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Limits of Science

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Dr. Steve Strogatz wonders if we've reached the limits of human scientific understanding, and should soon turn the reins of research over to robots. Cold, calculating robots. Then, Dr. Hod Lipson and Michael Schmidt walk us through the workings of a revolutionary computer program that they developed--a program that can deduce mathematical relationships in nature, through simple observation. The catch? As Dr. Gurol Suel explains, the program gives answers to complex biological questions that we humans have yet to ask, or even to understand.

Comments [31]

Michael Winn from Nh

Very enjoyable! The latter statements about lack of understanding of computed "answers" reminded me joyously of one of the all time best known: "42"

Dec. 22 2016 08:28 AM
khoi hoang

I don't think that humans' brain is limited. We just have not discovered things yet. Although, there are myriad issues that we can not explain, there are also a lot of things that we have discovered in the past century. Maybe it takes a long time to be discovered, it does not mean that it is undiscoverable. Furthermore, I think that we are already very intelligent when we create algorithm and computer. We should continue to use computer as a useful weapon to discover and to understand the subjects.

Oct. 12 2016 12:46 AM

This episode is mind-blowing. I believed that people will invent new kind of language (calculus) to explain the universal law, but I did not expect we already found it. Although we are not able to understand how it works yet, but there's no doubt that it's a great break though in human history, and I hold an optimistic view of understanding it, because we are pioneers, and we just began.

Oct. 11 2016 01:48 AM

Love this episode, due to this becoming a truth in many different avenues of life.

Mar. 03 2016 05:33 PM
Mike O'Dell from NoVA

When talking about the results of analsing the cell,data, you say, "We have the answer but we don't have the insightf."


The Insight IS the answer - the equation is how you test and demonstrate the understanding.

Without the insight, all you have is exquisite correlation - you have no causation.
If you don't know why it works, you cannot know that it works because your result
is not falsifiable.

If you are going to address these issues, which is very cool, you need to do the History of Science
homework first.

BTW - the Eureqa web site shows the program "discovering" the Lagrangian and Hamiltonian of the
double pendullum. Yes, it found two equations based on invariance - very powerful indeed. But
the ability to recognize the equations for what they mean was done by humans with huge experience
with those forms and how they explain things. Again, it certainly found the patterns, but it did nothing
to explain them or connected them to the rest of Mechanics. This last part is the Science, not the

Feb. 28 2016 01:14 PM
paul from Colorado

I mean ... how can I not think of this?

Feb. 28 2016 12:28 PM
Robert Thomas from Santa Clara

The whole program of reductive scientific investigation is to eliminate aspects of the observed world in order to perceive patterns that are obscured by the world. Theories of the world are models of verisimilitude with the world that must be simpler than the world, eliminating parts of the world. Else, the model would be the same as the world and reveal nothing unavailable to mere raw observation of the world.

That's why science is called "reductive".

Journalists: not philosophers.

Feb. 27 2016 05:11 PM

Plug it into the output of another computer calculating π ?

Feb. 27 2016 04:58 PM
B-dawg from A Short Time ago, in a Galaxy close, close by

Well, I've suspected for some time that humans may be too stupid to solve problems like cancer, nuclear fusion, and other things which have eluded us for the last 60 years. Maybe turning the problems over to machines (and perhaps replacing our bodies and brains with machines) is the next step in the natural evolution of our species.

Dec. 28 2014 10:52 PM
Mike R. from west coast

Instead of finding F=ma, it would be more amazing if it found the Hamiltonian of the double pendulum. Which it did! This page and video cleared up a lot of questions for me about the experiment and the method of symbolic regression used by Eureqa:

Nov. 12 2014 04:18 PM
Matthew from United States

Douglas Adams was quite ahead of his time.

The great computer Deep Thought takes 7 1/2 billion years to answer the Ultimate Question of Life, the Universe and Everything. When the answer comes back 42. No one understands. Deep Thought points out that they asked the wrong question and would have to wait billions of more years for the next computer to provide the Question.

Nice work, Adams.

Oct. 22 2014 04:29 PM
Robert Thomas from Santa Clara

F = ma can only be deduced from a set of true assertions that include the definitions of F, m and a. These definitions are made using one another, or with a chain of such definitions. This is a circular process which reveals nothing not already included in the initial assertions. The formulas used by the software can only confirm that the data converge on a result already implicit in these definitions.

This (illusory revelation from automata) is a consequence of the lamentable fact that few scientists have any education in the foundational structures or philosophies of mathematics or science.

David Hilbert confronted Kurt Gödel squarely. This lead to a strengthening of mathematics through recognition of its limitations and proper province.

