Category: science

On Nonlinear Noisy Key Agreement

TL;DR. A large number of post-quantum key encapsulation mechanisms (KEMs) and public key encryption schemes (PKEs) rely on noisy linear algebra problems. Interestingly, the addition of noise to make otherwise easy problems hard, is a strategy that remains restricted to linear algebra and fails to extend to nonlinear operations. This article explores why.

Noisy key agreement

Key agreement is a protocol by which Alice and Bob each send one message to the other and end up agreeing on a shared secret key. The eavesdropper Eve, who observes all messages in transit (but can’t modify them) remains incapable of computing this secret. The first such protocol was introduced by Diffie and Hellman and bears their names, but the general principle extends to generic algebras and not just commutative group theory.

For instance, let Alice and Bob agree on a common random integer G from a finite ring R, such as e.g. the set of nn matrices of integers modulo some prime p. Moreover, let Alice and Bob each sample their secret, a and b respectively, from this structure as well. They then exchange â = aG and b̂ = Gb, allowing both to agree on the shared key k = ab̂ = âb = aGb. Note that while the order of multiplication is important for matrices, by agreeing beforehand whose secret will be multiplied on which side of G, Alice and Bob circumvent this complication entirely.

Unfortunately, this protocol is completely insecure. Eve, who sees Alice and Bob agree on G before sending â = aG and b̂ = Gb, can compute G-1 and recover both Alice’s and Bob’s secrets, not to mention the shared secret key. Even if the ring disallows efficient computation of an element’s inverse, it remains extremely likely that there is a way to find the solution b to the system of linear equations Gb = b̂ and symmetrically for a.

The solution that makes the protocol a noisy key agreement protocol is to transmit only an approximation of aG and Gb. To see why this makes Eve’s task hard, observe how the error term 𝝐b = b̂ – Gb explodes: G-1b̂ = G-1(Gb + 𝝐b) = G-1Gb + G-1𝝐b = b + G-1𝝐b . Since G is a matrix with uniformly random coefficients, so is G-1 and multiplying that by another matrix 𝝐b — even if it has small coefficients — yields another random ring element that hides b much like a one-time pad.

However, the addition of small noise makes it difficult for Alice and Bob to agree on the same secret. Observe that Alice computes ka = a(Gb + 𝝐b) whereas Bob computes kb = (aG + 𝝐a)b. The trick is implied by the symbols’ case: instead of sampling uniformly random a and b, Alice and Bob sample a and b with small coefficients. If a, b, 𝝐a, and 𝝐b have small enough coefficients, then Alice’s view ka = aGb + a𝝐b is approximately the same as Bob’s view kb = aGb + 𝝐ab. As long as the difference a𝝐b – 𝝐ab is small enough, they can proceed to agree on an exact key with one additional message which either reconciles the two views or uses them in combination with error-correcting codes to transmit a wholly new message. In this last case, I like to refer the views ka and kb as shared noisy one-time pads or “snow-tipis”.

So how small should the secret elements a, b, 𝝐a, 𝝐b be? On the one hand, the secrets should not be too small because that reduces Eve’s search space. On the other hand, the secrets cannot be too large because then the difference a𝝐b – 𝝐ab is too large to enable either the reconciliation or transmission strategy. The situation is best described visually. While the unknown bits of the secrets do spread and multiply — and obscure Eve’s view — they also leave some bits of aGb intact; these bits can then be used as secret key material.

Incidentally, Ramstake, my own submission to the NIST PQC Project, does not quite follow this “intact bits” strategy of establishing common secret key material. Instead of having a few unknown bits at fixed locations, the secrets now have a few flipped bits at unknown locations. As long as the difference a𝝐b – 𝝐ab is not too dense, an error correcting code can help extract or transmit secret key material. Interpreting a darker shade of grey as representing a denser error distribution, this gives rise to the following analogous diagram.

 

Nonlinear Noisy Key Agreement

So why are there no nonlinear noisy key agreement protocols, or cryptosystems based thereon? Actually, that premise is not true. There is a submission to the NIST PQC project by the name of CFPKM whose underlying hard problem is polynomial system solving with noise (“PoSSoWN”). Alice and Bob compute their protocol contributions by evaluating a quadratic function f, which has small coefficients, in their secret vectors sa and sb, also with small coefficients, and by adding another small noise term. The underlying protocol is shown in the next figure. Unfortunately, despite the security proof, the cryptosystem was broken within weeks of the submissions’ publication.

