Sadly, You Should Ignore Non-Peer Review Nutritional Opinions

I was genuinely disappointed today with what I thought were some reliable sources of nutritional information in the blogosphere. The tipping point came when I was reading an article from (self-titled) "Authority Nutrition" against the adoption of a vegan diet. The first argument was a deficiency argument and the claim was that:

...B12 deficiency is very common in vegans, one study showing that a whopping 92% of vegans are deficient in this critical nutrient (1).

 I admit that, in the past, I have had a poor track record of actually checking references. I guess I was just too trustworthy, but because of all my recent pub-med crawling, I thought I would click on the reference. And I was sad. The claim made by Authority Nutrition only resembled what the reference said and a clearly crucial fact had been omitted. What the reference actually says in the abstract (in other words, all I had to do was click on the reference, without even reading the article):

Among subjects who did not supplement their diets with vitamin B12 or multiple vitamin tablets, 92% of the vegans (total vegetarians), 64% of the lactovegetarians, 47% of the lacto-ovovegetarians and 20% of the semivegetarians had serum vitamin B12 levels < 200pg/ml (normal = 200–900 pg/ml). However, their complete blood count values did not deviate greatly from those found for nonvegetarians, even though some had been vegans or lactovegetarians for over 10 years.

It is surely quite a different figure when those bolded statements are made clear. I am far from a representative socialite, but among vegans that I know, all of them supplement with vitamin B12 in some form. I am not sure whether it is more charitable to impute ignorance, carelessness or willful manipulation of the reader to the writer of the article, but it does not matter.

The unfortunate truth is that nutritional "facts" from these sorts of sources, as it turns out, are almost always misleading at minimum and plainly false in the worst of cases. Even the ones that claim to be based on facts, from people qualified to give advice on the area, can be wrong or misled; the diet advice you can receive on a popular platform in a small readable chunk will almost invariably lack the nuance of the original research and will equally invariably over-generalise. Studies are often not even done on humans, or are done on particular segments of the population in particular controlled environments. There are studies done, in fact, that demonstrate how poorly the results of other studies generalise to other portions of the population.

Even more unfortunate is the fact that the nuance and precision employed in the scientific literature often makes reading that literature inaccessible to the layperson. It is certainly possible to pick up the technical know-how to read and research the literature by yourself - but it takes a lot of practice to even break into one small subfield of the literature. Trying to get a good grip on a single topic is an excellent exercise if only to understand the complexity of even simple nutritional issues and why the researchers can do this as a full time job (without any of the glamour of a popular nutrition personality). Even after becoming proficient, there are few truths in nutrition that manage to actually transcend the bounds of the demographic studied to the general population, and fewer still that can be conclusively tied to some reductionistic element of a food. For example, the blood sugar effects of different foods cannot be tied to a single macronutrient (this video explains the research on berries and blood sugar). This implies that reductionistic accounts of nutrition of the ubiquitous "this was shown to be good so eat these other foods containing the compound" fail to account for the richness and complexity of foods as whole substances. The ineffectiveness of supplemental antioxidants compared to food-derived antioxidants is further evidence of this.

I sadly have to admit to myself that, not only is most of my popular level nutrition knowledge probably vastly over-simplified to the point of uselessness, but I am also unable to learn by going to popular sources. They are too unreliable and too simple. If I want to know what to eat - and I do! - I have to do my own homework. I may well post some of my findings here, but if you believe anything I have said, you will have to check my references for yourself.

All You Need to Know about Fundamental Quantum Mechanics

Quantum mechanics has got to be the hottest physics theory ever. Every successful theory in science is popular within that science - and quantum mechanics is the most accurate scientific theory of all time to date - but the popularity has decidedly left the Ivory Tower of academia. From quantum dishwashing to quantum real estate and practically everything in between, quantum mechanics seems to be the brainy version of adding sex appeal in marketing.

