# An Impossibly Enormous Calculation

## Main Question or Discussion Point

Is your curiosity piqued? Good. This is an open question and one that cannot be answered, but appoximated at best. The question is, what is the sum total of Humankind's energy consumption throughout all of Humankind's historical existence? Okay, so now you see the enormous and virtually impossibility of calculating such a sum, given that said energy is used in so many different manners in society, and after all, our historical records are themselves subject to great debate and inaccuracy. For that reason, I think its best to treat this question as an interesting exercise, rather than a realistically calculatable scientific endeavor. I will try to break this problem down into what I think are the components of its sum.

My defintion of how humankind consumes energy is this: Any energy used to sustain human life or build/maintain civilization. (I am open to other defintions)

How humankind consumes energy... A list of some...

1) Human body energy consumption (food) - Nutritionists will tell you that the average caloric consumption of an average human is 2000 kCals/ day. Of course, this number could vary greatly throughout history as famines, smaller humans, diets and a plethora of other factors influence this average. Some people even today, in the less fortunate countries are malnurished and receive less that 1000 kCals/day, while others in the wealthy nations consume in excess of 3000 kCals/day. So, if we don't nitpick every detail, I think a historical average of 2000 kCals/day is fine for a ballpark estimate of an average human's food energy consumption.

2) Work animals - This is certainly open to debate, but I think its important to also include the contributions of work animals in our calculation of human energy consumption. After all, using an oxen to til your field, or a horse to transport your carriage is a means by which humans also use energy, albeit not internally generated (but neither is electricity for that matter, which we will get to). So we can thus include work animals in our calculation of humankind's energy consumption.

3) Electriciy - Since the day Edison invented electricity that we could readily use and distribute, we have been using electric power for everything from lightbulbs to computers. World (electrical) power consumption has been well recorded in the last 50 years and certainly contributes a large amount of humankind's energy consumption.

4) Oil, gas, wood, etc. - Cleary these 3 fuel sources and many others have contributed and still contribute to humankind's energy consumption. Oil fuels our cars, gas our homes, and wood our fires. I think this simplification is of how we use these fuels is fine for our estimation and the data for oil and gas consumption is fairly well logged during recent times. Of course, its impossible to know how many chords of wood were burned during history to fuel our fires and cook our roasts, but we certainly can imagine it has been alot.

I am sure to have missed some other ways that human's have consumed power and leave them open for you to help fill in. Of course any estimate we would make on the historical aggregate of humankind's energy consumption is bound to be very inaccurate, yet still I think it is an interesting question to ponder and if we could get even within 3 orders of magnitude I think it would be a meritorious feat.

Hopefully, you will help fill in some of the details so we can together try to tackle this question in a meaningful scientific way. Citing data is our best hope. Such as world electricity consumption data, world caloric consumption, etc. I think the best unit we should use as our base unit is the Watt(W). We can readily converts kCals and other energy units into the power unit of the Watt when we are ready to.

My end goal would be having an estimate of humankind's historical aggregate power consumption in a fun an accessible phrase, like: Humankind has used 1,000,000 TerraWatts throughout history. Then we could make fun analogies like the Universe could have kept 100 light bulbs on for 10 billion years, or it could have let humanity use the power instead (this is an example and was not calculated correctly, but you get the point).

So lets have some fun and tackle this question together!

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russ_watters
Mentor
How accurate do you want the calculation to be? Since until quite recently, our energy consumption was rising geometrically, just calculating our consumption for the past 100 years will get you within an order of magnitude of the real answer.

Here's a start: http://en.wikipedia.org/wiki/Energy_consumption

World energy consumption in 2005 was 5E20 J, which is a rate of 15 TW or 130,000 TWh/yr. I've never figured the people themselves before, but 6 billion people at about 70W apiece is about 1 TW. Energy consumption in 1900 was at a rate of 0.7 TW.

That would probably put mankind's total consumption over its history on the order of 10 million terawatt-hours (your guess of 1 million wasn't bad).

Just to make sure you got it (you said it wrong), terawatts is a rate of energy consumption (power), not energy. What you're looking for is terawatt-hours of energy.

Sorry if the question was less difficult than you hoped... :tongue2:

How accurate do you want the calculation to be? Since until quite recently, our energy consumption was rising geometrically, just calculating our consumption for the past 100 years will get you within an order of magnitude of the real answer.
You have 10000 posts, so maybe I am wrong, but how does something rise geometrically?

World energy consumption in 2005 was 5E20 J, which is a rate of 15 TW or 130,000 TWh/yr. I've never figured the people themselves before, but 6 billion people at about 70W apiece is about 1 TW. Energy consumption in 1900 was at a rate of 0.7 TW.
You say energy consumption in 2005 was 15 TW and in 1900 it was 0.7 TW. I will estimate an average of 3 TW for this period, giving us 300 TW, or 2,600,000 TWh/yr.

As for world population, this is very difficult to estimate. 50,000 years ago there may have been 0.1 million people, 2,000 years ago there may have been 10 million people, 100 years ago there may have been 500 million people, today there are 6.7 billion. From this, I will extrapolate a guess on the average # of people over the ~50,000 years of humankind (VERY OPEN TO INTERPRETATION).

today - 1900

6.7 billion -to- 500 million = 2billion (rough average of humans alive in a single year between 1900 to present day)

2 billion x ~100 years = 200 billion people.

