Another "wow"

JamesG161

JamesG161

SBO Weather and Forecasting Forum Jim & John
Feb 14, 2014
7,605
Hunter 430 Waveland, MS
DayDreamer41 said:
show me 12,489,326,749 x 937,562,482
Click to expand
Actually even calculators or my computer cannot give you the correct answer, either.:yikes:

The old algorithm, I learned in school, could give you the real answer, by hand, if you could live long enough to do it or have enough pencils and paper to hand write it.

We landed a man on the moon using Logarithmic Addition and IBM computers that were only good for this precision...
12489 x .9376 ≈ 1.171 x E19 [ E meaning 10 times itself 19 times or 19 trailing zeroes]

Try this on your calculator...
2/3 = ?
If you get .6666666667 , it is lie.
Oh well...
But thanks to the IEEE 754 standard and low cost memory and high speed computation, we get a precision of...
https://en.wikipedia.org/wiki/256-bit

The answer I got, in my head, was 1.2 x E19 in about 10 seconds. I had to use a "pencil point" counter to get E19.:pimp:

The question is how precise you want the result.;)
Jim...
 
agprice22

agprice22

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Aug 3, 2012
2,542
Performance Cruising Telstar 28 302 Watkins Glen
Truly, the “new” math was intended to be intuitive. Stand at a cash register and calculate your total, your tax, and your grand total. You multiply the big numbers first and the small numbers second. We all do it automatically. Are we exact? No. It does not matter. We are not using it for science. We are using it for living. It works for that purpose. Beyond that, we would use other methods. It is not wrong. I just enjoyed her automatic reliance on the old tabulation methods with no awareness on her part.
I also enjoy how many scientifically minded, intelligent people we have right here who are sailors who enjoy the intersection of physics, mathmatics, mechanics, and nature. It is clear that we are inquisitive problem solvers.
Those traits will be passed on! Thank goodness!
 
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DougM

DougM

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Jul 24, 2005
2,242
Beneteau 323 Manistee, MI
I had some fantastic math teachers throughout my schooling. There was a lot of rote learning involved, and knowing the basic principles, I did well.
By contrast, my sons were taught what was then termed “modern math”. To this day I don’t think they could balance a checkbook without a calculator.
 
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jssailem

jssailem

SBO Weather and Forecasting Forum Jim & John
Oct 22, 2014
21,501
CAL 35 Cruiser #21 moored EVERETT WA
Yes Doug. It feels like we have lost a generation to machines. Calculators replaced slide rules.
Back when it was a tool to check my work it has now become a way to do the work. The issue is just going through a process is not necessarily going to assure you have the "Correct" answer for the problem you are trying to solve.
 
Will Gilmore

Will Gilmore

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Oct 19, 2017
7,774
O'Day 19 Littleton, NH
In my university physics class, the setup and logic behind the solution was more important than the number arrived at in the end. I got a 90 percent on a problem where I made a calculation error on step one, so every number in the problem was wrong after that. The professor recognized the error and gave me credit for doing the problem correctly.

-Will (Dragonfly)
 
agprice22

agprice22

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Aug 3, 2012
2,542
Performance Cruising Telstar 28 302 Watkins Glen
Will, exactly as it should be! School is to teach you to THINK! Thus, your thinking and understanding of concepts is displayed in your work. 1000 years ago, math, and math concepts, were considered magic, evil! The adherents were members of secret societies who feared revelation outside the society. Then, the concepts were known to few. Then, education brought those concepts to the masses. Now, electronics have supplanted the need to do the work... hopefully, the need to understand the concepts will NOT be next!
Sailors, and this includes the youngsters we see joining now, show an independent spirit, wanting to know how THINGS work. Sailors DO the work, learn the concepts, and enjoy the journey.
I OWN A SEXTANT. That should be our motto!
 
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Will Gilmore

Will Gilmore

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Oct 19, 2017
7,774
O'Day 19 Littleton, NH
agprice22 said:
The adherents were members of secret societies who feared revelation outside the society.
Click to expand
It was felt that certain levels of knowledge needed initiation to be exposed to because to learn the secrets of the Universe when unprepared, would cause deep fear and a break from sanity. The hermetic traditions go back to early Egypt and Babylon. The Pythagoreans were particularly interesting and influential.
A subject I find both very interesting and influential in my life.

-Will (Dragonfly)
 
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Will Gilmore

Will Gilmore

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Oct 19, 2017
7,774
O'Day 19 Littleton, NH
There is a story that a young Pythagorean initiate discovered irrational numbers. He brought his new discovery to Pythagoras while on an ocean voyage. Pythagoras was so insensed by the blasphemous idea that he threw the monk overboard.
Another version has the young monk being admonished by Pythagoras for revealing truths to the unprepared before their time. The monk later fell, accidentally overboard.
It is a little unbelievable, considering the intense loyalty of friendship and respect for life the Pythagorean ideals held, that being thrown overboard for having a "blasphemous" idea would be the reaction of Pythagoras. It is also a bit irrational;) to think that a mathematical thinker who studied triangles would not have already come to grips with the idea of irrational numbers. After all, the hypotenuse of the 45, 45, 90 triangle is an irrational number when the length of it's legs are set to one. It seems like Pythagoras would have already known that.
The history of Math has some fascinating events that have not only changed our world, but have been completely ignored in favor of far less interesting and uneventful facts.

-Will (Dragonfly)
 
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Mike4116

Mike4116

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Jun 7, 2004
350
Oday 28 East Tawas
Recently I tried to help my 11 year old grand daughter with some long division. As I went through the steps (I had learned) she began to explain to me the ADDITIONAL steps her new math required. It seems that in the quotient a step is added to place a digit over the dividend even if it is merely zero. As my head began to explode my wife stepped in to clear things up. Look, I hold a degree in statistics (lotsa' math) and this stuff makes no sense to me whatever. Long division is complex enough without adding extra, pointless steps to add to the complexity. It may make sense to a computer which calculates at the speed of light but to us pokey old humans the shortest path is still the critical path (PERT).
 
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JamesG161

JamesG161

SBO Weather and Forecasting Forum Jim & John
Feb 14, 2014
7,605
Hunter 430 Waveland, MS
Will Gilmore said:
After all, the hypotenuse of the 45, 45, 90 triangle is an irrational number when the length of it's legs are set to one.
Click to expand
It doesn't mater the same length size of the legs. What is irrational about the square root of 2?

√2= 1.4 for all practical purposes.;)

Jim...

PS: I remember 1.414 from pre-calculator days:pimp:
PSS: The hypotenuse is ≈40% longer than its legs.
 
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Will Gilmore

Will Gilmore

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Oct 19, 2017
7,774
O'Day 19 Littleton, NH

-Will (Dragonfly)
By the way Jim, the ancient Greek mathematicians didn't have the decimal point. o_O So, how did they do it?
 
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