“…if you want utility, don’t optimize expected utility because you’re bound to lose actual utility.” Ole Peters and Oliver Hulme, May 2025.
Expected-utility maximizers don’t maximize utility. – Ergodicity Economics
As ever, Ole makes it so clear. This wonderful note perfectly echoes our own claims around Sharpe World stalwarts, like Modern Portfolio Theory (MPT), that are explicitly optimizing to expected returns. Exactly as Ole shows, they are explicitly impairing actual returns.
“…agents who follow the prescriptions of expected-utility theory do not maximize utility in the long run; agents who follow the prescriptions of ergodicity economics, on the other hand, do maximize utility in the long run…We conclude: expected utility is a bad thing to maximize if you want to maximize utility” Ole Peters and Oliver Hulme, May 2025.
Inside the note, Ole provides a link to their coin-toss game at their website.
Figure 1: Expected vs Actual Utility in the Coin-Toss Gamble
Source: The infamous coin toss – Ergodicity Economics
We wrote about ergodicity and the coin-toss game way back in September 2020 Convex Strategies | Risk Update: September 2020 – Ergodicity.
“As usual, it simply comes back to the math. It is the flawed practice, throughout the industry, of applying ensemble averaging as though wealth were an ergodic progression, and therefore using simplistic short term, probabilistic, expected returns as a decision-making tool. Properly evaluated, investment returns must be evaluated as non-ergodic and evaluated with time averages. Each of us can only get the results that we get, we can’t get the average of results of a large group and cannot go back in time to change the results once received!” Convex Strategies, September 2020.
The alignment of the above picture to the multitude of portfolio examples that we show month after month ought to be obvious. Portfolio strategies that are optimized on the basis of expected returns/utility are realizing suboptimal actual returns/utility. Portfolios tuned to be resilient to the divergences from the mean of expectations, convex barbell portfolios, deliver far superior actual returns/utility.
Ensemble averages don’t drive actual compounding paths, in fact they impede them, geometric averages do. In Ole’s coin-toss example, the expected value of each toss is +5%. The geometric average is -5%. Something like the investment concept of Risk Parity, what most consider advanced-Sharpe World technology that improves upon the core premise of a 60/40 balanced portfolio, is based on the premise of targeting expected return and levering assumed diversification benefits based upon assumptions of the stability of historical volatility and correlations. It is, as we have said so many times before, an explicit recipe for volatility drag, exactly what Ole is showing in the divergence of actual utility from expected utility.
On the other hand, an example of a transformation of a traditional 60/40 balanced portfolio to something that is targeting actual utility, focusing on the time-averaged maximization of wealth/utility, would be something like our hypothetical Always Good Weather (AGW) portfolio. In AGW we take the capital tied up in the 40% bond allocation and split it between explicit loss mitigation and more participating equity risk. As a very simple example, in the below we compare the S&P Risk Parity Index 10% Vol Total Return Index (SPRP10T Index) to a transformed 60/40 where we have simply split the 40% bond allocation equally between the explicit loss mitigating strategy of the EurekaHedge Long Volatility Index (EHFI451 Index) and an allocation to a proxy of juiced-beta the Nasdaq 100 Total Return Index (XNDX Index). Thus, an AGW that is 60% SPX Total Return (SPXT Index), 20% Nasdaq, and 20% LongVol, rebalanced annually.
Figure 2: Hypothetical AGW 60/20/20 (blue) vs Risk Parity (red). March2009 – May2025. Compounding view
Source: Bloomberg, Convex Strategies
The AGW portfolio has less risk, more return. It has a lower Max Drawdown (18.4% vs 19.3%) and a lower Downside Volatility (6.4% vs 7.5%). It has higher CAGR (13.8% vs 9.1%), higher Sortino Ratio (2.1 vs 1.2), and a superior Convexity Ratio (1.09 vs 0.96). Most importantly, over circa 15 years, it has nearly 2x the terminal capital amount (816.65 vs 414.45). Actual utility!
One simply needs to understand that the red line is showing the actual utility of the strategy that was trying to optimize to expected utility, per Ole’s coin-toss image above. The blue line is the actual utility of a strategy that was optimized to time-average compounding through time, i.e. optimizing to actual utility. It is hard to argue that end capital holders wouldn’t prefer optimizing actual utility over optimizing expected utility!
