deety
how to bake π: an edible exploration of the mathematics of mathematics
eugenia cheng 2015 9780465051694
KUB: Things we know, believe, and understand. The most secure of truths.
KB: Things we know and believe, but do not understand. This includes scientific facts that are certainly true, even if we don't understand them. For example, I don't really understand how gravity works, but I know and believe it works. I know and believe that the earth is round, but I don't understand why.
B: Things we believe, but do not understand or know. These are our axioms, where everything else begins—the things we can't justify using anything else. For example, for me, there are things like love and the preciousness of life. I believe that love is the most important thing of all. I can't explain why, and I can't say I know for sure it is true—because what does that even mean?
After this things get a bit trickier.
K:
Things we know, but do not understand or believe. Is this at all possible? I think if you've ever experienced sudden grief or heartbreak you might have a sense of what this is like. Those numb days after the event when you know, rationally, that it really has happened, but you simply can't believe it, you can't feel it to be true in your stomach. And you certainly don't understand it. Perhaps extremes of good emotions feel like this too. Perhaps if I won the lottery I would, for a while, know that it had happened without understanding or believing it. Winning the lottery of love feels like that too, at least at the height of its ecstasy.
KU: Things we know and understand, but do not believe. Perhaps this is where we get to the next stage of grieving, when we have come to understand that this terrible thing really has happened, but we still don't believe it. But if you're in this state you're probably in some state of denial, because usually knowing and understanding something would make you really believe it's true.
Finally we have the following sections, which I suspect are empty.
U: Things we understand, but do not know or believe.
UB: Things we understand and believe, but do not know.
interview by nicola davis 2017
theguardian.com/science/2017/feb/26/eugenia-cheng-interview-observer-nicola-davis
beyond infinity: an expedition to the outer limits of mathematics
eugenia cheng 2017 not yet read
the art of logic: how to make sense in a world that doesn’t
eugenia cheng 2018 not yet read
positive attitude toward math supports early academic success: behavioral evidence and neurocognitive mechanisms
lang chen et al. 2018
http://dx.doi.org/10.1177/0956797617735528
from ‘sense of number’ to ‘sense of magnitude’ – the role of continuous magnitudes in numerical cognition
tali leibovich, naama katzin, maayan harel, avishai henik 2016
S0140525X16000960
infants distinguish between two events based on their relative likelihood
ezgi kayhan et al. 2017
dx.doi.org/10.1111/cdev.12970
5yr olds learn calculus
Link: theatlantic.com/education/archive/2014/03/5-year-olds-can-learn-calculus/284124/
moebiusnoodles
Link: moebiusnoodles.com/
mathematical model studies of the comprehensive generation of major and minor phyllotactic patterns in plants with a predominant focus on orixate phyllotaxis
takaaki yonekura et al. 2019
http://dx.doi.org/10.1371/journal.pcbi.1007044
"We developed the new model to explain one peculiar leaf arrangement pattern. But in fact, it more accurately reflects not only the nature of one specific plant, but the range of diversity of almost all leaf arrangement patterns observed in nature," said Associate Professor Munetaka Sugiyama from the University of Tokyo's Koishikawa Botanical Garden.
All in the angles
To identify the leaf arrangement of a plant species, botanists measure the angle between leaves, moving up the stem from oldest to youngest leaf.
Common patterns are symmetrical and have leaves arranged at regular intervals of 90 degrees (basil or mint), 180 degrees (stem grasses, like bamboo), or in Fibonacci golden angle spirals (like the needles on some spherical cacti, or the succulent spiral aloe).
The peculiar pattern that Sugiyama's research team studied is called "orixate" after the species Orixa japonica, a shrub native to Japan, China, and the Korean peninsula. O. Japonica is sometimes used as a hedge.
The angles between O. Japonica leaves are 180 degrees, 90 degrees, 180 degrees, 270 degrees, and then the next leaf resets the pattern to 180 degrees.
"Our research has the potential to truly understand beautiful patterns in nature," said Sugiyama.
The math of a plant
Sugiyama's research team began their investigation by doing exhaustive testing of the existing mathematical equation used to model leaf arrangement.
Leaf arrangement has been modeled mathematically since 1996 using an equation known as the DC2 (Douady and Couder 2). The equation can generate many, but not all, leaf arrangement patterns observed in nature by changing the value of different variables of plant physiology, such as the relationships between different plant organs or strength of chemical signals within the plant.
The DC2 has two shortcomings that researchers wanted to address:
No matter what values are put into the DC2 equation, certain uncommon leaf arrangement patterns are never calculated.
