Introduction

Let’s consider the relative humidity we have right now in Venice, Italy: 97% with a temperature of 8°C and a pressure of 755 mmHg. Pretty humid, right? What about a warm place, let’s say Buenos Aires, in Argentina? Right now they have a relative humidity of 55%, at a temperature of 23° and a pressure of 760 mmHg. Now, which place is more humid, between these two? In other words: in which of these two places the same volume of air contains the biggest amount of water? Are you sure you know the answer?

Some definitions and a formula

Rlative humidity is defined as follows

$RH\;=\;100\cdot\frac{e'}{e'_w}$

where ${e'}$ is the partial pressure of water vapour in air and $e'_w$ is the saturation vapour pressure with respect to water (the vapour pressure in air in equilibrium with the surface of water). We then have

$e'_w(p,t)\;=\;(1.0016\;hPa+3.15\cdot 10^{-6} p-\frac{0.074}{p}\;hPa^{2}) 6.112\cdot e^{\frac{17.62t}{243.12+t}}$

Here and in what follows we express pressure in hPa, with $hPa\;=\;10^2 Pa$, while $t$ is temperature in °C and $T$ is temperature in $K$, with $T\;=\;273.15+t$. Absolute humidity is simply given by

${\rho}_v\;=\;\frac{m_v}{V}$

where $m_v$ is the mass of vapour and $V$ is the total volume occupied by the mixture (Ref, chapter 4).

Physics of gasses

From the law of perfect gasses and considering that, according to Dalton’s law, in a moisture the partial pressure of each gas is the pressure it would have if it occupied the whole volume (Ref), we can also write

$e'\;=\;m_v\cdot R_v\frac{273,15 + t}{V}$

with $R_v\;=\;4.614\cdot\frac{hPa\cdot m^3}{kg\cdot K}$. Then, by substituting $e'$ and $m_v$ in ${\rho}_v$, we have

${\rho}_v\;=\;\frac{RH}{100\cdot R_v\cdot (273.15+t)}(1.0016\;hPa+3.15\cdot 10^{-6} p-\frac{0.074}{p} \;hPa^{2}) 6.112\cdot e^{\frac{17.62t}{243.12+t}}$

At the end of this post you find a simple code in Octave that calculates this formula and the plot.

If we apply now the equation for ${\rho}_v$ to the enviromental parameters relative to Venice, we find that one $m^3$ of air contains 8 grams of water; if we repeat the same calculation for Buenos Aires we find that the same volume of air contains 11 grams of water. In other words, today Venice is less humid than Buenos Aires in the same period, if we refer to the content of water of the air.

In the diagram below you can see the plot of absolute humidity in function of the temperature, for three values of relative humidity. So, for instance, 20 $\frac{g}{m^3}$ of water corresponds to a RH of 90% at a temperature of 24°C and to a RH of only 50% at a temperature of 35°C. The reason for this, beyond the mathematical formulae, is obvious: when the temperature of the air decrases, the ability of the moisture to retain water as vapour decreases accordingly.

Conclusion

Relative humidity is relevant for the subjective perception of heat (the more the relative humidity, the more difficult it is sweating for human beings, then the higher it is the perception of heat since we use sweating for cooling down). But if we are interested in the interaction of air and our lungs, for instance, relative humidity might be completely misleading and absolute humidity is likely the parameter to be considered (R).