The cryptanalysis exploits the observation that the keys computed by Alice and Bob differ only by the difference of element-wise products f(sa) ⨀ e2 – f(sb) ⨀ e1, which affects only the lower bits; whereas the high bits of both views are used for the session key. Importantly, these high bits are the same in b1b2, which is a value the passive adversary can compute as well.

So why is there no successful cryptosystem based on noisy nonlinear key agreement? The first observation is that the term nonlinear is really only relative to what the function’s arguments are. For instance, the expression x12 + 2x1x2 –x2 is nonlinear as a function of (x1, x2) but linear as a function of (x12, x1x2, x22, x1, x2, 1). By extending as we did here the vector of arguments of a function to a vector of all monomials occurring in that expression, any expression can be regarded as a linear function. In particular, both Alice’s and Bob’s computation of their proper views of the noisy secret key may be considered as linear transforms on some extended vector of monomials. This observation suggests a two-step approach to the diagrams above that indicate the source of secret key material: the second step captures the familiar linear noisy key agreement. The first step captures the extension of the original arguments into a vector of monomials.

This diagram highlights the origin of the problem: in order for there to be usable secret key material left at the end, the unknown bits in the extended vector of monomials must not be too many. In order for those unknown bits to not be too many, the unknown bits in the original arguments must be even fewer. However, this very salient feature makes these original arguments a vulnerable target for attack.

Conclusion

Why are there so few cryptosystems based on nonlinear noisy key agreement? My answer is twofold:

  1. Because any such protocol implies a linear noisy key agreement protocol.
  2. Adding nonlinearity to a linear noisy key agreement protocol makes it less secure.

 

On Catastrophic Anthropogenic Global Warming Theory

TL;DR. Skepticism is a virtue. But questioning catastrophic anthropogenic global warming theory seems to be a vice. We are told to believe that the debate is settled; there is scientific consensus that humans are the driving cause of global warming. Any skepticism at this point only serves to confuse policymakers and delay urgent political action. To the contrary, I contend that there is just cause for skepticism.

1. Introduction

Declaring any domain of knowledge as settled science is a characteristic result of the most anti-scientific attitude imaginable. It is the pinnacle of arrogance to claim any knowledge with absolute certainty; an intellectual offense surpassed only by the all-too-often following denouncement of all skepsis as anti-scientific bigotry. In contrast, science is exactly about challenging — and overturning, where appropriate — false beliefs. In the process of scientific investigation, some beliefs may wind up being reinforced rather than overturned, which is why all parties should welcome skepticism with open arms. Our confidence in the truth of scientific propositions comes precisely from our ability to question them. To hold a class of statements or ideas immune to scrutiny is not just akin to religion superficially; it shares its most fundamental tenet, namely the required leap of faith.

But a different standard seems to apply in the global warming discussion. The science is settled because there is 97% consensus among scientists who express opinion on the matter. A panel of experts has concluded that humans are the driving cause of climate change with a whopping 95% confidence1. The remaining skeptics serve only to delay urgently needed political action. In fact, since this delay will certainly cause catastrophe, the spreading of unerringly unreasonable doubt constitutes a prelude to crime. The skeptics who cannot muster the good graces to remain silent, should be put in jail in anticipation of their share of the responsibility.

Well, I am a persistent skeptic. And at the risk of social ostracism, of being associated with the other type of denier2, even of jail time, let me try to convince you that there is something wrong with this attitude. Starting with the philosophical foundations, and continuing first with the scientific theory and then discussing ideological bias, I think there is plenty to criticize and more than just cause for skepticism.

Disclaimer: while I am a scientist, I do not do climate science. My opinion is not that of an expert and if you believe I am factually incorrect somewhere or that you know an adequate response to some of the points I raise, please feel free to leave a comment or drop me an email. I do my best to weed out incorrect beliefs whenever possible.

