Mathematics is to science what a hammer is to a carpenter.
from Rob Reno
Mathematics is to science what a hammer is to a carpenter. It is a man-made tool (a language invented as needed) with an uncanny power to accurately measure physical reality. But it is not the only tool in a scientists toolbox, albeit an essential one and indispensable for creating an intersubjective verifiable intelligent discussion of the material aspects of the cosmos. But it is not necessarily a part of the higher realization of truth. The recognition of emergent phenomenon is not dependent upon mathematics. The observation that not only in the realms of life but even in the world of physical energy, the sum of two or more things is very often something more than, or something different from, the predictable additive consequences of such unions. The entire science of mathematics, the whole domain of philosophy, the highest physics or chemistry, could not predict or know that the union of two gaseous hydrogen atoms with one gaseous oxygen atom would result in a new and qualitatively superadditive substance—liquid water.
https://rwer.wordpress.com/2019/03/24/certain-decisions/#comments
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Real-World Economics Review Blog 
A bit overstated, but hooray for saying mathematics is a tool for science, it is not itself science.
Great comments, Rob!
Mostly true but essentially irrelevant. Discussion at the meta level may be true but of itself achieves nothing.
Only by the valid application of the scientific method will progress be achieved. Merely to say it needs to be done, whilst true is utterly pointless. Unfortunately this is frequently repeated on these pages. If the writers were to spend their time applying the scientific method, the quality calculus and empirical falsification to economic analyses, rather than saying something need to be done, they would most likely achieve something. Please actually apply the scientific method and achieve something.
Mathematics is nothing but the science of logic. Whatever is logical can also be formulated in the language of mathematics. If a science is unable to do this, it is not mathematics, not even science, but scientists who can not formulate their thoughts clearly and sharply enough, or simply lack mathematic knowledge. And by the way, science is different from naive belief just by logic. Simply, economics yet hasn’t done its mathematical homework.
Mathematics is the veil of economics used to confuse the masses.
“Mathematics is nothing but the science of logic”. OK, but it is a human (logical) construction. Classical sciences use only a very small part it to analyze and understand Nature. Engineers use it to design artificial (logical) instruments. The problem with economics is that they use this same small part of mathematics to analyze a sociological problem. We need a different part of mathematics.
“We need a different part of mathematics.”
No, you do not. The appropriate tools are the same, you only need to learn how to apply them.
Wisdom/Natural Philosophy is the best integration the ideal and workable, thought and action. Economics would best be the study of wisdom as it relevantly applies to that body of knowledge. A Wisdomics would be both what is most effective and what best served man, not the presently confused scramble for wealth dominated by the illegitimate business model of finance that is even more obsessed with wealth and power.
Absolutely true! The appropriate part of mathematics is the solving of differential equations over time. That leaves only a handful of papers to consider.
Great comment indeed, but economists lost the hammer decades ago, and were never capable of carpentry, which is an honourable profession. Without a thorough study of Political Economy, this “science” will not go a step forward. Unfortunately, it keeps going backwards.
One can’t (at the best) problematise the pertinent issues of our era, they need to be politicised properly. Little Greta is braver than the corrupt politicians and Economists put together.
New student of economics join every year, their “hammers” are fully intact and ready to be used. Just teach them how the tools are properly applied and it will be fine.
Yes Helen I agree with you “little Greta is braver than the corrupt politicians and Economists put together”
In spite of the fact that she has obviously been fed some extreme views, she certainly is a great example of a person; fearlessly dedicated to saving the world from self destruction.
Therefore I would suggest what we need to reform economics and save the environment is more Helens , not self serving extreme wealth, that corrupts politicians, and many academics
Ted.
“she has obviously been fed some extreme views” – patronising slander
It is sad to see otherwise intelligent individual stoop to patronizing slander of a child speaking truth to power. It is an attestation to the power of propaganda and anti-intellectual blindness that permeates certain segments of the population. Extremism is in the denial in the face of the overwhelming scienctific evidence of man made climate change (global warming). Truly, out of the mouth of babes comes wisdom.
I am saddened to think that some people think I have applied patronizing slander to a child. therefore I humbly state this was not my intention. Furthermore if I have given the impression that I have taken a patronising slanderous attitude to a child, then I publically ask for her forgiveness and again state it was not my intention.
For the record I am not a denier of climate change, rather I think we need to understand the history of climate change and then progress through to how we are accelerating that change. Next we need to not only stop causing pollution but actively employ ways to rectify the damage, eg rebuild rain forests, while at the same time keeping the cities running.
Back to brave HELEN whom I would rather describe as a dedicated young person, rather than a child, whose plea for meaning full conversation, needs to be acknowledged by all without prejudice Ted
Edward I know deep in my heart your are a kind and sincere human being and never intentionally meant to slandar a child. I think many a common man and women have been wronged by right-wing GOP propaganda pushing false narratives serving the monied wealthy class in with economic interest in perpetuating the status quo.
Our family once we’re on vacation in Canada and while sitting in a big snowcat on a glacier listening to the guide explain the stready decline of the glacier and the environmental consequences of global warming a group of older, feankyl arrogant, Americans snickered amoung themselves how these young “millennials” were brainwashed by “extremist” views. I said nothing. I regret not confronting their blatant ignorance on the spot, if for no other reason than the sake of my grandchildren’s future. Enough is enough of this wilful ignorance that that threatens our very planet. It is time to wake up and realize our generation has a lot to answer for.
Mathematics is one of the great cultural achievements of Sapiens. Every educated person understands the rudiments of numbers and measures and thinks and acts through this quantifying conceptual framework. In this way, mathematics helps provide the framework for the socially all-important practices of work, commerce, and economics. And as most of us now know, digital computers and the full range of information technology applications are exclusively the realm of mathematics. They are not possible without it. Mathematics is thus essential to the modern technological way of life and the culture that enshrines it in our lives. But mathematics is also a utensil in another way. It allows humans to invent and manipulate profound and abstract conjectures of the human mind about the form and relations of objects found only in the human imagination. Infinities, paradoxes, logical deduction, perfect harmonies, structures and symmetries, logics, sciences, and many other concepts exist, are explored, and put together only in human imagination using mathematics. Mathematics is the medium for abstracting, for turning flips via mathematics. One of these abstractions people hear about routinely is certainty, or lack thereof. Mathematics as a source of certainty has been in dispute for over 2000 years. The questions remain undecided today. Can mathematics provide certainty, necessity, and absolute universal truth. If yes, how? If no, how? So, in addition to an everyday practical role, mathematics seems to have also an epistemological role, an ideological role, and even a mystical role in human culture. We need to demystify mathematics; to show that for all the wonders we see in it, it remains a set of human practices, grounded, like everything else, in human cultures; particularly, in the case of mathematics material culture.
With all this clarity about mathematics and the role it plays in science, as well as the central part mathematics and sciences play in modern cultures, why would any member of a society of modern culture reject mathematics and science? Simple answer, those who reject mathematics and science are not members of a modern society. They are members of another society, with a different culture. For example, it is well known that plutocrats consider themselves not only separate from the ordinary crowd, but wholly distinct and superior to all other humans in terms of wealth, power, imagination, and success. Don’t believe me? Check the numbers of books written and published each year describing their specialness and/or giving “how-to” instructions on how to become like these “special” people. There is a biological component to this culture of specialness (the special are smarter, faster, concentrate better, live longer, etc.) but mostly the differences that matter are cultural (wealth, powerful in all its forms, status above all others, etc.). The special as superior stand above and outside science and mathematics. They certainly use science, but always to meet only their needs and under their tight control. They shape and bend, even redesign mathematics to serve their goals, but never allow mathematics to perform any greater function. In simpler terms they inhabit a non-scientific and non-mathematics (but still mathematical) culture. Following sociologist Charles Derber, we can call this and similar cultures sociopathic.