### Columbo and his memories

This was recently posted on that other blog, but on second thought it really belongs here, following a proud tradition of confusing thoughts about the arrow of time.

Inspector Columbo enters an empty apartment (*) and finds a dead body on the floor. He measures the body temperature and determines it to be 33C, while the room temperature is 21C. He could now use physics forensic science to predict quite well what will happen going forward. The dead body will continue to cool and a few hours later will reach equilibrium with the room temperature. He could even predict how several days and weeks ahead this dead body will turn slowly but surely into a decaying corpse.

But he is not really interested in that. He wants to predict postdict what happened earlier. Again, he can use thermodynamics to determine how many minutes earlier the body temperature was 34C, 35C, ... But when his postdiction reaches 37C he must stop. All he can postdict is the time of death, but he can not go beyond that point. Once his calculation reaches 37C he deals with a living human being and from the data he has he cannot postdict what that person was doing. It would not make any sense to continue his calculation - and he would have to stop at 100C anyways.

In some sense 37C is like a 'singularity' for his postdiction, which he cannot cross - quite remarkable, because we are used to thinking that the past is certain and the future is not; But here it seems to be the other way around. (Actually this case is not that special; In general, physicists are pretty good at making predictions, if they have the necessary initial data, but they are not good at all at making postdictions from the same data, which is why they normally don't do it.)

Later on, the clever inspector will find clues to what happened, fingerprints and other evidence - in other words he will find documents about the past. The truly amazing thing about those documents is that they fit together and tell a coherent story (e.g. the fingerprint on the door knob is the same as the fingerprint on the knife). Even more amazing is that in the end the killer will confess and tell the inspector what happened and his memory will match the story reconstructed from those documents.

Which brings us to the final question. Why do we have memories of the past but not the future? In other words, why does the inspector consider the dead body at the beginning of our story as evidence of a murder (which happened in the past) - but not as a document and memory of the rotten corpse it will be in the future?

Is it because he knows the future better than the past?

(*) There never was such an episode, but we can assume that he solved murder cases not shown on tv. Also, I am aware that he is actually a Lieutenant.