re: *Precision problems or the Problems with precision*

Your test effectively shows the problems with precision on display. The bigger problem is the application of or use of the different display values.

Lots of CS types never cross over to the business or banking side of computers much less the high speed transaction systems used by hedge funds and the like. Those systems are running complex modeling on supercomputers but suffer from the same issue although perhaps a bit farther out.

If you have ever attempted to calculate the interest rate on your mortgage or car purchase, you might have seen someone using a standard calculator in short display mode while filling out the forms detailing the interest rates and payments.

For the USA there are 2 versions of rates: a Stated Rate and an Annual Rate. The Annual Rate is generally more than the Stated Rate. The calculation difference is not only due to the way the interest rate is applied over 365 days but also by the undisplayed portion of the interest rate.

It looks small but MILLS count. Over time, they count up big.

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Search Term

Mill (currency)

- In the United States, it is a notional unit equivalent to a thousandth of a United States dollar (a hundredth of a dime or a tenth of a cent).

re: Orientation Precision

Testing on a not real old Android using calc app, P (portrait), L (landscape).

For comparison, G is google web calc (javascript), D is ‘https://www.desmos.com/scientific (also javascript), G and D on desktop FF.

sqrt(7)

P: 2.6457513110

L: 2.64575131106459059050

G: 2.64575131106

D: 2.645751311

sqrt(5)

P: 2.2360679774

L: 2.23606797749978969640

G: 2.2360679775

D: 2.236067977

sqrt(3)

P: 1.7320508075

L: 1.73205080756887729352

G: 1.73205080757

D: 1.732050808

sqrt(11)

P: 3.3166247903

L: 3.31662479035539984911

G: 3.31662479036

D: 3.31662479

sqrt(17)

P: 4.1231056256

L: 4.12310562561766054982

G: 4.12310562562

D: 4.123105626

Interesting. It sure appears to this Observer, that the Android calc app just truncates when changing from landscape to portrait mode. Also note that the browser output on both G and D do not display the last zero if there is one at the precision they want, even though they are rounding. The google calc web page is working with 11 decimal digits, but the desmos web page is working with 9 decimal digits. I’m not sure why they would be that different running on the same machine, in the same browser, but in different tabs. I’m not a javascript expert, nor do I want to be.

But, if you want precision, I would go with Android calc in landscape.

]]>re: *Orientation Precision *

- The phone was an iPhone 7 vintage.
- I don’t know what the Apple internal method is that is used to adjust the precision but if you flip the orientation of the phone and your display has sufficient non-repeating places the value will alter when you rotate the phone.
- It works the same for sqrt of 3 5 7 but I rarely play with values past those 3 numbers.
- The altered value appears to be rounded. eg terminal digits 78 for the short display and the long display is 776…. The differential was about .nnnn+04 or .nnnn+05 taken by subtracting the shorter number from the longer value. So .nnnn78[0] less .nnnn776.
- The iPhone also incorrectly returns ((sqrt of 3)sq) as 3. Same for 5 and 7. It appears to be a commonly accepted fudge in the calculator. Older calculators do not return the full integer value, they return a value less than the original number carried out to the precision level of the calculator.

I was surprised when I first showed the person about the precision that an old calculator in the desk returned the correct lesser value with the precision carry. But when the person tried it with their iPhone, it worked as expected and the ((sqrt)sq) rounded up the a whole number.

- As for the precision, the phone must carry the math value internally and the alteration takes place on the UI displayed image. Since you can flip the orientation back and forth and watch the value change without have to redo the calculation each time.

re: Observable Precision depends upon orientation

I would be curious to learn the specs of the phones used in your demo.

Were the different results truncated or rounded? Did you try some other values besides 7?

It reminds me of a System 360/44 with the magic go-faster knob.

The knob had 4 positions.

The phone accelerometer is logically only two positions for display purposes.

I am sure that does not matter for floating point precision on a smart phone, so I can only conclude that orientation to portrait mode just led to truncation instead of rounding. But, if that is not tbe case, that would be interesting.

Scroll down on this link to find 360/44. Interestingly, it had no microcode.

‘http://www.righto.com/2019/04/iconic-consoles-of-ibm-system360.html

A closeup pic of the knob can be found here:

‘https://www.twitter.com/kenshirriff/status/1120733559172370442

]]>Re : Green, Green, Green.

