You could probably even figure out the sum of all paths by using a geometric series.
But are these answers valid if the ring of points lies on a discontinuous surface, of if the surface is unwalkable?
If an engineer doesn’t know why he should be building something, then that something should be avoided. If he can’t explain why he designed a bridge in a particular way, then stay off the bridge! If his boss can’t explain why a bridge would improve traffic patterns, in some quantitative way, then it shouldn’t be built either. When these conditions are violated, it’s usually for the benefit of someone besides the engineers. A well trained engineer would not build a bridge to nowhere, or allow an unsafe shuttle to fly. These decisions are made by people who answer to social and personal pressures but not science or engineering principles. Part of the problem is greed, but another part is ignorance. Both will be big problems with AI, and studying humanities will not allow anyone to intelligently decide whether a particular machine resembling AI should or should not be built. They have no standing under which to make an argument. You can’t simply expect them to spew out some philosophy and convince a legal body that they understand the consequences of the machine better than those who designed it, and can quantify its purpose and abilities. You can’t effectively regulate what you don’t understand, and you won’t understand anything resembling AI in any meaningful way without some technical background. The precautionary principle is your only regulatory hope, and realistically that isn’t going to prevent AI malfeasance. Since we don’t know what this AI will look like, the answers to which technoligies should be suppressed must be picked up as its designers and observers go along. A solid background in science can’t just be picked up as you go along, if you’ve ignored it your whole life. But with a good background in some scientific area, other scientific expertise can be readily picked up along the way. I have no background in chemistry but now I work in a lab where biochemistry is a main focus. I’m picking it up to research level, but that would not be possible with a pure education in humanities. And the implications of any technoligy I may create? How could I expect someone to understand those implications without understanding the technology?
If critical thinking involves "knowing" when to apply equations, then critical thinkers must have experience applying equations. That comes from STEM education and not humanities. Understanding people and their motivations is surely important for selling stuff, and many other things. Fortunately there are (arguably) sciences that deal with these subjects directly - psychology and sociology.
And then you have to change it every three months. And not to anything you've used in the last decade.
That's to make you appreciate all the hard work involved in keeping with the diet - counting calories, reducing caloric intake month after month, huddling with a nutritionist, extra exercise and lots of yoga. Also there is stigma involved - some people have a very negative view of crossfit, and hate paleo by association. Some people just think that only an idiot would remove entire classes of food from their diet. Vegans avoid paleo because it involves eating animals or animal products.
Still, Hell no. It's fairly new and expensive, so every lab in the world is not going to have one. But it's commonplace enough that if it's used to support a result, it's not necessarily even advertised in the abstract. These results are cited by other labs as inspiration and support for their work, which in my view counts as usage. Moreover, its usage and acceptance has grown much faster than, say, the confocal microscope.
My altered state of consciousness is a superposition of worlds where Sagan is both right and wrong.
Veracity is not a property of an academic journal. It can refer to a statement. For an example of a statement lacking veracity, consider the assertion that 'does not produce fatal overdoses' is an adverse effect of cannabis.
The number from your rectal studies institute is probably more correct. The total number of people that have been imprisoned is likely much less than the number currently in prison.
Here are a few high-profile citations from the last year. Super-resolution microscopy on fixed cells is a big deal. That's not an argument against its worth. A technology need not satisfy all your wishes to be extraordinarily worthwhile. Current practices on a commercial system do not necessarily limit what is possible in a research setting. http://www.ncbi.nlm.nih.gov/pu... http://www.ncbi.nlm.nih.gov/pu... http://www.ncbi.nlm.nih.gov/pu... http://www.ncbi.nlm.nih.gov/pu... http://www.ncbi.nlm.nih.gov/pu... http://www.ncbi.nlm.nih.gov/pu...
Hell no. STED is widely used by neuroscientists. It has more than proven its worth.
So when banks routinely traded the fomc minutes in the milliseconds before the transcripts were released, we were only allowed to suspect an illicit symbiotic relationship?
Many moons ago Bernanke admitted that the fed has abetted LIBOR manipulation. It is therefore not news that the fed permits large-scale theft by banks. The news is that Goldman makes the underlying decisions, which is not really news, but signifies a shift in popular culture from conspiracy theory to conspiracy fact.
He seems to be arguing that diet and exercise do not improve quality of life before 75. I have news for this arrogant egghead who is obviously spoiled by his own good health: many of us NEED to focus on these things to maintain a decent quality of life before 75. It's not some silly obsession to cheat death. We must do this precisely because the modern sick-care system sustains the cushy status of bioethics "experts" who do very little to rein in the food and pharmaceutical companies who are responsible for the proliferation of widespread, chronic diseases such as diabetes, especially among the poor. This system fails those of use who are cannot adapt to some part of the modern industrial food and chemical complex. We're on our own, there are a lot of us, and obsessing about these things has been the only way we've been able to get our health on track. So instead of belittling the health-conscious, how about calling out public schools and TV advertisers that flood kids' minds and bodies with processed junk snacks? How is this different than passing out crack?? Why would anyone believe that poor diet and lack of exercise will have no effect until age 75, aside from an egocentric lack of personal experience? What kind of fantasy world is this guy living in?