## Matrix maths for quantum physics

Reading David Deutsch’s papers on quantum physics requires knowing some matrix maths. The papers are here

https://arxiv.org/abs/quant-ph/9906007

https://arxiv.org/abs/quant-ph/0104033

https://arxiv.org/abs/1109.6223

This post gives a brief account of the relevant maths.

### Complex numbers

First, a brief explanation of complex numbers. Ordinary positive and negative numbers have the property that the square of the number is positive, e.g. $1\times 1=1,5\times 5=25,-12\times -12=144$. An imaginary number is defined to have the property that its square is negative. The imaginary number i is the number such that $i\times i=-1$ and other imaginary numbers are just multiples of i. Also, $i\times -i = - (i\times i)=1$A complex number is a sum of an ordinary real number and an imaginary number, e.g. 1+2i is a complex number.

For a complex number $\alpha$ given by $a +bi$ the complex conjugate$\alpha^\star$ of$\alpha$ is defined as $a -bi$. Now, $\alpha \time\alpha^\star =a^2 +b^2 = |\alpha|^2$ and  $|\alpha|$ is called the magnitude of $\alpha$. For a real number  $\theta$$(\cos\theta)^2+(\sin\theta)^2 = 1$, so for any complex number, there is a real number $\theta$ such that $\alpha= |\alpha|(cos\theta+\sin\theta i)$. It also happens to be true that $e^{i\theta} = cos\theta+\sin\theta i$ and so a complex number$\alpha$ is sometimes represented as $|\alpha|e^{i\theta}$

### Matrices

These papers are about the multiverse as described by quantum mechanics. Each system exists in multiple versions that can interact in interference experiments. For any particular quantity you could measure for which there are multiple possible outcomes, there is one version of the system for each outcome. There is a finite set of possible measurement results for any finite system.

Let’s suppose that we have a system S and a measurement that could be performed on S with two possible outcomes +1,-1. There needs to be something in the theory that represents the transitions between each outcome. There is a complex number $n_t$ that describes each transition $t$: the probability of the transition is $|n_t|^2$. So for S the thing that represents these transitions would need 4 numbers: one for each pairs of outcomes$(+1,+1),(-1,-1),(+1,-1),(-1,+1)$. Now, a version of the system could do the transition $(+1,-1)$ and then it could do any of the transitions allowed from -1. The system could also do any -1 transition if it did the transition $(-1,-1)$.

What happens if two transitions happen one after another? The way to work out what happens is you list the set of possible states of the system. You can describe the first set of transitions as a square matrix whose elements are the numbers for each transition. So for the system S the matrix would read:

$\begin{bmatrix}n_{(-1,-1)} & n_{(-1,+1)}\\ n_{(+1,-1)} & n_{(+1,+1)}\end{bmatrix}$

The second transition would have a different set of numbers $m_t$ and the corresponding matrix would be:

$\begin{bmatrix}m_{(-1,-1)} & m_{(-1,+1)}\\ m_{(+1,-1)} & m_{(+1,+1)}\end{bmatrix}$

To work out the number for the composition of the transitions, you take the product of the transitions for which the final state of the first transition is the same as the initial state of the next transition and add them together. The matrix that describes the result of both transitions would be:

$\begin{bmatrix}m_{(-1,-1)}n_{(-1,-1)}+m_{(-1,+1)}n_{(+1,-1)} & m_{(-1,-1)}n_{(-1,+1)}+m_{(-1,+1)}n_{(+1,+1)} \\ m_{(+1,-1)}n_{(-1,-1)}+m_{(+1,+1)}n_{(+1,-1)} & m_{(+1,-1)}n_{(-1,+1)}+m_{(+1,+1)}n_{(+1,+1)} & \end{bmatrix}$

This is just the equation for the result of multiplying a pair of $2\times 2$ matrices. More generally, for a set of N possible states a set of transitions is represented by an $N\times N$ matrix. If two sets of transitions are represented by matrices A and B, the transition that happens if you do the transition described by A followed by the transition described by B is described by the matrix product of B and A, whose elements are $(BA)_{ij}=\sum_kB_{ik}A_{kj}$. For more than two transitions you just multiply more matrices, with the earlier transitions on the right and the later ones on the left.

