Earlier today the sunlight hit the top of my stapler, and I noticed the reflection on the wall did not match the surface of the stapler at all. Once I finished work, I took a look, to find that there was no obvious explanation for the pattern it was producing on the wall (photos below). I then tested it using my flashlight, which produced the same result. I did the same thing to the bottom of the stapler, which again produced an inexplicable pattern (photos also below). I took the stapler apart, to find that what I was seeing was the internal plastic structure –

The obvious answer is that it’s reflecting more at the points where there’s more plastic, just like a wall that’s harder at certain points will cause a ball to bounce back harder at those points. That is, light is kinetic energy, and when it hits a surface, the amount of material it passes through will, among other things, impact the percentage of light that reflects back, rather than being absorbed or passing through it altogether (producing in that case transparency).

The stapler is truly opaque, and so e.g., placing a finger below the plastic does not change the reflected pattern. Instead, it must be that the marginal difference in luminosity in the reflection really is due to the amount of plastic at a given point on the stapler, with the most dense points producing more reflection, and therefore greater projected luminosity. I did the same thing to the bottom of the stapler, which produced another inexplicable pattern that was plainly the result of the amount of plastic below a given point.

This can obviously be used as optical storage, that’s read with an ordinary light. The advantage is that reading with a light, does not require moving the object (c.f., a compact disc), and therefore reading should be basically non-destructive, even over extremely long periods of time. Moreover, plastic is really cheap, and this is not the nicest stapler, so I doubt the substance in question is worth very much. Storing an appreciable amount of information will require either a lot of plastic, or a small scale of production, neither of which should be a problem or expensive. And again, this could create basically permanent storage if it’s otherwise cared for and simply read. This is not the new USB drive, but it could be a new means of storing data permanently (e.g., government records).

Inflation

It dawned on me the other day that you might be able to completely eliminate inflation, given adequate supply. Just imagine an auction, where bidders submit bids to an order book, and the order book is processed by the seller in a manner that maximizes the seller’s revenues. This is probably what’s going to happen with any competent seller, since they will generally seek to maximize revenues.

Now imagine that everyone is aware of the seller’s reservation price, the supply being sold, and the demand. If we assume that supply is adequate to satisfy demand, there is no incentive on the part of any bidder, to bid above the reservation price. Now assume that we give every bidder more money, effectively increasing the money supply of the auction. It doesn’t matter, there’s still no incentive to compete, because everyone knows that there’s adequate supply.

This suggests that economies could benefit radically through regulation that requires transparency with respect to reservation prices, supply, and demand, and moreover, imposes an order book concept, like you find in financial market exchanges. This is not hard to implement, and it’s at least worth experimenting with, to see if e.g., sector-based inflation can be controlled.

Yield on Consumption

Preferences have long been considered by economists, and I don’t know who considered the question first. However, I do know that prior to Von Neumann, only ordinal preferences were well understood. An example of an ordinal preference is that you prefer apples to bananas. However, this is not a quantitative relationship, and instead places apples higher in an ordinal queue, with respect to bananas.

Genius that he was, from what I understand, Von Neumann flippantly solved the problem of cardinal preferences using lotteries. Specifically, he attached probabilities to outcomes, and then asked for the indifference point. So as an example, you could be indifferent to getting an apple with a probability of .2 (and getting nothing at all with a probability of .8), and a banana with a probability of .8 (and nothing with a probability of .2). If that’s true, then you view both lotteries (apple lottery and banana lottery) as equivalent, suggesting that you’re willing to take the significant chance that you get nothing in the case of an apple, because you like apples so much. You could argue that you like apples 4 times more than bananas. As a result, Von Neumann’s use of lotteries allows us to at least think objectively about cardinal preferences.

However, just because people assign such great value to e.g., apples versus bananas, doesn’t mean that they’ve solved a problem in economics. For example, just ask an alcoholic, whether they’d rather have a beer versus dinner, and you’d be shocked to find that at least some would go for the beer. In more precise terms, even if we can measure cardinal preferences, it doesn’t imply that human beings have tuned them to any reasonable metric. The question is then, can we measure the “correctness”, for lack of a better word, of the consumption behaviors of individuals. I believe the answer is yes.

Specifically, consumption will impact GDP. As a consequence, we could in a laboratory environment substitute one consumer good with another, throughout an entire economy, and measure the impact on GDP over time, versus a control economy that did not make use of the substitution. Though this is difficult to do in practice, we can nonetheless construct obvious thought experiments. For example, imagine instead of paying for internet service, everyone in the United States decides to eat $150 worth of candy every month, forgoing internet service. This will with near certainty have a negative impact on GDP, and eventually, a negative impact on health, which will again, have a negative impact on GDP. This simple experiment implies that the yield on consuming internet services is significantly higher than the yield on consuming candy.

This is deliberately a bit comical, but it’s an extremely serious idea, that would allow for objective preferences, that are simply correct, in the context of the returns they generate. In this view, societies that have objectively better preferences, will have higher GDP’s per capita.

It dawned on me last night, that it’s difficult to do worse than chance, when predicting a random variable. Specifically, if the lowest probability event in a distribution is e.g., , it’s not clear how you can achieve an accuracy that is lower than , but I’m not an expert on probability, so there could be a known result on point. I noticed this because one of my algorithms routinely performs worse than chance, and I never cared, because it uses confidence filtering to produce accuracy that is on par with other machine learning algorithms. See Information, Knowledge, and Uncertainty [1], generally. But it’s actually astonishing upon reflection. For example, try to underperform 50% accuracy using a fair coin. I don’t think it’s possible over a long run, though again there could be a result on point. In fact, if you can underperform chance, it suggests that you have information about the system. For example, if I know the next outcome will be heads, I could deliberately select tails. This will eventually cause my accuracy to be zero.

The net point being, that if your accuracy is under 50%, you actually know that your answer is probably wrong, which is actually positive information regarding whatever system you’re attempting to predict. Specifically, if your accuracy is less than 50%, then it’s more likely that the correct answer is in the compliment of your prediction (i.e., the set that contains every outcome other than your prediction). This sounds trivial, but it’s not, because it’s a different kind of information. When accuracy is above 50%, the most likely answer is a set with one element, asserting a possibility. When accuracy is below 50%, the most likely answer is the compliment of a set, excluding a possibility. In the extreme case, when your accuracy is significantly below chance, this allows you to exclude a possibility with high confidence, which is often useful. That said, it’s not clear how this could happen, but again, the algorithm I describe in [1], does exactly that, routinely.

One possibility, is that there really is a fundamental principal that accuracy increases as a function of the information upon which a prediction is based, and if you can reduce the information, or increase the information, you can achieve arbitrarily low or high accuracy, regardless of what you’re trying to predict. This is consistent with another astonishing observation I made, that you can actually predict random variables using the techniques I outline in [1], with high accuracy, which should otherwise be impossible. This does not contradict the laws of probability at all, since it’s only a subset of the output of a random source that can be predicted, but it’s nonetheless a counterintuitive, and potentially profound result.

I’ve thought a lot about the physical meaning of infinity, but it just dawned on me that a simple thought experiment suggests that infinity could be physically meaningful, in the simple sense of unbounded quantity: just consider the unbounded expansion of time. There’s no reason to assume that the Universe will ever vanish, even if all the mass and energy within the Universe does vanish. This posits a vacuum that exists, and persists through time, implying time is infinite, even if there’s nothing happening in that vacuum (i.e., it’s just an empty space that nonetheless exists).

Let’s dispense with that notion, and consider instead the mass and energy in the Universe itself. Fields can effectively destroy energy – just imagine light escaping from a massive object, it could red shift into literally nothing, if energy is quantized. However, fields cannot (to my knowledge) destroy mass. As a consequence, if all mass and energy were to vanish, it would have to be the case that all mass is converted to energy, and then destroyed via gravity. However, you can’t have gravity without mass, which implies that it is literally impossible for all of the energy in the Universe to be destroyed, since even in this view, you’d always have at least some mass. Therefore, time must be infinite, absent other assumptions.

If time is infinite, then it suggests the more general possibility of unbounded quantities, in particular, arbitrarily precise measurements. You don’t need the set of real numbers to have problems with predictions, you just need arbitrarily precise measurements, which would always imply non-zero error (i.e., the unexplored portion could always contain information). If the consequences of the error are meaningful, your predictions will be meaningfully wrong. Because humans have finite lives, if arbitrary precision is real, then it necessarily implies all predictions carry uncertainty.

My AutoML software, Black Tree AutoML, can already predict credit outcomes with no specialization at all. But it just dawned on me that with a bit of work, you can use any clustering and classification system to model credit in a meaningful way. First let’s define the relevant properties of a credit, which are its assets, and its liabilities, and for simplicity, we’ll include the equity capital of the credit in its liabilities. This will allow us to express a credit, at a given moment in time , as a vector , where each is the value of assets of type owned by the credit, and each is the value of liabilities of type owed by the credit. Because this is so abstract, this allows you to consider not only corporates, but SPV’s as well, and individuals.

Now let’s posit a dataset of credits , that were sampled over time. That is, is actually a time-series of a given credit, and we can evaluate , for any within some ordinal interval, though you could also consider specific periods of time as well. The overall gist being, we have observed and recorded the state of a given credit over time, in the form of the vector . We can therefore, pull all credits that are sufficiently similar to some new input credit , which will produce a cluster of similar credits. Because our dataset contains time-series data for each of the credits returned in the cluster, we can form possible future paths for . This will allow us to say, as a general matter, what the future of will look like, given its present state . Moreover, we can easily construct a probability of default, again using the cluster, since all of the credits in the cluster either paid or didn’t, though you could have some unknowns as well as a practical matter (i.e., those credits are still outstanding).

Applying this process repeatedly to the initial state of some credit , we will construct a set of possible future paths for , given that initial state. Specifically, first we find the cluster associated with . Then, we find the next state for each credit in that cluster. So, e.g., if credit is in the cluster associated with , we find the next state of in the cluster, which we can represent as . We do this again, for all such , and continue as desired, and this will produce a dataset of possible future paths for the credit, which will grow exponentially as a function of time, and at each ordinal interval of time, there will be some probability of default based upon the dataset.

My AutoML software is typically really accurate, so I would wager that if you use my software for the clustering step, you’re going to get great answers, and probably make a lot of money as a consequence, and so it’s another great reason to buy my software, which is comically better than everyone else’s.