Lance Mannion writes real gud, so I usually enjoy reading his essays, but this time he struck a nerve and for the first time I have to deeply disagree with him. He’s writing about math. He, personally, thinks he’s not good at math, so he regards it as unnatural.
Personal prejudice: Most people can’t do math. What we call math is actually simple arithmetic. Adding, subtracting, multiplying, and dividing. Calculating. What Jethro Bodine in his pride at his sixth grade education called cipherin’. Nobody does math, and can do math, until they understand why multiplying two negative numbers together produces a positive number. I’ve never understood that one. So I can’t do math.
I can cipher like a wiz, though. Like a sixth grader, at any rate.
This Paley Center panel discussion on Hidden Figures was interesting and I can’t wait to see the movie but I was a bit disgruntled by the way people on the panel who know better talked about math as if it’s all arithmetic and anybody can do it and do it well if they put their mind to it and get over the idea it’s too hard.
OK, that part I agree with. He’s right: math isn’t about the kind of number games you can play on a calculator. Mathematics isn’t about arithmetic, except for those parts of a big field that are. But then, after correctly stating that math is something more, he doesn’t really get it and ends up criticizing it for things it isn’t.
But I didn’t like it that learning to do math got implicitly compared with learning how to write a sentence that parses.
As the son of a physicist and computer scientist who, hard as he tried, never could get me to follow his math when he helped me with my homework, and as someone who was an A student in math in grade school but was stymied by ninth grade algebra and defeated in eleventh grade by calculus, and as the father of someone who has struggled with a severe math learning disability—dyscalculia they’re calling it these days—and is two daunting math courses shy of completing his degree, I’m here to tell you…
Math ain’t natural.
We don’t think in numbers. We’re not good at holding them in our heads. Most of us count “One, two, three, many” and then, if we’re forced to go higher, “Many more, and a lot!” and that’s as high or as complex as our numbers get.
That’s irrelevant, as he should know. Mathematicians aren’t necessarily thinking in numbers, either: they’re thinking about patterns, or relationships, or logic, or even geometry. Somehow, being unable to visualize numbers greater than, say, seven in our heads doesn’t seem to be an obstacle to considering infinity.
The thing that raises my hackles, though, is that word “natural”. I hate that word. It’s usually used to vaguely mean “the good things that I like” rather than “those unnatural abominations that perverted libertine over there likes”…like math. Or football.
And then, uh-oh, he abuses the “E” word. My wrath is immediately stoked.
Some of this is the result of biology, anatomy, and evolution—the evolution of bodies, and then the evolution of culture.
Evidence suggests that humans were talking to each other from the start, putting words to their feelings, coming up with ideas that could only be created with words, naming things. Naming things is what made us human. We evolved to speak and we evolved from speaking. Culture, art, and society are the result of words. We didn’t start counting until later when societies became more complex and more things needed to be sorted out. We can see our ancestors inventing math.
We don’t know precisely when language arose, so it’s hard to place it in relationship to other aspects of culture. Did the hominins who lacked language also lack art? We don’t know. So it’s hard to say that one is the prerequisite for the other. It’s also a definitional problem.
Did the first being we’d recognize as human speak? Or are we going to use speaking as the criterion for defining humanity? Maybe the first True Human was the bipedal ape who rose up from the grass with a rock in his hand, computed (without words, obviously) the parabola it would follow when thrown, and estimated the intersection of his rock’s path with the racing path of that tasty looking rabbit over there. Note that this isn’t the math of counting things, which Mannion unfortunately lapses into assuming here, but a different kind of understanding of the nature of motion that’s more physics than poetry (although I have noticed a tendency for poets to claim movement as an act of poetry; maybe scientists need to fire back and claim meter and rhythm as acts of physics and sensory biology).
But to return to the previous point: everything is natural, or nothing is. If we’re going to start labeling human specializations as unnatural, well then, singing ain’t natural. Dancing ain’t natural. Writing novels…what a weirdly unnatural thing for an animal to do.
All that stuff doesn’t just come “naturally”, whatever that means. People have to train to do it, they have to practice and practice, and there’s also an aspect of talent that you have to be born with. I can’t sing, unless you call off-key croaking “singing”, but I wouldn’t seriously declare that singing ain’t natural. Of course it is, because we do it.
