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Friday, May 8, 2009

What is wrong with you?

The short answer is that you have little sense of proportion.

Humans occupy the midrange of the dimension scale of our universe, between the Planck length and the distance to our cosmological horizon. Though the extent of this physical scale is virtually unfathomable, it is instructive to examine it mathematically. Let's choose the meter [m] as our unit of measure because it represents an easily grasped unit of length. For example, 1.8m is a typical height for a man.

At the small end of the length scale is the Planck length, which is the smallest distance or size about which anything can be known. This incredibly small size is 1.6×10^(-35)m [in scientific notation: 1.6 times 10 raised to the negative power 35]! That is 35 orders of magnitude (i.e., factors of 10) shorter than a man!

At the long end of the length scale is the distance to the edge of the observable universe, which is now located about 46.5 billion light-years away. We need to convert this length to meters. First, the number 46.5 billion is 4.65×10^(10) in scientific notation. Next, a light year is the distance light travels in one year, which is about 9.46×10^(15)m. Multiplying these two huge numbers give us 4.4×10^(26)m! That is 26 orders of magnitude longer than the hight of a man! Together with the 35 orders of magnitude on the short end, we have a length scale totaling 61 orders of magnitude with which to compare lengths!

Considering the immensity of the numerical sweep described above, it is small wonder that our brains have evolved to make absolute comparisons for only small numbered quantities, let us stipulate numbers in the range one to a million (to be generous). Everyone can visualize a single dollar bill. We can visualize ten of them, and even a wad of a hundred bills fairly easily. It gets increasingly harder as we progress to one thousand, ten thousand, and a hundred thousand individual bills. A million bills is a stretch.

I doubt anyone can visualize a billion individual dollar bills, which is a thousand times larger than my generous estimate of our capacity to visualize a million. What about a trillion, which is a thousand times larger than a billion? No. You. Can't.

Have you ever noticed how often people mix up the words million and billion when discussing the economy? I have, but I'm used to dealing with large (and small) numbers expressed in scientific notation. We may not be able to visualize large numbers, but we can conceptualize them. This means that we can't make sense of comparisons involving huge discrepancies unless we express them on a scale for which our brains are wired, namely meters when comparing lengths (for example). If we discuss money (for example) most people understand what it means to have an annual salary of $40,000 and that a cup of coffee costs about $1.20 anywhere (well, maybe not at Starbucks).

When President Obama asked his Cabinet to come up with budget-cuts totaling $100 million, many people saw how ridiculous that proposal was, because if the $3.6 trillion Federal budget was scaled down to a personal budget of $40,000 the President's $100 million cuts amounted to a mere cup of coffee.

So the President upped the ante. He is now proudly proclaiming Federal budget-cuts totaling $17 billion, which, he posits, is "big bucks even in Washington D.C."! Really, Mr. President? Really?

This "great new budget-cut" is 170 times larger than his first one. BFD! So now, instead of bragging about an annual cup-of-coffee, he's bragging about a cup-of-coffee every other day!

What is wrong with you? The short answer is that you have little common sense.

Post #742 What is wrong with you?


  1. You’ve hit on something that has fascinated researchers for a while now, i.e., people’s ability to understand a vast array of conceptual scenarios that are not accessible to our perceptual apparatus by adjusting them to human scale. Linguists love this because traces of the techniques we use show up in language—for example, in grammar and in conceptual projections and mappings as identified in metaphor theory and theories of blending or conceptual integration. It’s taken a long time for linguists, philosophers of language, and cognitive scientists to begin to understand how this works. But we’re all geniuses at it (especially if you happen to be someone’s kid or grandkid). Obama and his team are, without a doubt, geniuses at it. Which finally gets me to the point relevant to this post. Given that the president and his team are brilliant at projecting their agenda to human scale, why have they suddenly gone dumb when it comes to the budget?

  2. Thanx for your comments, tristein. As for your question (which may be rhetorical), I think there are several possibilities. First, they (by which I presume you mean the President and his advisors) may not have "suddenly gone dumb" but just continue to be too clever by half. They may be counting on the average voter to be too dumb to understand their cynicism. Of course, there are many voters who do understand what they are up to, but perhaps too few to make a difference in the polls. Second, the President may not be as smart as he thinks he is and as his worshipers believe Him to be. Third, a lot of people haven't gotten around to comprehending the difference between absolute and relative magnitudes. When making judgments about the merits of quantitative issues, it does not make sense to consider absolute magnitudes. Yes, a billion dollars is a lot of money when compared to a person's annual salary; but it's a pittance when compared to the Federal budget. The latter comparison can only make sense in terms of percent, which is a relative magnitude.

  3. I was wandering the halls tracing a troll's comment when I stumbled upon you and your site (you had referred to be as "an insolent whelp" in response to a comment I had made).

    While I will give you props for a well stated opinion, it seems puzzling that you ignore basic deficit to GDP ratios from an historical perspective. Furthermore, you ignore the current fiscal realities, and thereby place your well written logic outside the realm of humanity and into a vacuum. A vacuum which typifies the very limitation you seem to rail against in your post.

    You then compound this further by linking the genesis of your thought process, but fail to provide any links that are relevant and germane to the actual topic at hand. Which of course, I find puzzling. Are you doing this to prove an intelligence in hopes that you readers will be so enamored as to overlook your lack of supporting material for the article's main points?

    While this may be an act of arrogance, let us assume that you are simply unaware that there are people -with actual expertise in this area- who wholeheartedly disagree with your thoughts. Dr. Paul Krugman is one such person, who has and continues to advocate for far more spending in an effort to stave off what he believes will become the first Depression of the 21st century. But even if you find his opinion to be questionable, the historical precedents favor the current Administration's actions.

    Keeping that eye on history, it should also be pointed out that opinions such as yours were bantered about quite frequently only to be proven wrong. There are a number of books concerning the Great Depression, and if you are interested in a recommended reading list from me (I say this from one book lover to another without any desire to be rude), please drop me a note, and I would be happy to provide a list more inclusive and representative of my view than is possible here.

    Rick Beagle
    "insolent whelp"

  4. @Rick Beagle

    The point of my post was that the significance of an absolute magnitude can be argued ad nauseam, but its significance can only be made meaningful relative to some comparative magnitude. This is why people use ratios, such as per cent, to ground any such discussion in a meaningful context.

    P.S. The "insolent whelp" sobriquet was an allusion to Snoopy the Beagle in the "Peanuts" comics.

  5. Big Henry.

    I truly must have reading comprehension issues. The point of your article seemed to be a thinly veiled attempt to understand the wide based support for the Obama administration's "outrageous" spending, and in the process dismiss this support as some sort of intellectual deficiency.

    Having reread the article, yup, I had it right. You really ought to pick up a book on economics before you deride the opinion of the majority.

    Rick Beagle
    still "an insolent whelp".

  6. Dear Rick,

    Yup, you have reading comprehension issues. Far be it from me to deride the opinion of the majority.

    Peace out, dude.