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The Arithmetic of Growth: Methods of Calculation
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Cat: SCI |
Albert A. Bartlett |
11817u/18211r |
Title
The Arithmetic of Growth: Methods of Calculation
成長の算術的計算
Index
KeySus
Law of Sustainability; Smart Growth; 2^63 grains; Doubling time; Bacteria; Exponential expiration time; 10,000-year consumption;
Why?
- The author is a Professor emeritus, Physics, University of Colorado, whose makes stinging warning to current trend of exponential growth of consumption of such as population, non-renewable resources, etc. is worth to listening.
- We must seriously reconsider 'sustainability of our civilization', otherwise which would be crushed up by the burden of uncontrolled growth and our myopic mindset.
- The Fukushima disaster of nuclear plants in Japan occurred 2011.3.11 could be a turning point for us to reconsider what would be sustainability, or sustained availability, of human history.
- "sustainable growth" is an oxymoron.
- "Innumeracy" is the mathematical equivalent of illiteracy.
- Re: http://www.albartlett.org/index.html
- 著者はコロラド大学の物理学の名誉教授で、人口や再生不能資源などの幾何級数的な消費率の増加傾向に対し痛烈にな警告している。
- 我々は、我々の文明の持続可能性について真剣に再考すべきで、そうでないと制御不能の成長と近視眼的な精神の重圧でそれは崩壊してしまう。
- 2011.3.11の福島原発の悲劇は人類の歴史の持続可能性、即ち、いつまでも持続できることを再考する転換点となろう。
- "持続可能の成長"とは矛盾表現である。
- 数字音痴は、数学的には非識字と同意語である。
Key
phrase
Remarks
>Top
0. Disastrous dogma:
- We must educate people to the critical urgency of abandoning our religious belief in the disastrous dogma that "growth is good," that "bigger is better," that "we must grow or we will stagnate," etc., etc.
- We must realize that growth is but an adolescent phase of life which stops when physical maturity is reached. If growth continues in the period of maturity it is called obesity or cancer.
- Prescribing growth as the cure for the energy crisis has all the logic of prescribing increasing quantities of food as a remedy for obesity.
- >Top Laws of Sustainability (Bartlett 1994):
- Population growth and/or growth in the rates of consumption of resources cannot be sustained.
- The larger the population of a society and/or the larger its rates of consumption of resources, the more difficult it will be transform the society to a condition of sustainability.
- "Flying leap syndrome":
a person leaps from the top of a very high building. The free-fall is exhilarating. After each of the first few seconds of free-fall, the person concludes that all is well, and soon reached the logical conclusion that things will be alright forever.
- A spherical earth is finite, but a flat earth can be infinite in depth and lateral extent.
0.
破滅的なドグマ:
- "成長は善","大きいことは善","成長なくば停滞"などの信念は捨て去るべき。
- 成長とは、青年期だけであって、成熟すれば成長は止まる。もし成熟後も成長するならば、それは肥満か癌である。
- エネルギー危機の対策に成長を処方するなら、それは肥満の処方に食事量を増やせというようなものである。
- 持続可能性の法則:
- 人口増加 and/or 資源の消費率増加とは持続できない。
- 社会の人口が大きいほど、and/or 資源の消費率増加が大きいほど、その社会が持続可能な条件を達成することは一層困難になる。
- 飛び降り症候群:
人が高いビルの屋上から飛び降りたとする。自由落下は快活である。最初の数秒間は、その人は自分の結論が正しかったことを実感する。しかしまもなく物事の永遠の正しい論理的結末を迎えることになる。
- 丸い地球は有限である。但し、地球が平坦であれば、深さと面積の広がりは無限となる。
>Top
1. Lifetime of resources in years:
- Lifetimes of non-renewable resources for different rates of growth of consumption. (lifetimes in years)
Ann.Growth
Lifetime of resource in years
0%
10
30
100
300
1000
3000
10000
1%
9.5
26
69
139
240
343
462
2%
9.1
24
55
97
152
206
265
3%
8.7
21
46
77
115
150
190
4%
8.4
20
40
64
93
120
150
5%
8.1
18
36
56
79
100
124
6%
7.8
17
32
49
69
87
107
7%
7.6
16
30
44
61
77
94
8%
7.3
15
28
40
55
69
84
9%
7.1
15
26
37
50
62
76
10%
6.9
14
24
34
46
57
69
1.
資源寿命 (年):
- 消費率の変化による非再生資源の寿命（年): <左図>
- 例1: 資源寿命が300年もつ資源は、消費率が年6%の伸びの場合の寿命は49年となる。
- 例2: 消費率が年5%の伸びで18年の寿命の資源は、消費率が0%なら30年もつ。
- 例3: 消費率8%伸びで55年の寿命の資源は、消費率が3%伸びなら115年もつ。
>Top 2. Pseudo solutions:
- Growth management - smart growth:
- They don't save the environment. Whether the growth is smart or dumb, the growth destroys the environment.
