Groping in the Dark: The Untold Side of Research


Most scientific articles obey a formula that goes like this:

1. Here is the question I asked.
2. Here is how I answered the question.
3. Here is what I found.







Here is Albert Einstein expressing the same sentiment:




The growth of large corporations is related to energy use





United States (Source)


Trends Between and Within Countries (Source)





United States (Source)


Trends Between and Within Countries (Source)


Something doesn’t add up here









United States (Source)


Trends Between Countries (Source)

What about those other institutions?



United States (Source)



Trends Between and Within Countries (Source)



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  1. Some quick thoughts on the graphs.

    1, Energy usage per capita in your graphs for a year is actually a measure of power per capita. Because the definition of Power [Watts,GW]= energy [Juels,GJ]/ time [1 year]. People might figure that out some wont.
    a. Now given that, an electrical networks have limits or average power generations and distribution capacities. Probably the same for fuel distrebutions except ships can change countries.
    b. Cumulative production would be related to energy and individual production rate (of a factory) would be proportional to power given the same or simmiler efficiencies.

    2. You also might compare levels (cumulative sum of rates, integral in calculus) wich have less noise or fluxuations. Cumulative GDP would be some what a measure of wealth. I say this because econoimics puts more emphais on rates and rates of rates and much less emphasis on levels and accumulations. Whos rich who is poor. Firm size!
    a. So, if firm size is proportional to firm accumulation maybe quite related to integral or accumulation of GDP which would be related to Energy = accumulated power usage. Sum of your “energy/year” and gdp*(corprate share) over the years. Revenue and net revenue=profit adds to the capital account in accounting! And companies reivest from profit and loans to form productive capital equipment.
    b. You could use more than 2 dimientional plots to mix and max rates, levels, and accumulations.

    3. Have you plotted directions of the paths? Paths shows the actuall individual dynamics. The points would have the dates. Gnuplot can plot arrows showing the path direction using vector capability. An other way would be to color by decade or 5 years. Or, the date lables could be inserted for every 10 or 5th year.

    4. I see you use log plots which often show relationships.

    5. You can also brake down the power or energy usage by application of that energy. If that can not be done the type of fuel might give an indication less accurately. Gasoline is more for commuting (to work) and Deisel mor for moving product and production logistics.

    6. Smaller firms probably require much less of a commute per person. The oposite for larger ones in a different neighborhood and more diverse worker living locations.

    7. The power capacity could easily casued some what by firm size in addition to the other direction. The more money collected can effect power capacity of the power companies. A bi directional feed back. Of course electrification of countries has shown to be a good policy.


  2. I thought of some thing I have experienced might be related to your data.

    Some times plotting two exponentially growing quantities as a function of time on an log log x-y plot looks like they are correlated in time. I have done this and thought temporarraly that I have discovered some thing. But, what is actually going on is that they share a common variable time, t.

    Yet, do not dismiss with out being sure.

    Or, it could be two exponentialy growing things based on some other thing in common, a comon variable in the two functions. Maybe firm size and energy usage are effected by exponentially growing population? Energy usage is definately a function of population. (And, of course the common exponentially growing population share the common variable time. ) Firm size is also related to population. A nonlinear or exponential relation with population size could be involved in both, also.

    I think, this can be frequent in economics because many quantities are exponentially growing most due to exponental growth of population and the other to exponential growth of prices due to dillution of the currency and new credit money produced also effecting prices. Also, interest paid is an exponential growth inherent in economics.

    Any thing that has a near constant percent growth is an exponential growing thing or quantity in time. And, many organizations and firms The differential equation for this is Y´(t)= C*Y(t) or d/dt Y(t)=c*Y(t), where c is constant or is c(t) wich is nearly constant in the reial world. The solution to the diffential equatino is Y(t)=Y(t_initial)*exp(c*t). An example of this would be a bank account paying 20% interest at a continous rate with out withdrawing money, M(t)=100*exp(.2*t), where t is years and the inital deposit is $100. Econoimcs is full of this sort of thing, GDP of the US much of the time, population growth, price rises, energy(power) usage, labor suply, labor, etc., etc.

    Yet in economics if the fit is really good it might be dismissed as abnormal because much data is much more noisy. But, I have found when the fit is really good it is often do to an equation. Some times disapointingly I learn, an equation that is due to an economic definiton. For example, an equation with the defined quantity labor productivity, a defined efficiency of labor,, p.1 formula 1. Restated GDP=labor productivy*L


    • Your plots are percent on the vertical and logrithmic on the horizontal.

      The above precautions could apply for the following reasons: They might be related to the above because a percent growth is related to exponential ploted logrithmically. Or, if there is a nonlinear relationship.

      Or, most likely you have a real relationship. You might find a better relation, a third common variable, or an understanding from an expanded point of view.


  3. “but I could not find a problem in my methods.”

    There is a systematic way to detect and remove this kind of problem, every time!

    It is the consistant use of units in formulas, the unit coversion method (lime method). That is sufficient. But, there is also dimentional analysis. This seems like more work initially but is actually less work because it is nessesary to avoid lots of problems that cause more work.

    Economic notation seems rather bereft of units. This is one of the reasons for problems in economics. If units are not specified in measurements and calculations, physical calculations mean absolutly nothing. If a graph”s axis is not labeled with units it means very little, its wrong.

    Every good comparison shoud have the same units and dimentions. Both, sides of every equation should have the same units and dimentions. You might have to convert units to an other (usually of the same dimention) to match what your are comparing (inches to meters).

    Check out secondary and below science books where quantities are calculated. Work some problems to learn it.

    Example of a problem in economics is, Q, in the mythical supply demand curve. The dimention is not a quantity! But flow of a quantiy, change in quantity over time. Example units could be: 8 [Giga tones of iorn]/[year] or 8 Giga tones of iorn/ year. It is the addition (supply) or subtraction from inventory over a period of time.

    Converting Units With Conversion Factors
    Interpreting units in formulas | Mathematics I | High School Math | Khan Academy


    • Correctionion:

      I meant to say, (line method), but there might be other names for it today.

      I meant to say in the 6th paragraph, Check out secondary scienc books and below where quantities are calculated. Work some problems to learn it.


  4. More on the dimentional analysis solution:

    “Having the same units on both sides of an equation [or comparison] does not ensure that the equation is correct, but having different units on the two sides (when expressed in terms of base units) of an equation [or comparison] implies that the equation [or comparison] is wrong. ”

    Quotes to motivate economists to practice this:

    “In economics, one distinguishes between stocks and flows: a stock has units of “units” (say, widgets or dollars), while a flow is a derivative of a stock, and has units of “units/time” (say, dollars/year). ”


    How to Convert Units – Unit Conversion Made Easy


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