Mathematicians From The United States

"Stretching zones allows... buildings of different shapes using the same kinds of components."

"[[w:Recursion|[R]ecursive]] growth... In the case of... five fold symmetry there isn't uniformity. ...Instead of reproducing itself... it becomes steadily more intricate."

"The regular polyhedra are like seeds from which growths may appear. They are the connecting joints for the zonohedra."

"Zonohedra have bands of parallel edges. Any such band... can be stretched to alter the shape of the zonohedron. Stretching the band... does not alter any angles."

"The and the are duals of each other—the vertices of one match the face midpoints of the other and vice versa."

"The more you examine properties of objects and phenomena the more you find yourself presented with a few terms, usually simple, from a long series of terms. Often you cannot touch the terms which are further or lower in the series, but you can define the properties which they have. One gets the feeling of living in a container—one of an infinite number—to which are shunted objects and phenomena which have passed through one filter but can't pass through another; a great process like that which takes place in a gravel yard, only we are unable to see gravel other than that of our own size but sense that it exists in endless different piles beyond—everything from sand to planet sized boulders."

"The icosahedron and the dodecahedron have five fold symmetry. They cannot occur as crystals."

"The , because of its shape and the arrangement of its structural members is extremely strong, but its uses are limited because of the inflexibility of its shape. It is always part of a sphere... any variation would destroy the structural properties... It is complicated in structure and simple in shape. Zomes are simple in structure and complicated in shape."

"The joint must... be strong and inexpensive. If the joint is a ball and the A, B and C connections are... holes which the members screw into... holes of the same type... and the ends of all structural members are identical. ...[Y]ou can't make mistakes..."

"The graphs which demonstrate a huge dependence on fossil fuels are fine in one respect. They are alarming. But they are... [m]isleading... [in] that they blind people to obvious answers and prime them to a frenzy of effort in poor directions. Attention... to such... trains people to attempt to deliver what is shown in these accounting systems rather than what is needed."

"If you... remove the electric clothes dryer and install a clothesline the consumption of electricity drops slightly, but there is no credit given anywhere on the charts and graphs to solar energy which is now drying clothes."

"If you... ride and graze a horse... the horse's energy... does not appear on anyone's energy accounting."

"[W]e haven’t had the money... to tool up to manufacture the parts for the playground climbers on a competitive basis. The people... simply can’t afford to buy them. ...[T]hey just can’t hold their own in the market and so we’re not building them anymore."

"[T]he beadwall insulated window panels... this wonderful invention of David C. Harrison’s... a kind of super curtain that... transform[s] a clear dual-panel of glass into an opaque, well-insulated wall and back again."

"A few years ago Peter Van Dresser mentioned the Clothesline Paradox."

"Peter Van Dresser... built a solar heater here in New Mexico in 1956 or '58. We published his book, Landscape for Humans. One of the greatest forces... has been Harold Hay from California. ...I ...heard him in ’68 at the Solar Energy Conference. I had... a design and... modest success... Harold showed everyone... dead simple methods of doing the same job. He... completely changed my head around on how to attack these problems. ...[W]e’ve worked together a lot since then trying to bring some reforms into the Solar Society."

"I went to in Massachusetts for a couple of years and I went to UCLA for a year or two and then I went back to Amherst... I never quite fit... that... college thing. ...I joined the Army in 1960 and got married and Holly and I went to Germany... after I got out of the Army, I went to school in ."

"[W]hen you're experimenting, about 80% of the ideas you try are failures... But we put all these concepts together and they performed the first time. ...[W]e had pretested most of the ideas we incorporated into this [our] home. We'd never used aluminum-skinned, honeycomb-cored structural sandwiches and... no one had... fabricated a complete building from the material... but every architectural and engineering book mentions the possibility... The 55-gallon, water-filled drums... [W]e... knew the amounts of energy... such... could pick up."

"Some of our hardware is getting pretty good, but it... doesn’t make economic sense for most people. ...[O]ur zomes and heaters and so forth do not yet compete on a dollar basis with... conventional counterparts. It’s very exciting intellectually to work with these ideas but their validity will not really be proven until they start to replace... things they’re meant to replace."

