The Law of Contradiction

Transcript of the Opening Statement of Dr Li in the Hearings Concerning the Proposed Dissolution of the Stochastic Utopia Institute.

I’m here today as the CTO of the Stochastic Utopia Institute to speak in defense of the work that I and my colleagues do. I sympathize with the motivations behind this hearing today. The accusations against us are serious, and it is inherent in the nature of our work that it is difficult for the public to assess its benefit. But I believe most of the concerns arise from misunderstanding, and so I am very hopeful that today’s hearing can be productive for moving the conversation forward. We seek nothing less than the creation of paradise on earth, so I hope that at least our motivations have earned us some charity, however much you may be skeptical of our methods.

Some claim that you cannot change the past. This is false. But this mistake is forgivable, because the way in which the laws of physics allow us to change the past are subtle and difficult to understand. At the risk of belaboring our proceedings today, I’ll explain the nature of it to you all as I do to my undergraduates, because it is only through a proper and detailed understanding of the physical constraints that the proceedings today can be fully informed.

You can change the past. I repeat, you can change the past, but only if doing so is consistent with the Law of Contradiction. That is, you can change the past only if by doing so, you do not create a contradiction. This may seem difficult, or even impossible. Chaos theory and the butterfly effect would predict that any change one may make would have compounding consequences, and so even taking a single breath of air before your birth could cause you to never have been born.

But fortunately for us, there is a loophole. The Law of Contradiction is stronger than the laws of probability, and allows them to be broken. That’s what makes the whole enterprise work, and that’s how we detected the Law of Contradiction in the first place. If you’ll indulge me for a few more minutes of didacticism, you all are probably familiar with the famous Rubber Ball Experiment, at least by name, but I would like to walk through its details, because I believe it will be instructive. 

At time 0 minutes, person A walks into a room with two rubber balls in boxes, left and right. They flip a coin. If the coin is heads, they pick up the left ball. If tails, they pick up the right ball. Then they put that ball in the time machine, send it 30 minutes back in time, and write down their coin flip.

At time -30 minutes, person B takes the rubber ball from the time machine. They then put it in the right box, while its 30-minutes-younger twin is in the left box. Then they flip a coin. If the coin is heads, they trade the two balls between the boxes so that the time traveling ball is now in the right box. If tails, they leave them where they are. Person B writes down their coin flip, and leaves.

If both coins were heads or both coins were tails, we would have created a contradiction. The ball sent back in time would become disconnected from the original, since the original would never enter the time machine. A ball that comes from nowhere, and returns to nowhere, is physically impossible. But if one coin is heads, and one is tails, or vice versa, we haven’t created any contradiction. In that case the ball proceeds into the future as it normally would, just a little older from its short trip into the past.

This experiment has been conducted thousands of times, and 99.5% of the time, the coins don’t match, one is heads and one is tails, so no contradiction is created. If there were no possibility of contradiction, we’d expect the coins to match 50% of the time, as you can observe by flipping any two unrelated coins. But, because we’ve created the possibility of contradiction through time travel, the laws of probability break.

What happens in the remaining 0.5% of the time when the coins match? In those cases something else goes wrong with the experiment. Sometimes one of the people forgets which way the flip landed and follows the wrong instructions. Sometimes they trip and knock over the table and mix up the balls. One time a fire alarm went off, and the second person had to put the ball in the time machine much later, long after they had forgotten their coin flip. There’s a long tail of possibilities. But nevertheless, a contradiction is never created. By conditioning the experiment on such thoroughly random events as coin flips, we concentrate the resolution of the contradiction into those coin flips, rather than all the other ways the contradiction might be resolved. Just as Bell’s inequalities proved that quantum mechanics rules out local realism and that the laws of the universe must contain randomness, the rubber ball experiment has proved the Law of Contradiction without any doubt. 

When you’ve precluded half of the probability space in this way, the remainder tends to have stranger events, so we have to be careful not to push it too far. Fire alarms and tripping over your own feet are relatively ordinary occurrences, so it does not seem so strange when the experiments fail in this way. But suppose instead we used biased coins which would come up heads 99% of the time. In that case, the law of contradiction would preclude .99*.99 + 0.01*0.01 of the possible events, or 98.02%. In that scenario it becomes more likely that the experiment will fail in some outlandish way. The resolution of the contradiction would no longer be so concentrated in the coin flips, because their outcome would be less random. There are a lot of strange events whose probability is competitive with the 2% chance the coins will disagree, and so all sorts of unlikely mishaps would ensue. 

This same experiment was done with subatomic particles a few decades ago and that experiment also demonstrated the effect, but at the time, people were still skeptical of what it really showed. The time scales were short, and subatomic particles are probabilistic anyways, so many still thought that this behavior was just an unexpected consequence of a corner of quantum mechanics. But now that we’ve demonstrated it on the macro scale, people take the opposite stance. We now believe that quantum mechanics is itself a consequence of a universe that permits time travel. A purely deterministic universe doesn’t have any probabilistic slack. In such a deterministic universe, where only one outcome from any event is possible, any time travel would immediately create an infinite number of contradictions. But the universe we inhabit is probabilistic. And because it is probabilistic, it can resolve contradictions simply by choosing different, less likely outcomes.

