Free Republic

Oh, geez, could you be any more self-important?? George Washington you are not. The rhetoric here has become just as insufferable as that of DU.

For a few years this place was serious. Not anymore. It’s now little more than a lot of hot air. It’s no wonder your traffic is down & people are looking for other places to go. Thanks for the memories.

I had changed the hosts file on all of my computers to prevent even accidentally loading this site, and now I remember why. I will now uncomment those lines and leave your echo chamber, for good this time.

BTW, if you want to avoid FR, add these lines to your hosts file (/etc/hosts on most Linux systems, c:\windows\system32\drivers\etc\hosts on Win systems). Your browser will be redirected to Google when loading freerepublic.com.

74.125.227.136 freerepublic.com
74.125.227.136 www.freerepublic.com

My email to Carbonite:

“I am a small vendor in the business of providing IT support and services to other small businesses. Thanks for helping me to make my decision of whether or not to use Carbonite either personally or as a recommendation to my customers. Because of your withdrawal of support for Rush Limbaugh, I will not be using or recommending the use of your service to my customers. If at some future time you resume advertising on Mr. Limbaugh’s program I will reconsider my decision 6 months after your resumption of advertising.”

The DUmmies were flipping out in 2004 because GWB’s bus was made in Canada. I’m more amused by the fact that once again, Obama is doing what Bush did, but now the DUmmies and their ilk will give Obama a pass when they drilled Bush for the same thing.

OTOH, I’m surprised to see that some of them are actually criticizing 0 for some things, but I’m just as certain that his ineptitude and hypocrisy will not prevent them from voting for him.

Windows is the best operating system in the world, bar none. Linux starts with the letter L. Loser starts with the letter L. COINCIDENCE?????????????

Lazamataz starts with the letter L.

Just sayin' . . .

Graduate work is seldom worth much if it hasn’t been seasoned with a bit of real world work experience, following your undergraduate degree.

Agreed, and in my profession this may be doubly true. After earning a computer engineering degree 15 years ago, I decided to start a computer science master's program last Fall. My interest, commitment, and ability to learn are much higher than they were before, in spite of having other important things on the docket--a full-time job, 4 kids, volunteer work, etc. Going back to school has given me an opportunity to learn a lot of advances in computer science that have been developed in the 15 years or so since I finished my undergrad. I would never have used the word "fun" to describe school until I started grad school, and even though it's a ton of work, I'm having the time of my life.

Shouldn’t it say “because Americans work longer and take fewer vacations than almost any developed country, they enjoy unprecedented prosperity”?

Kids will just dump the raw veggies if forced to take them.

And they will get creative in doing it. The cameras will also snap a picture of the trays when they're returned to the kitchen for cleaning. Kids will take plastic bags to school so they can pack the leftover food and throw it away later, or they will take stuff in and add it to their plates to make it look like they ate less, or they'll pile the leftovers from 4 kids' plates onto 1. I could have a great time screwing with the minds of these researchers and bureaucrats. This is a complete boondoggle.

“But what is pi I asked the kid. He said nothing and left the room.”

Ask my 7 year old, home schooled daughter. Had you asked her, you wouldn’t have had such a snarky comment to post here.

My wife and I saw the 12:25 show also. I do not have much of a critical eye for acting and cinematography, so take my review with a grain of salt. :-)

Go. See. Atlas. Shrugged.

It’s not without it’s technical problems, but the message is too important to throw the baby out with the bath water.

Some things I noticed have been mentioned upthread — the acting was a bit rigid but not so much so that it was terribly distracting. The production was true to Rand’s work, as well as I can remember. (I read AS 3 years ago and had forgotten some details. I had completely forgotten Paul Larkin, for example.)

As has been mentioned, some of the villain characters were a bit underdeveloped. The viewer can see that there are several of them and get a sense of what they represent, but more of their hidden thoughts and objectives could have been brought out. It’s clear they’re up to no good when the Equalization of Opportunity bill is passed, but the underlying evil which drives such ideas could have been presented more explicitly.

When I came out of the theater I remembered Obama’s speech from Wednesday and thought of the similarities between it and and the looters in Atlas. One can barely distinguish the two.

My wife is a full-time mom and homeschools our 4 kids who range in age from 1 to 7. During this period of her life, most of her news and “outside world” information comes through me, and Atlas is no exception. As I read the book 3 years ago I would tell her about it as I went. She saw the movie with me today and at times I could see her wiping away a tear. The message of the movie is not lost on those who are willing to see that message.

As we left the theater, I was gratified to see a vanity plate on a high-end automobile which said “RGNOMX”. It warms the heart. ;-)

“Once again you rewrote the formula with a backslash”

It’s actually a forward slash.

Notice that nowhere in the following quotation does it mention greater precedence should be given to implied mult.

From http://jeff560.tripod.com/mathsym.html:

The convention that multiplication precedes addition and subtraction was in use in the earliest books employing symbolic algebra in the 16th century. The convention that exponentiation precedes multiplication was used in the earliest books in which exponents appeared.

In 1892 in Mental Arithmetic, M. A. Bailey advises avoiding expressions containing both ÷ and ×.

In 1898 in Text-Book of Algebra by G. E. Fisher and I. J. Schwatt, a÷b×b is interpreted as (a÷b)×b.

In 1907 in High School Algebra, Elementary Course by Slaught and Lennes, it is recommended that multiplications in any order be performed first, then divisions as they occur from left to right.

In 1910 in First Course of Algebra by Hawkes, Luby, and Touton, the authors write that ÷ and × should be taken in the order in which they occur.

In 1912, First Year Algebra by Webster Wells and Walter W. Hart has: “Indicated operations are to be performed in the following order: first, all multiplications and divisions in their order from left to right; then all additions and subtractions from left to right.”

