Physicists and Philosophers Debate the Boundaries of Science
quantamagazine.org
quantamagazine.org
Trying to fix the problem through weaker definitions of "testable" is desperation. All those smart people hate to face the fact that what they're doing may be total bullshit. This has major economic consequences for physicists - why should they be funded? Physics is funded because it produced the atomic bomb and semiconductors. Those came from the testable parts of physics. Untestable physics cannot produce engineering technology.
(The article says "no one has ever seen an atom". That's just wrong. There are lots of picture of atoms. Even pictures of atoms lined up to spell "IBM".[1])
[1] http://www.nytimes.com/1990/04/05/us/2-researchers-spell-ibm...
Physics is still a hard science. However, the edges of physics are difficult to test.
> In cosmology, you can only observe, not experiment
Saying that is like saying "we don't know evolution is true, because we don't see new species evolve every day". It's a naive approach to science.
In both cases, you can use theories to make predictions about new things to look for. e.g. http://tiktaalik.uchicago.edu/
> Physics is funded because it produced the atomic bomb and semiconductors.
Physics is funded because it's cool. And it still gets less funding than major sports leagues. So by your definition, the NFL is funded because it's part of a national defence strategy?
>Saying that is like saying "we don't know evolution is true, because we don't see new species evolve every day". It's a naive approach to science.
In general it's also true of almost all astronomical research, and large whacks of geology. Which is fine because experiments are just observations that scientists are the impetus for. Science works by gathering data, experiments just let us produce data to gather at our own speed instead of having to wait around for something to happen and hope we're looking in the right direction when it does. In the case of astronomy instead of relying on experiments to produce more data we mostly build better instruments.
Football isn't funded by the federal government at all, so your point about national security is just silly.
We do see new species evolve every day. We also see microevolution so commonly that it's a standard high-school biology task.
> Physics is funded because it's cool.
The point being made is that for a long time, it was common for physicists to look down their nose at other sciences "because what we do is real". Now they're finding themselves in the same boat.
Can you describe?
My memory of high school genetics involved experiments with Drosophila eye color, etc. which were really about the passing of genes and, sometimes, mutation. However these experiments didn't prove that natural selection or seemingly random mutation were necessarily what drove species to change over time to create new species based on their environment. I had to accept that. I also accept that people tell me human and chimp DNA is similar.
Theoretical physicists also attempt to explain things that they cannot see or experience, and if people believe it, they believe it.
Science, in part, requires faith.
Think of everything you think you understand about science and about our world. How much of it did you really prove with your hands, and how much instead did you just read or hear and understand to be true because others wrote or said it was true?
You can put your faith in theories, and that has proved practical for many physicists and biologists, just to name a few. A god or gods could also be driving those evolutionary processes in part, or could have set things in motion. Accepting religion and scientific facts both require faith, and that's ok.
Only at the bleeding edge, which you don't need to use in your everyday life. Most science-related things at human scale can be done with your own two hands; you don't require billion-dollar tools to fiddle with materials science, for example. Youtube is filled with videos of people doing human-scale science.
The whole 'science requires faith' argument is largely thrown out to give credence to religion. The problem with that argument is that the fundamental building blocks of science do not require faith, and you build from those. The SI units are convention - you can make your own. What constitutes validity is convention - you can decide your own way. You don't require faith to start doing basic science.
On the other hand, religion's basic building blocks require faith from the outset. Person X is divine, 'trust us'. God Y likes or doesn't like that, 'trust us'. And from these basic religious building blocks, whole edifices are built. For example, most catholics are unaware of how the bible was pieced together by committee. That information doesn't affect their day-to-day lives, however the religious rules that do affect them are based on those fundamental building blocks that are unverifiable by anyone. Faith is required because the foundational blocks are not verifiable at all.
This does not happen in science - you can verify the foundational rules yourself, and build as far along the tree as your interest and tooling allow. Theoretical physics existing in the 'faith' world is largely a canard - most science is not like this, and theoretical physics is at the exploratory edge of science, not at the core foundational blocks. In short, the Planck Length is defined by the meter which we can see and confirm; the meter is not defined by the Planck Length which we theorise about.
Not to mention that in general, 'scientific facts' are constantly tested, and 'religious facts' are not. The engineering capabilities of steel are in constant use in almost every part of our lives; if science was wrong about them, the material would fail in unexpected ways. The divinity of the christ figure... well, it isn't even testable. Christ is only divine to christians, but a steel bridge needs to hold up regardless of the mental state of the humans using it.
He means how do you know the speed of light is 186,000 mi/sec? Did you test it yourself? Or are you taking someone's word for it? It's one or the other.
> On the other hand, religion's basic building blocks require faith from the outset.
I think you and the guy above you used the wrong word. Instead of faith, I would have used "trust". I trust that Einstein and his peers who studied his work are correct in their assessment of his theory of relativity. I don't need to test it myself, I take their word for it. I trust them.
On the other hand, people who compare something like string theory to philosophy really have it backwards. String theory might be untestable right this second due to technical limitations (string theory does make quite a few unique predictions) but that doesn't mean it will remain that way forever. Hell, it may not be that way tomorrow with as fast as science has been progressing... This is in contrast to proving the existence of a God or deity which has zero hope of ever being testable because it's "inherently" untestable.
