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I got the update notice for Numbers this morning and it said (among other things): "Greatly improved accuracy using the enhanced 128-bit calculation engine".

As I remember my basic science, that is theoretically impossible, unless Apple Numbers has been making errors all along. I hope they mean "precision".

Still, mathematicians were calculating pi to many, many decimal places with just an 8-bit engine, so what does a 128-bit engine really do? And then I remember, even simpler Turing engines could calculate anything.
 


I got the update notice for Numbers this morning and it said (among other things): "Greatly improved accuracy using the enhanced 128-bit calculation engine".

As I remember my basic science, that is theoretically impossible, unless Apple Numbers has been making errors all along. I hope they mean "precision".

Still, mathematicians were calculating pi to many, many decimal places with just an 8-bit engine, so what does a 128-bit engine really do? And then I remember, even simpler Turing engines could calculate anything.
Here is the explanation from Apple:
About the increased accuracy of calculations in Pages, Numbers, and Keynote):
The new calculation engine dramatically improves upon previous versions by using a decimal representation of numbers throughout the calculation.
This actually does improve the accuracy of calculations that did not have a natural expression in base 2 but do in base 10.

To me, the most significant improvement in these new releases is the ability to place in-line equations, coming either from, say, Keynote's equation editor or from a TeX-based source, such as LateXiT. Pages has been able to do this with its own editor for a while, but not Keynote, which is where I really missed it. Hurray!
 


I got the update notice for Numbers this morning and it said (among other things): "Greatly improved accuracy using the enhanced 128-bit calculation engine".
As I remember my basic science, that is theoretically impossible, unless Apple Numbers has been making errors all along. I hope they mean "precision".
Still, mathematicians were calculating pi to many, many decimal places with just an 8-bit engine, so what does a 128-bit engine really do? And then I remember, even simpler Turing engines could calculate anything.
The terms accuracy and precision are often used interchangeably. They are not interchangeable terms. Each has a well-defined meaning. The term accuracy refers to the number of significant digits used to express a value. The more significant digits, the more accurate the value. A 128-bit calculation engine is more accurate than an 80-bit calculation engine is more accurate than a 64-bit calculation engine.

The term precision refers to the size of the unit used to measure a value. The smaller the unit, the more precise the unit. A micrometer is more precise than a centimeter is more precise than a meter is more precise than a kilometer. This is where things get interesting. Apple's new calculation engine is digital. Whether it is 64-bit, 80-bit, or 128-bit, it is still bits and all bits are the same size.

The term precision is inappropriate in this context.
 


Accuracy refers to how close a result is to what it should be. Precision refers to the representation of that result in the generated output.

For example, suppose you have an algorithm for generating the digits of Pi. If it outputs just "3", then you're accurate to one digit and have one digit of precision. If it outputs "3.0000", then you're still only accurate to one digit, but have five digits of precision. If it outputs "3.1234", then you're accurate to two digits with five digits of precision. If it outputs "3.1416", then you're accurate to five digits with five digits of precision.

Computer math, by its very nature, has limits to its accuracy - a function of the internal representation of the numbers, the number of bits used to represent them, and the algorithms used for the computation. But the act of generating output can produce precision far higher than the accuracy, especially if the internal and external representations are different (e.g. computing in base-2 and generating base-10 output).

Good programmers are aware of this and take steps to deal with it - for example, by refusing to generate output with more decimal places than the internal accuracy; or by doing computation with more bits than otherwise necessary, so the accuracy will be greater than the precision of the output; or by computing in base-10, which will be slower than base-2, but will avoid introducing errors that result from base conversion.
 


Accuracy refers to how close a result is to what it should be. Precision refers to the representation of that result in the generated output....
David's explanation of accuracy and precision is very good. Additionally, there is the concept of uncertainty, which is a description of what we don't know about a calculation or measurement. Generally, all the elements of error, such as accuracy, precision, resolution, etc., are RSSed , or each element is squared, added together, and then the expanded uncertainty is 2 times the square root of the sum of the squares.
 


Accuracy refers to how close a result is to what it should be. Precision refers to the representation of that result in the generated output.
I will quibble a bit with David Charlap. Accuracy is how close a value (input or result) is to reality. Precision is the number of digits in the value.

My good hard science teachers kept pounding this into our brains: "accuracy and precision are not related to each other." ... We got graded on both precision and accuracy, not allowed to have more significant figures in the result than in the input. If we ended up with more significant figures in our results than the measuring apparatus was able to provide, our grade was downgraded. There are some tricky calculations when trying to follow the degree of imprecision of the least significant figure through a set of calculations. Partial differential equations are your friends.
 