I can only imagine that advertising is the main reason for the flamboyant use of the word quantum, since it is essentially a fancy word for "smallest amount of some physical entity." For something to be quantised  means that it is made up of small indivisible quantities - for instance, spin of particles is quantised such that, for instance, electrons can only have some integer multiple of a half spin. So either these quantum products are "quantum" for their sexiness, or they are somehow quantised in such a way that is don't-ask-me-how relevant to the consumer. I suspect the former.

The other side of quantum mechanics (QM) in popular culture is not on the market but in the way people use QM to intellectualise their odd views about the world. For instance, there is esoteric views of "Quantum Healing" espoused by Deepak Chopra or wacky New Age perversions of the theory. Of course, to a physicist, all of that misuse of science amounts to a grand "quantum flapdoodle" (to use Murray Gell-Mann's term). In general, it is wisest to follow the advice of xkcd on this point when speaking to someone who has no background in actual physics:

But what if you do not want to be in the riff raff ignorant of quantum mechanics and rise to the lofty heights of someone who can honestly claim to not understand it? The fact of the matter is, quantum mechanics is weird because it operates on a different logic to what we are used to in "classical" physics. By all means, baffle your brains out by trying to picture interference patterns from double slit experiments with buckyballs (sixty carbon atoms arranged like a football) in terms of it acting like a wave and a particle. When you are suitably confused by that, perhaps you will appreciate that understanding the logic of QM gives far more insight, I think, into why QM seems so outlandish to us.

For those that are averse to mathematics, a career in quantum mechanics is not for you. Like most theories in physics, quantum mechanics has two parts:

1. Equations. 
2. Interpretations which explain how the symbols in the equations relate to real world phenomena.

But before you run away screaming that there are equations in physics, there is still some insight you can glean without actually looking at equations directly (something which some people avoid as much as looking at the sun for fear of burning their eyes). To begin with, the equations of QM are pretty well established. Unfortunately, the second element is not fundamentally agreed upon. Certainly, physicists can use the equations to make extraordinarily accurate predictions about the world from a "plug-and-chug" point of view, but there are wild divergences over what exactly is happening under the quantum mechanical bonnet. So a truly and absolutely conservative argument about quantum mechanics should probably only involve what the theory predicts - which unfortunately, has absolutely nothing to do with dish-washing, real estate, healing or, the darling of many quack worldviews, consciousness.

Still, the basic structure of the equations of quantum mechanics explains why we find it so un-intuitive: in QM, systems are described by states in Hilbert space. By contrast, classical systems are described by points in phase space. Even without really understanding what the Hilbert and phase spaces are, the underlying point is that the way we have to think about the inner workings of quantum compared to the more intuitive classical mechanics is fundamentally different. It would be, to use a crude analogy, like asking a car mechanic to work on a space shuttle: there are obviously certain similarities, but at the end of the day, car engines run off explosions which move pistons whereas rockets shoot fuel out their rear end to go forwards; they are incommensurate.

Let me finally state all the fundamental postulates of quantum mechanics:

• Physical systems are described by states in Hilbert space.
• Those systems evolve according to the Schrodinger equation (or equivalents, such as Heisenberg matrix mechanics and Feynman path integral formulation), given some Hamiltonian for the system (where the Hamiltonian is the functional of energy).

That is all. There is a rule for defining what something is and a rule for explaining how it changes in time. The state in Hilbert space is called the wavefunction and Schrodinger's equation is a wave equation, must like the one you would use in classical mechanics to describe a wave on a string, for instance.

Some physics-literate people may protest that I am missing an extra postulate. You see, part of the charm of quantum mechanics is that Hilbert space is mysterious and hidden. This means that you cannot actually measure wavefunctions - and this is quite the problem, because if you cannot measure wavefunctions and you hold that wavefunctions are what describe physical systems, then it would seem that physical systems cannot be measured. That has to be false, though, because we clearly measure things all the time. So they add in another postulate which explains measurements:

• The probability of measuring a system to be in some possible state is given by the Born rule, which "collapses" the wavefunction - in other words, measuring a system makes the wavefunction look like a very sharp spike at the value you measured.

