Many people in the world today have abandoned any rigorous sense of rationality in favor of a life of il-logic. This is an opportunity for those who have not to share and comment upon their experiences with the chronically illogical.
My sister took a job at a small diner that I frequented, and her immediate family members received a 10% discount on their bills. Anyhow, I took my brother there and we ended up putting our bills together. Since we both got a 10% discount, the lady ringing us up added up our subtotals - and then proceeded to subtract 20% from it, for each 10% discounted. In case there is anyone scratching their head about what's wrong with this:
If my bill is X and my brother's is Y, then the basic way to find out the discount would be (.10)X + (.10)Y = Discount. The waitress attempted to simplify the operation by combining the two bills and ending up with (.20)(X + Y) = Discount. Unfortunately, this isn't quite how it should go, since (.10)X + (.10)Y = (.10)(X + Y), meaning that she should have only taken away a 10% discount from the sum of our tabs.
But that's the world we live in!
I'm not surprised - most people have a hard time adding 2+3 any more and can't figure sales tax on $1 without a cash register. Not a calculator - a cash register that has a "sales tax" button.
To think they might understand even the simplest algebra is foolish.
I know where you are coming from here, wilderness. It distresses me a lot to see the dependence these days on technology to do the procedural thinking. I tell my students that math is the art of "you can't fool me," since it exercises rational thinking, rigorous proof, and problem solving - all essential elements of the ability to determine the validity of claims in a given axiomatic system (Godel aside, anyhow).
But, I still have faith that people will come around eventually. I fear, though, what it will take for that to happen.
It will probably take the fall of civilization. It takes effort to learn these things, and more effort to use them. Not much, but some.
Man is a lazy creature, particularly in the mental arts. A few truly enjoy learning and using their mind, but they are few.
Thus we will have to lose our crutches as a race before we can once more learn to walk without them.
Another of my favorite cases of illogic concerns the field of probability and prediction (I see this problem with students sometimes, as well). Suppose I am going step outside my door in a moment (this event alone is quite statistically unlikely for me, since I rarely leave my house after dark). It is a clear night - the probability of my being struck by lightning is exactly 50%. The reasoning behind this statement is that, after all, there are really only two outcomes in the trial: either I am not struck by lightning, or I am struck by lightning.
This isn't an error in "logic," per se, but rather is a result from the false assumption that the two events are equally likely, making it OK to invoke the favorite (ways the desired event can be true/ ways the event can happen total) formula for probability. Even so, it represents a misunderstanding that I have seen shake a person's trust in logic to provide logical answers, since it is obviously not a 50% chance that a person will be struck by lightning every time they step outside.
This reminds me of the old "argument from complexity" thing, but I don't know if I really want to bring that into this..
I sure did, but only because I didn't want her to make the same mistake with other customers and get into trouble for it. I'm not sure she understood, really, but I ended up paying the correct price in the end.
All's well that ends well, I suppose.
I worked with a guy who had just bought a new GM car and went to buy a towbar for it. The new towbar was $125.
He then priced a secondhand towbar for a Mercedes Benz and was quoted $25..... so naturally he went and bought himself a Mercedes and fitted the $25 towbar to it.
Makes good sense to me! Everybody needs a new Mercedes with a rusty, bent up, used towbar.
Can I have the GM?
He couldn't just go and buy a Benz, he had to justify it somehow!
On another occasion he ordered a new typewriter, (the GM would be a collectable by now!)
By the time the guy arrived with the typewriter he had convinced himself the salesman was evil, and threw him out!
earnest, are you kidding? That cannot be true!
Sadly it is true. He was smart enough to help the large insurance company he worked for (National Mutual) change their actuarial scale, and crazy enough to steal half a million dollars from his church fund for an aged home they were building. He started the project, then shot through with the money along with his baptist minister.
Worse, he was a magistrate!
Now, why is this even posted here? What's unreasonable about going out and buying a Mercedes so you can save a little on the towbar???
I love these kinds of things, I don't know why - they just amuse me a lot, I suppose.
While it is typical for people to think things are going downhill, IQ testing suggest that the tendency to use local categories and sound reasoning has actually been improving consistently over the last 30 years.
Are you referring, perhaps, to the Flynn effect? I heard about this in an adolescent psychology course that I took for teacher certification. Admittedly, it is true that the "bell curve" is skewed to the high end every time the IQ test is revised, suggesting that there are more "above average" IQ's than should statistically happen. However, further studies have pointed out that this is actually due to fewer "below average" scores than would be expected, and the number of "above average" and "high" are not much outside of the expected range.
To me, this does support the idea that, at least, unsound reasoning is becoming less prevalent - if you suppose that a low IQ corresponds with unsound reasoning, but that average and above average are necessarily "logical individuals." I do not think it particularly a safe assumption to make, since persons with very high IQ scores can behave and think very irrationally, as well.
At any rate, I would disagree that the Flynn effect (if that's what you're referring to) is an indicator of growing prevalence of logically-minded individuals in developed nations. However, I do agree that it should indicate a decline in illogically-minded people, which could still be relevant to what you were saying. So, I disagree - but I agree, as well.
If this is true and valid I must be running with the wrong crowd.
I gotta get off these forums!
I would disagree that the Flynn Effect says anything at all about intelligence.
But the increase does come predominantly from questions that test the formation of logical categories and understanding of logical sequences.
Basically is indicates a wholesale movement from philosophic logic (because most stone sink in water it is true to say stones sink) to scientific logic (because pumice does not sink in water it is false to say stones sink in water)
Education is not what it once was... I won't go into why. It would simply destroy the intent of the thread and lead it astray.
I dunno why, but I see a well educated articulate youth.
All the alphabetic young ones, such as the "Y" generation are light years ahead of where I was at their age, and I know a lot of kids from sports clubs to kindergarten.
Even the one's at pre-school are getting a great education. I see a bright new world from where I am looking.
Having followed my youngest boy's lacrosse since he was 8 years old, I know hundreds of young people who are doing well in life as young adults.
Yes, I do agree to a certain extent, though the culture of the youth varies with region and local culture. I've noticed the progression of algebra back way into elementary school, in some cases, where I didn't even hear the word at all until I was in 7th grade. Also, it seems like if you look at college coursework from back in the 40's through about 70's, you'll see a lot of things that look strangely familiar to anyone who's been through a public high school education.
Are they teaching algebra in elementary school? Or just calling the arithmetic I learned algebra?
My son came out of high school some 10 years ago and I really had a hard time helping him with his algebra. Everything he was taught was by rote, as if he were learning the multiplication tables. He had no idea of how to use anything he learned, and had no concept of what an algebraic proof consisted of.
As a consequence of course he repeated it in college only to go through the same thing and as a result of that, calculus was nearly his undoing.
I dunno either, Earnest. I know that as an electrician I don't get the brightest of the high school grads, but when they read a tape measure as "14 inches and a big mark and a little mark" I see a problem. When they can't add 1/2 and 3/4 I see a problem. When there is only one other man on the crew that can scale a 3/32" blueprint without an architectual ruler I see a problem.
It would probably help some if the US would come out of the dark ages and accept the metric system, but it won't cure it. Only real education can do that.
And maybe those dratted "down unders" as destined to rule the world.
That is a bit scary wilderness, I had not realised things were so bad in American education.
I do hear some complaints hear too, but often it's about kids not having enough hands on experience.
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