The Fibonacci spiral leaf arrangement pattern is by far the most common spiral pattern observed in nature, but is only modestly more common than other spiral patterns calculated by the DC2 equation.
A peculiar pattern
At least four unrelated plant species possess the unusual orixate leaf arrangement pattern. Researchers suspected that it must be possible to create the orixate pattern using the fundamental genetic and cellular machinery shared by all plants because the alternative possibility -- that the same, very unusual leaf arrangement pattern evolved four or more separate times -- seemed too unlikely.
One fundamental assumption used in the DC2 equation is that leaves emit a constant signal to inhibit the growth of other leaves nearby and that the signal gets weaker at longer distances. Researchers suspect that the signal is likely related to the plant hormone auxin, but the exact physiology remains unknown.
Rare patterns and common rules
"We changed this one fundamental assumption -- inhibitory power is not constant, but in fact changes with age. We tested both increasing and decreasing inhibitory power with greater age and saw that the peculiar orixate pattern was calculated when older leaves had a stronger inhibitory effect," said Sugiyama.
This insight into the inhibitory signal power changing with age may be used to direct future studies of the genetics or physiology of plant development.
Researchers call this new version of the equation the EDC2 (Expanded Douady and Couder 2).
First author of the research paper, doctoral student Takaaki Yonekura, designed computer simulations to generate thousands of leaf arrangement patterns calculated by EDC2 and to count how often the same patterns were generated. Patterns that are more commonly observed in nature were more frequently calculated by the EDC2, further supporting the accuracy of the ideas used to create the formula.
"There are other very unusual leaf arrangement patterns that are still not explained by our new formula. We are now trying to design a new concept that can explain all known patterns of leaf arrangement, not just almost all patterns," said Sugiyama.
Do it yourself -- ID the pattern
Experts recommend looking at a group of relatively new leaves when identifying a plant's leaf arrangement, or phyllotaxis, pattern. (In Greek, phyllon means leaf.) Older leaves may have turned (due to wind or sun exposure), which can make it difficult to identify their true angle of attachment to the stem.
Think of the stem as a circle and begin by carefully observing where on the circle the oldest and second-oldest leaves are attached. The angle between those two leaves is the first "angle of divergence." Continue identifying the angles of divergence between increasingly younger leaves on the stem. The pattern of angles of divergence is the leaf arrangement pattern.
Common leaf arrangement patterns are distichous (regular 180 degrees, bamboo), Fibonacci spiral (regular 137.5 degrees, the succulent Graptopetalum paraguayense), decussate (regular 90 degrees, the herb basil), and tricussate (regular 60 degrees, Nerium oleander sometimes known as dogbane).
abstract Plant leaves are arranged around the stem in a beautiful geometry that is called phyllotaxis. In the majority of plants, phyllotaxis exhibits a distichous, Fibonacci spiral, decussate, or tricussate pattern. To explain the regularity and limited variety of phyllotactic patterns, many theoretical models have been proposed, mostly based on the notion that a repulsive interaction between leaf primordia determines the position of primordium initiation. Among them, particularly notable are the two models of Douady and Couder (alternate-specific form, DC1; more generalized form, DC2), the key assumptions of which are that each leaf primordium emits a constant power that inhibits new primordium formation and that this inhibitory effect decreases with distance. It was previously demonstrated by computer simulations that any major type of phyllotaxis can occur as a self-organizing stable pattern in the framework of DC models. However, several phyllotactic types remain unaddressed. An interesting example is orixate phyllotaxis, which has a tetrastichous alternate pattern with periodic repetition of a sequence of different divergence angles: 180°, 90°, −180°, and −90°. Although the term orixate phyllotaxis was derived from Orixa japonica, this type is observed in several distant taxa, suggesting that it may reflect some aspects of a common mechanism of phyllotactic patterning. Here we examined DC models regarding the ability to produce orixate phyllotaxis and found that model expansion via the introduction of primordial age-dependent changes of the inhibitory power is absolutely necessary for the establishment of orixate phyllotaxis. The orixate patterns generated by the expanded version of DC2 (EDC2) were shown to share morphological details with real orixate phyllotaxis. Furthermore, the simulation results obtained using EDC2 fitted better the natural distribution of phyllotactic patterns than did those obtained using the previous models. Our findings imply that changing the inhibitory power is generally an important component of the phyllotactic patterning mechanism.
