It’s been a long, long day of teaching and meetings and lab work, and sometimes it’s good to get home and discover why it’s important to teach. Like by learning what a movie star thinks about basic math, along with his history of domestic violence.
“Since I was a child of three or four,” he says, “I was always wondering, you know, why does a bubble take the shape of a ball? Why not a triangle or a square? I figured it out. If Pythagoras was here to see it, he would lose his mind. Einstein, too! Tesla!” He shakes his head at the miracle of it all, his eyes opening wide, a smile beginning to trace itself, like he’s expecting applause or an award. And all you can do is nod your head and try to follow along. He just seems so convinced that he’s right. And that he is about to change the world.
“This is the last century that our children will ever have been taught that one times one is one,” he says. “They won’t have to grow up in ignorance. Twenty years from now, they’ll know that one times one equals two. We’re about to show a new truth. The true universal math. And the proof is in these pieces. I have created the pieces that make up the motion of the universe. We work on them about 17 hours a day. She cuts and puts on the crystals. I do the main work of soldering them together. They tell the truth from within.”
…
After high school, he attended Pratt Institute in Brooklyn, studying chemical engineering, until he got into an argument with a professor about what one times one equals. “How can it equal one?” he said. “If one times one equals one that means that two is of no value because one times itself has no effect. One times one equals two because the square root of four is two, so what’s the square root of two? Should be one, but we’re told it’s two, and that cannot be.” This did not go over well, he says, and he soon left school. “I mean, you can’t conform when you know innately that something is wrong.”
Ooooookaaaaaaaay.
He seems to be doing all right, despite the disgusting attitude towards women and the most useless and deranged ideas about math.
I feel sympathy for his professor, and relief that all of my students are a lot brighter than Terrence Howard.
Now I have to go to an evening meeting with a bunch of students.
Oh, fuck it…. just fuck it.
wat?
The world, especially the parts of it within the blast radius of the chemical plants he did not design, will be eternally grateful to the acting world for taking him in, and turning him from a career in Chem E…
At this rate, he’s going to design a machine with a wheel where pi is exactly three, and we’re gonna start getting mail from alternate universes.
mithrandir @4,
So, Terrence Howard is actually Bloody Stupid Johnson?
I had a student much like that. He insisted that if you divided by zero you got zero. I provided a half dozen proofs that his approach didn’t work, to no avail. When his test answers got marked wrong, he got really angry, and eventually went to the administration … who told him that I was right and he needed to get over himself. I don’t know if he ever changed his deep opinion, but he at least started answering test questions correctly … Sometimes that’s the best you get.
What the fuck did I just read? It’s so wrong, it’s not even wrong.
I never follow celeb news, and frequently don’t know who is who in a movie. I did know Howard’s face, though, and had appreciated his acting in Iron Man and The Salon.
Never going to look forward to his appearances again.
One of the many, um, interesting comments from his wife Pak:
Hey, seventeen hours a day soldering crystals will eat into one’s ability to get the housework done. That or maybe Howard starts counting dishes and doesn’t like that “two is of no value” or whatever the fuck he is trying to say in the article.
It’s probably just a coincidence that TimeCube.com recently had an outage…
Crip Dyke: “I never follow celeb news, and frequently don’t know who is who in a movie.”
Neither do I. I can’t even be bothered to check who that person was in Iron Man. What he said about basic math made me wince. I can’t imagine what would have happened if he hung on long enough to encounter the square root of negative one.
I customized my news feed to get me the basics (world, my country, health, science, tech, and a few other things). Though twice in the last month the software powers added “Entertainment” and “Sport” back in, so that I had to delete them yet again!
I can’t even can’t even, because there are no evens to can’t. Probably because he thinks the square root of 2 is itself, which is an even number and in despair the even has vacated the planet. There’s no more evens. I simply can’t.
Math is not metaphor. Metaphor is not objective reality. And objective reality isn’t poetry or metaphor.
One can use mathematics and objective reality as metaphor and poetry and one can *even* use the mathematics and science language in metaphor to display math and science language in opposition to the metaphorical and poetic result.
But YOU. CAN. NOT. use the metaphorical and poetic results to dictate math and objective reality. Objective reality is real and meaning is a one-way street. (Metaphorically, that is.)
*sigh*. This does get soooo frustrating at times.
Terrence Howard? Nope, never heard of ‘im ’til now. I’ve heard of Curly Howard, Moe Howard, and Shemp Howard, and he (by your post) reminds me of them but, of course, they were acting. Probably better actors too.
Rolling Stone is on a roll these days: hit pieces on both Donald Trump and Terrence Howard in the last couple issues. They haven’t so thoroughly trashed a celeb since they deep-sixed Billy Corgan. I wonder why celebs keep offering them interviews. Anyway, Howard is clearly disturbed, and I feel like mockery is kind of beyond the pale for someone who seems to have a mental illness. His battering and abuse deserve condemnation, but the other aspects of his condition are just kind of sadly pathetic.
@14 “Probably better actors too.”
Whatever else Terrence Howard is, he’s a very fine actor, without question.
If I put one pie into one group then I will get two pies? Mmmm, pie.
Also, if 1*1 is 2, then what is 1.1*1?
I’d ask that for the utter delight in watching his head explode.
@Rowan, #12:
Nice cant.
@holyPinkUnicorn, #9:
Well, if he’s washed one dish once, he’s washed it two times. And washing it when it’s already clean is a waste of effort!
There are only three important numbers– 1, 2, and 4. The rest and decimals are just conformists deliberately harshing your mellow. But they’ll all be gone in 20 years. (20 is a bigger type of 2.)
======
That’s actually a really good and subtle question and an excellent test to see how well people can utilize abstract concepts.
Good for you! It’s a pretty satisfying feeling, isn’t ….
Um, I think we can assume Pythagoras figured it o…
Um, now I *know* Einstein and Tesla would ha…
Um, I’ll just see myself out, shall I?
2.2, duh.
I would like Terrence Howard to forget about multiplication and square roots so that I can teach him about taking-N-groups-of-M-pies-and-counting-how-many-pies-in-total, how-many-groups-of-M-pies-make-N-pies-in-all, demonstrating that N-groups-of-M-pies equals M-groups-of-N-pies, extending to slices of pie…
@ #9:
‘Ymean he’s a total cipher? Flunk math & domestic involvement right there. Two strikes on one pitch.
He probably also believes pi are not square, Pi are round — cake are square.
Um… what if you told him that 2*1 is 2? How would he take that? I think he’s confused because 2*2 and 2+2 are 4, and that’s throwing him off.
Also… hey Matt? Can we not with the armchair psychology? Thanks.
I wouldn’t be surprised if some mathematician had proved, under some really strange axioms, hypotheses and fuzzy logic, that 1*1=2. I would like to see Mr. Howard demonstrate his proposition. Come to think of it, I would not.
In some ways mathematics crankery is the king of crankeries, since it’s often the basis or a strong supporter of other crankeries.
If 1X1=2, what does he think 1X2 equals? 3? Does he dispute that any number times one will equal itself, in general? Or is it only the case of 1X1 that he disputes? Is he somehow confusing multiplication with addition?
But what really boggles my mind is; how did he have this problem for the first time in COLLEGE?? Could he actually have never encountered 1X1 in elementary school or high school?
Whoa! Holy Fuck! You may be right. Then the square root would be 1/2 so half of 2 would be 1 and and his sentences would be more than just random things totally unrelated. … shit. Maybe he *is* just stupid.
The only way that is possible is if *everything* equals 0. Then 2 = 1 + 1 = 0 + 0 = 0 = 0*1 = 1*1.
Other wise (if there is more than one number):
a) 1 is never equal to 0 and
b) 1*1 is never equal to 1 + 1.
reason a: If a is not equal to 0 then a = a*1. a*0 = a*(1 – 1) = a – a = 0. 1 = 0 => a = 0.
reason b: If 1 + 1 = 1*1 = 1 then 0 = 1 + (-1) = 1 + 1 + (-1) = 1 which is impossible.
So if 2 = 1 + 1 then 2 can never equal 1*1 =1. Although 2 *can* equal 0.