Of course, for your standard fiduciary and Sharpe World practitioner, it is much easier to optimize to the known (assumed?) expected returns, than it is to optimize to the unknown actual future returns. Yet, it is precisely because we don’t know what will happen that tells us we should optimize to the divergences from expectations, rather than to the mean of expectations.
Figure 3: Hypothetical AGW 60/20/20 (blue) vs Risk Parity (red). March2009 – May2025. Monthly Scattergram and Return Skew
Source: Bloomberg, Convex Strategies
The green arrows highlight the performance in the two most extreme months, the 1-2 percentiles of monthly outcomes. These are the months that have the largest impact on the compounding path. As we always say, everybody is going to get their own 1 percentile of outcomes, inevitably.
It is the protection against the worst of outcomes, and the active participation in the best of outcomes, that will differentiate the long-term performance of terminal capital. Optimizing to the expected outcomes will impede compounding. The red strategy is diversifying against its participating risk through capturing positive carry, positive risk premia, in low correlated strategies. The blue strategy is explicitly diversifying against its participating risk through acquiring negative carry, explicit loss mitigating strategies.
As we can clearly see, positive carry may indicate positive expected return, but it does not equal positive actual return. Likewise, negative carry may indicate negative expected return, but it does not equal negative actual return.
As we said above, it is very difficult to adapt from one to the other, especially when all the standard tools revolve around pursuing expected returns/utility. Regulations and industry practices discourage Rational Accounting Man from pursuing solutions outside the impositions of Sharpe World orthodoxy. How do we advise people to make the transition from optimizing expected utility to optimizing actual utility? We encourage them to just do it. Just get started. Start freeing capital from ineffective portfolio diversifiers and start building explicit negatively correlating convexity into your portfolio, and taking the additional participating risk that it allows. Do a little bit every month, we expect that you will be better off, with a more resilient portfolio, and a lot more understanding in one year. Better again in three years we believe. And so on. Don’t sit around waiting to figure out how to fit a non-linear peg into your linear optimizer engine in hopes of it spitting out some magical precise weighting for something that it cannot know.
Sitting around and discussing it, month after month, year after year, and trying to use your old expected-return-optimization tools to find the right answer for optimizing a portfolio to the divergences from expectations, is not going to find a solution, we would suggest. Trial and error, learn as you do, is the answer to this puzzle.
As Nassim Taleb puts it in his fantastic book, “Antifragile: Things that Gain from Disorder”:
“…the simpler and more obvious the discovery, the less equipped we are to figure it out by complicated methods. The key is that the significant can only be revealed through practice.” Nassim Taleb, “Antifragile”, 2012.
We show picture after picture like the above blue line versus the red line. We are convinced that those that started the adjustment 5, 10, 15 years ago, are way ahead in their respective 40-lap Formula One race, and much better structured for the challenges that will, invariably, appear on the unknown future track. They also have the benefit of a lot of learning under their belt.
If we accept that optimizing expected returns/utility is suboptimal for maximizing actual return/utility, it behoves us to explore better alternatives.
“…it is downright irrational if one holds on to an old technology that is not naturalistic at all yet visibly harmful…” Nassim Taleb, Antifragile, 2012.
This all tracks exactly with our work on Boundedly Rational Agents (BRAs) and heuristic decision making. There are a whole bunch of things that we just don’t know (uncertainty) and a whole bunch of things that we cannot calculate (intractability). In such a world, a simple heuristic is to cut off the downside and maintain participation in the upside through an investment in the non-recourse leverage of optionality.
“Optionality is about getting the upper half of luck.” Nassim Taleb, Antifragile, 2012.
Here is a very simple visual over the last six-plus years.
Figure 4: CBOE Put Protect Index (PPUT3M Index – blue). Bloomberg US 60/40 Index (BMA6040 Index – white). CBOE BuyWrite Index (BXM Index – red). Jan2019-May2025
Source: Bloomberg
The interpretation could not be more straightforward. The PutProtect index (blue), buys put protection (takes on non-recourse leverage) and owns the underlying S&P market risk. For a fee, the option premium, it gets to participate in all of the potential upside and gets to forego extreme downside. The white line, a traditional 60/40 portfolio (white), has reduced its exposure to the downside by delevering its position and holding 40% of its capital in bonds. It is, going back to our race car analogy, managing risk by driving slowly. The BuyWrite Index (red), is owning the underlying equity risk and, we suppose in their minds, earning something of value for selling calls and foregoing the upside, while keeping the downside, of their exposure.