As far as string theory goes, one of the most obvious predictions are strings themselves. We cannot build an accelerator large enough to smash particles together at the speeds required to look for strings but that doesn't mean such a thing is impossible; such an accelerator already exists - supermassive black holes. They accelerate particles at the required speeds to look for strings.
I take someone's word for it, but here's the kicker: I don't care. That particular measurement doesn't affect me one jot if it's a different speed. I don't play with optics; the measurement affects nothing I choose to do. However, if I did care, I could work from first principles and find out; it's really well documented, and I can also create my own methodology. This is not true of religious requirements. Throw money in the plate on Sunday because this guy two thousand years ago was divine? There is no way I can verify that.
> Instead of faith, I would have used "trust".
I did leave out a bit saying that the GP was using two different forms of 'faith' that were apples and oranges, but left it out as I was already waffling. :)
However, you will find that as you do your own science, it pretty much always conforms to the rules found by people who have come before you. It's really only as you near the expansion fringes of science that you start getting conflicts with mainstream thought.
Again, this does not happen with religion, where often the argument becomes "god moves in mysterious ways" or "who can know his plan, but he does have one". Core rules that don't make sense with the observed world are often distorted with these phrases. There are definitely grey areas and fuzziness in science - biology has a lot of fuzziness - but there are still common behaviours that work regardless of your cultural background. Born into an Egyptian Coptic family, Christ is divine. Born into the Muslim family next door, Christ is a prophet, but not divine. The fundamental essences of science just don't move with cultural background like that; the resistivity of copper doesn't care about your state of mind.
There is definitely trust involved in science, but trust is a thing that can be broken and reshaped and is allowed to be examined and verified, where faith is not. Besides, if trust is broken, that's considered a fault on the part of the person providing the information. However, if faith is broken, that's considered a fault on the part of the person receiving the information.
But word choice is important - by saying "science relies on faith", the underlying agenda is that other things that rely on faith should be given the same level of trust, even though they don't expose themselves to the same level of inspection.
Physics is interesting in that both types of science are successful, where in say molecular biology or geology only one type dominates.
Guess who is thus interested in funding entertainment.
[1] http://jfi.uchicago.edu/~leop/AboutPapers/Boltzman.pdf [2] https://en.wikipedia.org/wiki/Brownian_motion
By contrast, the small bit work done on theories that have purely theoretical appeal is getting all the press, and in a way that needs to improve a lot before one could call it grossly misleading. Take for example the sentence,
“The imprimatur of science should be awarded only to a theory that is
testable,” Ellis and Silk wrote, thereby disqualifying most of the
leading theories of the past 40 years.
Some theories are so easy to test, a 4th grader in her science class can test it conclusively in half an hour. We don't even question these theories anymore, because they've been set in stone for centuries.
Some theories take millions of dollars and several years to test, but they're manageable by large research universities and governments. At the very edge of this range, we have things like the Large Hadron Collider testing the existence of the Higgs boson. That one actually cost a few billion dollars and several decades, but we could live with that.
Some theories will take trillions of dollars and several centuries to test. Perhaps it will be quadrillions of dollars and several millennia instead, or even several million years. Right now, we don't even know what kind of technology we will need to test string theory. Perhaps we'll need to evolve into something else before our brains can even imagine what it would take to test it. But eventually we'll get there, if we learn to accept that science is bigger than all of us and stop being so impatient.
The difference between these three kinds of "testable" are quantitative, not qualitative. It just looks qualitative because the quantities involved are so huge. But if someone cannot grasp the idea of a theory that takes aeons to develop and test, I don't think they're qualified to judge the merits of theoretical physics.
Sure they can. Build a particle accelerator with one million times the power of LHC. Not knowing and not having the technology are two different things.
Fifty years ago nobody knew how to test the Higgs boson theory either. That didn’t stop them from moving on and when the technology permitted it run the tests and solidify the hypothesis. String theory didn’t just popped out of the heads of physicists who had nothing better to do with their time. Parts of string theory are already tested, the discovery of the new particle that was semi announced last week at LHC was predicted by a model of string theory. That’s how science progresses, with little steps. So don’t get pessimistic, scientists have done huge progress in the last hundred years or so.
Lastly, let’s not forget how little funding science gets these days and how many different areas they have to cover. It’s not just physics, you have cosmology, space exploration, biology, energy, just to name a few.
It’s not science’s job to answer philosophical questions. If for example philosophers feel powerless because of the multiverse theory we should stop theorizing it? If it turns out that life and everything we know is just the result of a mere stroke of luck, one universe with the proper conditions popping out from a variety of trillions, what should science do about it?
All those smart people hate to face the fact that what they're doing may be total bullshit.
It’s funny saying something like that in Hacker News. Everything each and every one of us does has the potential to turn out as total bullshit. Every single day we write code that turns to be total garbage. And yet we’re doing it. You should watch the “Particle Fever” documentary. There you’ll see the reactions of physicists who favor supersymmetry in the possibility that it proves wrong. Everyone is devastated but they accept it. It’s part of the job. You make it sound like these guys are disillusioned. Scientists know perfectly well the consequences of following a wrong path in their career but they do it either way and we should be grateful to them, not despise them for it.
I'm not a physicist but pretty sure there's not one kind of physics. Applied physics is still hard science while theoretical physics does not lend itself as well to full scientific method. Both are highly valuable. When Einstein came up with special relativity he had no way to verify it in a lab but that turned out pretty well.
That's why some consider it physics inspired branch of math. For now.