This assumes we are working with fields (where 0 + a = a and 1*a = a and a(b+c) = ab +ac). If we aren’t working with fields then we can assume whatever the fuck we want and we can so 2 is equal to cat’s vomit as far as anyone cares.
Gad! Why the heck did I just do this? No-one actually cares.
I think college was probably the first time he was arrogant enough to believe he was right and the world was wrong and he would refuse to “conform.” Also maybe it’s a personal theory (based on one times itself requiring value) that he only developed in college.
Personally, I think what I’m not supposed do here involving armchair psychology beginning then but … we aren’t supposed to do that.
But maybe he completely missed the entire concept of multiplication and confuses it with addition (but then how the heck did he *get* into a chem engineering program?)
“because one times itself has no effect”… so yeah, I don’t think he accepts 1*a = a because that have “no effect”.
So…maybe. If multiplying by 1 has no effect then 1 can’t do anything so if 1 can’t do anything then adding 1 can’t do anything either. So this says 2, which is 1 + 1, has no value and “that can’t be”.[*]
Gad. *why* do I try to get into these guys’ heads? Because it’s so alien?
[*]Meanwhile there is no problem with add 0 having no effect because he’s fine with 0 having no value. *BUT* if you multiply by 0 you eliminate *everything*. That *IS* a *BIG* effect. *sigh*
Looks like he’s taking the loss of War Machine to Don Cheadle really badly.
I worked with a lawyer who had to use a calculator to multiply by 10. A finance lawyer. I guess it was better that he admitted he could not do math in his head, rather than doing it wrong. May be it’s like being color blind.
I really want to be his accountant! He’d have to drop the charges in court one I got him in the witness box!
Though I’d have to represent myself – I doubt I could find a lawyer with that kind of numeracy.
woozy @29:
I care! If you hadn’t beaten me to it, I would have posted something similar. The only correction I’d make is that we don’t even need to be working in a field – a ring is the minimal structure where we have a well defined “multiplication” operation with an identity element. Essentially, if we’re working in any mathematical structure which is not trivial (i.e. at least two elements) and where “1” and “times” have any kind of non-arbitrary meaning as commonly understood, then 1*1 is necessarily equal to 1. Of course, the difference between a ring and a field would be totally beyond Howard…
I think he’s been inhaling the solder fumes.
This brings back memories of being able to logically prove 1+1 = 2 and 1 * 1 = 1 then extend that to infinity. Now that was wasn’t easy to get your brain wrapped around. What this guy does not understand is that math can be counterintuitive but in this case the algebraic axioms state he’s wrong in a way that can be simply demonstrated using physical objects as suggested by Corey Yanofsky in #22. And then the idiocy of the square root of 2 is 1 (or 2), no it is not, it is 1.414214 (rounded up) which in this case, since it is a 2-root, if multiplied with itself would result in 2 again.
I wonder if his brain would have imploded if he would have been confronted with logarithms.
@sunburst(#26):
Not under really strange circumstances. Just need to work with a different set of axioms. Happens all the time, a good example are non euclidean geometries.
Multiplication isn’t even some obscure branch of maths that takes some ability for abstraction to understand it, it is directly applicable to real life situations.
3*2 = I eat 3 times 2 pies, A have eaten 6 pies in total.
This guy is literally saying: I eat 1 time 1 pie, A have eaten 2 pies in total.
I can’t even wrap my head around how you can get something like this wrong.
@29 woozy:
It also works if you use the symbol “1” to represent something other than the number we normally represent as 1. (Or in speech, the word “one” to mean something else.) I don’t think we can say that he’s using a different definition of “square root” from everyone, as this doesn’t explain his statement, “If one times one equals one that means that two is of no value because one times itself has no effect.” This implies he doesn’t believe that multiplying something by “one” will result in no effect. This might arise from confusion due to the colloquial use of “multiply” which implies an increase when used outside of a mathematical context. I also suspect that when he learned that the square root of 4 is 2, he internalized that as meaning “square root” meant taking half of something, then worked backward from there and wasn’t willing to reexamine his initial assumption when he found contradictory evidence.
Or – and this is my favorite explanation – his brain runs on a language like early FORTRAN, and he accidentally redefined “1” as the square root of 2. Yes, redefining numbers is something that was actually possible in FORTRAN.
[sigh] Since no one else seems to have said it…
1*1=2 for sufficiently large values of 1.
Obvious really
It didn’t work for Kim Davis and it won’t work for you, Mr. Howard.
So if I’ve got a £20 note, I can put it in an envelope and then I’ve got one envelope each with one £20 note in it. So that’s 1×1=2 £20 notes, which is 40 quid.
Does it remain £40 when I take it out of the envelope? And does anyone know what 1x1x1 is?
Reminds me of an idea Heinlein floated in Expanded Universe. Voting machine of the future. A smart 12-year-old walks in, solves a quadratic equation generated on the fly, is allowed to vote. Terrence Howard walks in, fails to solve his quadratic equation, voting machine locks, loud raspberry noise from the machine, Howard endures pitying looks from bystanders as he slinks out. Go hit the books, better luck next year.
Those familiar with Heinlein’s oeuvre will know which novel he was discussing when this came up.
LOL. When I logged in, the site asked me to prove my humanity by solving 3+7. No need to worry about Mr. Howard posting here.
Not sure why you (PZ) are bothering. There seems to be plenty of reason to complain about the way TH treats other human beings. Why bother with his strange ideas about mathematics? Masses of evangelical churches. right-wing politicians, and the Discovery Institute are not lining up to push Howard’s ideas into the schools. are they?
This kind of eccentricity is often found in creative artists. For example, some of the Russian Constructivists, in the 1920s, got the idea that sinusoidal motion was inherently more efficient than motion in a straight line. This led to some weird and funny imagined designs for future vehicles. But no one pushed to get this into Soviet schools — it was just laughed off by everyone else.
For now, forget it. Let me know when the first televangelist takes up Howard’s method of multiplication.
I’d like to sit down with him and some paper and round-ended scissors, making squares and rectangles.
See this 1×1 square, Terrence? What’s its area? 2? Ok, let’s run with that.
Let’s make two of them. The total area is 2+2. You accept that’s 4, right?
So, let’s tape those two 1×1 squares together to make a rectangle.
The long end of this rectangle is 1+1=2, right? Here, measure it if you want to be sure.
So, we’ve got this 1×2 rectangle with an area of 4. Are you feeling uncomfortable yet?
Here’s another square, this time 2×2. That also has an area of 4, right? You did say that 2×2=4.
So, if we fold this square in half, to make a rectangle with half the area, how come it exactly covers this other rectangle?
Put down the scissors, Terrence: they’re blunt anyway.
Wow, I like him so much as an actor, and I expected he’d be saying something positive and life-affirming, “stay in school, math saved my life,” that sort of thing. But that was something else. I don’t know what that was.
sunburst:
I’d like to get a better idea of what his geometrical models look like and what those are all about. The descriptions weren’t really enough to give me a clear mental picture. It obviously sounds bizarre and utterly useless for the kinds of math people normally want to do, but it could at least be internally consistent. (At some level it would have to be, if it’s something you can actually do with real physical objects.) Probably not especially interesting or original, but maybe it’s not totally arbitrary or illogical.
Whatever the shapes are like, the multiplication stuff (yeah, sure, it’s related, probably) doesn’t seem like it would need to be all that strange. I mean, you could say the first one times the second one is equal to one, and there’s also the second times the first which equals one. So, you simply add the results together and get two. That may not fit very systematically with his confused statements about square roots, but it could nevertheless be some idea along those lines. No, I don’t know when ideas like that could have useful applications, certainly not as useful as ordinary multiplication.
But if people are going to be criticizing it, they should be able to give a fairly detailed and coherent explanation of why ordinary multiplication doesn’t work that way. What bothers me is that some just scoff at it and mock him and assume he’s just an innumerate idiot who makes the trivial mistakes you want him to make, without offering any actual reasoning, as if math were just some piece of dogma in Plato’s heaven that fell down to Earth one day. Even if his reasoning is terrible or it’s not all put together in a coherent way (seems likely), that could actually be addressed, and in the mean time it’s sort of nice to see somebody actually cares about it (probably too much, if it’s actually interfering so much with his life) and is trying to be creative and think for himself about it. Just shitting on the guy doesn’t seem like a productive and mathematically-serious approach for somebody to take.
