# Einstein, Millikan, and the humanness of humans

It is fascinating and inspiring to study the history of science.  It is also remarkable how it is simply impossible for humans to not always be primarily driven by their humanness.  Sometimes this is incredibly useful, because it brings insights of the highest order; sometimes it is painfully debilitating, because it prevents seeing the obvious due to an intellectual stance that rejects an idea based on already acquired and strongly held notions.

To muddle the situation further, our humanness leads us to, over time, remember things in a way that suits us better right now, such that the same sequence of events are remembered and then interpreted differently depending on the circumstances, the mindset, and the knowledge as well as opinions we hold and have acquired since these events took place.

I am currently reading The Cambridge Companion to Einstein, a collection of fourteen essays by leading historians and philosophers of science that introduces his work in the historical and philosophical context in which it took shape and arose.  There are a few essays that discuss the photoelectric effect, the insight for which Einstein received his only Nobel prize.  This work of one of the most important in the history of modern physics because it was the foundation of quantum theory.  The fifth essay in the collection, The Experimental Challenge of Light Quanta, is by Roger Stuewer.

Many experimentalists ran many experiments to test Einstein’s theory that light was in fact quanta, little bundles of energy, whose energy depended only the frequency of the light with Plank’s constant as the proportionality constant: E = hv.  But surely it was Robert Millikan’s famous oil drop experiment that demonstrated beyond debate that all of Einstein’s predictions were in accordance with experimental reality.  Nevertheless, at the time, Millikan himself would not believe it.  He wrote in 1917, reflecting on his experimental testing of Einstein’s quantum theory of light that culminated in 1915:

Despite … the apparently complete success of the Einstein equation, the physical theory of which it was designed to be the symbolic expression if found so untenable that Einstein himself, I believe [my italics], no longer holds to it, and we are in the position of having build a very perfect structure and then knocked out entirely the underpinning without causing the building to fall.  It [Einstein’s equation] stands complete and apparently well tested, but without any visible means of support.  These supports must obviously exist, and the most fascinating problem of modern physics is to find them.  Experiment has outrun theory, or, better, guided by erroneous theory [Stuewer’s italics], it has discovered relationships which seem to be of the greatest interest and importance, but the reasons for them are as yet not at all understood.

But 33 years later, in his 1950 autobiography, he recalled, in a chapter entitled  The Experimental Proof of the Existence of the Photon, that at the meeting of the American Physical Society (APS) in April 1915 he presented “my complete verification of the validity of the Einstein equation” and then added:

This seemed to me, as it did to many others, a matter of very great importance, for it … proved simply and irrefutably I thought, that the emitted electron that escapes with the energy hv gets that energy by the direct transfer of hv units of energy from the light to the electron [Millikan’s italics] and hence scarcely permits of an other interpretation than that which Einstein had originally suggested, namely that of the semi-corposcular or photon theory of light itself.

What does this mean, and what does it tell us about not just Millikan, but about ourselves?  It shows us that the opinions, beliefs, ideas, notions that we hold of how things are will generally force us into a mindset that brings us to reject the obvious even in the face of “irrefutable” experimental evidence simply because we are not ready to accept it.  And it shows us that generally, each time we will recall something, each time we will bring something back from the annals of our memory, it will be reshaped by the mindset that we currently hold, which in turn is continuously reshaped and sculpted by information, acquired knowledge, and experiences we are presented with as we go about our daily lives.  This is certainly one of the hallmarks of our humanness; a hallmark of our being humans.  Is it wrong to distort history in this way?  Who’s to say.  Do we all do it?  Maybe.

# Implicitly Assumed

Has it ever happened to you to be, all of a sudden, struck by the realisation that something you had always believed to be the case, turned out to be different than what you believed? Maybe some lyrics in a song, maybe something about a silhouette or a logo on a sign. In that moment, what you realised was first that you were holding an assumption about something without knowing you were, and second that this assumption you held implicitly was wrong—it didn’t accord with the way things are in reality.

I think that one of the greatest difficulties we have in science is to avoid biasing our results and their interpretation based on these kinds of assumptions we hold implicitly. We learn that we should always be absolutely clear about the assumptions we make and state them upfront. And we do this. This is not the issue I am addressing here. The real problem is that of assumptions we are not aware we are making. And we are not aware because we either have no idea we are making that assumption, or because we have long ago forgotten that the method we are using in our analysis has a particular assumption that is embedded within it. Here is what I mean.

We have three scientists working with the same data set. The data was collected during a 10000 second observation of a star with an X-ray satellite and consists of a list of 5063 detected photons. This gives a mean count rate of 0.5063 counts per second, so basically, the detector was getting one X-ray photon every couple of seconds. Taking this list of times at which each of these 5063 photons was detected and going through it to count the number of X-rays per interval of 20 seconds, say, and then plotting the number of photons per interval on a time line, we construct a time series that is also call a light curve in astronomy and astrophysics. It looks like this:

X-ray time series of 5063 photons detected during a 10 ks observation and grouped in 20 s bins.