Western analytic philosophy entered a period of turmoil at the same time that physics was acclimating itself to Quantum Field Theory as the best available picture of the world, a program that has been progressing for a century. Contemporary analytic philosophy was not able to sensibly confront the complex ideas that emerged from scientific inquiry after 1950. The enervation of philosophical progress since that time hasn't lessened the need for a sober project to place science on a sound philosophical basis of the sort that Hilbert demanded for mathematics. Sadly, no new Hilbert seems available. Even if he were, who would pay his salary? Google?

Oct. 18 2014 07:06 PM
asdf from Utah

This segment reminded me of the Ted Chiang short story "The Evolution of Human Science."

Here's a brief snip:
"No doubt many of our subscribers remember reading papers whose authors were the first individuals ever to obtain the results they described. But as metahumans began to dominate experimental research, they increasingly made their findings available only via DNT (digital neural transfer), leaving journals to publish secondhand accounts translated into human language. Without DNT humans could not fully grasp prior developments nor effectively utilize the new tools needed to conduct research, while metahumans continued to improve DNT and rely on it even more. Journals for human audiences were reduced to vehicles of popularization, and poor ones at that, as even the most brilliant humans found themselves puzzled by translations of the latest findings."

Sep. 25 2013 03:53 PM

Good day! This is my 1st comment here so I just wanted to give a quick shout out and
tell you I truly enjoy reading through your blog posts. Can you recommend
any other blogs/websites/forums that deal with the same subjects?
Appreciate it!

Mar. 07 2013 06:53 AM

Listened to the Limits to Science broadcast today on WITF Harrisburg(8/31/12). The segment on the computer program to analyze complex problems was interesting but a bit overblown. The fact that the program identified F=Ma as the equation governing a double pendulum is more or less self-evident. F=Ma governs a simple pendulum, so it also must govern a complex penduluim. I kept waiting for the program to identify show some sort of pattern or complex chaotic attractor in the double pendulum behavior.

The other analysis of the workings of a cell was also overblown. Essentially, the program came up with an empirical equation describing the data it was given. Chemistry has used equations of this type for nearly two centuries. The Arrhenius equation, describing reaction rates was used for 50 years before why it worked was explained by the application of statistical thermodynamics by a string of authors. Empirical equations are useful, within their limitations. One of those limits is they do not get into the why of what is going on. They just provide a convenient tool. The why comes from application of more basic science, such as quantum mechanics, statistical thermodynamics etc.

Sep. 01 2012 09:22 PM
Scott Murphy from Oklahoma City

I wanted to comment on the equivalence suggested in this segment, between Newtons discovery of F=ma and Eureqa's derivation of the same law. I downloaded the eureqa program, and used it to find governing equations of a string. What is missing from a comparison between this work and the work of Newton is a discussion, not of the physical laws but of the available mathematics. The article makes a big point of saying that the eureqa is able to calculate F=ma or put differently; There is some quantity called force that is proportional to the instantaneous change in the instantaneous change of position of the pendulum. The Eureqa machine is capable of using calculus as a given. What made this task so hard for Newton was he had to create the calculus of instantaneous change. The problem that Eureqa solved is much more like that which a first year physics student solves( only, it did it with a much more impressive dataset) in that, thanks to Sir Isaac Newton, we have all the rules of calculus and mathematics to assist us. I don't want to act like this program isn't awsome though! Just not Newton awsome. Maybe next time.

Jul. 08 2010 10:20 AM
Skipper from Palo Alto, California

An expanded essay to elaborate on the first comment above: []

May. 18 2010 10:43 PM
amy obukuro from yokohama, japan

@skipper-- I just saw Stephen Wolfram's TED talk, too, and that's exactly what came to my mind when they were describing the Euriqa bot. That, and (along with everyone else, apparently), 42. Dear Mr. Adams, you have achieved immortality....:)

Apr. 29 2010 09:50 PM
Skipper from Palo Alto, California

The work of Stephen Wolfram is intriguing in this context of the increasing computational power that allows things like the Eureqa bot. He gave a TED talk this year that seems highly salient to this segment: []

Apr. 27 2010 09:56 PM
Arnold Lustiger from Edison NJ

Eureqa accurately modeled cell behavior, but the implication is that the information is of limited use because we don't know "why" the cells behave as they do. Newton also did not know "why" F=MA, yet we build bridges via such equations. The discipline of engineering is based on equations that we do not, nor need to, understand.

Apr. 25 2010 01:42 PM
Skipper from Palo Alto, California

The Wall Street Journal posted an interesting article last year entitled "A Wandering Mind Heads Toward Insight," a piece centered around the "aha!" moment as subconscious (but very involved) work in the brain.

If you daydream (which you do), the article might trigger some insight...