I doubt he realizes that he’s trying to remove the multiplicative identity from the number system. And he doesn’t realize all the trouble that will create.
Maybe he hasn’t given it any thought beyond 1 x 1 = 2. Does he think 2 x 1 is still equal to 2?
Because then he has to say that 2 = 4.
#43: The reason I focused on that was that I’d just come off an intense day working one on one and in small groups with real students, and was about to go off to an evening session with another group (and today is all about student questions, too — they’ve got an exam coming up, so I’m making an effort to get them thinking). So I was all tuned in to student-teacher interactions, and that story came up.
I agree that his behavior towards women is of far greater concern, and his math is just a bizarre eccentricity.
One drinks ones vodka
One sees double.
@ Anthoney “… And does anyone know what 1x1x1 is?”
A bloody small cube?
The square root of 2 should be 1, but unfortunately it’s 2? No, my calculator says it’s closer to 1.41 with a lot of additional numbers after that. He’s not only wrong, he’s wrong about what he thinks others think but are in fact wrong about. He’s might be fractally wrong.
Here’s a fun quote:
But what if it’s one cubic light-year of space or even one cubic mile of yogurt? That’s sorta big, isn’t it?
mmmm
yogurt
I prefer to make my own yogurt these days. It doesn’t even take a lot of effort, you just need a starting culture, so buy some live yogurt. Super markets around here sell some brands of live yogurt, but if yours don’t, then you might need to go to a health food store or something, dunno. Mix a bit – half a glass of yogurt at least – of that with 1 L of whole milk, spread it out over appropriate, clean, closable containers (I guess glasses) and incubate at about 40 degrees (Celsius, of course) over night and presto! When you’re running low on self-made yogurt, just use the last one for the next incubation phase. As long as you don’t get any contaminants in there, you can keep that going for several generations without having to use another live culture bought at the store.
The following comment would have been super cool if I could have slipped it in somewhere between 20 and, say 53, but it’s just a tad late now:
@19: Nice cant.
And even.
Also, I going to be using this for a while: there are no evens to can’t.
units may be an issue. 1 * 1 could be asking 1 apple times 1 orange = 1 apple *mic drop*. See no 2 involved in that there. Square root of 2 (apples) is a Wozniak (so to speak, to go off the rails, sorry).
slightly reminiscent of the snarky, “2 plus 2 equals 5, (for particularly large values of 2)”
After high school, he attended Pratt Institute in Brooklyn, studying chemical engineering
He attended some sort of a prat institute, alright.
I’m pretty sure I learned that the square root of two is 1.41, not 2.
So, he’s an idiot in addition to being a wife beater and misogynist? I am shocked.
http://jezebel.com/287242/terrence-howard-thinks-women-are-unclean-and-dressed-like-whores
Yeah. My statement that we have to be working in a field was pretty lame. Of course, we can be working in rings and quasi-rings and quasi-fields where we drop axioms. I suppose if you made something really stupid by dropping the distributive property (which means in essence there’s no necessary relation between addition and multiplication) we can come up with something rather meaningless where 1*1 = 1 + 1.
consciousness razor
I think people have been giving pretty decent explanations that multiplication is calculating the result of a number of groups with number of items. Hence all the discussions of pies and blocks and wallets.
To say that 1*1 means something other than taking one group of one item or to say that taking one group of one items somehow makes a second item appear is not a “trivial mistake”. It’s an incoherent statement. If *he* has some alternative definition of multiplication than it is *his* responsibility to explain what it is and even when he does he can’t simply declare the rest of the world wrong for using the conventional one. And he doesn’t have an alternative definition. He has some vague intuition that multiplying by one has to have “some effect” so 1*1 has to be something other than 1. Why 2? why not 37? And by insisting on giving 1*1 “some effect” he makes no definition of what the effect would be.
Frankly, to call him an “innumerate idiot” making “trivial mistakes” would be giving him too much credit.
====
Okay, I will grant you that conservation of measure is Plato dogma given on high. We make two assumptions that if we have a set number of things the number will be the same no matter how we shuffle or rearrange them, and we assume that no matter how many groups and items in each group that the actual number of total items will actually be some number. Those are dogma given on high but they are pretty fucking fundamental assumptions about reality.
The number of items of 1 group of items is the number of items in the group and, likewise, the numbers of singleton group of items is the number of items total as each singleton group corresponds to a single item. So it follows that 1*n = n*1 = 1 so although “multiplicative identity” and “field axioms” are Plato dogma they did not in anyway fall to the earth but we’re logically and well derived.
Moggie
Well, technically speaking we’ve never proven space is euclidean so in theory we don’t actually know that area is multiplicative.
Which I think is just the type of thing Terrence Howard would love to hear and consider profound with a deeper newer truth.
Yeah, that’s a subtlety that can really get missed. In multiplication it’s numbers and not units that get multiplied *unless* you have a meaningful mechanism for combining units. (Such as a man-hour, or a square foot.)
A cheap puzzle is
1 dollar = 100 cents.
1 dollar* 1 dollar = 100 cents * 100 cents.
1 dollar = 10,000 cents = 100 dollars.
I volunteer to carpet Mr. Howard’s house. Every time I carpet a 10 ft by 10 ft room I get to charge him for 200 sq ft of carpet. Sweet!
@ 6 Abner
Sounds like what a “smart” creationist would do in a biology or geology class about the age of the earth or speciation – give the “right” answer to the disbelieving teacher while knowing in his/her heart what is really true.
Some people always know in their heart what is right – you saw about 20k of them at an arena in Dallas yesterday.
re @60:
gotme! Not. The rules you violated is multiplying united numbers together producing the same unit. EG inch times inch = (square inch), you did inch * inch = inch. Error! !404!.
your specific example was mind boggling: dollars times dollars is … wha??? inconceivable, I stop at 100 dollars times 100 (unitless).
mixed units could help, EG: 1 (dollar per pocket) times 100 (pockets) = ?
[A:] 100 dollars.
…and so on and on.
I emphasize the “unit” importance, ’cause that so often saved my butt in science/engineering classes. “track the units, they’ll clue you the right way to form the equations to solution.”
@63:
Um, the puzzle wasn’t for *us*. It was for the students and the Terrence Howards of the world not really getting what multiplication is. That’s why I referred to it as a “cheap” puzzle. It was a cautionary tale of misapplying context of multiplication which “if 1*1 = 1 then multiplying by one has no effect and 2 is has no value; that’s can’t be” is. The puzzle was meant to be obvious and a humorous joke. I didn’t intend to seriously stump anyone (except possible an elementary school arithmetic student in which case it would serve as an instruction.)
It wouldn’t surprise me if there were an economic principal that would require square money but I have no idea what it would be.
re @64
sorry I forgot to include, that I did understand it was a joke, used as an example of misapplying the units rule.
my @63 was just “playing along”. sorry for the misunderstanding
Son, you can make up your own math, but you can’t fly a rocket with it.
Dammit, woozy, I’m really busy and only considered the standard algebraic structures, but now I’m really tempted to skimp on getting ready for my students’ induction week and trying to work out a properly minimal set of axioms such that 1*1 = 1, “2” can be sensibly defined as 1 + 1 and 1 =/= 2. Damn you.
So, if I were to give Mr. Howard $1 one time, could I get 8 quarters? Let’s do it a million times.
@67.
“trying to work out a properly minimal set of axioms such that 1*1 = 1, “2” can be sensibly defined as 1 + 1 and 1 =/= 2.”
Damn, I got lost in more than an hour paring it down. Only to come to the obvious and simple conlusion:0
a) distributive property
b) unique zero
Without the distributive property there is no relationship between addition and multiplication other than they use the same symbols. This is akin to playing checkers with chessman. Possible but pointless.
Examample: S = {0, 1, 2} .S;+ such that 0 + 0 = 0; 0 + 1 = 1; 0 + 2 = 2; 1 + 0 = 1; 1+ 1 = 2; 1 + 2 = 0; 2 + 0 = 2; 2 + 1 = 0; 2 + 2 = 1.