The script

% file name = absolute_humidity
% it calculates the absolute humidity given the relative humidity and the temperature
clear all
% constant for water vapour (J/kg*K)
Rv = 461.4;
% relative humidity (%), temperature (°C), pressure (mmHg)
RH = 55
t = 23
pHg = 760
% conversion to Pa (1 mmHg = 133.322365 Pa)
p = pHg*133.322
% conversion to hPa=100Pa
p = p/100;
Rv = 4.614;
% absolute humidity (kg/m^3)
AH = (RH/(100*Rv*(273.15+t)))*(1.0016+3.15*10^(-6)*p-0.074/p)*6.112*e^(17.62*t/(243.12+t))
% we now fix the RH and plot AH for variuos values of t
RH = 50
pHg = 760
p = pHg*133.322;
p = p/100;
for i=1:30
t2(i)=i+5;
AH2(i) = 1000*(RH/(100*Rv*(273.15+t2(i))))*(1.0016+3.15*10^(-6)*p-0.074/p)*6.112*e^(17.62*t2(i)/(243.12+t2(i)));
endfor
plot (t2, AH2,’-k’,’LineWidth’,3)
grid on
grid minor
hold on
RH = 70
for i=1:30
t2(i)=i+5;
AH2(i) = 1000*(RH/(100*Rv*(273.15+t2(i))))*(1.0016+3.15*10^(-6)*p-0.074/p)*6.112*e^(17.62*t2(i)/(243.12+t2(i)));
endfor
plot (t2, AH2,’-r’,’LineWidth’,3)
hold on
RH = 90
for i=1:30
t2(i)=i+5;
AH2(i) = 1000*(RH/(100*Rv*(273.15+t2(i))))*(1.0016+3.15*10^(-6)*p-0.074/p)*6.112*e^(17.62*t2(i)/(243.12+t2(i)));
endfor
plot (t2, AH2,’-b’,’LineWidth’,3)
xlabel (‘temperature (°C)’)
ylabel (‘absolute humidity (g/{m^3})’)
legend (‘AH for RH = 50%’,’AH for RH = 70%’,’AH for RH = 90%’, ‘location’, ‘NORTHWEST’ )

The equations of this blog post were written using $\LaTeX$.

Introduction

Some days ago, David Systrom offered an overview of his work on cardiopulmonary testing in ME/CFS during a virtual meeting hosted by the Massachusetts ME/CFS & FM Association and the Open Medicine Foundation. In this blog post, I present an introduction to the experimental setting used for Systrom’s work (paragraph 1), a brief presentation of his previous findings (paragraph 2), and an explanation of his more recent discoveries in his cohort of patients (paragraph 3). In paragraph 4 you’ll find a note on how to support his research.

1. Invasive Cardiopulmonary Exercise Testing

It is a test that allows for the determination of pulmonary, cardiac, and metabolic parameters in response to physical exertion of increasing workload. It is, mutatis mutandis, the human equivalent of an engine test stand. A stationary bike with a mechanical resistance that increases by 10 to 50 Watts for minute is usually employed for assessing the patient in a upright position, but a recumbent bike can also be used in some instances. Distinguishing between these two different settings might be of pivotal relevance in ME/CFS and POTS. I shall now briefly describe some of the measurements that can be collected during invasive cardiopulmonary exercise testing (iCPET) and their biological meaning. For a more accurate and in-depth account, please refer to (Maron BA et al. 2013), (Oldham WM et al. 2016). I have used these papers as the main reference for this paragraph, unless otherwise specified.

Gas exchange. A face mask collects the gasses exchanged by the patient during the experiment and allows for monitoring of both oxygen uptake per unit of time (named $VO_2$) and carbon dioxide output ($VCO_2$), measured in mL/min. Gas exchange is particularly useful for the determination of the anaerobic threshold (AT), i.e. the point in time at which the diagram of $VCO_2$ in function of $VO_2$ displays an abrupt increase in its derivative: at this workload, the patient starts relying more on her anaerobic energy metabolism (glycolysis, for the most part) with a build-up of lactic acid in tissues and blood (see Figure 1).

Oxygen uptake for unit of time at AT (called $VO_2$max) can be considered an integrated function of patient’s muscular, pulmonary, and cardiac efficiency during exercise. It is abnormal when its value is below 80% of what predicted according to patient’s age, sex, and height. Importantly, according to some studies there might be no difference in $VO_2$max between ME/CFS patients and healthy controls, unless the exercise test is repeated a day after the first measure: in this case the value max$VO_2$ for patients is significantly lower than for controls (VanNess JM et al. 2007), (Snell CR and al. 2013).

Another measure derived from the assessing of gas exchange is minute ventilation (VE, measured in L/min) which represents the total volume of gas expired per minute. The link between VE and $VO_2$ is as follows:

$VO_2\;=\;VE\cdot(inspired\;VO_2\; -\; expired\;VO_2)$

Maximum voluntary ventilation (MVV) is the maximum volume of air that is voluntarily expired at rest. During incremental exercise, a healthy person should be able to maintain her VE at a value ∼0.7 MVV and it is assumed that if the ratio VE/MVV is above 0.7, then the patient has a pulmonary mechanical limit during exercise. If VE is normal, then an early AT suggests an inefficient transport of oxygen from the atmosphere to muscles, not due to pulmonary mechanics, thus linked to either pulmonary vascular abnormalities or muscular/mitochondrial abnormalities. It is suggested that an abnormally high derivative of the diagram of VE in function of $VCO_2$ and/or a high ratio VE/$VCO_2$ at AT (these are measures of how efficiently the system gets rid of $CO_2$) are an indicator of poor pulmonary vascular function.