This Monday's XKCD comic, (Coordinate Precision) does a really good job of explaining precision. In this context (map coordinates), higher precision (adding more decimal places to the coordinates) specifies smaller regions on the map:
  • zero digits after the decimal point (integer count of degrees) is a pretty large region ("probably space-related")
  • 1 decimal place will identify a city
  • 2 decimal places will identify a neighborhood
  • 3 decimal places will identify a region of a street (small number of buildings)
  • 4 decimal places will identify a part of a building
  • 5 decimal places will identify a person-sized location in a room
  • 7 decimal places will identify a small drawing on a piece of paper
  • 9 decimal places will identify a grain of sand
  • 15 decimal places means "either you're handing out raw floating point variables or you've built a database to track individual atoms. In either case, please stop"
In the context, of course, "accuracy" refers to how close that coordinate (regardless of precision) is to the physical location it is supposed to be referencing.
 


A few days ago an Apple notification box popped up on my iPhone 6 (iOS 12.3.1) to tell me that time zones needed to be updated. Of course I agreed, but it on thinking about it, I wonder what is going on. Time zones don’t change that often....
 


Time zones don’t change that often....
Actually, they do. Linux users are very familiar with the tzdata package (that tracks the IANA database) frequently receiving updates.

Since time zones (and, more specifically, details like daylight-saving data) are the product of global political decisions and nothing scientific, they change far more often then you might think. There shouldn't be frequent changes for any single country, but for the aggregate of the entire world, there may be quite a lot each year.

Time, and software for tracking/managing time is far more complicated than most people realize. A few really good reads on the subject:
 



Ric Ford

MacInTouch
Apple warns against using solvents when cleaning their products.
But says nothing about alcohol per se:
Apple said:
How to clean your Apple products
... Use only a soft, lint-free cloth. Avoid abrasive cloths, towels, paper towels, and similar items that might cause damage.

... Don't use window cleaners, household cleaners, compressed air, aerosol sprays, solvents, ammonia, or abrasives to clean your iPhone.

... Don't use aerosol sprays, solvents, abrasives, or cleaners containing hydrogen peroxide that might damage the finish.
 


But says nothing about alcohol per se:
Well, alcohol can be considered as a solvent, but then again, water is a definitely a solvent, so it is a pretty broad prohibition. I have long used a water-dampened cloth to clean the aluminum on my MacBooks and even the keyboard (not enough water to seep into the keys). I use Klear Screen for iPhones and computer screens, which is supposedly alcohol-free (actually one safety sheet I found suggested the product contained siloxanes, often used in shampoos).
 



I'm still using an old Samsung SyncMaster 712n VGA monitor with a 2018 Mac Mini and Mojave 10.14.6. I switched it in Display Preferences to a lower scaled resolution to get bigger text, etc., but didn't like the crowded screen and switched back to my usual highest scaled resolution with 75 Hz refresh rate.

An odd thing happened.

Before, when I changed workspaces, there was a side-to-side sliding effect as one screen replaced the last. Now, the old screen fades out and the new fades in with no sliding effect. It's not a problem, just a surprise. I only mention it because it was unexpected.
 


Maybe a lawsuit similar to the 1948 one that broke up the film distribution system at the time would be appropriate?
The difference is that there isn't anything close to a monopoly in the TV and streaming video markets. There are literally hundreds, if not thousands of channels all producing original content, and they all compete with each other.

Back when it was only broadcast TV and most viewing areas only had 3-5 channels, you could make the case that there was a monopoly that needed to be regulated. Today, when any cable or satellite service offers hundreds of channels and there are almost as many (free and paid) streaming channels, it would be very hard to make that argument.
 


The difference is that there isn't anything close to a monopoly in the TV and streaming video markets. There are literally hundreds, if not thousands of channels all producing original content, and they all compete with each other.
I'd consider two aspects regarding the above.

For one, owning content and being an exclusive distributor thereof is always going to be problematic once the market becomes an oligopoly. Funnily enough, despite hundreds, if not thousands, of content creators trying to get into this market, the top 4-5 companies likely own something like 95%+ of the content being watched. Thus, conditions like Paramount in 1945 likely exist today.

