-1=e^ipi

I'll create a new thread to discuss the effects on the jetstream and I'll try to add some things like I'll try to quantify what kind of changes we will expect to the jetstream.

The label 'concern troll' is often used by people that cannot accept that there might be diverse opinions on a topic and that want to create a false dichotomy.

So where do the 6 year old transgendered people fit into this?

What prevents you from estimating, quantifying and monetizing the alleged damages from white collar crimes and comparing it to the damages for other crimes in other income groups? And how does white collar crime make the link between poverty and crime go away? Sorry, but your 99% occupyism isn't very convincing to me. Here, I'm trying to discuss the importance of reducing poverty to reduce crime rates, and you are trying to demonize income and somehow pretend the link away because the evidence doesn't fit with your predetermined dogmatic view. So that is what you say to people who present you with statistical evidence and an economic explanation for the link between poverty and crime? This sounds a lot like what the 911 truthers say when they are confronted with evidence. Oh look, another lawyer paper from before I was born. And again it does little statistical analysis or provide much evidence beyond opinion. But that is to be expected since lawyers are trained to approach things dogmatically. Look, the paper even contains an implicit ad populism fallacy in its abstract: 'the public generally ranks white-collar violations as serious' 'come back'? Did the casual link temporarily disappear or something.

@ eyeball, so you cite some random outdated 1970 opinion piece that does not try to measure or compare crime between income groups. Okay... 'white collar' crime exists. Your point? It doesn't make the correlation & causation between crime and poverty go away. Where as I cite a 2006 econometric article that uses data from 322 different metropolitan areas in the United States to examine the relationship between poverty and crime. It explains its methodology & the sources of data, and even after controlling for geographic location, race, age, unemployment and population density it still finds that poverty has a large, positive and statistically significant (beyond 5% confidence level) effect on crime. Somehow, I think I give 10000x more weight to the econometric study then the nearly half-century old lawyer paper.

You're welcome.

You can evaluate crime statistics on a per capita basis. Sigh... 3 minutes on google and I find this: http://economics.fundamentalfinance.com/povertycrime.php It is a very good regression analysis that controls for many variables. If you have any questions regarding how to read the regression tables you can ask me. There is this thing called democracy... where everyone gets a vote... Of course we could always follow the North Korean example and make everyone have the same level of income.

http://en.wikipedia.org/wiki/Ad_hominem

Why is WestCoastRunner commiting ad hominem fallacies against Bush-Cheney for being American?

Eyeball, type crime statistics by income in google or go to stats-can website or something. Like seriously. The correlation is well known and I explained the mechanism of causation. I'm also not really sure why you are trying to argue against a point that can be used to justify some income redistribution to reduce crime rates.

Squid, you said "by helping them it has been shown to be of net benefit to society". You put zero restrictions on under what conditions helping them leads to a net benefit. You did not include words like 'sometimes' or 'usually', so yes your statement is too strong. You also said that "one day it could be us". How does that not imply that every person is at risk of being poor? Is Bill Gates at risk of being poor? Or are some people not at risk of being poor? In which case how can you confidently use the word 'us'. Just be more modest in your claims. It is not my fault if your literal meaning and intended meaning differ.

They contribute by not rioting and stealing your stuff. Yes, presenting it as a moral issue is the wrong approach. Which is why I suggested rewording the question and gave 3 'arguments' for some level of income distribution that are less morally controversial and are relatively easy to evaluate empirically. 2 of the arguments I gave can even be potentially pareto improving. Are you advocating some central planning??? I do not think that the free ride term is imbued with morality. http://en.wikipedia.org/wiki/Free_rider_problem Your statement is too strong. Whether you have a net benefit or not depends on the amount redistributed, the economic inefficiency of redistribution, implement costs of a redistribution program, etc. Economic outcome is not something that is completely random.

Then we are in agreement.

@ Tim - I agree that circumstances where firms will change their decision are rare, but it does not mean that they do not exist given the billions of decisions people make on the planet everyday. With regards to the solar panel example, chose a sunny place like Australia and put the building in a remote location where they might have to install their own natural gas infrastructure and suddenly the costs between solar & natural gas come a lot closer. Maybe just change your claim from 'never' to 'usually not'? You didn't say those exact words but you have continually said that 'scientists have told us to change behaviour or we will face catastrophe' (paraphrasing). Such statements require some sort of a moral judgement (in order to say if something is good or bad) and are certainly outside the scope of science. Science doesn't tell us what we should do; It is a methodology for finding truth. Seriously, you are trying to legitimize your appeal to authority fallacies and correlation=causation fallacies? They are called fallacies for a reason, do not use them. There is a difference between referencing authorities as supporting evidence and using an authority reference as the entirety of you argument; the latter is fallacy. So if you are referencing something, you should explain the physical mechanism, relevance, etc. So if I ask a climate alarmist in this thread to explain their claim & the physical mechanism behind why they think that increasing CO2 concentrations will cause more extreme and more prolonged weather events and they respond, 'well the vast majority of scientists say so, here is an out of context quote from the conclusion of a scientific paper that i do not understand that justifies my claim', then they are using appeal to authority. And if they respond, 'there is more energy so things are more energetic... makes sense', then that is such a bastardization/misunderstanding of physics that it does not suffice as an explanation. In the case of correlation, you need to provide an explanation for why you think you have correlation; causation can be supporting evidence for correlation but it is insufficient on its own. There are also statistical tests for causation, which I will not get into, but many involve seeing which of the two data sets lags behind the other. There is a saying that if people repeat a lie enough times they will start to believe it. Be it with regards to religion, homeopathy, understanding of climate change, etc. With respect to your above statement, it is exactly the case. Climate alarmists keep telling each other this unproven claim over and over again that it has become a societal mass delusion. I also like how you use the word 'expert'... anyone an claim to be can 'expert' on something, doesn't mean they know what they are talking about.

I apologize if I misunderstood you are we are in agreement. Though 'The tax would never be high enough to change consumer choices because energy is a relatively small part of most people's expenses' somehow sounds incorrect to me. Does it have to be a real life example or can it be a theoretical one? If I can do theoretical, then this is simply a case of applying a pigouvian tax/subsidy. Example: a factory (which is small relative to other producers, so is a price taker) produces cars at a cost of of $19,750 dollars per car and can sell them at market price for $20,000. Each car produced emits 10 tonnes of CO2 (Thus a $500 social cost). Furthermore, the consumers that buy these cars are indifferent between having a car and not (i.e. zero consumer surplus). Without government intervention, the factory will make cars and sell them to consumers even though the social costs are higher than the social benefits. But if you implement a $500 pigouvian tax then this factory will no longer produce cars, which will increase the economic welfare of society. Example 2: an Australian company is decided whether or not to install a solar panel on their roof. If they install the solar panel then they expect that over it's lifetime it will produce energy at a cost of $80 per MWH. Alternatively they can decide not to install the solar panel and burn natural gas at a cost of $70 per MWh. However, burning natural gas emits 0.25 tonnes of CO2 per MWh (thus a $12.5 per MWh). Under no intervention, the company will decide to not install the solar panel. However, if the government implements a $12.5 per MWh pigouvian tax on natural gas (or a equivalent pigouvian subsidy on solar panels), then the company will decide to install the solar panel.

noone has responded to my post at the top of this page. Is it too long? Is it not well organized? Should I have split it up into multiple posts? Is it too hard to understand? Did I make an error anywhere? Should I start a new thread? :'( Please acknowledge my effort! It took a long time to write and derive some of that. Edit: if you don't understand/want to read it then at least read the summary at the end.