Respiratory exchange ratio (RER) is a measure of the effort that the patient puts into the exercise. It is measured as follows:

$RER=\frac{VCO_2}{VO_2}$

and an RER>1.05 indicates a sufficient level of effort. In this case the test can be considered valid.

Arterial catheters. A sensor is placed just outside the right ventricle (pulmonary artery, Figure 2) and another one is placed in the radial artery: they allow for measures of intracardiac hemodynamics and arterial blood gas data, respectively. By using this setting, it is possible to indirectly estimate cardiac output (Qt) by using Fick equation:

$Qt=\frac{VO_2}{arterial\;O_2 - venous\;O_2}$

where the $arterial\;O_2$ is measured by the radial artery catheter and the venous one is measured by the one in the pulmonary artery (ml/L). An estimation for an individual’s predicted maximum Qt (L/min) can be obtained by dividing her predicted $VO_2$max by the normal maximum value of  $arterial\;O_2 - venous\;O_2$ during exercise, which is 149 mL/L:

$predicted\; Qt\;max=\frac{predicted\; VO_{2}max}{149 \frac{mL}{L}}$

If during iCPET the measured Qt max is below 80% of the predicted maximum cardiac output (as measured above), associated with reduced $VO_2$max, then a cardiac abnormality might be suspected. Stroke volume (SV), defined as the volume of blood ejected by the left ventricle per beat, can be obtained from the Qt according to the following equation:

$Qt=SV\cdot HR\;\xrightarrow\;SV\;=\;\frac{Qt}{HR}\;=\;\frac{\frac{VO_2}{arterial\; O_2 - venous\; O_2}}{HR}$

where HR stands for heart rate. One obvious measure from the pulmonary catheter is the mean pulmonary artery pressure (mPAP). The right atrial pressure (RAP) is the blood pressure at the level of the right atrium. Pulmonary capillary wedge pressure (PCWP) is an estimation for the left atrial pressure. It is obtained by the pulmonary catheter. The mean arterial pressure (MAP) is the pressure measured by the radial artery catheter and it is a proxy for the pressure in the left atrium. RAP, mPAP, and PCWP are measured by the pulmonary catheter (the line in red) which from the right atrium goes through the tricuspid valve, enters the right ventricle, and then goes along the initial part of the pulmonary artery (figure 2).

Derived parameters. As seen, Qt (cardiac output) is derived from actual direct measures collected by this experimental setting, by using a simple mathematical model (Fick equation). Another derived parameter is pulmonary vascular resistance (PVR) which is obtained using the particular solution of the Navier-Stokes equations (the dynamic equation for Newtonian fluids) that fits the geometry of a pipe with a circular section. This solution is called the Poiseuille flow, and it states that the difference in pressure between the extremities of a pipe with a circular cross-section A and a length L is given by

$\Delta\;P\;=\;\frac{8\pi\mu L}{A^2}Q$

where $\mu$ is a mechanical property of the fluid (called dynamic viscosity) and Q is the blood flow (Maccallini P. 2007). As the reader can recognize, this formula has a close resemblance with Ohm’s law, with P analogous to the electric potential, Q analogous to the current, and $\frac{8\pi\mu L}{A^2}$ analogous to the resistance. In the case of PVR, Q is given by Qt while $\Delta\;P\;=\;mPAP\;-\;PCWP$. Then we have:

$PVR\;=\;80\frac{\;mPAP\;-\;PCWP}{Qt}$

where the numeric coefficient is due to the fact that PVR is usually measured in $\frac{dyne\cdot s}{cm^5}$ and 1 dyne is $10^5$ Newton while 1 mmHg is 1333 N/m².

