ishmael

Why is it better for the batter to hit a pitch a little distance down from the end of the bat, rather than close to the end, where the bat speed is clearly greater? It happens in almost every game. The announcer will say the ball didn't go as far because "he hit it off the end of the bat". How would one calculate where the sweet spot is?

Its not so crowded. If all six billion people were to gather into a crowd, fairly tightly packed at about six square feet per person ( about what you get in a movie theater), we could all fit into Rhode Island. Parking would be a hassle though.

Please indulge my naivete here. Is Einstein's famous equation a precise statement of the relation of energy and matter?, or is it just a way of saying there is a whole lot of energy locked up in matter? I just don't understand why the speed of light is used as the multiplier here. And what is the unit of energy that is the result of this multiplication? ergs, joules, volts.....?

These are drawings that Galileo made of the moon after turning his newly built telescope on it. http://outreach.atnf.csiro.au/education/senior/astrophysics/galileo.html Why did he draw such a poor likeness? This is not how the moon looks, either to the naked eye, or through a telescope. There is no big mountain range down the middle, with a giant round crater near the bottom. Is it because he was not used to a telescopic view? Or was there an agenda that distorted his view, or his drawing? Why not show the moon as it is? What was going on here?

Suppose you want to prove the statement "All crows are black". You can't do it logically, it has to be done empirically. One way is to go out and look at every crow and note its color. Every black crow would be a confirming instance of the statement, and increases (however slightly) the likelihood of the statement being true. The more black crows you see, the more likely the statement is to be true. The statement could only be proven if you could examine every crow and find that each is black. Now consider this: The statement "all crows are black" is the logical equivalent of "all non-black objects are not-crows". So if you go out and see a purple cow, that is a confirming instance of the statement, and increases the likelihood of it being true by an infinitesimal increment. But... a purple cow is also a confirming instance of the statement "all crows are white". How can one thing increase the likelihood of two opposite statements being true?

This is the only book I have read three times, over the years (30?). The author also wrote a follow-up book, called "Lila", wherein he expands upon his philosophy, the metaphysics of quality. It is more challenging than Zen. There is also an online community of Zen discussers.

I would submit that it is sometimes difficult to draw a line between selfish and selfless acts, even without considering whether it benefits the large Self of shared genes. We are social beings, often susceptible to the need for approval. The "selfless" act can be done with one eye on the resume. Is it too cynical to believe there is no such thing as a totally selfless act?

Isn't the question "how long does it take to fill the bucket"? Not how long does the faucet run. The bucket doesn't start filling until the first water enters it. Its true that the if the bucket is far below the faucet when the faucet is turned on, there is a time lag before it starts filling. Same for when you turn the faucet off, i.e. there is a time lag between turning the faucet off and the bucket being filled. If the bucket is close to the faucet, that water goes in with almost no delay. So there is a time difference in water entering the bucket. The shortest time to fill the bucket would be starting with the bucket low down, and finishing high up, and vice versa.

How does an atomic nucleus form if the charges are all positive? Why are the electrons not drawn into the nucleus? Are the regular laws of physics superceded at the atomic level? Does this sound bogus to anyone else?

There are some experimental sailboats that have been built using a tilting keel, adjusted with a powerful hydraulic ram inside the boat. I don't think any of these have wings on the keel, but they do have a ballast bulb at the tip of the keel. It works better than a fixed keel to keep the boat upright, but is very expensive and complex, and much more prone to problems than a simple fixed keel.

I think it takes more energy to produce the hydrogen than you get from using the hydrogen as fuel. Same thing with ethanol from corn.

The oblique angle doesn't change the question. The winter solstice has the most oblique sun angle, but its not the coldest day. The length of days and angle of the suns rays change in tandem. The lag is still the question

Today is the first day of winter. The shortest day of the year in the northern hemisphere. But it is not, on average, the coldest day. The coldest days come in January and February. Why the lag? I would think that least amount of sun should result in least amount of heat. The same lag happens after the summer solstice - the hottest days follow by a month or more. Obviously something other than the amount of sunlight is causing this. Is it the moderating effect of the oceans? I know the water takes longer to heat and cool than the land does (thus the sea breeze at the shore), but does it lag by a month or more? Is there something else?

I think the itch is the body's reaction to whatever the irritant is. The body produces histamines locally, and that is what causes the itchy feeling, not the insect bite or poison ivy or whatever. You can fool your body into producing excess histamines at the site of the itch by applying heat. But the body can only produce a certain amount of histamines in any limited amount of time. By applying the heat, you actually cause your body to use up all the histamines in that area for a while, and the itch stops. When the body has time to produce more histamines in that area, the itch returns. This is very useful information if you want some temporary relief, to get to sleep, say.

Perhaps I should have stated that the sphere must be at least 6" in diameter, but I believe that is implied in the original problem, as stated. What is amazing to me is that the answer is unique for all sizes of spheres, from 6" up to the size of the earth, and beyond. A six inch long cylindrical hole drilled through a sphere the size of the earth would be shaped as a 6" thick disc of approximately 8000 miles diameter. It would leave a very thin ring of material six inches wide and 8000 miles in diameter. This ring would have the same volume as a six inch diameter sphere with a cylindrical hole of zero diameter. Do the math. Amazing, no?

There is a unique answer, identical for any size sphere.

The education system in the USA is regularly attacked for being second class, at best. Many reasons are given, most reflecting the particular bias of the observer - teacher unions bad, parents coddle kids, too much homework, too little homework, too many video games, etc. I heard someone say that we, as a society, don't really want to fix the system, because if we had truly educated citizens, who would buy all the crap? And we do buy a lot of crap in this country. Its a huge part of the economy. Is this a conspiracy of some sort? Are we all complicit? Or is it just the way we have evolved as a society, with now so much inertia in the manufacturing, advertising, distributing, and consuming of this mountain of crap that we can't turn the damn thing around without a revolution or collapse?

This is from an old Martin Gardner book. A six inch high cylindrical hole is drilled through the center of a sphere. How much volume is left in the sphere?

Yes. that is a reasonable assumption, and makes the problem solvable. So what is your answer?

They get home 10 minutes earlier than usual. You are on the right track.

Yes there is.

A man takes the same train home every day, and his wife drives to the station to pick him up, meeting the train exactly as it arrives. One day he catches an earlier train, getting to the station an hour early. Its a nice day so he starts walking along the route that his wife always drives. She meets him along the way and drives him the rest of the way home. They get home 10 minutes earlier than usual. How long was the commuter walking?

"Now we are all sons of bitches." Oppenheimer after the first successful test of the atom bomb.

Some time ago I came across a description of a numbering system for some very large numbers (mind boggling, in fact) that involved numbers written within triangles, squares, and circles. I know it was a shorthand for some exponential calculation, but can't remember exactly what it was, and I can't find the reference - it was in a random book in my local library. Any help? Thanks in advance.

Do all of the symbols have to be used? Can you use ! (factorial)? Or exponents - e.g. 3 to third power is 27?