Appendix I: Market Data

Given the arguments made so far, it should not be surprising that certain patterns exist, albeit obscured, within seemingly random data, such as the stock market.

One test that anyone can perform shows such a hidden pattern. In this example, we have 14 months of data (632,869 values) from the 1-minute chart of Bitcoin/USD-Tether (BTC/USDT) from the Binance exchange from January 1, 2021, to February 14, 2022.

Start at the beginning of the data and take a series of values, such as 16, 24, 32, etc., consecutive values. In this example, we will use 16 consecutive values. This means we have 632,853 sets of 16 values (calculated as 632,869 minus 16), which looks something like:

Raw data

     1: [19695.49, 19646.79, 19607.03, ..., 19537.95]
        ...
632853: [42136.31, 42164.06, 42129.1, ..., 42194.44]

Then “normalize” the data to reduce each set’s values within the range of -0.5 to +0.5:

Normalized data

     1: [0.5, 0.20914, -0.02830, .... -0.44087]
        ...
632853: [-0.38965, 0.035047, -0.5, ..., 0.5]

Then apply a moving average (with a window of 3 values) to these normalized values:

Mean data

     1: [0.5, 0.20914, -0.02830,..., -0.44087]
        ...
632853: [-0.38965, 0.03504, -0.5, ..., 0.5]

Finally, round these values to a single digit:

Rounded data

    1:  [5, 2, 0, ...,-4]
        ...
632853: [-4, 0, -5, ..., 5]

The purpose of the above is to create sets of single values that represent the original values and, in the process, remove the ‘noise’ in the data.

We then split each set into two parts, the first 8 values and the last 8 values, sum the values of each part, and subtract the 1st part from the 2nd part.

For example, if we were using sets of 8 values, we’d have sets that look like this:

[-4, 0, -5, -3, -4, 1, -1, 5]

Splitting and summing the 1st part results in -12 (-4 + 0 + -5 + -3), and the 2nd part results in 1 (-4 + 1 + -1 + 5). Therefore, subtracting the 1st from the 2nd part results in 13 (1 - -12).

We now have a single number representing the relationship between the first and last half of every set.

We’ll call these values s1 for the 1st part, s2 for the 2nd part, and sd for the difference between s2 and s1.

To equate these values to something meaningful, such as the actual values of the transactions, we apply the same rule and sum all the original values together. We’ll call that value sv.

There are now 4 values for each set: sv, s1, s2, sd, for example:

-5221, -242, 135, -107   
358483, 69, -20, 49

If we plot the actual values (sv) against the difference (sd), we see a very familiar form, that of a wave or cycle:

Note: These plots were made with data sets of 63 values to increase the clarity of the plots

If we plot s1 against s2 we see another familiar form:

If we look at the plots of sv against both s1 and s2, we see 2 opposing ‘waves’, essentially a double helix:

This tells us that any sd with a value above 0 will yield profit, and any sd below 0 will lose money. The sd values form a curve, showing that (in this case) an s1 value between 50 and 100 (for 16 values, 100-150 for 63 values) is the most likely to return the most profit in s2.

In this way, we can identify potential patterns in market behavior.

This pattern is the same for any size sample, which means it can predict the next 8 minutes or the next 8 hours.

That is the theory, at least. In actual practice, when applied to trades on the Binance exchange against the 1-minute charts, going long on every transaction that has sd > 0 (along with some other control parameters) and closing at the first opportunity returned approximately 50% annually in backtesting during this specific period. This appears intuitively reasonable given we are only looking at 2 opposing forces, positive and negative.

To further test this…

Suspecting that my results might be due to something other than what I was testing for, I devised another test that used a different method on different data. My new algorithm looped through about a million data points of real-time closing prices for BTC/USDT. At every point, it took the previous 16 values and assigned a 1 to a value greater than the previous value or a 0 if less than the previous value. I then recorded the original value from positions 0 and 15, the first and last values, of each 16-element array.

This created 1,000,000 records that looked like:

0000000000000000, 20000, 21000
0000000000000000, 21000, 9000
0000000000000001, 32123, 31321
...
1111111111111110, 32101, 34321
1111111111111111, 32101, 34326

I wanted only 65,536 of these records (2 to the 16th power), one for each unique binary value, so I averaged all the amounts that had the same binary pattern (of 16 ones and zeros) to create one record for each of the binary values. For example, the two entries above of 0000000000000000 now become one entry:

0000000000000000, 20500, 15000

(20500 = avg(20000+10000), 15000 = avg(21000+9000)

Now, there are 65,536 entries, each with the average beginning and ending price of its 16 elements.

I plotted the percentage difference between the beginning price and ending price on the Y-axis and the value of the first 8 bits of each binary value on the X-axis. My assumption was that the Y-axis values, the % difference, would be generally random, so I was expecting to see something like this:

The above image is the plot of the average ratio of bullish elements (last price > first price) over bearish elements (last price < first price) for each binary value that begins with values 0 through 255

Instead, I got this!

The above image is just a small set to show the patterns. Plotting all 65,536 points looks like this:

Sorting the data by % instead of by hex values shows a more linear, less fractal pattern:

What is equally surprising (to me, at least) is the stepped aspect of the line.

