The various digressions I got into in my previous post on this thread has led me to write some more code to investigate another problem (mentioned briefly in earlier post) in more detail.

But first I want to waste a little of your time explaining my notions about “formal math” vs “numerical simulation” (I put these in quotes because I’m probably not using exactly the right terms). My notion here is that mathematicians (or math-oriented finance researchers) want to crank abstract math (isn’t all math ‘abstract’?), i.e. generate “proofs” via their long-appreciated methodologies. In contrast one can crank a bunch of numbers in the computer through an algorithm to investigate the same issue, BUT, the math types will denounce the computer simulation as insufficiently robust and in fact it’s just a guess as far as they’re concerned.

So here’s a simple example of that idea from my copy of *In Pursuit of the Unknown: 17 Equations That Changed the World* by Ian Stewart (the following formula is in the book but appears here courtesy of Wikipedia):

This equation, known as Euler’s Identity can illustrate my point. Presumably the incredible mathematician Euler “proved” this identity which to mathematicians means it’s totally true (even in alternate universes) for all possible values. Now e and i and π are some very interesting quantities, so the fact they would be related this way is very unobvious. e and π are known as transcendental numbers. While 1/3 is an infinitely repeating fraction 0.3333333… (forever more 3’s) transcendental numbers also have infinitely many digits but their pattern is unpredictable (it can be computed, however).

So a computer guy might “prove” Euler’s Identity (no one would, I’m just using this scenario to demonstrate my point) by computing e to the iπ’th via numerical methods. Since both e and π don’t have nice pretty values, like 1.0 (exactly) then the computations in a program must use some finite number of digits. Now there are algorithms to compute e and π to any arbitrary number of decimal places, but no matter how many we compute (say 1,000,000) there is still some small error when we plug these values into Euler’s Equation and thus the right-hand side, known through formal math to exactly 0, will actually have some finite (albeit small) value other than zero.

That bugs mathematicians. But as us engineers say “good enough for government work”.

But sometimes relatively naive programmers don’t actually understand computation in real computers using the builtin numbers in hardware. Now a third grader would know that 1/3 + 2/3 = 1, but if you actually try to compute that, say in C# with double precision numbers the result will not be one (first since the fractions infinitely repeat, but second, and worse, in base 2, they’re really icky fractions). You might be deceived if you merely print out your result (it will probably appear as 1), but if you look at the hex value of the actual double sum (or do calculation 1 – sum; it won’t be 0) you’ll see you got the wrong answer.

Now in my case I’ve bypassed that issue by assuming I won’t use hardware floating point numbers (nowhere near 1,000,000 significant digits), but it won’t matter that my BigFloat class will still have errors (both e and π are going to come from adding up many terms, each of which will be slightly wrong).

So I get it. Mathematicians can precisely say what their proofs mean; numerical calculation on a computer is always subject to various errors and thus can never “prove” anything. It can, however, still yield practical results as long as we’re careful in coding to understand the errors and minimize them.

But here was my point with Black-Scholes – yes, it’s neat and closed/formal math and therefore presumably true, for all possible values, BUT, to apply it to the real world you’re back in the realm of all those niggling little errors in computer programs, not to mention the much worse errors (but limited in scope and wrong at times) in your dataset. So all the nice assumptions you made doing that beautiful math aren’t worth diddly (or, IOW, are probably violated) when you apply “pure” math to the messy real world, especially cranking data through computers.

Now this post is already way too long to get to my new simulation, so I’ll make that another post back-referencing this prologue and thus close with this.

Not only did my first post trigger some ideas about a simulation, I also wanted to go back and read another book I read a long time ago – *When Genius Failed* by Roger Lowenstein, the story of the collapse of LCTM. Now this is connected to all my discussion because: a) the very same Scholes as the equation is named for was a principle in LCTM, along with various of his disciples, particularly Merton (who actually got the Nobel instead of Black because Black had died), so the story of LCTM is very much the story of Black-Scholes equation, but even more broadly this whole idea of beautiful theoretical math being applied in the real world – and failing spectacularly, and, b) all these guys and this financial theory was being devised at exactly the same time and exactly the same place as I got my financial training, i.e. MIT Sloan School in the 1970s. While I can’t claim much personal familiarity with these “geniuses” and I was a lowly Masters student, not a PhD and therefore not as heavily immersed in this stuff, at that time, I actually probably was a better computer nerd than any of them were, so I might be so bold, in such an apples and oranges comparison, to say my view of these issues, from computer POV, had perhaps as much validity as their POV from the formal math POV. And, of course, I can gloat, because they were proved spectacularly wrong, tripped up by exactly all the issues that arise in real computer programs on real data applied to real world problems.

