[I don’t actually expect most of those disclaimers to mean anything to you. They’re just there to shield me from pedants. All you need to think about is “How many times do I make a vowel sound in this word?”]
Math. Can’t stand it, can’t do it.
I, myself, don’t have trouble counting syllables, but I confess to ignorance regarding the terms used for describing parts of speech etc (IOW, what the hell is a dipthong? I’m sure I used it once, but it’s gone from my brain now.)
Re Pi. Ta, all. I said “it’s used as a constant” because doesn’t it stand alone, too? It’s a constant and number all by itself. For all I know, it’s an irrational number–and WTF are they, anyway?
GorillaMan–each individual word in your sentence re logs makes sense, but the comprehensive meaning eludes me. I never got to calculus, so maybe that’s why.
Most of math eludes me. I understand language intuitively–the subtext of grammar makes sense to me in a way I cannot articulate–but math has always been a “bash it into my head and hope it sticks” type of thing. When I studied to take the GRE for grad school, I took a practice test cold, just to see where I was. My math score was so low, it did not score, which (IMS) means I got less than 11 correct… I did manage to get a decent score (and didn’t need a good score for library school).
And what IS the golden triangle?
Interesting how, with one exception, every concept mentioned so far has been either from math or English class.
A diphthong is a vowel sound which, though it may act like a single atomic unit in the language, is actually phonetically produced by quickly moving the tongue from one vowel to another. For example, in English, the vowels in “bye”, “cow”, and “boy” are usually diphthongs; the first consists of moving from “ah” to “ee”, the second of moving from “ah” to “ooh”, and the third of moving from “aw” to “ee”.
I’ve always felt this is a failing of how math is usually taught - the absence of context.
For a long time, I thought I was incapable of math. I could never get past wanting to know what X meant. “Just solve for it”, my teachers would say. Yeah, but what does it MEAN?! And the word problems they started doing when I was a kid somehow never translated.
So it wasn’t until I took physics, where X actually stood for something. Suddenly… I could do math!
I remember looking at the equation for gravity, and having a burst of realization at what it meant, and its implications on mass and distance. What a feeling to get that from an equation, and I hate that I’ll probably never achieve it again from advanced math. I just don’t have the background for it, or the time to gain that background.
That aside, I’ve never understood the concept of poetry. What’s with all the indirect imagery and flowery language? Just say what you want me to understand!
Well, for the third, I mean the sound some people use for “aw”, though many people don’t. Others can think of it as the vowel in “ore”, only without the /r/ bit [imagine saying it an “r-dropping” accent]. Anyway, it doesn’t matter… the point is, the tongue moves from one place to another while you say “oy” (try stretching it out), so it’s a diphthong.
Also, think of Jenny of yore: “867-930-Nye-eeh-aye-in”. What’s going on there is that the diphthong in “nine” is being repeated, so you hear “ah-ee-ah-ee” instead of just “ah-ee”.
I did great at high school and college math; advanced algebra, geometry, trig, statistics, and calculus; anything involving memorizing and solving formulas, analyzing sets of numbers, and so on.
I completely sucked at elementary school algebra. Why? There was no problems with “solve for X”, which so much of it was. Where I had a huge problem was the “show your work” problem. I knew what X usually was, but I didn’t know why. A number popped in my head, I plugged it into the formula for X, and it fit; there’s your work, teacher.
Diagramming sentences, too. I would have gotten A+ grades in second grade English if I was any good at diagramming.
Er, 867-5309. Whatever, it was before my tye-ee-aye-im.
More math and English being brought up, I see. To me, the most intelligent thing ever said about mathematics education is Lockhart’s lament, though others may disagree.
They taught us orienteering in grade-school. So I’m counting it as at least partially academic. And I fail at it.
Math - no problem. I got through lots of calculus in college, can still do long division, add, subtract, multiply, divide in my head - easy-peasy-japanesy.
Language/Grammar - again, no problem. I read voraciously as a lad so this always came pretty naturally.
But I’m very poor at reading and following a map. Which is not to say I can’t follow directions - I just don’t naturally place them on a mental map.
I got chuckled at just yesterday - despite having lived in the area for years, I got stumped when a co-worker asked which direction IL-25 ran. Then another co-worker called me out further - “point in the direction of Chicago”. I had no idea. I mean, I knew it was southeast but had no clue whatsoever which cardinal direction I was facing.
I just can’t easily connect a map on paper to a physical place. I can get around just find, but I’ve learned that I do directions like this:
- Leave home, turn left
- Turn right at the river
- Turn right at the intersection with the candy store
- Turn left at the park
- Turn right at that junky old house with the missing shingles
- Voila! I’m at work.
I just have a really hard time thinking in terms of directions. Rather, it’s remember a sequence of landmarks to navigate.
Good to know re the dipthongs, thanks!
Another math conundrum for me was story problems. The only algebraic equation that made sense to me was d=r x t. I could manipulate that one endlessly. It made sense to me. And any story problem that had that equation as its focus I could solve. I cannot (at age 46) create a “math sentence” for something as simple as this:
Jill and Jody are in an circle of exercise stations, muscle strengthening alternated with running in place. If Jill stops at every station and Jody does every other, how soon will Jody catch up to Jill, if Jody starts 5 stations behind Jill? There are 20 stations in all.
No clue. Don’t care. Hate Jody and Jill and hope they both pull their hamstrings.
I worked in a bar and had to do quite a lot of mental arithmetic - oh sure, there was a cash register but it was embarrassing to have to use it to calculate the amount and then return to the customer to tell them.
Anyhow, the way I mentally add 27 and 35 is to add 30 and 40 then subtract 8. Or, in the bar, 4 bottles of beer at £1.85 would be £8 less 4 times 15p, hence £7.40.
Well, no wonder, the question is contradictory. If they are both alternating exercises, it can’t be the case that Jill is stopping at every machine and Jody is stopping at every second one. If Jill’s stopping at every machine causes her to alternate exercises, then the machines must alternate (running-muscles-running-muscles); then Jody, who is stopping at every second machine, would always be on the same kind of machine. If Jody wanted to skip machines while still alternating exercises, she would have to do every third machine.
Constants are numbers. They are just numbers that don’t change, whether that means ‘don’t change ever’ (like pi) or ‘don’t change within the context of a problem’.
An irrational number is a number that can’t be expressed as a ratio – that is, as one number divided by another number besides 1.
Any number with a set number of decimal places is rational, as is any number whose decimal expansion repeats. 5.2398458923475 (typed completely at random) is a rational number because it’s equal to 52398458923475 / 100000000000000.
As an irrational number, the decimal expansion of pi never terminates and never repeats.
You may have heard pi expressed as 22/7, but that’s just an approximation; 22/7 actually equals 3.142857142857 (3.142857 repeating). Pi can never be expressed as one number divided by another number except 1.
Don’t feel bad. According to legend, when one of the Pythagoreans discovered that pi was an irrational number, the rest of them were so offended that they had him killed for blasphemy.
Just to clarify, an irrational number is one which can’t be expressed as one integer divided by another integer. You could write π as π/1, if you like, but that’s not a ratio of integers.
Also, the Pythagoreans didn’t discover that π was irrational; that didn’t happen until the mid-18th century. Rather, they discovered that the square root of 2 was irrational.
There’s no contradiction. The bit about alternating describes the stations and is superfluous. All that matters is that Jill’s sequence is 6, 7, 8, 9, 10, 11 and Jody’s sequence is 1, 3, 5, 7, 9, 11. Therefore, after six steps, they’ll be at the same machine. You can set up equations and do it that way, but this is much simpler.
about math: I understand how some people just don’t get it, ever. Their brains just don’t work that way. Mine does though- math makes sense to me, always has, and hopefully always will. But when I was in fourth grade I, too, JUST COULD NOT GET LONG DIVISION. I remember sitting in the hallway bawling because everyone else could do it and I couldn’t. Then my teacher yelled at me for getting snot all over my math book.
There are a bunch of topics in biology I also can’t grasp for the life of me, but one fairly simple one is blood types. Antibodies, antigens, who can receive blood from whom, etc. I know it all makes sense, but when I try to think about it it gets all mixed up in my head.
Having reread the question, I see that it doesn’t, in fact, say that Jody is doing both every second machine and alternating exercises. However, it also doesn’t explicitly state that each of their sets is the same length, which we would need to know in order to work anything out.
If we assume that, then for every 1 set that Jane does, Jody does 2 sets. So:
JanePosition = JaneNow + RemainingSets [Jane’s position is her current position plus however many sets she does]
JodyPosition = JaneNow - 5 + (RemainingSets x 2) [Jody’s position is 5 behind Jane’s, plus however many sets she does x 2, since each set she moves forward 2 machines]
JodyPosition = JanePosition (We are trying to figure out when Jody catches up with Jane?)
So:
JaneNow + RemainingSets = JaneNow - 5 + (RemainingSets x 2) [replace JodyPosition and JanePosition]
RemainingSets = -5 + (RemainingSets x 2) [subtract JaneNow from both sides]
0 = -5 + RemainingSets [subtract RemainingSets from both sides]
5 = RemainingSets [add 5 to both sides]
So they will do 5 sets separately before they catch up to each other.
Ultrafilter’s way is definitely easier, but this is how to represent it with equations, more or less. Of course, it’s been a good 12 years since I’ve had to do this.
I see now that matt_mcl, in his definition of “irrational”, made special exemption for a denominator of 1, but that’s unnecessary and doesn’t accomplish what I think was intended; you can still express π as (2*π)/2, for example, and so on. Like I said, all the definition you need is that rational numbers are expressible as ratios of integers.
As for Jody and Jane, the equations are a bit overkill, like ultrafilter said. One other way of looking at it is that every transition, the distance between Jane and Jody decreases by 1 (since Jody moves 2 while Jane only moves 1); thus, since they start at a distance of 5, it takes just 5 transitions for them to end up in the same place. But ultrafilter’s approach is even easier.
Anyway, before investing too much time jumping over each other to offer new analyses of one arbitrary very simple problem, let us remember the point it was actually introduced to make: "No clue. Don’t care. Hate Jody and Jill and hope they both pull their hamstrings.
Alright, time for me to actually contribute something to this thread. I have a terrible time grasping statistics… by which I mean, it always seems to me that what’s being calculated is backwards from what I’d actually want to know. p-values, confidence intervals, and so forth. I toss a coin heads fifty times in a row and then say “Hm, I wonder if this coin is weighted”, so I go off and compute a p-value, something like “What’s the probability of a coin coming up heads fifty times in a row, given that it is unweighted?”. But that’s not really what I want to know! I want to know something more like “What’s the probability that a coin is unweighted, given that it comes up heads fifty times in a row?”… it seems like the practice of carrying out the former calculation is just based on erroneously conflating it with the latter one. And so it seems to me with practically every other major statistical tool; it seems like it’s all based on very elementary mistakes concerning conflation of converse conditional probabilities. And yet, it’s a large field, filled with presumably intelligent people who are all quite familiar with this concern and have a fine response ready to give. But it still hasn’t come to me…
Boy, I don’t hear that at all. No wonder I don’t understand them.