As you can see, it is rather unremarkable: a constant intensity with some fluctuations that all look pretty much like what we expect the statistical fluctuations to look like for a non-variable star. The way to look in more detail at the repartition of detected events in time, and in particular, to look for signs of periodic activity where something in the system would lead to regular, cyclical changes in the intensity, is to transform this intensity as a function of time into something that is a function of frequency. This is a mathematical operation that was discovered by Joseph Fourier and it is called a Fourier transform. The reason we can go back and forth from the time domain to the frequency domain with a Fourier transform to go from time to frequency and the inverse transform to go from frequency to time, is that they are two equivalent ways of presenting the same information, and there is no loss of information in going from one to the other.

The major difference between the time series and the periodogram is that in the time series each intensity value is independent of the previous and of the next. After all, the observation could have started or been stopped at any time, and each photon that is detected knows nothing about any other photon that we detected either before or after it. But to construct the periodogram each estimate of power for a particular frequency is calculated using all of the intensity measurements in the time series. The power at a given frequency can be thought of the measure of how well a sine curve of that frequency (inverse wavelength) matches the collection of intensities as a function of time. And so for each frequency, we can think of it as the mathematical version of drawing a sine curve over the data and measuring how closely it corresponds to the measurements.

All three scientists are interested in finding out if there is some kind of periodic signal in these data. The first scientist has a good implementation of a fast algorithm for computing the Fourier transform that they have been using throughout their very productive and prolific career analysing time series from X-ray emitting stars of different kinds, especially black holes. And therefore, this is what they do: the fast Fourier transform of the light curve, which looks like this:

Fast Fourier Transform of binned time series shown in previous figure.

If there is a periodic component in the emission then it should appear as a single spike at the frequency corresponding to the period of the modulation in the number of photons detected as a function of time. If there isn’t, then we expect an average of 2 with a variance of 4, and therefore quite a bit of scatter. So, in just a few seconds of looking at this periodogram, the scientist concludes, precisely as we would as well, that there is no clear evidence of a periodic signal, but seemingly just statistical fluctuations from a Poisson process with a non-variable average intensity.

The second scientist has also been around for a while, but has mostly worked in gamma-ray astronomy where, until rather recently, the number of detected photons was so low that every single one had to be very carefully considered, and that, for this reason, nobody ever grouped photons together into binned light curves. Instead, they had been using the Rayleigh statistic to calculate the power based on the exact time of arrival of each photon in the data set.

Computing the Rayleigh power for each possible period in order to construct a complete periodogram is orders of magnitude slower than computing the fast Fourier transform, but because there were so few photons, with sometimes so much time between each one, that the Rayleigh statistic was really the only reasonable tool to use to search for a periodic modulation in the arrival times. Naturally, this is what they do with this data set, with these 5063 photon arrival times, testing a lot more frequencies than there are in the Fourier transform—frequencies which are between each independent Fourier frequency. They use the Rayleigh periodogram to compute the power for 20 additional frequencies (so 21 times more than the FFT). This is exactly what allows the second scientist to look in very fine detail at what is happening in the entire spectrum, and especially also in between the independent frequencies. The result is this:

Rayleigh periodogram of event arrival times.

As you can see, we can’t see much from this periodogram. But because whenever they make a Rayleigh periodogram they always see a sharp rise in power at the lowest frequencies, they also always just ignore this, cutting it out of the view and rescaling the y-axis to see the rest of it better, like this:

Cropped and rescaled Rayleigh periodogram shown previous figure.

Lo and behold they discover that there is a peak that clearly stands out of the noise. Excluding the lowest frequency part, the peak stands out of the rest of the periodogram, which just looks like statistical fluctuations similar to those seen in the Fourier transform by the first scientist. The signal is very obvious, right there at a frequency of just over 4E-3 Hz. This is equivalent to a period of just under 250 seconds.

But is it okay to simply ignore part of the periodogram like that, and just focus on what looks interesting? Why is the signal so clear in the Rayleigh periodogram and absent from the Fourier transform? And why in the world does the Rayleigh periodogram have this sharp rise to huge powers at the lowest frequencies? Why doesn’t the Fourier transform have that? Can you really trust that the peak in the Rayleigh periodogram is indeed a signal and not just a fluke, a fluctuation similar to those that are seen at the lowest frequencies but that just happened to appear at a different spot?

As we saw earlier, a major difference between the Fourier transform and the Rayleigh periodogram is that the former is computed on a binned time series, which means it cannot take into account the time of arrival of each detected photon. And this is precisely what the latter does. But there is another major difference between them: the Fourier transform of a binned time series tests only independent frequencies. These are frequencies that correspond to periods that can fit an integer number of times in the time series.