the arms act as “anchors” in the bottom of the stroke; we are gradually pushing against these anchors as we gain speed, while elongating the rest of the body (by holding other arm in front and keeping legs extended) to help movement of body smooth through water
how to describe swimming speed
swimming speed is “proportional to the the length of the body in water”. but is this is really the case? actually how it should be said is “all other things being equal, etc.” the length of the body in water is an explanation for speed, not the cause of it. the cause is reducing resistance.
total immersion: the revolutionary way to swim better, faster, and easier
terry laughlin, john delves 2004
swimming made easy: the total immersion way for any swimmer to achieve fluency, ease, and speed in any stroke
terry laughlin 2001
triathlon swimming made easy: the total immersion way for anyone to master open-water swimming
terry laughlin 2002
on field expediency
amy olberding 2018
https://aeon.co/essays/how-useful-is-impostor-syndrome-in-academia
calculate
programmable scientific
pcalc
Link: pcalc.com/iphone/
dr drang on programmable functions
leancrew.com/all-this/2013/05/pcalc-2-8/
make downloadable layouts for pcalc
http://www.leancrew.com/all-this/2014/09/a-simple-pcalc-specialty-calculator/
may be useful for our carbon calculations
i built d100 and d6 functions
calca (ios)
Link: calca.io
count
momentum
tally2
Link: leancrew.com/all-this/2015/05/tally/
zero sum game
sl huang 2014
null set
sl huang 2014
critical point
s.l. huang 2020
factfulness ten reasons we’re wrong about the world – and why things are better than you think
hans rosling
reviving ancient chinese mathematics: mathematics, history and politics in the work of wu wen-tsun
jiri hudecek 2014
a primer of ecological statistics, 2nd edition
nicholas gotelli, aaron ellison 2012
probability theory: a first course in probability theory and statistics
werner linde 2016
the manga guide to calculus
hiroyuki kojima, shin togami
elements of stochastic calculus and analysis
daniel strook 2018
puzzle-based learning: an introduction to critical thinking, mathematics, and problem solving
zbigniew michalewicz & matthew michalewicz 2014
introduction to mathematics
alfred north whitehead 2017
a mind for numbers: how to excel at math and science (even if you flunked algebra)
barbara oakley 2014
advanced abacus: theory and practice
takashi kojima 2012
the numbers game: the commonsense guide to understanding numbers in the news, in politics, and in life
michael blastland, andrew dilnot 2008
the myth of ability: nurturing mathematical talent in every child
john mighton 2004
easy math step-by-step, second edition
sandra luna mccune, william d clark 2018
easy pre-calculus step-by-step, second edition
carolyn wheater 2018
it’s a numberful world: how math is hiding everywhere
eddie woo 2019
change is the only constant
ben orlin 2019
the math of life and death: 7 mathematical principles that shape our lives
kit yates 2019
gödel, escher, bach: an eternal golden braid
douglas hofstadter 1979
the efficiency paradox: what big data can’t do
edward tenner 2018
x + y: a mathematician's manifesto for rethinking gender
eugenia cheng 2020
weird math: a teenage genius and his teacher reveal the strange connections between math and everyday life
david darling and agnijo banerjee 2018 9781541644793
“You toss it once, and it comes up heads. It’s possible to prove that the probability of a head on the second toss is two out of three using Bayesian probability. However, the initial probability of a head was one out of two, and we didn’t change the coin. The Bayesian viewpoint says that while the first head will not directly affect the probability of the second head, it gives you more information about the coin that allows you to refine your estimate. A coin heavily biased toward tails is highly unlikely to flip heads, and a coin heavily biased toward heads is much more likely to flip heads.”
“Taking a Bayesian approach also helps avoid a type of paradox first pointed out by German logician Carl Hempel in the 1940s. When people see the same principle, such as the law of gravity, operating without fail over a long period of time, they naturally assume that it’s true with a very high probability. This is inductive reasoning, which can be summed up as follows: if things are observed that are consistent with a theory, then the probability that the theory is true increases. Hempel, however, pointed out a snag with induction, using ravens as an example.
