Children of the Cosmos by Sylvia Wenmackers

Sylvia Wenmackers

Essay Abstract

Our mathematical models may appear unreasonably effective to us, but only if we forget to take into account who we are: we are the children of this Cosmos. We were born here and we know our way around the block, even if we do not always appreciate just how wonderful an achievement that is.

Author Bio

Sylvia Wenmackers is a professor in the philosophy of science at KU Leuven (Belgium). She studied theoretical physics and obtained a Ph.D. in Physics (2008) as well as in Philosophy (2011). In her current project, she explores the foundations of physics, with a special interest in infinitesimals and probabilities.

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Sylvia Wenmackers

Full title

"Children of the Cosmos - Presenting a Toy Model of Science, with a Supporting Cast of Infinitesimals"

One sentence summary

As children of the Cosmos, we should remember this: "It is not nature, it is scientists that are simple." ;-)

Synopsis

- we are selected (2.1);

- our mathematics is selected (2.2);

- the application of mathematics has degrees of freedom beyond those internal to mathematics (2.4);

- and, still, effective applications of mathematics remain the exception rather than the rule (2.3).

Deleted scene

[Voice over for intro] On a particular planet in this Universe, a species evolved, the members of which had some crude tools for measuring and an organ for thinking. Using their tools, they were able to create somewhat less blunt tools. Soon, they thought themselves gods.

Goofs

Well, I forgot to include the original anecdote that got me thinking about this topic. [Trigger warning: armchair philosophy.] I attended a lecture in which the speaker claimed that "There is a matter of fact about how many people are in this room". Unbekownst to anyone else in that room, I was pregnant at the time, and I was unsure whether an unborn child. To me, examples like this show that we can apply mathematically crisp concepts (such as the counting numbers) to the world, but only because other concepts are vague (like 'person').

Trivia

This is the first FQXi contest that I participate in. My main goal was to compose an accessible piece, with the risk that it is too basic for the specialists on this forum.

Best wishes to all,

Sylvia Wenmackers

Gordon Watson

Sylvia,

Thank you for the lovely essay: not too basic for me; but then, I'm not too much a specialist. However: my subsequent re-readings have been punctured by my selection bias (toward maths, and it as the best logic). Heretofore largely subconscious, I thank you for the reminders (and they do you no harm).

The lead-in to your essay was another good one by Tom Phipps, "On Mathematical Misconceptions Masquerading as Physics." So I will need to return when these new thoughts clarify and cohere with my own essay. But, in short, they are trending something like this:

Nature talks to us in many ways (ready, willing and able; from big bangs to whispers and apples falling): but just one grammar (mathematics) governs all her languages, hence all her Laws.

So, following Tom, let's seek to reverse the pecking order in science: 1. Experimentalists. 2. Theoreticians. 3. Mathematicians. For, in seeking to understand Nature and her children, we must encourage her to address our biasses.

Enter the experimentalists! For, Nature seldom (if ever, in my experience) talking via mathematics, happily talks via niggles, laughs and rainbows to all who question her.

Thence cometh the theoreticians: Hopefully finding new Laws in new data; though forever to be tested against her (and oft found wanting).

Then the mathematicians, who, via one careless abstraction, cannot be tested against Nature nor reveal her Laws. But how lovely and eternal their universes!

Thus, for me, your disclaimer might better read: No parallel universes were postulated during the writing of this essay; though some were challenged.

With thanks again, and best regards; [link:fqxi.org/community/forum/topic/2491]Gordon Watson: Essay Forum[/link]. Essay Only.

James Hoover

Sylvia,

Quite interesting essay -- a timely argument in light of certain false discoveries like BICEP2. Selection bias I suppose is like confirmation bias which leans more toward science studies.

I love your selection of quotes by Einstein and Newton. Einstein's reminds me of the saying about democracy. In addition, the quotes are quite appropriate for your essay.

We might expect that peers of scientists, through peer review and their commitment to scientific truths would reveal fallacies, as they did BICEP2, and thus selection bias. Now confirmation bias in the political world and the polarized world doesn't have objective overseers on either side.

You might find my "Connection: mind, physics and math" of interest regarding what the union of mind, physics and math have accomplished.

Regards,

Jim

Sophia Magnusdottir

Hi Sylvia,

I like the way you address the question about the effectiveness of math, but I also think you miss the actual puzzle there.

Sure, we evolved by natural selection that would favor us being able to extract laws and regularities, so in a sense evolution worked towards a species that would end up using math to understand its environment. However, that doesn't explain why we find ourselves in an environment that displays such regularities to begin with. See, it is fairly easy to conceive of some mathematical structure that is just a complete mess, is chaotic, not causal, does not lend itself to a perturbative approximation and 2nd order differential equations with well-defined initial conditions etc. Why do we find ourselves in an environment in which that is the case? An environment that had these laws for us to discover?

Only reason I can come up with would be anthropic - quite possible life can't develop unless there are some regularities, in time or in space, ie self-similarities in some sense. But I don't think anybody knows how to make that argument precise.

In any case, I actually don't think math is all that efficient at all. Just look at all the things we cannot describe by math! Maybe you find some time to look at my essay, I think you would find we have some things in common, even though I pushed my argument into a different direction.