The longest period that can be tested for in a time series lasting T=10000 s can obviously not be longer than 10000 s since we cannot test for periods longer than the duration of the observation. A period of ten thousand seconds is equivalent to a frequency of 1/T or 1E-4 Hz. After that, the time series can be tested for a period of 5000 s that fits two times in the time series, and this corresponds to a frequency of 2/T or 2E-4 Hz. Next, it can be tested for a period of 3333 s that fits exactly three times in the length of the observation and corresponds to a frequency of 3/T or 3E-4 Hz. And so on. So, basically, the only frequencies that can be tested are multiples of 1/T up to 1/2dt, where dt is the timescale of the binning, which in our case was 20 seconds, and hence a maximum frequency of 1/40 or 0.025 Hz.

The Rayleigh periodogram, because it is unbinned and uses the exact times of arrivals of the detected events, has no restrictions on the frequencies it can test and for which it can compute the power. That is, it has no restriction in testing how well a sine curve of that frequency matches the rate at which the events were detected. This is why the periodic signal is clearly detected by the Rayleigh periodogram and not seen in the Fourier transform.

In fact, looking even closer at the periodogram we find that the periodic signal peaks precisely at 247 seconds, corresponding to 40.5/T Hz, which happens to be exactly in between two independent frequencies, those of 40/T and 41/T Hz. This is why it literally slipped between the Fourier transform’s fingers. The Fourier transform in this case is like too coarse a comb, a comb with too much space between its teeth, through which a small knot in your hair can just slip and pass unnoticed. Here is what it looks like when we zoom in around the peak and compare the two periodograms:

Zoom showing comparison between Fast Fourier Transform and Rayleigh periodogram.

The third scientist knows the Fourier transform as well as the Rayleigh periodogram, and understands where the differences between them come from. They have also understood why the Fourier transform does not have the huge rise in power at low frequencies—it only tests independent frequencies, while the Rayleigh periodogram does—it tests frequencies that are not independent and for which the powers are therefore correlated. They know that the reason why the Rayleigh periodogram does this is because it is computed as though it were calculating the power only at independent frequencies even if it isn’t. What needs to be done to avoid this—to correct for this effect—is to modify the Rayleigh statistic to account for the fact that we are testing frequencies that are not independent: frequencies (periods) that do not repeat an integer number of times within the span of the observation.

This is an analytical correction, something that can be calculated exactly. They do that and formulate the modification to the Rayleigh statistic with which they compute the periodogram of these data, the same exact 5063 photon arrival times. What they find is this:

Modified Rayleigh periodogram.

And to be absolutely sure that what they have computed is accurate, they compare the result with the Fourier transform. If the computation is correct, the powers at independent frequencies should match, and there should be no rise of power at low frequencies. Hence, they look closely at the low frequency part of the periodogram and find that they agree very well, exactly as they predicted, and exactly as they should. The comparison looks like this:

Comparison of Fast Fourier Transform and modified Rayleigh periodogram over entire frequency range.

The first scientist missed detecting the period in the data because they assumed that the Fourier transform was the best they could do in exploring the frequency space of these data, and that information of the independent frequencies was enough to fully characterise the signal when transforming it from intensity as a function of time to power as a function of frequency. The fact is, they most probably would never have known that there was a period in the data, because they would never have looked at these data again.

The second scientist detected the period in the data, but they were forced to arbitrarily cut out a part of the data, simply ignore it, and presume that the height of the peak was the correct power estimate for the periodic signal at 247 seconds. They did this because they had assumed that the Rayleigh statistic, which does not have any restrictions as to the frequencies it can test in a given data set, could be used to compute the power at any frequency, regardless of whether or not it was of an integer number of cycles within the observation duration.

The third scientist detected the periodic signal present in the 5063 arrival times of the detected X-ray photons, but unlike the second scientist, they did not exclude any portions of the data, and got an estimate of the power of the signal from which they could calculate precise and reliable quantities about the signal such as the probability of it having been a statistical fluctuation (1E-9), and the pulsed fraction of the signal, that is, the number of photons right on the sine curve with respect to the total (10%). Both of these, the second scientist would have gotten wrong. Not completely wrong, but wrong nonetheless.

How often does this happen in science? How often does it happen in medical trials? In trials testing a new critical procedure or a new drug? How often does this happen in industry? In testing of a new industrial machine or a new diagnostic technique?

How often does this happen to us in our own life? How often do we infer something, draw a conclusion, make a decision, and act based on assumptions hidden in our psyche so well that we are not even aware of them? Is there a way to overcome this problem?