I never made a claim remotely related to this... Again, science is incapable of assigning morality to a phenomena in order to call something a disaster. And again, using appeal to authorities and proclaiming that 'this is truth' without providing justification is the complete opposite of science. This is my biggest issue with the climate alarmists, they claim to support science while at the same time completely disregarding (i.e. spitting on) the scientific method. Yeah but this isn't your original claim... Your original claim was that energy prices do not affect the behaviour of individuals because it makes up a small fraction of there income. I pointed out that it has nothing to do with making up a small fraction of income and is due to energy having a relatively inelastic demand curve (people still need to get to work, go to the store, etc.); you can have a good/service that makes up a small fraction of income with an elastic demand curve. Your response is basically that the demand for energy is inelastic (in a much more crude way, though goods with elastic demands will also require a 'sacrifice' if a consumer chooses not to buy it)... which I agreed with... Why not just admit you made a false claim and correct yourself? Many, but not all. Either way, your claim was too strong (please revise it).

Anyway, I would like to discuss the implications of the changes to the jet stream and mid-latitude wind patterns as a result of an increase in CO2 concentrations. But before that it would be preferable if we can agree on our understanding of the mechanism and the effects that result from an increase in CO2 concentrations. (see above post) Anyway, I'll respond to a few random posts over the past few pages that annoy me slightly: How is the past not relevant to understanding the effects of changing CO2 concentrations for life on earth or for testing climate models that we use to make predictions? Please tell me what part/weather phenomena on earth acts as a reverse carnot engine (i.e. refrigerator)? None. Apparently energy and temperature have nothing to do with each other... Perhaps if you use some bizzare pseudo-science definition of energy to mean something comparable with qi then you can get away with it in your warped mind. Just because something is a small part of someone's expenses does not mean that there will not be a significant change in someone's behaviour in response to a tax. Though admittedly, demand for energy is relatively inelastic (which has nothing to being a small factor in someone's expenses). Tim, I think you are being a bit too strong in your claims. With regards to the issue of taxes/subsidies to deal with CO2 emissions, there are arguable significant externalities that are not internalized. Often these externalities can mean that something can have more societal benefit than its cost despite having a smaller private benefit than its cost. This kind of thinking really annoys me. Rather than trying to deal with the trade-off and argue that despite the costs, the net benefit of performing an action is positive, people conveniently pretend the trade-off does not exist so that they do not have to deal with it. What kind of bizarre Orwellian reality do you live in? Most research and development is done/funded by private firms/corporations and in many cases governments impose rules that prevent new technologies from being adapted, that's just the reality we live in. As I have stated many times before, Science does not tell people what they should or should not do! Science is a methodology to obtain truth about the universe we live in. Comments such as the one above are concerning because they indicate a large portion of the population does not understand what Science is and also indicate a large obsession with appeal to authority fallacies (which goes against the scientific method; people should be skeptical and use the science itself to make their arguments).

Because subjective morals still exist even if objective morals do not. Furthermore, decision rules can still exist, and methodology for finding the best course of action in order to benefit society overall can exist. Correlation does not imply causation and I would like to see the 'evidence' for your claim of a correlation. Also, the crime argument I gave is similar to what Dre argued in some of his/her posts (of course the wording used is very different). But it is well known that poor people commit more crime. Not quite. The depreciation can also include things like the deterioration of a person's physical or mental health due to being poorer (poor people are more at risk of physical and mental health issues). Certainly, there are some people that might not want to contribute to society ever, but you only need a fraction of the poorer people to want to work and contribute to society to justify the existence of the human capital effect. Furthermore, even if an individual is taking more from 'the rest of society' than they produce, that does not mean that increasing their human capital won't be beneficial for society (since they become more productive). Also, you are mixing up 'cost to society' with 'cost to the rest of society' since you omit that the poor individual in question is part of society. Another thing you need to remember is that people are not poor their entire lives. There is a large change in a person's income status as they age and income mobility in most developed countries is relatively high. If a person is poor and you reduce depreciation of their human capital due to income redistribution, later on they might be richer (and still have that undepreciated human capital) so they will be more productive than if no income redistribution took place. Another important point on the human capital argument is that there are human capital & technological spillover effects. Not everything can be internalized in society (particularly people participating in the free market place of ideas), and just by being surrounded by others with a higher level of human capital, your level of human capital will be slightly higher via some sort of osmosis effect of human capital. Example: if you are surrounded by individuals that know a lot about neuroscience, then changes are over time you will learn a bit of neuroscience just by talking to them. There is no 'destiny' required. You only need a correlation & causation from income level to physical/mental health. Yeah.. that is sort of the point. Poorer people make worse decisions due to lower levels of human capital/income, which can cause greater human capital depreciation. That sounds unfeasible or expensive to implement. And society is more favourable to supporting food, clothing, education & housing because these things have a greater effect on human capital. So even if you do not explicitly say it, you implicitly realize the importance of human capital. The only problem is that you have this strange concept of a 'bare-minimum' cut off value where if you support someone after this value there is no change in the human capital. There will still be a change if you go beyond the 'bare-minimum' but it will just be much smaller. The assumptions I made are not unreasonable and the conclusion is true under more circumstances. U > 0 is somewhat unnecessary but people generally agree that you get positive utility by having stuff. U' > 0 just means that people prefer to be richer. U'' < 0 just means that people get diminishing marginal returns to utility (i.e. $1 to a poor person means more than $1 to a rich person). The idea of having 'roughly equal' utility functions for individuals is primarily to exclude extreme cases where you have rich people by much more than you value poor people (should society value a person who is twice as rich as a poor person as twice the value as the poor person? I think most people would not agree with this). Obviously, different individuals have different utility functions (some people prefer jam over peanut butter for example) but we are primarily concerned with their overall utility based on their income if they are free to do with their income whatever they want. Your claim that I assumed income redistribution is efficient is completely false. I specifically said that inefficiency of redistribution can take place. I merely excluded the case of 100% inefficiency (i.e. if I try to take $1 from a rich person and give it to a poor person that that entire $1 will be lost due to loss of economic efficiency, bureaucrats, etc.). The initial implementation costs of setting up a redistribution program (i.e. costs independent of the amount redistributed that are zero if you do zero redistribution and positive otherwise) just have to be sufficiency small compared to the change in society's net utility from the performing the redistribution (which based on empirical analysis that I will not get into is roughly correct). But if you have these conditions (or similar conditions) then 'small' amounts of redistribution will increase society's net utility and 'large' amounts of redistribution will decrease society's net utility. It is a matter of choosing the correct value. Your question on 'small' cannot be answered without information on the specific utility functions of individuals, the economic loss in efficiency of redistribution, etc. I can't just arbitrary say '$5 is small'. But if you want me to do the mathematical proof that a small income-inequality-reducing redistribution from the Walrasian equilibrium leads to an increase in the sum of the utilities of individuals in a society then I can provide it for you.