> why should they be funded?
Until we have room temperature superconductors they are note done.
Rumors say that the more practical physicists have always been looking down on cosmologists for the same reason.
There are things that arise out of the mathematics and it seems like you think the answer is just ignore it since we do not have perfect tests right now. I agree that some claims are very grand without sufficient experimentation but I don't think we should throw the baby out with the bath water.
Equivocation:
You used "we" to mean government ("trillions on wars"), then private citizens ("hundreds of billions on sports..."), then back to government ("a few billion on producing knowledge"). "Our" war spending is certainly not related to "our" watching ESPN.
Red herrings:
War spending, lining corporate pockets, and private entertainment are unrelated to whether -- and to what extent -- fundamental physics should be government-funded. In fact, one may be a peace-loving socialist and still not believe that this research is the best investment for a nation's finite resources.
Begging the question:
You've assumed that research into string theory, multiverse theory, etc. produce knowledge, which is the very question being debated here. Knowledge is generally regarded as justified true belief [4] (albeit with qualifiers [5]). At issue here is whether one's scientific beliefs are adequately justified without empirical support -- i.e., whether we're producing any knowledge at all regarding this issue.
As a disclaimer, I was a researcher at a government lab for 5 years. In many cases, I believe scientific research is worth funding. That said, we should take care to present sound arguments regardless of the topic.
1. https://en.wikipedia.org/wiki/Equivocation 2. https://en.wikipedia.org/wiki/Red_herring 3. https://en.wikipedia.org/wiki/Begging_the_question 4. https://en.wikipedia.org/wiki/Belief#Justified_true_belief 5. http://plato.stanford.edu/entries/knowledge-analysis/
Seems a better critically minded approach is to consider their arguments - rather than brush them off by calling them desperate
An ordinary microscope, which employs optical lenses, could view objects
smaller than the wavelength of light. An electron microscope could view
smaller things with greater clarity than an optical microscope, but still
could not clearly view individual atoms.
So Binnig and Rohrer decided to build their own instrument – something new
that would be capable of seeing and manipulating atoms at the nanoscale level.
To do that, they began experimenting with tunneling, a quantum phenomenon in
which atoms escape the surface of a solid to form a kind of cloud that hovers
above the surface; when another surface approaches, its atomic cloud overlaps
and an atomic exchange occurs.
By maneuvering a sharp metal conducting tip over the surface of a sample at an
extremely small distance, Binnig and Rohrer found that the amount of electrical
current flowing between the tip and the surface could be measured. Variations in
this current could provide information about the inner structure and the
height-relief of the surface. And from this information, one could build a
three-dimensional atomic-scale map of the sample’s surface.
Also, knowing what's testable requires testing itself. Science has always been about incremental fraying at the edges of knowledge to answer 1 little question and open up 100 more. Things might not be perfectly testable today but that doesn't mean they won't be in the future or that we can't someone make progress with theory and models.
[1] http://researcher.watson.ibm.com/researcher/files/us-flinte/...
In my first language I think most people would agree that seeing involves visible light and eyes. We say the blind can't see, because their eyes don't work. We say that we can't see in the dark, because there is not light.
Sometimes we use see in a metaphorical sense, like "the blind see with their fingers". No one would confuse the fact that blind people gather some information about their surroundings with the help of their fingers with the fact that blind people just can't see. It's not the same thing.
I could agree that one can say "seeing" in regard to an atom in a purely metaphorical sense or poetical sense but that was not my interpretation of the original statement.
Maybe in English it's just different?
You can take a picture of a car and you can see a car with your eyes. You can take measurements of an atom and visualise that measurements but you will never be able to see an atom.
To put it another way: Imagine you and me took a picture of a green car. In your picture the car is green, in mine the car turned out blue. Would you agree that your picture is more realistic than mine?
The color of the atoms in the IBM visualisation is purely artistic. You will never be able to say green atoms are more realistic than blue ones. I’d even go so far to say the same applies for radius and shape in the IBM visualisation.
“no one has ever seen an atom" and no one ever will, because atoms don't exist in the visual realm.
We demonstrated interruptions of macroscopic duration in
a single trapped and cooled Ba+ ions’s 493‐nm
fluorescence. They are caused by transitions of the ion
into the ‘‘dark’’ 2D5/2 state.—Multiple simultaneous
jumps of three ions indicate cooperative interaction
with the light.
I'm not aware of a definition of atomic color but maybe that's a real thing in analytical chemistry, spectroscopy or some other field. I wouldn't be surprised.
Probably it's just the wavelength of the emitted light.
But yet, there isn't a crisis in physics at all since these theorists are so far removed from reality, I don't really care what they think. They don't really tell use anything useful or interesting so I tend to ignore them. Instead, I focus on things we do know exist but cannot explain, say astrophysical jets, pulsars, or supernovas. We know they exist and we can see them, yet we understand them very little. We have models that are getting better and better over time, but they all exist within the current understanding of physics. This is where physics really is. Whatever garbage the theorists put up on the arxiv can be ignored with little loss.
Instead, those of us "in the trenches" can continue our work trying to explain observed phenomena with our current theories. There is no need to add in extra dimensions or cohomology. Maybe, when we've done really understanding our current theories can we talk to those theorists again.
