1+1 = ?

Usually 2, unless 1 is an abstraction.
An interesting context to look at this in is the addition of ideas.

Let someone's idea be 1.

a. If another person has the same idea, putting those together gains nothing: 1+1 = 1.
A group that does not question ideas does not gain from its diversity and individuals.
The longterm trend of this group is just whatever the individual who originates the ideas (usually others just nod along) produces.

Let two people have different ideas, each is 1.
Since the ideas are not in agreement, a lot of different results can occur:
b. One of them bullies the other into accepting their idea: 1+1 = 1 (and time was wasted and feelings are hurt)
c. Consensus is not reached, nothing happens: 1+1 = 0 (lose-lose)
d. A compromise is reached where the overlapping parts of the ideas are kept: 1+1 in (0,1)
e. The ideas are used as the basis for arriving at a new, better idea: 1+1 in (1, inf)

These results are not inherently amazing or surprising, but they explain why certain systems work better than others. Scaling each of these up we see:

a. Popular dictator or religious leader
The populace accepts the mantra and goes with it. However, the group adapts slowly to changes and is not resilient to deterioration due to a poor leader. Eventually, a leader will be poor and the system will crumble.

b. Authoritarian regime
People learn that dissenting ideas will be fought and overridden. They either choose to stop resisting and society becomes a lower-functioning version of [a], or they continue having contradicting ideas which cause the regime to spend resources on enforcement and the system eventually crumbles due to inefficiency and resistance.

c. Current United States Congress
Nothing more to say.

d. Typical Congressional or Parliamentary system
Ideas are often severely hampered by the time they go into effect. Various special interests all tug an initially sound proposal in incoherent directions. However, it's less fragile than [a] because some members are always yanking in positive directions. The system has resilience from the many members involved.

e. Free market
Lots of people have lots of ideas. Some of them collaborate to produce super ideas. The super ideas win out over time. Other people have ideas that combine with the super ideas. The best combinations prove themselves to be the next wave of super ideas. The weaker ideas fade away. The system is most resilient and quickly evolving because there's incentive and freedom to create super ideas.

Make America Safe Again!

Trump's slightly shifted his message at the RNC. It sounds great in principle; who doesn't want to be safe? But what does this really mean? And what about the "again"? Are we not as safe as we used to be?

What does it mean to be safe? This is a rather nebulous question, but one reasonable approximation is the odds of "something bad" happening to you outside your control. I don't think most people consider falling off a cliff while playing Pokémon Go an example of an unsafe world; I think they're more likely to just throw a Darwin Award after the person.

"Something bad", in the way people talk about it, mostly refers to ending up dead. This, too, can be broken down into many buckets. Someone could get and die of cancer. We tend not to chalk these cases up to "being safe" unless there's ample evidence of some man-made hazard (like Fukushima). Generally, death from illness is less and less likely and I doubt will regress from one president to the next, so there's no way to say a particular president had an influence. Deaths from accidents (like car crashes) falls in a similar bucket.

Mostly, Making America Safe Again means you're less likely to get violently killed by someone who's attacking you for their ideological purposes and you had particular ability to avoid them. First things first, what baselines or expectations or norms do we have? Using this compilation of Terrorist attacks and related incidents (which, at a glance, seems reasonably complete), we can establish the number of such deaths per year, and per president. In the interest of modern-day discourse, I'm filtering this to 1980 and after. No one's political memory goes back past Reagan anyways and the draft was still in effect for most of the time before; subjective many to deaths in faraway lands that they probably wanted nothing to do with. So, let's just say that before Reagan, self-started wars were the leading such violators of American safety. Since military involvement is now fully voluntary, I'm content to say that bucket has dried up and has no bearing on this discussion.

I've exported the linked table to Excel, filtered for only dates after Jan 1, 1980 and removed all cases marked as accident (ACC). There are 4267 qualifying deaths (and 12068 injuries) over approximately 36 years (average: 118 and 335 per year). All else equal, a president should expect to see about 474 deaths and 1341 injuries in a term. Since all but Bush Sr** served two terms, they get to double their expected numbers. How did they do?

