Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Exponen'al growth and decay
Tell-‐tale sign of exponen'al growth – slow ini'al growth followed by rapid increase (we will quan'fy it in terms of marginal changes)
Tell-‐tale sign of exponen'al decay – rapid decrease followed by a slow-‐down in the rate of decrease
Stats Canada 2011 census data – need to learn more to be able to make a reliable predic'on
Hypoxic areas in oceans
Hypoxic (low-‐oxygen) areas in the world's oceans and large lakes (“dead zones”), caused by
“excessive nutrient pollu'on from human ac'vi'es coupled with other factors that deplete the oxygen required to support most marine life in boLom and near-‐boLom water.” (NOAA = Na'onal Oceanic and Atmospheric Administra'on)
read more (op'onal): hLps://oceanservice.noaa.gov/facts/deadzone.html
Lake Erie, Lower St. Lawrence Estuary
Number of dead zones
Diaz and Rosenberg, 2008. Science 321:926-‐929
hLps://scripps.ucsd.edu/programs/keelingcurve/
hLp://www.newsindata.com/home/2017/1/19/ne\lix-‐surges-‐in-‐2016-‐comcastnot-‐so-‐much
But … cannot con'nue forever (there is always limit to the growth)
One possibility … logis'c growth
the value at the 'pping point = ½ of the carrying capacity
'pping point, inflec'on
(red=number of infected; black=number of deaths)
Exponen'al curves in describing infec'ous diseases (Ebola)
These paLerns cannot con'nue forever (there is always limits to the growth)
op'onal: hLps://www.ny'mes.com/2020/02/29/health/coronavirus-‐flu.html?utm_source=pocket-‐newtab
Comparing seasonal flu and coronavirus infec'ons for poli'cal (and other non-‐medical) reasons is dangerous, oden unethical and does not help
How do we compare, for medical/research purposes?
What are the most important parameters?
Of the people infected, how many will die?
How easy/difficult is it for the virus to spread?
Of the people infected, how many will die?
Fatality rate/death rate
How easy/difficult is it for the virus to spread?
Reproduc'on number = how many non-‐infected people, on average, are infected due to a contact with an infected person
Note: Percent of what?
This slide and the previous one: it’s hard to precisely define the base rate (i.e., what is it the percent of)
To compare: the worst seasonal flu … R_0 is 1.3
What else is important?
Can we verify this?
How it spreads?
Tipping point?
The power of visuals …
Power of visuals … This is Nutella …
Power of visuals … This is the same Nutella …
Quan'fying exponen'al growth and decay
half-life = time needed for a quantity to decay to one half of its original amount
doubling time = time needed for a quantity to double, i.e., grow to twice its original amount
If a quan'ty grows/decays (Rate in percent)
Rule of 70: half-‐life, and doubling 'me up to 5% rate
Rule of 72: doubling 'me 5% or larger rate of increase
Dynamics of half-‐lives
Half lives of drugs
Note: alcohol does not decay exponen'ally
Why do we care about half-life?
sleeping pills: Zaleplon … 1 hour Doxylamine … 10 hours
pain/inflammation medications: Aleve … 12 hours Advil … 2 hours
What’s the difference?
Why do we care about half-life?
sleeping pills: Zaleplon … 1 hour Doxylamine … 10 hours
pain/inflammation medications: Aleve … 12 hours Advil … 2 hours
What’s the difference? (balance benefits vs. side-effects)
How much caffeine is there in a cup of coffee?
Ballpark: 240 mg of caffeine per cup
Health Canada standard for adults: 400 mg of caffeine per day
Half-‐life of caffeine … 4-‐5 hours
Amount of caffeine in a cup of coffee varies considerably depending on the coffee beans used and the size of the drink. For example …
Coffee …
source: hLp://www.caffeineinformer.com/'m-‐hortons-‐coffee-‐caffeine-‐content hLp://www.caffeineinformer.com/the-‐complete-‐guide-‐to-‐starbucks-‐caffeine
WARNING -‐ Caffeine can kill!