Side note: I will not go into why I think the Born rule is an unnecessary addition to the theory other than to say that I think the Everettian Quantum Mechanics is correct.

You can write that all in terms of the mathematical formalism, which is of course a necessary step, but if you leave this blogpost understanding nothing more than that fundamental difference between quantum and classical mechanics (ie, Hilbert vs. phase spaces), you will understand more than practically anyone outside of science. But why leave maths out of it when you can put it in for good measure? Here are the postulates in their mathematical glory:

Physical systems are described by states in Hilbert space which are written in Dirac notation with "bra"s (1) and "ket"s (2) (which together make bra-kets, or brackets):
$$\begin{equation}\label{eq:bra}\langle\phi\rvert \end{equation}$$ $$\begin{equation}\label{eq:ket}\lvert\psi\rangle \end{equation}$$

The bras are just the Hermitian conjugates of the kets - they correspond to the same vectors in the opposite sides of dual space.

Observables are the things you measure, and in quantum mechanics, they are described by Hermitian ("self-adjoint") operators such that: $$ \hat A = \hat A^\dagger$$

The possible results of measuring some observable are the eigenvalues of that operator. In other words, if you take the momentum operator: $$\mathbf {\hat p} = -i\hbar\mathbf{\nabla}$$

These systems evolve (change over time) according to the Schrodinger equation:

$$\displaystyle i\hbar\frac{\partial \psi}{\partial t} = \frac{-\hbar^2}{2m}  \nabla^2 \psi + V \psi$$

Or compactly and in terms of bras and kets:

$$i\hbar\frac{\partial\lvert\psi\rangle}{\partial t} = \hat H \lvert\psi\rangle$$ 

Finally, the Born rule can be written as (where x is just standing in for any observable, not necessarily an x coordinate):

$$P(x=a) = |\langle\phi(a)\rvert\psi(a)\rangle|^2$$

There you have it; that is all there is to fundamental quantum mechanics. Use your knowledge for good.

Laws of Nature as Patterns

An old definition of science could be that science is the study of cause and effect in nature. The idea that causality is the central idea in knowledge goes back at least to Aristotle's four cause analysis of the world and in many ways this is what people believe science does today. Instead of directly citing cause and effect, it seems to me that the intermediate notion of the "laws of nature" is interjected; science studies the laws of nature, which are about cause and effect in nature. Simple, right?

I want to propose an alternate idea based on how I view science and in particular, based on how I see modern science handling data. There's a caveat before I begin: as usual, I think much more about the canonical status of physics in science than I do of other equally legitimate branches of natural science. So what I say relates most to physics and (perhaps) the applicability slowly decreases as we move towards more qualitative sciences. Or it might not - my point is that I am making a stronger case for science as most exemplified in the hard, mathematical sciences.

Scientists do experiments and get data. This data is put often into tables or graphs and analysed, whereby models are produced which explain the correlations in the data by causal mechanisms. The model, if it is a good one, will make other predictions which can be tested to see if it is correct, and the more it passes those tests, the more credence it is given. That is the scientific method of observation, hypothesis, testing, conclusion. There are two very similar problems I see with this process: an error in data analysis and a deeper philosophical issue that Hume would have noted.

It is drilled into every data analysis/scientific statistics student that a correlation does not mean a causation and yet this explication of the scientific method clearly makes that jump. The justification is simple: eliminate as many variables as possible and the remaining correlations must be causation. That is simply mistaken and the history of science is rife with examples of deeper explanations being found of natural phenomena which destroyed the previously perceived causal mechanism.