So far I have only described transitions. What describes the system undergoing the transitions? The answer is more matrices. You need a set of matrices that can be multiplied by complex numbers and added up to give any other matrix of the same dimension. The reason is that you need a set of matrices that can be used to represent all of the possible transitions. For a system with N possible states you need $N^2$ matrices. If A is a transition matrix and M is one of the matrices describing the system then the system after the transition is described by $A^\dagger M A$, where $A^\dagger$ is the Hermitian conjugate of A: the matrix found by taking the complex conjugate of the entries and interchanging their indices. So the Hermitian conjugate of

$\begin{bmatrix}a & b\\ c & d\end{bmatrix}$

is given by

$\begin{bmatrix}a^\star & c^\star \\ b^\star & d^\star \end{bmatrix}$

The matrices representing the transitions are unitary, which means that $A^\dagger A = I$ where is the identity matrix that has 1s on the diagonal and zero on all off-diagonal entries. Some examples of unitary matrices:

$\begin{bmatrix}1/\sqrt{2} &1/\sqrt{2} \\ 1/\sqrt{2} & -1/\sqrt{2} \end{bmatrix}$

$\begin{bmatrix}1 &0 \\ 0 & i \end{bmatrix}$

Measurable quantities are represented by eigenvalues (the definition will given below, but requires some setup) of Hermitian matrices. A Hermitian matrix M is a matrix for which $M^\dagger = M$. Some examples of Hermitian matrices:

$\sigma_3 = \begin{bmatrix}1 & 0 \\ 0 & -1 \end{bmatrix}$

$\sigma_2 = \begin{bmatrix}0 & -i \\ i & 0 \end{bmatrix}$

$\sigma_1 = \begin{bmatrix}0 & 1 \\ 1 & 0 \end{bmatrix}$

$\sigma_0 = I = \begin{bmatrix}1 & 0 \\ 0 & 1 \end{bmatrix}$

These matrices are called the Pauli matrices. Suppose a matrix M and a vector v have the property Mv = av, where a is a number, then a is an eigenvalue of M and is an eigenvector of M. The first three Pauli matrices $\sigma_1,\sigma_2,\sigma_3$  all have eigenvalues +1 and -1. The eigenvectors for $\sigma_3$ are $latex[1,0],[0,1]$. The eigenvectors for $\sigma_2$ are $1/\sqrt{2}[1,1],1/\sqrt{2}[1,-1]$. The dot product of two vectors $v = (v_1,v_2\dots),w = (w_1,w_2\dots)$ is given by $v\dot w =v_1w_1+v_2w_2+\dots$. The dot product of two eigenvectors is always zero: they are said to be orthogonal.

A projector P is an operator such that  $P^2=P$. The projectors$I+\sigma_j,I-\sigma_j$ for the three Pauli matrices $\sigma_1,\sigma_2,\sigma_3$ have the property that $\sigma_j P = P$ or$\sigma_j P = -P$ . More generally, for any Hermitian matrix M there is a set of projectors $P_j$ such that $P_jP_k = \delta_{jk}P_j$ where $\delta_{jk} = 1$ if $j=k$ and 0 otherwise for which $M = \sum_j a_jP_j$ and the $a_j$ numbers are the eigenvalues of M.