2. Scientificity

Scientificity is the property of a theory that makes it suitable for scientific investigation. Informally, scientificity requires that the world in which the theory is true is different from the world in which it is false, and that by interacting with the world we can increase our confidence in the truth (or falsity) of that theorem. Falsifiability is a necessary requirement: an unfalsifiable explanation is one that is compatible with any phenomenon. Paradoxically, a good explanation is one that is not capable of explaining anything, but rather one that rules out particular phenomena. The notion is linked with information theory: a scientific theory is part of a model of the universe, and by interacting with the universe we extract information from it and incorporate it into the model. An unscientific theory is one that does not contribute to the model for being devoid of information about the world.

Scientificity is a binary variable, but falsifying is a process that can be easy or difficult. Among scientific theories there is therefore a spectrum of falsifiability difficulty, matching the effort required to test the theory in question. On the one end of the spectrum there are Newtonian postulates, which can almost be tested from the philosopher’s armchair. On the other end there are theories for instance about the inside of a black hole. It is difficult to test these theories, and consequently it is equally difficult to become confident about their truth value.

How does this relate to the climate change debate? Well for starters, consensus is immaterial. Assuming the existence of an accurate distinguisher for telling experts from non-experts, assuming the experts are doing science honestly, and assuming they are free of systemic bias, even then their consensus at best correlates positively with the truth value of the theory in question.

Also, note that “climate change” is the slippiest possible term to frame the debate with. Climate is by any reasonable definition the average weather over a suitably large time period. If this time period is large enough, then the climate is fixed by definition and any change is impossible. If the time period is short enough to be meaningful, then the average changes with the window over which it is computed, and then climate change is an immediate consequence of weather change. In other words, climate change being true or false is determined by how the term is defined rather than a reflection of the world we live in. Nevertheless, the presentation of the term “climate” as though not scientifically vacuous suggests a description of weather as a random noise signal added to an underlying steady state, which is then purported to be disturbed by human activity. This steady state theory of climate may be appealing to our mammal brains but is nevertheless assumed without justification and indeed, in contradiction to the prevalent creation and destruction theories of the Earth itself.

I much prefer the term “global warming” because it, at least, implies one bit of information about the world. If average temperature is observed to drop, then clearly global warming theory is false. However, this term is still troublesome because it captures wildly different scenarios in some of which the average temperature rises by a negligible amount and in others of which the temperature rise is catastrophic to all life on Earth. Phrased in terms of information theory: one bit is not enough. A meaningful debate on global warming must concern theories that explicitly state quantities. By how much will global average temperature increase one year from now? An answer to the same question except “one hundred years from now” is less useful because it is effectively unfalsifiable — especially if the implied political action must be taken before then. To be fair though, the quantity-free discussion is limited to public discourse; scientific reports, such as the IPCC assessment reports, are quite explicit in their quantities, as they should be.

Nor is discussion about the human component exempt from the requirement of being quantitative rather than qualitative. The theory “the globe is warming and humans are causing it” implies at most two bits of information about the world and is equally untenable in a meaningful debate. A proper theory must address to which degree humans are causing global warming and even answer hypothetical questions like how much the global average temperature would have risen if humans had not discovered fossil fuels. To its credit, the IPCC assessment report does make a claim that is falsifiable in principle3: an estimation of the temperature increase with and without mitigating action (among other climate-related effects). However, this theory and a complete causation theory are very difficult to falsify, chiefly because of the size of the time span that the predictions cover. To test them properly, we must compare observations far enough apart in time. And unless we go through this laborious and error-prone process of testing them we should remain accordingly unconfident about their truth values.

Nevertheless, the argument for causation does not derive from counterfactual data for the whole chain but from evidence supporting the strength of each link individually. While this stepwise approach is a sound methodology, it is easy to lose track of the forest for the trees and take evidence of strength in one link as evidence of strength in the entire chain. The situation is quite the reverse: one weak link can break the chain.

3. The Argument

The basic argument in support of anthropogenic global warming goes something like this:

  1. Since the industrial revolution, human activity has put tremendous amounts of $\mathrm{CO}_2$ into the atmosphere. $\mathrm{CO}_2$ levels are rising faster than they ever have before.
  2. There are quantum-scale simulations, laboratory-scale experiments, as well as city-scale observations indicating that $\mathrm{CO}_2$ behaves like a greenhouse gas, i.e., that it traps heat by absorbing infrared light but not higher wavelength radiation.
  3. There is pre-historical evidence that $\mathrm{CO}_2$ correlates positively with global average temperature on geological time scales.
  4. More greenhouse gases in the atmosphere means more heat from the sun will be trapped, thus increasing global average temperature.
  5. We are currently observing rising global average temperature. The temperature is changing faster than it ever has before.
  6. Therefore, human activity is causing this rise in global average temperature.