Microscopic time travel with subatomic particles has enough inherent quantum randomness that all contradictions are easy to resolve. A smaller subset of the quantum states become valid, but this poses no problem in the typical case. Macroscopic time travel does not have this property. Unless randomness is injected, contradictions become easiest to resolve simply by preventing the time travel from ever happening in the first place. It was in fact due to this property that all experiments in macroscopic time travel failed for several decades for seemingly idiosyncratic reasons. There were bizarre equipment failures, blown fuses, bad capacitors, steel with grain weaknesses, but it went beyond that. Climatologists have now in retrospect detected a statistically significant increase in severe weather at that time focused on the locations of those experiments. Lacking any other source of focused randomness, the weather became one of the easiest events for the universe to use to disrupt them. It was not until the rubber ball experiment that any succeeded. It seems absurd that such a low tech solution as a coin flip could make the difference between success and failure on top of the technological marvel of the time machine itself, but that is the universe we live in.

So now I believe that if you understand these constraints on how one might change the past, the motivation for the abstruse and controversial details of our operation become more clear. At the Stochastic Utopia Institute we seek to send people, missionaries we call them, back in time to change the worst events of our history, and thereby create paradise on earth. And yet our sending of those missionaries cannot be caused by those events, or we would create a contradiction. How can this be accomplished?

First, the way we select the time that missionaries will be sent to must not be caused by the event we wish to prevent. This seems superficially impossible. Of course if we wish to prevent an event, we must send a missionary to a time before that event, and so our knowledge of it pollutes our choice. But just as in the rubber ball experiment, we use randomness to get around this constraint. By randomizing the time to which we send the missionary, we ensure that there are possible worlds in which the event we wish to prevent was prevented, but in which we still, by chance, send them to that time. From the viewpoint of a universe in which the missionary was successful, they were simply unlucky, and sent by chance to a time with no terrible events to prevent. There is a tradeoff here, for the more we randomize the time to which we send them, the less the forces of probability are pushing against their success. But of course, if we send them to a time at which no pivotal action is possible, then they will certainly fail.

Much more difficult is preventing any causation from affecting the minds and experience of our missionaries, and this is the source of most of the controversy with our program. The missionaries must have no knowledge of the events they are attempting to prevent. If they knew of those events it would necessarily cause a contradiction if they succeeded, and so they would certainly fail. This is why we raise them from infancy in total isolation from the outside world with no knowledge of history. They must be taught only the general principles of right action, and such history, math, and science as predates any event we might wish to change. The majority of their instruction occurs only after they have come of age, once the pivotal event for their mission is selected, and we educate them to the extent we can on the history that occurred before the possible times they might be sent to, but no more. Some leakage is inevitable, but the greater the leakage, the lower the probability that they will succeed, because it forecloses more of the possible worlds in which they succeed.

Our critics consider the treatment of our missionaries to be cruel. And it is true that they have very little agency over their lives. They grow up without most of the comforts that people today enjoy. They are sent to a difficult period of history with little training. But the one thing that each of them does have is purpose, and we believe that most today would envy them that. Each of them knows, from birth, that they have great deeds to do. And when they finally enter the past, they know that the reason they exist at that time is to change the world for the better. Few of us could say that our lives had been put to so noble a use. Our critics who have sought to undo their isolation no doubt have their best interests in mind. But consider, if you knew that living a normal life would doom you to never fulfill your purpose on this earth, would you take that deal?

We believe that by sending people back in time, even with no foreknowledge of those times, but with the singular purpose of preventing calamity, we can create an equilibrium in which better events come to pass. But how can we test this? How can we know whether any of our missionaries have succeeded?

It is difficult, and we can never be completely certain. No known laws of physics allow an observer to observe a retroactive change to the universe in which it resides. But nevertheless we have circumstantial evidence. The secret is found in the distribution of times to which our missionaries are sent. Just like the Law of Contradiction in the Rubber Ball Experiment left its obvious fingerprints in our improbably synchronized coins, so does the work of our missionaries in the past cast a shadow on our random number generator.

Our organization carefully chooses which calamities in history we would like to prioritize to prevent, and accordingly set our random number generator to choose a random distribution of times around them. However, just like the coin flips, the distribution we ask of it is not the distribution we observe. Instead what we see is a uniform distribution over time, with notches cut out at the worst events in history. The events we wish to prevent the most are seemingly at times when some contradiction prevents us from sending missionaries there to prevent them. 

What could explain this? We do not believe that there is some inherent contradiction blocking time travel to those times. Instead, we believe this pattern is caused by survivorship bias. The calamities that our missionaries succeed at preventing are necessarily ones that we never learn about, while the ones that remain are only those which our missionaries were unable to prevent. If we are in a universe in which most of the calamities of history had been prevented by our work, the pattern we see is the pattern we would observe. The missionaries we send to peaceful pleasant times would be preventing calamities that consequently never occur, and so in our time we never become aware, and think of that time as pleasant and peaceful. So we believe that this distribution is good evidence that we have been wildly successful. 

The only exception to this pattern is found in the great plague of 1938, where despite successfully sending many missionaries to pivotal times before it, it still looms large in our history. Either these missionaries have all failed at their task, or they have prevented some calamity even greater than the plague. What calamity could be greater? We will almost certainly never know. A world in which our organization exists must necessarily reach a stable state where, despite our efforts, no action can be successfully taken to fix the calamities that remain. Yet we believe the existence of our organization is responsible for this equilibrium being as good as it is, and so we have no choice but to soldier on.

Leibniz believed that there was a solution to the problem of Theodicy, that an all loving, all powerful God could nevertheless create a world with evil. He believed that God must have chosen this world as “the best of all possible worlds,” and that constraints beyond our understanding dictated which worlds could be, and which could not be. We do not know if such a god exists. But we do know that we exist. And we know that we have the power to make our world, if not the best of all possible, then at least a little bit better. And we believe that we have evidence that we are doing so. As Stewart Brand said, “We are as Gods, and might as well get good at it.” Now that we have this power, power that the ancients ascribed only to God himself, how can we countenance giving it up? 

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