Incidentally, since I started my PhD in physics doing numerical relativity, my views on science have changed completely. I used to be interested in stuff like string theory, but actually sitting down and trying to do it left me feeling empty inside. Now that I work in an area that is very closely related to observations, I feel like I am actually learning something about the universe. It's hard to explain philosophically, but I really believe in experiments as the guiding principle of science. In my case, we see pulsars (2500+ of them) and we have yet to provide a full explanation of their nature. To me there is something more real and scientific about this then trying to explain multiverse theory but I don't know the words to describe it.
At the very least all of these theoretical developments bring us incrementally closer to understanding the structure of Quantum Chromodynamics. We still don't understand the theory enough to tell whether or not there are tetraquarks! All the effort put into theoretical physics and mathematical physics improves our mastery of the standard model.
tl;dr; don't call math garbage :[
I hate when theorists take some abstract crazy idea and then say the universe has 10 or 11 dimensions when they have no basis for saying that.
Einstein was a theoretical physicist. Without his theories:
* Japan might not have been defeated in WWII.
* There might be more coal power plants, because there would be no nuclear power plants.
* GPS probably would never have worked.
* We'd have fewer successful space missions.
* There would be no superconductive magnets.
* There would be no digital cameras or solar cells.
* There would be no lasers.
I could keep going if you want...
References:
https://en.wikipedia.org/wiki/Albert_Einstein
https://en.wikipedia.org/wiki/Theory_of_relativity
http://www.guidetothecosmos.com/present_wwe.html
As someone has pointed out above, these theroies are surely "untestable and unverifiable" for now but that doesn't make them unfalsifiable so we must not critisize the theorists just because we cannot test and verify them.
"We can invent as many theories we like, and any one of them can be made to fit the facts. But that theory is always preferred which makes the fewest number of assumptions."
And yet, physics ignores his LAST and FINAL conclusion about HIS theory:
"We may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an aether. According to the general theory of relativity space without aether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this aether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it."
Can you expand upon this? I'm unclear as to which of Einstein's theories you are referencing.
And why does everyone think that without Einstein we would somehow enter a 100 year long dark age?
He said "without Einstein's theories". Physics would probably have progressed about the same, albeit set back by a bit without the man himself, but all those technologies would still have been dependent on someone doing what Einstein did.
Not really; you're just confusing your opinion with some deeper truth :)
We can posit that people exist with the opposite opinion (they do) and it reveals that all we've learned is how your views on what's interesting in science have changed.
The question of: "what is true" is NOT so easy as most people think. It is in fact a damn hard question and depends on the basic axioms you accept. First you need a logic, and there are many logics out there, classical logic and mathematical logic as one of the most accepted ones. Classical logic as humanly understandable is for example much more accepted in philosophy then the mathematical one, because it is much more stricter.
This question was also part of physics in the till 1920s but basically got forgotten there and the blind accepted of mathematical logic due QM became standard. Blind, because this is not a questions young physicists get confronted with.
Every good physicist was also a philosopher, simply, you can't separate those. You can't build a physical model without basic assumptions. You have to at least assume there is "stuff" of some sort, you have to assume there are dimensions of some sort.
Roughly a year ago, I stumbled about the BSM-SG model from Dr. Stoyan Sarg. http://www.amazon.com/Basic-Structures-Matter-Supergravitati...
I got intrigued, it only needs 2 fundamental particles, 3 Euclidean dimensions and one law of attraction. As a philosopher I heart was instantly: WOW, I have to give it a try. Never could accept more the 3 dimensions due thought experiments into lower ones.
I really spend month thinking about this theory, pah, once I had to take holidays from work because I could not think about anything else ;) And then I clicked and everything started to make sense, really everything. Each quantum effect, general relativity, atoms, spectral lines, like everything. In fact, once you understand the crystallization process of a galaxy, how such complex structures like protons, neutrons and electrons come to be.
It is funny to have an answer to this super old philosophical question: why, why this complex world. Because it is bound to be. Enough fundamental particles, and those bulks are bound to be, they crystallize in a quite complex but simple process into protoneutrons (protons/neutrons) & electrons that are bound to build a stable galaxy. The laws inside a galaxy are always stable and behave the same with matter made from the same galaxy.
(There is a corner case but i highly irregular one).
Anyway, I started to promote this model because nobody else seems to. Started a non profit for it etc. I knew that promoting alternative physical models gets strong opposition compared to all other sciences, but knowing what bad assumptions are in the Standard Model I just laugh silently about their ignorance.
http://www.pnas.org/content/112/24/7426.full.pdf
This hole understanding made me personally much more critical. I tend to distrust everything that requires mathematical logic - when I have a physical model that requires only classical one, why should anything else in nature be true when not. I look much more openly at fringe sciences, the explanaitions make usually no sense for me now, I understand the process is quite fast tho.
Btw, pulsars are not so hard to understand: Chapter 12.B.6.4 but you need to understand chapter 1,2,3,6 at least, otherwise it will not make any sense.
Nowadays, as several philosophers at the workshop said,
Popperian falsificationism has been supplanted by Bayesian
confirmation theory, or Bayesianism, a modern framework
based on the 18th-century probability theory of the English
statistician and minister Thomas Bayes. Bayesianism allows
for the fact that modern scientific theories typically make
claims far beyond what can be directly observed — no one has
ever seen an atom — and so today’s theories often resist a
falsified-unfalsified dichotomy. Instead, trust in a theory
often falls somewhere along a continuum, sliding up or down
between 0 and 100 percent as new information becomes
available. “The Bayesian framework is much more flexible”
than Popper’s theory, said Stephan Hartmann, a Bayesian
philosopher at LMU. “It also connects nicely to the
psychology of reasoning.”
