to have various proofs or approximate proofs of them. He seems to have been interested in building a geometry on more materialist grounds, more directly as models of the real world, instead of the pure abstractions that held sway then (and, for that matter, now). This is not by itself a ridiculous thing to do: we are almost always better off for having multiple independent ways to construct something, because the differences in those ways teaches us not just about the thing, but about the methods we use to discover things. And purely abstract constructions have problems also: for example, if a line can be decomposed into nothing but an enormous number of points, and absolutely none of those points has any length, then how can the line have length? You can answer that, but it’s going to require a pretty long running start.

Trying to re-build the logical foundations of mathematics is an enormously difficult thing to do, and it’s not surprising that someone might fail to do so perfectly. Whole schools of mathematicians might be needed just to achieve mixed success. And Hobbes wasn’t able to attract whole schools of mathematicians, in good part because of who he was.

Hobbes achieved immortality as an important philosopher with the publication of Leviathan. What I had not appreciated and Jesseph made clear was that in the context of England of the 1650s, Hobbes’s views on the natures of God, King, Society, Law, and Authority managed to offend — in the “I do not know how I can continue to speak with a person who holds views like that” — pretty much everybody in England who had any strong opinion about anything in politics, philosophy, or religion. I do not know for a fact that Hobbes then went around kicking the pet dogs of any English folk who didn’t have strong opinions about politics, philosophy, or religion, but I can’t rule it out. At least part of the relentlessness and bitterness with which Wallis (and his supporters) attacked Hobbes, and with which Hobbes (and his supporters) attacked back, can be viewed as a spinoff of the great struggle between the Crown and Parliament that produced the Civil War, the Commonwealth, and the Restoration, and in that context it’s easier to understand why all parties carried on, often quibbling about extremely minor points, well past the point that their friends were advising them that the quibbling was making themselves look bad. Hobbes was a difficult person to side with, even when he was right, and a lot of his mathematics just wasn’t right. Some of it I’m not sure ever could be made right, however many ingenious people you had working to avoid flaws.

An amusing little point that Jesseph quotes is a bit in which Hobbes, making an argument about the rights that authority has, asserts that if the King decreed that Euclid’s Fifth Postulate should be taught as false, then false it would be in the kingdom. The Fifth Postulate, also known as the Parallel Postulate, is one of the axioms on which classical Greek geometry was built and it was always the piece that people didn’t like. The other postulates are all nice, simple, uncontroversial, common-sense things like “all right angles are equal”, the kinds of things so obvious they just have to be axioms. The Fifth Postulate is this complicated-sounding thing about how, if a line is crossed by two non-parallel lines, you can determine on which side of the first line the non-parallel lines will meet.

It wouldn’t be really understood or accepted for another two centuries, but, you can suppose the Fifth Postulate to be false. This gives you things named “non-Euclidean geometries”, and the modern understanding of the universe’s geometry is non-Euclidean. In picking out an example of something a King might decree and the people would have to follow regardless of what was really true, Hobbes picked out an example of something that could be decreed false, and that people could follow profitably.

That’s not mere ironical luck, probably. A streak of mathematicians spent a long time trying to prove the Fifth Postulate was unnecessary, at least, by showing it followed from the remaining and non-controversial postulates, or at least that it could be replaced with something that felt more axiomatic. Of course, in principle you can use any set of axioms you like to work, but some sets produce more interesting results than others. I don’t know of any interesting geometry which results from supposing “not all right angles are equal”; supposing that the Fifth Postule is untrue gives us general relativity, which is quite nice to have.

Again I have to warn that Jesseph’s book is not always easy reading. I had to struggle particularly over some of the philosophical points being made, because I’ve got only a lay understanding of the history of philosophy, and I was able to call on my love (a professional philosopher) for help at points. I imagine someone well-versed in philosophy but inexperienced with mathematics would have a similar problem (although — don’t let the secret out — you’re allowed to just skim over the diagrams and proofs and go on to the explanatory text afterwards). But for people who want to understand the scope and meaning of the fighting better, or who just want to read long excerpts of the wonderful academic insulting that was current in the era, I do recommend it. Check your local college or university library.

