Math is nothing but tautologies.

“The logic of the world, which is shown in tautologies by the propositions of logic, is shown in equations by mathematics.” Wittgenstein in Tractatus Logico Philosphicus (6.22)

> At one time, the stock market was closed at night and yet market indices often changed dramatically, even without a single share being traded. A hundred years ago, the Dow might close one day at 243 and open the following morning at 227, reflecting bearish overnight news. In that case, it is fairly obvious that the market moves on new information, not trading activity. To the extent that trading activity has any impact on prices, it is due to what the trading reveals about information held by various participants in the market.

Markets open using an auction: before the market opens, a bunch of bidders declare the price/qty they’re willing to buy at, a bunch of sellers declare the price/qty they’re willing to sell at, and at the moment the market opens, a single multi-party transaction happens immediately at the implied market clearing price. That transaction is special: it’s not attributed to any particular buyer or seller in transaction data feeds, and typically has a tick volume 1000x (or more) higher than the median tick volume during trading hours.

It may appear that markets are opening at different levels merely on new information, and new information absolutely affects it, and that market jump may not appear to move like the typical brownish motion of active markets… but that opening price is nonetheless the result of buying and selling.

Tautologies are useful to detect errors in reasoning, but not necessarily in actual policy.

The problem with tautologies is that usually the context where they are useful is very small.

As an example, lets use Equation of Exchange and Cambridge Equation. Defining "Money" (M in the equation) has become nearly impossible when there are so many liquid assets and instruments that act money like. Central banks can't reliably measure or control a single "quantity of money" in a way that reliably links to GDP. And because it's not causal model, just an equation, it does not explain anything interesting. All interesting questions are causal.

Tautologies are beautiful and helpful because they help people and are full of beauty.

  Tautologies are B&H because they confound intuition (H) AND are truthful (B)

If a stock tanks is it sellers with info selling to market makers? So a sell off.

Honestly I think any economic minister, such as the chancellor in the UK should be required to read this. It's amazing in a time when they champion growth, without understanding these relationships.

I love a good tautology like Clarke's "Any sufficiently advanced technology is indistinguishable from magic", but sometimes enough is enough!