No Fooling, a Really Cute Story Based on Infinity
This happened a while ago. I kept meaning to blog it, mainly to economize on my telling it to relatives, but better late than never. My son Clark is 6. Here is our exchange:
Clark: Daddy why can’t there be a biggest number?
Bob: Because no matter how big a number is, there is always a bigger number.
Clark (puzzled): Why?
Bob: OK, let’s say a guy comes up to me and says, “Hey, I know the biggest number!” Then I would say, “Oh yeah, what is it?” And the guy would tell me, “It’s a billion billion.” But then I would just add 1 to it, and say, “A ha, a billion billion and 1 is a bigger number. So you made a mistake when you said you thought of the biggest number.”
Clark (after a pause): What guy are you talking about?
Bob: Just any guy. I’m saying, if anybody tries to think of the biggest number, I’ll always be able to do that trick–where I add 1 to it–so they can’t do it. They’ll always lose.
Clark: What if a girl asks you?
[I ran through the same thing with a girl asking me…]
Clark: OK I want to tell the story!
Bob: Sure go ahead.
Clark: So what if a guy came up to me and said, “Hey Clark, I know the biggest number! It’s 100 billion!” Then I would say, “No, 100 billion and 1 is bigger! You’re wrong!”
Bob: Right, good job. So he didn’t really think of the biggest number after all, did he?
Clark: No.
Bob: And you can always do that.
Clark: OK let me tell it again with Sam [name possibly changed–a kid from his class].
Bob: OK.
Clark: So what if Sam came up to me and said, “Hey Clark, I know the biggest number. It’s 50 googol.” But I would say, “No Sam you’re wrong! 50 googol and 1 is bigger!” But Sam gets mad so he would start shouting and say, “I DID TOO THINK OF THE BIGGEST NUMBER CLARK!!”
Somehow, I don’t think my attempts at an abstract proof worked. Join us next week when I describe the awkward moment in a parent/teacher conference when I had to explain to the math teacher that Clark’s “imaginary numbers” were based on the square root of -1, not numbers who were his invisible friends.
Potpourri
* Aristos sends this video of a policeman telling people he’d pulled over that he should have executed them. It’s true that the offense (threatening to kill them) isn’t as bad as in plenty of other videos we’ve showcased, but this one makes the cut because the people are being fairly cooperative. (I.e. in the other videos where, say, a cop starts pounding the heck out of somebody, usually it’s because the person was resisting arrest or some such thing that escalated the situation.)
* Just to give you guys a heads-up, at some point I am going to explain why my approach to cash balances–and not Wenzel’s–can rescue us from this insanity.
* Joe Salerno touting his new book.
* I’m too busy to experiment, but word on the street gives a thumbs-up to Google+. This is a fascinating episode, because it shows how fleeting a market “monopoly” is. When the Facebook movie came out, the social network seemed invincible. Not only was it dominant, but it was literally a network–so how could anyone displace them? And yet Jeff Tucker explains how Google+ seized on Facebook’s flaws.
* The unsaturated von Pepe sends this interesting link trying to explain fiat money using game theory. However, I don’t get the use of backwards induction in step 1 of the argument. Are they assuming a finitely repeated game, so there’s no value for the fiat money in period N, hence no value in period N-1, etc.?
* You know how little kids wonder whether a lion could beat a polar bear in a fight, etc.? Well did you ever wonder what would happen if crazy inflationist Scott Sumner took on the crazy inflationist MMTers? Here ya go, courtesy of the above link.
* Last week I outlined Mises’ proposal (in the Theory of Money and Credit) for linking a fiat currency back to gold. It’s not as easy as you might think.
* Then today I explain the logic of coupons and other price discounts.
* The creator of “KrugmanIsWrong.com” is running for office. However, he needs to be careful, as Jon Stewart would have fun if his campaign ever gets traction.
* Check out these graphics that Tony sent me, showing the size of our unfunded liabilities in terms of $100 bills.
Jesus Insults Gentiles?
I know there are some serious difficulties with passages from the Old Testament, where the Lord (e.g.) literally orders the Israelites to kill infants. In the past I’ve offered some thoughts on this heavy subject.