Strictly speaking, the argument is not logically valid, although it does seem convincing somehow. Let us dissect it properly, starting with premise 1.

  1. Since the industrial revolution, human activity has put tremendous amounts of $\mathit{CO}_2$ into the atmosphere. $\mathit{CO}_2$ levels are rising faster than they ever have before.

It is certainly true that human activity since the industrial revolution has put enormous quantities of carbon dioxide into the atmosphere, as the following graph shows. (source, script)

Confused? Well, the graph you might be familiar with uses the same data but rescales the vertical axis to focus on the 0-500 parts per million range. Here it is, for reference.Both graphs describe the same thing: the increase in atmospheric $\mathrm{CO}_2$ content, which is (presumably) driven primarily by human industrial activity. One graph is useful for illustrating the relative increase of $\mathrm{CO}_2$, i.e., 140% increase since 1850. The other graph is useful for illustrating the absolute increase — or properly speaking relative to the level of oxygen, which is after all what the carbon dioxide is displacing when it enters the atmosphere as a result of burning fossil fuels.

The point of this graph trickery is that there is no objective way to decide beforehand what does and does not constitute “tremendous” amounts of added CO$_2$, as “tremendous” is a relative term and thus requires a benchmark. The only way to decide whether this 140% increase is massive or insignificant is after determining the effects caused by this increase. Even a 1000% increase can be judged to be mild if the resulting effects are barely noticeable.

More generally, the presentation of the premise as saying that the $\mathrm{CO}_2$ increase is tremendous and faster than ever before is a bit of a straw man as neither fact is necessary for the argument to work. This point addresses only the alarming quality that is absent from the minimal formulation, “Human activity has put measurable amounts of $\mathrm{CO}_2$ into the atmosphere.”

  1. There are quantum-scale simulations, laboratory-scale experiments, as well as city-scale observations indicating that $\mathit{CO}_2$ behaves like a greenhouse gas, i.e., that it traps heat by absorbing infrared light but not higher wavelength radiation.

I do not dispute the individual statements made in the premise. Nevertheless I would like to point out that the implied conclusion, that $\mathrm{CO}_2$ is a greenhouse gas on a global scale, does not follow. $\mathrm{CO}_2$ has many subtle interactions with the complex biological and geological ecosystems that it is a part of. The focus on the heat-trapping properties and effects of the gas in isolation ignores the many terms of the equation that are introduced by its interaction with its environment. For instance, according to current understanding, both the ocean and vegetation on land absorb $\mathrm{CO}_2$. How does this absorption affect trapped heat? It is easy to come up with plausible mechanisms by which the carbon dioxide based heat trap is exacerbated or ameliorated, and whose truth cannot be determined beyond a shadow of a doubt from laboratory experiments alone.

  1. There is pre-historical evidence that $\mathit{CO}_2$ correlates positively with global average temperature on geological time scales.

Indeed there is. A clever piece of science in action — several pieces, actually — have enabled researchers to dig into polar ice and determine the temperature as well as carbon dioxide levels of the past, ranging from yesterday to 400 000 000 years ago. The near exact match spurred Al Gore to mock in his film about truth, “did they ever fit together?”, as though the point is contentious. Here’s a graph. They do fit together. (source 1, 2, script)It has become a cliché to point out that correlation does not equal causation, but unfortunately that task remains necessary. In fact, there is a very good reason why the “$\mathrm{CO}_2$-causes-temperature to rise and fall” theory is a particularly uncompelling one in light of this data. It is because the $\mathrm{CO}_2$ graph lags behind the temperature graph by 900 years or so, as the next cross-correlation plot shows4 (same script). That time lag is short enough to be unnoticeable on the 400 million year scale, but long enough to seriously reconsider the theory. The position that the pre-historical temperature and $\mathrm{CO}_2$ record supports the $\mathrm{CO}_2$-causes-temperature theory, is untenable. If anything, it supports the opposite temperature-causes-$\mathrm{CO}_2$ theory.Despite the minor inconvenience of having a time mismatch, the $\mathrm{CO}_2$-causes-temperature theory survives. The adapted argument is that $\mathrm{CO}_2$ level and temperature are both causes and effects, locked in a positive feedback loop. Temperature affects $\mathrm{CO}_2$ but $\mathrm{CO}_2$ also affects temperature. The mockery5 continues on skepticalscience.com: “Chickens do not lay eggs, because they have been observed to hatch from them.”