Consider a simple theory - bear attacks will be very low in the UK forever. Consider an alternate theory - bear attacks will be low until 2016 and then the bearpocalypse happens. Both theories have passed all attempts at falsification - they both accurately predict that bears haven't so far eaten very few people.
The Bayesian approach is to assign a prior distribution to various theories of this nature. Because there are infinitely many possible priors, most exceedingly complicated (because the set of priors of complexity < C is finite or at least compact), we'll need to (eventually) assign low probabilities to high complexity ones. This gives a natural derivation of occams razor as well, at least as an asymptotic law.
A very readable approach to this is a post by Scott Alexander: http://slatestarcodex.com/2014/09/03/the-guardian-vs-inducti...
Wikipedia is also pretty good: https://en.wikipedia.org/wiki/New_riddle_of_induction
I don't think this would be a very compelling argument for Occam's razor if you didn't already believe it. This argument says you can't assign high probability to all "complex" theories, but it doesn't seem to say that the high probability theories must be simple. You could use any criterion at all to single out a high probability subset.
Lim_{complexity -> infinity} P(theory having fixed complexity) = 0
Stated more precisely, fix a prior distribution, then for any epsilon > 0, I can find a complexity cutoff C (which depends on the prior) so that P(any theory with complexity > C being true) < epsilon.
This doesn't mean that P(theory|complexity) is monotonically decreasing, that would be a much stronger claim.
I don't know how this isn't a compelling argument, it's a provable mathematical statement.
jwmerrill's razor: points in the plane should be considered to be close to the origin unless there is evidence otherwise.
Is this a reasonable law? As reasonable as Occam's razor? I think probably not, but I don't have a strong opinion. One interesting thing to note is that the law doesn't say where the origin is (similarly, Occam's razor is vague about what exactly is meant by "simple" and "complex").
Finite asymptotic form: for any finite point set, there is a distance D such that no point in the set is further from the origin than D.
Continuous asymptotic form: given any function from points in the plane to non-negative numbers which has a finite integral, there is a distance D such that the integral of the function over the region that is further from the origin than D is less than any epsilon_1, and such that the function is everywhere less than any epsilon_2 on this region except perhaps on a set of measure 0.
The asymptotic forms are provable mathematical statements, but I think it would be a mistake to say that either of them is a very compelling argument for the original statement of "jwmerrill's razor."
Without intending to call you out in particular (I don't know what opinions you hold), I think people sometimes accept some odd logic in probability theory that they would be less likely to accept in other contexts. Bayesian probability theory provides practical solutions to a lot of interesting problems, and I personally wish people would emphasize those cases more, and make fewer sweeping statements about it being a consistent theory of all of the scientific method.
I don't really know why you don't think that the asymptotic forms are evidence in favor of this - a prototypical probability distribution on the real line is a bump somewhere with a decaying tail. And that "somewhere" is far closer to the origin than points out in some arbitrarily distant tail.
Now obviously if you want to make stronger claims about a specific origin, you'll need to specify a particular probability distribution, and justify why that's the right one. I agree that a non-asymptotic Occams razor is an additional assumption.
But you also get pretty far with the asymptotic theory. Consider a theory of "green" as compared to a theory of "bleen" (namely that green turns to blue after some time T). You have a prior with some probability that only green exists (say 50%), and also a 50% chance that green turns to blue after some time T. But now you have a continuous distribution over T.
Now suppose you want to make a prediction - e.g., H = "the grass will be green, not blue, at t=50". When you compute a posterior, you reject all values of T < 0 (supposing the present time is 0). Also, all values of T > 50 actually yield the same prediction as "only green exists". So the only way you can get a prediction of blue at time 50 is if 0 < T < 50. Of course, the more time you spend gathering data, the further into the tail you move and the less likely it is that your posterior will predict blue. I.e., Bayesian stats even with very few assumptions gets sensible results eventually.
I do in fact hold the view that Bayesian probability is a consistent theory of the scientific method, and also of how humans should update their beliefs when new evidence is gathered.
(Minor nit: your continuous asymptotic form isn't slightly wrong for this purpose, f(x) need not approach zero. Counterexample: f(x) = 1 for x \in [1, 1+2^{-1}], [2, 2+2^{-2}], etc, f(x) = 0 elsewhere. That integrates out to 1/2 + 1/4 + ... = 1, but lim_{x -> \infty} f(x) doesn't exist.)
[I'm also a bit surprised you are being so heavily downvoted. I don't think you are right, but you are hardly so crazily wrong that you should be greyed out.]
Is the asymptotic relevant though? Physical theories are finite and generically quite small, and we have no a priori way to fix C.
It is still a minority position.
Predictably, as a hardcore supporter of Popper's version, I don't think this problem will be solved.
Andrew Gelman is the author of the most popular of the advanced "Bayesian Data analysis" text and is considered the standard.
He says false, bayesian falsificationism is better than confirmation theory and deborah mayo founder of error statistics essentially agrees with him.
http://www.stat.columbia.edu/~gelman/research/published/phil...
The use of Bayesian statistical methods in papers is reasonably normal, although still the minority position.
The use of Bayesian falsification or confirmation theory as a philosophy of science is increasingly common.