If you have two different systems $S_1,S_2$, the transition matrices and the matrices representing the system’s state can be represented by tensor products of the matrices representing each system. The tensor product of two matrices A,B is denoted as $latex A\otimes B$ and is represented by

$\begin{bmatrix}a_{11}B &a_{12}B &\dots \\ a_{21}B &a_{22}B&\dots\\ \vdots& \vdots & \ddots \end{bmatrix}$

For example

$I\otimes \sigma_1 =\begin{bmatrix} 0 & 1 & 0 & 0\\ 1 & 0 & 0 & 0\\ 0 & 0 & 0 & 1\\ 0 & 0 & 1 & 0 \end{bmatrix}$

A function f applied to a Hermitian operator $M = \sum_j a_jP_j$ is given by$M = \sum_j f(a_j)P_j$.

I think that covers most the matrix stuff you need to know to read those papers. More stuff on matrices can be found in Quantum Computation and Quantum Information by Nielsen and Chuang, which also has exercises.

## Criticism of Jay Joseph on Twin Studies and psychiatry

The Trouble win Twin Studies: A Reassessment of Twin Research in the Social and Behavioral Sciences by Jay Joseph is about twin research and the way psychiatrists try to use it to argue that some behaviour is controlled by genes. It illustrates some bad misconceptions about evolution. It also includes misconceptions about the sort of arguments that are worth making against psychiatry.

Knowledge about what you want to do and how you want to do it is what explains the stuff you do. Anything else is just a particular circumstance in which you use the knowledge you already have. If you go to the supermarket and they have run out of hummus and buy some other snack instead that doesn’t necessarily change your preferences, it just changes what you do in that particular situation. So then what matters for assessing behavioural genetics is concerned is what knowledge you use to make decisions and the properties of that knowledge.

Evolution is a knowledge-creating process. Genes contain information about how to set up an organism that will make copies of those genes. That knowledge was created by variation and selection of genes. The variation takes place by genes mutating. The selection consists of genes either managing to make bodies that make copies of those genes, or not. The fact that copies are made of the successful variants of genes is important because otherwise there is no way for many small changes to build up over evolutionary time. If every small change was lost to the next generation, then no knowledge would be created because there wouldn’t be any selection.

For humans, genetics is irrelevant to behaviour, assertions to the contrary notwithstanding. People think and make decisions and have ideas: culture. Culture is also a knowledge creating process. A person produces some variation on current knowledge. That variation either manages to get copied in books, in people talking about it and thinking about it, or it doesn’t get selected and it dies. This has led some people, like Richard Dawkins to suggest that evolving ideas should be treated as analogous to genes in some ways:  he called the evolving ideas memes. The best existing treatment of memes is in The Beginning of Infinity by David Deutsch. A person can change his mind a lot faster than he can change his genes. And the selection process for an idea doesn’t necessarily involve implementing the idea immediately. So an idea can go through a phase in its development where it couldn’t be implemented without the idea being destroyed. As such, if a gene and an idea address the same issue the idea will evolve faster and the selection pressure on the gene will cease. These differences mean that ideas explain differences in behaviour between people, not genes.

Jay Joseph makes a different argument against behavioural genetics. On pp. 99-100 of the Joseph book he writes:

In recent years much attention has focused on epigenetics, which refers to genes switching expression on and off in response to environmental events and challenges, without alteration in the DNA sequence. Furthermore, these epigenetic changes can be passed down to the next generation independently of DNA inheritance. As the psychologist John Read and his colleagues Richard Bentall and Roar Fosse put it, “epigenetic processes turn gene transcription on and off through mechanisms that are highly influenced by the individual’s socio-environmental experiences.” They believed that “the implications, for research, mental health services and primary prevention, are profound” (Read, Bentall, & Fosse, 2009, p. 299).

Although some genetically oriented researchers have attempted to integrate epigenetics into their existing arguments and theories (e.g., Plomin, DeFries, et al., 2013, pp. 146–149), recent findings in epigenetics and other areas provide additional support to environmental theories of behavioral differences. This is because it is now known that the environment, and especially the perinatal environment, can influence gene expression. This is, according to Charney, “particularly prevalent in the human brain and probably [is] involved in much human behavior” (Charney, 2012, p. 331; see also Meaney, 2010).

