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HP calcs are really not that accurate..
12-02-2017, 12:40 PM
Post: #21
RE: HP calcs are really not that accurate..
(12-02-2017 10:56 AM)Gerald H Wrote:  Aristotle? He claimed women have a different number of teeth from men. Discredited.

I'm reminded of Robert Recorde:

http://www.hpmuseum.org/forum/thread-3223.html

I couldn't have said it better myself (in old English!)

Tom L

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12-02-2017, 02:50 PM
Post: #22
RE: HP calcs are really not that accurate..
(12-02-2017 10:37 AM)DA74254 Wrote:  Thanks again, and to emphasize; it was not my intension to step on anyones toes.

You can learn a lot here, depending on how you ask a question, if you have thick skin....

You can pose the same question in different ways, for example:

1. "How does one do XYZ?"

or this way:

2. "There is no question that the best way to do XYZ is [insert simple/dumb explanation here], right?"

and you will get vastly different responses. The former is likely to get fewer simple answers, including the universal (and generally appropriate) "RTFM", while the latter will provide many more elaborate and insightful answers, often leading to a series of competing solutions, each successively improving on the last.

But you may take a few small bruises in the process... Of course they heal, and you've learned a lot in the process.

@Pauli - Regarding "256 digits are far more than you'd need to represent the diameter of the universe in terms of the planck length"

Awesome statement, it just captures and states the point better than any other phrase possibly could express it. And it's cool!

And as a bonus, you've no doubt caused a lot of folks to google 'planck length'. Sure, I knew it was small, but not that it is essentially the very definition of smallest possible. Like I said, Cool!

--Bob Prosperi
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12-02-2017, 03:07 PM (This post was last modified: 12-02-2017 03:07 PM by pier4r.)
Post: #23
RE: HP calcs are really not that accurate..
(12-02-2017 02:50 PM)rprosperi Wrote:  2. "There is no question that the best way to do XYZ is [insert simple/dumb explanation here], right?"

and you will get vastly different responses. The former is likely to get fewer simple answers, including the universal (and generally appropriate) "RTFM", while the latter will provide many more elaborate and insightful answers, often leading to a series of competing solutions, each successively improving on the last.

Almost like the Cunningham's Law

And I agree with the point that every thread can be a source for new input.

Wikis are great, Contribute :)
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12-02-2017, 03:47 PM
Post: #24
RE: HP calcs are really not that accurate..
(12-02-2017 02:50 PM)rprosperi Wrote:  You can learn a lot here, depending on how you ask a question, if you have thick skin....

You can pose the same question in different ways, for example:

1. "How does one do XYZ?"

or this way:

2. "There is no question that the best way to do XYZ is [insert simple/dumb explanation here], right?"

and you will get vastly different responses. The former is likely to get fewer simple answers, including the universal (and generally appropriate) "RTFM", while the latter will provide many more elaborate and insightful answers, often leading to a series of competing solutions, each successively improving on the last.

I agree that option 1 is generally not the way to go. For me personally, it tends to make me suspect that the person asking the question is looking for someone to do their homework for them.

Whether option 2 is right is a matter of taste. I find that it if you're actually making an effort yourself, it works perfectly fine to simply be honest: "I'm trying to figure out how to do XYZ. The best I've been able to come up with is <insert description of algorithm here>."

Not everyone has a taste for unpleasantness, and people who are genuinely willing to share their knowledge don't need to be prodded into action with provocatively-phrased statements, and might even by turned off by them -- "I'd be happy to help, but this person is being an ass, so f--- them."
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12-02-2017, 04:05 PM
Post: #25
RE: HP calcs are really not that accurate..
(12-02-2017 03:47 PM)Thomas Okken Wrote:  Whether option 2 is right is a matter of taste. I find that it if you're actually making an effort yourself, it works perfectly fine to simply be honest: "I'm trying to figure out how to do XYZ. The best I've been able to come up with is <insert description of algorithm here>."

