Tomorrow, freedom reaches retail shelves bearing PCs. That’s the day M$ throttles supplies of licences for “7” to OEMs. Eventually, the backlog of “7” machines will trickle out and consumers will only be faced with “8*” which many hate. Inevitably, consumers will ask retailers if they have anything else. There will be ChromeBooks and perhaps, other GNU/Linux distros or naked PCs. Inevitably, OEMs will see demand for “8*” subside and they will start installing GNU/Linux seriously. M$’s next release is looking less interesting with each go round. Finally, there’s competition on retail shelves. Consumers have several attractive alternatives on retail shelves already: Android/Linux, Chrome OS, and some other GNU/Linux. They will welcome more choice, especially at lower prices and in smaller packages. M$ is already giving away licences there. There’s a rumour that M$ will actually pay OEMs to install the OS on certain machines. Can you see the environmentalists complaining about piles of new PCs going to the landfill?

Perhaps freedom won’t turn on like the flick of a light-switch. It will be a gradual process that’s been going on for a while but it will be faster now. People I meet are still wondering what to do about XP. “7” or “8*” or Wintel are not on their radar any longer. They are thinking that if Android/Linux is what I like, why do retailers only offer Wintel on retail shelves? They are thinking that something must be available and they are finding GNU/Linux. On their own. That’s the game-changer. That’s the shift in mind-share.

## About Robert Pogson

I am a retired teacher in Canada. I taught in the subject areas where I have worked for almost forty years: maths, physics, chemistry and computers. I love hunting, fishing, picking berries and mushrooms, too.

DrLoser wrote,

“Last time I heard, rocks plunge vertically downwards.”I guess we shouldn’t let mathematicians do physics…

$latex x = x_{0} + v_{x_{0}}t $

$latex y = y_{0} + v_{y_{0}}t + \frac{1}{2}gt^{2} $

The locus of points $latex ( x,y ) $ is a parabola. $latex (v_{x_{0}},v_{y_{0}}) $ is it’s initial velocity/direction. It’s still a rock falling freely regardless of the initial conditions.

Oh, I think it’s too early to give up on the specious “ballistics” analogies, Robert.

Last time I heard, rocks plunge vertically downwards.

Naturally you will have a graph to demonstrate this particular straight vector. And none of that parabolic nonsense this time, please.

Took me a long while to write my correction, Robert, and I apologise for that. But at least I correct myself as soon as I can.

When was the last time you corrected yourself?

For example, are you going to admit any time soon that a least-square fit on

a mere five data pointsis, to be as polite as possible,not really the done thing in polite circles?Probably you shouldn’t let wannabe amateur mathematicians like me play with numbers, either …

First, a correction of fact. The

discriminantis in fact b^2 – 4ac, and not the square root, as I stated. I also incorrectly lumped it in with the axis of symmetry, which is plain wrong.And, gaaah … I used the quad best fit numbers based on my back-calculation of Robert’s five data points, which were imprecise enough to give me an imaginary square root of the discriminant. On Robert’s own a, b and c, the discriminant is roughly 373.

So that’s me pretty much comprehensively wrong. Oh well, back to the welding classes.

I finally gave up on fat-fingering my calculator and resorted to Python. On Robert’s figures, the x-intercepts for this make-believe parabola are December 2017 and December 1998.

Which is where this “analogy” thing comes in. If this analogy is to stand up, Robert, we have to believe that Microsoft’s share of web-pages was

zeroin December 1998.Clearly, it wasn’t.And if it wasn’t, there’s no reason to suppose that the analogy holds, and that there is an axis of symmetry, and that the End of M$ Days is going to happen in December 2017, either.Where’s the missing part of the analogy? Well, this is interesting in a way. You can’t

entirelymap M$ page views to a continuous parabola, but you can certainly take a more general “dynamic model” view of the phenomenon.1) What stops a bullet travelling along the x axis? Well, obviously, the ground. (Or a deer, whichever comes first.)

2) What is the determinant force that causes a bullet to drop to the x-intercept? Ignoring other minor forces, it’s gravity, pure and simple.

I’m not going to spend much time on (1): if you really think there is an exact mapping between a bullet hitting the ground and Microsoft somehow having

no page views whatsoeverin December 2017, then I’m afraid you’re hopelessly lost to civilisation and you need to stop thinking likeoiaohm.But (2) is the far more interesting part of the analogy. I’m sure you are aware, Robert, that for the duration of a bullet’s trajectory between muzzle and destination, there’s basically only that one force (gravity) acting upon it. We can begin the analogy by stating that the y-axis is entirely dependent on gravity. If gravity vanishes — to establish the basis of this analogy — then the bullet never drops. There is no x-intercept.

Not so with page views since 2010 or so. One “force” is web views via desktops, laptops, notebooks, etc. This “force” was present from 1991 onwards and is still present.