If epigenetic changes can be inherited then that’s just more of the same kind of things that genes do. Epigenetics is sometimes described just in terms of the influence of some genes switching on and off in a way that changes the activity of other genes. In that scenario, epigenetic is not any kind of exception to genetics, it is just a consequence of the content your genes. However, suppose are some inherited non-genetic chemicals as some people claim: call them epigenes. You just use the epigenes in addition to genes to explain behaviour. They act in almost exactly the same way as genes. They only go through selection once per generation. They can only act by building something that works first time. Any differences are minor compared to these similarities. The twin study people could respond by saying they’ll just test for these epigenes too.

If the epigenes can’t be inherited they don’t contain much knowledge since there is no opportunity for error correction, so they can’t be very important for behaviour, as in the “supermarket is out of hummus” example.

What about psychiatry? Trying to argue that there’s a different biological mechanism for behaviour than those psychiatrists talk about doesn’t matter at all for reform of psychiatry. Let’s say that Joseph totally won the argument and psychiatrists started looking for epigenetic stuff and trying to “treat” it. That, in and of itself, wouldn’t matter at all. Who cares whether psychiatrists use your genes or what happened to you in the womb as an excuse for involuntary treatment? The psychiatrists would still be treating people involuntarily unless you argue specifically against involuntary treatment. This is a moral issue not a scientific issue and you can’t settle it by arguing solely about whether X causes Y. You have to argue that a person is morally responsible for his behaviour, and that imprisoning a person without trial is wrong, and those are moral and philosophical issues, not scientific issues.

## The right number of NHS beds

There has been a lot of news in the UK over an alleged crisis in the NHS: the government run system of hospitals in the UK. The British Medical Association, who are a trade union for doctors, claims that overnight beds in the NHS have declined. The government disagrees and they’re arguing over how the figures are collected.

This argument will drag on for a while and then sputter out and everyone will be pissed off. The reason it will sputter out is that there is no objective way of settling this issue. Neither the BMA nor the government knows how many beds people want or anything else. There is no prospect of finding this out as long as we have an NHS. Since the NHS is funded by taxes no patient has any choice about whether to fund it. As such, a patient can’t decide there were not enough beds and withdraw his financial support of the NHS. So NHS funding and resources have nothing to do with whether patients are satisfied.

A patient might say he wants more beds, but if there are more beds there is less of something else: MRI machines, say. Patients should be offered hospitals with different combinations of beds, MRI machines etc and left to choose which combinations to fund. Arguing about numbers of beds is irrelevant. What matters is people actually getting what they want, which the NHS can’t deliver.

## Quantum information storage in atoms

In a previous post I explained a little about why Seth Lloyd said that anything can be a quantum computer if you shine the right kind of light on it. Quantum information can be stored in electronic states of atoms. Those states might in principle be used for quantum computation. And those states can be manipulated by shining light on the atom. A more complete account can be found in these lecture notes. This post will be a very short summary in which I indicate some of the physical effects taking place in atoms. The subject overall is very complicated and mathematical so I can’t do much more than summarise it in a blog post.

A stable state for an electron around an atom is one in which its expectation values for measurable quantities don’t change over time. These states are states of constant energy and they form a discrete set that can be labelled by integers starting at zero, typically labelled by the letter n. The electron’s state isn’t fully described by how much energy it has, its orbital angular momentum also plays a role. The total amount of orbital angular momentum is labelled by another quantum number l. The orbital angular momentum in the z direction is also relevant and is labelled by another number m. Finally, an electron also has a type of intrinsic angular momentum called spin. The spin can only have two states and those a labelled by the letter s that can only take values -1,1. States of electrons around atoms are then described in terms of those values (n,l,m,s) that are called quantum numbers. Now, the amount of angular momentum an electron can have is related to its energy. Having angular momentum gives the electron energy. So an electron with a particular energy can’t have too much angular momentum or it will have more than is compatible with the amount of energy it has.