Apr. 23 2010 03:20 PM
Glenn Dewar from Astoria, NY

LOL, the minute that they said that Eureqa gave them the correct answers about cellular function but that they still didn't know why all those systems worked the way they did, I thought - They got the answer but didn't know what the question was... it's Deep Thought!

It's great to see that I wasn't alone in thinking that Douglas Adams would have been very amused by his prescience.

Apr. 20 2010 11:48 AM
Skeptic from Urbana, IL

I'm not impressed by that discussion. It seems to me to be just another way of introducing magic and mysticism into science. There have always been complex systems (like the movement of planets) that are first approximated with various equations, followed eventually by a deeper understanding. And I think it's also wrong-headed to single out biology as being uniquely complex. The evolution of a solar system (without life), for example, is not a trivial exercise in physics. In fact, I suspect that the operation of single cells will be completely defined (for all practical purposes) long before the evolution of large systems in the universe.

Everyone wants to feel like they are living in special times. And there is always the temptation to jump to the conclusion that, because something is now difficult to understand, that we have reached our limits in some special way that makes us special.

Apr. 20 2010 10:30 AM
Michael D from DC

Michael S:
You can download Eureqa and try it out at:
(they also have available their datasets downloadable somewhere)

I haven't had a chance to try out Eureqa, but have used a different data mining program, Weka, which is a little easier with reading in files and can support nominal data, like text (but in fairness, Weka is in its 3rd major release).

Comparing the two would be like comparing apples to oranges. Eureqa is intended for finding scientific laws, Newton's second law for example, whereas Weka searches for classification models, like comparing apples to oranges.

Apr. 19 2010 10:16 PM
Michael Segel from Cambridge MA

Does anybody know where I can learn more about eureka?

Apr. 18 2010 02:43 PM
Sandi from Madison, WI

I was a little disappointed that the discussion on The Limits of Science didn't include Thomas Kuhn's "The Structure of Scientific Revolutions".

That warm, fuzzy "Aha!" moment in the grand world of science is a (pardon me) paradigm shift. And sadly, those of us living in the old paradigm cannot even vaguely imagine the new paradigm until one creative mind can see it differently. (See examples: Galileo, Newton, Einstein)

Apr. 12 2010 08:30 PM
Skipper from Palo Alto, California

Douglas Adams was brilliant satirist as much as prescient predictor of our eventual technological capacity (insofar as Deep Thought is like Eureqa). The unfathomably simplistic answer of "42" and the consequent quandary that faced the receivers of the answer to Life, the Universe, and Everything in H2G2 is partially intended to make us aware that we are limited in our abilities of comprehension. But it's also there to show that meaning is not inherent in an answer. 42 is the answer to uncountable questions (e.g. "What is six times seven?") and Douglas Adams chose it bearing this fact in mind; consider that if the answer Deep Thought gave was a calculus equation 50,000 pages long, the full insight of his satire might be lost on us poor readers, who naturally assume a result so complicated is likely to be accordingly meaningful, when in fact it is no more inherently accurate or useful in application than an answer of 42.

Apr. 12 2010 02:29 AM
Elspeth Suthers from Boston, MA

I am so glad that I am not the only one who instantly thought of 42 when listening to this segment.


Apr. 11 2010 02:46 PM
Aaron Petcoff from Woodbridge, Detroit, MI

What is six times seven?

Apr. 10 2010 11:29 AM
David A Keary from Kansas City, MO

All I can think of is 42, and how Douglas Adams seems to have seen this coming long ago.

Apr. 08 2010 03:27 AM
Skipper from Palo Alto, California

I share Steve Strogatz' concern about our impending scientific uselessness. I do wonder, though, if it's merely imminent or already arrived. After all, what is human language to the Eureka bot but a superfluous step to repackage the formula into a less precise, linguistically bound representation? If one considers mathematics to be the most concise description for phenomena, hasn't the bot already had the purest insight?

I think part of the reason we don't think of the robot as having 'true' human-like insights is because the robot doesn't have other systems to consider or imagine. That is, Eureka doesn't think about how human understanding is affected by the discovery. When Newton discovered his famous F=ma law he reached the same ultimate conclusion as the robot. The difference was that Newton, a human-concerned machine, ascribed meaning to the formula by associating it to systems that have meaning for humans, namely physics and consequently engineering and technology. A robotic scientist doesn't have other complex systems to consider (at least until we program them to care about speaking our language). When Eureka reaches a profound insight about the phenomena it observes and displays the final formula, it has already discovered everything that is inherently meaningful.

There's clearly a greater question about meaning in this story, but meaning is an area needing insights all its own. I'm thankful Radiolab is unafraid of challenging its listeners with these issues!

Apr. 06 2010 05:41 AM

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