Clearing some basic fundamentals in math, science and other subjects

realgoogler · Post by **realgoogler** » Thu Dec 30, 2010 1:27 am

As we cruised past the school/college days learning new concepts in math and science, I am sure there were some things that raised questions within us but we did n't pursue seeking answers and moved on. I am opening this thread so that those can be cleared.
It may appear naive but not for ourselves. I am proposing to leverage experts/laymen in this forum to address those.

Here are some of mine
RG1. Why is standard deviation calculated the way it is ? Why can't it be a average of absolute difference between samples with respect to average ?
Why do they think standard deviation calculated the way they do is more representative of deviation ?

RG2. To measure angles, why did they chose 90 degrees for right angle. Won't life be simple if the angles were 100. Where did 90 come from ?
Similar question for minutes, second, hour, day why 60, why 24 ? why don't you approximate in 10s ?

RG3. why is the natural logarithm ? how did they discover "e" and why is it so significant.

boca · Post by **boca** » Thu Dec 30, 2010 2:33 am

realgoogler;358495
RG2. To measure angles, why did they chose 90 degrees for right angle. Won't life be simple if the angles were 100. Where did 90 come from ?
Similar question for minutes, second, hour, day why 60, why 24 ? why don't you approximate in 10s ?[/quote]
Why does the circle have 360 degrees? Blame it on the Babylonians (passed down from the Sumerians) and their sexagesimal (base-60) system. That is what I read. :)

http://en.wikipedia.org/wiki/Sexagesimal

As to the rest, I was strictly taught not to ask why. I passed. :)

boca · Post by **boca** » Thu Dec 30, 2010 2:39 am

realgoogler;358495RG3. why is the natural logarithm ? how did they discover "e" and why is it so significant.

Here is an interesting take on "e" as the "constant of compounded growth"

http://www.recoveredscience.com/constanteofgrowth.htm

I think that the logarithmic table was a result of this, though formalized much later. Seems plausible. :)

realgoogler · Post by **realgoogler** » Thu Dec 30, 2010 3:38 am

Thanks boca2blr for digging those up. I m still working on digesting why e is good base for natural logarithms.

To clarify on the following
[quote]
RG1. Why is standard deviation calculated the way it is ? Why can't it be a average of absolute difference between samples with respect to average ?
Why do they think standard deviation calculated the way they do is more representative of deviation ?

[/quote]
Consider samples 1, 5, 15
mean is 7
so if somebody asked me to calculate deviation measure I would do
( (7-1) + (7-5 ) + (15-7) )/3 = 16/3 = 5.33

The conventional formula is square root of ( sq(7-1) +sq(7-5) + sq(15-7)/3 )
square root of (36 + 4 + 64)/3
square root of (104)/3 = 5.887

Why is 5.88 is a good measure deviation measure than 5.33 for the given sample set ?

boca · Post by **boca** » Thu Dec 30, 2010 3:58 am

realgoogler;358525Thanks boca2blr for digging those up. I m still working on digesting why e is good base for natural logarithms.

To clarify on the following

Consider samples 1, 5, 15
mean is 7
so if somebody asked me to calculate deviation measure I would do
( (7-1) + (7-5 ) + (15-7) )/3 = 16/3 = 5.33

The conventional formula is square root of ( sq(7-1) +sq(7-5) + sq(15-7)/3 )
square root of (36 + 4 + 64)/3
square root of (104)/3 = 5.887

Why is 5.88 is a good measure deviation measure than 5.33 for the given sample set ?

In other words, why standard deviation and not mean deviation.

See if this helps -> http://www.leeds.ac.uk/educol/documents/00003759.htm

BTW, got it from http://mathforum.org/. If you have any more questions on maths, that site is better for answers.

Similarly, anything on Physics, go to http://www.physicsforums.com/

realgoogler · Post by **realgoogler** » Thu Dec 30, 2010 5:05 am

boca2blr;358527In other words, why standard deviation and not mean deviation.

See if this helps -> http://www.leeds.ac.uk/educol/documents/00003759.htm

BTW, got it from http://mathforum.org/. If you have any more questions on maths, that site is better for answers.

Similarly, anything on Physics, go to http://www.physicsforums.com/

Thanks you! you rock !!
So this consistency argument seems to be the key
When drawing repeated large samples from a normally distributed population, the standard deviation5 of their individual mean deviations is 14% higher than the standard deviations of their individual standard deviations (Stigler 1973). Thus, the SD of such a sample is a more consistent estimate of the SD for a population, and is considered better than its plausible alternatives as a way of estimating the standard deviation in a population using measurements from a sample

stup123 · Post by **stup123** » Thu Dec 30, 2010 8:06 pm

I was trying to think if I ever had such doubts in school and i cant remember a thing

but when I came across SSY, Sidha Samadhi Yoga where they suggest that we eat raw veggies..all those biology digestive system class came back in a flash.Dont recall any organ in the human digestive system that said "used to break down raw foods" .
Also first part of it in our text book in school was Oesophagus and it helps in digesting cooked food.I used to wonder what will happen to raw food..On a lighter note,Is it ok to eat raw veggies?

boca · Post by **boca** » Thu Dec 30, 2010 10:00 pm

realgoogler;358542Thanks you! you rock !![/quote]
Thank you for asking the questions. It helped brush up on the basics. :)

realgoogler;358542So this consistency argument seems to be the key
When drawing repeated large samples from a normally distributed population, the standard deviation5 of their individual mean deviations is 14% higher than the standard deviations of their individual standard deviations (Stigler 1973). Thus, the SD of such a sample is a more consistent estimate of the SD for a population, and is considered better than its plausible alternatives as a way of estimating the standard deviation in a population using measurements from a sample

Well, I read further and the experts are not convinced with the actual reason. At some point, it went beyond my scope of understanding statistics.

However, this guy's explanation, I like. :)

http://amarsagoo.blogspot.com/2007/09/making-sense-of-standard-deviation.html

rabtag · Post by **rabtag** » Thu Dec 30, 2010 10:07 pm

"e: The story of a number" by Eli Maor may interest you. Has been on my wishlist for a while, I liked the author's interview on a radio and he sounded like a very good Math teacher with great love for the subject. If I do read it anytime soon will post my review. One of my good math teacher used to say that e, pi and golden ratio are the nature's constants of our physical world as they occur in so many different areas of sciences.

P.S: Thank you for starting this thread. Hope to learn some from you learned people.

cabo · Post by **cabo** » Thu Dec 30, 2010 10:46 pm

stup123;358665I was trying to think if I ever had such doubts in school and i cant remember a thing

but when I came across SSY, Sidha Samadhi Yoga where they suggest that we eat raw veggies..all those biology digestive system class came back in a flash.Dont recall any organ in the human digestive system that said "used to break down raw foods" .
Also first part of it in our text book in school was Oesophagus and it helps in digesting cooked food.I used to wonder what will happen to raw food..On a lighter note,Is it ok to eat raw veggies?

From what I remember of the GI physiology, Digestive enzymes are produced from mouth ( saliva), stomach, intestine. Pancreatic enzymes and bile are also essential. Oesophagus does not helps in digestion except may be mechanical breakdown and food mixing by peristalsis.

As far as I know, most raw food is digested except for grass etc which has high cellulose. As we have evolved, the now vestigeal structure- the appendix no longer produces the enzyme cellulase needed for digestion of grass.