President	Deaths	Injuries
Reagan	51	327
Bush Sr**	182	54
Clinton	587	2101
Bush Jr	3072	9005
Obama	241	591

The statistically very difficult thing here is that over 70% of the total comes from a single event (9/11), so everyone else is below the average. It can also be argued that the first WTC attempt *could* have been successful, and that was under Clinton's watch. But, let's just stick to what actually happened.

We can also sort and see when the largest events occurred. I'm going to semi-arbitrarily pick all the events with at least 10 casualties:

Bush Jr	New York City, New York	2759	8700	TER-islm	crashing of two hijacked planes into World Trade Center towers, causing fires and collapse
Clinton	Atlantic Ocean, Massachusetts	217	0	TER-islm	intentional crash of Egypt Air flight off Nantucket Island by copilot
Bush Jr	Alexandria, Virginia	189	200	TER-islm	crashing of hijacked plane into Pentagon
Clinton	Oklahoma City, Oklahoma	169	675	TER-right	truck bombing of federal building, causing partial collapse
Reagan	San Juan, Puerto Rico	97	140	CRI	three employees set fire in Dupont Plaza Hotel; most fatalities were in the hotel casino; the employees were in a labor dispute with the hotel's management
Bush Sr	New York City, New York	87	0	CRI	arson fire in social club
Clinton	Waco, Texas	86	25	CRI	Branch Davidian cult members kill 4 ATF agents, injure 16, when agents raided their compound in Waco, TX; 10 cult members killed; compound was sieged until 19 Apr when another raid was attempted and the compound burned down
Obama	Orlando, Florida	50	53	TER-islm	shooting attack at nightclub
Bush Sr	Atlantic Ocean, Puerto Rico	47	0	CRI?	explosion in gun turrent of battleship U.S.S. Iowa off Puerto Rico kills 47; Navy cites some evidence of sabotage
Bush Jr	Somerset County, Pennsylvania	45	0	TER-islm	crashing of hijacked plane into rural area of Pennsylvania, following attempt by passengers to regain control of aircraft
Clinton	Rancho Sante Fe, California	39	0	CRI	discovery of mass suicide by 39 members of Heaven's Gate cult, tied by cult members to Comet Hale-Bopp
Bush Jr	Blacksburg, Virginia	33	17	CRI	shooting attack at Virginia Polytechnic Institute
Obama	Newtown, Connecticut	28	3	CRI	shooting attack at elementary school kills 20 children and 6 adults; shooter killed himself and had killed his mother earlier that day
Bush Sr	Killeen, Texas	24	20	CRI	shooting attack at Luby's restaurant
Reagan	San Ysidro, California	22	19	CRI	shooting attack at McDonalds restaurant
Obama	San Bernardino, California	16	23	TER-islm	two attackers killed 14 and injured 21 at a county employee meeting and Christmas party; both attackers were killed hours later in a shootout with police in which 2 police officers were injured
Reagan	Edmond, Oklahoma	15	6	CRI	shooting attack by postal employee at post office
Clinton	Littleton, Colorado	15	27	CRI	mass shooting at Columbine High School by two students; 12 students and 1 teacher killed, 21 students and 2 teachers killed; both gunmen killed themselves
Obama	Binghamton, New York	14	4	CRI	shooting attack at immigrant center
Reagan	Wilkes-Barre, Pennsylvania	13	0	CRI	shooting attack
Obama	Foot Hood, Texas	13	44	TER-islm	shooting attack at Soldier Readiness Center at Foot Hood
Obama	Washington, DC	13	3	CRI	shooting attack at Washington Navy Yard
Obama	Aurora, Colorado	12	58	CRI	shooting attack at movie theater; suspect was arrested afterwards; suspect had booby-trapped his nearby apartment with explosives which were successfully disarmed by police
Reagan	Philadelphia, Pennsylvania	11	0	CRI	police assault on headquarters of radical black group Move starts fire
Obama	Alabama	11	6	CRI	multiple shootings at residences and businesses in Samson and Geneva, AL
Bush Sr	Jacksonville, Florida	10	4	CRI	shooting attack at GMAC office
Bush Jr	Red Lake, Minnesota	10	7	CRI	shooting at Red Lake Indian Reservation school

The worst incidents happened under Bush Jr and Clinton. Bush Sr and Reagan are next, and Obama is last in this ordering. Obama is also second-to-last in per-term deaths and injuries.