Yet today I want to bring up something that is more trivial and yet as always puzzled me more:
21 Then Jesus went out from there and departed to the region of Tyre and Sidon. 22 And behold, a woman of Canaan came from that region and cried out to Him, saying, “Have mercy on me, O Lord, Son of David! My daughter is severely demon-possessed.”
23 But He answered her not a word.
And His disciples came and urged Him, saying, “Send her away, for she cries out after us.”
24 But He answered and said, “I was not sent except to the lost sheep of the house of Israel.”
25 Then she came and worshiped Him, saying, “Lord, help me!”
26 But He answered and said, “It is not good to take the children’s bread and throw it to the little dogs.”
27 And she said, “Yes, Lord, yet even the little dogs eat the crumbs which fall from their masters’ table.”
28 Then Jesus answered and said to her, “O woman, great is your faith! Let it be to you as you desire.” And her daughter was healed from that very hour.
This particular story never sat well with me. I would not have expected Jesus to talk like that, given His actions in the rest of the gospels.
Griping About My Mac
I realize this is going to be more controversial than the work of Charles Murray, but sorry Mac fans: I switched earlier this year and I don’t see what the big deal is. I am probably going to stay a Mac user because they are just so much prettier, but that’s hardly what I thought going into this.
Specifically, I abandoned my PC when it would freeze up all the time. If I had to give an online lecture, I would re-boot the computer to try to get it back to its best operating ability. Yet I would have to do it a good 15 minutes before the class started, because that is just how long it would take for my PC to “calm down” after re-booting. If I tried to open applications and actually use the computer after only, say, 2 minutes following a re-boot, then it would be ridiculously slow.
Well, things aren’t that bad yet, but they are getting there on my MacBook. During the past week, if I come to it fresh and try to start using it, I just budget into my schedule that I will have to wait up to 3 or 4 minutes for the computer to be “ready” for me to actually use. Up until that time, the aggravating color wheel will spin if I have the audacity to try to, say, check my email.
Discuss.
Overdose: The Next Financial Crisis
I was on a panel at FreedomFest offering commentary on this short documentary. I thought it was great. (I was sitting next to Andrew Schiff. Poor guy had a bunch of people come up to him, talking about his brother and his dad.)
Is Krugman Adding an Epicycle Regarding Debt Default?
In standard economic/financial analysis, without having libertarian views about government spending, I would think the standard answer would be, “If the US government defaults on its debt because of political squabbling, that is bad for the economy.” Just like, in standard analysis, government spending crowds out private spending, and government deficits raise interest rates.
But Krugman has been telling us for two years now that these are not normal times. In fact, just about everything you think you know about fiscal issues is the exact opposite when we’re in a liquidity trap.
Because of this, I would have supposed that Krugman would have to admit that if those stubborn Republicans actually triggered a debt default, that this would somehow create jobs. (Normally it would be bad of course.) Nick Rowe made an argument along these lines (read him in the original, I’m not trying to summarize him).
Ah but we can’t have that. The Republicans are always bad, whether in a boom or a bust. So here’s Krugman explaining why:
In fact, I’d argue that [a US government bond default] is in fact contractionary, because it raises interest rates even in a liquidity trap. How, you ask. Well, here’s a first cut.
What we normally say in a liquidity trap is that the Fed is keeping short-term interest rates at zero, which is as low as they can go because below that cash dominates bonds. And the Fed achieves that zero rate by being willing to buy short-term government debt whenever the rate threatens to rise above zero.
But now introduce the threat of default. This makes short-term debt worse than cash, unless it offers a sufficiently positive interest rate. Yet we’ve just posited that the Fed is ready to buy bonds to keep the rate at zero. So what happens? In a simple model, investors sell *all* short-term US debt to the Fed.
Then what? In practice, the hawks at the Fed might force Uncle Ben to stop the purchases, out of fear of too great an expansion in the monetary base. (Misplaced fear, but never mind). But suppose the Fed does in fact buy all the short-term debt. Then there is no longer a market interest rate on that debt. But there is still a “shadow” rate, the rate at which private investors would be willing to buy short-term US debt — and that rate can easily go well above zero.
