How’s my math (reasoning) Part 2

[ChrisGreaves]

Toronto city boasts roughly three million people.
About half of Toronto’s population live in high-rise apartments.
About half of Toronto’s population work in high-rise office buildings.

I assume a person leaves their home about once a day. High-rise dwellers would use an elevator twice a day – once out, once back. 3,000,000 elevator trips.
I assume that half of Toronto’s population is at work, and about a half of them work in a high-rise office. A person goes to work once a day. Office workers would use an elevator twice a day – once up to the office, once out. 1,500,000 workers, 750,000 in high-rise offices twice a day, so 1,500,000 elevator trips.
That would mean of the order of 4,500,000 elevator trips per day in Toronto.

I would think that on average there are two people per elevator trip; significantly more at start-of-work and end-of-work in office towers, but mostly one per elevator car during the day in apartment and condominium buildings.
Which suggests 4,500,000/2 or 2,250,000 door closings behind the-last-person-aboard each day in Toronto.

If I consider 350 days in a year as a balance between 365 residential days and 240 office days, I get 350*2,250,000 or about 800,000,000 door-closing events (that is, the door closing behind the last-person-aboard) in Toronto, a city of 3,000,000 people.

I can’t remember the last time someone got trapped in an elevator in Toronto; probably three years ago.
To the best of my knowledge no-one has been sliced in half by a malfunctioning elevator door since I arrived here in 1982.

That’s, say, 30 years multiplied by anything from 400,000,000 to 800,000,000 door-closing events.
If I average out at 600,000,000 over 30 years I get 18,000,000,000 door-closing events in 30 years.

Not a single person sliced in half or dragged to their death as the car moves up or down.

That says a lot for the engineering behind the elevator car door closing mechanisms. They are to all intents 100% safe in terms of unattended and automated door closings.

For the life of me I can’t understand why a significant number of people I talk with worry about fully automated trains, in particular that the doors might close on them while they are leaping aboard a subway car or streetcar.
It’s true that if you are a last-minute boarder in Toronto the subway car door opens, the guard frowns at you, and then re-closes the door.
But elevator door mechanisms have an unblemished record, as far as I can see.

[BobH]

Is this what long winters capped by snow in April do to the psyche?

[HansV]

All (reasonably) modern elevators have safeguards built-in that prevent them from moving up or down while the door is open. These safeguards can be bypassed for maintenance and in case of emergency, but that requires special action.
I suppose that fully automatic trains would have similar safeguards to prevent them from departing while a door is still open.

There are quite a few driverless underground/metro/subway lines: see List of driverless trains.

[Rudi]

Your reasoning seems reasonable...but now I'd like proof of your numbers.

[BobH]

For a time, I used to commute through the Hartsfield International airport in Atlanta. It has 5 terminals that are connected by driver-less subway trams. Whenever a tram enters a terminal loading area there is a rush of people to board the train. The doors open and attempt to close automatically, but often there is that person intent upon crowding himself in instead of waiting for 3 minutes for the next tram to arrive who holds the door open delaying everyone. It became the habit of a group of regulars to taunt and embarrass anyone who rude enough to cause the delay. After a number of years not commuting through Atlanta, I was surprised on an occasion when I once again passed through and experienced the delay and harassment of the perpetrator. I don't know if the practice continues. Probably not. Someone is sure to have complained to airport officials who probably consider it a terroristic threat, these days.

I am very, very glad that I no longer need to travel by air in the US!

[viking33]

Office workers would use an elevator twice a day – once up to the office, once out.
--------------------- 1,500,000 workers,


Chris,
You didn't include anyone going up or down for lunchtime? Double your numbers?

[BobH]

Office workers would use an elevator twice a day – once up to the office, once out.
--------------------- 1,500,000 workers,


Chris,
You didn't include anyone going up or down for lunchtime? Double your numbers?

Or inter-floor trips which are quite common in office skyscrapers.