• jcckeith 12:30 am on Wednesday, 14 January, 2015 Permalink | Reply

From what I understood about this post was – aside from the king is god’s annointed and thus is always right and whatever he says is the rule regardless of its veracity – was that all accepted mathematicians of the day stuck with the classical models of mathematics, which in truth, can be difficult to use much less completely comprehend. So Hobbes wanted, like so many people these days, for mathematics to have a much more reasonable, understandable basis? From what i gather from your post, he offered various proofs for his assertions but none were complete or at least none proved his assertions when provided for peer review? And from what else you have said, this Hobbes guy had the deck stacked against him from the beginning because of his background in philosophy?

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• Joseph Nebus 12:08 am on Thursday, 15 January, 2015 Permalink | Reply

Largely, yes, although I’m hesitant to declare exactly what Hobbes wanted because I haven’t read anything more than excerpts of his work, and he did a lot of work over the course of decades, and it can be hard to tell what the point of original work is until after it’s been thought and reworked, completed, and refined. In many ways mathematical constructs are like inventions, with the first ideas of something a complex and barely functional kludge that requires a couple generations of work to make into an elegant and understandable whole, and Hobbes’s mathematics didn’t get those generations of work.

I think it’s fair to say he wanted a more materialistic mathematics, thinking of the lines you draw with straightedge and pencil and the circles you draw with compass and paper. There’s obvious need for that, especially if you want to do something like turn an abstract concept into an actual machine or building or canal or such. But it isn’t the same kind of work that mainstream mathematics was doing at the time, so in some ways he was working in a different field from other mathematicians.

Hobbes’s background in philosophy didn’t by itself hurt him; the fields of mathematics and philosophy blur together on many points, and were even more blurry then. Both fields have about equal claims to Descartes as a founder of their modern incarnations, after all, and Berkeley and Pascal and Leibniz as lesser but still noteworthy figures. Philosophers can be surprised to know mathematicians get to put in a claim on Kant as one of their member; I’m sure the reverse happens. It was a more fluid era.

However, Hobbes’s particular philosophy worked against him, because it was frightfully controversial (then and since) and thus made it harder for people to stand behind him. And it put him politically at odds with the Oxford and Cambridge establishments — there was a fierce battle about how the Universities should be reformed and how free they ought to be — and these were the people who would form the Royal Society and the mainstream of English mathematical thought.

And, yes, Hobbes didn’t manage to prove the big impressive things he wanted to prove, including some results that carried implication like pi being (if I have it correctly, as I can’t find the page for this right now) equal to 3.2, which everyone by then knew could not be so.

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• Boxing Pythagoras 1:44 pm on Wednesday, 14 January, 2015 Permalink | Reply

If you liked Squaring the Circle, you’ll likely enjoy Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World, by Amir Alexander. He also touches on the Hobbes/Wallis feud, but talks about a number of other related discussions from 17th Century mathematics on the philosophical nature of the field.

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• Joseph Nebus 12:09 am on Thursday, 15 January, 2015 Permalink | Reply

I’ve been looking at that! I’ve enjoyed Alexander’s other books, and mostly been figuring out whether my reading list has gotten short enough to start adding new things to it.

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• Aquileana 10:16 pm on Sunday, 18 January, 2015 Permalink | Reply

Excellent post Joseph … I can’t but congratulate you!.

“Homo homini lupus”, as Hobbes would say!.

All the best to you. Aquileana :D

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• Joseph Nebus 1:20 am on Monday, 19 January, 2015 Permalink | Reply

Oh, I’d forgot that Hobbes quote, which is silly since it’s one of his top ones.

Thanks kindly; I’m glad you enjoyed the post.

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