StrictlyLogical

I'm not sure you have connected each step in this hypothetical "proof". How about this [taking K as the additive identity element: K = (K + K)] So K*x = (K + K)*x = K*x + K*x = 2*K*x Using the unitary operator "-" K*x - K*x = 2K*x - K*x or 0 = K*x for any x.

Well that sounds a little more safe... at least the eco-terrorists would have to do some legit research on their own before ruining the world.

I do not doubt an enviro-terrorist will soon unleash such plastic attacking organisms into the biosphere with little thought to unintended consequences. Soon people will have throw out their disintegrating plastic hooks, hangers, pens, waterbottles, computer equipment, TVs, previously safe electrical appliances, recycling bins, and replace rotting composite patio planks, vinyl siding on their homes, car interiors, and replace crumbling and unsafe plastic-based safety equipment all crumbling slowly before their eyes. So much for my "permanent" CD collection... oh well, we'll just release another plague of organisms into the biosphere to take care of the first plague.

Is it really so arbitrary though? The unknown is not the unknowable. We know the things are of nature and that they have attributes, and generally know the kinds of things there are and at least the kinds of attributes and properties things have. We know even more in specific contexts. We do not know everything about an unexplored desert, but we know that it is a desert, and what usually lives there. I think we rightly fear the risks of the unknown, because we now know of dangers which we remember we were completely unaware of early enough in childhood, risks of rattlesnakes, risks of poison ivy, risk of avalanche, radiation poisoning, electric shock.... these were not unknowable, but they were unknown to us, specifically, before we learned of them. We are not omniscient, but we have enough experience to know that those things of nature of which we do not know include some which are dangerous, so it is reasonable to assume there are dangers you do not know of, whether individually, or undiscovered by Man... lurking in the unknown places... but so there does opportunity await. No one reaps the reward of taking risks without lack of some knowledge... without the lack of any knowledge, there would be no risk. Risk is in the unknown future, the unknown reaction to your product, the unknown amount of gold deposits in a potential mining site... so the potential for a boon lies in the untraveled places as well... which is why things that are new are often exhilarating, filled with both fear and excitement. Had we treated the dangers and also the opportunities of the unknown as non-existent rather than real potentialities for harm and growth, we never would have pushed the boundary to make the unknown, the known, and we would never have braved the unknown for their bounties nor been properly prepared for their peril.

Perhaps, but benevolence could be seen as extending beyond that (and I may perhaps be extending it beyond what Rand meant) in the literal (and religious) sense of "Ask and it shall be given". The real issue is, what are you asking for and by what means are you asking, which is really only one thing... the thing you ask for is the consequence of your means of asking regardless of your intent. You ask when you act, or fail to act. What you ask for, are the totality of consequences of your acting or not acting in the full context of reality. In that sense, the universe gives, in spades. Work hard to understand and master a craft or skill and reality rewards you, directly in response to what you do and how you do it, but what you ask cannot be merely equated with what you wish or intend. Wishing for fish, by looking in an apple tree is NOT asking the universe for fish, intending to get better at basketball by painting pictures is not actually "asking" the universe for skill at basketball... that requires the proper action. Reality gives perhaps when you thought you weren't asking... but in some sense you were "asking for it", even if there were no possibility for you to know it. Even just choosing to remain alive in a difficult to predict world, is in a sense its own way of asking for it.. all of it. And don't be fooled by the idea of not asking for anything. Doing literally nothing is a way of asking ... specifically, for death. Standing under a crumbling cliff, also is asking for death (or injury), and indeed it may be given, more so, if you can shake the rock with a sledgehammer, or have the knowledge to find the right bit of cliff just ready to fall. In a very real sense to reality, which is not "interested" in your good or ill, this is benevolence, absolute unquestioning, consequential benevolence. This is an incredibly powerful idea, especially when one is engaged in seeking the knowledge and experience required to know HOW to ask reality in just the right way. So, the connection between fallibility and reality is precisely in the what and how of your "asking for it". The more you know, the better you can act in asking, and the more likely what is given is what you intend... the greater the causal connection between what you intend to ask for and what you actually do reap from what you do. One thing to keep in mind though, is the distinction between the manmade and the metaphyscially given... in some sense reality does give in a way that other humans do not. Humans can make mistakes and they can lie and evade... they can react very differently when you "ask" of them in the same way... of course you can shift your thinking a bit, and think of human beings as that part of reality which is capricious and whim ridden and prone to error, or you can choose to separate the benevolence of reality itself from your assessment of society and the people in it. I think the latter approach is more intelligible.