The argument that we should switch to Bayesianism in situations where we cannot sample from the likelihood function (ie: perform an experiment which yields evidence distinguishing one hypothesis from another) is a special kind of bullshit where the attempt at "science" is being packed into prior formation to favor someone's pet theory.
You could say the same for phlogiston or N-rays. Falsifiable hypotheses that actually get falsified are dropped from science, but the process of falsifying them is a scientific activity.
It is a demarcation criterion. Falsifiability is definitely a very good attribute but it is necessary, not sufficient.
BTW, is astrology actually falsifiable? I'm under impression that astrologists deliberately strive for unfalsifiability exactly to avoid falsification which could cast doubt on their wisdom.
It is. Just do the following experiment:
Find, say, ten persons and an (or many) astrologists and let them create a horoscope (say, either a prognosis for the future or description of character traits) for these 10 persons, where only the exact time and location of birth is given to the astrologists.
After that give all ten horoscopes to all ten persons and let them rank. Now just formulate some sensible statistical model and voila - falsified.
Of course, if the proponents of astrology choose to present it in a non-falsifiable way, then it is not science from the get-go.
When astrology was conceived, it was actually respectable science, if that concept had existed then, and it led to the development of astronomy. If you can predict the flooding of the Nile by the rising of Sirius, what else might the heavens show you?
I think it was Carl Sagan who said that "soft sciences" are actually "cargo cult sciences".
Out of your ten people, two are astrology haters and respond that everything is false, two are astrology nuts and respond that everything is true, two respond at random because they can't believe you are bothering them with such bullshit, two respond at random because they think you are CIA agent trying to read their mind, two respond mostly true because horoscopes are deliberately vague and they will find confirmation for most of the claims if they try hard enough.
So you get 55% true. With sufficiently large sample size p-value goes down and you claim that astrology is valid.
As if your aunt hasn't been telling you that for your whole life...
I dislike the outcome this experiment is measuring. I’m not an expert on horoscopes (and wouldn’t want to be one), but to me the primary purported function of horoscopes is to predict the future. As such people might not necessarily be able to say beforehand whether their own horoscope is more correct than that of someone else†. How should they know? But that is easily fixed: Just ask them to rank the horoscopes after the purported predicted time frame …
Altogether this seems like a solid setup to me, though. It would be fun to conduct this, but ultimately pointless. Astrology is just a too low hanging fruit.
(A potential issue might be people’s awareness of stereotypes associated with their astrological sign. I’m not sure how big a role those play of how important and consistent across different astrologers those are – as I said, not an expert – but if stereotypes associated with astrological signs are consistent and generally well known people might be able to identify the correct horoscope just based on the knowledge of those stereotypes, not any predictive power of the horoscopes.)
It was Feynman using the term cargo cult science. And he was not only talking about soft science, he was more generally talking about all of science. And it was not a general condemnation, it was about saying that “cargo cult science” is always a possibility and obviously an issue, but not that it is always an issue. Though I would definitely agree with you in saying that quantitative soft sciences suffer the most from cargo cult thinking.
It’s a paradox, really. “Soft science” is actually really hard. Measuring people and people’s behavior is a nightmare. There are so many variables, so many complex, ever-changing systems. We are at the limits of what we can achieve and our measuring instruments are extremely blunt and imprecise.
Because it’s so hard we are currently not even trying to solve many of the hard problems there. Because we just don’t know how. As such we limit ourselves to simple stuff and the people who are adept at doing the hard stuff (but not as hard as soft science, since that is so hard, no one knows how to properly do it) are doing things that are easier to nail down, with fewer variables – like physics.
And quantitative soft science limits itself by necessity to simple stuff. It simplifies without understanding the underlying complexity. And often slips into cargo cult thinking doing that …
—
† Though I actually think this is the real function of horoscopes: People have to be able to identify with them and think that they fit them when they are reading them. It’s entertainment. That’s why they are full of platitudes and not very specific.
Good point.
And that's the experiment I meant. Some will lie to swing the result to their liking, some will respond with bullshit for whatever other reasons. And the rest may easily respond "mostly true" if the author of those horoscopes has enough skill to make them sufficiently truistic and vague, which is what they typically do. Like, "something important will happen to your life in the next month because Jupiter blah blah blah".
My point is: horoscopes are unfalsifiable by design. Or by evolution with mutations, selection and stuff - whatever floats your boat.
The question you ask is whether people are able to identify their own horoscope, not whether they think the horoscopes are correct, i.e. they might well believe that on a 1 to 10 scale their horoscope is a 7, but if they then also score all the others at 7 (on average) then the horoscope had no predictive power. Basically, all the other horoscopes act as a control. It’s a quite elegant setup.
That experimentation in physics has slowed down to 18th century levels doesn't mean science is over, it just means the low-hanging fruit is over and we will have to continue slogging through theory before we discover new experiments.
Science has always relied on philosophy for its underlying direction, it's just obvious again. It took 2040 years before science/math could answer Zeno's paradoxes. If you can't handle the slog you're not really a scientist, you're a technician.
Another thing somewhat impacted by this issue that people don't think about is that we might not be able to keep up this pace in research for things like string theory for non-scientific reasons: specifically, science funding has flat-lined while the number of students entering the fundamental research fields is increasing. Really, particle physics is probably one of the most saturated fields in theoretical physics today.