I suppose if we want to Make America Safe Again, we should bring back zombie Reagan. If that's not feasible, let's give Obama a 3rd term. His track record demands it.

An Apple (R) a day keeps the DoJ away

Couple kills 14 people in San Bernardino; they are determined to have terrorist ties.
iPhone with potentially valuable law-enforcement data is recovered.
FBI asks Apple for help retrieving data, Apple declines.
FBI takes them to court, judge orders Apple to help.
Tech world gets behind Apple's appeal centered on privacy and back-doors.

This is where we are now. It's been incredibly disappointing to me to see so many tech-involved people (Apple included) blatantly misrepresent what Apple has been asked to do. The narrative is that the FBI would get a backdoor that they (or hackers) could freely use to access any encrypted data in the future. This is not at all the case, and is a very important point in the discussion:

 "Apple’s reasonable technical assistance shall accomplish the following three important functions: (1) it will bypass or disable the auto-erase function whether or not it has been enabled; (2) it will enable the FBI to submit passcodes to the SUBJECT DEVICE for testing electronically via the physical device port, Bluetooth, Wi-Fi, or other protocol available on the SUBJECT and (3) it will ensure that when the FBI submits passcodes to the SUBJECT DEVICE, software running on the device will not purposefully introduce any additional delay between passcode attempts beyond what is incurred by Apple hardware."

This would be a custom OS that prevents the booby-trap of locking down the device after a handful of incorrect passwords. The FBI's approach afterwards would be to brute-force their way in by guessing the pin code. This is also a very important distinction. The details of how the device is encrypted are fairly technical (Apple seems vague on details because their devices use magical fairy dust, but it's likely very similar, or identical, to Windows bitlocker). The key takeaways here are that

1. The FBI is not actually accessing anything to do with the real encryption of the data.
2. The FBI is exploiting the relatively weak pin that lets the underlying hardware decrypt far more securely locked data. In other words, your data is only as secure to attack as guessing your 4- or 6-digit pin in a handful of tries is.
3. There is no general alternate route to the data provided to the FBI or anyone else who gets a hold of the device

Apple, like other technology companies, has been asked to (and complied with) dig up data on customers by law enforcement. Why in this case are they resisting? There are numerous possibilities, some more rational than others. The following have been explicitly cited:

Apple is fearful the custom OS will get into the wrong hands
This is probably the most valid concern. I can't imagine they can't negotiate some arrangement where they recover and hand over the unencrypted data, but never hand over the OS to the FBI. Essentially, guarantee they maintain custody of said OS bits and move on.

It sets a bad precedent that the government can have Apple build custom OS
This seems silly to me. This is an example of requiring technical assistance to gather data. This happens all the time. When the FBI collects phone records, or cloud-stored info, or identities from an account, etc, they call the affiliated company, present a warrant, and the company gets the data for them. The FBI does not have the technical capability to get this info without help; in fact, doing so would require them hacking databases which is not kosher.

People have a right to privacy
I'd scoff far louder if Google were making this claim ... but let's stick to the case at hand. Yes, people have a right to privacy. Law enforcement can't randomly peek into my house to see if something is amiss. That requires a warrant, just like the one the FBI has for the phone, just like the ones they need to call Verizon and get phone logs, etc. This, to me, is absolutely no different.

It compromises encryption for all
This is simply technically false and has been a completely erroneous part of the discussion. No, we should not compromise the quality of encryption. No, that's not happening in this case.

Compelling companies to write custom software is a slippery slope towards encryption backdoors
I don't think this is true. I think the road to encryption back doors is independent of this. Companies are already 'compelled' to write certain code; for example anyone working in healthcare or finance has to comply with very strict auditing guidelines. No one is dictating particular lines of code, but some very specific features have to exist.

Apple wants to look like the technical leader of privacy
Bingo! Sell more iPhones! I can't imagine this isn't a/the top internal reason.

But other tech companies all back Apple, Apple must be right
Yep, cuz people are dumb and none of the other big players want to look like law-enforcement pawns to these technically illiterate people. Or to the technically semi-literate who have misconstrued all of this.