I apologize for the delay in my reply. I had half of this written in 2013 (including all supporting references), but trying to decipher Waldo-speak, especially given that Waldo ‘ran-away’ from the discussion on page 29 isn’t the most appealing thing. Especially when Waldo refuses to even acknowledge something as basic as ‘the climactic conditions of Earth, during which multi-cellular life evolved and flourished, is relevant to the discussion of climate change in terms of understanding the environmental impacts of climate change’. Also, I've been really busy with real life stuff. I'll give an explanation of my understand of various claims regarding the slowing of the jet stream below. waldo, on 31 Dec 2013 - 6:07 PM, said: nice! You've now really upped your game to formally include NOAA (along with your earlier reference to NSIDC) in your alarmist labeling. Should we throw NASA into that mix, as well? How about Environment Canada? Are there any existing government organizations, or scientific based institutions, or academia, or intergovernmental organizations, etc., that you don't label as alarmist? Why do you consistently misinterpret what I say? I never said NOAA is a climate alarmist organization. I said that all climate change related organizations have been influenced by climate alarmism to some extent and individuals within these organizations may be climate alarmists. This is why you should directly evaluate the scientific models and evidence presented rather than use appeal to authority fallacies. waldo, on 31 Dec 2013 - 6:16 PM, said: I certainly have no obligation to provide you with diddly If you want to make a bunch of bogus claims without sufficient supporting evidence or reasoning then that is your choice. But it will not make a convincing argument nor be effective in making people change their positions. waldo, on 31 Dec 2013 - 6:16 PM, said: In any case, related papers have been cited... if the papers don't meet your claimed "scientific prowess", I suggest you contact the authors directly. You may also want to throw a challenge/comment in against any of the papers you feel are lacking in meeting your "expertise". You certainly have a ballsy approach for someone who couldn't even read a basic article reference and follow the direct bread-crumb trail laid out for you... repeatedly laid out for you! Blah blah, same dodge of providing sufficient evidence or explaining the scientific models behind your unclear claims. Of course the reason you keep dodging is because you do not know/understand the scientific models to explain them. Being a climate alarmist that approaches the issue of climate change dogmatically, you are only interested in out-of-context sentences from conclusions of scientific papers that support your climate alarmist conclusion and rely primarily on strawman, ad hominem and appeal-to-authority fallacies to make your arguments. waldo, on 31 Dec 2013 - 7:03 PM, said: I'd suggest, purposely ignore. Clearly, the video is a high-level presentation on the weather effects of Arctic amplification relative to the shifting jet-stream pattern. You think that presentation was 'high-level'? Then I guess some of the links & explanations I'm about to provide will be too much for your science-n00b brain. waldo, on 31 Dec 2013 - 6:36 PM, said: no - the concept of Arctic/Polar amplification speaks to the propensity for high Northern latitudes to experience enhanced warming... or cooling... in relation to the rest of the Northern Hemisphere. Yes, it's the same thing as global temperature gradient reduction. - - - - - Discussion on trying to figure out jetstream related claims by climate alarmists: Anyway, I guess that I'll continue from my last post. For the benefit of other people reading this thread, as well as trying to understand each other's claims, I'll briefly summarize what my understanding is of the relationship between the equatorial-polar temperature gradient, Rossby waves, properties of the jet streams, and resonance pressure phenomenon for the Northern mid-latitudes: Now I repeatedly asked Waldo to clarify his claims regarding the physical mechanisms behind which a decrease in the global temperature gradient (arctic amplification as he calls it) results in an increase in the frequency of resonance phenomena of planetary waves. In science, it is important to understand the physical mechanism by which physical phenomena occur. Of course Waldo could not answer this basic question since he is a science n00b that approaches the issue of climate change dogmatically. So to understand the claims I had to do my own 'research'. Below is a decent 'intro' video that briefly explains some of the relevant concepts. http://www.youtube.com/watch?v=_nzwJg4Ebzo It includes a number of relevant facts (that Waldo conveniently omits) such as the jet stream shifting poleward & stretching, but I will not get into it now. The video is self explanatory, but I will point out that it doesn't properly explain the physical mechanism by which a decrease in the global temperature gradient increases the frequency at which the jet stream forms resonance phenomena. It does explain that since warmer air has a greater volume than colder air, if one looks at the earth's isobaric (for science n00bs, isobaric means constant pressure) contour, they will notice that it is higher at the equator than at the poles; effectively the isobaric contour slopes downward towards the poles. If there is a decrease in the global temperature gradient, then this will decrease the downward slope, which will supposedly slow down the jet stream (how this is the result isn't explained in the video). The video also shows some crude correlations between zonal wind and sea ice as justification for this connection between the speed of the jet stream and arctic amplification. But other than that the video is insufficient to explain this supposed phenomena. http://arctic-news.blogspot.ca/2012/12/polar-jet-stream-appears-hugely-deformed.html Here is a somewhat useful link. It is a bit climate alarmisty and it does make some false claims such as "Accordingly, the Northern Temperate Zone used to experience only mild differences between summer and winter weather, rather than the extreme hot or cold temperatures that we've experienced recently.". This claim of course makes no sense in the context of a discussion of the resonance of planetary waves (which supposedly affect intra-seasonal temperature variation not inter-seasonal temperature variation) and the fact that a reduction in the global temperature gradient reduces (rather than increases) inter-seasonal temperature variation. They even have a ridiculous 'diagram of doom'. However the above link has a link to http://www.srh.noaa.gov/jetstream/global/jet.htm This NOAA site is less biased and is useful to effectively explain the 3 different tropospheric cells for each hemisphere and the mechanism by which a reduction in the global temperature gradient will decrease the speed of the jet stream: - Since the isobaric contour slopes downward towards the poles, air at the top of the troposphere will move poleward via gravity. - The earth has a higher centripetal velocity at the equator than at the poles. The centripetal velocity as a function of latitude is R*ω*cos(θ), where R is the radius of the earth (approx 6371 km), ω is the angular frequency of the earth (2π/(24hours)), and θ is the latitude. The effect is that as the air moves poleward, it gains eastward velocity relative to the ground below. - The acceleration at which the air moves poleward is approximately proportional to sin(arctan(M)) = M/sqrt(1 + M^2), where M is the slope of the isobaric contour, since the force that moves the air poleward is the downward force of gravity. - However, if the air is moving faster relative to the ground below it, then it will experience a friction/air-resistance