Again, optimizing to expected return/utility, would say that the holdings in bonds and the premia received on selling calls had positive expected returns. Turns out, they have lower actual returns/utility than the negative expected value of the option premia spent to own the downside protection against the underlying equity exposure by the PutProtect strategy. The PutProtect strategy got the “upper half of luck.”
One of our heroes, Gerd Gigerenzer, lays out these three simple heuristic rules in his opus “Bounded Rationality: The Adaptive Toolbox”:
- “Simple search rules. The process of search is modelled on step-by-step procedures, where a piece of information is acquired, or an adjustment is made, and then the process is repeated until it is stopped.
- Simple stopping rules. Search is terminated by simple stopping rules such as to choose the first object that satisfies an aspiration level…Simple stopping rules do not involve optimization calculations, such as computations of utilities and probabilities to determine the optimal stopping point.
- Simple decision rules. After search is stopped and a limited amount of information has been acquired, a simple decision rule is applied, like choosing the object that is favored by the most important reason – rather than trying to compute the optimal weights for all reasons…”
This is such a great step-by-step explanation of, for example, the wonderful Total Portfolio Approach research from GIC (Singapore’s sovereign wealth fund) and JP Morgan Asset Management (JPMAM) that we have referred to many times before (eg. Convex Strategies | Risk Update: September 2024 – “Emergence”.)
GIC-ThinkSpace-Building-A-Hedge-Fund-Allocation.pdf
They searched across their chosen universe of hedge funds. Evaluating them across dynamics such as correlation to an equity benchmark, performance during major drawdowns, reliability of that performance, and some measure of alpha.
Figure 5: GIC/JPMAM Universe of Hedge Funds and Performance during Equity Drawdown. Jan2011-Dec2023
Source: JPMAM, GIC, HFR, and Pivotalpath
They stopped when they had classified the underlying hedge fund performance by factors of portfolio contribution; 1) Loss Mitigation, 2) Equity Diversifier, 3) Equity Compliment, 4) Equity Substitute.
Figure 6: GIC/JPMAM Classification of Hedge Fund Contribution Factors. Performance during Stress. Annual Alpha. Average Correlation to Equity Benchmark. Jan2000-Dec2023
Source: JPMAM, GIC, HFR, and Pivotalpath
They decided to choose the factor that favoured an optimization across the entire portfolio, based on a limiting factor of not more than 20% in a hedge fund allocation, that resulted in the best Sharpe Ratio. They did two versions. One where they optimized the hedge fund allocation on a standalone basis and the other where they optimized the entire portfolio. (Side note; we are not sure why, in a Total Portfolio Approach mindset, they need the optimization to the standalone hedge fund piece.)
Figure 7: GIC/JPMAM Portfolio Optimization to Sharpe Ratio Determinant. Jan2000-Feb2023
Source: JPMAM, GIC, HFR, and Pivotalpath
The results speak for themselves. In the standalone hedge fund component, Loss Mitigation gets 60% of the 20% (12% of the total portfolio) of the hedge fund allocation. In the full portfolio optimization, 100% of the 20% goes to the Loss Mitigation factor, which reduces risk sufficiently to allow for a further reduction in the bond allocation by 2%, adding to the equity weight by 2%.
We love this work from GIC/JPMAM. It is a near-perfect example of our Boundedly Rational decision heuristics. Just a straightforward analysis, without any nonsense about made-up expected returns, that optimizes to the one thing they have decided matters, ie total portfolio performance. Why bother with the complexities of trying to figure out and optimize to the expected returns of all the different strategies when that explicitly does not optimize actual returns? We cannot commend this work highly enough.
We say “near-perfect” because we would advocate three very simple changes to their search, stop, decide process.
- Expand the search to include Explicit Loss Mitigation Strategies, eg Long Volatility strategies.
- Don’t stop at simple measures like correlation. Go beyond to measures of convexity like downside correlation, downside volatility, downside beta.
- Decide based on a metric more conducive to the ultimate objective of improved compounded outcomes. Replace Sharpe Ratio (the Wittgenstein Ruler of investment performance) as your decision metric with Sortino Ratio.