- It's like buying a ticket on the Titanic. You can be smart and go first class, or you can be dumb and go steerage. In both cases, the result is the same. But given the choice, most people would go first class.
- Creating jobs:
- If the equilibrium unemployment rate is 5%, and a new factory moves into town, the hiring at the new factory may lower the unemployment rate to 4%. But then new people move into the town to restore the unemployment rate to the equilibrium value of 5%. But this is 5% of a larger population, so the number of unemployed people has increased.
- Instead of building exclusionary walls, you drive up real estate prices to a very high level so that people can't afford to move into the community.
- >Top Building highways:
- The fallacy arises because of the fact that the construction of the new highways generates new traffic, not previously present, to fill the new highways to capacity.
- Regional planning:
- Regional planning dilutes democracy. A citizen participating in public affairs has five times the impact in his city of 20,000 as he would have in a region of 100,000 people.
- The regional "solutions" are usually designed to accommodate past and predicted growth and hence they foster and encourage more growth rather than limiting it. Regional solutions enlarge the problems rather than solving them.
- Population growth destroys democracy: Isaac Asimov responded:
- Bathroom metaphor; if 2 people live in an apartment and there are two bathrooms. Everyone believes in freedom of the bathroom.
- If 20 people in the apartment with 2 bathrooms, no matter how much every person believes in freedom of the bathroom, there is no such thing.
- In the same way, democracy, human dignity, convenience and decency cannot survive over population.
- The more people there are, the less one person matters.
- Smart growth:
- "Smart growth" was the magic key to the achievement of sustainability. A central ingredient in smart growth is regional planning; regional planning encourages more population growth, and population growth is unsustainable. It is thus clear that smart growth can't solve the problems.
- Smart growth destroys the environment.
- Dumb growth destroys the environment.
2.
欺瞞的な解決:
- 成長の管理 - スマートな成長:
- いずれも環境問題の解決にはならない。
- それはタイタニック号の切符を、スマートに一等船室に買うか、やぼったく三等船室に買うかの違いである。いずれでも結末は同じである。しかし許されるなら多くに人々は一等船室に乗りたがるだろうが。
- 雇用増大:
- もし失業率が5%で均衡していて、町に新工場が建設され、新規雇用で失業率が4%に下がる。すると新たな人々がその町に流入し、また元の失業率5%に5%戻る。但し、これは人口が増加した結果の5%なので、失業者数は増加する。
- 人口流入を排除的する壁を作る代わりに、不動産価格が非常に高くなり、その町への人口流入が抑えられることになる。
- 高速道路建設:
- 新たな高速道路の建設によって、それ以前にはなかった新たなトラフィックが増加して、新規の高速道路の容量を埋め尽くす。
- 地域開発計画:
- 地域開発によって民主主義が希薄化する。人口10万人の地域が、人口2万人の町では、一人の市民参加は5倍のインパクトを持つ。
- 地域ソリューションは、通常は、過去に想定した成長モデルに沿っており、成長を抑制するのではなく、更なる成長を推し進めるものである。地域ソリューションズは問題を解決するというより問題を拡大する。
- スマートな成長:
- スマートな成長は持続性達成のためのキーワードとなっている。その中心概念は地域計画である。即ち、地域計画は一層の人口増加を図っており、人口増加は持続できない。従って、スマートな成長では問題は解決できない。
- スマートな成長は環境を破壊する。
- バカな成長も環境を破壊する。
>Top 3. The game of chess:
-
Sq. numbers
Grains on the sq.
Total grains this far
1
1
1
2
2
3
3
4
7
4
8
15
5
16
31
6
32
63
64
$2^{63}$
$2^{64}-1$
As
a reward for the invention a mathematician asked the King to place 1 grain of wheat on the first square of the chess board, double this and put 2 grains on the second square, and continue this way, putting on each square twice the number of grains that were on the preceding square.
- >Top On the last square one will place $2^{63}$ grains, which is approximately 500 times the 1976 annual worldwide harvest of wheat. This amount is probably larger than all the wheat that has been harvested by humans in the history.
- the increase in any doubling is approximately equal to the sum of all the preceding growth!
- >Top On 4/18/1977 President Carter told, "in each of these decades (1950s and 60s), more oil was consumed that in all of man's previous history combined."
- Doubling time is 10 yr. The growth rate is 70/10 = 7% /yr.
- The world population in 1975 was 4B, and it was growing at the rate of 1.9% /yr, which would double in 36 yr. The population would grow to a density of 1 person/m2 on land surface of the earth in 550yr.