So in my next post of this series I’ll finally get to the model I’ve already done which will be the basis for expanding into more general solutions. So bye for now.

## What everyone is overlooking about Apple Pay

I used to be a big fan of Apple but as they drifted into a new world my enthusiasm dropped. I have some current Apple products but I pick and choose, so naturally I have the superior Kindle (and its content ecosystem) over iBooks (and its corrupt pricing). The whole incident with books shows you exactly who the new Apple is. Since Amazon had a huge lead and Apple, in books unlike in music, was not highly regarded, they used a simple trick – bribe the booksellers to do deals with Apple instead of Amazon. Now back when they did this I keep screaming – look what they did to music publishers. When Apple is the monopolist they squeeze their suppliers; when someone else is the leader Apple appears to be on the side of supplier, until, of course Apple wins, then they’ll put on the squeeze.

This is the overlooked issue in Apple Pay. People are looking at what Apple is doing TODAY, when they’re trying to ingratiate themselves into controlling your money and ignoring what they will do in the FUTURE when they hold the monopoly. We’ve seen this before, over and over, say esp. at Facebook – old policies designed to attract users are quickly reversed when Facebook can now monetarize something by changing policies, and, poof, guess what, your EULA changes at the whim of Facebook and you have no choice but to accept it.

Do you really think Apple, once they own retail, won’t collect personal information and sell it? Do you really think they will leave those billions lying on the table and not scoop them up?

Sure they’re saying no collection of personal information TODAY, but what happens when their system is nearly universal. Do you have an ironclad, court-enforceable contract that says they can’t change that policy? And are you stupid enough to believe they won’t when they can get away with changing that policy and tracking everything you do and selling that to the highest bidder.

What people need to realize about modern mobile technology is YOU ARE NOT THE CUSTOMER. You are PRODUCT. You exist to be mashed and molded into something that can be sold to those enterprises who ARE the customer. Whatever “benefits” you believe you’re getting are not goodness-of-the-heart (of businesses that certainly have no heart, only profit maximizing) can be recalled in an instant, the very instant where whatever adverse effects the policy change has are less than the benefits. Sure a few people may protest Facebook and drop out – they counted that in their model, but most of the rest of the people are sheep and will go along and Facebook gets $N.MM dollars each – something lost, something (more) gained – done deal.

Why is everyone so naive about this having seen it over and over? Do you think Apple is doing this just because it’s cool. Isn’t the idea that they will say whatever they have to to gain entry to your wallet and once it’s in their possession they will then do whatever they want to make money make sense to do. Apple Pay costs them something – where’s their return?

And as we’re now seeing Apple is the iPhone company, not really much else. Their other product lines are minor. Now Apple knows this but much of the world doesn’t. So big surprise that their latest mandatory iOS updates break older phones. When you have one product and that product can physically work for years, but the only way you get ever increasingly sales is to get people to discard their old phone for new, AND, you’ve run out of real new ideas and/or fashion tricks (isn’t gold case just totally the reason to upgrade, oh sure), then forced obsolescence is their only marketing trick.

So you lock yourself into Apple Pay and somehow merchants get browbeat into using it and then Apple controls most retail payments. Guess what – you’d better plan on a new phone every six months as Apple breaks your old one and now you can’t get your coffee. Don’t think they’ll do this – exactly why not? Because they’re nice guys (sure), because of legal reasons (exactly which are those), because of bad customer relations (sorry, you’re not the customer anyway), because of competition (sure you’ll switch to Beta because you’re mad at VHS). Apple knows we’re sheep, just as Facebook and Twitter know we’re sheep, and their business strategy is simple: 1) tell us what we want to hear in order to get a hold on us, 2) change polices to whatever makes them the most profit.

I hope I can go to my grave without every buying an iPhone (or worse an iPad). OTOH, I hope I can get iPods forever. And with Microsoft building junky OS’s now, I might even switch back to Macs. But the iPhone is drugs and I refuse to be an addict. I don’t much want Android or Microsoft either, I don’t want to be a phone zombie from any vendor (it’s getting where I may have to budge on this but then I’ll get the cheapest POS I can possibly stand). So naturally any attempt Apple is making to require me to use their iPhone – well screw them. They can yank my credit card (or even cash, or my Starbucks card) out of my cold dead fingers or I’ll just go off the grid before I’m forced to use Apple as my bank (hey, Goldman Sachs, scumbags that they are, aren’t even in the same league as Apple when it’s a monopoly).

So stuff it Apple. And folks, get a clue – forget your trendy fashion statement sense of Apple (hey, Steve is gone to the great alternative medicine and design center in the sky, today’s Apple has no heart at all). Don’t help Apple run the world and then eventually tax you more than your state or federal government can dream of. Stop Apple Pay!

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