S; * such that 1*1 = 1; 1*0 = 0; 1*2 = 2; 0*1 = 0; 0*0 = 2; 0*2 = 1; 2*1 = 2; 2*0=1; 2*2 = 0.
You see what I did there? S+ and S* are both Z3 under addition but for S* I switched the symbols for 1 and 0. Trivial and pointless. And it fails distribution.
Uniqueness of 0: 1 + 1 = 1 => 1 = 0. Thus with distrubitive law: b = b*1 = b*(1 + 1) = b + b => b = 0 for all b. Therefore a trivial set.
Now, the question is: How can we build a set with distributive law and zero not unique where 1 + 1 = 1 and 1*b = b for all b? Well, I’m sure we can. not sure of the point but:
Well, lets try it: S = {a, 1} 1 + 1 = 1.
1 is mult. identity so a*1 = a; 1*a =a. and 1*1 = 1.
a*1 = a so a+a = a*(1 + 1) = a*1 =a
So unknowns are a + 1; 1 + a; a*a
Eight possiblities. … Oh, screw it. I have things to do but I’m sure 2 or maybe even 4 of them but at least 1 will work out.
…. to be continued….
I know what I’ll be wasting my time on today. *sigh*
A bit late here, but… WTF?
I’ve no idea who this eejit is — albeit other comments suggest an wannabe-actor — but I suspect a remedial education, starting at the level of “this is a finger” and “this is how to use fingers to count” is advisable, and exceptionally taxing.
Anyway, simplest case I could come with where 1*1 = 1 and 1+1 = 1 and a(b+c) = ab + ac and (b+c)a = ba + ca for all a ,b, c and there is at least two elements:
S = {a, 1}. 1 + 1 = 1. 1*1 = 1. a + x = a = x + a for x = a or 1 and a*x = a = x*a for x= a or 1.
So minimum requirement that 1*1 != 1 + 1. Unique zero and distribution and non-trivial. (In my example 1 is a zero as x + 1 = 1 + x = x for x = a or 1, but it isn’t unique as a + a = a as well.)
Meanwhile 1*1 =2 and 2 !=1 is simply a contradiction in terms. 1*1 = 1 unless “1” has no meaning. Plato has so determined it to fall to earth.
Let me defend his math dyslexia (of course his attitude towards women is disgusting and not to be defended)
Math’s difficult: I’m sure I can go look up statistics on how most students don’t get as far as Algebra 2, and dread any mention of just the word “math”, and that its teaching should be improved. At least Howard’s thinking about math, I’d imagine the majority of people simply look at an equation, shiver, vomit, and then ask someone else to do it.
And isn’t questioning basic things like “is 1*1=2??” how you *learn* math? Shouldn’t the process be something like: you read some book/solve some problem, don’t understand something, go to a teacher, who promptly replies that what you don’t understand is completely trivial and stares you down until you say ok and move on, but you still don’t understand your problem *at all*, and then, 2 years later, “……..Ohhhhh! Holly shit!”. The problem isn’t that Howard posed that question, or that he couldn’t have been an engineer or mathematician if he wanted to(he *ABSOLUTELY* could have, this point must really be stressed). It’s that he gave up (it’s also that he was too focused on the Pythagoras’ and Einstein’s and Tesla’s of the world…. but then, I imagine that’s also a common issue that can’t be ridiculed out of existence).
He doesn’t have math dyslexia. Math dyslexia is confusing numbers, not understanding how fractions work, assuming (a + b)^2 is the same thing as a^2 + b^2. Math Dyslexia is tossing your hands into the air and wondering why oh why is it so hard and why doesn’t it make any sense.
It is *not* deciding that you are smarter than every other mathematician in the history in the world and you are the only one who understands it and everyone else is wrong.
Questioning is fine but you also have to listen to the answers.
Yes, that’s a bad way to teach. But he doesn’t still not understand the problem. He has created a batshit incorrect understanding and convinced himself it must be right because he must be the one person in the world with the courage not to conform. He was *not* beaten and broken down.
No, it’s that he insisted the answer had to be what he thought it was, that it couldn’t possibly be what everyone else for milenia thought it to be, that he refused to try to understand what the question was and insisted it had to reflect something entire off the wall and incoherent.
Oh, for fuck sake. !!NO!!!. Nobody who insists an utterly meaningless and incoherent belief that 1*1 =2 and simply refuses to believe one group of one item is one item but that some utterly misapplied idea that if multiplication by 1 “has no effect” means no other completely unrelated operation with one can have any effect either, and who solves this non-existing problem be arbitrarily making up an “effect” out of nowhere which is unrelated to anything else and incompatible with the entirity of 6,000 years of mathematics, such a person can *NEVER* be an engineer or a mathematician.
He did nothing of the sort. He insisted he was right and the entire study of mathematics was wrong. He is convinced the entire world will recognize his “new truth” and he spends 17 hours a day convincing himself he’s tapped into the real truths of the world that eluding Einstein, Pythagoras and Tesla. That’s not giving up.
That’s refusing to face reality. And expecting reality to bend to you is … wrong. And definitely worth deriding no matter how good an actor or how tough and tragic his life has been.
oh, geez
I have bad news…
woozy, @73
You’re in the habit of turning down students then, are you? Should every math undergraduate be assigned a therapist, who, upon finding that a student a) believes some unorthodox and strange thing, and b) is unwilling to give that up when prodded (probably because of a *combination* of not really understanding their error, even after a competent explanation, and wedding themselves and their success to that crazy belief), should summarily recommend expulsion?
Take Erik Andrulis as an a example(PZ wrote about him a few years ago, link below) of someone who became a biochemist at case western, despite believing that everything can be explained by torus’ (quantum gravity, biochemistry, psychology, the moon…). That theory’s just as insane as Howard building weird shapes in his garage. Yet Andrulis made it through, probably because he was able to keep the crazy bottled up until he was in a secure enough position.
I’m not defending how these people dismiss the entirety of their field, in the pursuit of being a New Einstein. I’m advocating that we don’t flush them down the toilet, or the initial impulse that made them imagine their heterodox universe.
http://freethoughtblogs.com/pharyngula/2012/01/27/the-comparison-to-jabberwocky-is-inevitable/
gakxz1, 75
If there is someone who has made it past grade school trying to claim on a test or project that holding up one finger on one hand means they are holding up two fingers… no, they should not pass. Pretty much everyone has weird beliefs about something or other, but crankery about such basic math is not conducive to success in any field requiring math. It would be nice if the teacher tries to explain it many times in many ways before giving up, but attempting to use such crankery in the engineering design process would lead to non-functioning and/or dangerous products.
woozy:
How do you know any of this? Couldn’t both sorts of issues be causes here, along with numerous other things we haven’t even considered yet? What makes you insist on one?
The double-negative would mean he does understand. And I have no idea how that’s supposed to connect with the possibility that he’s been exposed to bad teaching, contradict it, or whatever it’s doing. Rhetorically, it leads us back into the story you’d prefer to tell, but that is all you’re doing.
This is becoming a long story. How do you know any of it?
Do you have any idea what his life has been like? I don’t. Do you know about any instance in which he actually explained his reasoning in any appreciable amount of detail (however faulty it may be), what he meant or what he had in mind when he made the statements this arts/culture magazine published without further explanation or context? I don’t know that either. How convinced are you that you must be right?
MattP:
I doubt he means anything like that. You’re merely attributing that to him. You can think of it lots of different ways. It can be a geometrical idea, like finding the area or volume of something (or the mathematical representation of something analogous to that, without actually being a quantity of space). It can be thought of as a shortcut for adding together groups of physical objects (unless you’re multiplying something other than integers). It can just be a specific method of manipulating terms in an equation or mathematical expression. It’s a very powerful and flexible mathematical tool, so it can do lots of stuff, which doesn’t much look like any of the other stuff, except in an exceedingly abstract and hard-to-pin-down way. Who knows which sorts of concepts he’s actually working with? Nobody can read his mind, so how exactly are we supposed to tell, if it’s going to be based only on a handful of short quotes from a Rolling Stone article, without assuming any bullshit that isn’t actually in it?
PZ: “The reason I focused on that was that I’d just come off an intense day working one on one ”
and so now you’re 2! Got it.