The other force is new: phones, tablets, Chromebooks if you will — and this “force” has no analogy whatsoever to ballistics. After all, you don’t suddenly get a second equivalent of

gravitymidway through the trajectory, do you?Your graph, and your vaunted R-square, is therefore

completely worthless, because there are actuallytwocomponents of the measure on the y-axis here. One is the bog-standard “desktop” market, and the other … may beentirely orthogonal. Or it may not.But, if it

isn’tentirely orthogonal, then you have to be honest. You have to accept that the PC market (for want of a better word) is saturated; and the mobile market (ditto) is yet to be saturated. Here are the best figures I can come up with:PCs 2010-now: 1.4Bn – 1.6Bn

Mobiles 2010-now: 0.1Bn – 1.6Bn

Yourtheory is that Gnu/Linux will take over because mobiles will take over from PCs. This is not borne out by the numbers. In fact, if you combine the numbers for this “new market” with your graph, the M$ PC web page views basically turns into a boring old straight line.But let’s assume that the mobile market is not yet saturated. Let’s assume that its share of web page views keeps on growing, in an upwards parabola. (This is a stupid assumption, but whatever.)

Absolutely

none of thissuggests that Microsoft is losing share of the only thing it cares about — the lucrative desktop market — does it?DrLoser, abusing mathematics endlessly, wrote a bunch of stuff…

No matter what refinements you give the analysis, you can’t change the shape of that curve. M$’s share of page-views is plunging like a rock.

Now, passing on from the sheer joy of using the Birth of Christ (give or take four years) as the zero abscissa for Cartesian co-ordinates, we proceed to the analysis of the metaphor itself. Is a wild parabolic extrapolation off five data points similar in any way to the ballistics of a gunshot?

One important property, as I mentioned yesterday, that a theoretical parabola possesses, and a gunshot does not, is that it is a

continuous function. A true parabola has an axis of symmetry — the x-coordinate can be calculated as -b/2a.Robert’s rather naff fit (caused by an inadvertent total failure of numerical analysis) places this axis at an x-coordinate of 1981.65 …

… which would suggest that Microsoft page views peaked in early August 1981. Just about when the first IBM PC hit the market! Those fiends, their timing was immaculate!

Also almost ten years before the Birth of the Web … but nobody ever denied that ole Bill Gates was very much ahead of his time.

Not that it matters, because in fact I left out one tiny little detail: the axis of symmetry should really include the

discriminant. In which case it is actuallyimaginary(it has anicomponent of -509, give or take). This is because b^2 is greater than 4ac on Robert’s numbers.You don’t see many parabolas in the real world with an imaginary axis of symmetry, do you?

That’s possibly because, in the real world, you leave experimental physicists to doink around spot-welding cloud chambers and the like, and let people with some sort of clue about mathematics do the hard numerical yakka.

On my fit (five orders of magnitude better, I should remind Robert), the axis of symmetry has an x-coordinate of -1.5872. No imaginaries involved!

This gives a far more believable figure of Peak Microsoft Web Page Views being in roughly May 2008.

Well, I seem to have strayed a little from my immediate aim of discrediting Robert’s bizarre analogy, simply on the basis of analogy. I’ll try to get to that a little later.

But in the mean time, the maths suggest an unexpected conclusion:

You can play with numbers at home, kiddies — they won’t catch fire! But for goodness’ sake, don’t let a physicist play with them on your behalf!The American “economy” today reminds me of East Germany in years past. The State dictates what will be manufactured and offered for sale. In the DDR gray government employees made those decisions. In America, the Federal Reserve Bank is the defacto government and makes those decisions.

It doesn’t matter if anybody buys anything from Microsoft (and a number of other big American “brands”). The Fed prints the money (out of thin air) and gives it to its mates who often pretend to run companies. If the companies produce scrap it doesn’t matter as the Fed or its minions will continue “lending” to them indefinitely — or until the USD collapses.

One further important correction:

“I believe that ballistic partial parabolas with a

negative“a coefficient” are, shall we say, relatively rare.”Wait, sorry, I got the sign wrong.

This is glorious.

You’re actually claiming that, mathematically speaking, and if you ignore the effects of the time-line, that the natural saturation point of Microsoft Web Views is actually so massively negative that

most of the little green men in the Milky Way“un-watch” the Web?I am

entrancedby that conclusion. If only it were possible.A small note on the respective coefficients, btw. As noted,

ais an invariant between the two fits.Yours:

b=4021.33714285714

c=-4247376.45714286

Mine:

b=-3.22092857142858

c=89.2987142857143

I believe that ballistic partial parabolas with an

acoefficient are, shall we say, relatively rare. This may be a topic for future examination.However, the main thing I note here is that

mycoefficients justsoundright. Apart from anything else they are both within the range covered by the y-axis (did I mention that the y-axis in this case is “fully closed?” Possibly not. Small mathematical detail there).Yourcoefficients, though obviously produced by the same equation,soundsilly.Another way to look at it is this: if

xdid not exist (which in terms of the real world means that the timeline is irrelevant), what can we deduce about the base constant ofy?Given

yourfigures, we can “deduce” that the percentage saturation of Microsoft products in the Page View domain is, errrrr … let me see ….112,000times the current number of page views.We’re going to need a much bigger Earth for this one, boys.

