A billion here a billion there pretty soon youre talking about well pretty soon no one has a clue what youre talking about.
And as President Barack Obama prepares to unveil his 2010 budget thats becoming a daily headache for Republicans.
After $787 billion for a stimulus plan $700 billion for a financial markets bailout and $410 billion for a proposed end-of-2009 spending plan getting folks fired up about whether the 2010 budget is $3.6 trillion rather than say $6.3 trillion is not just a political challenge; its a cognitive one.
Human beings have a hard time differentiating between millions and billions and trillions let alone the numerical subsets thereof. To most of us it just registers as a whole lot."
As the mathematician Ronald L. Graham once said Our brains have evolved to get us out of the rain find where the berries are and keep us from getting killed. Our brains did not evolve to help us grasp really large numbers or to look at things in a hundred thousand dimensions."
Or as Rep. Jeff Flake (R-Ariz.) put it: I catch myself in almost every interview saying millions instead of billions. Its tough weve never dealt with numbers this big."
But the natural tendency for people to tune out specific quantities somewhere between the Ms and the Bs has created a particular challenge for Republicans seeking to spark outrage at the amount of money being spent to shore up the sagging economy or to pay for government operations.
Part of the problem is that a majority of voters seem to agree that the government needs to spend a whole lot" of money in the service of economic recovery: A USA Today/Gallup Poll released Wednesday indicated that 40 percent of Americans thought the stimulus bill was about the right size and another 14 percent thought it should have been bigger.
It is hard then to get people excited about the difference between $787 billion and $478 billion both of which are equally abstract if not equally large sums which is perhaps one reason why House Republicans alternate stimulus proposal which carried the latter price tag failed to gain much traction with the public.
It hasnt stopped the Republicans from trying. Flake says he has tried putting the deficit in terms of the total national debt or the gross national product but hes not sure it really resonates.
Sen. John Thune (R-S.D.) hoped to make an impression by pointing out on the Senate floor that a trillion dollar bills would make a stack 689 miles high.
Senate Minority Leader Mitch McConnell (R-Ky.) has been employing a Bible-based comparison: If you started the day Jesus Christ was born and spent $1 million every day since then you still wouldnt have spent $1 trillion."
When Thune talked of a trillion dollars he meant the $787 billion that would end up in the stimulus plan. The catch putting the math aside is that most Republicans didnt want to spend no money on the stimulus; their stack would have been 418 miles high. In other words still a whole lot" of money.
David M. Schwartz author of How Much Is a Million?" a childrens book that uses fanciful illustrations to explain the differences between a million a billion and a trillion thinks folks such as Thune may be doing all they can.
I think that the best we can hope for is to make them more concrete. Nobody will ever get a real feel for a trillion dollars. But relating them to human-sized things or a human time scale I think we can wrap our minds around them."
He explains the difference thusly: Each step from million to billion to trillion is times a thousand. If you think of it in terms of time seconds and go to a point a million seconds from that youll have gone 11½ days into the future. A billion seconds turns out to be 32 years. Youll reach that in 2041. A trillion seconds is 32000 years. I like to say that I have a pretty good idea of what Ill be doing a million seconds from now I have no idea what Ill be doing a billion seconds from now and I have an excellent idea what Ill be doing a trillion seconds from now."
Still he adds I dont think it will ever be completely meaningful. I dont think anybody will ever understand a trillion dollars the way they understand $10."
John Allen Paulos a professor of mathematics at Temple University and the author of Innumeracy" isnt sure even comparisons such as Thunes or McConnells are concrete enough to be useful. Pointing out that a trillion dollars laid end to end extends from x to y doesnt help much since it attempts to explicate an abstract notion with one just as abstract."
Rep. Jeb Hensarling (R-Texas) says he doesnt see the big numbers as a problem; he just takes out his calculator and makes them smaller.
When youre talking about this dizzying array of numbers I try to relate it to a working household" he says.
For example by his math the stimulus bill is going to cost the average American household roughly $10000. Says Hensarling: Thats a number everyone can understand."
Perhaps. But if you take Hensarlings calculations a few steps further you learn that his $10000 is $1000 a year for 10 years which works out to less than $3 a day. When the cost of financial stability can be related to a latte or a lottery ticket mightnt you start to see it less as a massive financial burden and more as well a bargain?
The problem is there is no way for the average voter to tell. What is a fair price for the recovery of the economy or to operate the country? A hundred billion dollars? Five trillion? A dollar a day for a decade? Ten dollars a day for two decades? The typical American doesnt have the tools to make a cost-to-value calculus for the items on offer so he or she must rely upon those who claim they can and who do the best job presenting their case.
It is possible that the public will hit its threshold for federal debt in the Gallup Poll 54 percent of Americans said they were worried about it. But that limit is less likely to take the form of the number of dollars spent than the number of companies or industries the public is asked to bail out a number people will be able to count to on their fingers yet that still may seem like a whole lot."
However Paulos thinks the GOP has already hit upon its best tactical option: working with the publics trouble with numbers rather than trying to fight it. Paulos says the numerically challenged nature of the typical voter has already allowed the Republicans to glom onto a few million" for a project or provision likely to offend the publics sensibilities knowing that they can depend upon the average American not to understand how insignificant that amount is relative to the overall proposal or bill.
In other words expect the GOP to continue to attack its big-number problem by thinking small say about the size of a mouse.