- Compound interest on an account in the savings bank causes the account balance to grow exponentially. 5% compound rate will grow in 500 yr to $72B.
- One can see that our long national history of population growth and of growth in our per-capita consumption of resources lie at the heart of our energy problem.
3. チェス・ゲーム:
- ご褒美として、チェス盤の最初のマス目に１粒の小麦粒を、２番目にその倍の２粒をというようにもらうとすると、64番目のマス目には$2^{63}$個の小麦粒となる。
- これは1976年の世界の小麦生産量の500倍となる。これは、歴史上の小麦の総生産量より多くなるという逸話。
- 2倍で増加する量は、それまでの合計量にほぼ匹敵。
- 1977/4/18カーター大統領曰く、"1950年代、60年代は、それまでの人類の全石油消費量よりも多かった。"
- これは10年間で倍増。増加率は年7%となる。
- 1975年の世界人口は40億人。増加率は年1.9%で、36年毎に倍増し、550年後には地表面に1人/平米の人口密度となる。
- 5%複利の預金の場合、500年後には$72Bとなる。
- エネルギー問題の確信は、人口が増加していること、かつ一人当たりの消費量が増加していることにある。
>Top 4. Exponential growth in a finite environment:
-
Time
Full
Empty
11:54
1/64 (1.5%)
63/64
11:55
1/32 (3%)
31/32
11:56
1/16 (6%)
15/16
11:57
1/8 (12%)
7/8
11:58
1/4 (25%)
3/4
11:59
1/2 (50%)
1/2
12:00
full (100%)
0%
>Top The last minutes in the bottle:
- Bacteria grow by division so that 1 bacterium becomes 2, the 2 divide to give 4, etc.
- The number of bacteria grows exponentially with a doubling time of 1 minute.
- One bacterium is put in a bottle at 11:00 am and it is observed that the bottle is full of bacteria at 12:00.
- Q1: When was the bottle half-full? Answer: 11:59.
- Q2: At what time would a bacterium in the bottle first realize that they were running out of space? Answer: Probably 11:57, when the bottle is only 12% filled and 88% open space.
-
11:58
Bottle #1 is a quarter full
11:59
Bottle #1 is half full
12:00
Bottle #1 is full
12:01
Bottle #1/#2 are full
12:02
Bottle #1/#2/#3/#4 are all full
Q3: at 11:59, bacteria look offshore on the outer shelf and discovered three new empty bottle. The discovery quadruples the total space resource known to the bacteria. How long can the bacterial growth continue if the total space resources are quadrupled?
- Answer: Quadrupling the resource extend the life of bacteria by only two doubling times; 12:02
4. 有限の環境での指数関数的増加:
- 瓶の中の最後の時間
- バクテリアが１分ごとに２倍に分裂するとする。
- バクテリアの数は１分毎に倍増する。
- 11:00に１匹のバクテリアを瓶に入れて観察する。12:00には瓶はバクテリアで満杯となるとする。
- Q1: 瓶の半分が満たされるのはいつか？ A: 11:59
- Q2: 瓶のバクテリアは、いつ空き空間が不足することに気付くか？ Ａ：多分11:57頃。その時、瓶の12%が満たされ、空き空間は88%となる。
- Q3: 11:59にバクテリアは外界を探索し、新たな空き瓶を３個発見した。この発見は利用空間は4倍となった。ではこれによってバクテリアの増加はいつまで期待できるか？
- A：利用空間が4倍になったとしても、バクテリアの命は倍増時間の２倍だけ延長される。即ち、12:02
>Top 5. How long will US oil fuels last?
- Dr. M. King Hubert estimated how long US oil resources will last.
- US crude oil (48 states):
- Ultimate total production: 190 B barrels
- Produced to 1972: 96.6 B barrels
- % of ultimate total production produced to 1972: 50.8%
- Annual production rate 1970: 3.29 B barrels
- Note that the rate of US domestic crude oil production increased 8.27%/yr exponentially from 1970 to 1930, with a doubling time of 8.4 yr. If this growth rate of production stopped and was held constant at 1970 rate, the remaining US oil would last only (190-96.6)/3.29 = 28 yr.