A couple Facebook discussions yielded numerous other claims, but they fall into the technically inept bucket so I'm not even going to address those. Bottom line is this narrative has fallen far from the scope of reality and entered a world of fearmongering most tech people seem to think only exists in the GOP around Planned Parenthood and persecutions on Christianity. We make fun of them for being ridiculous, let's turn that same analysis on ourselves.
 

Driving the Ford Mustang

Upon arrival to Phoenix, I was offered a swap from whatever I had rented to a Mustang for no extra cost. I said sure.

The car looks pretty nice from the outside, and the interior finishes are better than I remember from previous generations. I often say that of the American car companies, Ford got their shit together first, and this continues to show. One thing that continues to confound me is the sheer size of the car. It's huge, but doesn't feel particularly spacious. The trunk is a weird shape that not much fits into, and the seats don't offer excessive room. It's 14" longer and 8" wider than my Acura RSX and feels more cramped inside. So, that's weird.

The next thing I noticed is just how enormous the hood is. I can't see over it at all, and it definitely makes me feel uneasy about where the car ends. The windows are also relatively small and high, the doors also limit sideways visibility downwards, meaning it takes a while to not feel like I'm going to run over curbs. Forward 180 degree visibility is otherwise good (like to avoid other cars), but rear quarter is non-existent. Compounding this is a pair of very small side mirrors; after a couple days driving this thing I'm still a touch uneasy during lane changes.

The power is good enough, its handling is generally good, though a little vague. It feels like there's a few inches of play in where the car will end up, which is usually ok, you just have to get used to it and trust it. It definitely feels more like a cleaver than a scalpel, to use familiar tropes.

It has a froofroo feature: when unlocking the car, it shines a pony on the ground by the door. I can't come up with a reasonable use for this, so I'm just assuming it's new-age car bling?

The interesting new feature on this car is that the seats are vented. I'd often wondered if it made sense to route the hvac through the seat. I can imagine it'd help cool the seat itself down quickly, which is a huge deal in hot climates with strong sun. The amount of heat a leather seat can soak up is surprising and also causes unavoidable horrific back sweat. For whatever reason the venting is through the bottom of the seat, up. So you're sitting on (as opposed to leaning back onto) an air-conditioned layer which does nothing for the aforementioned back sweat. And frankly, sitting on a cold air jet kinda tingles in a weird way. I find it not unpleasant, but just kinda weird. So that answers that, at least for me. It's February now and only 80 out so I can't really test the extreme heat theory part of this .. .maybe that would change my mind.

What are the odds!? **

** - given various pre-conditions.

"If you're ever sad, just remember the Earth is 4.543 billion years old and you somehow managed to exist at the same time as David Bowie"

This has been making the rounds on Facebook following Bowie's recent death. It's pretty amazing, right? Except not really. Because while I could certainly calculate an infinitesimal probability that two human lifespans overlap in a 4.5 billion year window, that's simply not the right constraint for the claim. For one, humans, and written history of particular individuals, has only existed for a few thousand years. Already our odds are a million times better than before. Furthermore, such sentiments tend to come out right when someone well-known dies, in which case there's a 100% chance that anyone reading such a sentiment is alive at the same time. And therein lies a perhaps unintuitive truth: that we only perceive when we exist, so anything we perceive sets a very significant condition on any probability we might think about. If the problem is simply "what are the odds you're alive at the same time as a famous person who just died (or while they are alive)", the real odds are something, but the odds, to you, are 100%. You only perceive in the case where you are also alive, thus limiting the conditional probability significantly.

There are a number of similar realizations. A friend recently posted a picture of her great grandmother, along with the story behind the picture. It was taken to commemorate buying a ticket for the maiden voyage of a certain ship named the Titanic. Gram had gotten out of line to tend to something with the kids who were not on the ship, and by the time she'd gone back, boarding had completed and gates were closed. She missed the ship, and therefore the iceberg, due to unlikely random circumstances. My friend effectively was saying, "look how close I came to never being here". But in the same vein, had she never been born, she wouldn't know it. Alternatively, being born guarantees that the unlikely event did occur. Again, allowing for perspective alters the odds.