A billion here a billion there pretty soon youre talking about well pretty soon no one has a clue what youre talking about.
And as President Barack Obama prepares to unveil his 2010 budget thats becoming a daily headache for Republicans.
After $787 billion for a stimulus plan $700 billion for a financial markets bailout and $410 billion for a proposed end-of-2009 spending plan getting folks fired up about whether the 2010 budget is $3.6 trillion rather than say $6.3 trillion is not just a political challenge; its a cognitive one.
Human beings have a hard time differentiating between millions and billions and trillions let alone the numerical subsets thereof. To most of us it just registers as a whole lot."
As the mathematician Ronald L. Graham once said Our brains have evolved to get us out of the rain find where the berries are and keep us from getting killed. Our brains did not evolve to help us grasp really large numbers or to look at things in a hundred thousand dimensions."
Or as Rep. Jeff Flake (R-Ariz.) put it: I catch myself in almost every interview saying millions instead of billions. Its tough weve never dealt with numbers this big."
But the natural tendency for people to tune out specific quantities somewhere between the Ms and the Bs has created a particular challenge for Republicans seeking to spark outrage at the amount of money being spent to shore up the sagging economy or to pay for government operations.
Part of the problem is that a majority of voters seem to agree that the government needs to spend a whole lot" of money in the service of economic recovery: A USA Today/Gallup Poll released Wednesday indicated that 40 percent of Americans thought the stimulus bill was about the right size and another 14 percent thought it should have been bigger.
It is hard then to get people excited about the difference between $787 billion and $478 billion both of which are equally abstract if not equally large sums which is perhaps one reason why House Republicans alternate stimulus proposal which carried the latter price tag failed to gain much traction with the public.
It hasnt stopped the Republicans from trying. Flake says he has tried putting the deficit in terms of the total national debt or the gross national product but hes not sure it really resonates.
Sen. John Thune (R-S.D.) hoped to make an impression by pointing out on the Senate floor that a trillion dollar bills would make a stack 689 miles high.
Senate Minority Leader Mitch McConnell (R-Ky.) has been employing a Bible-based comparison: If you started the day Jesus Christ was born and spent $1 million every day since then you still wouldnt have spent $1 trillion."
When Thune talked of a trillion dollars he meant the $787 billion that would end up in the stimulus plan. The catch putting the math aside is that most Republicans didnt want to spend no money on the stimulus; their stack would have been 418 miles high. In other words still a whole lot" of money.
David M. Schwartz author of How Much Is a Million?" a childrens book that uses fanciful illustrations to explain the differences between a million a billion and a trillion thinks folks such as Thune may be doing all they can.
I think that the best we can hope for is to make them more concrete. Nobody will ever get a real feel for a trillion dollars. But relating them to human-sized things or a human time scale I think we can wrap our minds around them."
He explains the difference thusly: Each step from million to billion to trillion is times a thousand. If you think of it in terms of time seconds and go to a point a million seconds from that youll have gone 11½ days into the future. A billion seconds turns out to be 32 years. Youll reach that in 2041. A trillion seconds is 32000 years. I like to say that I have a pretty good idea of what Ill be doing a million seconds from now I have no idea what Ill be doing a billion seconds from now and I have an excellent idea what Ill be doing a trillion seconds from now."
Still he adds I dont think it will ever be completely meaningful. I dont think anybody will ever understand a trillion dollars the way they understand $10."
John Allen Paulos a professor of mathematics at Temple University and the author of Innumeracy" isnt sure even comparisons such as Thunes or McConnells are concrete enough to be useful. Pointing out that a trillion dollars laid end to end extends from x to y doesnt help much since it attempts to explicate an abstract notion with one just as abstract."
Rep. Jeb Hensarling (R-Texas) says he doesnt see the big numbers as a problem; he just takes out his calculator and makes them smaller.
When youre talking about this dizzying array of numbers I try to relate it to a working household" he says.
For example by his math the stimulus bill is going to cost the average American household roughly $10000. Says Hensarling: Thats a number everyone can understand."
Perhaps. But if you take Hensarlings calculations a few steps further you learn that his $10000 is $1000 a year for 10 years which works out to less than $3 a day. When the cost of financial stability can be related to a latte or a lottery ticket mightnt you start to see it less as a massive financial burden and more as well a bargain?
The problem is there is no way for the average voter to tell. What is a fair price for the recovery of the economy or to operate the country? A hundred billion dollars? Five trillion? A dollar a day for a decade? Ten dollars a day for two decades? The typical American doesnt have the tools to make a cost-to-value calculus for the items on offer so he or she must rely upon those who claim they can and who do the best job presenting their case.
It is possible that the public will hit its threshold for federal debt in the Gallup Poll 54 percent of Americans said they were worried about it. But that limit is less likely to take the form of the number of dollars spent than the number of companies or industries the public is asked to bail out a number people will be able to count to on their fingers yet that still may seem like a whole lot."
However Paulos thinks the GOP has already hit upon its best tactical option: working with the publics trouble with numbers rather than trying to fight it. Paulos says the numerically challenged nature of the typical voter has already allowed the Republicans to glom onto a few million" for a project or provision likely to offend the publics sensibilities knowing that they can depend upon the average American not to understand how insignificant that amount is relative to the overall proposal or bill.
In other words expect the GOP to continue to attack its big-number problem by thinking small say about the size of a mouse.