Hey, who knows, maybe singing — something with a rhythm and tones — preceded language, even. Perhaps australopithecines got together in great choruses and hummed and beat drums and sang to express their mood, all while calculating what frequencies went together best to make pleasing chords. Don’t know. Wouldn’t past ’em. Humans are weird, and the first ones wouldn’t have been constrained by any expectations, you know?
So please, avoid trying to justify your prejudices by claiming your preferences are “natural”. It turns out we’re all capable of whipping that one right back at you, so it’s a poor argument.
But I do usually agree with Mannion, so I’ll conclude on one point we both share. He’s not a fan of the current STEM fad.
I hate the word neo-liberal. But I only know it as an online epithet. Progressives use it as an all-purpose insult for liberals and Democrats who don’t adhere to any point of their programmatic political doctrine, and as such it has whatever meaning the user gives it because it suits his purposes or feelings at the moment. Which is to say it has no real meaning. But if it does have any meaning in the real world, it’s when it describes the self-interested principle that social good is best achieved by letting capitalism take its natural course. If it saves money or makes money and some of that money is used to promote the general welfare, then hooray! And if that’s what it means, then our colleges and universities have become hotbeds of neo-liberalism.
STEM is a neo-liberal dream.
Promote STEM and the government will throw money at your school. Promise the kids good jobs and they’ll flock to your school and more government money will follow. Target minorities and girls in particular and even more money sluices in. And look at the good you’re doing while you build the endowment and hire more administrators. Those kids get a first class education (Never mind that most of their classes are taught by grad students and adjuncts.) and will likely get good jobs when they graduate. They’ll become productive members of the wealth producing elite and isn’t that the whole purpose of education and of life, in general?
I’m a STEM guy in a STEM field teaching students STEM who personally benefits from the parent/student bias for STEM degrees, but I agree, STEM alone is a terrible idea. We should be promoting a balanced education, where scientists-to-be need to learn some history and language and music and all that social science/humanities stuff. I deal with students all the time who regard all those requirements outside science and math to be a waste of time, and are focused entirely on zipping through their education as quickly as possible so they can get a job in a science- or engineering-related occupation. It’s a terrible attitude. Didn’t they pay attention to Alexander Pope?
A little learning is a dang’rous thing;
Drink deep, or taste not the Pierian spring
Oh, right, they’re STEM majors, and they would never even hear of Pope unless we forced them to take those literature courses, which they think are a waste of time. They don’t know what the Pierian spring is, either, because they’re all hoping to grow up to be David Gelernter.
You know Gelernter, the guy who might be Trump’s science advisor.
In Gelernter’s view, the future of higher education will involve a focus on STEM subjects while “throwing out” the arts and humanities. Online courses will become commonplace, but not without evolving, and students will need a “digital guides or mentors” to carry them through online education.
Degrees themselves will become a thing of the past, Gelernter writes as they’re “gradually be replaced by certified transcripts.” Rather than a university conferring the degree, a “transcript” — that is, coursework showing that a student has successfully learned a given set of material — will be “vouched for” by a trusted institution like a think tank, newspaper, museum, or research lab.
Jebus. Throwing out the arts and humanities is a great way to build a generation of short-sighted, unimaginative, uneducated blockheads who might be able to code or mix reagents, but that’s about it.
How about if we do it all, balanced and in moderation? Or would that be too “unnatural”, especially when it requires an alliance of mathy people and non-mathy people?
Obviously he uses the term “natural” in a way that isn’t meaningful. On the other hand it is true that language arose at least a couple of thousand years before writing, and that math remained rudimentary (mostly just counting) for another 8,000 years or so; developed in a couple of spurts with the Greeks and the Arabs, and then took off after the 19th Century to a vast new universe. Writing and music have changed over time, but they haven’t expanded in the same way and they are much older. So there is something quite different about math.
However, as for people who don’t think they can grasp advanced algebra and calculus, I’d say for the most part they just haven’t been taught well. There are people of highly unusual mathematical aptitude but for the most part, I think most of us have the faculties to grasp college math. But some people need a good teacher.