The electron’s stable states give probabilities for the electron to be in a given region. Those probabilities can be plotted in various ways, e.g. – drawing surfaces inside which the electron has some high probability of being found. There are websites full of such plots so I won’t reproduce them here.

Since the states I described are stable, and they are labelled by a discrete set of quantum numbers they an be used to store qubits. There are restrictions on how those values can be manipulated. If you want to change the values of the quantum numbers of an electron then are trying to change its energy and angular momentum, which are conserved quantities. So if you want to increase the energy and angular momentum, you have to shine light on the atom that is carrying the relevant amount of energy and angular momentum. And if you want the atom to drop to a lower energy and angular momentum state, the light has to be able to carry away that energy and angular momentum.

Manipulating atoms with light requires using coherent light: light where different versions of a photon are related to one another in controlled ways. This allows you to control the whether they arrive at different places at the same time or different times at the same place and that sort of thing. This requires using lasers. So researchers making quantum computers will try to pick atoms with transitions where the energy matches those available in relatively inexpensive commercially available lasers. It is also possible to arrange for photons to have a particular amount of orbital angular momentum with the right equipment.

## Stefan Molyneux vs rational parenting

Stefan Molyneux is known among libertarians as an advocate of peaceful parenting (PP). PP is not the same as TCS and I thought I’d look at an interview he did on the topic and explain what’s wrong with his position.

I’m not going to explain everything, but I’ll pick a few things that stuck out as bad.

Before I say anything about Molyneux, I’ll post a few links about TCS:

http://fallibleideas.com/parenting-and-fallibility

Most parents make children do stuff they don’t like and tell a story about why they do this. The parent is coercing the child because the topic is important, e.g. – education, health. But then if the topic is important, it is important for the advice to be right and you ought to welcome criticism regardless of its source. So if you can’t convince your child of idea X that’s a criticism of X and you shouldn’t coerce him into acting on it.

TCS also has a theory of what’s going on when you feel emotionally coerced. Coercion involves a person acting on one idea while he has other ideas that he wants to enact and hasn’t resolved that conflict:

TCS claims that it is always possible to avoid coercion:

TCS also claims that people are universal knowledge creators. A person can learn or create any knowledge that it is possible to create. See Chapter 2 of “The Beginning of Infinity” by David Deutsch.

———————–

Molyneux states that spanking and raising your voice are violations of the non-aggression principle. But he doesn’t seem to have anything to say beyond that on philosophy of parenting.

————————-

Molyneux recommends parenting books such as Parental Effectiveness Training. A quick look on Google reveals the following link:

http://parenteffectivenesstraining.blogspot.co.uk/2013/12/christmas-gifts-you-wish-they-hadnt.html

It’s about people buying gifts a child wants and his parents don’t want. It’s bad to want to prevent your child getting a gift he wants. Parents should want to help their children get more of what they like, rather than sabotage happiness.

————–

At about 22 minutes Molyneux sez he is willing to sacrifice some of his daughter’s privacy to tell stories about her that will help others.

This is very bad cuz sacrificing your child’s interests for any reason is a bad idea. The parent should offer guidance and resources that will help promote the child’s interests.

———————–

Starting at about 24:00 somebody asks a question about what a parent should do when a child makes a rational argument to the effect that he should have more snacks or sugar. Molyneux replies by saying a person will sometimes feel ambivalent about the right thing to do. He sez that the tongue loves sugar but the belly likes less since you’ll get sick. So you have to go without stuff you want. He also relates a story where he denied his daughter a cookie because she had previously had hot chocolate.

So Molyneux does not think it is possible to live without coercion. There are some things you will be ambivalent about. And to deal with that you have to sacrifice.

Molyneux’s control over what his child eats is also bad. If you can convince your child not to eat something with arguments that might be okay if the child is interested in the arguments.

Also, being worried about diabetes over a cookie after hot chocolate doesn’t sound rational.