"Many other Zomeworks ideas... as... black 55 gallon drums behind glass... (the "drumwall") have... become classics..."

"High above the roofs of... Martineztown, one of Albuquerque's oldest s... a growing army of... structures...point south to capture sunlight... [for] two large buildings... Zomeworks Corporation, one of the nation's earliest companies."

"There is a mistake-proof flange joint for both A and C connections if one hierarchy is introduced. You must always orient the joint to suit A lines."

"[T]here's Dave Harrison's bead wall. I teach... classes at the University of New Mexico and Dave... one of my students... said. "...I've got this idea of building a wall out of two panes of glass... and you can blow Styrofoam beads between the panes at night to insulate the wall." ...Here's a problem ...nobody has thought of a way to solve. I've tried... and... Harold Hay has... and... a lot of others... Dave Harrison has the answer! ...[A] ...low-tech ...answer ...simple ...easy to understand, that a heating and ventilating man in any town can fix... [W]e’ve made a deal with Dave so that he’ll get a big part of any royalties we realize..."

"Solar energy advocates are continuously humiliated by being shown "energy pies." Slices are assigned to coal, gas, oil, hydroelectric and even nuclear. but is evidently too small to appear."

"[I]f folks don’t like the idea once they’ve given it the once-over, we’ll be glad to buy the plans back at the full $15.00 purchase price."

"If you install interior greenhouse lights the electricity... is faithfully recorded. If you grow the plants outside no attempt is made at an accounting."

"If we use the figure of 0.5% efficiency (Ayres and Scarlott)... we have consumed... 2,000,000 BTU/person/day of sunlight in producing the 10,000 BTU/person consumed. Solar energy then fills over 2/3 of the new energy pie."

"Why wouldn't it be fair to expand the slice—4% (1973—Bureau of Mines) given to hydroelectric power by a similar factor of efficiency—for the solar energy consumed in raising the water to its working head?"

"[O]ur next concern in heating the building is what keeps the earth warm..? What supplies the United States with the energy to maintain an average temperature of 60 degrees Fahrenheit as it spins in empty space at absolute zero? This is a heating contract that no oil company would be quick to try and fill."

"[I]t is very important to examine what the limits of an accounting system are—to know what the numbers and quantities... really mean."

"It would take an enormous crew of experts to determine the efficiency of different orientations of windows, different arrangements of shade trees, etc... To ignore these efforts and only to reward the purchase of "off the shelf hardware" is to further the disease of narrow minded quantification."

"If you purchase certain kinds of hardware to exploit solar energy it will be accounted for and credit will be given to the sun. If you depend on more customary old-fashioned uses of solar energy, growing food, drying clothes, sun bathing, warming a house with south windows, the sun credit is totally ignored."

"[W]e would be much better informed if alongside every graph showing our use of oil, coal and uranium there were also an indication or the total energy received from the sun. Since we can't do without it, let's not omit it from our accounts."

"In the case of the United States a conservative estimate of the solar energy received in one year might be... Twenty nine thousand three hundred quadrillion Btu as opposed to the 62 quadrillion shown as used during 1968 by the U.S. Bureau of Mines."

"The effect of clothes and blankets on heat loss is naturally investigated by everyone."

"A sniper scope or camera... that shows... temperatures as... colors would be an enormous help to the investigator. 30 minutes with such... could be as valuable as a week's work... without it. ...[N]ature ...treats you to such a view of the window or skylight with a pattern of frost. ...[S]eals ...[are] the entire problem."

"First of all, there are problems that no one knows how to solve. There are problems that have been studied but untouched, or problems on which there is partial progress. There are problems that sound compelling when formulated, but which no one has thought of yet. There are concepts which are very useful in solving problems .. or which perhaps ... sound very natural and compelling when formulated, but have not been formulated yet. And all of these things interact. So, by solving problems, one is led to concepts — and, by thinking about concepts, one is led to problems."

"Working with Eli Stein is amazing. There are good teachers and there are great teachers — and then there is Eli. He was simply the best teacher, I believe, of advanced math, I believe, in the whole world, by far. ... he conveyed a spirit of optimism. ... He has a wonderful style of explaining math — in which almost all of the effort of explanation goes into finding the right point of view and getting the essence of the problem."