My personal feeling is that this happens a lot. It is admittedly hard to measure and quantify, but I suppose with enough time and consideration that it could be done, at least for a handful of cases as the one presented here.

About overcoming this fundamental problem that does at first sight appear unsurmountable for the simple fact that we are biased by something we are not aware of being biased by, I think a solution is, by keeping this issue in mind, to not settle for something that can potentially, even hypothetically, be improved upon. In this way, we at least open up the possibility to go on finding more and more suitable methods, more and more accurate estimates, and more and more reliable answers to the questions we seek to answer.

# Reflections on what it is to be a scientist

What is it to be a scientist? What do scientists mean and understand by the word “scientist”? What do non-scientists mean and understand by that same word “scientist”? Are non-scientists really not scientists? And are scientists really scientists?

You get up in the morning, go pee, wash your hands and face with cold water, brush your teeth, and go have a good drink of water. You have a shower, get dressed, maybe have some coffee or tea, maybe breakfast, and then go to work. You get to the office and you start working on whatever it is that you were doing the day before, or start working on something new, but typically of a very similar nature as to that of what you were doing yesterday, the day before, the day before that, and for possibly years and decades.

This “work” that you do can be anything: preparing your next class of history or economics, literature or philosophy, geography, biology, chemistry, physics or math, to be presented later that day or next week to your grade 6, grade 9 or graduating students; it can be preparing for your next meeting in which you are presenting to potential investors your revolutionary idea for a project that will be so lucrative it will make Facebook look amateurish; it can be looking through tables of numbers in accounting spreadsheets to track expenditures and sales to make sure that your business is doing good and can continue to function as it has for years in this unpredictable market of consumers regulated by their likes and dislikes, their moods and fashions, their hopes or fears about the evolution of the national economy, and on and on; it can be to set up your cash, making sure you have enough of all the different types of coins and bills, and then starting, from the moment the store doors open, to ring things in from the first customer that lines up at your cash to buy their groceries for the day or the week, continuing this routine of welcoming and greeting them politely, passing all their items, obviously withholding any judgement on their person for buying those things, helping them bag their stuff and wishing them a pleasant day, over and over again from morning to night.

Of course, it can also be to sit down at your desk with your steaming cup of green tea, open a book, and start to read about the history of the second world war from the Chinese or Japanese perspective, about the comparative evolution of our species following the last ice age in the Fertile Crescent and North America, about writing style and how to craft the perfect sentence, about the relationship of butterfly species and birds on the different continents and climates, about the visual display of quantitative information, about political stability and civil unrest in developing countries in the latter half of the twentieth century; or it could be Plato’s dialogues, Galileo’s Messenger from the Stars, Newton’s Principia Mathematica, Darwin’s On the Origin of Species, Kant’s Critique of Pure Reason, Wittgenstein’s Philosophical Investigations, Popper’s Logic of Scientific Discovery, Savage’s Foundations of Statistics, Jaynes’s Probability Theory — the Logic of Science, or anything else from the countless works available for us to read, available for anyone to read at any time given their willingness and effort to read it.

Does what we do define who or what we are? No, it doesn’t. Does what we do tend to define the way we consider and perceive the world? Yes, it does. Does what we read, have read, think about define who or what we are? No, it doesn’t. Does what we read, have read, think about tend to define the way we consider and perceive the world? Yes, it does.

The persona of ‘the scientist’ dates back several centuries, if not millennia, all the way to ancient Egypt, Persia and Greece, where those who wondered about the functioning of the physical world, measured positions and motions of celestial objects, and worked out ways of both keeping track of things as well as calculating and estimating quantities related to physical phenomena, always stood out from the population, and had very privileged positions in society as holders of secret knowledge and deeper truths about the inner workings of the physical world. In many ways, this is still true today, albeit much less so, because scientists are enormously more numerous than they would have been several thousand or even a as little as a hundred years ago, when they were really extremely rare.

But what do twentieth century philosophers like Wittgenstein, Popper and Bertrand Russell mean when they use the word scientist, when they discuss what it means to speak the language of a scientist, to think like a scientist, to perceive the world like a scientist? Do they talk about those famous few that have marked the history of science but that are also remembered for it? Scientists like Copernicus, Galileo and Tycho Brahe, Rene Descartes, Blaise Pascal and Isaac Newton, Jacob Bernoulli, Leonard Euler and Karl Friedrich Gauss, Pierre Simon Laplace and James Clerk Maxwell, Karl Pearson and Ronald Fisher, Niels Bohr, Max Planck and Erwin Schrodinger, Bernhard Riemann, Hermann Minkowski and David Hilbert, Hendrik Lorentz and Albert Einstein, Roger Penrose and Stephen Hawking, Enrico Fermi and Richard Feynman, and so many more uniquely gifted people whose work and discoveries we have studied and admired, often marvelled at as senior university students, but whose persons, personal traits, tendencies beliefs, social behaviours and familial relationships most of us know nothing about. Is this important or is it irrelevant?