Caffeine powder is extremely toxic
white powder (legal for now) sold as a dietary supplement; usually taken before a workout, as energy booster, or to control weight gain
a heap-‐full teaspoon of caffeine powder could contain 3200 mg of caffeine! so 1/16th of a teaspoon is roughly 1 cup of coffee
Steady growth of 7% per year means that the doubling 'me is roughly 10 years
the rule of 70 gives 70/7 =10 years The rule of 72 gives 72/7 = 10.3 years
Examples of quan''es doubling in ten years
hLp://www.telegraph.co.uk/educa'on/universityeduca'on/9664927/Cost-‐of-‐university-‐accommoda'on-‐doubles-‐in-‐10-‐years.html
hLp://www.stats.govt.nz/browse_for_stats/snapshots-‐of-‐nz/yearbook/people/popula'on/grown.aspx
hLp://www.bbc.co.uk/newsround/37294729
hLp://www.cbc.ca/news/canada/saskatchewan/saskatchewan-‐diabetes-‐doubles-‐1.3524509
hLps://nccnews.expressions.syr.edu/2016/09/21/digital-‐ny-‐student-‐loan-‐debt-‐doubles-‐in-‐10-‐years/
Visualizing exponen'al growth
1+ 2 + 22 + 23 ++ 2n−1 = 2n −1
Geometric sequence (case: doubling)
The sum of all doublings for the first doubling to some doubling
Next doubling minus 1
=
1+ 2 + 4 = 8 −1= 7
1+ 2 + 22 + 23 = 24 −1= 15
1+ 2 + 22 + 23 + 24 = 25 −1= 31
Message:
the last doubling interval generates an amount which is larger than the total of all previous amounts
Doubling 'mes and reserves
Oil: in 1950s, 1960s, doubling 'me was about 10 years; now doubling 'me is longer; projected reserves will last 30-‐40 more years under present consump'on paLerns
Coal: doubling 'me about 35 years, reserves will last for about 150 years; if increased by 5% per year, reserves will last for 45 years
Natural gas: 100-‐250 years (lot less ader coal and oil are exhausted)
Doubling 'mes
Need for electricity: in 1990s it was 12 years; slowing down, but might increase (electric cars)
Freshwater withdrawals: in 2000s it was 32 years; slowing down as climate changes
Steady growth in limited environments
We start using a resource at 11am
Doubling 3me = 1 minute
It is now 11:55am
55 doubling 3mes elapsed
11:55
We have exhausted just 3.1% of our resource
Popula3on has reached 3.1% of its carrying capacity
11:56
We have exhausted just 6.2% of our resource
Popula3on has reached 6.2% of its carrying capacity
11:57
We have exhausted 12.5% of our resource
Popula3on has reached 12.5% of its carrying capacity
11:58
We have exhausted 25% of our resource
Popula3on has reached 25% of its carrying capacity
11:59
We have exhausted 50% of our resource
Popula3on has reached 50% of its carrying capacity
12:00
We have exhausted 100% of our resource
Popula3on has reached 100% of its carrying capacity
12:00 no problem – we discovered three new planets
12:01
12:02
Important ques'on:
When do we realize that we need to take ac'on? When is it too late?
Long term?
Popula'on in the world is currently growing at a rate of around 1.14% per year.
The average popula'on change is currently es'mated at around 80 million per year.
Annual growth rate reached its peak in the late 1960s, when it was at 2% and above.
Historic and projected yearly growth rates
fast enough?
Rate of increase Doubling 'me (rule of 70)
1 % 70 years
1.14 % 61.4 years 1.2 % 58.3
1.5 % 46.5 1.8 % 38.95 2 % 35
so each person living for 61.4 years witnesses the World popula'on doubling
Beyond absolute maximum:
Total land mass of Earth is 148,939,063 km2
In 14 to 15 doublings (880-‐921 years), the popula'on will increase by a factor of between 2^14=16,384 and 2^15=32,768
7.8 billion will increase to over 255,590 billion, i.e., about one human per square metre of land
Beyond absolute maximum
Total land mass of Earth is 148,939,063 km2 i.e., (round off to 150) 150,000,000,000,000 m2
255,590 billion people is 255,590,000,000,000
So more than one human per every square metre of land
United Na'ons es'mates and predic'ons
What is human popula'on’s carrying capacity?