"Charles Fefferman (Charlie) is a mathematician of the first rank whose outstanding findings, both classical and revolutionary, have inspired further research by many others. He is one of the most accomplished and versatile mathematicians of all time, having so far contributed with fundamental results to harmonic analysis, s, , , quantum mechanics, fluid mechanics, and , together with more sporadic incursions into other subjects such as neural networks, financial mathematics, and crystallography."

"What I like about mathematics is the interplay with other people. And that generates extra energy — because it really helps you think."

"When a student picks a research topic, the decision is influenced by the research interests of the advisor, the state of the field in which the problem lives, the personality of the advisor, the chemistry between them ... who else in working on whichever problem. It's immensely complicated. And asking for a sort of simple prescription for how to assign research problems — it reminds a little of the question of how to decide who should marry whom."

"That geometric considerations enter in a decisive way in many questions of harmonic analysis is by now a well-known fact. In explicit form such ideas arose first in the estimation of the of surface-carried measure; they have since played a key role in averages over lower-dimensional varieties, restriction theorems, in connection with the study of s and Fourier integral operators, and in application to linear and non-linear s."

"(edited by Noga Alon, Jean Bourgain, Alain Connes, Misha Gromov, and Vital D. Milman; quote from p. 434)"

"Two events related to clergy sexual abuse have touched the figure of Prevost. The first dates back to the early 2000s, when, as Augustinian provincial in Chicago, he was involved in a case of hospitality to a priest already convicted of paedophilia. The second, more recent, concerns his episcopate in Peru: he allegedly handled an investigation into two priests accused of molestation with little transparency."

"Sinner: The ball, there it is. If you want to play a little. Pope Leo XIV: But we'll break something here! We'd better not."

"It will be a pontificate in continuity with the magisterium of Pope Francis. I am very happy about that. This is what the majority of the cardinals wanted ... but with a style of their own. [...] Pope Leo XIV, in his first message, spoke of a “synodal Church.” Having participated in the work of the Synod, we have a Pope who knows synodality, who understands it, who dares to be synodal. There will not be a revolution, but an evolution."

"It’s shocking, mind-numbing, mind-blowing. How do you describe that? I don’t know. I still haven’t figured out how to tell anybody what I feel, other than out of my head, crazy with happiness, pride, joy, love for my brother.When he made his appearance, then it became real. It’s one thing to hear the name, but when Rob came out onto the balcony and we saw him, it just brought tears to my eyes. You know that’s my little brother. He’s now pope. I don’t know how to describe it spiritually. He was special. When we were kids and went to play games, he wanted to play priest. How many little kids want to play priest, you know? As soon as he got out of eighth grade, he went directly into the seminary. It was like he knew what he wanted to do, and more power to him, and he’s been quite successful at it, right?"

"I don't think I'm revealing any secrets when I write that a long and warm round of applause followed that ‘I accept,’ which made him the 267th Pope of the Catholic Church. [...] I met Cardinal Prevost years ago, in connection with a thorny issue involving the Church in Peru. Even then, I saw in him a sense of balance, calmness, love for people and attention to detail. [...] Pope Leo XIV, he continues, is well aware of the world's problems, as he demonstrated from his very first words from the Loggia, evoking a ‘disarmed and disarming’ peace. [...] I am certain that he will find strength in the grace of the Lord, in his experience as a religious and in the example of the great Father Augustine, whom he mentioned in his first speech. We are close to him with our affection, our obedience and our prayers."

"Please join me in thanking Our Lord for the election of Pope Leo XIV, Successor of St. Peter, as Shepherd of the Church throughout the world.The Shrine of Our Lady of Guadalupe in La Crosse has a particularly strong bond with the Roman Pontiff, especially through its affiliation with the Papal Basilica of St. Mary Major. I urge all pilgrims and friends of the Shrine to pray fervently for Pope Leo XIV that Our Lord, through the intercession of Our Lady of Guadalupe, St. Peter the Apostle and Pope St. Leo the Great, may grant him abundant wisdom, strength and courage to do all that Our Lord asks of him in these tumultuous times. May God bless Pope Leo and grant him many years."

"I met Leo XIV in Peru, and I was struck by his serenity. He is the right man to lead the Church."