There simply isn't enough room for everyone to study what they want. Therefore, given the "zero-sum game" situation we have, we need to decide where it's beneficial to spend our tax dollars and time researching...or most likely, governments who barely understand how to balance a budget will decide it for us. Given that string theory's only argument at this point is suspect amongst a plurality of traditional scientists, it seems like low-hanging fruit to be picked off the funding tree.
Regarding the "keep researching" line in higher level theory that the end of the article and you seem to be promoting...I think yes, you will always have people researching something out there, although honestly, the people who will be able to will most likely be at a certain number of institutions which can be enumerated on one or two hands. The rest of theoretical particle physics? I guess the sustainability of that program is dependent on the stress tolerance of physics graduate students and post-docs for the time going forward.
The other way out is to, you guessed it, work in research that is testable, and leads to fancy toys the beltway boys can appreciate.
This is probably not true. All kinds of money is being poured into physics research to create better batteries for example. It may be indirect, but there's a ton of money going into physics research.
On second reading of your post, you may be implying it isn't zero sum due to more money going to the applied physicists, leaving some for the stringy guys. It might be true, my impression is that it isn't enough[0], but I could be wrong.
[0] This is somewhat out of my ass, but it is tempered by colloquia at my university I've attended where this comes up from time to time.
This is not research (in particular not physics research) but engineering or development.
"In this revolution, research has become central; it also becomes more formalized, complex, and costly. A steadily increasing share is conducted for, by, or at the direction of, the Federal government. Today, the solitary inventor, tinkering in his shop, has been overshadowed by task forces of scientists in laboratories and testing fields. In the same fashion, the free university, historically the fountainhead of free ideas and scientific discovery, has experienced a revolution in the conduct of research. Partly because of the huge costs involved, a government contract becomes virtually a substitute for intellectual curiosity. For every old blackboard there are now hundreds of new electronic computers. The prospect of domination of the nation's scholars by Federal employment, project allocations, and the power of money is ever present and is gravely to be regarded. Yet, in holding scientific research and discovery in respect, as we should, we must also be alert to the equal and opposite danger that public policy could itself become the captive of a scientifictechnological elite."
Well, nice that we managed to heed one of Eisenhower's warnings.
I further disagree regarding your take on the "underlying" basis of science. Science begs philosophy to explain its (irreducible) mathematical foundation, where the said foundation ("basis") has a few un-canny givens/axioms in its bag of tricks.
Empiricism was the line drawn a few centuries ago. And just like the 'magna carta', the latter day "sages" apparently have determined the ancient ones were in error ..
[post-comment-edit: 1] Roughly speaking. To set bounds, above would consider Einstien a good citizen of 19th century science.
And that's only if we assume calculus answered them. Which is not the absolute consensus of logicians/mathematicians.
Many seem to believe they are simply about limits and that's all, but they may also point to a more fundamental aspect of reality. E.g. from Wiki:
A suggested problem with using calculus to try to solve Zeno's paradoxes is that this only addresses the geometry of the situation, and not its dynamics. It has been argued that the core of Zeno's paradoxes is the idea that one cannot finish the act of sequentially going through an infinite sequence, and while calculus shows that the sum of an infinite number of terms can be finite, calculus does not explain how one is able to finish going through an infinite number of points, if one has to go through these points one by one. Zeno's paradox points out that in order for Achilles to catch up with the Tortoise, Achilles must first perform an infinite number of acts, which seems to be impossible in and of itself, independent of how much time such an act would require.
Another way of putting this is as follows: If Zeno's paradox would say that "adding an infinite number of time intervals together would amount to an infinite amount of time", then the calculus-solution is perfectly correct in pointing out that adding an infinite number of intervals can add up to a finite amount of time. However, any descriptions of Zeno's paradox that talk about time make the paradox into a straw man: a weak (and indeed invalid) caricature of the much stronger and much simpler inherent paradox that does not at all consider any quantifications of time. Rather, this much simpler paradox simply states that: "for Achilles to capture the tortoise will require him to go beyond, and hence to finish, going through a series that has no finish, which is logically impossible". The calculus-based solution offers no insight into this much simpler, much more stinging, paradox.
A thought experiment used against the calculus-based solution is as follows. Imagine that Achilles notes the position occupied by the tortoise, and calls it first; after reaching that position, he once again notes the position the turtle has moved to, calling it second, and so on. If he catches up with the turtle in finite time, the counting process will be complete, and we could ask Achilles what the greatest number he counted to was. Here we encounter another paradox: while there is no "largest" number in the sequence, as for every finite number the turtle is still ahead of Achilles, there must be such a number because Achilles did stop counting.
If in logic you assume/imagine something, and reach a contradiction, then your reaction should be to reject that assumption.
In this case we reach the conclusion that Achilles cannot note all the positions.
The problem, and the whole point of the thought experiment, is that the assumption is tied to Achilles being able to make the distance, so we should ditch that too.
I'm of the opinion that Achilles and the Tortoise is solved by there being a smallest distance, a pixel (Not smallest measurable. Smallest period.)
I make amends with Achilles' Arrow by believing the universal clock is independent of the moments that it measures -- like the internal clock of a computer's being independent from a pixel arrow moving across a pixel screen.
The paradox is illogical anyhow, it fails to equate simple v*t=s.
That's one solution yes, but whether the universe is continuous or discreet is not a "solved" problem in physics in general. The lowest resolution could just be a "sampling restriction" (or quantum laws etc) and not the actual reality. There have been some experiments to discern between the two cases, but nothing conclusive IIRC.