1900 - 1 A.D.

500 million -to- 10 million = 50 million (roughly)

50 million x 2000 years = 100 billion people

1 A.D. - 48,000 B.C.

10 million -to- 0.1 million = 0.5 million (roughly)

0.5 million x ~50,000 years - 25 billion people

ADDING THE PEOPLE TOGETHER, we get:

200 billion + 100 billion + 25 billion = 325 billion people have lived during mankind's existence. (extremely rough of course, but logically sound)

You said human's use 70 W, this is not calculated correctly. I specifically said to use the number of 2000kCal/day as a reference, which gives us ~96 W, which is pretty far off from the 70 W you said. So we multiply 96 W x the 325 billion people and get ~30 TW total biological consumption.

Adding 30TW (biological consumption) to 300TW (electrical consumption), we get: 330TW total.

That would probably put mankind's total consumption over its history on the order of 10 million terawatt-hours (your guess of 1 million wasn't bad).

Just to make sure you got it (you said it wrong), terawatts is a rate of energy consumption (power), not energy. What you're looking for is terawatt-hours of energy.
Correct.

Sorry if the question was less difficult than you hoped... :tongue2:
Or more than you thought? :tongue2:

Danger
Gold Member
The answer is 3. Case closed.

The answer is 3. Case closed.

Borek
Mentor
You have 10000 posts, so maybe I am wrong, but how does something rise geometrically?
http://en.wikipedia.org/wiki/Geometric_series

Note that if you assume geometric series you don't need any other assumption to calculate amount of electric energy consumed in the given period. Specifically you don't have to

I will estimate an average of 3 TW for this period
as this average can be easily calculated.

Same holds for the number of people.

2 billion x ~100 years = 200 billion people.
Do I understand you correctly that your approach tels us that there were around 50 billions people living on the Earth in 21st Century? 7 years at almost 7 billions?

Or do you mean peopleyears?

And am I right reading from your post that you assume 96 W used per YEAR per one person?

I am with russ_watters here - if you assume geometric increase in population and energy consumption (and data we have seem to support this idea) you just have to find out a0 and r and use general formula for the sum. Not that hard.

But for the people energy consumption I would go easier route.

http://en.wikipedia.org/wiki/Earth_Population#Number_of_humans_who_have_ever_lived

Assuming there were around 100 billions of people living on the Earth all the time, assuming average life span of 30 years (open to debate), assuming 2000 kcal per day (open to debate), assuming 365 days per year, assuming 4.128 J/cal gives 9.2*1021 J or 2.5 EWh. Around 6 orders of magnitude more than your estimates. Looks to me like you forgot days per year and k in kcal.

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Danger
Gold Member
I didn't read it the first time; that's why it was so easy to answer. :tongue:
(Maybe I should have put a smilie after my post, but I thought that is was so obviously a joke that it wasn't necessary.)

Thank you Borek. You have cleared up some of my mistakes and have breathed some nice insights into this post. So what do you estimate the total is in Watts?

Danger, what was obviously a joke? Answering a question before reading it? :)

Danger
Gold Member
Danger, what was obviously a joke? Answering a question before reading it? :)
Yup, since it wasn't anything even vaguely resembling a real answer.

Borek
Mentor
Thank you Borek. You have cleared up some of my mistakes and have breathed some nice insights into this post. So what do you estimate the total is in Watts?
You don't measure energy consumption in Watts. My estimate of human biological energy consumption was given - 2.5EWh.

How is that equation going? I'm going to eat lots of food for the next couple of weeks just to screw up your calculation!!

Yup, since it wasn't anything even vaguely resembling a real answer.
YOu are a strange breed mr. danger, very strange indeed.

Danger
Gold Member
YOu are a strange breed mr. danger, very strange indeed.
Thank you. (You're just realizing this now?)
It was a facetious response to the title of your thread, not its contents. '3' was the simplest answer that I could think of to an impossibly enormous calculation.

Borek
Mentor
Borek
Mentor
'3' was the simplest answer that I could think of to an impossibly enormous calculation.
42 is a better known universal answer to the much more complicated question

Thank you. (You're just realizing this now?)
It was a facetious response to the title of your thread, not its contents. '3' was the simplest answer that I could think of to an impossibly enormous calculation.
I understood immediately you answer (as, I'm sure, most of the others) and I found it funny. I probably would have answered in the same way (but with another number ).

Danger
Gold Member
42 is a better known universal answer to the much more complicated question
Oh, well, of course we all know that's the real answer... but there are copyright issues.

Borek
Mentor
Oh, well, of course we all know that's the real answer... but there are copyright issues.

Danger
Gold Member
Well, not copyright so much as it not being original. I'm sure that the number itself falls under 'fair usage'.

[/HIJACK]

Oh, well, of course we all know that's the real answer... but there are copyright issues.
But with a proper transformation of units, the answer is exactly the same.

Danger
Gold Member
:rofl:

Thank you. (You're just realizing this now?)
It was a facetious response to the title of your thread, not its contents. '3' was the simplest answer that I could think of to an impossibly enormous calculation.
Don't worry, Danger.

You got a chuckle out of me.

Where did Russ go? It seems he backed down from my rebuttal as it outmatched his. Don't be a coward, I love being proved wrong.