In 1913, Second Course in Algebra by Webster Wells and Walter W. Hart has: “Order of operations. In a sequence of the fundamental operations on numbers, it is agreed that operations under radical signs or within symbols of grouping shall be performed before all others; that, otherwise, all multiplications and divisions shall be performed first, proceeding from left to right, and afterwards all additions and subtractions, proceeding again from left to right.”

In 1917, “The Report of the Committee on the Teaching of Arithmetic in Public Schools,” Mathematical Gazette 8, p. 238, recommended the use of brackets to avoid ambiguity in such cases.

In A History of Mathematical Notations (1928-1929) Florian Cajori writes (vol. 1, page 274), “If an arithmetical or algebraical term contains ÷ and ×, there is at present no agreement as to which sign shall be used first.”

Modern textbooks seem to agree that all multiplications and divisions should be performed in order from left to right. However, in Florida Algebra I published by Prentice Hall (2011), a problem asks the student to evaluate 3st2 ÷ st + 6 for given values of the variables, and the answer provided comes from dividing by st. A representative for the publisher has acknowledged that the expression is ambiguous and promises to use (st) in the next revision.

“Once again you rewrote the formula with a backslash to satisfy your computation method. Throw that calculator away”

The original question was because of 2 calculators which had the expression written with a backslash. The expression in question properly has a backslash.

There is a definite difference. Computers require a more rigid set of rules for solving expressions than humans do, even for mathematics. However, it isn’t a question of which discipline is more rigid or precise. It’s a matter of defining the semantics of the mathematical grammar. In the 48/2(9+3) expression, if the implicit multiplication is given higher precedence than the parentheses, the answer is obviously much different than if implicit and explicit multiplication have the same precedence. Many, if not most, computer scientists and engineers have given equal weight to implicit and explicit multiplication (PEMDAS) and this has probably influenced mathematicians and textbook writers. The notable exception is TI, and even they have now changed their algorithm.

I’d like to see the algorithm used by the online calculators to parse the problem text. To give different answers, they have to be parsing the text differently. Most likely they’re doing something like

48/2(9+3) => 48/2*(9+3)
and
48÷2(9+3) => 48/(2*(9+3))

The expressions after the => can be calculated directly in the languages used to build the sites.

The calculators in question used /. See the pictures of the 2 calculators at the top of the thread. I can’t say for sure, but the link you’re looking at is almost certainly pre-parsing the problem text before evaluating it, and it’s “rewriting” the problem differently for the / and ÷ cases.

Google gives 288 for both / and ÷. Bing gives 288 for / but does not calculate with ÷. Matlab, C, C#, PHP, JavaScript, bc, Python, and the HP50g all say 288.

What does this mean? Math, like other languages, has evolved over the years. The implied multiplication question is still being asked, which is evidence of the continuing evolution. In the last 4-5 decades or so (and probably as a result of the development of computing,) implied multiplication has come to have the same precedence as explicit multiplication. This is evident in the fact that so many languages and computing platforms give 288 as the answer to the problem in question. Very few give an answer of 2. Even though some TI products produce 2, TI has changed their approach so that newer products say 288.

Perhaps you should publish a paper and explain to the people who wrote the arithmetic parsers for Google, Microsoft, HP, GNU, etc. why they are giving the wrong answer.

Nice example, except it’s given only to show an ambiguity which arises when people don’t follow the standard order of operations. A previous post indicated that the mathematicians and/or engineers at TI do not give implicit multiplication higher precedence.

“Note that different software will process this differently; even different models of Texas Instruments graphing calculators will process this differently. In cases of ambiguity, be very careful of your parentheses, and make your meaning clear.”

The original post in the thread asks why 2 calculators give different results. From Dr. Math on mathforum.org:

“In my research for another Dr. Math “patient,” I found that some calculators have experimented with this rule [implied multiplication]. Calculators have somewhat different needs than mathematicians, since they have to take input linearly, one character after another, so they are forced to make a decision about it. On the TI Web site I learned that they deliberately put this “feature” into the TI 82, and then took it out of the TI 83, probably because they decided it was not a standard rule and would confuse people.”

Summary: implied multiplication is not a standard rule, and the programming of the TI calculators was consequently changed.

“The only thing being distributed is 2(9+3).”

Not in the video link you posted.

If the expression were limited to a single, stand-alone distribution, your obsession with it might matter. However, you ignore the order of operations to arrive at an incorrect answer.

Watch the first 20 seconds of this video to understand how to evaluate the expression in question.
http://www.youtube.com/watch?v=k-VJjfw90jc

Evaluate the operations inside the parens first. Then evaluate div and mult operators from left to right. Finally, evaluate add and subt operators from left to right.

“Nothing to brush up on. I’m right. Anybody that comes up with 288 is wrong. Thanks for the advice, though.”

Tell us why you’re right. FYI, if you are right, that means that Excel, Google, bc, and programs written in C, C#, PHP, JavaScript, and my HP50g are wrong. If you’re right it should be easy to explain.

Before you can ask, I’ll tell you why 288 is right. The order of operations is

Parens
Mult and Div (equal to each other)
Add and Subt (equal to each other)
Operators with equal precedence are evaluated from left to right.

48÷2(9+3) =
48÷2(12) = [Because operations inside parens are evaluated first]
24(12) = 288 [Because mult and div have equal precedence & evaluated L to R]

Where is the error in my work?

“As you have said, the answer is 2. I’ve done more math in my life than I care to admit (I’m a civil engineer). Having said that, a few more parentheses would have made the equation alot less ambiguous.”

You’d better brush up a bit, then. Otherwise, perhaps you can explain how you arrive at an answer of 2?