A positive feedback loop is possible but it would be highly surprising. Very few natural processes actually have positive feedback loops. It is the same mechanics as that of bombs: the combustion rate increases the pressure, which then increases the combustion rate. When positive feedback loops do occur in nature, for example in population dynamics, their extent tends to be limited due to natural stabilizing mechanisms such as disease or predators.

What is more likely to be the case, is that $\mathrm{CO}_2$ and temperature are in a negative feedback loop. $\mathrm{CO}_2$ causes temperature to rise (or fall), and the resulting increase (decrease) in temperature affects $\mathrm{CO}_2$ in turn, but the magnitude of these effects dies out exponentially. In this scenario, it would be true that some amount $x$ of added $\mathrm{CO}_2$ would cause another amount $y$ of temperature increase; but an additional $x$ of $\mathrm{CO}_2$ would cause strictly less than $y$ temperature increase. The two are in an equilibrium which can be moved by a perturbation in either input; but the system responds by making another shift of the equilibrium that much more difficult. In chemical systems, this mechanism is known as Le Chatelier’s principle.

The point of this discussion is not to debunk the $\mathrm{CO}_2$-causes-temperature theory; Le Chatelier’s principle probably is at work and if so, the $\mathrm{CO}_2$-causes-temperature theory is true in a literal sense despite being dominated by the temperature-causes-$\mathrm{CO}_2$ component. The point is rather that this theory is firstly not supported by the ice core data and secondly limited as a tool for prediction — as it certainly flies in the face of catastrophic predictions. Nevertheless, the bomb analogy, though it is erroneous, is certainly a far more effective tool of communication; and presumably that is the reason why skepticalscience.com features a Hiroshima counter so prominently on its sidebar.

Criticism of delivery aside, it is worth addressing a common counter-argument to the $\mathrm{CO}_2$ lag objection, namely that “about 90% of the global warming followed the $\mathrm{CO}_2$ increase.” If that argument is valid, then surely so is, “100% of the $\mathrm{CO}_2$ increase followed the global warming.”

  1. More greenhouse gases in the atmosphere means more heat from the sun will be trapped, thus increasing global average temperature.

No counter-argument here beyond criticizing the triviality of this truism. Trapping solar heat is precisely the defining property of greenhouse gases. As raised in the counter-argument to premise 2, the question is whether $\mathrm{CO}_2$ satisfies this definition, something that cannot be inferred from small-scale experiments alone.

  1. We are currently observing rising global average temperature. The temperature is changing faster than it ever has before.

Unless you distrust the data, the observation that we are currently observing a warming trend is quite inescapable. A simple web search churned out the following surface air, surface sea, and satellite data. (source 1, 2, 3, script)However, the second part of the premise follows neither from the first part nor from the plot and is in need of a citation. In fact, the plot illustrates precisely why the proposition “the rate of change is faster than ever” is very difficult to defend.

For starters, the “rate of change” is not explicitly present in the data. One has to infer it by dividing the temperature difference by the time difference associated with two samples. While rate or velocity in physics is defined as the limit of this fraction for time difference going to zero, computing this ratio from the data inevitably magnifies the measurement noise. The best you can do is consider trend lines over a time interval large enough to average out the noise. Make the interval too short, and your trendline reflects only noise; but make it too large and any human effect will be averaged out with the noise. There is no objectively right way to choose interval size. This paradox suggests the philosophical point that maybe “rate of change” is not the right way to think about temperature change to begin with. The notion is not practically usable and really reflects an unjustified ontological presupposition: the “rate of temperature change” exists, has a definite value, and produces different measurement outcomes depending on this value. Nevertheless, this ontological criticism merely reflects the difficulty of defining in precise terms what the current “global temperature” is.

Second, the data reaches back only so far, and is less fine-grained the further back you go. We only have satellite data from 1980 onward; weather balloons since the end of the 19th Century; thermometers since the 1720’s. However, a compelling argument for the temperature change being faster than ever should present an accurate temperature graph spanning a large stretch of history. The requisite data simply does not exist.

There are secondary, indirect records that do reach further than the invention of the thermometer. Clever scientists have attempted to reconstruct earlier temperatures from ice cores (i.e.,  isotope ratios of air bubbles trapped in ice), tree rings, lake and ocean sediments, and so on. However, these proxy sources require careful modeling and calibration of whatever natural process records the temperature or temperature change and stores this information until readout. The accuracy of this data is limited by the degree to which the models approximate these natural processes, which is by nature very difficult to falsify. Moreover, the further back in time you go, the coarser the data becomes. The question then arises, to which degree can the sharpness of the observed recent temperature rise be explained as the by-product of the resolution mismatch? Joining together recent thermometer data with biological or geological proxy data to produce a graph resembling a hockey stick, suggests that the data’s accuracy is roughly uniform across time. The addition of error bars or an uncertainty range reflects the graph makers’ optimism that the inaccuracy is quantifiable to begin with.

  1. Therefore, human activity is causing this rise in global average temperature.

Even if you accept all the premises and pretend that the conclusion follows syllogistically from them, it is worth noting how little this conclusion actually says. Human activity is contributing to a global temperature increase. It does not follow that this temperature increase is catastrophic, will raise sea levels, will kill polar bears, will cause crop failures, draughts, monsoons, or even effect the weather one iota beyond the slight temperature change. All these projected secondary effects require separate arguments that can be questioned independently of the first. And yet by some sort of unspoken agreement, the entire disagreement about global warming centers around the first argument. The motte-and-bailey technique of sophistry comes to mind to describe the situation: by only defending a small but more defensible premise, the alarmist can get away with claiming a far larger conclusion.

The catastrophic effects is only one implied consequence of the anthropogenic global warming argument. The second implied conclusion is the mandate for political action. However, even if we accept a list of projected catastrophes as being the consequence of burning fossil fuels, then we must still weigh the benefits against the drawbacks before such a political mandate can be justifiable6. The obvious and under-emphasized benefit of fossil fuels is its enabling of an industrialization and market economy that has lifted more people from the clutches of grinding poverty than any other object or idea throughout human history. This achievement puts the discovery of fossil fuels on par with extinction level events in terms of importance on geological time scales. If global warming does not pose a threat of equal or greater magnitude, and if its solution does not present an alternative to fossil fuels that enables us to maintain our present living standards, who is to say climate neutrality is preferable to affluence? An affluent society might be better off dealing with the consequences of climate change than an impoverished one dealing with adverse weather conditions.

4. Political Bias

4.1 Libertarianism

People often accuse me of mixing ideology with reason, in particular with respect to the man-made climate change debate. Being a libertarian, I favor free markets and condemn government intervention. The scientific consensus on global warming unequivocally mandates immediate political intervention, and as such conflicts with my libertarian views. Rather than re-evaluating my political ideology, I choose to ignore the scientific facts. Or so the accusers would have me believe.

This accusation fails to convince because it is predicated on a misconception of libertarian legal theory. In fact, assuming the correctness of catastrophic anthropogenic climate change, there is a justification for political action7 in response to carbon emissions. And reviewing this libertarian basis presents an opportunity for providing much-needed focus for the scientific questions whose answers are supposed to justify violence.

In the libertarian tradition, violence is only justifiable in response to prior aggression, on behalf of the victim and against the perpetrator of said aggression. The purpose of this violent response is not retribution but restitution: to reinstate the state of affairs prior to the aggression; to make the aftermath independent of whether the initial aggression had or had not taken place. Also, the crime and responsive violence are committed by individuals; not by communities or societies. No group of individuals has rights that the individuals that make up the group do not, and therefore class guilt and class indemnification (that does not reduce to individual guilt and indemnification) are intolerable. The victim must be able to demonstrate ownership of the object of aggression as well as deleterious effects on said object. Lastly, the chain of cause and effect from aggressor to deleterious effect on the object must be demonstrably true.