We made a little effort at adapting to these improved heuristics and added the EurekaHedge Long Volatility Index (an index of the performance of long volatility hedge fund managers), what we have dubbed “Explicit Loss Mitigation”, then tried to replicate the GIC/JPMAM analysis.
Figure 8: Universe of Hedge Funds including Explicit Loss Mitigation. Performance during Equity Drawdown. Jan2011-Dec2023
Source: Bloomberg, Convex Strategies
The jump in performance during drawdowns, from the Explicit Loss Mitigation, clearly stands out. It is the same again in their stress vs alpha vs correlation view. (Note, due to data access constraints, we have used different start dates, 2005 vs 2000, than GIC/JPMAM.)
Figure 9: Hedge Fund Contribution Factors including Explicit Loss Mitigation. Performance during Stress. Annual Alpha. Average Correlation to Equity Benchmark. Jan2005-Dec2023
Source: Bloomberg, Convex Strategies
Again, even to the naked eye, the results jump off the page.
Finally, making the adjustment to Sortino Ratio as the decision factor, along with the inclusion of Explicit Loss Mitigation, generates the below.
Figure 10: Portfolio Optimization, including Explicit Loss Mitigation, to Sortino Ratio Determinant. Jan2005-Feb2023
Source: Bloomberg, Convex Strategies
Now, with the addition of Explicit Loss Mitigation, and optimized to downside volatility, ie Sortino Ratio (as opposed to annual volatility, ie Sharpe Ratio), again 100% of the 20% constraint of the hedge fund allocation goes to Explicit Loss Mitigation. The difference is, the far greater impact the Explicit Loss Mitigation has on the (actual) risk measure of downside volatility (how, in anybody’s mind, is foregoing upside volatility risk management?), allows for a reallocation of the entirety of the remaining bond weighting to additional participating equity exposure.
In this example, from an historic perspective, the optimal barbell 80/20 portfolio is ‘same risk, more return’. But, as we always say, “history alone is a poor measure of risk”. It only tells us what did happen. As with our above example comparing the PutProtect Index to the BuyWrite Index, our convexity improved portfolio, with highly asymmetric negatively correlating exposure and greater upside participating weights, always had more protection against bad occurrences that could have been and more participation for better outcomes that might have arisen. It is optimized to divergences, optimized to actual utility.
One of the very best voices on the real-world implications (above and beyond just the world of finance and economics) of Bounded Rationality, is our dear friend Dr. Pippa Malmgren. Her latest Substack note, “Heartware”, is an absolute must read. As an extra gift, our other friend Grant Williams, interviewed Pippa on his “Hundred Year Pivot” podcast series, giving Pippa free reign to weave her thread around this concept, and made it available (truly a gift) to the whole world.
As you read Pippa’s note, and listen to her interview with Grant and Demetri, keep in your mind the principles that we discuss so often in these pages – the importance of tacit knowledge, skin-in-the-game, accountability, convexity, acceleration and deceleration, Bounded/Ecological Rationality, and our own concept of the God Particle (the infinitesimal point of convexity). You put good brakes on your car, not to drive slowly but, rather, to drive faster, safely. You avoid the unrecoverable so you can advance toward the unimaginable.
Just like Pippa’s “Dry Brain vs Wet Brain” aligned so perfectly with our own “Probability vs Possibility” (Convex Strategies | Risk Update: March 2023 – Probability vs Possibility), so too does her “Heartware” align to our concept of the “God Particle”. As she puts it in her note:
“It is the heart that connects the rational and the imaginal.” Pippa Malmgren, “Heartware”, May 2025.
It is the point between acceleration and deceleration. The point between playing offense and playing defense. The point between participating and protecting. It is Mandelbrot’s fractals. It is convexity.
“This strangely echoes one of our most ancient stories, the story of the God Indra’s efforts to create reality by casting a net out into the universe. It connected all people and things. At the point of connection between everything is a unique jewel. Our universe shines in the brilliance of these infinite jewels.” Pippa Malmgren, “Heartware”, May 2025.
How does Pippa advocate advancing forward and overcoming established paradigms? In our words, she says “just do it”.
“We are hesitant to abandon a well-established paradigm and a clear set of rules and assumptions because new paradigms have not yet been established. If we shifted our focus and leaned into our heartware, into our right hemisphere, and into a world where we are the gift (not the job), we might find a greater willingness to embrace changes that our amplified left hemisphere is now generating at ever-greater speed. Instead of resisting change, we’d be better at embracing it.” Pippa Malmgren, “Heartware”, May 2025.