There was a forth Green…

Prof Lucie Green.

https://en.m.wikipedia.org/wiki/Lucie_Green

Now for the coincidences…

You might remember I’ve mentioned Mullard House (Torrington Place), and UCL as places I’ve had involvment with. Oh and well I guess most here know I have an interest in satellite design/construction and Space Weather as well.

Well… As well there is a photograph that used to be on the wall at UCL in which both she and I are standing… Taken at a meeting we both happened to be attending.

Oh and you will possibly also remember I’ve also mentioned I’ve twice tossed a UK copper “two pence” coin and had it not just land but come to rest on it’s edge or rim. The first time was at school in “Mr Pearson’s” Maths class and we were doing probability…

I once actually sat down and worked out a formular for the probability of a coin landing –but not comming to rest– on the edge some years ago (it’s tedious and has a lot of assumptions). But… The round “one pound” coin he did 10,000 flips with should have landed on the edge, a lot more than the 14 times he mentioned. It works out around 1.3% or 130 times or say ten times his quote which suggests he was counting “at rests”.

As for that heads tails triplets game for gambling… A long time ago I mentioned on this blog I can toss a coin and have it land which ever way you call, irrespective of if you call before the toss, whilst it’s in the air or covered on the back of my hand… And no it’s not magic, but my son when he was around seven, thought it was. And his very nice maths teacher was quite impressed when I gave her ten correct calls followed by ten incorrect calls at the “show the parent” evening. She was even more surprised when I got my son to work out how one of the demonstrations worked.

So yes the world is full of coincidences…

But sometimes the odds of them are way smaller than you would expect. For instance on that “people in a photo” he should have mentioned the chain length. That is although you and I have never met, you probably know someone who knows someone, who…. Who knows me with around only five or six someones in a chain for something like 8 in ten people in the first world continents (scary thought when you consider how close that brings you to the last US President đ

]]>Re : Data points.

“Note that the number of functions on R^2 is a bigger infinity than the real numbers”

Which is what simple logic will tell you.

A point in N dimensional space has an infinite number of functions in every dimension that go through it. Thus from R to R^2 effectively goes from one dimension –line– to two dimension –plane– gives you an infinity of infinities and so on.

“This means that Matt Parker was right, âfitting a set of data pointsâ is no supportive evidence at all for any model to be true.”

Which is the point I’ve been making…

]]>re: *any level of precision you want as long as youâre prepared to ignore enough data. *

While taking care of “sadmin” (1) at the bank recently, I had a discussion with a young banker about precision and it’s importance to arbitrage; how even a small difference can have a big impact.

Using their phone calculator, I had the person take the sqrt of 7. With the phone upright there was @8 digits of precision. When flipped sideways to science mode there was @13 digits of precision.

They didn’t get it.

I explained if they thought a commodity was worth the 8 digits of precision, and I could buy the same commodity at a lower price, ~04 or ~05 differential, I could sell them a lot of that commodity before they figured it out.

Once the light went on, the phone accelerometer got a good workout…

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1) Sadmin = new word for me. The administration and notifications needed to resolve and conclude the business affairs of the dead.

]]>You can find any pattern you want to any level of precision you want as long as youâre prepared to ignore enough data.

Note that the number of functions on R^2 is a bigger infinity than the real numbers, Gamow even claims that it is aleph-2.

Irrespective of whether Gamow was right, there is an infinite number of contiuos graphs going through any finite set of data points. This means that Matt Parker was right, “fitting a set of data points” is no supportive evidence at all for any model to be true.

]]>Re : What happens when maths goes wrong/bad,

With respect to “wrong”, your quote of,

âYou can find any pattern you want to any level of precision you want as long as youâre prepared to ignore enough data.”

And with respect to “bad”,

“There are lies, damn lies and statistics.”

The classic example of both is “death by sugar” foisted on the world by “Ancel Keys” the father of the nutritionaly poor K-Ration during WWII that hurt so many US soldiers, and make billions for the corn sugar industry by giving hundreds of millions life shortening diseases like type II diabetes.

Oh and we are very likely to see the same sort of scandle come out over mRNA vaccines.

]]>serendipitous

What are the odds? Green, Green, Green.

Just over an hour long Matt Parker talk from 2019. Touches on many subjects that we have discussed. Many means greater than small values of 2. A lot of insightful stuff and also a lot of humour. Recommend watching when you have a moment in time. Relativistically speaking of course.

The title of the talk is:

What Happens When Maths Goes Wrong?

“You can find any pattern you want to any level of precision you want as long as you’re prepared to ignore enough data.”

‘https://www.youtube.com/watch?v=6JwEYamjXpA

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