math 2uu3 lecture 9Hypoxicareasinoceans...

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

We have exhausted just 3.1% of our resource

Popula3on has reached 3.1% of its carrying capacity

We have exhausted just 6.2% of our resource

We have exhausted 12.5% of our resource

We have exhausted 25% of our resource

Popula3on has reached 25% of its carrying capacity

12:00 no problem – we discovered three new planets

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)

math 2uu3 lecture 9Hypoxic*areas*in*oceans*...

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math 2uu3 lecture 9Hypoxicareasinoceans...