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How to increase your IQ level ?

Thermal said:
OP would be snickering at all these little brains and their bufoonish commentary, but he graciously recluses himself from commenting, just checking regularly on the thread to see how the lesser minds are getting along.
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His spider sense is obviously tingling
 
You can test the accuracy of your system's sine routine by using it to calculate the sine of 29 degrees.

I have reason to believe the correct result of that calculation, rounded to 50 decimal places, is

.48480962024633702907537962241577656827665747683687​

(I believe that is the correct result because it's the result I calculated using the series expansion of Abramowitz and Stegun equation 4.3.65, which is the same as the series expansion shown by Wikipedia. I used exact arithmetic of unlimited precision for the series expansion. The only source of inaccuracy in my calculation was in my conversion of 29 degrees to radians, for which I used the first 65 decimal digits of pi. I don't believe that 65-digit approximation to pi could have introduced enough inaccuracy to affect the 50-digit result shown above, but I haven't actually done the numerical analysis needed to prove it doesn't.)

If that calculation doesn't expose the source of Python's inaccuracy using numpy.longdouble, then I can use the first 100 digits of pi to convert 29 degrees to radians, followed by exact arithmetic of unlimited precision for all subsequent calculations. Somewhere in there we'll see where Python is going wrong.
 
JayUtah said:
For C++, yes I get the same answer as you did, as expected, since it's the same IEEE double precision arithmetic. Using Python's numpy.longdouble type (IEEE quadruple precision, 128 bits) I can improve it to 29.000000000000000003.
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Okay, I was able to reproduce that result using Python on my system.

I was also able to establish that the reason Python is printing only 19 or 20 digits of a numpy.longdouble is that the significand of a numpy.longdouble (on my system, and apparently on @JayUtah's as well) is approximately 64 bits, not 128.

(I say "approximately" because examining the low-order bits that Python's print function doesn't want to reveal is not entirely trivial, and I wasn't too concerned if my conclusion is off by a bit or two. The main point here is that the significand is far short of 128 bits.)

(Edited to add: By the way, I checked my previous calculation using 200 digits of pi, and got the same result as when I was using only 65 digits of pi.)
 
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Might as well post this:
Code: 
import numpy as np

bits = 0
x = 1.0

while x < x + 1.0:
    bits = bits + 1
    x = 2.0 * x

print ("Default float precision is", bits, "bits.")

bits = 0
x = np.longdouble(1.0)

while np.less(x, x + 1.0):
    bits = bits + 1
    x = np.multiply(2.0, x)

print ("NumPy.longdouble precision is", bits, "bits.")
After putting that into a file named precision.py, and running it on my system:
Code: 
$ python precision.py
Default float precision is 53 bits.
NumPy.longdouble precision is 64 bits.
 
Thermal said:
OP would be snickering at all these little brains and their bufoonish commentary, but he graciously recluses himself from commenting, just checking regularly on the thread to see how the lesser minds are getting along if anyone's clicking the links to his site.
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FTFY
 
Ron Obvious said:
I had a primary school teacher who complained that "kids today" would just whip out their slide rule and get an answer without really understanding the question or the answer....
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Actually, to get the right answer using a slide rule, you have to be able to understand the question well enough to be able to figure out the magnitude of the answer.
 
zooterkin said:
I learnt to use one, though I can't remember if we were actually taught at school, or my dad taught me (he was a Physics teacher) or I found it in a book. I was never particularly proficient, though I remember I always had a slide rule in my briefcase, and there's certainly more than one in the house now somewhere. Calculators came in while I was at secondary school; my dad had one of the first Sinclair Scientific calculators, which used RPN. We weren't allowed to use them in exams, though; can't remember if that applied to slide rules (I suspect it did, since many had all sorts of formulae printed on them).
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I had a basic calculator in the early 80s in primary school. I got a scientific calculator , a Casio fx100, in secondary which was allowed in the Leaving cert exams. Though my programmable fx8500G was not.
In college I didn't do maths as subject but as a module so exams were open book; I used the fx8500G and a Poqet with PCMCIA memory card loaded with Derive.
 
I'm assuming I knew at one time what logs were. I went through Calc 2, and aced it, so I'm sure we hit them prior to that. Damned if I can remember though. Maybe if I listened to some groovy tunes, it would all come flooding back?

Memory is such a pain in the ass. After six months of high school French in a Catholic school, I can still belt out the Notre Pere without missing a beat, and can stumble through simple French speaking interactions.
 
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@wise47 writes, "The original text on which I based the initial post in this thread can be found here: How to increase your IQ level ? How to improve your IQ ?"

Yes, Gregory, we're well aware of where to find your publications. But this is a discussion forum, not your personal blog. No one here is obliged to read your publications since you can't demonstrate a willingness to discuss them. You have amassed several pages of comment and criticism which are not answered by your simply referring back to your original statements.

In the larger sense, some of us have taken the time to comment on all your writings at least to some degree, and at great length on other parts of your writing. Continuing to call yourself a scientist while ignoring scholarly courtesy is rude and pretentious.
 
W.D.Clinger said:
I was also able to establish that the reason Python is printing only 19 or 20 digits of a numpy.longdouble is that the significand of a numpy.longdouble (on my system, and apparently on @JayUtah's as well) is approximately 64 bits, not 128.
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That's good work, thanks. longdouble is one of those alias types defined as "at least this big and possibly much bigger." In the documentation, "much bigger" is given as 128 bits and specifically described as IEEE quadruple precision. But after looking more closely, the numpy on my laptop is too old to allow longdouble to be aliased to numpy.float128. And thanks also for the code that determines precision.
 
wise47 said:
If someone has 120 IQ points, they can try to reach 1200 points.
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No, they cannot.

Your method of measuring and scoring I.Q. is entirely something you made up. It has no connection to the system that produces scores clustered around 100, therefore the scores are not directly comparable. This has been explained to you extensively by people with proper experience and knowledge. Why are you still peddling something that has zero scientific basis and zero scientific utility?
 
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