A subset of patients with exercise intolerance presents with preload-dependent limitations to cardiac output. This phenotype is called preload failure  (PLF) and is defined as follows: RAP max < 8 mmHg, Qt and $VO_2$max <80% predicted, with normal mPAP (<25 mmHg) and normal PVR (<120 $\frac{dyne\cdot s}{cm^5}$) (Maron BA et al. 2013). This condition seems prevalent in ME/CFS and POTS. Some of these patients have a positive cutaneous biopsy for small-fiber polyneuropathy (SFPN), even though there seems to be no correlation between hemodynamic parameters and the severity of SFPN. Intolerance to exercise in PLF seems to improve after pyridostigmine administration, mainly through potentiation of oxygen extraction in the periphery. A possible explanation for PLF in non-SFPN patients might be a more proximal lesion in the autonomic nervous system (Urbina MF et al. 2018), (Joseph P. et al. 2019). In particular, 72% of PLF patients fits the IOM criteria for ME/CFS and 27% meets the criteria for POTS. Among ME/CFS patients, 44% has a positive skin biopsy for SFPN. One possible cause for damage to the nervous system (both in the periphery and centrally) might be TNF-related apoptosis-inducing ligand (TRAIL) which has been linked to fatigue after radiation therapy; TRAIL increases during iCPET among ME/CFS patients (see video below).

3. Latest updates from David Systrom

During the David Systrom reported on the results of iCPET in a set of ME/CFS patients. The $VO_2$max is lower in patients vs controls (figure 3, up). As mentioned before, $VO_2$max is an index that includes contributions from cardiac performances, pulmonary efficiency, and oxygen extraction rate in the periphery. In other words, a low $VO_2$max gives us no explanation on why it is low. This finding seems to be due to different reasons in different patients even though the common denominator among all ME/CFS patients of this cohort is a low pressure in the right atrium during upright exercise (low RAP, figure 3, left). But then, if we look at the slope of Qt in function of $VO_2$ (figure 3, right) we find three different phenotypes. Those with a high slope are defined “high flow” (in red in figure 3). Then we have a group with a normal flow (green) and a group with a low flow (blue). If we look then at the ability to extract oxygen by muscles (figure 3, below) expressed by the ratio

$\frac{arterial\;O_2 - venous\;O_2}{HB}$

we can see that the high flow patients reach the lowest score. In summary, all ME/CFS patients of this cohort present with poor $VO_2$max and preload failure. A subgroup, the high flow phenotype, has poor oxygen extraction capacity at the level of skeletal muscles.

Now the problem is: what is the reason for the preload failure? And in the high flow phenotype, why the muscles can’t properly extract oxygen from blood? As mentioned, about 44% of ME/CFS patients in this cohort has SFPN but there is no correlation between the density of small-fibers in the skin biopsies and the hemodynamic parameters. Eleven patients with poor oxygen extraction (high flow) had their muscle biopsy tested for mitochondrial function (figure 4) and all but one presented a reduction in the activity of citrate synthase (fourth column): this is the enzyme that catalyzes the last/first step of Krebs cycle and it is considered a global biomarker for mitochondrial function. Some patients also have defects in one or more steps of the electron transport chain (fifth column) associated with genetic alterations (sixth column). Another problem in high flow patients might be a dysfunctional vasculature at the interface between the vascular system and skeletal muscles (but this might be true for the brain too), rather than poor mitochondrial function.

The use of an acetylcholinesterase inhibitor (pyridostigmine) improved the ability to extract oxygen in the high flow group, without improving cardiac output, as measured with a CPET, after one year of continuous use of the drug. This might be due to better regulation of blood flow in the periphery. This paragraph is an overview of the following video:

4. Funding

The trial on the use of pyridostigmine in ME/CFS at the Brigham & Women’s Hospital by Dr. David Systrom is funded by the Open Medicine Foundation (R). This work is extremely important, as you have seen, both for developing diagnostic tools and for finding treatments for specific subgroups of patients. Please, consider a donation to the Open Medicine Foundation to speed up this research. See how to donate.

The equations of this blog post were written using $\LaTeX$.

# Six Months

So, it seems that I am improving again. Six months ago I came back from Argentina, where I spent the boreal winter. I felt better there, as I usually do during summer, in Italy. Feeling better means being able to think, to read, to do calculations, to draw. To exist, in one word. And also to move around a bit, which is not truly relevant for me, though.

I came back to Italy at the end of March (blog post), sure that I would have had other months of improvement ahead of me, given that we were at the beginning of Spring. But it hasn’t been the case, I got worse: For six months I haven’t thought, and I have been living horizontally, in silence. There were days in which it seemed that I was starting to improve (like when I recorded this video), but then it didn’t last. I can’t remember these six months, in my subjective time they sum up to a week or less.

Not sure why it happened: perhaps the 48 hours of the chaotic journey back to Italy damaged me so badly that it took half a year for me to regain the status quo ante, or maybe the strange flu I got in March, while in Argentina, made the disease worse. In the life of an ordinary person, this would be a rather exceptional episode, for me it is the rule: the improvements are the rare exception. I have lived like that since I was 20.

