
“When we do mathematics, we touch immortality.” - nature24
https://www.quantamagazine.org/20161020-science-math-education-survey/?code=3048
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FabHK
There is the ontological position that mathematical truths are "out there",
independent of us, and we are merely "discovering" them. As such, they're
eternal, and you could argue then that you "touch immortality".

But apart from that, I find this sort of talk unhelpful. It's a bit like
Schopenhauer who thought that instrumental classical music gave access to the
innermost truth of the universe (I'm paraphrasing from memory here) - what
hogwash.

Lastly, the headline has not much to do with the article, has it?

~~~
JoeAltmaier
So, the value of PI is a human invention? That's hogwash.

~~~
omalleyt
The concept of "circle" is a human invention, in that a perfect circle has
never been observed in the universe. The value of pi follows immediately as a
derivative human invention.

~~~
justifier
I would argue the 'perfect circle' is inherent in every circle, similarly to
how it is inherent in your dismissal of it

But if you require a more direct understanding I would say there is a perfect
circle in every rotation

~~~
kordless
The _possibility_ of a perfect circle exists in this universe, but the last
digit we are aware of is definitely a posteriori. In other words, the
_description_ of a circle is prior knowledge given it allows calculating pi,
but the actual values are post observational knowledge, given they must be
calculated and continue to be irrational forever. (At least as far as we
know.)

It would take an infinite amount of power to calculate every digit in pi,
given pi itself is irrational, even while describing _how_ to calculate it is
rational.

~~~
justifier
You are moving someone else's goalposts

I answered where circles are in our universe and you then try to change the
original intent of omalleyt's question to mean a symbolic representation of pi

> It would take an infinite amount of power to calculate every digit in pi

Calculating pi is so simple life without nervous systems does it

Now, expressing that value in our limited yet overly verbose base ten symbolic
representation would indeed require infinite recursion

~~~
kordless
I'm not aware of a means by which goal posts can exist in a philosophical
debate around rational vs. irrational thinking. Both types of thinking are
valid, but I can see how and why some tend to argue for absolute rationality
at all times.

~~~
justifier
I apologise, I thought you were implying that what omalleyt 'really meant' was
a perfect circle is data we can calculate

It seemed to me you were changing the question that was being asked, and a
question asked implies an answer, or 'goal post'

But if you were just developing new inquiry stead building off omalleyt then I
apologise and would hope to encourage like critical thinking in the future

.. Thinking on it 'goal posts'.. and 'soap box' elsewhere in this thread..
lacks a timeless quality, I really should have left it out ;P

~~~
kordless
I asked my daughters friend why pi was irrational, and she said "because you
have to calculate it". The knowledge of those calculations cannot be given,
but the way to calculate it, with a bit of suffering, can.

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ThomPete
I think a better way to describe this is that you touch reality.

It's important to remember that for all the books written about physics in
layman terms, especially quantum physics, there comes a time when words don't
cut it and only math allow you to continue the conversation.

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hzhou321
>> “the math that’s being taught has no relevance to my life"

I think our math education do fail in that way. Math essentially is a logic
system where you set up premises and derive and make sure everything is
consistent. That can be applied to real life such as accounting and physics,
or it can be applied to an artificial game -- number theory is such a case.
Our education emphasize on the latter part, and it is quite irrelevant to real
life, and it is hard. I am in mid-life now and on reflection, fractions, for
example, had zero use for my life, and I am in the career of scientific
computing. What we need is a concept level of understanding of mathematics --
realizing that the key idea of mathematics is basically consistency. Most
importantly, the math required in the real life is not hard -- it is
necessarily intuitive. What the education we receive is the technical gaming
part of mathematics, e.g. how to actually find the roots of quadratic
equation. I don't really remember the formula now, but I now have an intuitive
understanding of the quadratic curves and the meaning of roots. And the same
goes for quintic equations. It is not hard at all. I roughly sketch out the
curve and I immediately have a rough idea of where the roots are. And at work,
it is simply an exercise in programming. It is hard following the way in our
education, though.

The purpose of education is to show them that knowledge exists, but not the
knowledge itself. Knowledge itself is misleading. It is more important to
recognize what you don't know than to remember what you know.

To clarify, I personally do not hate math. And I respect the discipline of
mathematics. However, doing math (the way our education system assumes) is
just like doing music or art, or playing star craft, it is not for everyone.

PS: on further reflection, not only useless, the concept of rational number
has been quite damaging in our understanding of the real world.

~~~
justifier
I was thinking about education last night and here is the idea I am
developing.. I encourage ongoing criticism

Students study varied subject matter but only one subjects' grade 'matters'
and can be chosen by the student

Personally, I think our maths education suffers from a lack of freedom.. I do
think it can be for anyone but only because I believe anyone can bring to it
whatever they'd like, whereas education tells you what areas need to be
studied and how

is competition the foil of expression?

~~~
baobrain
Could you elaborate?

For example, What would motivate a student to put towards any effort in their
non-main courses if it doesn't affect their grade?