force. The force of air resistance is approximately proportional to the square of the velocity. This means that if the net acceleration is zero then the poleward velocity of the air is approximately proportional to sqrt(sin(arctan(M))). - As said earlier, the centripetal velocity of the ground is R*ω*cos(θ). If we consider some air at the top of a cell/troposphere that initially has no velocity relative to the ground and moves poleward by an amount dθ in dt time, then the air's new eastward velocity relative to the ground is R*ω*sin(θ)*dθ. Since the rate at which air at the top of a cell moves poleward is simply R*dθ/dt, this means that the eastward velocity of the air relative to the ground is now proportional to ω*sin(θ)*sqrt(sin(arctan(M))). - The important thing to note here is that sqrt(sin(arctan(M))) is a positive monotonic transformation of M. This means that the eastward velocity of air at the top of the air cell relative to the ground depends positively on the isobaric slope of the air. - If we consider the air below to be an ideal gas of approximately equal temperature and constant pressure PV = nRT, then a small change in the temperature of the air is proportional to a small change in the volume of the air. And if the volume of air is some polynomial function of height, then a small change in the temperature will be proportional to a small change in the height of the air. Note that 'a small change in temperature is proportional to a small change in height' is true in more general circumstances (it's simply a linear approximation for small changes); I used the ideal gas argument for convenience. - Therefore, the poleward temperature gradient of the air is proportional to the poleward height gradient of the air (which is approximately the same thing as the isobaric slope of the air). This means that the eastward velocity of the air at the top of the air cell relative to the ground depends positively on poleward temperature gradient of the air. This implies that for small changes, a change in the temperature gradient will be proportional to a change in the eastward velocity relative to the ground below. - The areas where two tropospheric cells meet have the highest temperature gradients in the hemisphere. This is what causes polar jet streams to form between Polar & Ferrel cells and what causes subtropical jet streams to form between Ferrel & Hadely cells; jet streams are just fast eastward moving masses of air at the top of the troposphere. - If one decreases the global temperature gradient, then one will decrease the temperature gradient between two cells, which will therefore decrease the speed of the jet stream. Note that this still hasn't explained how the decrease in the speed of the jet stream results in an increase in resonance effects. It is also helpful to point out a few things: - The reason why Earth has 3 troposphere cells in each hemisphere as opposed to more or less is due to the properties of present day Earth. There is strong evidence that suggests that during the Cretaceous period on earth, there was only 1 cell per hemisphere. Jupiter on the other hand has at least 8 cells per hemisphere (you can see them as alternating light and dark bands on Jupiter). As an aside, Jupiter has had significant climate change over the past few decades (which is one of the reasons I prefer to use the term global temperature gradient rather than 'arctic amplification' as the former is more generally applicable and can be used when discussing other celestial bodies). - It is also relevant to point out that the jet streams shift poleward during the day and equatorward during the night. In addition, the jet streams shift poleward during summer and equatorward during winter. The below two links might also be useful for someone reading this and wanting to better understand the connection between a change in the global temperature gradient and resonance of planetary waves. http://skepticalscience.com/jetstream-guide.html http://blog.ucsusa.org/wacky-weather-a-warmer-arctic-and-a-slower-jet-stream-is-there-a-link-194 However, please note that neither of the above 2 links explain the physical mechanism by which a slowing of the jet stream (or other eastward moving air) will increase the rate at which we have pressure and/or jet stream resonance phenomena. They just use this as a 'given' and the closest thing to an explanation provided is something along the lines of 'slower jet stream makes it have a higher amplitude and meander more, which increases its chances of getting stuck'. Such a justification is poorly described, an oversimplification at best and misleading/incorrect at worst. However, I did manage to find a theoretical model/explanation that explains why a slowing of the jet stream 'might' increase the frequency of these pressure phenomena. http://geosci.uchicago.edu/~nnn/LAB/DEMOS/RossbyWave.html The above link is useful and you might need to enable flash player to see the video of the forced Rossby waves. They use a rotating annulus with water inside to represent the northern hemisphere, but the physics and equations used are mostly valid. The above link also helps to explain some phenomena. However, it is a bit insufficient as it doesn't explain the origin of some of its equations, and the equations are for a rotating annulus and different than for the Earth. Furthermore, many of the claims made by climate alarmists often relate wavelength, amplitude, group velocity, frequency of resonance phenomena and other things to the speed to the jet stream, so better analysis is needed. Anyway, after having consulted various sources on the subject I have a sufficiently good understanding of the connection between the zenith velocity of the jetstream relative to the Earth's surface and the wavelength, amplitude, group velocity, frequency of resonance phenomena, etc. If you are interested, Here are two decent pdfs on the subject: http://www.columbia.edu/~irs2113/3_Circulation_Vorticity_PV.pdf http://www.ocean.washington.edu/courses/oc512/rossby-waves-gfd109-lec5a-07.pdf But basically the physics are as follows: - Suppose you have an air mass that is moving faster than the rotation of the planet and is moving in the same direction as the rotation of the planet (example: air at the top of the troposphere that has moved pole ward via gravity). Note that this applies to both jet streams as well as air in the mid latitudes that generally move west to east (air at the equatorial regions and polar regions move east to west). And suppose that this air moves over a ridge (such as the Rocky Mountains, the Himalayas, the Ural Mountains, the Appalachian Mountains, the Alps, etc.). - As the air mass goes over the ridge, it is compressed vertically & adiabatically (since no heat is transferred to surrounding air by the compression). For an ideal gas, an adiabatic compression implies that PVγ = constant, where P is pressure, V is the volume and γ > 1 is the adiabatic index. Thus pressure must increase. However, if the pressure of the air mass is greater than the surrounding air (which is the same as the air mass before adiabatic compression), then there will be a net outward force on the air mass which will cause an adiabatic expansion in the horizontal direction until the pressure of the air mass and the surrounding air equalizes. But if the pressure is the same than the volume must also be the same since PVγ = constant. Thus the air mass will be compressed vertically but expanded horizontally and keep the same area. - Suppose this air mass is a rotating cylinder with constant density ρ, radius Q, height H, volume V, mass M and an angular frequency of ω. The moment of inertia of a rotating cylinder (about its axis of rotation) is simply 0∫Mr2dm = 0∫Vr2ρdV = 0∫H0∫Q0∫2πr2ρ r dθ dr dV = H*Q4/4*2π = 0.5MQ2. Then the angular momentum of this air mass due to the rotation of the air mass about itself is 0.5MQ2ω. However, you also have an angular momentum due to the fact that this cylindrical air mass is located on the Earth, which is rotating. If we are only concerned about the angular momentum in the radial direction then this angular momentum will consist of two components. The first is due to the fact that the air mass is spinning around the earth's axis MR2cos2(φ)sin(φ)Ω, where R is the radius of the Earth, φ is the latitude and Ω is the angular frequency of the Earth. The second is due to the fact that the earth's axis and the rotation axis of the cylinder are not necessarily perpendicular 0.5MQ2sin(φ)Ω (note that both of these components are in the radial/up direction). Note however that one of the components does not depend on Q, the radius of the air mass. - Thus, by conservation of angular momentum (Newtonian physics) in the upward/radial direction we have 0.5MQ2ω + 0.5MQ2sin(φ)Ω = constant. But M is a constant (by mass conservation) so Q2(ω + sin(φ)Ω) = constant. But volume is constant and V = πQ2H, so (ω + sin(φ)Ω)/H = constant. For this rotating air mass, we define its relative vorticity to be η = abs(curl(v)) = ∂vy/∂x - ∂vx/∂y, where x is distance in the zenith direction from the axis of rotation, y is the distance in the azimuthal direction from the axis of rotation, vy is the velocity of part of the air mass in the y direction relative to the ground and vx is the velocity of part of the air mass in the x direction relative to the ground. If we take a point in this air mass with cartesian coordinates (x,y,h), then vy = xω and vy = -yω. Thus η = 2ω. Using this we get the potential vorticity conservation equation: (η + f)/H = constant, where f = 2Ωsin(φ) is known as the coriolis parameter. - Now back to the air mass that is moving eastward, has zero initial relative vorticity and going is over a ridge. Suppose for simplicity sake that the ridge is short & wide relative to the height & radius of the air mass and that the ridge has a height of dh and a width of W. When the air mass is over the ridge, its height must decrease so by conservation of potential vorticity f/H = (η + f)/(H-dh) => f*(H-dh) =(η + f)*H => η = -fdh/H. Thus the air mass goes from zero vorticity to obtaining a negative vorticity (i.e. it starts to spin clockwise in the northern hemisphere). Suppose for simplicity that the initial eastward velocity of the air divided by the width of the ridge is large relative to this new vorticity. Then eastward velocity is approximately constant so -fdh/H = η = ∂vy/∂x - ∂vx/∂y ≈ ∂vy/∂x. Thus the acceleration is constant, so the poleward velocity of the air mass after it moves across the ridge (initial poleward velocity is zero) is W*∂vy/∂x = -f*W*dh/H, which is negative. - So basically, after some non-rotating eastward moving mass moves over a ridge, it will have zero-vorticity, the same eastward velocity and a negative poleward velocity (i.e. it will be heading to the equator). Note that this applies to all 'small' pertubations/ridges since you can just consider other shapes to be a sum of infinite ridges with constant height and varying widths. For larger perturbations/ridges the effect will still be the same but the eastward velocity after the air mass moves over the ridge will decrease to compensate for the ∂vx/∂y term. In the context of the jetstream traveling over the rockies, ignoring the ∂vx/∂y for simplicity sake is reasonable. - Anyway, after the air mass goes over the ridge, it now has zero vorticity and is moving towards the equator. However, as the air moves towards the equator, potential vorticity must be conserved but two things happen. f = 2Ωsin(φ) decreases since we are moving towards the equator, and H may increase (as gravity becomes effectively weaker due to a larger centripetal force, and the air mass may expand due to becoming warmer). If the time scale is small (which is reasonable in the context of the topic) we can ignore the warming effect. - The centripetal acceleration of the earth at the equator is v2/R = (RΩ)2/R = RΩ2 = (6371 km)*(2π/24h)2 ≈ 0.03 m/s2. The acceleration due to gravity for earth is approximately -9.81 m/s2. This means that the net radial acceleration on the earth's surface as a function of the latitude is g = -9.81 m/s2 + cos2(φ)*0.03 m/s2. For a small change in latitude dφ, the new acceleration is g = -9.81 m/s2 + cos2(φ+dφ)*0.03 m/s2 = -9.81 m/s2 + cos2(φ+dφ)*0.03 m/s2 - sin(2φ)dφ*0.03 m/s2. Note that pressure is defined as force per unit area. Thus the downward pressure of a point in the air mass must be equal to gravitational force acting on the air above it per unit area. So P α g/Q2. But we also know that for the cylindrical air mass, V = πHQ2. But since pressure and volume are constants (as explained earlier) we have H α 1/Q2 => gH = constant or g α 1/H. - For the effect of a change in the coriolis parameter, for a small change in latitude dφ, the new coriolis parameter is f = 2Ωsin(φ+dφ) = 2Ωsin(φ) + 2Ωcos(φ)*dφ. From conservation of potential vorticity we have (η + f)/H = constant. This plus g α 1/H implies that (η + f)*g = constant. Thus, for a small change in latitude, we get (η + 2Ωsin(φ))*(-9.81 m/s2 + cos2(φ)*0.03 m/s2) = (η + dη + 2Ωsin(φ) + 2Ωcos(φ)*dφ)*(-9.81 m/s2 + cos2(φ)*0.03 m/s2 - sin(2φ)dφ*0.03 m/s2). Neglecting all non-linear displacement terms gives: (η + 2Ωsin(φ))*(-9.81 m/s2 + cos2(φ)*0.03 m/s2) = (η + 2Ωsin(φ))*(-9.81 m/s2 + cos2(φ)*0.03 m/s2) + dη*(-9.81 m/s2 + cos2(φ)*0.03 m/s2) + 2Ωcos(φ)*dφ*(-9.81 m/s2 + cos2(φ)*0.03 m/s2) - sin(2φ)dφ*0.03 m/s2*(η + 2Ωsin(φ)) => 0 = dη*(-9.81 m/s2 + cos2(φ)*0.03 m/s2) + 2Ωcos(φ)*dφ*(-9.81 m/s2 + cos2(φ)*0.03 m/s2) - sin(2φ)dφ*0.03 m/s2*(η + 2Ωsin(φ)) => dη/dφ = -2Ωcos(φ) + (η + 2Ωsin(φ))*sin(2φ)*0.03 m/s2/(-9.81 m/s2 + cos2(φ)*0.03 m/s2) - Note that the first term is on the order of 2Ω, while the second term is on the order of 2Ω*0.03/9.81. Thus the second term is about 300x smaller then the first term and we can neglect it to get: dη/dφ = -2Ωcos(φ) - Similarly, we could have also introduced other effects of potential vorticity such as the fact that the isobaric surfaces are not necessarily parallel to the radial direction, the fact that the air may warm due to an increase in sunlight, the fact that the earth isn't perfectly round, etc. But by far the most dominant effect on the change in vorticity due to a change in latitude is the coriolis effect. - Integrating both sides of dη = -2Ωcos(φ)dφ gives η - η0 = -2Ωsin(φ) + 2Ωsin(φ0), where φ0 is the initial latitude and η0 = 0 is the initial vorticity. If we only consider small perturbations such that φ = φ0 + Δφ, where φ0 >> Δφ, then we get η = -2Ωcos(φ0)Δφ. - Note that η = ∂vy/∂x. Since the air mass follows it's velocity over time, we have ∂y/∂x = vy/vx => η = ∂vy/∂x = ∂(vx(∂y/∂x))/∂x. For small deviations/perturbations vx >> vy so we can treat vx as a constant. Thus vx∂2y/∂x2 = η = 2Ωcos(φ0)Δφ. If we use y = Rφ to represent the distance in the azimuthal direction and y0 = Rφ0 to be the initial 'displacement' from the equator then we get ∂2y/∂x2 = 2Ω/vx*cos(φ0)*(y-y0)/R. But this is of the form ∂2y/∂x2 = -k2*(y-y0), where k = sqrt(2Ω*cos(φ0)/(R*vx)) is the wavenumber. This differential equation has the following general solution: y = y0 + D*cos(kx) + E*sin(kx), where D,E are arbitrary constants and k = sqrt(2Ω*cos(φ0)/(R*vx)). - Taking the second derivative gives: ∂2y/∂x2 = -Dk2*cos(kx) - Ek2*sin(kx). We know that initially (after the air passes over the ridge) the relative vorticity is zero. But vx∂2y/∂x2 = η. Therefore, substituting in x = 0 for the second derivative yields 0 = η0 = -Dk2*cos(0) - Ek2*sin(0) = -Dk2*cos(0) => D = 0. - This means that the first derivative can be written as: ∂y/∂x = Ek*cos(kx). We know that initially, the velocity in the y direction is = -f*W*dh/H = -2Ωsin(φ0)*W*dh/H. Thus (-2Ωsin(φ0)*W*dh/H)/vx = (vy/vx)0 = (∂2y/∂x2)0 = Ek*cos(k*0) = Ek. => E = (-2Ωsin(φ0)*W*dh/H)/(vx*k) = -sin(φ0)*W*dh/H*sqrt(2ΩR/(cos(φ0)*vx)). Thus the equation of the azimuthal displacement of this air mass as a function of the zenith displacement is: y = E*sin(kx), where E = -sin(φ0)*W*dh/H*sqrt(2ΩR/(cos(φ0)*vx)) and k = sqrt(2Ω*cos(φ0)/(R*vx)). - Now let us examine the effects of changing the zenith velocity vx (due to say a decrease in the temperature gradient due to global warming): - The wave number k is proportional to 1/sqrt(vx). And by definition, λ = 2π/k => the wavelength is proportional to sqrt(vx). This means that a slower velocity will lead to a shorter wavelength. - The amplitude, abs( C ), is proportional to 1/sqrt(vx). This means that a slower velocity will lead to a larger amplitude. - With respect to the frequency of resonance phenomena, you have resonance when the circle around the earth's axis at the central latitude is equal to a whole integer number of wavelengths. I.e. 2πR*cos(φ0) = 2π*sqrt(R*vx/(2Ω*cos(φ0)))*i, where i is any member of the natural numbers. Now whether there is an increase or decrease is the frequency of resonance effects is very chaotic and depends not only on the change in temperature gradient, but how this temperature gradient varies over the year, on the distribution on ridges that can cause these waves (I.e. on the earth's topology), on the interaction with other weather events, etc. But what we can do is make a statement about how the frequency of resonance effects changes in general (i.e. what happens to the density of states when we change the velocity of the air mass?). - We have a resonant state when R*cos(φ0) = sqrt(R*vx/(2Ω*cos(φ0)))*j, where j is any positive integer. Note that for a constant central latitude we have j*sqrt(vx) = constant => j = constant/sqrt(vx). To get the density of states for the velocity, we simply take the derivative of j with respect to vx, which yields (density of states) = dj/dvx = constant*(-0.5)*vx -1.5. This means that the a slower velocity will lead to a larger density of states. So it is not unreasonable to expect that a slower velocity will lead to a higher frequency of resonance phenomena. - Note that the above is the result of a standing wave (does not move in time). This explains why the jetstream usually dips equatorward after it hits a ridge (such as a mountain ridge) or dips poleward after it reaches an ocean, etc. And from the above we can determine a rough relationship between the speed of the jet stream and the frequency of resonance phenomena. However, it is also useful to determine the group velocity of a moving wave, since the jetstream is not completely stationary, to get a rough idea of how quickly the jetstream passes over an area (and to examine some of the claims by others about the speed at which the jetstream moves). - To get the speed of the jetstream, we need to look for plane-wave solutions to the conservation of potential vorticity (η + f)/H = constant. If we ignore the effect of the change in the height of the air mass (which is reasonable since, as explained earlier, the coriolis parameter dominates). This implies 0 = d(η + f)/dt = dη/dt + df/dt = ∂η/∂t + (dx/dt)*(∂η/∂x) + (dy/dt)*(∂η/∂x) + ∂f/∂t + (dx/dt)*(∂f/∂x) + (dy/dt)*(∂f/∂y). - But f = 2Ωsin(φ) = 2Ωsin(y/R) => ∂f/∂t = 0, ∂f/∂t = 0, and ∂f/∂y = 2Ωcos(y/R)/R = 2Ωcos(φ)/R. Furthermore, vx = dx/dt and vy = dy/dt. So we end up with: 0 = ∂η/∂t + vx*(∂η/∂x) + vy*(∂η/∂y) + vy*2Ωcos(φ)/R. - If we consider a wave that is flowing in the zenith direction with a mean zonal flow of u, then we can define vx = u + Δvx. Notice that for small perturbations, U >> Δvx and U >> vy. Thus we get the approximation: 0 = ∂η/∂t + u*(∂η/∂x) + vy*2Ωcos(φ)/R. - Now suppose we introduce a scalar 'stream' function where the gradient of the stream function gives the velocity of the wind at any point. I.e. we define a function Ψ(x,y,t) such that vx = ∂Ψ/∂y and vy = -∂Ψ/∂x. Then using our definition of relative vorticity, we have η = ∂vy/∂x - ∂vx/∂y = -∂Ψ2/∂x2 - ∂Ψ2/∂y2 = -∇2Ψ. Thus the differential equation becomes: 0 = ∂∇2Ψ/∂t + u*∂∇2Ψ /∂x + ∂Ψ/∂x*2Ωcos(φ)/R. If we consider small perturbations then we can treat 2Ωcos(φ)/R as a constant, so we get: 0 = ∂∇2Ψ/∂t + u*∂∇2Ψ/∂x + β*∂Ψ/∂x, where β = 2Ωcos(φ0)/R. - To look for plane-wave solutions in the zenith direction, we let Ψ = real(exp(ikx - iσt)), where i is the imaginary number, k is the wave number and σ is the angular frequency of the plane wave. Substituting this into the differential equation yields: 0 = ik2σΨ - iuk3Ψ + iβkΨ This yields the dispersion relation σ = (uk2 - β)/k. - To get the group velocity of this wave, we simply differentiate σ with respect to k to get: vg = ∂σ/∂k = u + β/k2, where u is the mean flow in the zenith direction and β = 2Ωcos(φ0)/R. - To get the wave number k, set the time derivative of the differential equation equal to zero to yield: 0 = u*∂∇2Ψ/∂x + β*∂Ψ/∂x. Substituting in stationary plane wave solutions Ψ = real(exp(ikx)) yields : 0 = -iuk3Ψ + iβkΨ => uk2 = β => k = sqrt(β/u) = sqrt(2Ωcos(φ0)/(u*R)), which is what was obtained earlier. - Thus we get: vg = u + β/sqrt(β/u)2 = 2u ≈ 2vx - Thus the group velocity is approximately proportional to the zenith velocity. I.e. if the zenith velocity is slower, then the wave pattern will move more slowly across the planet. Furthermore, not that the group velocity is in the same direction as the zenith velocity (i.e. the group velocity is eastward). - Note that the group velocity might not be that relevant for say North America where the waves are more or less stationary saves forced by the Rocky Mountains and other mountain ranges. The group velocity might have more meaning in Europe where there are less topologically significant features and the jetstream is coming from the Atlantic Ocean. However, in the case of North America, one could argue that the primary change in the shape of the jetstream is caused by variations in the zenith wind speed since we showed that the wavelength is proportional to sqrt(vx). - It is reasonable to expect that variance in the zenith wind speed should be approximately proportional to vx (i.e. just scale all wind speed values up by the same value). If this is true then the change in the wind speed over time should be approximately proportional to the mean wind speed vx. Thus (∂/∂t)λ α (∂/∂t)sqrt(vx) = 0.5*(vx)-0.5*(∂vx/∂t) α (vx)-0.5*(vx) = sqrt(vx). - Therefore, even if one claims that the group velocity has little physical meaning, we still get the result that the rate at which the jetstream and other Rossby waves change depends positively on the zenith velocity. Of course the dependence relationship is slightly different (group velocity proportional to vx compared to change in wavelength over time proportional to sqrt(vx)). - Using this information, it might be useful to examine the claim that if the wind speed of the jetstream is lowered due to a smaller temperature gradient, then this will lead to longer droughts/floods and 'prolonged extreme weather events'. The frequency at which a moving jetstream passes over a mid-latitude region is 2vg/λ. Since λ α sqrt(vx) and vgα vx, we get that the frequency is proportional to (vx)0.5. - Thus, a decrease in the wind speed of the jetstream will lead to a DECREASE in the rate at which the jet stream passes over a mid latitude region; thus longer droughts or floods could be expected. Note however, that this does not apply to resonance phenomena of standing waves. For resonance phenomena, the rate at which you move out of a resonance state will be proportional to (∂λ/∂t)/λ, but since both ∂λ/∂t and λ are proportional to sqrt(vx), we get that the rate at which the jetstream moves out of a resonant state is independent of the zonal wind velocity of the jetstream. Thus there is no reason to believe that a change in the duration of resonant phenomena will occur as a result climate change based on the physical mechanism described above. - Another thing that one should take into account when evaluating the claim that a decrease in the wind speed of the jetstream will prolong weather events is the effect of the change in the amplitude of the jetstream. As explained earlier, the amplitude is proportional to 1/sqrt(vx). This means that as wind speed decrease, amplitude will increase. However, if amplitude increases then now regions that were previously outside of the amplitude of the jet stream are now within the amplitude of the jetstream (Northern Canada, Southern Europe, etc.). Thus the jetstream will now occasionally pass over these regions, which will reduce the duration of weather events in these regions (since they will now vary more between high and low pressure). - The last thing to check is if the strengths of the high and low pressures systems change as a result of the decrease in the wind speed of the jetstream (since an increase in the strengths of the pressure systems could lead to more extreme weather events). Note that by conservation of potential vorticity we get η + 2Ωsin(φ) = constant (H was ignored because its changes are negligible as explained earlier). Since the vorticity at φ0 is 0, we get η = -2Ωcos(φ0)Δφ. Thus the vorticity at each latitude only depends on the latitude and not on the wind speed of the jetstream (due to the domination of the coriolis effect). - Since the pressure corresponds directly with the vorticity (if something rotates opposite of the rotation of the earth it becomes a region of high pressure and if something rotates in the same direction as earth it is becomes a region of low pressure), this means that the strengths of the high and low pressures at each latitude are UNCHANGED. Thus it is unreasonable to expect a change one way or another in the severity of weather events based on this change in the strength of the jetstream. - The one exception to the above is for regions that are now within the amplitude of the jetstream that were not before. These regions will now experience greater variation in their pressures over time, which one could argue could lead to more severe weather events. But this comes with the consequence of less prolonged weather events as explained earlier. - One consolation to the climate alarmists is that since the magnitude of high and low pressures remains unchanged while the wavelength gets shorter (λ α sqrt(vx)), one could argue that the magnitude of the pressure differential along the same latitude is proportional to approximately 1/sqrt(vx)). Therefore, a reduction in the global temperature gradient could lead to greater longitudinal pressure differential (and therefore maybe greater wind speeds). Of course, this is due to having slower eastward moving wind speeds in the first place... so the net effect is difficult to evaluate (we would need to look at the exact topology of the earth to determine the magnitude of pressure variation & wavelength of Rossby waves at different latitudes in order to compare the two changes in wind speeds). Summary of effects of increased CO2 concentrations on jetstream: - Increasing CO2 concentrations will lead to uneven warming between polar and equatorial regions due to the T4 nature of black body radiation power emission and the fact that polar regions will experience a greater loss in albedo due to melting ice. - This uneven heating reduces the global temperature gradient, which reduces the temperature differential between the Polar, Ferrel and Hadley cells in the troposphere. - The reduction in the temperature gradient between cells means that the height gradient at the top of these cells decreases in magnitude. Since the velocity of air in the jetstream is due to the loss of centripetal velocity as air falls from equatorial regions to polar regions along the top of the tropopause, the reduction in temperature gradient leads to a reduction in the speed at which air 'falls' towards the polar regions. - Since air resistance is proportional to the velocity squared, the speed of the jetstream is roughly proportional to sqrt(sin(arctan(M))) ≈ sqrt(M), where M is the slope of the height. Thus the speed of the jetstream is roughly proportional to sqrt(ΔT), where ΔT is the temperature differential across the two cells. - From conservation of momentum + considering the adiabatic expansion/compression of a rotating ideal gas on earth, we get the conservation of potential vorticity equation (η + f)/H = constant. - By considering an air mass moving eastward over a ridge, from conservation of vorticity we get that this air mass forms a standing wave pattern. Examining this standing wave pattern tells us that: - The wavelength is proportional to sqrt(vx), a slower velocity will lead to a shorter wavelength. - The amplitude is proportional to 1/sqrt(vx), a slower velocity will lead to a larger amplitude. - The density of states is proportional to vx -1.5, a slower velocity will lead to a larger of density of states, which means we should expect an increase in the frequency of resonance phenomena. Note that true change to resonance phenomena are extremely chaotic and to fully understand the effects one has to take into account the Earth's exact topology, variation in wind speeds over time, etc. This is especially true since for the northern polar jet stream, the perimeter around the earth at its latitude divided by its wavelength is often on the order of a single digit number. - Looking at planewave solutions to the potential vorticity equation allows us to examine a moving wave pattern. We find that: - The group velocity is proportional to vx; a slower velocity will lead to a slower group velocity. This means the wave form will move more slowly across the earth. - By comparison, the change in the wavelength of the standing wave pattern over time is proportional to sqrt(vx). This still gives the conclusion that a slower velocity will lead to a slower change in the wave pattern over time. - Looking at the frequency at which a moving jetstream passes over a region, this is proportional to (vx)0.5. Thus a slower velocity leads to decrease in the frequency at which weather events occur & an increase in the duration of weather events. - In the case of resonant phenomena due to forced standing waves, this is independent of the wind speed of the jetstream. Thus no change to the duration of resonance phenomena (corresponding to extreme droughts or floods) should be expected. - The strength of high and low pressure systems as a function of latitude will remain basically unchanged by this reduction in the speed of the jetstream, since their vorticities are primarily due to the corolis effect (i.e. changing the speed of the jetstream does not change the rotation rate of the Earth). - For areas outside of the old amplitude of the jetstream that are now within its amplitude, they should experience more weather variation, shorter duration of weather events, and an increase in the severity of weather events. - Arguably, the mean magnitude of the longitudinal pressure gradient is proportional to 1/sqrt(vx), so will increase due to a slower jetstream. This could lead to higher localized wind speeds. But since the cause is lower wind speeds in the first place, the net effect is difficult to evaluate. So my question to Waldo is 'can we at least agree upon the effects of increasing CO2 on the jetstream?'. (Note: I used various characters such as Greek letters. Tell me if you cannot see some of them.) (Edit: made several changes to make the post more readable.) (Edit 2: I made a new/better version of this post with estimates of expected change here: http://www.mapleleafweb.com/forums/topic/23461-effectsimplications-of-climate-change-on-jetstreams/) (Edit 3: Fixed error regarding the change in the frequency at which a jetstream will pass over a region.)

Personally, I am a nihilist so I do not believe that objective morality exists. Which is why I wanted you to rephrase the question. You have some control since you can vote and talk to others to change your opinions. Furthermore, the fact that your behaviour is affected by things such as level of taxation should always be of concern to policy makers. (I.e. your control is small but non-zero). And regardless of if you have control or not should not demerit the question of asking if income redistributing policies are good for society. I agree that this belief and similar beliefs are common in our society and I do not agree with these beliefs. However, that does not mean that some level of income redistribution isn't good. I'll give you 3 'strong' arguments that can be used to justify some income redistribution: Crime Argument: Poorer people tend to commit crimes at a greater rate. There are a number of reasons why this occurs but this is expected even for rational individuals. Poorer people have less to lose by committing crimes (and roughly the same amount to gain), so poor people have a lower expected cost to commit crimes. This means that there is a greater expected net benefit to commit a crime if you are poor. So the result is poorer people tend to commit crimes. If you income supplement poor people then this reduces the crime rate (of course this will make the richer people poorer, which will increase crime, but it will not be enough to offset the crime reduction due to diminishing marginal utility of income). Human Capital Argument: Individuals accumulate human capital throughout their lifetime. This means education, skills, etc. It takes a long time and many resources for individuals to acquire this human capital (they have to be raised from birth, go into the public school system, maybe do university, maybe take various training sessions,etc.). Note that most of the costs of giving someone human capital is not internalized and most of it is paid for by the government and/or parents. If people have extremely low income they are at a higher risk of dying, more susceptible to physical and metal illnesses, malnutrition, poor fitness, etc. The effect is that if a society has more people in low income situations, it will have a higher rate of human capital depreciation, which means a lower level of human capital (which is expensive to replace as now you have to have someone have a new child, have them be raised for 2 decades, etc.). The reduction in human capital per capita means a lower income / less production per capita, which means society is not better off. Now if you were to say 'well we could just have less people, so the effect on human capital per capita does not change if a poor person dies', you forget for a society like Canada, we have an extremely low population density and could benefit from economies of scale. So either way, society is worse off from the higher rate of human capital depreciation. Utilitarian Argument: If we were to make a claim that society should try to maximize the sum of the utilities of the individuals. And furthermore, assume that the utilities of individuals (as a function of income) are positive, have a positive first derivative, have a negative second derivative and are roughly the same for all individuals (these are fairly reasonable assumptions since it is just saying people prefer more income, they have diminishing returns to income and we value everyone as roughly equal). If these assumptions hold, then if we were to perform a very small amount of income redistribution from a rich person to a poor person (and we start from the walrasian/Market equilibrium), and we also assume that the implementation costs of implementing a redistribution program are relatively small, then as long as the loss of economic efficiency from that income transfer is less than 1, there will exist some level of income redistribution that increases societies overall utility. Note that large levels of income redistribution will decrease society's overall utility due to increasing effects of loss of economic efficiency.

I do not disagree with your first 2 sentences, but the 3rd sentence is not implied from your second. You can have welfare benefits that exceed the prevailing wage if you also income supplement people that have low income wages.

There is a difference between holding a belief out of necessity and holding a belief out of faith. At some point you need to have beliefs in order to make decisions. Belief in our perceived reality is necessary since it is the only information we have to make decisions.

I'm not sure that I like the wording of the question. You use the word 'responsibility' to the poor, which implies there must be moral justification. Would you prefer to use the question 'Why should society implement policies to help lower income peoples?" which is more objective and can avoid more morality issues?

I explained this earlier in depth (see my first post). If there are no gender roles then gender identity becomes somewhat meaningless beyond biology. A girl that likes sports or lego should not be considered 'a female that identifies as male' but 'a female that likes sports & lego'.