———

At about 28 minutes he sez a parent should dictate to a child the way he would dictate to himself. He sez he heard that crack cocaine is good but he forces himself not to do it. He sez his test for making his child do something she disagrees with now is whether she’ll thank him later.

If you had an argument that persuades you that taking crack cocaine is a bad idea, then you wouldn’t be tempted by it. So saying you are tempted by crack cocaine is an admission that you have no such argument. And if you can’t come up with an argument against crack cocaine, you have to kinda suck as a philosopher. Crack is a waste of time that you could be spending learning interesting stuff and new skills.

———

At about 43 minutes Molyneux sez that intelligence has a genetic basis. But people are universal knowledge creators, so genes can’t explain what a person achieves. Only his choices and ideas explain that. Molyneux also sez personality is fixed by the age of four. But personality is a result of ideas, including ideas about how to act. If those ideas are bad they can be improved at any age.

## r/k selection political theory is rubbish

This essay has been touted by some people on the right as being a great explanation for liberal (lefty, not pro-liberty) and conservative political positions.

The essay is no good. The essay starts by describing a biological theory called r/k selection theory, which are related to how animals evolve under different resource constraints. I will mostly take the biological descriptions as accurate, except where they are in conflict with basic biology. I will also wait until the end of the post to explain that all biological explanations of behaviour differences between people are crap. The explanation is coming but I want to explain why I consider this specific analogy bad.

If there are lots of resources, then an animal will tend to breed a lot and take less care of its young. For example, rabbits in a field with grass might never be able to eat all the grass in the field. As such, they can make lots of offspring and if some get picked off it’s not a big deal for the rabbit’s genes. So the species in this environment of plenty will tend not to be interested in fighting or contending for resources. These animals will also be willing to sleep around because this results in more copies of their genes. This is called the r selection strategy.

The author of the essay then writes:

Since group competition will not arise in the r-selected environment, r-type organisms will not exhibit loyalty to fellow members of their species, or a drive to sacrifice on their behalf.

This is dumb.

First, no animal will sacrifice itself for a random member of its species. At most the animal will sacrifice itself for relatives who have some of the same genes. Genes are the unit of selection because they can be copied. A species cannot be copied and so is not the unit of selection. This is basic biology. The author could have worked out this was a dumb thing to say by reading “The Selfish Gene”.

Second, the author sees sacrifice as positive. Humans can create explanatory knowledge. Sacrificing yourself gets in the way of you developing better knowledge that could improve your life and the lives of others: it is a bad idea. The death of some random rabbit isn’t a big deal because the rabbit can’t create explanatory knowledge. All of the knowledge it has is instantiated in its genes. So if a copy of those genes is destroyed to preserve five copies in other animals this is a gain for the genes not a loss.

Here in the r-strategy, we see the origins of the Liberal’s tendencies towards conflict avoidance, from oppositions to free-market capitalism, to pacifism, to demands that all citizens disarm so as to avoid any chance of conflict and competition.

This is also dumb. Liberals are in favour of the government increasing taxes. They are are in favour of escalating conflict with productive people. And liberals want citizens disarmed partly to make it easy for the government to prey on them. So liberals are in favour of conflict.

Another strategy emerges if a species is in an environment where resources are very scarce. The animals are in favour of being willing to fight for resources. They are ranked by their ability to compete. And such animals will tend not to sleep around as much because they only have a limited number of chances to copy their genes and have to try to weed out bad genes in advance of having offspring. An example of this might be lions. Lions have to hunt for food. So the strategy for lion genes to get themselves copied is to rank other holders of lion genes according to their ability to hunt. And a lion may be more willing to die to preserve copies of its genes in its offspring or other relatives because dying would free up resources. This is called k selection.

The conservatives are allegedly k selected, which explains their habits like faithfulness to spouses and competing for resources instead of begging the government for stuff. This analogy also fails. Conservatives want to reduce taxes, which reduces violence used by government and the government’s ability to use violence.