This shadow rate, in turn, is — if I’m getting this right — the rate that feeds into the determination of longer-term rates. So we should expect rates to rise all along the term structure.
What gets tricky here is the question of whether private borrowing costs rise in tandem. For corporate bonds, maybe not. But the GSEs pay rates that are tied to the cost of government borrowing, and they are the main sources of housing finance, so mortgage rates would probably rise.
I like Rowe’s take on this, and not Krugman’s. Krugman has been pounding the table saying, “These Chicago School morons don’t even get basic macro. Look guys, draw your diagrams. Right now the market clearing interest rate is negative. The Fed can’t push rates negative. So that’s why we’re in recession.”
So, if the fear of default pushes up nominal interest rates, then the market-clearing rate can become positive. Meaning the lower bound is no longer binding. Meaning Krugman’s own case for Big Government falls apart.
Funny how Krugman only likes macro 101 when it supports his case.
The Economics of Large Cities
Some light reading to get your week going. I draw on some obvious facts of the world and try to explain them using economic reasoning. For example, do you know why the best steakhouses are typically in a big city?
Law and Knowledge
One of my favorite themes in the Bible is that God’s laws help us. We should follow them in order to navigate this world better. God knows things about the world that He created that we do not, and so even if a particular law doesn’t make sense to us, we should trust that God isn’t giving us bad advice.
However, unlike physical laws, when it comes to God’s laws for our relationships with Him and each other we have a choice whether to obey. You can’t violate the laws of physics, but you can sin.
Since I love this sort of thing, I was blown away by these passages from Psalm 119 that I recently stumbled upon:
9 How can a young man cleanse his way?
By taking heed according to Your word.
10 With my whole heart I have sought You;
Oh, let me not wander from Your commandments!
11 Your word I have hidden in my heart,
That I might not sin against You.
12 Blessed are You, O LORD!
Teach me Your statutes.
13 With my lips I have declared
All the judgments of Your mouth.
14 I have rejoiced in the way of Your testimonies,
As much as in all riches.
15 I will meditate on Your precepts,
And contemplate Your ways.
16 I will delight myself in Your statutes;
I will not forget Your word.17 Deal bountifully with Your servant,
That I may live and keep Your word.
18 Open my eyes, that I may see
Wondrous things from Your law.
19 I am a stranger in the earth;
Do not hide Your commandments from me.
20 My soul breaks with longing
For Your judgments at all times.
…
45 And I will walk at liberty,
For I seek Your precepts.
46 I will speak of Your testimonies also before kings,
And will not be ashamed.
47 And I will delight myself in Your commandments,
Which I love.
48 My hands also I will lift up to Your commandments,
Which I love,
And I will meditate on Your statutes.…
60 I made haste, and did not delay
To keep Your commandments.
61 The cords of the wicked have bound me,
But I have not forgotten Your law.
62 At midnight I will rise to give thanks to You,
Because of Your righteous judgments.
63 I am a companion of all who fear You,
And of those who keep Your precepts.
64 The earth, O LORD, is full of Your mercy;
Teach me Your statutes.…
71 It is good for me that I have been afflicted,
That I may learn Your statutes.
72 The law of Your mouth is better to me
Than thousands of coins of gold and silver.
…
95 The wicked wait for me to destroy me,
But I will consider Your testimonies.
96 I have seen the consummation of all perfection,
But Your commandment is exceedingly broad.
…
97 Oh, how I love Your law!
It is my meditation all the day.
98 You, through Your commandments, make me wiser than my enemies;
For they are ever with me.
99 I have more understanding than all my teachers,
For Your testimonies are my meditation.
100 I understand more than the ancients,
Because I keep Your precepts.
101 I have restrained my feet from every evil way,
That I may keep Your word.
102 I have not departed from Your judgments,
For You Yourself have taught me.
103 How sweet are Your words to my taste,
Sweeter than honey to my mouth!
104 Through Your precepts I get understanding;
Therefore I hate every false way. [Bold added.]
Recent Comments