The scientist’s persona is defined by a complex mixture of ideas, beliefs, prejudices and other intellectual constructs rooted in a collective consciousness in which everything is distorted. We add to this the powerful attraction we tend to have to myths and tales, and our love for making important figures of the past larger than life, greater than great, more singular, more unique, more unusual, more special than anyone alive that we can actually see, encounter, speak to and interact with in person, even if hypothetically. Why all of this seems to be the way it is, no matter which human collective we consider, indeed is a good question whose answer could probably be found by digging into evolution and anthropological, into everything we can find out about our human ancestry, hoping to help elucidate deeply rooted psychological tendencies and behaviours we, as members of this race of homo sapiens, all share together.

But regardless of the actual details and the level of sophistication or refinement of what great scientists and mathematicians, great philosophers and thinkers, great historians and sociologists, or anybody else may have meant when speaking and referring to the notion of ‘the scientist’, it cannot have been and still cannot be anything other than an agglomeration of complex entangled intellectual, cultural, emotional and psychological constructs. Therefore, the unavoidable conclusion is that philosophers speaking of ‘the scientist’ are speaking of what they think and what they believe this is or should be. They are speaking of that complex mental construct they have developed and formulated in some way, undoubtedly to a level that satisfies their own requirements of intellectual and philosophical rigour, but that, in the end, bears little connection to the practical reality of what it is to be a scientist.

An innumerable number of interesting and useful questions can be posed, and an equally innumerable number of valid and different answers can be put forth in regards to this question of what it is to be a scientist. Does this mean it is not possible to agree on what is meant by it? Or does it mean that this is, in fact, quite hard to do?

Are we a scientist if we have a Bachelor’s degree in a scientific discipline? Anyone who does, knows that by the end of a Bachelor’s degree, what we know is that we have barely touched upon the rudiments of the discipline we have spent three or four years studying up to this point. And for most, it is almost embarrassing to be presented or even considered to be a scientist after graduating in physics or chemistry or biology or whatever other scientific field of study. So, the answer is definitely no.

Are we a scientist once we have spent another two or more years studying and working hard on much more advanced subjects towards a Master’s degree? Here again, doing this only serves to show us how little we know about the process of doing research and about the actual scientific foundations of the research we are participating in under the supervision and guidance of our thesis adviser. This is especially obvious if we are surrounded by or in contact with other graduate students working on their PhD with several more years of experience, and to whom we continuously turn for help and advice, these senior student who appear to us so knowledgeable and so wise from our perspective. So, are we a scientist once we have finished and defended our Master’s thesis, something that may have seemed to us a remarkable and maybe even gruelling accomplishment, but which to any doctoral student who has been through it is now seen for what it actually is: a baby thesis, a warm up for the real thing, for the real thesis that is the doctoral thesis.

Are we a scientist when we finish the course work for our PhD? When we finish the research project we chose or were encouraged to tackle? When we finish writing our doctoral thesis after three, four, five or more years of studying, reading countless papers and books, trying hard to understand things we don’t understand over and over again to eventually understand some of them, rarely completely and usually only superficially, but without knowing it, and only later, upon uncovering yet another level of understanding, realising it? When we defend the thesis and have this moment of great personal satisfaction and maybe even pride?

Of course not! We feel like we are just now allowed to enter the lowest ranks of research workers like our supervisors and their colleagues, those who have been doing research for decades, many sometimes started before we were even born, and we are a new kid on the block who mostly knows things that everyone else in the field knows, with possibly a few tiny bits that we might know a little better than some, but usually only in our skewed perspective and restricted exposure both of which are the result of isolating ourselves in order to complete the work that we have either set for ourselves or that has been set before us.

So, are we a scientist when we have that PhD that we can when we choose to place before or after our name? No, we are not. At least not relatively speaking. Although when we go out in the world and exchange with ‘regular folks’, those who have not spent five or seven or ten years in graduate school, we realise that we speak a different language to a certain extent; we realise that we see things, maybe most things, quite differently than they do, and this no matter what we are talking about, regardless of the actual subject of our studies; there is a different perspective on things, which is difficult to describe but definitely palpable and usually recognised. But when we interact with mature research workers we time and time again are forced to recognise how little we know and how much we still have to learn just to be able to exchange at a level that is sufficiently high to be interesting and useful.

When do we become scientists? Is there a moment at which we begin to feel that we are a scientist? Is there a point at which research workers consider someone to have become part of their peers? Is it possible to actually identify this in an objective way? We could say: when you have published a refereed paper, when you have published ten or twenty, or when your papers have amassed a certain critical number of citations; when you have given your first conference presentation, or when you have given ten or twenty of them; when you have given your first seminar, taught you first class, given your first series of lectures; when you have given your first invited review talk or your tenth. We could go on and on in this way, listing milestones and achievements, but can any of these actually determine at what point we can be considered or consider ourselves to be a scientist?