[DaveA]

Or all of the people that live out side of the area that commute every day.
So you numbers are way out of the ball park?

[BobH]

Toronto city boasts roughly three million people.
About half of Toronto’s population live in high-rise apartments.
About half of Toronto’s population work in high-rise office buildings.

...(some snippage occurred here)

Do we know if the set of those who live in high-rise apartments also are in the set who work in high-rise office buildings? Drawing on set theory classes of about 50 years ago, it seems that to the extent that the 2 sets overlap, the numbers grow. Given the relatively high numbers in each set, one might expect that the joint set is pretty large.

So, Chris, how would that affect your calculations and your conclusions? I ask only because there might still be some snow and I would hope that the question would distract you.

[ChrisGreaves]

Thanks to all who had replied by the time I took a snapshot of the thread back on the 15th. I have tried to REDUCE the number of posts to Eileen’s Lounge by accumulating my responses into one post.


BobH> Is this what long winters capped by snow in April do to the psyche?

Hi Bob, No. It is a reaction to the crowds who object to anything at all on principle.
In this case, discussing driverless trains with Torontonians causes an eruption of fear “What if the doors close on a passenger?”. (It happens on a daily basis in Toronto on the subways and buses and streetcars, even with drivers, guards etc, but that’s no reason to object to driverless trains on some principle).


HansV>All (reasonably) modern elevators have safeguards built-in that prevent them from moving up or down while the door is open.

Quite so. It was my musings on elevators that led me into this. Elevator door malfunctions are, as far as I know, absolutely non-existent.
I am amazed at the engineering/technology that has accomplished such a high standard that we take it for granted without a thought. To me it is a modern miracle.

HansV> There are quite a few driverless underground/metro/subway lines:

In Jacksonville FLA there are trains that are not only driver-less, but are also passenger-less. I made six trips on the SkyTrain last February, and excepting the first trip, I was the only passenger in the car.
Note to Lounge Pedant: You know quite well what I mean by “passenger-less”.

Rudi>Your reasoning seems reasonable...but now I'd like proof of your numbers.

Proof is hard to come by.
For purposes of discussion about vermicomposting of kitchen waste I’ve asked the Toronto City to provide numbers about dwellings; they are incapable of providing the data. They are worms.
Most articles about recycling nowadays quote a figure of 50% for the proportion of Toronto citizens who dwell in high-rise buildings.
Even “high rise” is poorly-defined, but three or four storeys seems to be the threshold figure .
See for example the excerpt (attached) from page 5 of “the newspaper” of the University of Toronto March 2014 vol XXXVI (http://www.thenewspaper.ca" onclick="window.open(this.href);return false;)


BobH> …a group of regulars to taunt and embarrass anyone who rude enough to cause the delay.

Sadly this is Toronto, home of the timid Canadians who are too shy to ask a person to remove their bag from a seat and will therefore stand for the whole trip, thereby blocking the passageways and doors and leading to perennial cries of “overcrowding”. The same people who don’t protest when crowds try to exit a streetcar by the front doors, instead of the rear, thereby causing the car to delay and miss yet-another-green-light with the attendant (literally!) larger crowd at the next stop, the longer delay, and the growing crowd of empty streetcars trailing behind the mother-of-all-confusion.
Torontonians are too polite for words. In a line-up, step backwards six inches and step on the toes of the person behind you, and THAT person apologises to YOU!
Gaaaaaah!


viking33> You didn't include anyone going up or down for lunchtime? Double your numbers?

Could do. It seems that about 50% of office workers DON’T have time to pack a brown-bag lunch, but DO have time to spend 15 minutes dropping down to the food court, standing in line for ten minutes (see “toes” above) and fifteen minutes getting back to the desk.
I could refine the model to take account of, say, 50% who go out for lunch, 25% who go out for coffee in the morning and in the afternoon, and then there are the legal clerks who spend so much time in transit between their desks and the cafeteria that they take eight weeks or more to make a copy of a Final Order from the Superior (hah!) Court of Canada.
But I digress …
I was looking for a first-approximation to the number of closure-events per year in Toronto.
There has to be closure


BobH> Or inter-floor trips which are quite common in office skyscrapers.