All ravens are black, so the theory goes. Every time a raven is seen to be black and no other color—ignoring the fact that there are albino ravens!—our confidence in the theory “All ravens are black” is boosted. Here, though, is the rub. The statement “All ravens are black” is logically equivalent to the statement “All nonblack things are nonravens.” So, if we see a yellow banana, which is a nonblack thing and also a nonraven, it should bolster our belief that all “ravens are black. To get around this highly counterintuitive result, some philosophers have argued that we shouldn’t treat the two sides of the argument as having the same strength. In other words, yellow bananas should make us believe more in the theory that all nonblack things are nonravens (first statement), without influencing the belief that all ravens are black (second statement). This seems to fit with common sense—a banana is a nonraven, so observing one can tell us about nonravens but tells nothing about ravens. But it’s a suggestion that’s been criticized on the basis that you can’t have a different degree of belief in two statements that are logically equivalent, if it’s clear that either both are true or both are false. Maybe our intuition in this matter is at fault, and seeing another yellow banana really should increase the probability that all ravens are black. Adopting a Bayesian stance, however, the paradox never arises. According to Bayes, the probability of a hypothesis H must be multiplied by this ratio:
Probability of observing X if H is true /
Probability of observing X
where X is a nonblack object that’s a nonraven and H is the hypothesis that all ravens are black.
If you ask someone to select a banana at random and show it to you, then the probability of seeing a yellow banana doesn’t depend on the colors of ravens. You already know beforehand that you’ll see a nonraven. The numerator (the number on top) will equal the denominator (the number on the bottom), the ratio will equal one, and the probability will remain unchanged. Seeing a yellow banana won’t affect your belief about whether all ravens are black. If you ask someone to select a nonblack thing at random and they show you a yellow banana, then the numerator will be bigger than the denominator by a tiny amount. Seeing the yellow banana will only slightly increase your belief that all ravens are black. You would have to see almost every nonblack thing in the universe and see that they were all nonravens before your belief in “All ravens are black” went up significantly. In both cases, the result agrees with intuition.”
“In 1931, several years before leaving Austria and joining the Institute for Advanced Studies at Princeton, where he became a close friend of Albert Einstein, Gödel published two extraordinary and shocking theorems—his first and second incompleteness theorems. In a nutshell, the first of these theorems showed that any system of mathematics that is complex enough to include ordinary arithmetic—the kind we learn in school—can never be both complete and consistent. If a system is complete, it means that everything within it can be either proved or disproved. If it’s consistent, it means that no statement can be both proved and disproved. Like a bolt out of the blue, Gödel’s incompleteness theorems revealed that, in any mathematical system (apart from the very simplest), there will always be things that are true but that can’t be proved to be true. The incompleteness theorems are analogous in some ways to the uncertainty principle in physics in that they expose fundamental limits to what can be known. And like the uncertainty principle, they’re frustrating and inhibiting because they show that reality—including purely intellectual reality—behaves in ways that prevent us from being omniscient about everything that we try to penetrate with our minds. To put it bluntly, truth is a more powerful concept than proof, which, for a mathematician especially, is anathema.”
how to remember equations and formulae: the leaf system
james smith & phil chambers 2014
listening to music at low volume
we can build with imagination what the piece is meant to sound like (especially if we have heard the piece before), whereas with high volume you have no choice in the matter, it is thrust upon you.
sealant–adhesive
silicone
can also be used as an adhesive in limited situations
soudal silirub+ s8000 premium silicone adhesive & sealant 310ml
comes in clear and white opaque varieties (have only used opaque so far)
soudal.com/soudalweb/images/products/4201/ID239_Silirub plus S8800_België_Engels.pdf
solvent–free, suitable for high–movement joints; unfortunately they use a fungicide, would prefer biocide–free sealant like the s2000 range but not available locally
have used to seal sink, bath, doors and windows, low–impact reused fencing–as–shed–roofing as well as in some situations where would otherwise use sugru (sugru is expensive but worthwhile)
requires a sealant applicator to apply, am using the rectangular end of a bamboo chopstick for shaping
eventually mildew will grow on the sealant if in constantly–moist areas like the kitchen sink
does not stick to cling–film or sospy surfaces (“no adhesion on PE, PP, PTFE and bituminous substrates”) so for example, to seal door, stick cling–film to doorstep using masking tape (or leftover silicone on previous day) and proceed to seal between door and doorstep using silicone
sticks well to paper and tissue paper, so to remove still–unset silicone from skin or surfaces, rub on paper or tissue
emissions of tetrachlorobiphenyls (pcbs 47, 51, and 68) from polymer resin on kitchen cabinets as a non-aroclor source to residential air
nicholas j. herkert et al. 2018
https://doi.org/10.1021/acs.est.8b00966
arrange in batches
process notes
time scheduling
cleaning
maintenance
scheduling and adding timed alarm for recurring tasks lets you “decide in advance” what you will be doing, removing the procrastination of infinite choice when you could decide to do anything.