And what of this language, this language of scientists? Is it that a scientific training changes the way we understand the meaning of common words used in everyday language, or is it that the somehow different and possibly expanded worldview, to a greater or less extent, brought about by going through the process of scientific training, that everyday things, words and meanings are perceived and interpreted in a different and possibly wider general context that allows a more subtle understanding of not just these things relating to the specific subject of the training, but to everything else as well. Does this mean that it is not possible to agree on what different words mean by agreeing on a definition for them? Certainly not. Does it mean that communication between a scientist, whatever that is, and a non-scientist is not possible or not really possible because of the unbridgeable gap between their different worldview that causes an unsurmountable obstacle in their respective abilities to convey what each one is trying to express? Certainly not.

For all of the physical sciences, the universal language is that of mathematics, and it does not depend on culture, religious background, country, gender, skin colour, age, or whatever other superficial characteristic we might have inherited or learned from our family, friends, peers and larger social context. In any other field of science or anything else, for that matter, the specificities of language that are developed in time, and that we usually refer to as jargon, but which involves not just specific kinds of words, but also particular sentence structures, as well as speaking and writing styles. Are these somehow only accessible to those in the particular field of research?

Not really, are they? There is nothing fundamental about this jargon, this way of using words and sentences to express specific kinds of information. It is only a matter of learning it, which only requires exposure and time. To a great extent, to understand the language that is specific to a branch of science or other field of research, we do not even need to have formal training in that field, but only enough exposure to acquire these language-related skills.

Could a Galileo be imagined to be brought from his seventeenth century world into Roger Penrose’s twenty first century classroom on differential geometry in multi-dimensional non-euclidean spaces and understand even a handful of the words he would be speaking? Rather doubtful. On the other hand, could Galileo explain to Penrose his measurements and calculations on evaluating the acceleration of different spheres of the same size but of different materials on inclined planes? Absolutely! Could Galileo, given enough time, learn the vocabulary as well as the mathematical details required to grasp and follow Penrose’s lectures on curved non-euclidean spaces? Surely he could. Is there some kind of unique and special mindset that a scientist has, and that sets them apart, granting them access to hidden, secret aspects of the world, physical and even metaphysical? This was believed for many centuries and by most people, including those scientists themselves, but this is now not very believable, is it? Is it true that a career and a lifetime devoted to scientific inquiry and investigation, to the study of evermore complex subjects and mathematical formalism, the continual pursuit of deeper and more complete understanding of any particular problem in a field of scientific research work can lead to ever deepening insight into the function of and interactions between the phenomena that we observe in the physical world? Absolutely! Are these incompatible conclusions? Not in the least.

The importance of language for communicating, for expressing ideas and conveying what is intended to be conveyed, is enormous: there is no doubt about this. So great is it that it is far easier to be misunderstood or at least not well understood, than it is to actually succeed in making ourselves understood in the way we intended. Every research worker who has been to a conference, given and listened to presentations, and in that setting interacted with other research workers from different cultural and linguistic backgrounds knows how difficult it can be to express oneself in a way that ensures we can be understood, and how difficult it sometimes is to understand what others are trying to express and convey. Pushing this point to the extreme, we could conclude that we always only partially express what we want to convey, and always only partially understand what others are trying to convey. And yet, even if this is, in many ways, more of a tautology than something to be argued, we do succeed in conveying meanings, often of exceedingly high complexity and sophistication, especially in regards to a wide range of very technical scientific matters, that are understood by our peers, at least enough to continue the scientific dialogue and related research activities.

What about the way we function in our life outside of our research work: what do we believe about ourselves, about others, about the world and the universe? Do we believe in a God, a omnipotent or omniscient God, a benevolent God watching over us? Do we, as so many billions all over the globe, pray to our God for health and prosperity, for long life and success, for help and guidance through difficult decisions and difficult times, for a speedy recovery from illness, for our children, for our parents, for our brothers and sisters, for our cousins, uncles and aunts, for our friends? Do we believe in hell or in karma, in the existence of a soul, of an afterlife or in reincarnation? Do we believe that the societal rules of conduct defined by and through the religious and cultural frameworks that evolve within this society and that have been transmitted to us as they have to everyone else, have something inherently important, inherently fundamental, that they have something that inherently sets them above and beyond our ability or even our right to question their validity or just their practical usefulness? Do we believe that what we believe to be ethically right is actually right, and what we believe to be ethically wrong is actually wrong?