If the plot is changed to only use the first 8 bits when plotting (instead of all 16 bits), we get essentially the same plot repeated in a series of “octaves”.

This second test suggested that any sequential 16 prices (in real time for BTC/USDT at least) will tend to end higher when there are more DOWN than UP values in the first 8 prices. Conversely, they will tend to end lower when there are more UP than DOWN values in the first 8 prices, regardless of what the other 8 values are doing.

This supports the first example that also states that any delta value that is above 0 (meaning the 1st part is less than the 2nd part, i.e., there are more DOWN values than UP values in the first part) will yield profit.

The Tholonic idea here is that even within random or unpredictable data, the laws of cause and effect create patterns that create balance. When there is an imbalance on one side, it is predictable that this will soon be followed by a compensating imbalance in the opposite direction. While it is impossible to predict where the balance point will exist in the future, given that there are unpredictable opposing forces constantly exerting pressure, what can be predicted is the potential opposing force to the current dominant force.

However…

These patterns are the same for any series of random numbers. When I ran these same tests using random numbers between 1 and 1,000,000, the result was visually identical. It works with market data because that, too, is random, for all intents and purposes. So, while these patterns do not tell us anything new about market data specifically, they do tell us something about the cyclical nature of even the most unpredictable events.

Applying Newton’s 2nd law to the Market

Note: This is very ‘beta’.

Here is a more detailed example of the earlier reference to Newton’s law and how it might apply to finance.

Below, in row A, we have the historical price data of the cryptocurrency Ethereum, recorded every 15 minutes from December 12, 7:45, to December 13, 17:25. The squiggly line is the raw data, and the overlaid smoother line is the moving average of the day’s trades.

We assign the following concepts in the following manner:

Voltage (V), the potential between the highest and lowest points of energy, is assigned to the difference between the opening and closing price for each 15-minute period, as this represents the price potential for that period.

Current (I) is the quantity of energy that is moving, which we assign here to the volume of trades that have taken place in that time period.

With these 2 values, we can calculate the following:

Resistance (R) is calculated as R = V ÷ I, representing the asset’s theoretically ideal value or price. We refer to this value as the Balanced Price, but in reality, the actual agreed-upon price is rarely this value, as you can see in Row G, which compares the Balanced Price (R) with the actual price. Interestingly, while the Balanced Price is calculated, the actual price is the result of the resistance between the seller wanting a higher price and the buyer wanting a lower price.

Power (P) is also calculated as P = V × I (but it is not clear what P represents yet).

In the above image on the right, there is a legend that shows the formulas used to describe these values. This requires a bit of explanation. Each value of P, V, I, and R can be calculated using 3 different formulas with the remaining 3 values. When we do this with electricity or matter, all 3 formulas for each value give the same result, as expected. Here, however, they give slightly different results. For example, calculating R₁ = V ÷ I, R₂ = V² ÷ P, and R₃ = P ÷ I², we’d expect all three values of R₁, R₂, and R₃ to be the same, at least in the case of electricity, but here they are all slightly different. However, when all 3 band values are added together, they form the exact same pattern as that of R₃ = P ÷ I². This is the same for all 4 formulas, and the above formulas have the same pattern as the totals. This is why we say the above formulas describe rather than calculate the values because all 12 formulas can do the calculations, but only 4 formulas seem to describe them.

The issue here is that even though we should be using the R₃ formula, we can’t because we do not have the values for P, as we only have the values V and I we can only use the R₁ formula. R₁ and R₃ are not the same, but they are very close (R₁ light, R₂ bold):

If we were to show all 3 R bands, it would look like this:

When these 3 bands are added together to form 1 new band, we get a single band that, when normalized to the same scale as the single bands, is exactly the same as the single band formed by I² ÷ P.

Here are the other bands as well:

This last one is a surprise because we are actually seeing all three bands; they just happen to be exactly the same for all the formulas!

Tholonically, this is very interesting because, if you remember, V is the N-source, and P is the result of the N-child. If you look at P and V, you will notice how similar they are:

This would then suggest that I and R should be opposites, which they are:

We might then expect to see the closing prices fluctuate in-between these two bands, but it seems pretty clear that the closing price follows the R line (below).

If we multiply them, we get V, as V = I × R, and if we look at the difference between them, we get something very close to R again:

In order to make these bands comparable, all the data of all the lines were normalized to the minimum and maximum of the closing prices, but the rise and fall of the values were still too extreme to properly compare. We took the nth root of the number to fix this. In these examples, n = 8 and anything after 8 was pretty similar. See the charts on the right to understand the ranges for these lines.

The R band appears to be consistently predictive of the closing price, and I suspect that if we understood more about the other lines, we could build a pretty decent market indicator.

This model seems to work better for shorter windows, like 15 minutes, than larger windows, like 24 hours.

As a test, considering we are looking at this tholonically, below is a chart where the black line is the value that is (V ÷ R) × (V ÷ I), which we’ll call the adjusted indicator. This curve is similar to the P curve but different enough to make a pattern more obvious.

For those who analyze the market, here is this model (using the Tradingview platform) applied to stocks, commodities, foreign exchange, and crypto: