OldChemE

I think there is a careful distinction to be made. "getting back" at some one can lead to a bad situation, and anger that cold hurt you. One the other hand, if the person showing intolerance and hatred can be made to experience the logical consequences of their behavior, benefit can result. This is much the same situation as crime and punishment. The legal punishments established for certain crimes are (in theory at least) balanced by the severity of the crime-- and are fair. Revenge, on the other hand, is not considered right. When I was teaching it was not uncommon for individual students to behave badly toward others on occasion. As a Teacher, I did not let the students "get back" at the individual, but I did apply school-sanctioned punishments, so that the intolerant student experienced consequences that were clearly connected to their behavior.

Fiber does not necessarily mean poor nutritional foods. For example-- eating lots of vegetables (particularly things like Broccoli) will give you plenty of fiber. Certain fruits and beans provide a similar benefit in terms of fiber. All you need to do is eat a little less meat and fewer highly processed foods.

Logically, your equation should work fine. It is mathematically equivalent to multiplying the number of elements in the sequence by the mean number of the sequence, which always gives the sum. To see why, lets look at this set: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. To get the sum we could add 10+1, then 9+2, then 8+3, 7+4, 6+5.... all of which add to 11. The mean of the sequence is 5.5, which is just (10+2)/2. If we multiply this mean by the quantity of numbers in the set (10) we get 55, which is the sum of 10+1, 9+2, 8+3, 7+4 and 6+5. The equation that corresponds to my example is ((n+k)/2)(n-k+1), and your equation can be manipulated to match this equation.

Those who pass laws must be 100% subject to the same laws. For example, Retirement systems and medical care for legislators and government officials have to be within the Social Security and Medicare systems. If they had to depend on it they would be more likely to try to get it right.

If you look at the history of earthquakes in Southern California you will see something very interesting. The San Andres fault has a sort of "dogleg" or hockey stick bend in Southern California. The pressure from the northward movement of the Pacific Plate, along the San Andres fault, pushes against the dogleg. On a diagonal line roughly to the Northwest from this dogleg, there is a history of additional earthquakes, not on the San Andreas fault. From an engineering perspective, it is as if the pressure at the dogleg is stretching the crust to the northwest, or maybe even (some day) forming a new fault line to the northwest branching off the San Andreas fault. The Ridgecrest Earthquakes were on this diagonal from the San Andreas fault.

I see the logic behind your point-- its a good one. I just think that in science we are not nearly as close to the point of knowing as much as there is to know. When it comes to ultimate knowledge I think we are barely to the beginning of the "S". Of course, I realize I cannot prove this.

Yes, but history shows that here is a new "S" curve for each new technology. As long as Science is used to discover we will likely continue to produce more "S" curves. One very exciting thing about Science and Engineering is that we do not yet know what we do not know.

We've been seeing similarly cooler summer days in my part of Northern Nevada. But-- to my view it seems to correlate to global warming. What has happened is that the past couple of winters, especially this last one, have been much warmer. 9 years ago, when we moved here in retirement, we hit nightime lows of -25 F on several occasions, and had snow. This past winter we rarely dropped lower than +10 F, and had very little snow. Instead, we had lots of rain, and the rain continued into the spring. Now we have groundwater at the surface, and frequently the evaporation builds unseasonal cloud cover-- so we are seeing slightly cooler days than normal for the summer. To my relatively untrained eye it looks to me like the overall warming (and associated evaporation) is bringing more moisture to the high desert and the effect of that moisture is to moderate the extremes-- giving warmer winter/cooler summer.

I cannot see how any of the above statements logically follow from the definition of Emotional Intelligence. Maybe I have the wrong definition?? According to Wikipedia: Emotional intelligence (EI), emotional leadership (EL), emotional quotient (EQ) and emotional intelligence quotient (EIQ), is the capability of individuals to recognize their own emotions and those of others, discern between different feelings and label them appropriately, use emotional information to guide thinking ... Emotional intelligence - Wikipedia It seems to me that a high capability to recognize ones own emotions and discern the emotions of others would be very beneficial to relationships.

hint: Look up the rational zeroes theorem, then look at synthetic division, and work from there

Perhaps the way to improve peer review is to not make it blind. Circumstances are admittedly different, but I once worked in the Nuclear power industry, and every engineering document was required to be verified by a separate engineer. This was a form of peer review. The difference was that the name and signature of the review engineer was placed on the publication along with the name and signature of the originating engineer. If the document turned out to be wrong, the reputations of both the originator and the reviewer were on the line.

You haven't said whether these numbers are the result of a specific calculation, or whether they are experimental observations. They very much appear to be exponential decay, but not all the numbers fit perfectly. My scientific calculator suggests that a reasonable mathematical model (assuming exponential decay) could be y = (2870)*(0.576)^x, where x =1 for the first term (the 2025 term). Exponential decay does have a long tail as you suggested.

The amount of matter in a sphere is only proportional to the cube of the radius if the sphere is of uniform density. It is the volume that is proportional to the cube of the radius. If the density if not uniform, the relationship is totally case-dependent. Either way is says nothing about a "preferred location." We don't have to be where the planet is if we are someplace else-- such as in orbit.

Early man was essentially powerless in nature. He could hunt and forage for food, build shelter and care for a family, but he and his family were largely at the mercy of the natural elements. Having the intelligence to be dissatisfied with this situation, man began to wish for something better and to visualize beings who had power over the elements and did not have human limitations. This is the origin of Gods. Thus, early gods tended to reflect the needs of mankind: Gods of the hunt, the harvest, and of all things good in life. As mankind grew and developed into larger tribes and had territorial conflicts, the Gods of battle and war emerged-- because a warrior who could win was what mankind needed. As man recognized the limitations if death and yearned for more life, gods became immortal. When civilizations developed and mankind had a better lot in life, such as early Grecian and Roman societies, mankind yearned for pleasures that the moral standards of society tended to limit, and the immortal gods emerged that had to power to have limitless love affairs and debauchery. In simple terms, our Gods have always tended to represent the things we wish we could have in life but cannot always have due to our human limitations.

Omnivore for sure. I love veggies and meat. I try not to eat meat from any animal with an encephalization quotient over about 1.

Agreed. over a very short distance two great circles could appear to be parallel, but still ultimately converge.

I'm not certain-- but I try. The internet makes it possible for people to say things and be aggressive in ways that they would probably never do in face-to-face conversations. I try to avoid this and behave in the same manner I would in conversations with friends. Civility is important to me.

Whether or not parallel line converge on a sphere depends on how you define parallel. If you define parallel classically, as two lines of which corresponding points remain equidistant (such as latitude lines on earth maps), then they also do not converge on the surface of a sphere. Lines of longitude (again speaking in terms of maps) might appear to be parallel on some maps, but they are 'great circles' and are not parallel.

There is nothing inherently "unclean" about sex as an expression of love-- sex is simply one valuable facet of a successfully intimate relationship.

The title question and the discussion seem to be at odds. Parallel lines (the title question) being massless creations of geometry do not converge-- ever. The only exception is in art, where an artificial convergence point is selected for parallel lines in order to create the illusion of perspective. But, in fact the parallel lines do not converge. Beams of light, on the other hand, being subject to gravity, would presumably converge at some point (assuming they started out parallel but close enough for the very small gravitational effect to bring them together). The problem is proving this by experiment-- for all the reasons given above.

I appreciate the responses-- but I don't think the question has been answered. If x = 1 and y = 3 then the GCF of x2y2 becomes 9, which does not satisfy the constraints of the problem. If x = 3, then the GCF of both terms becomes 81, which does not satisfy the constraints of the problem. If x = square root of 3, then the GCF constraint is satisfied, but x then is not a positive integer, which violates the other constraint of the problem. I'm still trying to understand how both constraints of the problem (x and y both positive integers, and the GCF of both terms = 27) can be satisfied with the available answers.

The arrangement of elements in the periodic table was done before we had extensive knowledge of electron orbitals and all that. The original(s) of the periodic table were based on atomic weights and the reactive properties of the elements, not their electron structures. The Halogens all have nearly complete outer electron shells (missing only one electron), and are rather aggressive about stealing an electron to fill that outer shell. Thus, they tend to form ions with a -1 charge. That led to the classification called halogens. Technically, Hydrogen is also just 1 electron away from filling its outer (and only) electron shell, but Hydrogen usually (but not always) gives up one electron forming a +1 ion instead of stealing a second electron-- a behavior more like lithium, sodium and the others in its group.

In my spare time I work as a substitute teacher. In High School math today, students were working on a standardized practice test to prepare for the ACT exam. The following question baffled me. Given x and y are positive integers, such that both x2Y2 and xy3 have a greatest common factor (GCF) of 27, which of the following could be a value of y? The available answers are 81, 27, 18, 9 and 3 I ruled out 81, 27, 18 and 9 as values of y because in all cases y2 would be greater than 27, so the GCF could not be 27. It appears the intended answer is y = 3. However, if y = 3, then x2 y2 becomes 9x2. In order for this to have a GCF of 27, x2 must contain at least one factor of 3. If x2 contains a single (or odd number) factor of 3, then x must contain a factor of square root of 3, and x will not be a positive integer, which violates the problem statement. If x2 contains two (or an even number) factors of 3, then x will contain one or more factors of three, and the GCF will be at least 81, which violates the problem statement. What am I missing?? Any thoughts? Thanks

I too agree that given sufficient time the works would be reproduced-- but there is no guarantee that the works would be produced in any finite time. The catch is that, if the letters are being produced at random, multiple repetitions of previously produced patterns may occur. In other words, this is different from a computer produce methodically working through all the permutations of letters. Thus, we can posit that the works of Shakespeare will eventually be produced but we cannot know that it will occur within any arbitrarily large finite time.

he example of 6 + 6, 4 + 8 and 8 + 4 is different from 6 bolts and 6 nuts, 4 bolts and 8 nuts and 8 bolts and 4 nuts because the first set are pure numbers, the second are things. In other words, let x = bolts, y = nuts. Then your two examples form to : Numerical equivalence: 6 + 6 = 4 + 8 = 8 + 4 But for nuts and bolts 6x + 6y does not necessarily equal 4x + 8y which does not necessarily equal 8x + 4y Said differently, that which holds with pure numbers need not hold when representing numbers of things.