too many facts

Ludwig Wittgenstein began to write his Tractatus almost exactly hundred years ago and the little book would become quite important for the development of positivism and analytic philosophy.
It begins with proposition 1: "Die Welt ist alles was der Fall ist."
This is usually translated as "The world is all that is the case."
followed by proposition 1.1: "The world is the totality of facts, not of things."

But I think there is a problem with this proposition.
Let us begin with a simple fact, e.g. F1 = "I am."
This is a truly basic fact and I can immediately add another one: F2 = "I know that I am, i.e. I know F1."
But there is now another fact: F3 = "There is more than 1 fact."
We can now construct an infinite number of facts from these three facts: Fn = "There are more than n-2 facts." with n=4,5,...
An interesting question is if we can count all facts and I think the answer is No.
Let us assume that all facts form a countable set {F1, F2, F3, ...}
We then have another fact for each subset; e.g. F' = "{F1, F2, F3} is a subset of all facts."
But the power set of a set S (the set of all subsets of S) always has higher cardinality than S itself.
Therefore one cannot count all facts and in fact (!) they do not even form a well-defined set.

The set of all finite English sentences is countable and so is the set of all Turing machines. In other words, neither mathematics nor the English language is capable to handle the world of all facts as envisioned by Ludwig Wittgenstein (*).
Unfortunately, he never really discusses this.

I am aware, that almost all facts stated above are statements about other facts without reference to much else. We never really got beyond "I am." and "I know that I am." and "I know that I know ... that I am."
It would seem that something like Russell's type theory would be needed here.
But the Tractatus does not do that, so I recommend to jump straight to proposition 7 and skip all the stuff in the middle.


(*) A while ago I showed that a seemingly straightforward definition of "possible worlds" leads to something that cannot be handled by set theory, i.e. math as we know it.
I think it is amazing that already all the facts that follow from two basic facts are too many to be properly handled by set theory; notice that none of the facts I considered is self-referential or otherwise ambiguous.


#LastNightInSweden



After what happened Friday night in Sweden, the country prepares for the worst...

But perhaps a great bass line makes the nights in Sweden bearable...

links

"So, to summarize: in the past fifty years, education costs have doubled, college costs have dectupled, health insurance costs have dectupled, subway costs have at least dectupled, and housing costs have increased by about fifty percent. [] I worry that people don’t appreciate how weird this is. [] But all of the numbers above are inflation-adjusted."
SSC about the Cost Disease.

"A lot of people thought the explanation was obvious; unfortunately, they all disagreed on what the obvious explanation was."
SSC highlights comments about the Cost Disease

"What we’re seeing now is that anyone can be grabbed on their way through customs and forced to hand over the full contents of their digital life."
Don't bring your phone on a flight to the US.

"US forward bases and surface deployments are hostages to advanced missile capability and would not survive the first days of a serious conventional conflict."
Stephen Hsu on preparations for a Pacific war.

"... it will be a great pleasure when, in ten years, I can say: I told you so."
Sabine predicts the future of fake news.

"Trump’s younger supporters know he’s an incompetent joke; in fact, that’s why they support him."
A brief history of 4chan, from anime to Trump.

Clyde Stubblefield passed away yesterday.
You have probably heard his beat many times without knowing it.

prospect theory

Lee mentioned prospect theory in a comment, but before we discuss behavioral economics, I would like to establish your risk aversion. So please answer the following without thinking too much about it:
Imagine that you delivered a service or job, which is worth 100$ dollars.
Would you prefer to get paid 100$ immediately, or would you be willing to wait 1 week for your payment and receive 101$ then?
This is not a trick question, just a simple question about what you would prefer.


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added later: The 101 option is equivalent to an annualized interest rate of 67% and very few investments provide for this kind of return. One has to either have a very high risk aversion or face severe liquidity constraints to reject it. But if you ask friends or family you will get mixed results (try it).
This kind of delayed gratification experiment has also been performed many times by behavioral economists; in one typical case the interest demanded ranged from 5% to 240% per month . And in the famous marshmallow experiment half the children rejected an offer to double an asset they desired in 15 minutes. Not even high frequency trading can provide for such high returns.

This raises three questions:

i) Why are real interest rates so much lower?

ii) Why do behavioral economists never point out this discrepancy?
In the linked piece a guy who demands 5% per month is described as having a “flat discount function”.

iii) Finally, is behavioral economics relevant for the real economy and financial markets?

In my opinion the answer to i) is quite simple: Real interest rates are not set by cash strapped students or little children or any single person, but liquid markets dominated by large investors. But even an odd lot investor would probably think different about interest rates when she purchases bonds, than when asked the above question.

I admit that ii) is a real puzzle to me, but perhaps I am not familiar enough with the literature.

My answer to iii) is that our everyday experience just does not scale very well to the overall economy and financial markets in particular. There are many reasons why we may prefer the immediate payment of 100$ in everyday life. Perhaps we are worried that we might forget about it, it is a hassle to chase a payment one week later and perhaps such an offer would be somehow strange in real life and raise suspicion. Also, marshmallows taste much better than money.

Don't get me wrong, I think experiments uncovering behavioral bias and economic fallacies are interesting and one should know about them. The sunk cost fallacy is one of my favorites.
But I do not expect that behavioral economics is the secret sauce that will help us understand macro economics or financial markets better. What is missing imho is some kind of "renormalization procedure", which scales individual behavior to macro economics.

Reading, Fast and Slow

I still did not finish Kahneman's book (*), but I would like to share just this one thought about it:
He references a lot of interesting experimental results, I guess on the order of a hundred. If each result is flawed with e.g. a probability of 1% , it would mean that there is likely at least one misleading result (with probability approximately 64%) in the book.

I think Kahneman would actually appreciate this kind of skeptical slow system 2 thinking.
And indeed we already know one such faulty result. It is especially embarrassing that he describes the Florida effect as "an instant classic" and writes "the results are not made up, nor are they statistical flukes".
I think the study claiming that stocks with simple ticker symbols show better performance should be re-examined too...


(*) It is the kind of book where I take lots of notes and double check things. But I am also lazy.

What's going on?



One important ingredient (fwd to 3:30) was foam.

opportunity cost

"Maybe, just maybe, these aren't the final days of the Republic.
A more likely outcome to the Trump Show is probably something far more prosaic. Maybe we'll look back on his presidency not as a dystopian nightmare, but instead as a total and complete waste of our valuable time."
link

I think after four years of this everybody will be exhausted.

added later: A bit about the prime minister of New Zealand from 1975 to 1984 ...


added even later: But then there is Moby. Yes Moby! If he really has this insider information it would be final proof that we live in The Matrix imho.

why I am not afraid of AI (yet)



I bought those two books weeks ago from you Amazon!
Why do you still show me this ad - everywhere?
Your AI and surveillance capabilities clearly suck;
and you are supposedly the biggest and best new digital economy company.

In other words, I think it is silly to worry about the superintelligence of machines taking over (*), even if they learned how to play Go recently...


(*) If you are the typical interweb person with short attention span, who does not want to read a long text, here is my advice: Scroll down to the picture with a robot in front of Comedy Lab and read the argument about the superjoke ...

added later: The machines already beat us at standardized IQ tests. I do not take this as evidence of super-intelligence, but as proof that IQ tests are not measuring intelligence (i.e. the acquisition of knowledge and skills to solve problems); even if they are somewhat correlated when testing human beings.



added even later: So who does Google think I am?




added much later: Scott Alexander about AI and all that.