And now, because I usually get worse at the end of September, I know that I am about to start my descend to Hell again. And this time I can’t move to the austral hemisphere, because of the pandemic. So what am I supposed to do in the few days of life I have left? I’ll do what I have always wanted to do: applied maths and drawing, with only very short term goals. Something that I can finish.

I share these private vicissitudes only because I think that it is important to let the world know about this struggle. It seems unlikely that I can discover the reason why this curse has stricken my life, but I will continue studying this phenomenon: most of what I study, when I can, is about new tools to apply to my own biology.

# The indiscreet rotation

The world must be wonderful, beyond the muffled atmosphere of these rooms and the obstinate curtain of encephalopathy; now that Autumn is still a harmless chrysalis, an apparently unlikely threat, while the industriousness of men swarms again, in search of untouched paths.

The Autumn of intellectual and material adventures, of encounters and discoveries, remains an unfulfilled promise, which I nevertheless do not give up on cultivating. Because I don’t know if Ulysses kissed his stony Ithaca during this season, but I like to think so.

I am perpetually mocked by the indiscreet rotation of the wall clock, which turns on the spot; while Rilke’s panther remains trapped in my chest.

When I got sick, about 20 years ago, for the first time I started thinking about diseases and loss of health. And I remember coming to the conclusion of how fortunate I was, from a physical standpoint. Not of how fortunate I had been in the past (that was obvious), when I could conquer mountains, running on rocks with my 15 Kg bike on the shoulders; no, of how fortunate I was in that very moment, while confined at home, mostly lying horizontally. I was fortunate, I could still move my hands, I had still all my body, even if I couldn’t use it in the outside world, even if most of the usual activities of a 20 years old man were far beyond reaching, I realized how fortunate I was. And after 20 years I still say that, as for the physical functioning, I am a very lucky man. There are even some years, during the core of the summer, in which I can run for some minutes in the sun. I am blessed.

I am aware that this might offend some patients, but I think that those who have ME/CFS in the vast majority of cases are fortunate too, from a physical standpoint. Yes, it is annoying to need help from others for so many things, but with assistance and some arrangements, you can go on with a productive life… unless you have cognitive impairment.

Actually, I never felt fortunate concerning my cognitive functioning. That has been a true tragedy, I have lost my entire life because of the cognitive damage, by any means because of the limitations of my body. I would have had a meaningful life (according to any standard) even with physical limitations way worse than mine if I had had a functioning brain. But I lost it when I was 20 before I could get the best from it and that is the only real tragedy.

As an example of what I am saying, consider a person like Stephen Hawking: he has been a prolific scientist, he had a stellar career (literally), he shaped our culture with his books for the general public, he was a father of three, and so forth. And yet for most of his life, while he was doing all these things, his physical functioning was way worse than the one of the average ME/CFS patient (worse even of a very severe patient, probably). For many years he could use only the muscles of the head. That’s it. Think about that. Was he missing or invisible? Definitely not!

Was he a disabled man? Yes, technically speaking he was, but in fact, he has never really been disabled, if we judge from his accomplishments. He once said that the disease somehow even helped him in his work, because he could concentrate better on his quantum-relativistic equations¹.

So what I am saying is that if we consider the physical functioning in ME/CFS, it is a negligible problem in most of the cases. The only thing that matters is the impairment in cognition (in the cases in which it is present), especially if it starts at a young age (consider that after you reach your thirties there is very little chance that your brain will give a significant contribution to humanity, even if you are perfectly healthy, so it is not a big loss if you get sick after that age). That is disastrous and there is no wheelchair you can use for it. For all the other symptoms you can find a way to adjust, just as Hawking did in a far worse situation.

This might be one of the reasons for the bad reputation of ME/CFS: there isn’t awareness about cognitive issues, no one talk about them (and in some cases, they are in fact not present at all). But I am pretty sure that the real source of disability in these patients, the lack of productivity, is due to their cognitive problems (when present). Also because in a world like ours, you can work even without using most of your muscles. It is not impossible, I would say it is the rule for a big chunk of the population.