Hume would have heartily agreed with this objection and would defiantly disagree with anyone who tried to maintain that, whilst correlation does not equal causation, a lot of correlation does, in fact, equal causation. His problem was two-fold: the assumption that the correlations of the past will hold in the future is only based on the observation that the correlations of the past have so far held true in the future. But that is circular, since in effect it says that the future is causally equivalent to the past because the past is causally equivalent to the past. But again, Hume had a deeper problem that simply the problem of induction. His biggest reason for scepticism is that causality was not a superficial relation between objects, in fact, we never really perceive causality at all, we perceive effects and infer causation. He called this "customary conjunction", or basically, correlation. For all this scepticism (and Hume unlike others branded with this title really was a sceptic), Hume did still believe in cause and effect, he simply thought it was beyond our knowledge.

I am not sure if I believe in cause and effect, but I propose right now the weaker claim that science does not study it. Science studies data to produce laws of nature which are expressed mathematically because, at bottom, the laws of nature are patterns in observable variables or parameters. In other words, the laws of nature are patterns of numbers that describe nature. Let me give an illustrating idea to stir the intuition of this proposal and consider how this relates to epistemology and the metaphysics of causality (if causality exists at all).

Think of the positive integers: 1, 2, 3, 4, ... They form a nice set whose properties can be analysed to yield fascinating mathematics. Relations can be defined on this set giving it order, taking a pair of numbers to another in the set by multiplication or addition, and so on. The tools of mathematics are about seeing mathematical structure in the integers, seeing what symmetries it might have, trying to see what patterns it has. A simple pattern in the integers is that the numbers are alternating odd, even, odd, even.

What if we tried to apply the tools of old fashioned science to the integers? It would yield fictitious language about causality to something which exists independent of causes: the fact that 2 is even is not caused by the fact that 1 is odd, even though we could conceivably speak of it that way. Many of the properties of the positive integers can be spoken of in terms of causality, but it is a fiction of our language, not a fact about the set itself.

So, I claim, it is in science. Equations like Newton's laws are mathematical statements which should not be thought of in terms of causality but in terms of patterns. It is still possible to make if-then statements: If a force is applied, then an acceleration will occur. That is a statement about what the second law predicts and codifies. It is also important to note that I am not simply saying "science produces equations that have no necessary connection to what really exists." This view is not scientific anti-realism, it is congruent with a critical realism about science.

It is important to dispel the objection that I am merely playing with words and the if-then statements are exactly equivalent to causality statements. But I refer back to the case of mathematics: it seems clear that "if you add one to an odd number you get and even number" is not equivalent to "adding one to an odd number causes an even number." The first is true, and the second uses perverted language to try and express, it seems, the first statement.

The pattern view has several advantages: for starters, it is epistemically conservative and codifies what the science actually shows rather than trying to make it jump over the correlation-causation barrier in the data. It is robust to quibbles over the meaning and nature of causality, in particular, it allows for a less stringent requirement on the necessary conjunction between a state of affairs and its antecedents; the pattern view may allow, once specified, the derivation of if-then statements, but it does not have to. Patterns can in principle be random or ordered.

It also avoids infinite causal regress problems. It seems intuitive to some (though not all) that causal chains must have a beginning (whether the causal series be per se or per accidens as Thomists would distinguish). But it does not seem to be obvious that patterns need to have a beginning: sure, the pattern of odd, even, odd, even in the positive integers has a beginning because it has a first member. But the integers have no first member because they stretch from negative infinity to infinity - and yet they still have the pattern of odd, even, odd, even. What is not definable is whether the first element was odd or even, because there is no first element.

But even if we take the positive integers, it still does not need for there to be something before the first member for the pattern to continue ad infinitum. To ask "what caused the first member of the positive integers" is a senseless question. Similarly, it may very well be the case that nature had a beginning and it is self-contained. The objection that "but it had to have had a cause, science demonstrates that!" is simply not true. The universe could be just like a set which starts at time zero and continues to infinity without  quibbling over whether there was anything at t = -1.