Aliens, Forecasts, and the Shape of Signal Space

I’m going to do a remix of this earlier article. The feedback I got was: “The preamble made sense, but the math lost me.” That’s fair. This time there will be almost no math. You’ll just have to picture things in your head. My mission here is to educate highly intelligent potential stakeholders who may not be mathematicians.

Our Thesis

At AlphaNova, we believe there is room for possibly millions of predictive forecasts. That’s why the search for new signals — especially the way we’re doing it — is not only warranted but essential.

One critical point: you don’t want to just average millions of signals. That would be like piling noise on top of signal. A simple example will make this obvious. (And for the record, AlphaNova doesn’t average — we use deep learning to combine forecasts intelligently.)

Contrary to much of the consensus, we believe more signals are better, provided they are managed correctly. We’re in good company here: Renaissance Technologies is widely thought to discover signals with machines and data, not hand-built economic models. Humans simply cannot design millions of forecasts. The space is too vast.

Relative Forecasts

We focus on forecasting the relative returns of a universe of assets.

Relative means: how well will each asset perform compared to the average of the others. This is the backbone of long–short trading: long what’s predicted to outperform, short what’s predicted to underperform.

You can think of capacity in two dimensions:

• Time: more observations = more degrees of freedom.
• Space: more assets = richer geometry, and vastly more degrees of freedom.

A Stylized Example: The Time Dimension

Time is the easier dimension. More observations give you more signals, due to what we might loosely call “seasonality.” The growth is linear.

Imagine trading BTC daily:

• You hire one analyst who can perfectly predict the return on January 1. Every other day, they’re a coin flip. You’re forced to trade $100k nominal every day. One good day, 364 coin flips. Result: a dreadful Sharpe ratio.
• Now suppose you hire 365 analysts, one for each day. Analyst #1 is perfect on Jan 1, Analyst #2 on Jan 2, and so on. Each is random on the other 364 days.

If you just averaged them, you’d drown in noise. But if you selectively listen to the right analyst on the right day, you’re right every day. In this toy world, your Sharpe ratio is infinite.

The lessons are clear:

1. Time adds linear degrees of freedom. 365 days = 365 potential signals. Double the days, double the signals.
2. Naive averaging is fatal. What matters is smart, selective ensembling.

So time is helpful, but the payoff is linear. To see where the exponential elbow room comes from, we need to look at space.

The Space Dimension

Here’s where things get interesting. Because of how relative returns are normalized, the geometry of forecast space depends on the number of assets — and it lives on a sphere. It may not be the everyday sphere you know, but for our purposes, it behaves the same way.

The Alien One-Shot Landing Game

The Alien One-Shot Landing Game is a thought experiment to explain the geometry of forecast space.

• The setup: imagine aliens arriving from space. They can sense Earth’s magnetic field but can’t see. Their mothership tells them: “There’s something special about the North Pole,” but not which pole is which.
• The rule: each alien gets only one attempt to land somewhere on Earth.
• The goal: land as close as possible to the North Pole.
• The analogy: each alien represents a forecast, and the North Pole represents the true relative returns. An alien that lands close to the Pole is like a forecast that is close to being correct. Aliens landing on the same spot are redundant, and aliens landing on the South Pole are maximally wrong.

This is more than just a story. The analogy is surprisingly precise from a mathematical perspective: forecasting relative returns really does reduce to a geometry problem on spheres.

Playing the Game

Version 1: Two assets → two points
With just BTC and ETH, forecast space collapses to two poles: North and South.

• If one alien hits the North Pole, that’s the perfect forecast.
• Another alien can only pile on top (redundant) or land at the South Pole (perfectly wrong).

There’s no elbow room for more aliens to do something “different but still good.”

Version 2: Three assets → a circle
Add SOL, and the forecast space opens into a great circle: the union of the 77th Meridian East (running through Delhi, Colombo, Bangalore) and the 103rd Meridian West (passing through Oklahoma City, Monterrey, and into South America).

Now the aliens can land anywhere on this circle. Those north of the equator are “closer” to the Pole and thus useful forecasts.

• The distance from the Pole to the equator is about 6,200 miles.
• If aliens must be at least 1,000 miles apart, you can fit about 12 aliens on the northern arc.

That’s already a big improvement over the two-asset case: 12 non-redundant forecasts instead of just 1.

Version 3: Four assets → the whole sphere
Add AAVE, and the forecast space becomes the entire globe.

Now aliens can spread across the northern hemisphere. With the same 1,000-mile spacing, you can fit on the order of 100 distinct aliens, all reasonably close to the Pole.

This is the geometric explosion: going from 2 → 3 → 4 assets increases the elbow room not linearly, but superlinearly.

And Beyond: Higher Dimensions

With 5, 10, or 100 assets, the geometry generalizes to higher-dimensional spheres. These are hard to visualize, but the principle is the same: the “surface area” of these spaces grows dramatically faster than linearly.

That’s why we say there’s room for millions of forecasts. The geometry itself guarantees it.

Why This Matters

Accuracy matters — being close to the North Pole is good. But redundancy kills value — multiple aliens landing on the same spot are wasted. The value comes from diversity: aliens spread out across the northern hemisphere, each one distinct, each one adding value.

Time gives you linear growth. Space gives you exponential elbow room. That’s why AlphaNova is building machines to search signal space — and deep learning to combine them intelligently.

That’s how we move from thousands of forecasts… to millions.

If you know how to blend these forecasts intelligently and not just take the average, the rewards are absolutely massive. If you’re an investor, let’s have a chat https://www.alphanovafund.com/. If your an aspiring scientist, sign up on our platform https://www.alphanova.tech.