Not everyone has a taste for unpleasantness, and people who are genuinely willing to share their knowledge don't need to be prodded into action with provocatively-phrased statements, and might even by turned off by them -- "I'd be happy to help, but this person is being an ass, so f--- them."

Oh, I agree with you, and I'm not advocating using style 2; I guess I was not clear, I'm just commenting on what I've observed over the years.

In fact I've found that the very people whose replies and opinions I seek most, generally will not reply to such taunts, except occasionally to correct another reply.

I think your final phrase captures it well!

There is no doubt that making a sincere effort first, followed by an honest and direct request for help is the way to go here. It always results in lots of replies, and even if the ultimate question isn't answered (sometimes there is no answer) one always learns something new in the process (as do most of the readers).

--Bob Prosperi
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12-02-2017, 10:43 PM
Post: #26
RE: HP calcs are really not that accurate..
(12-02-2017 02:50 PM)rprosperi Wrote:  @Pauli - Regarding "256 digits are far more than you'd need to represent the diameter of the universe in terms of the planck length"

Awesome statement, it just captures and states the point better than any other phrase possibly could express it. And it's cool!

I almost went with represent the volume of the universe in terms of. I don't think this is quite so neat but it is even more mind boggling.


As for asking questions, Thomas's variation of approach 2 is my favourite: I've tried, I've got something is there a better way? Being less confrontational can often avoid the need for thick skin.


Pauli
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12-02-2017, 11:51 PM
Post: #27
RE: HP calcs are really not that accurate..
Spoiler alert: shameless plug below. But it's all true nonetheless...

(12-01-2017 09:09 PM)DA74254 Wrote:  In my opinion, there should be no reason that we should not have, say, at least 256 digits/decimal points accuracy. That goes for any device capable of doing "2+2".

How about 2000? Search for newRPL.

(12-01-2017 10:37 PM)brickviking Wrote:  In addition, while computers have gobs of spare memory and awesome (!) floating point processors, calculators do not. Most calculators are not expected to be connected to the wall just to plain work (or charge their batteries after 9 hours of use), they're expected to work after 6 months (or more!) of use just the same as when the battery was first put in. This requires serious compromises in the choices of CPU or multifunction chip so as to make best use of the limited energy resources available from batteries.

Not completely true - see newRPL. Same CPU, battery and RAM requirements as the 39gs/40gs/50g. May not be perfect but does what the OP suggested (>256 digits) without much compromise.

(12-02-2017 10:37 AM)DA74254 Wrote:  I have been lied to, and I don't like it.

Well, some good came out of this. My slight ADHD/ADD, which demands things set square still prefers the "good" answers from the lying calcs, though I myself, upon reading the HP article linked here and the explanations from you, sets things "square" in a better way.

You can have it both ways. If your precision is sufficiently high (as you suggested), but you only display a limited number of digits, it creates the illusion of the perfect answer (2.00000000000000000000000), but if you subtract 2 you'll still see the 1.3E-254 error, which is the "truth" behind the scenes. That will give you the peace of mind that you are not being lied to.
By the way, that number is the actual answer from newRPL with 256 digits setting, doing the 5 iterations of sqrt/sq).
My way of thinking aligns well with yours. If you have enough numerical precision, you don't need to "lie",and you need to worry less about roundoff error propagations after thousands of operations.

I'm not sure I mentioned before in this post, but you should check out newRPL! :-)

PS: My apologies to everybody, I'm really bad at marketing...
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12-03-2017, 12:10 AM
Post: #28
RE: HP calcs are really not that accurate..
(12-01-2017 07:49 PM)DA74254 Wrote:  I put 2 on the stack and sqrt it 5 times, then squared it back. All my 5 HP's returned 1.99999999979 instead of 2.0. That goes for the Android Pro version as well.

I ran this in NQ41, which uses double precision floating point numbers, subtracting 2 and got the following result.

Code:

Welcome to NQ41 (Not Quite a -41!)
Version 0.003
Copyright © 2017 Craig Bladow. All rights reserved.
This experimental software is released for the sole purpose of testing and feedback and without warranty of any kind.

Input commands and numbers, separated by spaces, and press return.
A space or return after a number is the same as the command 'enter'.
Use 'exit' to quit and 'catalog 3' for a list of commands.

> 2 sqrt sqrt sqrt sqrt sqrt x^2 x^2 x^2 x^2 x^2 2 -
x: -3.5527e-15 y:0.0000 z:0.0000 t:0.0000 l:2.0000

>

Check out NQ41!
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12-03-2017, 01:19 AM
Post: #29
RE: HP calcs are really not that accurate..
(12-01-2017 09:09 PM)DA74254 Wrote:  there should be no reason that we should not have, say, at least 256 digits/decimal points accuracy

This is bait.
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12-03-2017, 01:47 AM
Post: #30
RE: HP calcs are really not that accurate..
Inspired by some other thread (where I looked at the pros and cons [but mainly the cons, the pros getting enough support already] of QPI and PSLQ), I just realised that we can "deal with" some of the issues raised in this thread in a more sophisticated and more defensible way if instead of sneaky extra digits we use (auxiliary, stateless) CAS and functions like QPI and PSLQ behind the scenes.

Would we still be talking about "lying" then, i.e. in particular when the auxiliary CAS does not know the provenance of the floats? Presumably you would need a mechanism to indicate how accurate your floats are...

More generally, how useful, magical, dangerous, perfect, .... would such a CAS-backed numerical calculator be?
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12-03-2017, 01:49 AM
Post: #31
RE: HP calcs are really not that accurate..
Might I suggest
[attachment=5379], [attachment=5378], [attachment=5380], [attachment=5381]
for perusal / edification as well as common reference.

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12-03-2017, 02:31 AM (This post was last modified: 12-03-2017 02:39 AM by AlexFekken.)
Post: #32
RE: HP calcs are really not that accurate..
(12-03-2017 01:49 AM)SlideRule Wrote:  Might I suggest
Sorry, haven't read the books (yet). But I think I did get a decent training in the principles covered, and this prompted me to write up this rant:

My previoius post reminded me of literally the first two basic principles that I learned when I started studying physics (and mathematics) at university in 1976:

1 - a number is totally meaningless if you don't specify its units
2 - a number is also totally meaningless if you don't specify its error margin

Now 1 is usually implied by context, but 2 still seems to be consistently neglected, sometimes even by people who did read the books and should know better (e.g. Feynman wrote that error margins for a number of space shuttle components were clearly reverse engineered from the requirements).

Now back in 1976 we had to rely on custom applications to process data with error margins. But I wonder why this is still the case now. My favourite, somewhat biased :-), answer is:

It is politically incorrect to teach scientifically correct thinking to the masses. It might hurt their brains, or worse, they might pick it up.

But still, should we not have an abundance of (freely available) tools now to do, for example, interval arithmetic? And should these not be the standard in scientific education by now. Clearly, this is much more fundamental and important than e.g. CAS or graphing capabilties.

And then threads like this would not even exist...
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12-03-2017, 02:43 AM
Post: #33
RE: HP calcs are really not that accurate..
(12-03-2017 01:19 AM)Sukiari Wrote:  
(12-01-2017 09:09 PM)DA74254 Wrote:  there should be no reason that we should not have, say, at least 256 digits/decimal points accuracy

This is bait.

Ahh, but such sweet bait. And it had the purpose of extending the conversation even further. That's not always a bad thing…

(Post 140)

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12-03-2017, 02:46 AM
Post: #34
RE: HP calcs are really not that accurate..
(12-03-2017 02:31 AM)AlexFekken Wrote:  Sorry, haven't read the books (yet). But I think I did get a decent training in the principles covered, and this prompted me to write up this rant:
I don't consider your expository a rant but rather significantly aligned with my undergraduate studies in Physical Science & Civil Engineering. My only departure is with respect to Numbers versus Measures, but this is a nuance adopted from my professors. Since I seldom venture into PURE MATHEMATICS, I also have difficulty with numerical quantification of physical measurements and an absence of attendant units / error. Please continue to press to test

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12-03-2017, 03:24 AM (This post was last modified: 12-03-2017 07:51 AM by AlexFekken.)
Post: #35
RE: HP calcs are really not that accurate..
(12-03-2017 02:46 AM)SlideRule Wrote:  My only departure is with respect to Numbers versus Measures,

Thanks, I agree of course. The two principles came from a physics lecture on measurement and data processing (a mandatory first lecture) so that narrowed the context.

