Friday funny – Logarithmic Scales are for Quitters Without Enough Paper

Log Scales are for Quitters

From XKCD: A webcomic of romance, sarcasm, math, and language.

Hat tip to Dr. Brian Mays, one of the more prolific contributors to the Atomic Insights comment threads.

About Rod Adams

20 Responses to “Friday funny – Logarithmic Scales are for Quitters Without Enough Paper”

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  1. Engineer-Poet says:

    I regularly feature XKCD in my “Morning Snort” selection on Multiply (and now LiveJournal).

  2. Cyril R. says:

    Well, that’s certainly funny, but not entirely accurate. Log scales are for scientists who know what a log scale is and does. It can be convenient to recognize certain patterns that are not linear in a normal scale.

    A more accurate point, maybe not so funny, would be that log scales are not helpful for public relations. Most people don’t understand a log scale, in fact they have trouble with anything beyond quadratic.

    I would suggest surface area – using squares – as a reasonable public relations tool, to cover the point of energy density. You’d have a big square versus a speck.

    I tried to make the point of energy density in a number of simple drawings:

    http://energyfromthorium.com/forum/viewtopic.php?f=39&t=2757

    The responses indicated that the quadratic (surface) comparison is better for getting the point across than third power (volume) comparisons.

    • Brian Mays says:

      Personally, I would avoid using an area, since the graphic will end up understating the difference that you want to emphasize.

      As Edward Tufte explains:

      There are considerable ambiguities in how people perceive a two-dimensional surface and then convert that perception into a one-dimensional number. Changes in physical area on the surface of a graphic do not reliably produce appropriately proportional changes in perceived areas. The problem is all the worse when the areas are tricked up into three dimensions …

      Conclusion: The use of two (or three) varying dimensions to show one-dimensional data is a weak and inefficient technique, capable of handling only very small data sets, often with error in design and ambiguity in perception. These designs cause so many problems that they should be avoided: The number of information-carrying (variable) dimensions depicted should not exceed the number of dimensions in the data.

      – Edward R. Tufte. The Visual Display of Quantitative Information, Second Edition. Graphics Press LLC, Cheshire, Connecticut. 2001.

      In addition, you have to worry about such effects on your audience as the Ebbinghaus illusion.

      • Cyril R. says:

        But I need multiple dimensions to deal with all those orders of magnitude difference. Otherwise I can only use a friday-funny type cartoon. Which doesn’t actually give you a feel either, it’s funny but wrapped up paper is worse than a surface area, if you want to convey a serious message.

        • Steve says:

          I think these two views can be reconciled. It depends on the difference between the things you are comparing.

          If you are comparing two things that have similar sizes, then it is bad to more into 2 or 3 dimensions. As I heard it put very well recently, it is very had to tell just by looking how much more pizza is in a 10inch than a 12inch.

          But when things being compared are massively different, like in this cartoon. I think moving to 2 or 3 dimensions is really useful. Llike Cyril R’s drawings.

  3. Josh says:

    I had come across an article that compares the flux density of various forms of energy using energy per square meter as a tool. If I’m not mistaken the figures were (Mw/sqm):

    Solar: 0.001
    Coal: 10
    Fission: 50-200

    I’ll try and dig up the source. It also spoke about spent nuclear fuel as a valuable resource, not waste.

  4. gmax137 says:

    xkcd has a nice graphic using areas to represent radiation doses, see
    http://xkcd.com/radiation/

  5. Brian Mays says:

    Logarithms? We don’t need no stinkin’ Logarithms!

    • James Greenidge says:

      Can’t Google it up, but isn’t there a figure that were the sun made of coal it’d burn out in 15,000 years?

      James Greenidge
      Queens NY

      • Brian Mays says:

        Well, there’s something related to that.

        William Thomson (a.k.a. Lord Kelvin) once used a limit on the age of the sun as an argument against Darwin’s theory of biological diversity through the slow process of natural selection, which would require more time than the sun could possibly last according to his calculations. His figures were based on the amount of energy available from gravity (the best source available to his knowledge at the time), not coal, and the age was given in millions of years. Of course, we now know that nuclear fusion drives the sun and it lasts for billions of years.

        Somehow, I think that this history has been transformed into a story about scientists once believing that the sun is made of coal. Perhaps this came about because Lord Kelvin once explained his theory of an initially very hot sun slowly cooling by giving up its energy as radiating its heat away “like a hot coal.” But I don’t know.

      • Cyril R. says:

        One thing I find interesting about the sun is the low power density.