Secondly, there is the question whether there is an appetite to break up large monopolies or oligopolies. I'd argue there has been no real interest in this direction ever since big business co-opted both parties, starting with the AT&T breakup. Too much money at the trough to make it through committee, never mind a general vote. See what happened with Microsoft in the late 90's.

As far as remedies go, the easiest remedy is to legally bar content owners from also being the sole distributors (and/or being owned by the same parent company). Perhaps the fees that a distributor can charge would have to be capped FRAND-style, and content would have to be made available at the same price to all distributors.

However, be careful what you wish for, as that kind of remedy could have also prevented the likes of Netflix from getting into the content development game!

I don't see this getting better until it's so blatant for so long that all goodwill for the large media conglomerates has evaporated. That's how anti-trust got started in the first place. It's not like the railroads controlled all forms of transportation, it's that they owned so much of the most efficient means back then to move goods in bulk that they could value-price.
 


I'd consider two aspects regarding the above....
I think an issue is that the content business is moving much faster than the regulatory apparatus can keep up with, which often results in unintended consequences much worse than the problem being addressed. It is not just the content industry that is moving so fast. For example, does the US Constitution protect against surveillance or search without a warrant by a drone 100 feet above your house? Decisions have been made that it is ok over your house but not okay on the ground outside your house.

When ATT was a relatively unchanging entity in the 1930s, or even up into the 1950s, regulation was a lot simpler. The trade-off between a regulated monopoly and funding universal, affordable service really worked. But one seemingly simple decision upset the apple cart, when a couple of court decisions forced ATT to allow third parties to connect to their network. This resulted in MCI competing against ATT's long distance, which effectively ended the monopoly.

I think the current issue of what to do or not do about Facebook and the like is difficult. The power of Facebook is far greater than any prior media company. Sometimes an issue can be addressed by simply ending special protections and letting the company be exposed to normal business checks and balances. It is amazing how many entities are exempt from normal laws. The National Football League is one example, in that it is exempt from anti-trust laws.
 


Because I don't want to be stuck with iOS 12, I want to upgrade from my iPhone 6 Plus to the iPhone 8 Plus. Due to my physical disability, I sometimes have trouble with unintentional touch input; therefore, to be truly comfortable, I (personally) still need an iPhone with a home button.

My question for those of you who moved from phones with a truly physical home button to the "haptic" version on the iPhone 7 and 8: was it a weird experience, or did you find it to be a relatively easy adjustment?
 


Ric Ford

MacInTouch
... My question for those of you who moved from phones with a truly physical home button to the "haptic" version on the iPhone 7 and 8: was it a weird experience, or did you find it to be a relatively easy adjustment?
I actually found the difference to be surprisingly subtle and completely non-problematic — to my surprise — going from an iPhone SE to an iPhone 7. There's even an extra advantage to the haptic home button: you set the sensitivity of the button, as you like it best, choosing among three difference force levels required for activation.

Settings > General > Home Button: Choose your Click

There are also touch sensitivity settings for 3D Touch:
iPhone User Guide said:
Adjust touch settings on iPhone
...
On models with 3D Touch, you can control the sensitivity of 3D Touch or turn it off.
  1. Go to Settings > Accessibility > Touch > 3D Touch.
  2. Do one of the following:
    • Choose Light, Medium, or Firm sensitivity to adjust the amount of pressure needed to activate 3D Touch. Light sensitivity reduces the amount of pressure required; firm sensitivity increases it.
    • Turn off 3D Touch.
 



There are a few 256GB iPhone 8 Plus refurbs currently, at $599.
Thanks, Ric. Unfortunately, I don't have the funds ready to go just yet. Hopefully, I'll be as lucky when the time comes... if not, 128 GB will still be a nice upgrade from the 64 GB that I have now.

But that raises an interesting question in my mind: Does Apple only offer unlocked iPhones as refurbs, or is Apple capable of turning any formerly carrier-locked iPhone into an unlocked iPhone, because all the radios are present but simply disabled via firmware?
 


I actually found the difference to be surprisingly subtle and completely non-problematic — to my surprise — going from an iPhone SE to an iPhone 7. There's even an extra advantage to the haptic home button: you set the sensitivity of the button, as you like it best, choosing among three difference force levels required for activation.
Settings > General > Home Button: Choose your Click
I'd agree with that: haptic is absolutely no big deal - it feels good and just works pretty naturally.

The big surprise to me is how much I prefer FaceID over TouchID - I expected to hate it, but it works pretty darn well overall and seems faster than TouchID for me. I don't miss the Home button at all.
 