SwissMicros seems to be working on the right sort of hardware (big multi-line display) for a true scientific calculator that would meet our demands.
Now just waiting for someone to implement Free42+\(\delta\) :-)
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12-03-2017, 05:46 AM
Post: #36
RE: HP calcs are really not that accurate..
(12-03-2017 02:43 AM)brickviking Wrote:  
(12-03-2017 01:19 AM)Sukiari Wrote:  This is bait.

Ahh, but such sweet bait. And it had the purpose of extending the conversation even further. That's not always a bad thing…

(Post 140)

Mathematica ran quite nicely on a Next machine with, by today's standards, a very modest 68k processor, I think there could be a market for a Wolfram calculator. One could conceivably create a Pi shield with a handheld calculator form factor ala the PocketChip which I also own and quite like, and simply use the free Mathematica that Steven Wolfram was kind enough to release on that platform, even.
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12-03-2017, 07:46 AM
Post: #37
RE: HP calcs are really not that accurate..
(12-02-2017 10:43 PM)Paul Dale Wrote:  
(12-02-2017 02:50 PM)rprosperi Wrote:  @Pauli - Regarding "256 digits are far more than you'd need to represent the diameter of the universe in terms of the planck length"

Awesome statement, it just captures and states the point better than any other phrase possibly could express it. And it's cool!

I almost went with represent the volume of the universe in terms of. I don't think this is quite so neat but it is even more mind boggling.


As for asking questions, Thomas's variation of approach 2 is my favourite: I've tried, I've got something is there a better way? Being less confrontational can often avoid the need for thick skin.


Pauli

Actually, you can't calculate the volume of the universe. It has no volume as it is flat Wink

Lookey heerey:
Space.com
Scientific American
Wikipedia

Esben
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12-03-2017, 08:54 AM
Post: #38
RE: HP calcs are really not that accurate..
(12-02-2017 11:51 PM)Claudio L. Wrote:  newRPL commercial..
I've been looking at that site every now and then.
Not wanting to "do something" with my precious 50G, I'd ask here; can it be run on the 49G+ as well?
I'm more inclined to use that calc as an experimental thingy than my 50G.

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12-03-2017, 10:03 AM
Post: #39
RE: HP calcs are really not that accurate..
(12-01-2017 10:18 PM)Paul Dale Wrote:  What are you trying to represent that requires so many digits?
How can you possibly measure something that accurately?

256 digits are far more than you'd need to represent the diameter of the universe in terms of the planck length.

256 digits may be an overkill when dealing with physics problems, but there are other problems where they may be not enough.

Some authors have used the double-exponential quadrature method to compute some definite integrals and then the PSLQ algorithm to ascertain closed form solutions involving elementary functions and well know constants that solve such integrals. Such approach relies on computing such definite integrals with a large number of digits, not in the hundreds, but in the thousands. So in this universe do exist interesting problems that demand high digit counts.

(12-02-2017 07:42 AM)DA74254 Wrote:  And yes, I know exactly how big my land plot is in square plancks (just over 5,5x10^72)

Thus, apparently, you only needed 2 digits to measure your plot in square planks.

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12-03-2017, 11:34 AM
Post: #40
RE: HP calcs are really not that accurate..
(12-03-2017 07:46 AM)DA74254 Wrote:  Actually, you can't calculate the volume of the universe. It has no volume as it is flat Wink

Apart from being trivial to calculate the volume of a two dimensional object (it's zero), the universe being flat doesn't mean it is two dimensional. Flat has a special meaning in this context which is defined by curvature and quickly heads away from Euclidean to Riemannian spaces and manifold theory. I knew this stuff thirty odd years ago but the details have faded away.


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