Another friend's grandfather flew on bombers during WW2. If I recall right, he was one of the first to successfully complete 25 missions without being maimed or killed. He then met a nice lady, they had a son who also met a nice lady, and my friend became. How lucky he is that his grandfather was one of the few who survived! This is essentially the lottery winner concept. Someone gets lucky, and only because they got lucky are they there to evaluate it. Sure they got the winning ticket, but the ones who didn't, never found out. They never even knew tickets were being passed out.

The notion of "how lucky I am to be here" is funny too. Every single one of us has defied great odds to be here. I myself am born to a father who would be dead at age 2 weeks had a Russian bomb detonated when it hit the next building, a mother who survived some serious lung problems as a child and capsizing into a stormy lake as a teen, a grandmother who had to walk through the raging winter to get away from incoming Russian troops, another grandmother was had been ordered shot if she tried to sneak the kids away, and two grandfathers who were POWs during WW2. Many others weren't so lucky; their prospective offspring are not around to ponder their unluckiness.

Some wonder how we, as a race, have defied cosmic odds to exist in this universe. Isn't it a miracle? Maybe, to some other observer. But to us, the only possible odds are 100%.

A week with an RDX

My wonderful little Acura RSX-S had to go to the doctor for a transplant. The seatbelt buckle wasn't quite right and was causing the airbag light to come on (which could end with the airbag not deploying, I suppose). This was diagnosed in 5 minutes by regular mechanic, but since he doesn't do warranty service and Acura of Bellevue ("AB") does, he sent me there to get it fixed.

I checked into AB on Dec 30. They told me they'd get back to me by the afternoon. They also quoted me an estimate of $144 for the service (which I hope won't be on my bill because, warranty). They were nice enough to give me a loaner: an Acura RDX. Not really my top choice, but whatever, it's for a day ... until AB called late Dec 30 to let me know that they'll need to replace the buckle and need to order the part. I'd have to keep the loaner until Jan 2. They then called me on Jan 2 to let me know that, just kidding, it won't be here til Jan 5.

Aside about AB: I had already told them the issue was diagnosed by my guy when I dropped the RSX off in the morning (actually, told them when I booked the appointment on Dec 22). It still took them a full day to diagnose it and get the part ordered (or at least I'm concluding that from when they called me). That delay could absolutely affect when the part gets in. I really wish there was some reference concept where they could have just ordered the buckle based on my guy's diagnosis even before I dropped the RSX off. Sure, they could spend some time to confirm it, but they'd be ready and we'd all be done by now. I'm still curious to see what happens with the $144 estimate, hopefully that will just disappear.

So now I've got this beast mobile for a week. I'm not a big-car guy, so this isn't really up my alley and thus I'm not going to looooove driving it around. But that's ok. I can still try and take an objective look at the car. Marisa immediately commented that it "is really nice to sit up high" and that "it looks really good in our garage". She also commented that the seats are really nice. That's all great. In fact, the car overall is hard to fault. The 279 peak hp and 252lb-ft peak torque drag its 3800 pounds around quite easily; acceleration is good for the most part, the engine sounds great. The seats are great, there's plenty of space and all that. The general interface is clean, things are where I'd expect them to be (though Hondas are pretty consistent car-to-car, so it could just be that I'm used to them). I personally don't love the whole navigation system center console thing, but that's me being generally grumpy about such things.

What about my quibbles? Sure, I find the following weird:
1. The shift lever for the auto has a button that you kinda pull up instead of pull back. Marisa and I both found it weird, but this is the kind of thing you get over by the 3rd time and stop thinking about.
2. The driver's side mirror's outer edge is curved to give a very wide angle of view, which is distracting because the edges of what you see in the mirror are heavily distorted.
3. The seat heaters (and the heater in general) take a while to get going. The seats in Marisa's Jetta, for example, will feel warm within 10 seconds. The RDX takes a couple minutes. The RDX also takes a minute or so to start blowing hot air. I think this is a philosophical thing with Honda; they don't want to add an electric heater to their HVAC? My RSX is also a little slow to get the heat blowing.
4. I don't like the material used for the steering wheel. It's too smooth and I'd worry it'd slip if my hands were sweaty. Marisa said the same.