Ric Ford

MacInTouch
The big surprise to me is how much I prefer FaceID over TouchID - I expected to hate it, but it works pretty darn well overall and seems faster than TouchID for me. I don't miss the Home button at all.
While I agree about that, I find the user interface changes for removal of the Home button pretty annoying, because they reverse previous behavior, confusing things when switching between older and newer iPhones. Specifically, the newer (e.g. iPhone X) Face ID phones locate the Control Center at the top, where you have to swipe down from the top-right corner to get it, the inverse of earlier iPhones (e.g. iPhone 7), where you swipe up from the bottom.

(Additionally, the gesture for invoking the app switcher/quit interface seems perversely difficult to perform — swiping up from just the right point in at the bottom to just the right point in the middle — and I wonder if this could be by design, given Apple's arguments that apps shouldn't ever be quit because Apple supposedly manages everything so brilliantly.)

#userinterface #appleuserinterface #ui
 


While I agree about that, I find the user interface changes for removal of the Home button pretty annoying, because they reverse previous behavior, confusing things when switching between older and newer iPhones. Specifically, the newer (e.g. iPhone X) Face ID phones locate the Control Center at the top, where you have to swipe down from the top-right corner to get it, the inverse of earlier iPhones (e.g. iPhone 7), where you swipe up from the bottom.
(Additionally, the gesture for invoking the app switcher/quit interface seems perversely difficult to perform — swiping up from just the right point in at the bottom to just the right point in the middle — and I wonder if this could be by design, given Apple's arguments that apps shouldn't ever be quit because Apple supposedly manages everything so brilliantly.)
#userinterface #appleuserinterface #ui
Okay, yes, now that you've mentioned it, I'll walk back my enthusiasm a bit - I did find adapting to the new swipe-up/swipe-down/app-quit behavior to be pretty annoying - must've forgotten all about that. I find it particularly irritating in landscape mode - many inadvertent activations if I'm gaming. Not sure how I would've solved the problem differently without a physical button, but I do recall this bit of interface hide-and-seek being extremely annoying when I got my iPhone X.
 


Ric Ford

MacInTouch
I did find adapting to the new swipe-up/swipe-down/app-quit behavior to be pretty annoying - must've forgotten all about that.
What's even more annoying than adapting after an upgrade is having to switch between two devices that work in completely opposite ways on a frequent basis. Not cool.
Not sure how I would've solved the problem differently without a physical button...
It would be quite simple to dedicate a tiny bit of space at the bottom to this, but that obviously runs counter to the design goal of maximizing display space, which also results in losing information at the top while pushing the remaining icons up into the edges of the ugly Face ID frame. (I guess "function" won over form here, but both ugliness and destruction of consistency are hard to stomach.)
 


On another subject, in System Preferences, General pane, Recent Items, you can set the number of recent items. In my case on one machine, the selection of None does not work, and the number is stuck at 50. Somewhere there is a field that is stuck. Do any of the gurus know how I can use Terminal to find that field and enter 0?
 


While I agree about that, I find the user interface changes for removal of the Home button pretty annoying, because they reverse previous behavior
And that is the other reason I intend to upgrade to the iPhone 8 Plus, as opposed to a newer phone. I know that it will be necessary to upgrade to a phone that lacks a home button eventually, but I will cross that bridge only when I must.
 


Ric Ford

MacInTouch
And that is the other reason I intend to upgrade to the iPhone 8 Plus, as opposed to a newer phone.
I have to say, if the size of the iPhone 8 Plus (barely larger than an iPhone Xr) is acceptable, it seems like a great phone to me, with its extra "telephoto" (i.e. portrait) lens and its standard FHD (1080p) display resolution, plus the IPS display that doesn't color-shift like OLED displays, nor burn in. (I don't speak from experience, however, having spent most of my time with the wonderful iPhone SE, which is a better size for many of my uses.)
 


I have to say, if the size of the iPhone 8 Plus (barely larger than an iPhone Xr) is acceptable, it seems like a great phone to me...
Yep. It's the same size as the 6 Plus, which I got because I have larger fingers that make typing on a smaller screen a more... error-prone experience. I'm also excited at the thought of having 3D Touch, among other improvements.
 


To be sure, Apple's cycle of abandoning support of OSes and other factors such as security updates and browser updates is irritating. The only rationale I can think of is, simply, a base venal decision on the part of Apple, although I cannot really believe in the notion that to maintain support would be a noticeable expense to Apple.