I meant to write that language arose a couple of hundred THOUSAND years before writing, of course. (You should have a comment editing function.)
Heh. I got my degree in STEM – the hard mix of geology and physics (Geologists hate math and Physicists hate rocks and outdoors).
The knowledge that gave me the most bang for the buck were all humanities, because I’m around sweaty, gassy, messy humans all the time, we share a culture and often interact.
I’m talking about Philosophy (how to think and argue), Women’s studies (seeing bias around us all the time), Classic Lit (understanding contrasts between our culture and others, and how to observe), Sociology (where values come from and why people act “funny”), etc., etc.
Think tanks are trusted institutions?
Son, it ain’t Maths, it’S just you…
+++
We’re currently school shopping for our eldest (middle and high school). Many schools advertise that they’re STEM schools. That’s all good and nice, but I never see a “language school” or “history school”. Though the one we want to choose is an Arts as in drawing and acting school.
That’s for consistency. For example, the distributive law wouldn’t work otherwise. e.g.:
(2-1)x(3-1) = 1×2 = 2; and
(2-1)x(3-1) = 2×3 + (-1)x3 + 2x(-1) + (-1)x(-1) = 6 – 3 – 2 + (-1)x(-1) = 1 + (-1)x(-1)
The only way to reconcile these is if (-1)x(-1) = 1.
I look forward to receiving my Sociology degree from the Daily Mail. It, too, won’t be worth the paper it’s written on.
PZ, I fail to see the big problem (beyond his poor word choice). Language is both biological and social. Counting isn’t biological in the sense that language is, or we wouldn’t have counting systems based alternately on fingers (base-10) or knuckles (base-12, minus thumb), and all languages would have arithmetical counting schemes (they don’t, some merely have one, slightly more than one, and slightly more than that). I take the article to be using the term “natural” really to mean “biological basis” and nothing more.
I mean, really, everything I learned in graduate linguistics is reinforcing what he’s saying to me. That doesn’t mean there’s an interesting point in any of it, just that it isn’t an inaccurate one.
It is a bit far to say “words” fed intelligence, though. And that is a definitional issue. The animals with the biggest brains relative to their body mass all possess some kind of communication, and communication comes in other forms than the sign/signified relationships making up human communication. Also few real linguists anywhere are willing to define what a word is. Same with “language”. These terms are broad and useless when it comes to academic description.
I had a similar thought as soon as he (after noting the difference between arithmetic and mathematics!) smooshed it all down into counting. It’s far easier to write a program for counting than it is to write one for walking on two legs without falling over and accurately throwing projectiles. And yet the sort of neural processing necessary for the latter two things predates humanity. That complex calculations are being done without language doesn’t make them less complex.
I will say there is one flaw, and that is perhaps a failure to perceive the difference between philosophy and utility. Communication, which feeds intelligence, is not in itself a philosophy, yet you can create and explore a philosophy of language. Likewise mathematics is a philosophy, but it can be used without proving it works. Some of the most basic concepts in arithmetic were not proven to logical satisfaction until the 20th century, but they worked just fine, and were discovered just as easily the cart before the horse.
I suspect that the position of Trump Advisor is one of the best places for philistine idiots like this Gelernter fellow – if there’s one thing Trump is famous for it’s not taking other people’s advice.
In the Middle Ages there was a common notion that higher learning literally had a seat and kingdom of its own, which lodged with the most enlightened and glorious kingdoms of the day. First it flowered in Egypt, then among the Greeks, then the Romans, and finally (so Otto of Freising would have it in his Gesta Friderici) among the Germans of the Holy Roman Empire. One might suggest that in the years since Learning has migrated to the USA, as Germany devolved into fascism, and is all set to move once more now America is going the same way…
The fact that multiple cultures independently came up with the idea of building observatories and had them work out how to predict eclipses and other astronomical phenomena suggests we are pretty well wired for doing complex math.
Similarly, we have attestation of multiple independent inventions of counting systems, in support of the independent inventions of bureaucracy.
cartomancer: cool story, but it elides Mesopotamia, Persia, India, China, Japan. As well as Mesomerica, though it was totally independent.
Opposing math and arts is a bit sad.
Math can be be quite beautiful to the trained eye, and elegance is a sought after quality in mathematics and algorithmics.
And of course you can use math to create or better understand a lot of work of art.
As someone who does write code, I’m glad I had classes in art and humanities. It helps me to think about problems in different ways which in turn improves the quality of my work.
oh man, without anything actually “triggering” the thought, when he talked (wrote) of how special math is and how primitive man didn’t Count, until there was enough stuff to talk about how much each one got. I remembered recent discoveries of crow behavior, and how, surprisingly, they think numerically. Given a group of 10 seeds and one of 11; they will methodically count to find out which has more. And not just dive on the one configured to look bigger.
.
My primary math education class repeated Set Theory the first few months in each grade until algebra. Burning into out brains that numbers are just symbols of how many and how to group them. That arithmetic is not just symbol manipulation rules, but descriptions of how sets cn be combined together, divided, etc. *ugh* ….
—
The thing about the common perception of math that frustrates me, is ‘anything with numbers’ is called math, and the pride people take in avoiding math. One example of the former is a phrase a friend used, “I’m bad at math so Sudoku is not my kind of puzzle” to which I just gasp. Sudoku is NOT math, numbers are just the symbol used but totally irrelevant to the puzzle itself.
Algebra is not just abstract thinking about abstractions. It’s a tool to answer realworld questions about everyday questions.
Q) If my dinner will be for 5 people and my recipe is for 4 people, how much more of each item do I need?
A) do algebra.
and so forth.
*spit*
[ramble …]
?
.
I started college as a math major with an eye towards computer engineering. And, though I could do the math (quite well), I could never see what the numbers were trying to tell me. I think that may be a difference between someone who is truly exceptional at math and the rest of us. Just as a baseball player who is exceptional can read the pitch coming at them based on the angle of release, the spin, the arc, and decide to swing or not to swing in a tiny fraction of a second.
But to claim that, since not everyone can ‘see’ what the equation is saying, math is not natural is absurd. Just as claiming that, since we cannot all ‘see’ what is happening with a ball, that swinging a club is unnatural.
I guess that early hominin languages involved blowing bubbles underwater.
You are all missing the most important point ,why do Americans call it Math instead of Maths like wot we British do ?.
Also ,why do Americans pronounce solder as soder ?.
Music may be older than language…. No idea, but it’s certainly possible. But it may be pointless or even counterproductive to make such distinctions at some point. After all, you might notice that there are some musical aspects of language, linguistic functions of music, drawing aspects of writing, mathematical or logical aspects of basically anything we do, etc. So, I figure many of these things may have been developing together as a big interconnected web of abilities. Which was first? Probably a large assortment of things we don’t consider modern academic fields in their own right.
However, harmony may not be at the core of it, historically speaking. I’d guess that we started out with simple rhythmic and melodic components. You repeat stuff in time, making some kind of significant or at least recognizable pattern. That gives a performer something very easy to do, and others can join in by doing the obvious thing of repeating (at the same or different times) what that performer does. Maybe that’s in order to communicate something, maybe it’s just obsessing over a pattern you happen to like…. doesn’t seem to make a difference.
What you probably wouldn’t do at first is have a bunch of different performers doing different things, according to some (very abstract) harmonic principle or another — that seems too complicated. If you’ve got that sorted out, then you were already prepared to have them all do (more or less) the same stuff, at the same time or in succession. We probably didn’t have any proto- conductors, choreographers, impresarios, etc., to organize such things, certainly no theorists to make sense of what that was supposed to be about. But it seems like less of a problem for a fairly small, leaderless group of people to simply mimic each other — that’s not hard and seems to “come naturally” to people (scary scare quotes right there) — which basically suffices to get some sort of music.
One of the things I don’t like about the STEMpocalpyse is that there are always lines drawn very carefully around what is supposed to be considered “science, technology, engineering, math.” Music, for instance, is not included, despite all of the scientific/technological/engineering/mathematical work which forms part of the discipline. But serious question here: when my musical work involves bits of physics, math, psychology, sociology, even computer programming nowadays … then in exactly what sense is it “not STEM”? I’m sure there may be a sense out there according to some silly person or another, but I don’t think I have a use for it. History, linguistics, philosophy, and so forth, are also “not STEM” for these purposes, which is apparently the purpose of funneling ever larger wads of cash into specific fields, as well as to ensure we all know who’s the boss and what is best in life. Only very specific types of science and engineering, along with pure mathematics oddly enough, get to count. Why? Well, just because, I guess. There doesn’t seem to be a good reason. But if you’re really just interested in the cash or whatever it is, then just own up to it and say so. You don’t need to invent all sorts of confused rationalizations for what you’re doing and expect everyone else to happily play along.
