Not your usual #science #blog

well this is of course a wonderfully written address

It makes a very good point of why we should be teaching mathematics better, and why we should be teaching better mathematics. It wonderfully describes the pleasures and challenges and necessity of learning new mathematics. It is absolutely correct about how we should approach and treat the students who are interested in mathematics.

it also does absolutely nothing to address professional mathematical research. This article is not about or for people who are at or beyond PhD level.

“Math is very important because iPhones and gravity”, we and the students are told. I highly doubt that chromatic homotopy theory has or will ever have any impact or importance for anyone outside a hundred people community of like-minded mathematicians. As much as I hate the “if you can’t explain to your grandmother argument…” it does have a certain merit, but the moral should not be “then you don’t understand what you’re doing” but “you are probably in a historically wrong field”. 

Of course math is wonderful and beautiful and important….Except that not all math is beautiful – and most “live-action” math is far from being so. Math is beautiful because we polished it over dozens of years. Not a single theorem that you prove in grad school or beyond will be beautiful. Maybe someone in 10 years will rediscover it, put it into a broader context, apply newly-established techniques, write a textbook, and two generations later some students will read your theorem and marvel at the beauty of math. You won’t. You will hate your theorem for not being beautiful – because at that time it won’t be.

Except that not all math is important. Do you think that all the math we learn is all the math there ever was? Do you think that every PhD thesis that has ever been written is a small part of a small proposition is one of your textbooks? 

I hear that argument often – yes what I’m doing is not immediately important, but it just means someone else will not have to do that, can build on that etc.. But do you really believe that? Do you really believe that there is a certain uniform progression in mathematics, and that every single brick laid down by every single PhD student is a foundation for something that will some time in the future be used by someone outside the narrow community of experts? If so, godspeed. I hope you have great time in grad school (but you probably won’t). 

SpaceX Falcon 9 first stage in the final moments of its flight during the launch of the Iridium-1 mission earlier this month.

Carrying a total of ten Iridium-NEXT satellites, Iridium-1 starts the process of replacing the legacy Iridium satellite phone network. These satellites have much longer design lifespans, higher bandwidth, and can handle far more traffic than their predecessors… and the lack of the large polished aluminum transmitter plane arrays will finally eliminate the infamous “Iridium Flares” that have plagued stellar photography and observations for the last 20 years.

Roaring aloft from Vandenburg AFB’s SLC-4 at 9:54am PST, the Falcon 9 headed south out over the Pacific Ocean with the ten satellite of the Iridium-1 mission safely tucked away in the fairing atop the second stage.

The first stage carried the second stage and payload through the thickest part of the atmosphere and added about 1/7th of the downrange velocity needed to reach orbit before detaching and flipping end-for-end and firing three of its nine engines for several seconds to reduce its downrange velocity and put the stage on a rough course for the targeted LZ, the Autonomous Spaceport Drone Ship (ASDS) “Of Course I Still Love You”.

This was followed by the entry burn, a unique aspect of the Falcon 9 mission profile. Due to the high speeds of entry and the lack of a high-performance thermal protection system, SpaceX has adopted what the industry calls “hypersonic retropropulsion” to protect the first stage as it reenters the atmosphere. This slows the stage from 6 times the speed of sound to about 2.5 times, and provides a much finer trajectory correction to help put the stage on track for recovery.

While all this excitement is happening with the first stage, the second stage has been pushing to orbit, going from about 1km/s to, at this point, around 5.5km/s. (For those of you who don’t know metric, that’s REALLY freaking fast.) The fairing which has protected the ten satellites of the payload has been ejected, as it no longer needed to keep even the most tenuous wisps of atmosphere off the satellites.

Back at the first stage, the four sets of grid fins at the top of the booster have steered the stage to a pre-determined point in space above the ASDS, and the centermost engine lights for a fourth and final time. With a maximum thrust of nearly 100 tons, the engine provides an incredible thrust to weight ratio at this point in the flight. As a result, the engine is throttled back to around 70%, which is still a staggering 70 TONS of thrust… which is still more than the stage weighs!

Careful management of that thrust allows the onboard computer to put the stage at a dead stop right as it touches down on the ASDS, and the stage has successfully been returned to Earth.