The following one is an interview with Norwegian neurologist Kristian Sommerfelt, in which he points out some analogous considerations. He has done some research on ME/CFS with the group of Fluge and Mella, including the well-known study on pyruvate dehydrogenase. From the subtitles of the video (minute 3:38):

“This [the cognitive problem] is a very typical ME symptom and some of what I believe causes the main limitation. I don’t think the main limitation is that they’re becoming fatigued and exhausted by moving around, walking, running, or having to sit still. If it were just that, I think many ME-patients could have had a much better life. But the problem is that just actively using the mind leads to problems with exactly that, using the mind. It comes to a stop, or slow down, depending on how ill they are.”

¹ It seems that Stephen Hawking had a very unusual presentation of Amyotrophic Lateral Sclerosis (ALS): one half of those with this disease die within 30 months from the first symptom; moreover one out of two ALS patients has a form of cognitive impairment which in some cases can be diagnosed as frontotemporal dementia [R]. So, Stephen Hawking was somehow lucky, in his tragedy, and he doesn’t represent the average ALS patient. I mentioned his case as an example of a person with very severe physical impairment and no apparent cognitive decline, not as an example of the average ALS patient.

The following video is meant to be a presentation of both the blog and of myself. As I started improving again, some days ago, I decided to record this monologue, so that there could be a video memory of my struggle.

This winter I have spent almost three months in South America, to see if I would have improved during the austral summer, as I usually improve during the Italian summer; and in fact, I did improve. When I came back to Italy (in March) I had a relapse, though. For the last three months, I have been mostly horizontal, without reading or thinking for most of the time.

Now I am climbing the mountain again: I started my rehabilitation reading novels some days ago, then I switched to simple calculations and now I have written my first small code since March. And when I will reach the cognitive level I had about 20 years ago just before I got sick, I will lose everything for months (or years) and I will have to wait without thinking much (despite my best efforts) until I can start all over again…

The myth of Sisyphus has been shaped after me.

# My saviour

One of my short-lived summer improvements (2013). During all these years, as soon as I started feeling better, I opened my books, even before taking a shower and having my hair cut. Happy as a child for most of the time, but also profoundly saddened for the time lost, especially at the beginning of the improvement, when I could realize how much time had passed from the previous positive phase.

Each time I had to start exactly from where I had left many months or even years before (the longest gap has been 5 years without studying). I had to do a cognitive rehabilitation each time, learn again how to read properly, how to do math, how to discipline my thoughts, how to code. It is a hard process each time. And then, a few weeks after, when I recovered enough to function mentally, I relapsed again.

I am pretty sure that only this complete, obsessive devotion to studying has saved me from very bad cognitive disability.

Before getting sick, coding and math had taught me how to think. Then, when I became ill, each equation I wrote, each drawing and code, all those efforts made to bring my soul back from wherever it was, they kept me alive for all these years.

# My first time with LaTeX

Each mathematical formula I have used in my blog till now was an image: I wrote them in a Word document using the equation editor by Microsoft (that I like very much), then I captured the screen and saved it as an image and then I uploaded them in my blog.

In the past, I tried to find a way to write them as text, without succeeding. But in fact, it is possible, using the LaTeX syntax and a few HTML commands.

These are the first “true” mathematical formulae present in this blog. I will use this page to test the LaTeX syntax for mathematical expressions (a handbook is available here).

$\int_{A_1}\int_{A_2}\frac{\partial \Psi(x,y)}{\partial x}dxdy$

$i\hbar\frac{\partial}{\partial t}\left|\Psi(t)\right>=H\left|\Psi(t)\right>$

A symbol within the paragraph: $\pi$. A inequality within the paragraph: $x_i>0$. This is an example of an expression with a pedix that has a pedix: $f_{X_1}$.

# The time machine

I am aware that these are just messages floating in the silence, stored somewhere in the planet as binary numbers. I am writing to myself, mainly, from my remote hiding place.

I have travelled through ages, without really being part of them. All alone with my problem. As a patient with a rare disease that doesn’t even have a proper description, I do not belong to humankind.

But humans have paradoxical behaviours, they care more about a man who lived five thousand years ago in the north of Italy, trapped in the ice of our highest mountains, than of clochards that live right now in pain and loneliness in their community. So it might be that generations from now, someone will find these notes, an archaeologist who will try to build my story, from fragments of what I left behind: drawings and calculations. Mathematics is a universal language, after all, and to some extent, even art is universal; not always but often, good art is forever.

If I fail my mission, history will never record my existence. But it might be that at some point in the future someone will find these notes frozen in the ice of a planet long forgotten by humans themselves, as we now have forgotten Africa, the place we all come from.