Edit: clarity and accuracy

~~~
justifier
Exactly, it would be unnecessary

The student could just coast through a course.. they would have to sit through
all lectures and would be assigned problems and reading but only one course
would track their retention

I feel this is basically already what is happening in education with the
prevalence of students' creative ways of undermining the current grading
paradigm

But with the ancillary benefit that a student would be freed to actually do
the work to foster an interest in at least one subject

Also, the student could be free to explore other subjects in ways outside of
the means of tracking retention

I was pushing my math research since I was a child but instead was forced to
abandon it and had calculus forcibly replaced as 'how I should think about
mathematics' even though I fundamentally disagreed with its concepts

If I was free from the stress of doing poorly from the standpoint of grades I
could have focused my interest on my own mathematical insight and simply
allowed my education to expose me to calculus

wherein I would have retained an appreciation for mathematics and developed
one for the practicality of calculus practices

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vinchuco
Immortality, meanwhile, rolls its eyes. Still, it's interesting to see what
motivates people to learn something (or to stay away from it). Better put:

>"When you take a course in Euclidean geometry is not the teacher putting a...
learning program into you? ...You enter the course and cannot do problems; the
teacher puts into you a program and at the end of the course you can solve
such problems. ...Are you sure you are not merely "programmed" in life by what
by chance events happens to you?" \- Hamming

I'm curious as to how different mathematics would be for two otherwise
identical civilizations but with distinct average lifespans. In alternate
Earths where lifespan is 40 or 200 years, what's the state of mathematics in
2017?

~~~
everybodyknows
As Hamming describes, it was very much for me: 8th grade plane geometry feels
now like an intellectual awakening. The satisfaction of proving "pons
asinorum", by Euclid's method, followed by vexation at learning I had
overlooked the much simpler reflexive approach.

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ivan_ah
It's surprising to see so few math haters in the hexagon (the thin outer
shell). I'm guessing there is a self-reporting bias, since if you hate math
you wouldn't really want to fill in this survey...

It's also interesting to note that many of the haters direct their hate
towards rote learning tasks like arithmetic calculations and memorizing
multiplication tables, which makes me think that they don't really hate math
but rather the way it is taught. I'd hate math too if I saw it as following
procedures blindly! Perhaps with better computer math tools[1], future
students won't be forced to learn "manual labour" math tasks, and instead
focus on "white collar" tasks like modelling and abstraction.

[1] SymPy is the best computer algebra system ever:
[https://minireference.com/static/tutorials/sympy_tutorial.pd...](https://minireference.com/static/tutorials/sympy_tutorial.pdf)

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Bluestrike2
God, some of those quotes about how some early math teaching techniques hurt
people's appreciation and understanding of the subject are depressing. I still
remember the anxiety and even embarrassment caused by timed drills in
elementary school that seemed to harshly pit student against student.

It took me until college to realize that I was just coasting through math
courses and not really investing myself in the subject. Perhaps in an effort
to avoid those long-ago memories? Everything started to click in college.
Interestingly enough, it was my enjoyment of programming and study of
philosophy that really helped to push me. That, and sitting in a calculus
class and realizing that I had to either dive in or be royally screwed.

It's a shame that such stories are so common.

~~~
captain_clam
Dear god, the timed drills. I distinctly recall the tremendous anxiety evoked
by the ultra-competitive nature of those drills in elementary school, and
especially the subsequent feelings of failure when comparing my performance to
that of my peers.

It must have been that bitter flavor of failure that first inured me against
mathematics...it didn't help that the rest of my K-12 education never even
attempted to demonstrate the enormous beauty of maths. In fact, until I
discovered calculus on my own terms between high school and college, I
understood mathematics to be nothing more than the practice of applying rote
formulas to arbitrary equations. There was no rhyme or reason to the quadratic
equation...it was just one of many "rules" pulled from the mathematical
"rulebook," and math was simply the practice of recognizing when this
arbitrary rule applied, and then applying it.

Therefore, for most of my life, math was not seen as a creative or exploratory
discipline, and in fact the very opposite: One's ability in math was
completely contingent on their memorization of rules and simply following
them. It was purely robotic, the domain of tightly-wound, uninspired
automatons. It was for squares, not free-spirited creative souls like myself!

Though I am disappointed to think of the heights and wonders I could have
visited by now, had I been given a proper introduction at a younger age, I am
no less excited by the wonders ahead of me, and the many years I have left to
explore them. :)

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danidiaz
“Mathematics has the inhuman quality of starlight, brilliant and sharp, but
cold.” —Hermann Weyl

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imh
Can we get a title change? About half of the people seem to be commenting on
the HN title instead of the article content.

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tluyben2
Did not read the article, but that was my feeling when I first touched math
and (almost at the same time) wrote my first code.

Using Coq, Idris, Haskell, Purescript, Mercury and k give me that sense still.
Anything that takes a long and hard time to think about.

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lngnmn
Which, along with infinity, does not exist.

The ability to produce an infinite series of numbers (by adding another one)
does not constitute a proof of existence of anything infinite outside one's
mind.

Good philosophers, like Leibniz and the Indian tradition, which includes early
Buddhists, have postulated this, but popular memes are much stronger.

The ability to notice some inherent patterns of natural phenomena, such as the
ratio of a circle's circumference to its diameter, does yield this ratio to be
immortal, or any other inferred constant.

Math does not exist outside people's minds (contrary to the popular discourse
from the Zen And Art Of Motorcycle Maintenance). Only a few of what we call
conservative forces and different forms of what we call energy (or matter if
you like) which are different aspects of the same That, to which human
categories are inapplicable.

~~~
keiferski
Once, just once, I would love to open the comments of a philosophy-related HN
article and not see a middlebrow dismissal [1] as the top comment.

[1]
[https://news.ycombinator.com/item?id=4693920](https://news.ycombinator.com/item?id=4693920)

~~~
Ar-Curunir
It's a slight variant of the Dunning-Kruger effect; people have just a little
knowledge of some field, and can therefore dismiss entire decade's worth of
thought on the matter.

~~~
lngnmn
What is wrong with dismissing entire decade's worth of superstitions,
astrology, alchemy, metaphysics and theology?

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swayvil
Mathematics touches immortality like fractals touch infinity and circles are
endless.

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zentropia
For me when I see some physics equations is a mystic experience.

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jayeshsalvi
Despite Gödel's incompleteness theorems?