“If we put humans at the center of our thought process instead of the system, we’ll get very different answers.” Pippa Malmgren, “Heartware”, May 2025.
From an investment perspective, if we put the actual utility of the capital owner at the centre, we will get very different answers. Thank you, Pippa!
Another very worthwhile read comes from our friend Ben Hunt in a recent edition of his Epsilon Theory, “Beyond Nudge”. He too has been generous enough to open this note up to the entire world.
In this wonderful note, Ben warns of the ‘nudging’ inherent in the evolution of our interactions with the various advances in AI systems.
“The meta of first-gen LLMs was to be a magician performing a trick. We would ooh and ahh when the trick was performed well, boo and throw tomatoes when it wasn’t. But we knew that we were watching a magic show. Today’s LLMs have a meta beyond that. They are now a magician performing a trick of a magician performing a trick. We don’t see this new, encompassing magician. We think we are still watching the old magician … Ta-dah! Oh, what a clever trick! Just as I suspected! … while the new, encompassing magician weaves his Charm spell invisibly, imperceptibly, so that we don’t even realize we’re in a new, encompassing theater. We don’t even realize we’re experiencing a new, encompassing trick.” Ben Hunt, “Beyond Nudge, May 2025.
We have long analogized the workings of LLMs to those of Sharpe World. Both are using simplified assumptions of historical frequency to ‘nudge’ our acceptance of their answers as representing something in the vicinity of truth. They are both trying to get us to accept that optimizing expected utility is the best way to pursue actual utility. We, Ben, Pippa, Gerd, Nassim, would all disagree (we believe) and caution against succumbing to this siren song. We will stick with Claude Shannon, there is no information in the expected.
For a great real-world example of managing to expectations, while getting unintended actual utility, we need look no further than our friends at the Bank of Japan (BOJ). BOJ Governor Ueda provided the below opening speech, and accompanying charts, at the annual BOJ-Imes Conference.
“New Challenges for Monetary Policy” Opening Remarks at the 2025 BOJ-IMES Conference Hosted by the Institute for Monetary and Economic Studies, Bank of Japan
The gist of Governor Ueda’s opening comments revolve around justifying their ongoing insistence that they have yet to achieve their price stability target of 2% annual increases, despite being above that level with their explicitly proclaimed measure of price stability for now 38 consecutive months.
Figure 11: Japan (blue), US (red), Eurozone (green), CPI/HICP yoy% changes
Source: Bank of Japan, Ministry of Internal Affairs and Communication, Haver
Yet, as he shows, BOJ policy rates remain far more accommodative than their peers. Indeed, with BOJ at roughly their most negative real policy rate in history!
Figure 12: Japan (blue), US (red), Eurozone (green) Real Policy Rates
Source: Bank of Japan, ECB, FRED, Haver, Ministry of Internal Affairs and Communication
As has been the case for some time now, Governor Ueda informs the listeners that “underlying inflation” remains below 2%. He poses, on everyone’s behalf, the obvious question.
“What constitutes underlying inflation?
In principle, it refers to inflation excluding temporary factors. But in practice, there is no perfect data series that capture this concept. Instead, it must be judged from the totality of data and information on the economy, making communication with the public challenging. We have often faced harsh criticism for a perceived lack of clarity.
One variable we closely monitor to assess underlying inflation is inflation expectations.” BOJ Governor Ueda, May 2025.
Figure 13: Japan CPI y/y% change (blue) and Inflation Expectations (red)
Source: Bloomberg. Consensus Economics Inc, “Consensus Forecasts”. QUICK, “QUICK Monthly Market Survey <Bonds>, Bank of Japan, Ministry of Internal Affairs and Communication
In the fine print, a footnote beneath this chart, they detail that “the composite index of inflation expectations” is based upon 10y-year ahead staff estimates. There is that old expected utility bugaboo again! The BOJ is optimizing their policy setting to their own internal (made-up) estimates of expected inflation. The chart, reasonably clearly, shows that they are not managing to optimize to actual inflation.