One group of one item is a total of one item. Two groups of one item each is a total of two items. One group of two items is a total of two items. One group of two items and one group of one item is a total of three items. Two groups of two items each is a total of four items.
One meter (length) times one meter (length) is one square meter (area). One square meter (area) times one meter (length) is one cubic meter (volume).
Two meters (length) times one meter (length) is two square meters (area). Two square meters (area) times one meter (length) is two cubic meters (volume).
Words have meanings, and the very first classes in engineering (statics and dynamics) drill into your head over and over and over: “keep track of your units”. He could be using some unit system where one length multiplied by itself is equal to two unusual units of area, but uncommon units does not make 1×1=2 a universal truth. One cubic meter is equal to 2000 half-liters, but it requires at least one extra multiplication operation to perform the unit conversion and does not make 1×1=2000 a universal truth. None of it can make the square root of two equal to either two (as he claims) or one (as the article says that he claims his teachers told him).
MattP, @79
You know, it’s possible to do something (homework, exams) without completely understanding what you’re doing, or what it means. I don’t know anyone who hasn’t “just” memorized formulas for some upcoming exam, without knowing a thing about what they actually mean/how they’re derived. Ideally yes, complete understanding should be strived for. Practically, there’s often not enough time.
Howard made it through high school and attended college (I’m going by what’s on this blog: I’ve not actually done more than skim some of that article). Do you think he *actually* wrote 1*1=2 on an exam? No: he did everything he was told (including keeping track of units, I’ll assume). That doesn’t mean he understood everything, or that he didn’t harbor reservations. It’s even a bit strange to say he was speculating about multiplication: it just served as a proxy for his worldview.
At any rate, what exactly are we arguing about? He didn’t publish a paper trying to disprove all the mathematics that’s ever been done. He just related, in an interview, that he has some fanciful ideas, which mostly amounts to arts, crafts, and quixotic speculation about “multiplication”. How horrible!
Consciousness razor:
“How do you know any of this? Couldn’t both sorts of issues be causes here, along with numerous other things we haven’t even considered yet? What makes you insist on one?”
“ Do you know about any instance in which he actually explained his reasoning in any appreciable amount of detail (however faulty it may be), what he meant or what he had in mind when he made the statements this arts/culture magazine published without further explanation or context?”
“How convinced are you that you must be right?”
“I doubt he means anything like that. You’re merely attributing that to him.”
“You can think of it lots of different ways. It can be a geometrical idea, like finding the area or volume of something (or the mathematical representation of something analogous to that, without actually being a quantity of space). It can be thought of as a shortcut for adding together groups of physical objects (unless you’re multiplying something other than integers). It can just be a specific method of manipulating terms in an equation or mathematical expression.”
“It’s a very powerful and flexible mathematical tool, so it can do lots of stuff, which doesn’t much look like any of the other stuff, except in an exceedingly abstract and hard-to-pin-down way. Who knows which sorts of concepts he’s actually working with? Nobody can read his mind, so how exactly are we supposed to tell”
gakxz:
You’re in the habit of turning down students then, are you? Should every math undergraduate be assigned a therapist, who, upon finding that a student a) believes some unorthodox and strange thing, and b) is unwilling to give that up when prodded (probably because of a *combination* of not really understanding their error, even after a competent explanation, and wedding themselves and their success to that crazy belief), should summarily recommend expulsion?
“Do you think he *actually* wrote 1*1=2 on an exam?”
“That theory’s just as insane as Howard building weird shapes in his garage.”
“ Yet Andrulis made it through, probably because he was able to keep the crazy bottled up until he was in a secure enough position.”
“It’s even a bit strange to say he was speculating about multiplication: it just served as a proxy for his worldview.”
THE. GUY. THINKS. ONE. TIMES. ONE. EQUALS. TWO.
This is not eccentric. This is not offbeat and original. This is not an alternative world view. This isn’t simply not understanding and giving up. He isn’t wrong and doesn’t understand why— he thinks anyone who believes otherwise grew up in ignorance.
He is simply out and out wrong.
woozy
What are you doing with your formatting?
You’ve lost me.
Well, if you represent the points on the complex unit circle by their phases, then indeed
θ*φ = θ + φ
woozy:
You’re right! So what’s he still doing on TV, why hasn’t the FBI taken him away in handcuffs? I’ve always said we should return to stockades in town centers: finally, there’ll be a place for all those B-actors who get confused with multiplication. I’ll start saving up rotten fruit…
gakxz1
One of the many types of post on this blog is the posting of the kooks with either exceedingly stupid or batshit insane ideas. Then we the readers marvel at the utter stupidity or batshit insanity of these ideas. Believing that 1 * 1 = 2 is probably the batshittiest of insane ideas ever presented here, and it is a huge fodder for marvelling at. It is far, far, far more insane then anything Erik Andrulis ever proposed. It is more stupid then anything Ken Ham has ever blathered on about. It is an utterly insane idea divorced from any coherence or understanding of reality. The idea is utterly indefensible.
And yet for reasons utterly beyond me, you and conciousness razor are attempting to defend these ideas. And now apparently you are attempting diffuse by equating ridicule of the idea to criticism of the person holding the idea. Did I *say* that he should be taken off television? Did I say he is a less worthy human being for being batshit ludicrous and arrogantly stupid and delusional? No, I merely said 1*1 = 2 is batshit insane, belief that he and he alone have stumbled on the truth and that in 20 years the world know the “new truth” is arrogant and delusional. And the ideas are *all* of these things.
Why are you defending these ludicrous ideas?
====
chiagu
The bold are cr or grakx comments and the blockquotes are direct quotes of the Howard article that explicitly counter the comments made. cr claims I can’t know what howard means when he says 1*1 =2; that he doesn’t mean it in the mathematical sense; the I can’t judge him for believing this cause I never heard what he actually said etc. *all* of these are countered by his comment that he very much did say this, he did mean it arithmetically and literally. gakx seems to think Howard was just a poor student who never had mathematics explained and was just dismissed when he tried to ask for help. That he never wrote 1*1 =2 on an exam. But, no, he believes he has a truth that will revolutionize what children will learn 20 years from now when the are freed from ignorance. He argued with professors what 1*1 equals and left the program because he “refused to conform.” etc.
===
Well, that is clever. But I don’t think that’s quite is kosher. It’s not the *angles* that are being multiplied but the complex numbers that are being represented by the angles. Technically that equation should be e^iθ*e^iφ = e^i( θ + φ).
I kind of see what he means: it does seem unfair multiplying by 1 doesn’t do you any good. Maybe he’s open to negotiation? Suppose we offer 1*1=1.5?
Rob:
Oh, but that can’t be right, because woozy has already proved somewhere that his assumptions about the applicability of elementary math are always and everywhere relevant. You must also be insane or have the education of a third-grader, if you don’t have an orthodox understanding of every minute detail of complex algebra. Everybody knows that.
gakxz1:
Come on, he’s undoubtedly an A-list actor. He should be offered some kind of amnesty.
woozy:
You’ve made several empirical claims about what his life has been like and what caused him to have these ideas which warrant criticism. The fact that they warrant criticism does not imply he arrived at them as you claimed. So there is no reason to believe, nor is there any actual evidence, for the claims you’ve made.
And I’m not actually defending anything, since as I’ve said, I don’t know what his ideas actually are. It would help to know more.
Saying anybody (or a statement they make) is “batshit insane” is not a valid psychological diagnosis. I also can’t imagine how you’re not making judgments about his worth as a person, or that it doesn’t cause splash damage for others, who you’d also call “insane” for some other arbitrary reason.
As an aside, I use various sorts of math in music, and the fact that it’s sometimes used in unconventional ways doesn’t bother me in the slightest, nor does that mean it’s “batshit insane.” I’d like you to consider a kind of perspective which isn’t one a professional mathematician has, one another sort of person might take to be significant about certain abstract mathematical or logical concepts. Having a more expansive or liberal view of what they could mean in some contexts, or how they might be used metaphorically perhaps, instead of something extremely literal and simplistic (like raising one finger on a hand equals raising two fingers), is in fact something people do. It’s not really that unusual, even when it isn’t a rigorous form of conventional math. But historically, it’s also how people have come up with new ideas in math or new ways of applying math, despite the fact that they’ve been told by dogmatic people like you that what they’re doing is somehow crazy and/or sinful.
I never said he doesn’t mean it in a mathematical sense. There are multiple meanings of multiplication. He may be wrong about all of them. But you haven’t shown that, and you’re not trying to understand anything about where he’s coming which can’t be derived from a few vague quotes in a magazine. How can I take your criticism seriously?
You can do so… but you were just trying to suggest you’re not being judgmental. If you were backstepping before, what are you doing now?
Again, why do you say “But, no…”? That does not contradict the claim that it was explained to him inadequately or didn’t involve dismissiveness (dismissiveness of the sort you and others have demonstrated in this thread). However confident or optimistic he may actually be (that sort of thing can’t actually be revealed conclusively by a quote), it would not inform us at all about how ignorant he is of any explanations of his mistakes that he may have been given, nor would it tell us how adequate those explanations were, nor would it say anything else about how he’s been treated because of it. If math is logic, how about you try using some yourself, instead of fallacious horseshit like this?
woozy:
Let me extend an olive branch and say that I’m not advocating that we all act very seriously and not say one critical word about a B actor (sorry consciousness razor, being in Crash doesn’t cut the A list in my book) who has some strange beliefs. It’s sort of like when that elderly parishioner painted over a mural of Jesus in that Spanish Church: hilarious! But are you saying I’m not allowed to mention that, well, math’s very difficult for a lot of people? Or that variations of this are not as uncommon as you might think, or believing that 1*1=2 (and I am in no way amending my original comment: he *ABSOLUTELY* could have become a mathematician, if he were so inclined) should not be grounds for dismissing someone, or their potential? Even if they were wrapped up in a giant conspiracy theory: the goal should be to *unwrap* them, and then guide them towards mathematics. Because, his initial insight (that there’s more to math than just handing in homework, and that it can be worth spending hours in a garage) is great, is something many people do not realize, and would’ve been worth preserving.
No I did not.
I never made any claims about how he arrived at them other than his own incoherent staments about 1*1 having no effect and that’d make two which is the square root of four valueless.
The only claim I made is that 1*1 =2 is a batshit insane idea. Are you saying it isn’t?
“This is the last century that our children will ever have been taught that one times one is one,” he says. “They won’t have to grow up in ignorance. Twenty years from now, they’ll know that one times one equals two. We’re about to show a new truth. The true universal math.”
“How can [1*1 equal one?” he said. “If one times one equals one that means that two is of no value because one times itself has no effect. One times one equals two because the square root of four is two, so what’s the square root of two? Should be one, but we’re told it’s two, and that cannot be. …I mean, you can’t conform when you know innately that something is wrong.”
There! Now you *do* know precisely what his ideas are:
a) 1*1 = 2
b) 1* 1 can not equal 1.
c) This is a new universal truth that in 20 years children will learn and be liberated from ignorance.
d) the square root of 2 = 1.
e) schools teach that the square root of 2 = 2. Which can not be.
There *now* you know precisely what his ideas are.
I use very specific to say his ideas were batshit insane. I never said he was batshit insane and I never made any psychological diagnosis. The only judgement I make of his person is that he believes and espouses an extremely batshit insane idea. And I stand by that.
Um, and I did? If you are using mathematics, you are using mathematics. But if you are using actual mathematics you will not conclude 1*1 =2 or be able to use 1*1 equaling 2 because that is simply meaningless and impossible.
When one speaks metaphorically or poetically one isn’t doing math at all. That’s fine. Laurie Anderson had a bit about “Everyone wants to be number 1 and nobody wants to be 0 but there isn’t enough room for everyone in between” which is fine and good. But it isn’t mathematics and she never claimed it was (not seriously, it was a performance piece). Howard is either not speaking metaphorically or he is confusing metaphorical with empirical quantitative existence. He claimed 1*1=1 is empirically wrong and that 1*1 =2 is new universal truth.
Yes, by apply it consistently and knowing what they are doing. Can addition not be commutative? What will be the consequences of that and what are the required axioms to make the statement meaningful? What results if Euclid’s 5th postulate is modified? But in doing so and any new mathematics that arises, the results will be consistent and meaningful in some framework.
a) He means specifically the mean of multiplication that we teach children and that, to him, is the only meaning as 1*1 = 2 is a new universal truth and 1*1 =1 is ignorance.
b) multiple meanings of multiplication but limited meanings of 1 in context to multiplication. As I pointed out 1 + 1 can equal 1 in other non-group or trivial number systems.
I don’t care how he came to his conclusions nor do I have any idea how well or poorly he was explained the concepts as a child nor whether he understood them or not. That was all pure conjecture on gaxkz1’s part. His statement *now* that 1*1 = 2 is what I deem ignorant.
You are one the most intelligent and reasoned people I have ever come across, but you have a persistent and compelling compunction to read one hell of a lot into statements that were simply not there.
An article about Hunter says he states 1*1 =1 is wrong and 1*1 = 2. That is wrong, weird, stupid and *extremely* mockable. That is *ALL* anyone in this thread has *ever* said about his ideas.
Olive branch accepted
Of course you can say that and of course it is true. Biology, english composition and poetry are very hard for me. But I don’t, when confronted with a concept I can not comprehend, insist I am right and the world is wrong and that this is the last generation where children will learn that rhyme means the ends of words sound alike because I figured out that’s impossible and that rhyming most mean that the have the same number of letters.
Well, I could be an opera singer if I had the voice. A belief that 1*1 =2 is a *huge* stumbling block and an indication that one needs to go back to the *very* beginning.
Well, sure. And there is more to English composition and scribbling out crib notes about the Great Gatsby, but if I’m incapable of stringing together a coherent sentence, I have failed to come across what that more could possibly be.
Ugh, one more rant. Woozy: 1*1=2 is NOT as batshit an idea as you imagine it to be. Here’s why, and then I’m out:
When I was in 8th grade, I came up with a system (that I called the “OF” system, for reasons best known to my 8th grade self) by which you should only use certain rational fractions (I picked 4 of them, but I forget which ones, maybe ½, 1/3, 1/4th, and 1/5th) to section things up (I think I only thought that applied to sectioning up social science statistics, because… reasons…). I was, by the way, taking Algebra 2 in 8th grade (so by your logic, that I believed what I did should’ve made me fail every test I took). Luckily for me (and, I imagine, for the rest of us) I dropped that idea a few months after I came up with it. So, hurray! I later found out that the ancient Egyptians also only decomposed things into certain rational fractions, which felt greatly reassuring (not because I still believed my “OF system”, but because it felt nice not to be alone).
I’ve had plenty of similarly silly ideas, and have run into others (either other students like me, or, later, students I TAed) who believed one misconception or another. You don’t dismiss those students! Or call their ideas batshit crazy, even if they fervently, and heatedly, believe them. You do your best to provide an explanation, and then try to sympathize in some way (“Physics is indeed difficult, and I’ve had my share of misconceptions. I recommend this or that, and you can come see me anytime”). These ideas, very much including 1*1=2, are in no way batshit crazy (nor is it crazy to believe you are changing the world… that’s also common, and for many people, including me, believing that your idea is earth changing soon gives way to a crushing sense of “how could I have believed that, I’m a worthless human being”)…
At any rate, I’ll tell you what’s more batshit then 1*1=2. The republican presidential candidate who is currently #1 in the polls, got there because he believes that we should deport over 10 million people. And he got into politics only because he believes that our current president was not born where all the evidence says he was.
Some samples:
Your claims that he’s “batshit insane” are personal judgments about him, which do also amount to claims of some sort about him and his life history. They’re vague, but they don’t fail to have such implications.
Not so. See above. Maybe you don’t pay attention to all the things you’re claiming, but that’s not my problem.
Nope. Do any of those actually look like precise, rigorous and unambiguous mathematical theorems to you? It looks like his ideas aren’t precise enough to know precisely anything about them.
I can’t say I understand what the fuck this hair-splitting is about either. You said he’s delusional. Do ideas have delusions, or can ideas themselves literally be insane? Don’t just put it into words that you think will let you off the hook — what could that literally mean?