That's "affirming", not refuting. Something jams when things cannot slip, and otherwise would: it's just a matter of friction at the contact points, gears/cogs are equivalent to very high friction which does not allow slippage, whereas normal rolling surfaces (wood, rubber, metal etc). when there is an inconsistency of speed between touching surfaces, would tend to skid or slip. True for a "track" which is single rigid object (with a sort of stair step) moving at a single speed. But you could use a double wheel type thing, for example, to slide or feed work pieces, packages, or whatever, underneath it, shallower ones at one wheel and thicker ones at the other. Those different objects would be conveyed, at different speeds. The key I think is to remember the purpose of the exercise is not to impress others or improve other people's thinking (when not asked to) but to clarify one's own. I think in this case the problem is actually ill-posed, and uses a kind of fundamental misdirection. I will try to explain this in a future post. If anyone seems interested.

A good relaying of information in an intuitive manner. I think something equivalent to this is the first thing that comes to mind when most dispel the ghostly paradox. I think it very possible, in some people's minds, with mechanical experience and understanding, no feeling of paradox would even emerge in the first place. Although no one has really touched on this here, nor in a similar thread elsewhere, imagine clock technicians, and factory workers, at the height of the industrial revolution who worked with gears, and wheels, and pulleys, and belts, and axles, gear boxes, and conveyors and all manner of rotating, intermeshing, winding and unwinding, force and distance multiplying components... imagine their working with all manner of these, for 16 hours a day, day in day out for years, maybe working at multiple facilities and seeing multitudes of "contraptions" of various sorts. In such a man, I would bet (and none too little an amount of money either) that the intuitive knowledge of rotation, gear ratios, pulleys, multiple rigid wheels or gears connected to a single axle and the effect thereof, would cause the man to look at the "posed" conundrum, and scratch his head... not for the lack of any knowledge and understanding but for the lack... of any lack of it, and in particular the lack of any "strange feelings" of mystery/paradox/puzzle which others might be eager to have him reaffirm.. but which he simply does not have. Paradox needs some ignorance... not too much (that's simply bafflement) and certainly, not too little.

What I find fascinating about this wheel issue, is that a full enough description of the actual motion of the wheel and its parts relative to the ground and its frame of reference is, arguably (theoretically), all that is required to dispell the apparition of paradox from the mind of one capable and willing to understand fully, for when the confusion at issue is removed and reality laid bare... what else needs to be said? There are different descriptions of that reality with different focii and different levels of completeness, which nonetheless will be sufficient to dispell the misgivings, depending upon the mind in which the irksome feeling of "paradox" resides, the particular form the paradox takes, and the particular sum of integrated and connected knowledges and intuitions of the person, which allows them to, by thier own routes, untie themselves from the Gordion knot. It's fascinating to note that minds differ so much they will argue endlessly whether or not some particular truth told in a certain way about the non paradoxical thing (in reality) is in fact enough to dispell the misapprehensions. That there is so much disagreement over which truth among many "really works" points mainly to the way paradox and misapprehension, errors of the mind, lodge themselves, they must be of widely varying natures and magnitudes. Who am I to say your realization has not led you out of the labyrinth? When I see that I require mine to escape. Many are the different ways our minds are each led astray and knotted up, and so too, many are the different ways which work to lead us each aright and unknot our thinking.

