I've been pursuing something of a project in recent months. The project has been to convince people that budgets matter. That they're not one-day stories or dull documents that we have to pretend to care about.

They're a moment when politicians put numbers down on a page. Numbers we can check and question. In those numbers — in the tables in the back, and the assumptions fed to the Congressional Budget Office — we can see the decisions the parties make when they're forced to choose between competing priorities and constituencies.

But the numbers don't matter if we don't force them off the page and into the world voters actually inhabit. Which brings us to David Brooks' Friday column:

"Under (Rep. Paul) Ryan, (President) Obama charged, 10 million college students would get their financial aid cut by $1,000, Alzheimer's research would be slashed, 200,000 children would lose their chance to enter Head Start.

"Where did Obama get these specifics? He imagined them. He imposed some assumptions that are nowhere to be found in the Ryan budget. He compared Ryan's reduced spending increases with proposed growth, not current levels."

Brooks is right: Obama did offer specific cuts that don't appear anywhere in Ryan's budget. But only because Ryan refused to provide the specifics himself.

Ryan, whose budget was approved by the House but stands little chance in the Senate, has said how his cuts will be distributed on the category level. He's clear on the size of hit that "non-defense discretionary spending" will take. But he hasn't said how those cuts will be distributed among the programs in that part of the budget. His numbers stop at the water's edge of the real services and programs people use. And so the White House, to try to make them real, made a assumption — arguably, the only assumption they could make: They assumed that when Ryan said he would cut X category of spending by Y percent, those cuts would be distributed equally among the programs in that category. And the Ryan camp — echoed here by Brooks — called foul.

I spent 24 hours trying to unravel the Ryan camp's argument that the White House is imposing unfair assumptions on their budget. In particular, the assumption they're upset about is the White House's claim that their budget will mean 10 million college students get their financial aid cut by $1,000. Unpacking this gets a little complicated, and it requires getting into some budgetary weeds, but it's also a good case study of what happens when you start trying to estimate the Ryan budget's effects on real programs.

Under current law, Pell grants are scheduled to receive $30.5 billion in 2014. $24.5 billion will come from "discretionary spending." $6 billion will come through "mandatory spending."

Ryan's budget says that Pell grants "would be fully funded through discretionary spending." And it says that the category of discretionary funding that includes Pell grants will be cut by 19 percent. This leaves two options for what happens to Pell grants:

• Ryan's budget erases all the funding they get from the mandatory side of the budget and then cuts their discretionary funding by 19 percent. That would blow a $12 billion hole in the program. That's what the White House assumed.

• Ryan's budget doesn't cut Pell grants by 19 percent. Instead, it cuts them by somewhat less than 19 percent, but it cuts other domestic discretionary programs by much more than 19 percent. That's pretty much what Ryan's office is arguing.

However, if he's not cutting Pell grants by as much as the White House thinks, he's cutting other things by more. But he won't say what. Obama "imposed" the simplest of all assumptions: equal cuts across-the-board.

There's a bottom line here: You can't cut spending without cutting spending. But Ryan wants to have it both ways: He wants to get the credit for cutting spending, but he doesn't want to have to propose specific spending cuts. Oh, and he doesn't want anyone to extrapolate what those cuts would be, either.

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Of course, even Ryan's supporters should see the problem here. If these cuts are too unpopular to detail, then they're going to be too unpopular to pass. If the only way to defend Ryan's budget is to beat back any attempts to make it specific, then it's an empty, useless document.

If Ryan's budget is to pass, the defense has to be that his cuts are worth it, or necessary, or at least better than the alternative. On Pell grants, for instance, his office accurately argues that the White House's plans for Pell are unfunded after 2015. They also argue that the Pell program isn't well targeted, and that increasing student aid so quickly is driving up the cost of tuition. And they argue, more broadly, that debt and tax increases pose such dangers to the American economy that painful cuts are a superior option.

These are all arguments we can, and should, have. But in the end, we're also going to have to have an actual discussion of how and where Ryan intends to make his cuts. And a discussion of where Ryan is going to find the $4.6 trillion to pay for his tax cuts.

To try to protect Ryan from that discussion is to let the two parties retreat back into the bromides that allow them to so effectively obscure their visions, and our choices.

And it is also, in the end, to say that Ryan's budget is not defensible, or at least it requires choices that cannot be defended to the public. That would be an interesting revelation — and it would mean Ryan's budget has told us something important about the workability of his vision — but I don't think it's the point Brooks is trying to make.

Ezra Klein blogs about domestic and economic policy for the Washington Post, where this column first appeared.