I have no idea how to tell if that’s generally true or not, but what makes you think he’s doing this sort of math? How exactly can you tell that Rolling Stone didn’t report about some metaphors he likes, since you don’t actually have an opportunity to speak with him directly and ask questions to clarify?
But that’s impossible. A person can’t be a number. It’s nonsensical bullshit. It’s ruining America. Blah, blah, blah.
Well, now there are more options suddenly. So, exactly how could confusing some things render him insane or constitutionally incapable of ever having worked successfully in a STEM field? Assume he got the best and clearest and most thorough exposition on the subject imaginable — how could be confused on the subject, despite that, be a reason to believe that? How is that not saying something about him, and on what basis do you conclude that?
Aren’t you confused here? I won’t read through again to check, but he didn’t speak in terms of empirical truth. And math isn’t empirical. Since you’re confused (or maybe since you misspoke), do I get to say you’re a total crank and utterly incapable of whatever I happen to care about?
Interestingly, a lot of physicists and mathematicians are very, very serious about wacky ideas like the “mathematical universe.” Should they lose their jobs, because they’re confused (or disagree) about some obscure point or another in metaphysics or epistemology?
Oh, I see. So, they were “consistent” with something (but obviously not previous mathematics which was inconsistent with their new idea). And they knew what they were doing, but not until after they did it. That’s when they knew. Before that, they were doing something inconsistent and therefore insane. Zero and imaginary numbers, indeed! You crazy mathematicians. How do you come up with such weird crap?
What makes you think there is no conceivable framework whatsoever, in which this is at least consistent or meaningful? That’s an incredibly easy standard to meet. How could you possibly have such knowledge about all conceivable sets of ideas?
I don’t care how he came to his conclusions nor do I have any idea how well or poorly he was explained the concepts as a child nor whether he understood them or not. That was all pure conjecture on gaxkz1’s part.
If you don’t care and you’re not conjecturing about any of it yourself, you have no business disagreeing with any of it. Maybe you don’t care now, but that’s not actually what you had been doing.
He was apparently ignorant before, and if so, he clearly hasn’t learned since. You presumably don’t think he forget what he used to know before, so I don’t get how I’m supposed to understand the meaning of this.
Is it like the way people have read a lot of things into Howard statements, which are simply not there? Because instead of saying I’ve been “defending” it like you did before, maybe you could acknowledge that that is what I’ve been saying.
I do take it seriously that many things people say (if it’s clear they’re serious and literal about them) have implications that they may not make very explicit. Bringing those things out into the open isn’t a problem, and in fact I think it can be helpful in showing what is wrong about an idea or else clarify something about it. However, making shit up is a problem. I get that you care about math and dislike people who abuse it — I’m like that too — but I think you’re trying to express your frustrations (as understandable as they are) by assuming the worst, rather than being careful about what you’re saying and reading, to make sure you actually know what you’re talking about. You evidently know some things about math, of course, but that is not the only thing you need to know about in this case.
That’s just transparently false. The thread would be quite a bit shorter or more repetitive, if that were the case. You apparently think it’s acceptable sometimes to exaggerate, oversimplify, say something provocative, inaccurate, misleading, metaphorical…. So how do know for sure when somebody else isn’t doing the same thing? Is there some special reason why we should draw the line at math? Is that sacred territory, or do you say things about it that are wrong as well sometimes? Also, have you never read a celebrity say something a little bizarre to Rolling Stone (or any magazine) before, and have you never wondered why they’re saying it or whether it’s an accurate and comprehensive presentation of their actual views?
Sorry, missed a blockquote, in the paragraph beginning with “I don’t care how he came to his conclusions….”
That’s actually not sufficient for being an opera singer. And you do literally have a voice.
Just felt like inexplicably being a total hardass about something pointless for a moment. Carry on.
@92
Not sure how your imaginative “OF” system compares with 1*1 = 2. How does “OF” lead to 1*1 = 2? Your “OF” systems seems fine to me with no fundamental inconsistent ideas or mistaken concepts. I might be a bit perplexed as to *why* you are doing it but you were doing nothing wrong.
(In my senior seminar, one of my classmates seminar topic was Egyptian fractions.)
And no, I’m not talking about teachers telling students to their face their ideas are batshit (although god knows, I *never* had a university professor who had any compunction or problem with that). I’m talking about an idea of a celebrity stating a preposterous idea in public for the scrutiny in readers. I don’t know what the nature of his “argument” with the professor was but the upshot is he, Howard, came to a very mistaken conclusion.
@96
I was just trying to relate how it’s possible to believe silly things sometimes (a part of me wants to self consciously stress that I didn’t believe that for more than a few months…)
Anyway, we agree (obviously) that 1*1=2 is silly. We also agree that it’s fine to have a laugh over that. What we haven’t agreed on, from the beginning, basically boils down to what you say in your first response to me:
I fundamentally disagree with that, and have given you my reasons. Well, you don’t agree with me, so there it is. Cheers mate.
@93
“think” “maybe”. These were conjectures with no claim of inside knowledge to verify.
That was in response to gaxkz1 claim that his issue *was* math dyslexia. His ideas can not be dismissed or explained away with math dyslexia which gaxkz1 has no reason to believe he has. Math dyslexia (or math anxiety or simple math difficulty) may or may not explain why he doesn’t understand what 1*1 is but it doesn’t explain his insistence that 1* 1 = 2 and his believe that this a universal truth that has eluded mankind for millennia.
He *doesn’t*. He believes 1*1 =2. No-one who understands the problem can come to that conclusion.
This was in response to gaxkz1 belief that Hunter simply found math hard and fell between the cracks of unsympathetic teachers. That would explain why he can’t do math but it wouldn’t explain why can’t but thinks he can.
They aren’t theorems because the are false. But they seem like precise, rigorous and unambiguous mathematical statements to me.
1*1 =2 seems imprecise to you? He is stating 1 * 1 = 2. What the heck is imprecise about that. 1 * 1 can *not* be 1. This is the last century that children will be taught the ignorance that 1*1 =1. 1*1 =2 is a new universal truth.
What the heck is imprecise about any of that?
Howard is delusional because he believes 1*1 =2. 1*1 = 2 is a delusion. An *idea* is insane if it is irrational, preposterous, inconsistent with reality. Are you claiming that believing in insane ideas by definition means a person is insane? If not, I did not claim I knew he was mentally ill or that mental illness is his only explanation. But I do claim that 1*1 =2 is an insane idea.
I am reacting to what Rolling Stones wrote. If Rolling Stone was mistaken and libel this poor guy then that is on Rolling Stones. If the claimed Obama claims 1*1 =2. The idea that 1*1 = 2 is still batshit insane.
Because 1*1 does not equal 2.
Well, first of all Howard is not talking about an alternative framework. He is talking about the framework in which we teach children the fundamentals of math.
Second of all we can’t merely make up definitions to mean what we want. This is the old Well, no-one can actually be an atheist because God can have different definitions for different people and no-one can disbelieve all of them. In any system the terms “multiplication” must mean something in concept of producing something by combining terms and the number “one” must mean a unit entity. If the concept of “unity” is a quantitative one then multiplication on a unit quantity is itself a unity quantity. (If a foot is a basic unit of length and multiplication is an area produced by perpendicular lengths then a square foot is the basic unit of area. It’s a definition.) If on the concept of “unity” is an identity operation on a binary operation then 1*1 = 1 by definition.
Howard, in stating (or, if you prefer the Rolling Stone image of Howard is being quoted as stating) that he is speaking of the basic multiplication we teach children. That is the idea the numbers are units of counting and multiplication m*n is the amount resulting from m groups of n. The result of 1 group of 1 is 1.
What’s not there? Rolling Stone presented him as saying 1 * 1 can not be 1 and 1*1 = 2. Those statements are there. They are there for the world to see.
At this point I seriously don’t know what you are talking about. I don’t think Howard is a two-bit actor as a result of what he says. (His ability to act has nothing to do with what he might say.) I don’t think he is a threat to the education of children. I don’t have any opinion about his supposed spousal abuse.
I simply think he said an extreme bizarre and *wrong* statement that is very compelling and fascinating in its complete and bald wrongness.