Also conservatives are taking the side of makers: people who make new stuff. This position requires thinking that we have not reached the limits of what resources are available and so we can experiment with new ideas to make progress. This contradicts the premise of this r/k selection stuff. This is the most serious defect of the r\k selection theory, it denies the possibility of an open-ended stream of knowledge and resource creation. The reason to take the side of the makers is you want new and better stuff and ideas. It is not because you want to scrape by in a world where you have to murder other people to survive. This r\k selection political stuff is evil shit.

The real reason for parents to take responsibility for their children is that children can create an open-ended stream of benefits. Children and the adults they grow into can create new explanatory knowledge including knowledge about how to do stuff better. But to create knowledge people need to have good ideas about critical discussion, how to test ideas, how best to try them out and that sort of thing. To convey such ideas to their children, parents have to be willing to spend a lot of time and resources on their children rather than spending lots of time on sex. As such, responsible parents don’t spend a lot of time sleeping around. Since conservatives favour personal responsibility, they will tend to sleep around less.

All biological explanations of differences of ideas and behaviour among humans are garbage, including the r\k theory. Humans create knowledge through cultural evolution: evolution among memes. Some memes get selected, others do not. The selection time for a meme is of the order of seconds, the selection time for a gene is of the order of a decade. In addition, memes include explanatory knowledge about how stuff works and why it works that way, unlike genes. For both of those reasons, we should expect behaviour differences between people to be a result of different ideas, not different genes.

## The power of inductivism

NOTE In this post, I take it for granted that inductivism is false. For criticisms of inductivism and an explanation of better ideas, see Objective Knowledge, Chapter 1 by Karl Popper, Realism and the Aim of Science Chapter I by Popper, The Fabric of Reality by David Deutsch, Chapters 3 and 7 and The Beginning of Infinity by David Deutsch, Chapters 1,2 and 4.

On an e-mail list that is now defunct, Elliot Temple asked:

What makes the idea of induction so powerful that people who normally don’t care about abstract philosophy – ones who don’t pay much attention to conjectures and refutations as the method of creativity, and certainly aren’t interested in knowing a lot about evolution – remember induction vividly, like it, bring it up on their own, and insist they do it despite it being ridiculous, extremely vague, proven not to work, and many other problems?

People like to think that science has some definite way of finding ideas and deciding which ideas are good and bad. They think of science as an authority. Science says what is true and what is false, what is good and what is bad. This is plausible if you don’t understand much and take seriously what you see on news sites, or in magazines or whatever. Science provides us with great stuff like iPhones and cancer treatments, so it must be always be right.

Inductivism is a vaguely plausible story about why science is an authority. Scientists just look at nature and nature tells them what is true. And nature proves the scientists right when they do experiments.

If science is an authority, then you don’t have to think much. There are some ideas you like. You look around for an authority to prove your ideas true. Then you can say that if somebody disagrees with you, your critic is scientifically illiterate. And you can do that not just on factual issues, but on moral issues too. For example, people for and against transsexualism like to pretend that their preference is scientific.

So inductivism is the backbone of the worldview of a lot of people. If you take it away, you’re attacking their whole understanding of the world, including all of their moral and factual knowledge. They can’t imagine any replacement.

The true theory also makes the strategies inductivists use for getting along in life look a lot worse. Science is created by guessing solutions to problems and criticising the guesses. So you shouldn’t take everything a scientist says as gospel because he’s guessing. And that means you should actually engage in critical argument rather than just insult people and pretend your insults are scientific.

The inductivist also fears that any alternative will cause a lot of conflict. Suppose that controversial moral issues can’t be solved with certainty by saying vague stuff about scientists proving something or other and claiming anyone who disagrees with you is a moron. Then people will actually have to discuss moral issues. And they think that their incompetence at discussion will lead to lots of inconclusive and long winded arguments that result in bitterness and distrust.

Such problems could be solved by trying to understand the world, and understand better moral ideas, but that takes effort most people don’t want to make. And they don’t feel confident about their ability to understand anything.