Basic Math


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37 minutes ago, Carborendum said:

But the truth of the matter is that, believe it or not, the answer really is 5! 

By what rules?

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There used to be a TV game show called "Are You Smarter than an Eight Year Old?" where adult contestants tried to answer questions that would typically be given to eight year old kids.

In one episode the contestant was given something like 20-10×0. The answer he gave was wrong anyway, but the show host told him the true answer was zero because "anything multiplied by zero gives zero".

The show producers were bombarded with complaints from mathematicians, who said the answer was 20 because the multiplication should be performed first.

The producers consulted the question setter - a teacher of eight- year-olds, who defended her answer by saying "eight-year-olds are taught to do their sums left to right" and the TV producers stuck to that.

Which would have been fine if the show had been named "Do You Do Your Sums the Same Way as an Eight Year Old?"

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3 hours ago, Carborendum said:

and believe the answer is 5.  How ridiculous!  People will say.

Was it Snagglepuss who used to say "ridicalicalicalous"? I cannot find a single YouTube video of him saying it. (Plenty of him saying "Heavens to Murgatroyd".)

I would love to be able to do a Snagglepuss voice, but it never comes out right.

Edited by Jamie123
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1 hour ago, Jamie123 said:

The producers consulted the question setter - a teacher of eight- year-olds, who defended her answer by saying "eight-year-olds are taught to do their sums left to right" and the TV producers stuck to that.

Which would have been fine if the show had been named "Do You Do Your Sums the Same Way as an Eight Year Old?"

No, the only thing that would have been fine is if they'd taught 8 year olds right from the start instead of saying: "Do it left to right." followed by "Remember when we told you to do it left to right? Well, we lied."  :SMH:

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21 minutes ago, zil2 said:

No, the only thing that would have been fine is if they'd taught 8 year olds right from the start instead of saying: "Do it left to right." followed by "Remember when we told you to do it left to right? Well, we lied."  :SMH:

A lot of math scholars will joke about the difference between mathematical theorist and mathematical application.  The jokes usually go around the theoretical mathematicians being sorely disappointed whenever some low-level mathematician (engineer) finds an application (or a new application) for their pure unadulterated theory.

Personally, I have always been an advocate of the “Keep it simple – stupid” or KISS theory of approach to anything.  Parentheses are an integral part of mathematical theory (across all variations of mathematical theory).  I believe children ought to be taught to properly avoid ambiguity and always use parenthesis to properly express mathematical thinking and process.

I believe the proper use of mathematics will always produce a singularity of answer and that this proper use best defines true science (such as the various engineering disciplines) – unlike the pseudo sciences that produce a variety of answers to please the various students (such as psychology and various therapies).  Clear thinkers produce clear thinking and results and leave uncertainty to those that love uncertainty and uncertain results.

 

The Traveler  

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1 hour ago, Traveler said:

I believe children ought to be taught to properly avoid ambiguity and always use parenthesis to properly express mathematical thinking and process.

This is how I code. I said above that JS (or any computer language) does... such-n-such. But if I were coding it I wouldn't write 

230 - 220 / 2

I would write 

230 - (220 / 2)

to be explicit.

Edited by The Folk Prophet
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6 hours ago, Jamie123 said:

In one episode the contestant was given something like 20-10×0. The answer he gave was wrong anyway, but the show host told him the true answer was zero because "anything multiplied by zero gives zero".

The show producers were bombarded with complaints from mathematicians, who said the answer was 20 because the multiplication should be performed first.

The producers consulted the question setter - a teacher of eight- year-olds, who defended her answer by saying "eight-year-olds are taught to do their sums left to right" and the TV producers stuck to that.

But the question is, How are they taught to do their products? Apparently they are not taught correctly.

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14 hours ago, Vort said:

 

I had high hopes for this video, but it doesn't really get to the nub of the problem: it only nitpicks (quite validly) at one of the intermediate steps, but proves the answer us numnuts arrived at by dumb luck happens to be correct.

The major issue for me is that if i^i is 0.20787958 and also 0.000388203 (and a whole bunch of other numbers) then by the foundational axiom that if A=B and B=C then A=C we must conclude that 0.20787958=0.000388203, which is as wrong as saying that 1=-1, which was Presh Talwalkar's objection to our "numnut" approach.

Now that always reminds me of...

undefined

...though no one pretends that the Trinity is anything but a mystery.

The only solution I can think of is that "equality" in the statement x=i^i does not identify an equivalency, but a kind of "predicate" which applies not only to x but to other numbers as well. We use this sort of language in "big O" notation anyway for example:

image.png.d03f245c179656b737d0ef9b377599b7.png

does not imply that f(x)=g(x). It is merely a statement about how fast the functions grow. (I've always thought big O notation was very sloppy, and I hardly ever use it.)

We could define the answer as an infinite set

image.thumb.png.9e2b37d959df41f56f97b3fb1f943ea3.png

 

Edited by Jamie123
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