        The power production by fusion in the core varies with distance from the solar center. At the center of the Sun, theoretical models estimate it to be approximately 276.5 watts/m3,[54] a power production density that more nearly approximates reptile metabolism than a thermonuclear bomb.[b] Peak power production in the Sun has been compared to the volumetric heats generated in an active compost heap. The tremendous power output of the Sun is not due to its high power per volume, but instead due to its large size.

        http://en.wikipedia.org/wiki/Sun

        Fusion scientists want to put the sun in a box. Apart from the box being torn apart every 5 minutes at full power, obviously putting a compost heap in a box isn’t going to power countries. A more accurate depiction is that fusion scientists want to put a high energy density hydrogen bomb in a box. Of course, that is not exactly good public relations.

  6. James Greenidge says:

    Ultra-creative! Is there no media cartoonist out there who’d pick this up just for public service enlightenment reasons??

    James Greenidge
    Queens NY

  7. David says:

    Brian,

    Super! Exactly the type of communication that ordinary people can relate to!

  8. AtomikRabbit says:

    “Warning: this comic occasionally contains … advanced mathematics (which may be unsuitable for liberal-arts majors)”

    Ouch! (obviously Rod gets a pass here)

    It would be interesting to see the assumptions and calculations behind the numbers. I assume he is oxidizing the hydrocarbons completely, and fissioning 100% of the uranium and taking credit for the delayed energy in the fission product decay (about 5% is lost unrecoverably as anti-neutrinos). Randall, If you are reading this please clarify.

    Despite these nerdly quibbles, the cartoon makes a convincing case for the energy density trump card of nuclear fission. As James says, it’s too bad this is never slapped down on the table in front of most mass-media consumers.

    • Steve says:

      Yes, I find even pro-nukes (and I am one of those) sometimes over-egg these numbers.

      If you fission an nucleus of U235 you get about 200MeV (for order of magnitude, neutrinos and subsequent fission product energy can be ignored)

      If you burn one atom of carbon you get about 4eV of energy.

      This would give you a difference of 50 million.

      This is a bit unfair because a uranium235 atom is heavier than a carbon atom.

      So in terms of energy density the difference is a factor of 2 million.

      This is a bit unfair because coal is not pure carbon so the factor is more like 3 million. (this is what is used in the cartoon)

      But this is for a block of U235, for pure uranium in it’s natural state (unenriched) only 1 in every 140 odd nuclei are U235 so this gives a energy density factor of 20,000 (this is what should have been used in the cartoon IMO, unless further clarification is given)

      Uranium as it transported as yellow cake probably has an energy density of more like 10,000 diffence to coal, because it isn’t pure uranium.

      Enriched Uranium is more energy dense, this gives a factor of 100,000 with coal (this is what is used in the famous ANS fuel pellet – 10g pellet having as much energy as a ton of coal)

      If you start taking about Uranium ore, 1% ore would have a factor of 200 difference with coal.

      and 0.1% ore would have a factor of 20 difference with coal.

      Now, I’m perfectly happy if the cartoon means pure U235, and I’m also happy if the cartoon means complete fissioning of uranium in a breeder reactor. He doesn’t say either. (I would actually be more comfortable if he has used thorium instead of uranium because there would then be less room for doubt).

      But I must say, I often hear that a “uranium fuel pellet contains a million times more energy than coal” or even “yellow cake is a million times more energy dense than coal”, when talking about LWRs, and I think it’s misleading. The actual numbers are incredible enough.

      • Cyril R. says:

        Yes, even if we use our relatively primitive (no offense intended – some recent designs are quite advanced) light water reactors, that use only 0.5% of the theoretical potential of the ore, the difference is so large, it is indicative of the potential of nuclear fuels.

        However, as recently discussed here, I must disagree with mass-based energy density focus. Volume is at least as important. If it weren’t, natural gas would be a lot more attractive (it actually has higher energy density per unit mass than petroleum, but that underestimates the fact that it’s a gas of low density… a barrel of oil contains a lot more energy than a truck full of natural gas at atmospheric pressure). If natural gas had a high volumetric energy density, it would likely be predominantly used as transport fuel over petroleum, even today.

      • Brian Mays says:

        You do realize that it’s just a cartoon, and the actual values, even if they are off by an order of magnitude or two, are inconsequential to the joke, don’t you?

        The best way to ruin a good joke is to provide too much information.

  9. Steve says:

    Agree. An even better argument against concentrating on energy/kg is hydrogen. It’s MJ/kg is off the chart, but by volume, much less impressive.

  10. AtomikRabbit says:

    It appears that Randall has also solved the “paucity of pro-nuclear PR” conundrum: http://xkcd.com/1019