Do we question these beliefs that we hold? Do we question all of our beliefs and convictions? Do we recognise how strongly conditioned everything about our selves actually is? Do we recognise the extent to which this conditioning defines not only what we perceive, but also what we are actually able to perceive, what the way in which our attention is configured allows to perceive, irrespective of the actual biochemical and physiological function of the senses, nerve endings and central nervous system? Do we see what the eyes see, hear what the ears hear, feel the breathing of the body as it breathes, feel what the fingers and the skin all over the body actually feel? Or are all of these details ignored, overshadowed by our attention contracted and focused on some thought, feeling-tone or discursive conversation we are having with ourselves while going through the motions of doing what we do from the moment we wake up to the moment we go to sleep, never actually consciously seeing, hearing, touching and feeling anything other than our thoughts, our stories, our memories and our most often recurring and almost always paralysing feeling-tones?

Can we be said to be scientists—actual scientists, real scientists, true scientist—if we don’t question into absolutely everything about the way we know and learn, sense and feel, perceive and cognise, imagine and believe, conceive of and conceptualise, recognise and interpret, and in the end, how we express anything at all? Can we be said to be scientists if we do not strive to reconcile into a coherent whole all of the knowledge, beliefs and information we hold about ourselves and the world in all of its forms? Do most scientists live in this way: questioning thoroughly and uncompromisingly into everything without any discrimination nor censorship? No, they don’t; definitely not. Does, in fact, any working scientist do this? Maybe one or two here and there, but without any doubt, very very few, vanishingly few. Could most scientists, all of them even, live in this way? Yes, indeed, they could.

How is it possible, for example, to spend a lifetime studying and trying to understand the inner workings of supermassive black holes and everything about them, their vicinity and their interaction with and influence on these surroundings, and yet never wonder what happens scientifically speaking—biochemically, physiologically, metabolically—when we take a sip of orange juice or Coca-Cola, when we take a bite of a sandwich or piece of pizza? Does it make sense to spend so much time thinking and considering certain things, and not others, which are to all practical purposes infinitely more important for the survival of this being as a living organism? Does this behaviour seem contradictory?

Well, it may to some when put in these terms, but it is nevertheless normal, it is the norm, the standard way in which we tend to behave and tend to be, not just amongst scientists but amongst everyone, or at least, practically everyone. This separation, this segmented, disconnected, fragmented life filled with piles of bits and pieces, shards and splinters which together seem to make up its entirety, and this remaining so without triggering any sense of awkwardness or that there is something fundamentally off about this painful lack of coherence and cohesion between all of these separately considered broken pieces that what we nonetheless, maybe by force of habit, call our life.

To be starkly truthful, isn’t this questioning into absolutely everything, not merely hypothetically, but practically, not merely once in a while and not merely with our thoughts, but with the whole body-mind in each and every moment, again and again, and over and over throughout life, what every thinking human being should do? Do most people live in this way? No, they don’t; definitely not. Does actually anyone live in this way? Surely some do, but here again there is no doubt that their numbers are also vanishingly small in the global human population. Could most people, everyone even, live in this way? Indeed, we could.

With all of this in mind, having cast such a light on the subject, what would we say about what it means to be a scientist? What would we say about what it means to be a thinking human being? What would we say about coherence and cohesion in our own life? And what would we say to Wittgenstein or Popper about their notions of ‘the scientist’, ‘the life of the scientist’ or ‘the language of the scientist’?

# Remarks on the relation of scientific theories to physical reality

A few days ago at the dinner table, my son mentioned that one of their Theory of Knowledge teachers had explained to them on that day that gravity was not a force, but instead that it was an epiphenomenon in the sense that it arose as a consequence of the presence of mass and energy in spacetime. My immediate reaction was to specify that this was true in the framework of Einstein’s Theory of General Relativity, but that as revolutionary, elegant, subtle, and incredibly successful as it was and is, General Relativity is, as all other theories are, a theory nonetheless, and that theories are descriptions of nature that we construct to explain and understand, at least partially, the phenomena we observe.

No matter what it is that we are observing, no matter how microscopically small or astronomically large, no matter how simple of complex, no matter how subtle or coarse, no matter how rudimentary or sophisticated the instrumental methodology, the observation or measurement is inherently distinct from the phenomena being observed, it is removed from it. This precedes conceptually the modern quantum mechanical tenet that the act of performing a measurement affects the system to which the measurement is applied. The former is a statement about the inherent distinction and separation between the phenomena, the observation and measurement of a manifestation of it, and thus also the interpretation that is given to the observation. The latter underlines the fact that, in the quantum mechanical view of the world, a system is a weighted probabilistic mixture of different states that coexist until a measurement is made, at which point the `wave function collapses’, forcing the system to be found in one of these possible states, and the instrument tells us which state that is.