Provided one has a wherewithal to not confuse the supposed metaphor with actuality. Thorns are not *literally* put on roses to remind humans that life will always have trouble. Similarly the power of loved squared can conquer the single linear force of hatred is a fine math metaphor but it doesn’t mathematically mean anything sensible.
I’m merely mocking a preposterous statement.
If Rolling Stone misrepresented Howard’s statement then Howard has been grieviously abused (because they made him look like an idiot). However one can still mock the ideas presented. If rolling stone misreported then that is on rolling stone.
Perhaps, I overstated that. Anyone can overcome problems and become anything once they figure things out. But my point was 1*1 =2 is a *fundamental* misconception. Continuing to believe such a strong misconception and/or fundamental noncomprehension is incompatible with coherent science. Okay, perhaps these creationists and weirdos can fake their delusions and get a degree. But they can not develop any science *based* upon or supporting the wrong idea. Because it is a wrong idea.
So, anyway… I just wrote this piece of music. Instead of having a rational tempo like 3/4 time and 4/4 time it has a tempo in square-root-of-two time. (Hmm, actually *could* that work? I meant it as a joke but…)
I’ve known *lots* of people who believe wrong ideas. (That seems to be a residential hazard of living in Northern California). Most are flaky (we are evolving into plants because plants don’t consume life and are more highly evolved because it is conscious) but a few (those closest to my family) are delusionally schizophrenic (urine turns into gold after 1,000 years). I know *many* people who somehow simply can’t not see metaphor in every thing. That pi is irrational must be a metaphor for the unknowable transcendence of human conciousness or something. They almost seem to believe that if there is any counter intuitivity in math that mathematicians must have made it up that way to express a metaphor. The thing is, they *can’t* go on or get past this and actually understand what math is actually saying (and more importantly why) because they hold onto these ideas. Math, and reality, might actually work by other rules.
I mean no, I was never suggesting that anything (publishable, say) would *directly* come out of his theories. My guess of how to handle a student like Howard (assuming lines of communication stay open): say their beliefs are fine as long as they keep going with their more sober work (homeworks, exams), suggest that they keep an open mind (if you can manage that without sounding condescending), recommend some good reading material (probably expansive texts that talk broadly about mathematics), and stay open, as a teacher, to revisiting the subject in the future. I think if the student is dedicated to (say) math, then they’ll work things out as time goes by. Plus, their initial ideas might serve as a motivator, and might suggest future areas of interest (even if my “OF system” scheme wasn’t the masterpiece I’d have envisioned it, it might perhaps lead to an interest in Egyptian mathematics, and, say, a good summary paper).
That’s not to say that, in real life, things are ever that cut and dry…
Uhh… what?? How is it not incorrect or not using mistaken concepts,* to claim you should only use particular fractions (for certain purposes)? Maybe go through the criteria you’re using, to explain how you decided this. I don’t get it. I don’t see how you can seriously say that it isn’t wrong, on so many counts. Numbers other than a handful of fractions can and should be used for all sorts of things. Making arbitrary limitations like this is certainly no guarantee of consistency, not just because the larger set of rational numbers (e.g.) can be used consistently. And to me it looks like an obvious case of conceptual confusion or some sort of misapprehension. It is not the right sort of idea to have about applied math, it is not useful in any obvious way, the reasons are probably impenetrable and misguided, etc. So what exactly are you thinking of, when you say something like this is “doing nothing wrong”? It doesn’t appear to be the very same mistake as Howard’s (who knows what that really is), but that’s not the issue at hand.
*Don’t worry, gakxz1. Everybody has silly ideas sometimes, especially kids.
You said you didn’t care about conjecturing about such things. Of course you don’t have that knowledge, which is the point I’ve been making. If I just say something, I don’t need to preface it with “I claim to have inside knowledge to verify” in order for that to be implied.
If I say “I think 2+2=4,” it doesn’t come across as if I’m suggesting that I’m not really sure about it. That can be done verbally by emphasizing “think” a certain way, but that meaning is not implied when it’s simply written down somewhere without verbal (or visual, etc.) cues. Also, if I say “maybe 9/11 was an inside job” or “maybe she asked for it,” it likewise doesn’t generally sound, if in context I’m not clearly dismissing the idea but am putting it forward as a serious proposal, like I don’t actually believe that or that I’m making no claim to that effect. And while we’re at it, if you say “it’s probably X,” you’re literally saying there is a fact it’s probably X, or that there is a fact of the matter about X with the degree of probability you’re claiming for it. These words can give you some kinds of wiggle room when making vague or uncertain claims, but they simply don’t make things disappear entirely. It just doesn’t work that way.
In any case, using that kind of suggestive language, to urge us in the direction of the claim you want to make but avoiding making explicitly, is enough for my purposes. It isn’t based on evidence, and it is something you have no good reason to do. At the moment, I’m not criticizing the exact way in which you performed the claim, so you don’t need to try to correct me by telling me that you did it in a specific way with specific magic words, or why you did it that way instead of doing it some other way.
I’m criticizing the fact that you’re doing it. And I’ll criticizing you for doubling down and continuing to contradict that fact even now, after I pointed it out. Because that’s just dishonest.
Well, I hardly need to mention this is clearly about him as a person. You can stop pretending as if you’re somehow talking about something else now. Can we at least agree about the facts we’re both capable of understanding perfectly well?
I don’t recognize “insane idea” as a well-formed and meaningful concept, independent of calling a person insane (or calling their sanity into question). Ideas don’t think, and sanity or insanity is (to phrase it one way) a description of organized or disorganized thought processes. That’s simply what it is. Irrational means it is without sufficient reason. Preposterous is something that’s highly implausible or hard to believe. And inconsistent means there’s a contradiction, logically speaking or compared to some physical fact about the world.
Ideas and claims can be all of that, but they don’t think, so they can’t literally be sane/insane. It’s preposterous (read: highly implausible) that you actually and literally believe ideas can be sane or insane, because even if we disagree occasionally you don’t in my experience tend to say (and sincerely mean) things which are so totally ridiculous. The much more plausible explanation is that you’re using coded language, which really is about the person or their behavior. Is there any reason why I shouldn’t conclude that?
By the way, it would make more sense if you didn’t pick all of those to describe the same thing. If you’re saying it’s inconsistent, there’s no point in mentioning any of the others. It’s simply not possible, whether or not anyone attempts to give any sort of reason for it, and whether or not you find it hard to believe. There could not be genuine reasons for making an impossible thing seem plausible to you, so what could be the purpose of mentioning any of that, if you really do know enough to back up your impossibility claim? It comes off a bit like a bad lawyer/cop reading off a laundry list of trumped-up charges, in the hopes that at least one of them might stick.
Anyway, if you’re going around saying things like this are “insane,” you may as well start accusing people of witchcraft too. You’re not making mathematics look any more serious or respectable when you do this. With friends like this, why would it need enemies?
I’m not suggesting they did anything like that. Printing his actual words isn’t libel. The fact they’re his actual words (assuming that’s the case) doesn’t mean they give us the whole picture or even a good understanding of what part of the picture really looks like. I’ve said more than a few things in my life, so this sentence right here — the one I myself really am writing at this very moment — doesn’t tell you everything you need to know to understand me, what I’m thinking, what this line of thought is about, or much of anything really. It’s much less than complete information, and the meanings of words and the intentions behind them aren’t something that itself can be presented to you in those very words. So your interpretation of them is always something to be careful about, which is one reason why repeatedly quoting things at me verbatim does not get us anywhere productive at all (also, I’ve already read them more than once, thank you). I don’t think you’re actually that naive about this sort of thing, so what is there not to get?
Along the same lines, earlier in the thread, I said I wanted to see the figures he was making, because it would give me a clearer understanding of what precisely it is that I was probably going to reject as pointless garbage. The fact that you’ve sort of jumped the gun isn’t so much what bothers me, compared to the fact that you really seem to confidently believe that you have impeccably and unquestionably good reasons for doing so. I don’t think it’s really all that well-founded or airtight. It would be nice to actually know, since of course I think he’s wrong about standard multiplication, what is going on, what sort of mistakes he’s making, what he really means by it if he doesn’t literally mean every last word. You do not know that, because that information (whatever it might look like) simply isn’t present in any form that could be a reliable/useful answer to questions like that.