In the context of global warming, the object of aggression might be crops, a house on the shore, or snowy ski slopes, just to name a few. The deleterious effects might be draught, a sea level rise or a hurricane, melting snow. The aggressor would be every individual who emits carbon dioxide; and they would be responsible in proportion to the quantity of their emissions. The task of the global warming scientist would be to demonstrate the chain of cause and effect from $\mathrm{CO}_2$ emissions to the aforementioned deleterious effects. Alleged perpetrator and self-declared victim would present their cases before an independent arbitrator and all parties would be allowed to question the opposition’s arguments and evidence. The validity of the scientific argument would not be decided, as it is now, in the court of public opinion; but rather in the court of a professional judge, or group of judges, who stand to lose both reputation and livelihood if their ruling is not convincing and fair. Moreover, if this ruling is later overturned on the grounds of a bad court procedure or ignored evidence, this group of judges gains complicity in the perpetuation of the crime. In contrast, in today’s society, the validity of the scientific argument is decided by popular vote, and altogether by individuals who do not personally suffer the consequences of an incorrect determination.

I would be remiss to neglect modifying the accusation at the onset of this section in a way that does make sense. As a proper libertarian, I recognize bullshit arguments for state expansion for what they are. With this perspective in mind, what is the likelihood that I would be overzealous in my determination of logical fallacies in an argument that is easy to misconstrue as supporting state expansion? My honest answer is “quite high”. However, I write this essay while consciously aware of this answer, and I invite all corrections mandated by an honest pursuit of truth.

4.2. Other Ideologies

If the determination of validity of a complex scientific theory is a probabilistic process, then one would expect the proportion of believers to non-believers to reflect the strength of the argument. If the determinators and propagators of the scientific consensus reports are correct, then this consensus itself constitutes a strong argument in favor of the theory’s validity. This argument fails, however, if the determination of validity is systematically biased. If it is possible for my political ideology to influence my determination of validity, then certainly people of other political ideologies are not exempt, especially when they are not consciously aware of their biases.

Anti-market bias is a documented phenomenon even among people who do not openly advocate the abolition of capitalism. Individuals with this bias will be predisposed to the belief that industrial activity is harmful, and that government intervention is necessary to curb its harmful effects. It goes without saying that the opposite is true: industry is overwhelmingly positive for human well-being and in those cases where it is harmful, the adverse effects of government mitigation inevitably outweigh the benefits.

Mother Nature is a human archetype present in a wide array of cultures throughout history. The pre-historic human tribes who were predisposed to the belief in the spirit of the environment no doubt had an evolutionary advantage over those who were not. Early humans who avoided over-hunting or over-burning because that would anger the Earth-goddess were inadvertently improving the conditions for life in their environment, thus benefiting them indirectly because they were in symbiosis with it. Modern-day environmentalists likely tap in to this archetype, even when they don’t explicitly worship Gaia. Nevertheless, the existence of this bias does not void all environmental concerns.

Sponsorship Bias is the tendency for science to support the agenda of whoever paid for it. It is the reason why published papers are required to disclose its funding sources, so that critics know when to receive strong claims with more or fewer grains of salt. Sponsorship bias is frequently attributed to institutes that are critical of global warming alarmism such as the Heartland Institute and Prager University, owing to their funding coming in part from oil companies. However, the same argument works in reverse as well: if being funded by oil money skews the science towards supporting oil interests, then so does being funded by government programs skew the science towards supporting government programs.

5. Conclusion

Some time before leveling the accusation of ideological investment, people ask whether I believe in global warming, usually with negated-question grammar. I find the question particularly telling because the choice of words highlights the distinction between religion and science. On the one hand, “belief” refers to an unconscious worldview or a conscious leap of faith. On the other hand, a “belief” can be a working model of the universe and source for testable hypotheses. Only the second sense is meaningful8 in a scientific context.

The catastrophic anthropogenic global warming theory is just that — a theory, looking to be falsified or borne out by the evidence. An admittedly cursory examination of this evidence raises more questions than it answers, and chiefly of an epistemological nature. Rather than welcoming the skepticism and criticism as a means with which to refine the science, the alarmists dismiss the skeptics and critics as dangerous ideologues and their arguments as religious superstition. However, it is precisely the orthodoxy, the irrational confidence of believers, the call to sacrifice, the state sponsorship, the demonization of heretics and the call to jail them, that have more in common with the ugly end of religion than with open discussion and an honest search for truth. Climate change is not a question for religion. Let’s return to science.