Here's something to ponder. Assuming the Riemann Hypothesis is true, would that monkey type out a proof of the RH before it got to Hamlet? I guess it depends on if the proof can be expressed in fewer words than the word count of Hamlet.
My wife had knee replacement surgery two weeks ago. She was given an epidural for the procedure and it worked well for her. Our two children were born back in 79 & 82 (20th century) and epidurals were available but only as some sort of last resort so she did not get them.
Science is partisan, at least the 'science' being addressed in this article, because the funding for this science comes from a finite source and there are competing demands placed on this finite source. As any competent scientist knows, taking something from a finite source leaves less in the source. There are differing ideas and beliefs, some partisan (including those of the esteemed Mr. Colbert), on how best to divide up this finite source.
Oh if religion wasn't responsible for "massive cultural destruction" then mankind would have invented something else to do it (whatever is meant by "massive cultural destruction").
Please include me also in contacts. I developed anosmia about 8 years ago (well before COVID). I truly wish there were some sort of 'cure' that would restore even a small amount of my sense of smell.
This is good news considering that the Galapagos Turtle is endangered. The mom has been in the Philadelphia Zoo since 1932 and has never had offspring till now. Here's to wishing the children a long and healthy life and many children.
Thanks for the reference to the video. I watched it a few weeks ago and was befuddled by it. How can the ball just randomly start rolling in a random direction? It seemed to me that an obvious explanation would be that there is air flow in the environment and with the ball balanced in an unstable position that some air movement would easily nudge the ball off balance. I understand the diff eq of motion with the singularity but it seems to me that a ball balanced at the apex of any radially symmetric convex surface would eventually commence rolling, due to fluctuations in the air flow.
It is more than a little disappointing that a solar plant in the desert cannot survive. While birds, who were killed at the plant by the thousands each year are rejoicing, those of us who seek a cleaner form of energy have been dealt a significant setback. Can industrial scale solar be made to work barring some new more efficient method to turn light into electricity?
What am I missing? I can sit in my den and watch SpaceX and now Blue Origin launches, in real time see the telemetry data, see stage separation, reentry burns, etc, etc. As for Saturn V, to quote the Byrds "I was so much older then..." but I don't recall any of that. Doesn't film require taking the exposed product to a lab for after the fact processing? While the Blue Origin images this morning were not nearly as good as the SpaceX, to me the images are absolutely incredible. I am a serious amateur photographer and I do still shoot film on occasion but I see little dynamic range differences now in 2025.
I love this CGonaB site. I used it several times myself including for my similarly titled "Go west (not so young) man" diary documenting my XCountry ride in 2007. I didn't own a cell phone then (did they even exist then?). I used paper maps and had a small laptop to make my diary entries. I generally did them sitting outside town libraries (they were usually closed in the evenings when I arrived in towns) and most internet sites then were non-password and publicly accessible. I haven't made any documented treks since 2012 but still send the website money. You can see my "Go west..." diary here:
https://www.crazyguyonabike.com/doc/?o=3d2&doc_id=2579&v=LL
Well, the OED definition of 'recall' is "official order to return to a place" and a software update or fix requires no return to the place of purchase. I wonder how may legally defined 'recalls' Microsoft Windows has experienced with each new version.
It's a shame the title begins with 'Mathematica', makes one think the book is about the Wolfram software. That's the first thing I thought of when I saw the title. Hopefully Wolfram doesn't sue him for copyright violation or some such infringement.
"...anyone else would have handled it differently", yes, and very likely we would not have gotten the COVID vaccine as quickly as we did and hence Biden would not have been able to set us out on the road to the pandemics end (and been able to come out of his bunker). Who knows how much longer the pandemic would have lasted and how many more might have died had Trump not cut out the red tape and fast-tracked the pharm industry on the road to a cure.
It would be interesting to see a comparison of lane effect, say for instance, re-running a race after let's say a weeks rest with the top finishers now nearest the side walls and the lowest finishers in the center lanes. Oh and for incentive, let's say the average of their two times determines the winners.
Today's Wall Street Journal (Jun 20) has an article "Europe has a new Economic Engine: American Tourists", where this is written:
"While Germany’s economy is flatlining, Spain is Europe’s fastest-growing big economy. Nearly three-quarters of the country’s recent growth and one in four new jobs are linked to tourism."
I have never run into this alleged issue. In fact, we have several times booked AirBnB homes in the town of my youth and hosted Thanksgiving Dinner for my elderly mom and siblings who are themselves visiting and staying in AirBnB's. Yes, we asked the hosts before booking if we could cook and host a Thanksgiving Dinner and received their OK.
I truly love AirBnB and have stayed in them in most all my business and pleasure travels to Europe, Canada, Israel and across the USA.
Yeah, or the Wash Post or NYT or MSNBC. As for Fox, listen to the Howard Kurtz show on Sunday mornings, he provides a nice, dare I say "fair and balanced", analysis of media coverage of news stories from the previous week.
Can't all these many people who want the technology purchase it today? I think for every new hobbyist that comes along only because of this saw there will be five less hobbyists who stay away because of cost.
One can do this mentally easily enough. 52! = 525150....321, and there are 26 even numbers in this progression, so we have 26 powers of 2. Taking them out, there are 13 of those even factors divisible by 4, but we already took out the first 2 from each so we have 13 more 2's, giving 26 + 13 = 39. Now on to factors divisible by 8, they are half of those that are divisible by 4, so half of 13, giving 6 more 2's (52 is not divisible by 8 so we round down). Thus so far we have 39 + 6 = 45 two's in the factorization of 52!. On to numbers less than 52 that are divisible by 16, that's half those divisible by 8, so 3 more, getting us to 48. Finally there is there is the factor 32 = 2^5 of 52! giving us one more 2, hence 49. i.e. for p a prime, the largest k such that p^k divides n! is given by k = Floor(n/p) + Floor(n/p^2) + ... + Floor(n/p^t) where p^(t+1)>n
I must have missed something since the title of the linked IEEE Spectrum article calls out MIT and IBM yet the text of the article says nothing about either. The only source mentioned is the lead researcher who's from Georgia Inst of Tech.
Another excellent math youtuber is the mathologer. He has humor, great graphics, clear explanations, all while expounding on challenging topics. Here is a representative sample
https://www.youtube.com/watch?v=LFwSIdLSosI
With more and more cameras everywhere we are coming to the end of the "who done it" investigative novels and movies and TV shows - at least those set in current times. Who needs a Sherlock with amazing logic and investigative skills when all the police and investigators need do is get recorded camera data. Police shows are becoming boring as they simply go from one camera to the next to discover the perp.
Yes, we have increased safety, and those intending to do us harm have less assurance of getting away with it, but something is lost (I'm not sure what it is exactly) in the knowledge that as we go about our lives we are being continually watched and there is less and less potential mystery and uncertainty in what's taking place around us and/or by us.
A few years back I attended the RSA Conference in San Francisco and stayed at an AirBnB in Haight-Ashbury district. I discovered a nearby restaurant, Zazie, that advertised on their web site they were "proud to be tip free" so I tried it. I had dinner there more than once over my week stay in SF and it was so nice to get a credit card receipt with no space for tip and a reminder from the server that no tip was wanted. The service was great and the prices did not seem excessive compared to other places.
Many of the comments here have discussed how without tips paying a living wage would compel higher prices. I ask, what's the difference between a higher up-front price on the menu for the item or a lower price with the expectation that at payment you'll pay 20% more? I prefer the simplicity and less pressure of a bill with no space for "tip", that the price you see on the menu is the price you will pay when finished eating.
Despite some discussion regarding blur and ghosting over 3 exposures, I am unable to grasp how the shown photographs of people have no blur given each is constructed from 3 distinct exposures. The time for the 3 exposures must have spanned minutes despite being outside in sun with each individual exposure made at a reasonably fast shutter speed. How did the subjects manage to stay perfectly still? The group photo of children in a grassy meadow has them in various positions, some awkward, yet they are all quite sharp. How can kids stay perfectly still in those various positions over 3 large format exposures?