Nothing terrible really, which is a lot more than I can say for some other cars I've driven around.
There is, however, one other thing and this surprised me because it seems so un-Honda. The transmission is slow. There's really no two ways about it: shifts take a long time. I noticed while driving it in D that while it has very nice acceleration once going (like from 30 to 50, or even from rolling to whatever), it's a little sluggish off the line. To debug this more, I popped it over into Sport mode and drove it around with the paddle shifters.

First, the car doesn't really like to stay in 1st gear if you're not flooring it. In my couple trials, it flipped over to 2nd around 3000 rpm (despite the 6500 rpm redline). As most people who drive stick can attest, cars get a little twitchy in 1st, so maybe this is ok. But, the shift takes about 1.5 seconds (whether I initiate the shift with the paddle or not):

Click (+) paddle, instantly see dash show next gear, wait 1.5 seconds, see RPMs actually move (meaning that's when the next gear was actually engaged). The same delay is present between every pair of gears. If you double-click the paddle, it won't show confirmation. The dash will show the next gear, then the gear will engage, then there's a little pause, then the dash shows the 2nd next gear, then that gear will engage. A double-click has an end-to-end runtime of about 4 seconds, with a distinct ambiguous middle zone before you know that the 2nd shift is coming.

This lead to a curious realization: the car would be better served without a 1st gear (or just have 1st be a 'low' gear, out of the way for usual driving). Sure, getting to 20 takes a touch longer, but there's enough torque that you can't remotely make full use of 1st anyways. 2nd isn't much slower, and it avoids one slow shift while getting up to normal speeds. I started just flipping the car into 2nd after stopping, and the driving experience was a lot better.







 

Terminal betrayal velocity

A friend posted a story from the internet that goes:

A couple decided to commit suicide. They'd had some rough times and chose to jump from a building. When they got to the top, they counted to 3 and the woman jumps. The man watches her fall for about 8 seconds when a parachute opens. Who betrayed whom?

Her comment? "Must be a tall building!"

Of course I took it upon myself to figure out just how tall that building is. This is more interesting than a basic equations of motion problem because the use of a parachute necessitates allowing for variable forces, both during the initial freefall and then during the slowing down process after the chute opens. To frame up the initial fall, we can write, generally:

[1] d/dt D(t) = v(t)
[2] d/dt v(t) = a(t)
[3] a(t) = F(t)/m

These are our base, non-specific equations. The force diagram on the woman has 2 components: mg down (which we'll define as the positive direction), and kv up, where k is some constant aerodynamic coefficient; air resistance can be crudely modeled as proportional to velocity. We have additional data as well. We know that a person in freefall will reach a terminal velocity, Tv, and that value is generally stated as being about 50m/s. I'll use this value for the calculations, but if you feel they aren't right, you're welcome to use alternate values in the final equations. So, at the point of terminal velocity we know that kTv = mg, and thus k = mg/Tv.

[3.1] a(t) = (mg-kv(t))/m
[3.2] a(t) = (mg-mgv(t)/Tv)/m
[3.3] a(t) = g - gv(t)/Tv

We can do a quick sanity check here: as v(t) -> Tv, acceleration indeed goes to zero as expected. The next step involves solving the differential equations [2] and [1]. While this could be a fun exercise in math process, I'll defer to Wolfram Alpha diff eq solver. Known boundary conditions (notably that velocity and distance are both zero at time=0) will be used to solve for constants that appear as a result of integration steps.

[2.1] d/dt v(t) = g - gv(t)/Tv
[2.solved] v(t) = c1 exp(-gt/Tv) + Tv
[2.boundary] v(0) = 0 = c1 + Tv, thus c1 = -Tv
[2.final] v(t) = Tv - Tv exp(-gt/Tv)

[1.1] d/dt D(t) = Tv - Tv exp(-gt/Tv)
[1.solved] D(t) = c2 + Tv t + Tv Tv exp(-gt/Tv) / g
[1.boundary] D(0) = 0 = c2 + Tv Tv / g, thus c2 = -Tv Tv / g
[1.final] D(t) = Tv Tv exp(-gt/Tv) / g + Tv t - Tv Tv /g

Solving for distance fallen and speed after 8 seconds yields her status as:
D(8) = 196 meters down
v(8) = 40 m/s

We're now at the stage where her parachute is opening. Based on a combination of movie scenes and the shortest base jump I could find, it appears it takes about 2 seconds for the chute to open. During this time I'll assume it has negligible braking force, and I'll simplify and assume the woman would continue to fall at v(8) = 40 m/s and thus finish this stage at 276 meters down and still going 40 m/s. Clearly I've simplified here, but due to the short duration of the stage, the effects are not terribly material on the final calculations. Others suggest the time could be as low as 1.2 seconds (derived by dividing the claimed 200 feet distance to open by terminal velocity of 50 m/s). That would put a lower-bound on her fall at 244 meters.