It does seem very job-oriented too: you’re training people to do a particular type of work, as opposed to simply providing opportunities to learn (full stop) and at the expense of doing anything else with their lives (since any of this shit takes time and money). Also, I just can’t make sense of a position that wants to put an emphasis on STEM, while also trying to promote anything like interdisciplinarity. You’re either prioritizing certain fields or you’re not; and “interdisciplinary” work between chemists and physicists, for example, does not exactly look like the gold standard of what is possible in that regard. It all just feels extremely limiting and myopic and more than a little pathetic, which doesn’t feel right in an academic setting.
Yes, lets dump the humanities and turn everyone into technologists. It will mean fewer people around asking potentially subversive questions about things like justice, freedom, responsibility to others, and so on.
(Retired engineer-cum-philosophy-student here)
Um. “Not natural”.
In order to braid a sling to herd animals, well, you need an understanding of numbers. In order to weave a piece of cloth, same thing. Those activities have been going on for a fearfully long time, at least 20,000 years, and possibly far longer.
The evidence and the conclusion don’t seem to go together. Unless by “not natural” you mean “something that I. personally, do not like.”
Pretend you’re walking on a number line. Start by facing positive infinity. Every time you see a minus sign, do an about-face.
In other words they’ll be obsessed with keeping taxes low and government out of their life, since they won’t know what government is for or how it works, they’ll be entertained by the basest amusements, and they might have opinions about the world (or even, perish the thought, political beliefs) but they’ll lack the background to explore them or the skills to express them beyond an obscenity-laced text message. What little knowledge of philosophy, beauty of morality they do have will be provided by their megachurch.
Who would benefit from such a system, you ask? I dunno.
People who use “neo-liberal” to refer to Democrats, don’t understand what “neo-liberal” means.
#19: Wait, what? Brits pronounce the “l” in “solder”? More grounds for our revolution.
It seems to me that he’s also thinking that there’s just one kind of math, that there’s no difference between theory, calculating, estimating, visualizing, constructing proofs, analyzing proofs. I’m not a mathematician but it sounds to me like his problem is that he doesn’t understand his problem. He’s just not thinking very well.
My impression is that most fields are sub-specialized. My field (computer security) hasn’t been around very long at all, and it’s already got a dozen things I’d identify as sub-specialties. You can be top drawer in one sub-specialty and not in another. In some cases, skill in one is oppositional to the other.
We didn’t start counting until later when societies became more complex and more things needed to be sorted out.
Crows can count. Elephants can count. Humans couldn’t count until societies became complex?
It’s useful to be able to figure out how many people it’ll take to carry piles of stuff, so you know how many of the tribe to summon. It’s very important to be able to tell the tribe how big the raiding party is. Etc. Methinks he talketh through his hat.
@27: I figure that some sort of ability to do basic rough quantification, comparison and logic are wired-in to the brain. To update Kronecker: Evolution invented the integers; all else is the work of humans. (More or less).
Math/numbers are not real things…they are useful fictions. nothing more.
Tell that to the IRS during an audit. ;)
#25, PZ:
Wait, Minnesotans don’t? This USian has always pronounced the el. It’s the d I don’t pronounce. The way I say it is more like soul-jurr.
Apparently language doesn’t come as naturally as we thought!
Oh wait, never mind, I’m thinking about the word “soldier.” Language is hard :/
@#31, malta:
Is it possible you are confusing solder, the metallic stuff used to hold electronics together, with soldier, someone who kills people for a living with governmental sanction?
#19 #25
…What? Are there people that don’t pronounce the l in that? So solder instead sounds like …soda? WTF
The opposite of a $50 profit is a $50 loss (50 * -1 = -50). The opposite of a $50 loss is a $50 profit (-50 * -1 = 50). I don’t even get what’s so hard to understand about this. There’s no other way for it to work. Do you have trouble understanding double negatives in English??