Important message:
Building more housing, producing more food, building more highways, etc. WILL NOT WORK IN THE LONG TERM
We have to REDUCE the rates of increase of popula'on and resources; actually, in the long term, the rates of increase will have to be zero, or nega've (e.g., more people die than are born)
Popula'on increase
Large families Motherhood
Medicine/public health Sanita'on
Peace, law and order
Agriculture and research
Clean air
Ignorance
Popula'on decrease
Small families Contracep'on
Disease
War, violence
Famine
Pollu'on
Government control
Popula'on increase
Large families Motherhood
Medicine/public health Sanita'on
Peace, law and order
Agriculture and research
Clean air
Ignorance
Popula'on decrease
Small families Contracep'on
Disease
War, violence
Famine
Pollu'on
Government control
So, in the longer term:
In 50-‐60 years … Human popula'on will reach its carrying capacity (10, 12, 14 billion?) stop increasing, and quite possibly start decreasing.
In 120-‐150 years at best … We will run out of oil, coal and other non-‐renewable resources.
In ??? years … Securing fresh clean water will be a huge problem.
Dominant mode of living is reduc'on.
Distant future …
10,000 years from now – humanity is likely to be ex'nct (based on Carter catastrophe argument, a.k.a. Doomsday argument)
Uniform distribu'on (Human Randomness Assump'on): we could be 95% certain that we are within the last 95% of humans ever to be born.
Exponen'al regression
hLps://scrippsco2.ucsd.edu/
Keeling curve data (CO2 concentra'on)
Download data from the site ... general informa'on
Into exponen'al regression:
URL hLps://keisan.casio.com/exec/system/14059930754231 (also on 2UU3 web page)
Correla'on coefficient is almost 1!
Looks like a line, but when we graph a larger por'on of it … (next slide)
Range is too small, cannot see exponen'al well … use sodware:
Extrapolate:
CO2 = AeBx = 337.687e0.0046(time in years)
when x = 40, CO2 = 337.687e0.0046(40) = 405.91
This extrapola'on is an underes'mate:
in March 2020: 413.31 parts of CO2 per million
Calculator: to compute e0.0046(40)
SHIFT ln ( 0.0046 x 40 ) =
Exponen'al regression (data from before, where we used linear regression)
Year Average Global Temperature in Degrees C
1950 13.96
1960 13.98
1970 14.02
1980 14.21
1990 14.36
2000 14.56
Extrapolate to predict in 2010 …and compare with 14.61
enter data, as usual …
hLp://keisan.casio.com/exec/system/14059930754231
Strong posi've correla'on
Exponen'al model extrapola'on:
In 2010 ('me = 60) … 14.6181 degrees C (the actual value is 14.61)
In 2020 ('me = 70) … 14.7458 degrees C (don’t know the actual value)
In 2030 ('me = 80)… 14.8747 degrees C (increase of 1.07 degrees C over 1880)
Recent quote from scien'sts “And the 1.5 degrees C temperature "guard rail" could be exceeded in just 12 years, in 2030.”
In 2030 ('me = 80)… 14.8747 degrees C (increase of 1.0747 degrees C over 1880)
… so not 1.5 degrees C as claimed (which means that other models, or more data, were used for the 1.5 C increase predic'on)
Logarithmic scales
Comparing disasters
What are the values of data points in this graph?
logarithms replaced by true values
Linear grid consists of equally spaced lines ... logarithmic grid:
Logarithmic scale on the ver'cal axis .. why logarithmic?
seismograph
record of seismic waves
Richter scale is logarithmic scale
Lots of data – visualize! Math suggests how
What does this graph represent?
Peak break-‐up 'mes based on facebook (UK data)
Related Documents