"Fictional problem", in the sense that a "paradox" must involve some disconnect with reality. Reality has no problems, the problems are thus fictional. No hypothetical shape, event, situation, process, system, etc. which is obvious and behaves exactly as "expected" or "intuited" was ever called a "paradox". Neither was anything which was judged too new or too complex to understand. Differential geometry is not a paradox to a musician, it's just something he/she does not have training in and does not understand, but he has no reason to suspect "paradox". A paradox requires an experience that something is amiss... but there are no contradictions in reality (no matter how many opposing forces, collisions or disagreements) there is only existence and existence is identity. So the "problem" is fictional, in the same way an illusion introduces a fiction... reality is what it is, but something about what we see, and should understand, is off kilter, and we know it. At least for those who experience the particular paradox... the feeling of paradox requires a certain thinking process to get a person in the wrong place to sense that disconnect, and in truth, different people are often led in different directions... I think in a sense the more something appears or seems opposite of what one assumes it obviously should appear or seem like, the more paradoxical it is. Since reality is NOT at fault, our sense and assumptions of what things obviously should appear or seem like, IS.

Boydstun: Following up on my musings about the study of mental errors leading to "mirage" paradoxes... How do you feel about engaging one-on-one with me, in a Socratic, dispassionate, impersonal, and objective discussion, aimed at discovering exactly what is going on when one falsely perceives, at first blush or on an intuitive level, an "issue" or "problem" when presented with the kind of "description" or set-up presented for this rolling disc?

You are at an intellectual advantage, whether by nature, nurture, or self made and you’ve shown that once more. I do begin to wonder whether as a compliment or adjunct to philosophy (perhaps it already forms part of it) the study of what leads the mind astray, causes confusion, gives rise to the appearance of paradox etc should not have a more prominent place, perhaps even outranking epistemology (maybe it’s a small subset of epistemology) in importance … it seems to me that insufficient knowledge was never the cause of all the woes of a man or mankind but the over abundance of false impressions and ideas masquerading as knowledge. Perhaps the study of fools is the path to wisdom?

Is it possible to "dissect" the paradox to identify exactly where and how (perhaps even why) one is "potentially" led astray? Clearly, some people were and possibly are of the kind who see this as being some problem or riddle... they perceive a paradox... is it of any use for us to try to understand why? Should we merely chalk it up to a fictional problem in a bad thinker's mind, and dismiss it completely from our thought and effort?

Hello everyone. Something for the Physicist, Mathematician, and Philosopher in each of us. What do yo think about this? https://en.wikipedia.org/wiki/Aristotle's_wheel_paradox

I really like this summary, it is concise, and quite excellent: I really love that! As for this: I cant reword it anywhere near as eloquently as your excellent summary but trying to tie them together I would state that the following is true (however awkward). You can separately evaluate the method as good or bad, insofar as you can judge whether it is consistent with or contrary to principle, but you cannot evaluate an object outside of its context of method, and moreover, you cannot evaluate the object at all when it is obtained by irrational action because it is moral principle that sets the intelligible context (a commensurable standard) for evaluating that object in relation to your other values." WRT breakfast but only by looking at it in the context of how I obtained it... I do not know why I am being so picky about language here... you know what you are talking about and you said the best bits! You win! Again an excellent summary !

How are the intermediate steps of the terraforming as such actually profitable? A process of baking bread involves spending resources and energy, all in negative territory, on a moderate timescale... gathering together, mixing ingredients, kneading, assembling and then baking. For at least (let's just say it's an hour) the whole process is complete outlay of effort, energy, resources, i.e. its all spending/investment... profit is only possible once the bread is baked. It then has a greater value than the separate ingredients etc. (otherwise no one would bother to bake bread) and a profit can be reaped from the investment of time and effort etc. WHAT IF... terraforming is just like that... except the time scales for expenditure before any return is possible, is much greater than the life of any person? WHAT if the sheer amount of energy and resources FAR exceed anything a tourist shop, space tours, or MacDonald's toys might earn? An eight year old could promise to move a mountain one shovel full at a time, and do a song and dance about how selling lemonade at its base (as well as with your investment) will fund the endeavor in stages, starting first with him before he hires a "crew". I would suggest you not count on any actual return on investment promised in connection with the actual moving of the mountain being complete, but think of the entire thing as an investment in a lemonade stand business... because that is the only thing you would actually be investing in or getting anything back from.