OTOH,

mybase constant is89%saturation.Which do you prefer, Peak Microsoft at 89% and declining, or your somewhat bizarre figure of Peak Microsoft at a substantial proportion of the Milky Way?

Do physicists really have so much faith in Our Lord that they calibrate their x-axes in Annos Domini, Robert? How very touching.

A brief lesson in mathematics; well, two, actually.

1) The ballistic trajectory from a gun (and let’s ignore coriolis effects and wind resistance and so on — may I recommend

GEBC?) is, strictly speaking, only a partial parabola. The bullet starts at the gun and ends on the surface. The parabola is not complete. Rather, we use aparabolic equationto approximate the resultant path. This may sound like nit-picking, but wait a while until I get to the subject of analogies.2) In mathematics (as opposed to home-brew physics), we generally start with an adjusted Cartesian origin of (0,0). This is a very useful convention, because it allows us to limit the Numerical Analysis effects of plugging in what we mathematicians call “Very Large Numbers.”

When using a Least Square Quadratic Regression fit, as I’m sure even physicists are aware, you require powers of x up to x^4. Now, x^4 where x is 2000+ is aVery Large Number. x^4 where x < 10is not. Shall we deal with a more malleable x-axis? Let’s do that.I’ve taken the liberty of back-calculating your five data points, Robert (I forgot (3), didn’t I? A mere five data points is risible to a mathematician). Here, I think, they are:

(2010, 89.3), (2011, 85.06), (2012, 78.8), (2013, 70.505), (2014, 60.18)

I now subtract 2010 from each x co-ordinate and apply Least Square Quadratic Regression.

Confirming that there are no glaring errors in this conversion, I note that the

afactor isidenticalto your calculation:a = -1.01464285714286

b = -3.22092857142858

c = 89.2987142857143

r-square = 0.999999971130651

Youwillbe pleased, Robert!I’ve just come to essentially the same numerical fit as yours, and yet

myfit has a r-square ofseven nines, whereas your pitiful little effort — not bad for a mere physicist, but not really good enough — only has an r-square oftwo!See what a tiny little “brief lesson in mathematics” can teach a physicist, Robert? Naturally,

oldermanis sorely in need of a “brief lesson in physics” from an eminent MSc in the subject such as your good self. But apparentlyyouare sorely in need of a “brief lesson in mathematics” from somebody who, like me, is merely an extremely competentamateurin the subject.But I digress. What does all this mean? I’ve spent a lot of time trying to get the maths under some sort of control, so I’ll leave you to ponder before I make a further post pointing out your obvious fundamental errors of analysis.

“I assume it bears some resemblance to â€œmind-shareâ€, that is folks are not thinking of M$ when they browse with */Linuxâ€¦”

You assume…?

More entertainment IMHO.

As an aside, have you ever attempted any of the kinds of desktop related tasks on any device running Android? I own two of them (a Motorola Droid running 4.4.2 and a samsung Galaxy Tab pro S 10.5 (also I believe running 4.4.2). They are quite good for what they do, but even the 10″ samsung tablet is too awkward to do anything more than take rough notes.

Desktop computers will be around for quite a long time IMHO, Robert Pogson. And vast majority of them will be running windows applications.

olderman wrote,

“â€œThatâ€™s the shift in mind-share.â€Nope, itâ€™s actually a fantasy on your part Robert Pogson.”

Kelvin:

“I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind”Well, here’s describing M$ share of page-views on the web (desktop, mobile, tablet, and, what the Heck, console), according to StatCounter. I assume it bears some resemblance to “mind-share”, that is, folks are not thinking of M$ when they browse with */Linux…

A brief lesson in physics… That curve is a parabola, the path a heavy shot follows. It’s “free fall” in other words. Assuming it carries on, the mind-share will drop more each year until you hit bottom in a few years.

“Thatâ€™s the shift in mind-share.”

Nope, it’s actually a fantasy on your part Robert Pogson.

Thanks for the entertainment.

Once ChromeOS is fully merged with Android, it’s game over for M$.

“Five years ago, Google co-founder Sergey Brin predicted that Android and Chrome OS would likely “converge over time”.

“Microsoft has repeatedly emphasized its “One Windows” strategy, which will unite phones, tablets, and PCs under a single operating system. Today, the Windows market is fragmented between Windows Phone, Windows RT, and Windows 8 — three separate systems which aren’t fully compatible with each other.”

Imagine the touchpad as your OLED screen.. 😛

One can only hope…. Fingers crossed 🙂