Agreed; I could fake up a percentage to account for intra-office inter-floor travel.
I’d then have to discount those who made a trip out for coffee, a trip back to a floor other than the normal floors, then a trip back to the home floor.
I’d also have to factor in those businesses that employed a mail-clerk …
Then some women’s libber would protest


DaveA> Or all of the people that live out side of the area that commute every day. So you numbers are way out of the ball park?

Hi Dave; see all the above especially the simplicity of the model.
I could argue that the resident population, say 3,000,000 is augmented by 1,000,000 who travel in from the suburbs and inflate the office elevator figures by 33%, but at this stage I was/am unwilling to fire up Excel for a first approximation.


BobH> Do we know if the set of those who live in high-rise apartments also are in the set who work in high-rise office buildings? Drawing on set theory classes of about 50 years ago, it seems that to the extent that the 2 sets overlap, the numbers grow. Given the relatively high numbers in each set, one might expect that the joint set is pretty large.
So, Chris, how would that affect your calculations and your conclusions? I ask only because there might still be some snow and I would hope that the question would distract you.

Thanks BobH. Rain Yesterday during my walk through Mt Pleasant cemetery. Sunshine today, so I’m staying inside IN CASE it rains later.
I agree that the sets overlap.
I had hoped to address the overlap in my text:-
CG> I assume a person leaves their home about once a day. High-rise dwellers would use an elevator twice a day – once out, once back. 3,000,000 elevator trips.
I assume that half of Toronto’s population is at work, and about a half of them work in a high-rise office. A person goes to work once a day. Office workers would use an elevator twice a day – once up to the office, once out. 1,500,000 workers, 750,000 in high-rise offices twice a day, so 1,500,000 elevator trips.
That would mean of the order of 4,500,000 elevator trips per day in Toronto.

Now it has been about 50 years since I “did” set theory, so I may be in error.

[viking33]

Chris,
I have tried to REDUCE the number of posts to Eileen’s Lounge by accumulating my responses into one post.
-------------------------------------------
Go back to answering individual posts. Much too long a post to keep my attention.

[Rudi]

Much too long a post to keep my attention.

You are only supposed to attentively read the section under your name

[Rudi]

Thanks to all who had replied by the time I took a snapshot of the thread back on the 15th. I have tried to REDUCE the number of posts to Eileen’s Lounge by accumulating my responses into one post.

Chris.....one HECK of a summary....you deserve a and some

[BobH]

Howdy, Chris!

Might I get back to you on vermiculture some time? I've started a compost pile and built several table top gardens to use the Mel Bartholomew Square Foot Gardening method. As I get more involved, I think I want to try vermiculture to get the castings to add to the mix and maybe even to the compost mix.

[HansV]

You're opening a can of worms!

[ChrisGreaves]

You are only supposed to attentively read the section under your name

I hate to disagree with you, Rudi but I thought, in making that long-winded post, that anyone interested in the thread would end up reading all my eight(?) individual responses anyway.
I'd ha' thought a digest was, well, easier to digest wholesale rather than piecemeal, to speak mixed-metaphorically.
I think.

[ChrisGreaves]

Chris.....one HECK of a summary....you deserve a and some

In all seriousness, I File,savedAs the web page and mused over it for three days. My response was more in the order of a single response to the accumulated wisdom of The Lounge. I was responding to the collective consciousness.

[PaulB]

... the accumulated wisdom of The Lounge. I was responding to the collective consciousness.

Resistance is futile. You will be assimilated.

[Rudi]

Resistance is futile. You will be assimilated.

Says Dr. Who!

[NotQuite]

Resistance is futile. You will be assimilated.

Says Dr. Who!

I believe it was The Borg !!