The fundamental point I am referring to, which, when expressed plainly, is as obvious as obvious can be, is this: a description of a phenomena is not that phenomena—it is a description of it; a theory about the physical world, a theory about the physical reality we observe is not the physical world, it is not physical reality—it is a description of it. This is so easy to see that it is not debated and obviously shouldn’t be. However, we, as scientists and philosophers, regularly, and in fact, too often make statements, adopt stances and draw conclusions that undeniably demonstrate that this most fundamental point about the relationship of the theories (to which we tend to be so dearly attached) to physical reality is not well understood, and the point is muddled in our appreciation of the scientific process in which we are engaged.

To hold that gravity is not a force but the manifestation of the fact that objects follow geodesic lines defined by the curvature of space-time which in turn is defined by the distribution of matter and energy illustrates the point well: we have substituted a beautifully accurate and successful description of the physical world as it pertains to the motion of bodies and particles, a jewel of a theory that is as elegant, far-reaching and as awesome in its descriptive as in its predictive powers, for an expression of how reality actually is, what gravity in itself is.

This is the first point I raised and explained in response to his mention of what the teacher told them in class. The supportive argument I used as an illustration of this was that in quantum field theory, another very successful theory that underlies all of modern particle physics, does, in fact, in stark contrast to Einstein’s classical Theory of General Relativity, treat the forces of nature as acting through the mediators of that force, bosons, that travel back and forth between the two particles, `carrying’ the force which is quantised in these boson force mediators. This is why it is described as a quantum theory of fields: everything is quantised into particles, including all the forces of nature, all of these particles are treated mathematically as fields pervading space-time, and gravity is quantised and carried by the graviton, even if the latter is the only one of the bosons that has not (yet) been detected. The other ones—gluons for the strong force holding quarks and anti-quarks together; $W^+$, $W^-$ and $Z^0$ for the weak force responsible for radioactive decay; and photons for the electromagnetic force—have all been detected long ago and studied in a great deal of detail for decades now. Therefore, in the framework of the modern quantum theory of fields, gravity is a force mediated by the graviton; not an epiphenomenon that manifests as a consequence of the energy distribution dependent curvature of space-time. Furthermore, most attempts to reconcile General Relativity with Quantum Field Theory are based on the scientific framework defined by the second of these theoretical pillars of present-day physics in which forces are forces carried by gauge bosons.

Each time we succeed in understanding an aspect of the physical world more deeply and in subtler details, even if this understanding is flawed in some way that is not apparent to us, each time we succeed in developing a consistent theory with greater descriptive and predictive powers than the previous theory we had for this aspect of the observable physical world, the natural tendency is to claim and actually feel that now we finally understand how this works and how things are. But by the very fact that we have witnessed a multitude of both large and remarkable as well as small and incremental advances in our theoretical descriptions of the natural world, we are forced to appreciate the fundamental point that descriptions are only descriptions and will never be in any way equivalent to the actual phenomena that they describe.

In the same way that scientists and philosophers have pondered, discussed and argued about the meaning and consequences of the General Theory of Relativity on how we view nature and physical reality, they have done this, and in fact most likely to a greater extent, in relation to the interpretation of quantum mechanics, coming up with various paradoxes and conundrums in the process, which on the whole, instead of elucidating or clarifying issues, have only made the doctrines and theoretical implications appear stranger and more difficult to grasp. But here again, we suffer from the same problem: taking a description of reality, extracting meanings from this description about how reality or nature actually is, and then being intrigued and surprised by the counterintuitive consequences and paradoxes that arise from doing this.

To take the example mentioned above that deals with the collapse of the wave function, the fact that we describe our partial knowledge of the state in which the hydrogen atom finds itself as a superposition or co-existence of a set of different states with different probabilities for manifesting themselves, does not mean that this is so, it does not mean that this is how nature is. And the fact that when we make a measurement we find a particular state does not mean that prior to the measurement the system was in a quantum mechanical mixture of all the states. It is a description that works very well to describe certain physically observed phenomena in our laboratory experiments and therefore we use it. But it should not be interpreted as a statement about how nature in itself or physical reality in itself actually is; it is only a clever description that works in certain settings when certain boundary conditions are fulfilled.

This inquisitive human mind has always sought to understand. This understanding has grown evermore sophisticated and subtle over the centuries and millennia. The inherent human trait of clinging and holding onto whatever seems most solid in an attempt to make it feel most solid has led scientists and philosophers time and time again to believe in scientific theories as being expressions of how nature actually is, to equate a successful description of a physical phenomena to a statement about what the phenomena in itself is. Pursuing the intellectually challenging but stimulating and satisfying exercise of seeking increasingly sophisticated and subtle, extensive and ideally even all-encompassing explanations of natural phenomena through modern scientific theories has muddled the point further by continuing to ascribe to nature qualities derived from the interpretations we make of these theories. I think we should be more careful about this.