-- Sophia

Gordon Watson

Dear Sophia (and Sylvia),

As a local realist, I'm keen to study and learn about the nature of reality. Thus, as I say in my essay, I seek to ensure that there is nothing relevant missing, and nothing irrelevant found, in the models that I develop. Hence the maxim: "Every relevant element of the subject physical reality has its counterpart in our analysis; and there are no irrelevancies."

So, for me, Sylvia nails two points that seem to be missed by many:

(i) "For each abstraction, many variations are possible, the majority of which are not applicable to our world in any way; p.5." Sylvia here speaking to my own need for caution.

(ii) "In my view, mathematics is about exploring hypothetical structures; p.4." Sylvia here recognising a branch of mathematics that differs markedly from my own: for my maths is about exploring concrete elements of physical reality; motivated because ...

... out of such studies, a small ubiquitous constant emerges:

h = Planck's constant, the quantum of action.

Such action then helps me give my answer [.] to your concerns above

"Sure, we evolved [based on the quantum of action] by natural selection [based on the quantum of action] that would favor us [based on the quantum of action] being able to extract [based on the quantum of action] laws and regularities [based on the quantum of action], so in a sense evolution [based on the quantum of action] worked [based on the quantum of action] towards a species that would end up using math to understand its environment [and discover the the quantum of action]."

"However, that doesn't explain why we find ourselves in an environment that displays such regularities to begin with." Now WHY is always a great question; but too often recursive. So let me answer personally: In that the quantum of action was undoubtedly in the environment before I was, I understand why I find myself in an environment that displays such regularities: because without them, neither this concrete environment nor this concrete I would be here to exchange ideas with concrete you and concrete Sylvia!

Hoping this quantum-like contribution helps, and with my very best regards;

[link:fqxi.org/community/forum/topic/2491]Gordon Watson: Essay Forum[/link]. Essay Only.

Georgina Woodward

Hi Sylvia,

A very enjoyable read. I did find it accessible and thought provoking.

Re thinking the unthinkable- I think we can think about the unthinkable without actually being able to think it : ) If I look at a cup I see one viewpoint of it. However emanating from its surface is potential sensory data- that has the potential to give many different views. The whole truth of what it, the object, is would be like taking all of that data at once, not a tiny sub set, and forming an image. If an amalgamated manifestation is formed showing all viewpoints at once, the many different outputs would not allow clear definition of any singular form -too much information at once would cause the image to be a blur.

So while we can imagine viewpoints not seen individually we can not imagine all of them at once. The source of all potential manifestations, the object, is not altered by which manifestations of it are or are not fabricated. So the source object might be considered to be before and after observation in a superposition of all orientations, relative to all possible observers. Only when a manifestation is formed by an observer is it thought to be as it is seen -one viewpoint rather than all. This is a transition across a reality interface, the observers sensory system in this case, ( that transition corresponding to hypothetical wave function collapse ) from what is independent of observation to what is observed to be. Leaning not towards an abstract Platonic realm of perfect mathematical objects, that you mention, but a realm of concrete absolute source objects and complete information.

Good Luck , Georgina

Dipak Bhunia

Dear Dr. Wenmackers,

Thanks for "Children of Cosmos". You are rightly said regarding selected roles of such "Children of Cosmos" or "mathematizing mammals" where you have concluded:"we are selected" and "our mathematics is selected" as well.

But from where or how that selection came from? Or who made that selection? Probably you are not conjecture to mean to have direct intervention of GOD? Rather, if such a selection is a kind of logic or pattern (the term what you have used) followed through casual steps (in cosmological evolutions) onward arrow of time (as like as Darwinian steps in biological selections by same nature) would be understandable.

However, instead of such "mathematizing mammals" centric views about the nature (it may include universe or multiverse but makes no differences) to link the physics and mathematics, why one could not think the same nature as if a huge set of some intrinsic elements e.g. all hardwares (to deal with physics) plus all softwares (to deal with mathematics), and all "innate cognitive abilities" in those "Children of Cosmos" (to deal with neuro-cognitive cyber-sciences) are fundamentally emerged out from the combinations of such hardwares & softwares to explore that nature through all "Toy models of science" no matter how many times are modified onward cosmological arrow of time? Because such "Children of Cosmos" is also a part of that nature.

Thanks

Dipak Kumar Bhunia

Rick Searle

Dear Sylvia,

I loved your essay, and you have a wonderful writing style. In large part I agree with you- that our mathematical thinking has been selected for by nature as part of our ability to recognize patterns. I also agree with you that there are limits to this sort of mathematical thinking.

What I wonder though, is if mathematical "thinking" is selected for, not just in humans, but in animals- such as was shown to be the case in the "Honeycomb Conjecture" how can we say that it is not a property of the world that exists independent of humans?

The conclusion of your essay where you suggest we need to practice intellectual "judo" to see beyond mathematics to other ways of structuring the world I found especially intriguing. Do you have any hints as to what such thinking might entail?

Again, really enjoyed your essay. Please take the time to check out and vote on mine:

http://fqxi.org/community/forum/topic/2391

Best of luck in the contest and all of your endeavors,

Rick Searle

Marcel-Marie LeBel

Sylvia,

Wondering about the pieces of the puzzle, we tend to forget about the board; that which underlies all the pieces and allows them to exist in the first place.

"Could our cosmos have been different - so different that a mathematical description of it would have been fundamentally impossible" I don`t think so. We are the universe looking at itself; our logic, our maths are that of the universe.

Best of luck,

Marcel,

Marcel-Marie LeBel

Sylvia,

Wondering about the pieces of the puzzle, we tend to forget about the board; that which underlies all the pieces and allows them to exist in the first place.

Best of luck,

Marcel,

Edward MacKinnon

Sylvia,

A very stimulating essay. I differ on the selection process. For 95% of human existence humans, like their hominid predecessors lived in small Hunter-Gatherer groups. Here Darwinian evolution was operative in a way that it is not now operative. Most individuals did not live long enough to reproduce. This inculcated the dispositions needed for survival, willingness to sacrifice for the sake of the group and some form of altruism within the group. Mathematics could develop only when a more sedentary life style developed. In the very different universe you consider I doubt if hominids could have survived.

Edward MacKinnon

Sujatha Jagannathan

In accordance with your work, I would like to get answers from you :

If MAN is born only because mathematical bound how the physics came in this picture?

If everything are here in numbers with no texture and color which inanimate and animate would live?

Regards,

Miss. Sujatha Jagannathan

Harry Ricker III

Dear Sylvia, Good job on this essay. It is a better essay that the ones I have read so far. However, as I read, I became less and less convinced of you thesis and at the end felt unsatisfied. You are on the right track regarding the selection effect. In my opinion this issue is not complicated. We invent the universe as we imagine it to be. That process involves mathematical imagination. A lot of that is not effective as being persuasive in terms of explanation. Yet some of the imagination works well as in classical physics. But that is based upon infinitesimal calculus. As you show that is not correct mathematics. So we invent some new mathematics that fixes the problem. I think the real question ought to be how is it possible for wrong mathematics to be so effective in physical science. That is because as we learn we discover that the math used before is wrong in many ways. So we are constantly reinventing the math to fit the universe. I think this is because humans want a mathematical universe, not because the universe is mathematical.

James Hoover

Sylvia,

Time grows short, so I am revisiting essays I've read to assure I've rated them. I find that I rated yours on 3/13, rating it as one I could immediately relate to. I hope you get a chance to look at mine: http://fqxi.org/community/forum/topic/2345.

Jim

Sylvia Wenmackers

Dear Jim,

Thank you for both of your comments. I finally got round to reading and commenting on your essay as well.

Best wishes,

Sylvia

Sylvain Poirier

Hello. In your essay you wondered how "to imagine a world that would defy our mathematical prowess", in fact you mean : that would be anything else than highly mathematical in the way it was found.

In my essay I gave some precise expressions of how remarkably mathematical the universe is, what does this precisely mean. Moreover I do hold that, aside the remarkably mathematical aspects, there are also non-mathematical aspects, and I gave a precise sense to this claim.

Other descriptions of the remarkably mathematical character of the universe, showing that it really means much more than tautological consequences of the human ability to do mathematics (which you unimaginatively assume to be all what it might mean), are given in other essays: those of Peter Woit, Alexey and Lev Burov and Martin Seltmann.

David Hestenes

Sylvia,

Here are a few points for you to consider.

There are patterns in nature, but only reproducible patterns can be modeled with mathematics.

When there are reproducible patterns that we cannot model with our mathematics, we invent new mathematics to do the job. That is where most math comes from and why it works so well.

You say that probability and statistics informs statistical mechanics. I submit that the opposite is closer to the truth. On this point see

"Probability Theory, the logic of science" by E.T. Jaynes

-- one of the great books of the twentieth century!

.....David

Sylvia Wenmackers

Dear David Hestenes,

I am grateful for your comment.

I am very fond of the work of E.T. Jaynes! For instance, in my course on the philosophy of probability theory, I teach his analysis of the chord paradox. But I take your point: my statement about statistical mechanics was sloppy at best.

Best wishes,

Sylvia

Cristinel Stoica

Dear Sylvia,

I enjoyed reading your essay. Indeed, we understand the world, at least as much as we do, because we are its children, and this may explain why our math is effective in our physics. The four elements, in particular selection, support very well your thesis, and the example of non-standard analysis is well chosen. The style is eloquent, pleasant and funny just as much as it should be (I loved the disclaimer). I am very glad I didn't miss your essay!

Best wishes,

Cristi Stoica

Sylvia Wenmackers

Dear Christi,

Thank you for your positive comment!

I had already read your text, but waited for the deadline to submit all my comments in one batch: it is now in your forum.

Best wishes,

Sylvia

Michel Planat

Oups: "it is not nature, it is scientists that are simple".

Thanks Sylvia, I agree with most you are writing, a truly Darwinian essay.

Michel

Sylvia Wenmackers

Dear Michel,

Thanks for your kind comment. I also wrote a reply to yours.

Best wishes,

Sylvia