That being said, I will miss Safari's ease of virtually on the fly modifications. I find the method for disabling JavaScript in Firefox to be a ridiculous exercise.
 


To be sure, Apple's cycle of abandoning support of OSes and other factors such as security updates and browser updates is irritating. The only rationale I can think of is, simply, a base venal decision on the part of Apple, although I cannot really believe in the notion that to maintain support would be a noticeable expense to Apple.
It's an inevitable consequence of their rapid-release schedule of a new version every year.

Maintenance isn't free. Every release they support means another platform which they must have ongoing testing, patching and deployment. We can argue how many releases is reasonable, but they don't come for free.

That having been said, I've never been a fan of the rapid-release schedule. If Apple would put out major releases every two years, then existing releases would (probably) maintain support for twice as long and there would be time for a release to stabilize before it is replaced with the next one.
 


I think Apple's product trajectory is headed toward the next generation MacPadBook Pro: the entire internals will be encased in a high thermal transfer epoxy, solving the thermal throttling issues and conveniently making the entire unit a throwaway if anything goes wrong, like the battery becoming old. It will follow the new Apple mantra of "Replace not Repair."

In parallel development, Apple will move to a subscription model for its OS - if you don't pay the monthly fee, your hardware will cease to function. This fee will be set to industry-leading levels because stock price, also funding social justice.

This will be introduced in macOS 19.84, and following Apple's new naming scheme of California islands, it will be named Alcatraz. You can get onto the island, but you can't get off.

User interface guidelines, hardware design, and reliability will be whatever Apple says is insanely great, never mind what actual users experience. Apple's new software slogan will be, "Suck it up, buttercup."
 


I think Apple's product trajectory is headed toward the next generation MacPadBook Pro: the entire internals will be encased in a high thermal transfer epoxy, solving the thermal throttling issues and conveniently making the entire unit a throwaway if anything goes wrong, like the battery becoming old. It will follow the new Apple mantra of "Replace not Repair."
The exact opposite of the design philosophy of the new Mac Pro, so with respect, I doubt it.
 


I guess the iPhone 11 Pro Max {$1349} isn't so expensive after all:
Washington Post said:
Motorola’s Razr flip phone is back as a folding-screen smartphone, for $1,500
The good news: A phone can fit in your pocket again. The bad news: It’s twice the price of an iPhone {low end}.
And what durability! {my emphasis}
The new Razr uses a flexible screen and hinge that can be folded and unfolded for at least two years, Motorola says.
Hmmm, my LG LX225 flip phone has lasted more than 10 years and is still going strong.
 


I've posted here before about wanting to upgrade from the iPhone 6 Plus to the 8 Plus but, the more I think about it, I would be foolish to intentionally put myself more than a single generation behind, if I'm going to spend money on a new phone... unless I want to find myself behind the curve once again – and sooner than I had hoped.

Therefore, I have a question for the community: I have large fingers; that's what drove me to get the 6 Plus rather than the 6. Can anyone who has made the move from a 6/7/8 Plus to the iPhone XR/ iPhone 11 (non-Pro) comment on whether the reduction in screen size (not resolution) has been a problem, specifically with regard to using the keyboard?

The XR and 11 are the only two models in consideration, so that is why I am concerned about sizing. I think they're just about identical, right?
 


Can anyone who has made the move from a 6/7/8 Plus to the iPhone XR/ iPhone 11 (non-Pro) comment on whether the reduction in screen size (not resolution) has been a problem, specifically with regard to using the keyboard?
I switched up from the iPhone 6 (not the 6 Plus) to an iPhone XR a few months ago, which is somewhat different from what you're asking about. And I can't say whether the keyboard experience has changed in any way for me.

But the only way you'll be able to truly determine that for yourself is to physically try each out, side by side. At some point, it takes a visit to a store that stocks both models you're comparing.
 


Ric Ford

MacInTouch
Therefore, I have a question for the community: I have large fingers; that's what drove me to get the 6 Plus rather than the 6. Can anyone who has made the move from a 6/7/8 Plus to the iPhone XR/ iPhone 11 (non-Pro) comment on whether the reduction in screen size (not resolution) has been a problem, specifically with regard to using the keyboard?
This very good iPhone size chart might be helpful:
PaintCode said:
(I'll also note, although you may already realize this, that it's possible to select remarkably tiny areas on the screen by touching very lightly.)
 


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