The final stage is to figure out how long it takes for the chute drag to slow her down to a speed she'll survive. We can reuse equations [1.solved] and [2.solved] with new boundary conditions. Tv in this case is the descent speed with the chute open, which I'll call about 5 m/s.

[2.boundary.stage3] v(0) = 40 = c1 exp(-gt/Tv) + Tv = c1 + Tv, thus c1 = 35
[2.final.stage3] v(t) = 35 exp(-gt/Tv) + Tv
[1.boundary.stage3] D(0) = 0 ** = c2 + Tv t - 35 Tv exp(-gt/Tv) / g = c2 - 35 Tv / g, thus c2 = 35 Tv / g
** - I'm re-referencing her position here as zero, this can be trivially added/shifted to the previous stages.
[1.final.stage3] D(t) = 35 Tv / g - 35 Tv exp(-gt/Tv) / g + Tv t

The last thing to figure out is how long it takes her to slow down to a speed she can still land reasonably safely. I'm not sure what the number is, but let's say 2 Tv = 10 m/s. That's the equivalent of jumping from about 15 feet. It'd hurt, but she'd survive. Using [2.final.stage3] and solving for t:

[2.final.stage3.survival1] v(t) = 2 Tv = 35 exp(-gt/Tv) + Tv
[2.final.stage3.survival1.1] Tv = 35 exp(-gt/Tv)
[2.final.stage3.survival1.2] Tv ln (Tv / 35) / -g = t
[2.final.stage3.survival1.3] t ~= 1 second

As an alternative, suppose we want to get to 1.2 Tv for a practically terminal velocity landing
[2.final.stage3.survival2] v(t) = 1.2 Tv = 35 exp(-gt/Tv) + Tv
[2.final.stage3.survival1.1] Tv = 175 exp(-gt/Tv)
[2.final.stage3.survival1.2] Tv ln (Tv / 175) / -g = t
[2.final.stage3.survival1.3] t ~= 1.8 seconds

Plugging in our two values will give us a reasonable upper and lower bound for how much distance she needs after the chute opens.
[1.final.stage3.survival1] D(1) = 20.3 m
[1.final.stage3.survival2] D(1.8) = 26.3 m

The final stage is quite rapid, and slowing down considerably more only costs an extra 6 meters. Let's assume for comfort, she'd want to get to the slower speed. Adding up the 3 stages yields 196 in freefall, 48 to 80 while the chute is opening, and another 26 to slow down. To be on the safe-ish side, let's take the max of each stage and say the building needs to be at least 196 + 80 + 26 = 302 meters (991 feet) tall. In essence, this could be done off, with rounding, any building over 1000 feet (or nominally 100 stories) tall.

There are only a few buildings in America that this story could plausibly have happened on. There are only 17 that are formally tall enough, and a few of those are coming within feet of the exact minimum height. However, a number of those don't qualify because they don't have a platform that's high enough. For example, it's doubtful that anyone could jump outwards enough from high enough on the Empire State Building or Bank of America Tower to avoid significantly outcropping lower layers. The New York Times and Chrysler buildings definitely fall into this category, and judging from other photos, the Bank of America Plaza and US Bank Tower are similarly problematic. The bottom end of the tall-enough buildings all seem to be box-shaped enough that they would support our scenario. All in all, this could happen in maybe 10 or 11 specific places, but would have to be in New York, Chicago or Houston.

What's fun to note is that even from full terminal velocity, the distance needed to open a chute and slow down to safe landing speed is under 150 meters. Scaling this up to the tallest building in the world, Using [1.final] and D(t) = 680 allows for 18 seconds of free-fall! Intense!