This speech begs us to re-quote economist Jeremy Rudd from our September 2021 Update – “The Challenge of Measurement (convex-strategies.com/2021/10/19/risk-update-september-2021/). His note, “Why Do We Think That Inflation Expectations Matter for Inflation? (And Should We?)”, needs to be forwarded along to anybody involved at the BOJ.
“Mainstream economics is replete with ideas that “everyone knows” to be true, but that are actually arrant nonsense.” Jeremy Rudd, Federal Reserve Board, September 2021.
https://www.federalreserve.gov/econres/feds/files/2021062pap.pdf
We will just throw in a quick array of pictures that might provide some clarity to the BOJ’s predicament. The below pictures show 2yr, 10yr, and 30yr government bond yields, along with the CPI year-on-year percent changes, across the US, the Eurozone and Japan.
Figure 14: US Treasury 2yr (white), 10yr (papaya), 30yr (purple) Yields and CPI yoy% (blue). Jan2007-May2025
Source: Bloomberg
Figure 15: Eurozone Govt Bond 2yr (white), 10yr (papaya), 30yr (purple) Yields and CPI yoy% (blue). Jan2007-May2025
Source: Bloomberg
Figure 16: Japan Govt Bond 2yr (white), 10yr (papaya), 30yr (purple) Yields and CPI yoy% (blue). Jan2007-May2025
Source: Bloomberg
What do we see? US yields are well above their current inflation rate, they have a moderately steep yield curve, after circa two years or so of an inverted curve. Eurozone government bond yields are wrapped around the current inflation rate, they have a moderately steep yield curve, after also having a couple of years or so of an inverted curve. JGB yields are well below the current inflation rate, they have a very steep (and aggressively steepening) yield curve, they are yet to have experienced (caused?) an inversion of their yield curve.
What has that meant to bond investors over the last dozen or so years?
Figure 17: US Treasury Total Return Index (LUATTRUU Index) in Real (deflated by CPI Index) and Nominal Terms. Jan 2013-March 2025
Source: Bloomberg. Convex Strategies
Figure 18: Eurozone Govt Bond Total Return Index (LBEATREU Index) in Real (deflated by HICP Index) and Nominal Terms. Jan 2013-March 2025
Source: Bloomberg, Convex Strategies
Figure 19: Japan Govt Bond Total Return Index (I29067JP Index) in Real (deflated by CPI Index) and Nominal Terms. Jan 2013-March 2025
Source: Bloomberg, Convex Strategies
Not good. As we are inclined to ask, “who’s gonna buy the bonds?”. If, as Governor Ueda says in the above speech, Japan is lagging behind the others, it does not bode well for attracting enthusiastic buyers of JGBs!
BOJ, much like our advice to fiduciary investment managers, should “just do it”. Stop trying to optimize to expected outcomes, it will continue to explicitly impede actual utility. Start trying to optimize for actual outcomes. That means building convexity, flexibility, acceleration and deceleration, into their policy process. It means applying some of Pippa’s heartware, operating in the connection between the rational and the imaginal. It means small steps of trial and error, not teams of Sharpe World practitioners huddling around each other doing the same old, same old.
One last picture. We could do this with all the above countries/regions (US, Eurozone, Japan and more) but, to keep it short, we will suffice with this global view. They all would look some version of the same story.
Figure 20: MSCI World Index Total Return (blue). Global Bond Aggregate Total Return (red). G7 CPI Index (white). Jan2013-May2025
Source: Bloomberg, Convex Strategies
We were heard to proclaim, at the recent Sohn HK Conference (you can find the link at the Media Tab on our website Media | Media), “The biggest opportunity cost in the modern history of investments has been sitting on bonds.” This picture (and all the ones if we showed it country by country) ought to reinforce that bold declaration. Also, anybody that thinks financial repression is only a ‘future risk’ hasn’t been paying attention.
Just do it. Start putting brakes on your race care and start experimenting/learning how to, safely, drive faster. Back to Pippa, she discusses legendary race car, and before that ambulance, driver Tazio Nuvolaru.
“Where did his racing skill come from? Race car driving is one of the most technologically complex undertakings around since the invention of cars. But, it was not his skill as an engineer that made the difference. It was his heartware. It came from being an ambulance driver in WWI. He was so greatly concerned for the lives of the war victims that he learned to drive extremely fast.” Pippa Malmgren, “Heartware”, May 2025.
Tazio didn’t figure it out with some complex math, he learned it by doing it.
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