I take a seriously dim view to people who don’t understand math. It’s just about the basis of logical and critical thinking. I suspect it angers people because it’s the only subject in school that actually requires you to think and understand the subject instead of memorizing and parroting back answers. It saddens me, because I think a lot of math illiteracy comes from shitty teachers who think math should be as rote and mindless as the way they poorly teach every other subject (https://www.reddit.com/r/pics/comments/3pmyh3/teachers_logic_in_grading_math/). Yeah, dyscalculia is a real thing, but difficulty with numbers or mental arithmetic shouldn’t interfere with understanding core logical principles, like why taking away a negative results in a positive.
You know what I loved about math as a young radical? Math is objective. It’s not dependent on simply trusting a source of information; you have absolutely no way of personally verifying everything in a history textbook, but you can test for yourself the quadratic formula. Because of its objectivity, math is the school subject least affected by teacher bias (but sadly not immune to it: http://www.slate.com/blogs/xx_factor/2015/02/10/teacher_bias_in_math_new_study_finds_teachers_grade_boys_more_generously.html) Math shows that the universe itself runs according to consistent, understandable rules. Math implies that there is a reason behind every seemingly arbitrary event.
And on a transcendent level, all spirituality is vulgar compared to mathematics. Math is the engine that powers the universe. Math is the closest real thing to God.
@34 Holms
Everywhere I’ve been in America, “solder” is pronounced like “sodder”, like someone who sods.
When I read this I thought I’d remembered supporting evidence for “math is not natural”. About 10 years ago I read an article about the Piraha tribe in the Amazonian rain forest. Their language contains no numbers. Anecdotal evidence showed that in the absence of language providing a framework for numbers they thought in logarithms. So are we built for numbers or logarithm?
Here’s a simple question:
If humans doing math isn’t natural, then why did geometry develop independently in the empires of Babylonia, Egypt, Greece, China, and India?
The fact that “knowledge of mathematics” seems intensely correlated with “extremely successful civilization” ought to mean more to most people.
@38: Because large agricultural civilizations all have plots of land to mark out and divvy up.
If 1 = one he could try maths in English, or math in American.
“Throwing out the arts and humanities is a great way to build a generation of short-sighted, unimaginative, uneducated blockheads who might be able to code or mix reagents, but that’s about it. ”
Isn’t that the point? It’s like George Carlin said, all they want are people just smart enough to fill out the paperwork and keep the machines running.
“as someone who was an A student in math in grade school but was stymied by ninth grade algebra and defeated in eleventh grade by calculus”
What the author of that statement has not realized is that he has tacitly admitted that he is good at memorizing things but he totally lacks comprehension. I noticed this trait in some students nearly 50 years ago in grade school and even through early high school. My daughter then independently noticed it in some of her classmates as well and told us about it. Some people get through life using rote memory alone, while others actually seek to understand the actual principles.
As an addendum to the above, people who complain about failing technical test questions because the question being asked is not identical to any examples that they were taught, even though the question uses exactly the same principles that they were taught, is a solid example of rote memorization vs knowledge.
“That’s a question that I have never seen the answer to before now, so it is totally unfair!” is the battle cry of the rote memorizers.
Yeah, with the sodder/ sold-er thing I was thrown off the first time I heard it too. It’s like hearing a Brit say “aluminium”.
@zetopan- I have done fine in every course I have ever taken in my life, including math, but I have to admit that I have never been at a school that was very good at teaching comprehension. You go through most of your younger years learning rote, and then they jump you into principles with narry a word. I am under the impression that was what common core was supposed to counter-act.
@39 stevewatson
The question wasn’t “what problems did these societies solve with geometry?” the question was “if math is so unnatural, why did these societies independently arrive at geometry for the solution?” Why didn’t they seek to solve issues like landownership through ways that come more “naturally” to humans?
I’d wager you already know this, but I’d feel remiss not to point out that mathematics developed in all those empires *way* beyond the formulae you’d need for agriculture, or *any* practical purpose, really. Ancient cultures were exploring abstract math functions in the BCs that were a radical revolution when they were discovered in Europe in the Victorian era.
That’s just what’s so amazing about mathematics. Most fields of knowledge are driven by need. Math, ultimately, is driven by pure exploration. So much of mathematics was discovered just by people wondering “hey, what happens if I do this?”
zibble:
The fact that we can use math so effectively shows that we care about whatever consistent, understandable descriptions we’re able to conjure up about how the universe “runs.” We work hard to represent it as well as we can, and that tends to pay off … sometimes. Maybe that view is a little less grand than yours, but at least I think I can wrap my head around it.
I don’t think it’s much of a surprise that reality is consistent (how understandable it is to you or to me or to Donald Trump is maybe another question). What would it be like if it were inconsistent? I’m not too sure what that would even mean. It presumably wouldn’t be like anything in particular, because it would also not be like that particular thing.
For that matter, I don’t think anything has some kind of consistency-making powers … how would that work? What precisely would something be doing if that were the job this thing is supposed to have? Why would something be needed to fill this job for anything? I mean, do I need to have a special guardian angel of my own, making sure I’m consistently whatever it is that I am? Or can I simply be whatever I am, which certainly looks to me like it entails, without any additional help from anybody or anything, that I’m not whatever I’m not? Maybe multiply entities is okay in this case, but even if it is, exactly what is it supposed to accomplish?
No, it doesn’t. If in fact an event is merely seemingly arbitrary, that fact implies there is a reason behind it, since it is not arbitrary as it seems. Math doesn’t determine such things — as I said, physical events just happen, and we use math to describe them. Absolutely nothing requires us to believe there must be a reason for everything. I know very well that there are natural or physical explanations for many, many things, but I have not once seen any bit of math or logic worth taking seriously which implies that nothing is arbitrary. I have no idea how that would be done, but please go ahead, do it in mathematical style and show your work.
Uhhhh, but seriously, there’s no real thing like that either. The universe needs no power to “run” and has no engines. It is something out of which you could make engines, if you’re into that sort of thing. But as far as I’m aware, there’s just the universe we live in, nothing transcending it or beyond it or governing it, in any sense of the words, or urging it somehow to do whatever the hell it does. The fact that it does stuff (and doesn’t do other stuff), whatever the hell that happens to be, well … that’s a decent place to begin I guess, but it’s not a conclusion that you had to reach.
@ Zibble, 35.
Okay. I’ve got to delurk for now as a mathematician. Or a math-student at the very least.
No. I’m sorry. I would like that to be true and lay claim to logic and critical thinking, there are principles that can be considered that, but mathematics isn’t the only source. There is, for example, philosophy laying also claim to these. What I would consider “mathematical logic” is in many universities a part of CS.
Okay, could be a case of country matters. Where I live, sure, you may do with some success a lot of subjects by rote memorization. In truth, you can do that with math too. Math isn’t unique, even in this regard. But where I live, every subject is pretty much taught by introducing some underlying principles and how to apply them. Understanding is in some way required for the best grades.
From what I’ve understood of american education, I’d say even math is really easy to pass just by rote memorization there.
What.
Let me repeat that: What.
You don’t test quadratic formula. You prove the quadratic formula. Math is objective, sure. Math is the only science where you can PROVE something. Because math is on a fundamental level completely abstract. You take some axioms and rules of inference and then you can prove results, and they remain the same, forever. They are true. Assuming of course, we continue to assume that the axioms are true and the rules of inference produce only true results. (For those axioms and rules of inference). Math makes absolutely no statements about “reality” or the “universe”. Math as a system has no implications like you claim or anything. Math doesn’t power the universe. Because mathematics makes no claims about reality. Mathematical models are used as a way to explain some (real-world) phenomena. There is a world of difference between these.
Okay, some nitpicking. If you consider math a part of reality, metamathematical results about mathematics may speak about reality. But that is one completely different discussion.
from what I read here it could have been written by someone else with a much better grasp of humor and been rather funny but he just sounded dumb instead the jokes did not really work.
uncle frogy
It’s also a bad sign when someone applies the word “evolution” to subjects outside the scope of evolution theory… Like culture. It is a strong indication of sloppy thinking.
While I agree that the focus on STEM to the exclusion of humanities and other such subjects is a detriment and should be averted, one also has to keep in mind the point of view of the student. When I had to take a class outside my major I was often reticent not because I thought the class was worthless, but because a 3-credit course was another few hundred bucks I had to shell out. And, yeah, it sucks that the primary focus of school has been driven toward getting a job, but for the students it is their focus for a good reason. As someone who’s degree is in political science and psychology with a minor in English, I often kick myself for not getting a “practical” degree, because it set me back. It’s really hard to care about how well rounded your education was when you’re working 60 hours a week at $12/hr and still barely getting by because you spent time earning essentially a “worthless” degree rather than learning a trade, getting a job focused degree, or simply jumping into the job market and earning experience (which these days is often more valuable than a 4-year degree). The days of just any college degree getting you a job are long over. For a lot of folks it’s specialize or starve.
As Kevin Anthoney points out (#6) the rule for multiplying negative numbers is simply a matter of consistency, e.g. with multiplication of numbers assumed to be commutative.
But it is possible to construct a fully consistent arithmetic where a negative times a negative is a negative (although – spoiler alert – it is generally much less convenient to use that version of arithmetic.) For complete details, as well as some fascinating history of mathematics, see Alberto A. Martinez’s book Negative math (Princeton University Press, 2005)
http://press.princeton.edu/titles/8026.html
“Maybe the first True Human was the bipedal ape who rose up from the grass with a rock in his hand, computed (without words, obviously) the parabola it would follow when thrown, and estimated the intersection of his rock’s path with the racing path of that tasty looking rabbit over there.”
With assumed permission, I’d like to bring in some physics to this excellent biology board. With the same assumptions (no friction, point masses of rock and earth, and Newton’s Physics) needed to claim the rock path is a parabola, one actually finds the rock path to be elliptic. Without Newton’s assumptions the path is neither parabolic nor elliptical. If one threw the the rock harder (i.e. faster and higher) the rock could go into an elliptic earth orbit. In the early part of its ‘parabolic’ path the rock wouldn’t know if it would clear the mountain on the horizon and thus should maybe be on an elliptic path. The truth is, it was elliptic all along. It’s the same for any thrown object such as a baseball or bullet. Nearly everybody commonly thinks the path is parabolic. Why does the parabolic path notion persist? Nearly every introductory physics text explains that for short paths it’s OK to assume the earth is flat, which makes the path parabolic. The mathematics of parabolas is simpler than the math of ellipses.
Bah. Being able to provide a transcript as described just means you were present for the classes. If you are being generous, it could assume you passed the finals in each, meaning you showed some basic ability to regurgitate the material on command.
Neither have much bearing on comprehending a subject in a way that allows you to do original work in it. And this ain’t just sciences. When I’m running a milling machine, I set up a work holding based not on some exact book example, but upon an understanding of how it generally works and the underlying principles those book examples were trying to teach.
@46 consciousness razor
It would mean that the laws of reality could be suspended or broken by supernatural means. Really, though, you couldn’t have worked that out for yourself before taking that condescending tone?
It used to be a very common belief that, at some level, mathematics would break down or be prone to unsolvable errors, because the universe was, at its core, of divine origin and not natural, and thus our human means of understanding the universe (like math) would be insufficient. That’s why Bertrand Russell helped write the Principia Mathematica, which proved the foundations of mathematics using symbolic logic.
I didn’t say “requires” I said “implies”. It’s not absolutely proven but it’s a fair inference.
“Engine” as in a physics engine, like the kind programmers use to replicate the nature of forces in the real world. I don’t see what there is to disagree with there, the comparison is so direct it goes beyond metaphor.
Please stop trying to argue against what I’m saying as if I believe in god. It’s not committing the pathetic fallacy to get a little poetic.
@47 begemot
Until you start getting into algebra and calculus and trigonometry, as zetopan (42) pointed out.
You can do both. All I’m saying is you don’t have to know shit about mathematical proofs to take a ruler and check the veracity of the equation itself.
The word was -implies-.
You can accuse me of equivocating between “math” and “physics”, and that’s fair, but I still feel you’re being a bit of a tedious bore.