a (flexible) schedule can ease the way between tasks and help us return to continue work on a task. flexibility is important for dealing with unexpected events
輪舞 revolution
奥井雅美
Link: run-workflow
断罪の花～guilty sky～
DANZAInoHANA
小坂りゆ
Link: run-workflow
漢字
ココロ…まだアナタのキヲクの中で
カラダ…探してる足りないワタシを
今日も何処かで誰かの流す涙
冷たく笑う運命を生きていく事
なくせないもの握りしめながら
ワタシは今もここにいるの
☆枯れない花は美しくて
ゆるぎない思いを胸に咲き続けた
ちぎれた雲の断罪の空
止まらない哀しみを抱き締めていた
どんな“痛み”にも『始まり』はあって
いつか訪れる『終わり』を待ってる
あの日アナタに感じた温もりも
気付けば手が透けるぐらい色褪せてた
失っていく音ばかり増えて
全てを捨ててここにいるの
枯れない花は美しくて
ゆるぎない思いを胸に咲き続けた
ちぎれゆく愛 残酷な夢
止まらない哀しみを抱き締めていた
この世界は
真実という
孤独を必要とした
アナタの影
アナタの夢
追いかけてた…
なくせないもの握りしめながら
ワタシは今もここにいるの
☆繰り返す
未来、求めて…
踊りつづけて…永遠に…
english
ココロ…まだアナタのキヲクの中で
kokoro… madaanatanokiokunoNAKAde
my heart… is locked in your memories
カラダ…探してる足りないワタシを
karada… SAGAshiteruTArinaiwatashiwo
my body… i seek for i have none
今日も何処かで誰かの流す涙
KYOUmo DOKOkadeDAREkanoNAGAsuNAMIDA
today i will once again see someone somewhere shed tears
冷たく笑う運命を生きていく事
TSUMEtakuWARAuSADAMEwoIkiteikuKOTO
and again it’s my destiny to return nothing but a cold smile
なくせないもの握りしめながら
nakusenaimonoNIGIrishimenagara
as i hold on to this fate that cannot be abandoned
ワタシは今もここにいるの
watashiwaIMAmokokoniiruno
i stand here right now
☆枯れない花は美しくて
KArenaiHANAwaUTSUKUshikute
like the beauty of an eternal flower
ゆるぎない思いを胸に咲き続けた
yuruginaiOMOiwoMUNEniSAkiTSUDZUketa
stubborn feelings still bloom in my heart
ちぎれた雲の断罪の空
chigiretaKUMOnoDANZAInoSORA
shredded clouds in a guilty sky
止まらない哀しみを抱き締めていた
TOmaranaiKANAshimiwoDAkiSHImeteita
embraced tightly a neverending sadness
どんな“痛み”にも『始まり』はあって
donna"ITAmi"nimo HAJImari waatte
every pain has a beginning somewhere
いつか訪れる『終わり』を待ってる
itsukaOTOZUreru Owari woMAtteru
and an ending that surely awaits
あの日アナタに感じた温もりも
anoHIanataniKANjitaNUKUmorimo
the warmth i felt in you on that day too
気付けば手が透けるぐらい色褪せてた
KIDZUkebaTEgaSUkeruguraiIROAseteta
faded softly away in my open hands
失っていく音ばかり増えて
USHINAtteikuOTObakariFUete
only sounds of lost hope seem to grow louder
全てを捨ててここにいるの
SUBEtewoSUtetekokoniiruno
i threw away everything to be here now
枯れない花は美しくて
KArenaiHANAwaUTSUKUshikute
like the beauty of an eternal flower
ゆるぎない思いを胸に咲き続けた
yuruginaiOMOiwoMUNEniSAkiTSUDZUketa
stubborn feelings still bloom in my heart
ちぎれゆく愛 残酷な夢
chigireyukuAI zankokunaYUME
dying love, cruel dream
止まらない哀しみを抱き締めていた
TOmaranaiKANAshimiwoDAkiSHImeteita
embraced tightly a neverending sadness
この世界は
konoSEKAIwa
this world
真実という
SHINJITSUtoiu
needs a solitude
孤独を必要とした
KODOKUwoHITSUYOUtoshita
called truth
アナタの影
anatanoKAGE
your shadow
アナタの夢
anatanoYUME
your dreams
追いかけてた…
Oikaketeta…
i chased after them…
なくせないもの握りしめながら
nakusenaimonoNIGIrishimenagara
as i hold on to this fate that cannot be abandoned
ワタシは今もここにいるの
watashiwaIMAmokokoniiruno
i stand here right now
☆repeat
未来、求めて…
MIRAI, MOTOmete…
wish for the future…
踊りつづけて…永遠に…
ODOritsudzukete… TOWAni…
and dance on… to eternity…