5. ,米国の石油資源はいつまで保つか:
- 米国
石油生産
- 究極の全生産量: 190B bbl
- 1972までの生産量: 96.6 B bbl
- 年間生産量(1970): 3.29 B bbl
- 米国国内石油生産量増加: 8.27%/y
- 生産倍増までの年数: 8.4y
- 残存石油量(1970レベルでの生産と前提): 28y
- >Top
% annual growth
US 48 states
US 48 states + Alaska
US 48states +Alaska +Oil shale
World
remaining oil
World oil + oil shale
World oil + 4x oil shale
0%
28.4
31.4
62.8
101.0
113.0
147.0
1%
25.0
27.3
48.8
69.9
75.4
90.3
2%
22.5
24.4
40.7
55.3
59.0
68.5
3%
20.5
22.1
35.3
46.5
49.2
56.2
4%
19.0
20.4
31.4
40.5
42.6
48.2
5%
17.7
18.9
28.4
36.0
37.8
42.4
6%
16.6
17.7
26.0
29.8
31.2
34.6
7%
15.6
16.6
24.1
27.6
28.8
31.8
8%
14.8
15.7
22.4
25.7
26.8
29.5
9%
14.1
14.9
21.1
25.7
26.8
29.5
10%
13.4
14.2
19.9
24.1
25.1
27.5
Exponential expiration time (EET) in years of various estimates of US oil reserves for different rates of growth of annual production.
- US annual production rate is 3.29 B barrels/yr.
- World annual production rate is 16.7 B barrels/yr.
- "What will life be like without petroleum?"
- Modern agriculture is based on oil-powered machinery and on oil-based fertilizers. Modern agriculture is the use of land to convert petroleum into food.
- As a result of overpopulation and resource limitations, the world is fast losing its capacity to feed itself.
- More alarming is the fact that while the world population doubled its numbers in about 30 yrs the world doubled its energy consumption within the past decade. Moreover, the use of energy in food production has been increasing faster than its use in may other sectors of the economy.
- Absolute upper limit of crude oil:
The volume of petroleum in the earth cannot be larger than the volume of the earth. The volume of the earth is 6.81 x 10^21 barrels, which would last for 4.1 x 10^11 yr if the 1970 rate of consumption of oil held constant with no growth. If the rate of consumption of petroleum continued in 7.04%/yr, this earth full of oil will last only 342 yr!
- Coal resource:
- Conclusion:
If we want coal to last until US's tricentennial (2076). the rate of consumption will have to be held below 3%.
- If we want coal to last 200 yrs, the rate of growth of annual consumption will have to be held below 1%/yr.
- >Top 10,000-year consumption:
The epoch of the worlds's use of its fossil fuels is shown on a time scale of human history form 5000 yrs ago to 5000 yrs in the future. The vertical axis is the rate of consumption of fossil fuiels measured in units of 10^14 kWh/yrs.
(Redrawn from Hubbert's Fig.)
- 生産比率毎の枯渇予想年度<左表>
- 前提：
- 米国年間生産量：： 3.29 B barrels/yr
- 世界年間石油生産量：16.7 B barrel/yr
- 石油が枯渇するとどのような生活になるか
- 近代農業は、石油によって支えられている (農機具＋化学肥料)
- 世界の過剰人口と資源の限界によって、世界は食糧不足になる。
- 世界人口は30年毎に倍増し、世界の石油消費は10年毎に倍増してきた。さらに、食料生産におけるエネルギー消費は他のどの産業よりも大きい。
- 究極の上限:
地球全体が石油で出来ているとすると、その量は、6.81 x 10^21 barrel。これを1970年の石油消費増加率で計算すると、4.1 x 10^11年もつ。石油消費が7.04%/yrで増加すると、342年しかもたない。
- 石炭の場合:
米国建国300年祭(2076)まで保たせるためには、石炭消費率の伸びを年3%以下にする必要ある。
- あと200年もたせるためには石炭消費率の伸びは1%以下にする必要ある。
- 歴史上の化石燃料消費 (5千年前から5千年先の未来まで)：現在が如何に異常なエネルギー浪費の時代があることか！
Comment
- >Top This thesis is a 21C version of "The Limits to Growth" 1972, based on the report of The Club of Rome.
- The issue is getting clearer in the beginning of 21C.
- この論文は、ローマクラブの報告に基づいた"成長の限界" (1972)の21世紀版である。
- この論点は、21世紀になってますます明らかになってきた。
Title |
The Arithmetic of Growth: Methods of Calculation |
成長の算術的計算 |
|---|---|---|
Index |
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KeySus |
Law of Sustainability; Smart Growth; 2^63 grains; Doubling time; Bacteria; Exponential expiration time; 10,000-year consumption; |
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Why? |
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Key phrase |
Remarks |
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>Top 0. Disastrous dogma:
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0. 破滅的なドグマ:
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>Top 1. Lifetime of resources in years:
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1. 資源寿命 (年):
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>Top 2. Pseudo solutions:
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2. 欺瞞的な解決:
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>Top 3. The game of chess:
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3. チェス・ゲーム:
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>Top 4. Exponential growth in a finite environment:
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4. 有限の環境での指数関数的増加:
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>Top 5. How long will US oil fuels last?
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5. ,米国の石油資源はいつまで保つか:
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Comment |
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