>The paradox is illogical anyhow, it fails to equate simple vt=s.*
That's not being illogical. vt=s is not logic, is just a formula that we deduced and which matches what we see in everyday life (and in fact it's not absolute, e.g. when it comes close to the speed of light etc).
The paradox just checks whether vt=s is compatible with certain descriptions of the chain of events that look intuitive at first.
Mind blown! Wat? If it's falsified then it's just wrong, i.e. it had the potential to be science before it was proven to be wrong and now it isn't. He seems to be confused about the chronology of theories. If I make up a theory based on complete bs and it just happens to be falsifiable and then falsified then I wasn't doing science. I don't know of any falsifiable theory that was just pulled out of a hat, was recognized as one but wasn't immediately falsified (if there is one then he has a point.) If I come up with a theory and work hard to make sure it's falsifiable then I was doing science even if the theory was later falsified.
Science dies the moment things that are untestable becomes "a new kind of evidence".
If we can't test something because whatever reason, like we don't have enough energy, the fact that we know we can't test it is in fact valuable. We will have to find methods or ways to get there in the future.
Until that , we can't be sure. Fine. We know we don't know.
But falsifying this fact and believing in evidence that does not exist is believing we know things that are unknown to us.
This is dogma, religion, philosophy, but not science.
Nothing wrong about religion, or philosophy, but it is not science.
#1: "Only game in town": ZERO viability (perhaps negative). Ether was the only game in town before relativity. Geocentricism was the only game in town before it wasn't. Gods were the only game in town before science.
#2: "Y grew out of X (and X is solid)": ZERO viability (perhaps negative). It's essentially a corollary of the exact same rationale. (e.g. X = Maxwell's Equations, and Y = Ether). Everyone is thinking along the lines of X, and the only thing they can come up with is Y.
#3: "Unexpectedly delivered explanations": THIS is a big deal. Or at least it may be. This is what (I hate to say "philosophers of science", depicting "armchair philosophers", but rather "scientists of science") need to be focusing on. In essence, it asks: can mathematics (sometimes) be considered an experimental science, in the Popperian sense? I think it could, if formalized, and would allow us to tackle on some of these nasty questions more definitively, but I have no idea what that formalization would be. However I'd be very interested to see if etherian theory had any "unexpectedly delivered explanations" before Einstein. THAT is worth investigating.
The former's still chugging along pretty good, with things like the "invisibility cloaking" and all sorts of condensed matter stuff.
Ironically, since Upanishads, there is a maxim, popularized by Buddha, that we should strive to "see things as they are" instead of worship nonsense produced by society of mediocrity.
No better advice, probably, could be given. We are in the situation quite similar to that one of 6th-7th century AD, where almost every person who could barely write produce volumes of "religious" and "philosophical" doctrines, commentaries, commentaries to commentaries and similar crap (so called Tantric Buddhism texts, which are available in museums).
Nowadays, people who were barely graduated and had, lets say, not quite developed, highly constrained, too specialized and excessively brainwashed minds are doing "research", that egotistic pompous meme-joggling we could read in any so-called academic journals.
So, let's try to see things as they are, not misuse math to produce modern hymeras and mumbo-jumbos.
And at what point in its development and study do you abandon a theory that nobody has yet invented a way to test?
Theories like String Theory tend to fall into the first, possibly dabbling with the second option. Researchers are already starting to work on ways to test string theory, with promising results. It's quite likely that within 20 years, we might be able to do just that. While things like the many worlds interpretation of quantum mechanics or multiverse theories tend to fall on the "maybe in 1,000 years, but probably never" category.
I think the real question is: How patient are we?
If you mean we're going to be hearing about the Many Mystical Worlds of Quantum Physics from Deepak Chopra types for the next 1,000 years, I'd say "not very" is a reasonable answer.
Perhaps a better question is at what point does philosophy become physics? Finding a way to test the theory, and doing so, may be such a point.
String theory's critics are sure that it isn't. I've even heard it said that it only has the prominence it has because a noisy generation of physicists elbowed out competing projects.
If you don't have a testable theory in the short term, should you carry on trying to refine that theory in the absence of evidence, or should you spend more time on competing theories that perhaps have more chance of being open to experimental verification in a reasonable time frame?
The list of open, unsolved, and unexplained issues in physics isn't small. Continuing to prioritise one theory and gambling that it works out eventually is a classic sunk-cost error.
Clearly if you propose a theory that requires an experiment so advanced (or circumstances so rare) we can't hope to do it in 20 years, it's still a valid scientific theory. What about 50-100 years? What if it requires technology so advanced it's nearly unthinkable that we will ever attain it? This is when it becomes a philiosophical gray area. It's not a clear cut case what is verifiable and what isn't, since the theory is valid before our ability to verify it.
https://en.wikipedia.org/wiki/Atomism
You could also derive the Atomic nature of matter through math though, as infinitely devisable sets end up with paradoxes that don't match up with reality (think banarch-tarski)
You can do all this without an idea how to test it.
The philosophers that invented atomism probably thought about how the might see their atoms directly. I wonder how many "crazy" ideas were dreamed up that sounded impossible, that are now easy experiments to do today.
Theory is important, even if it sounds impossible today, because we have a history of redefining what is "possible" throughout the history of science.
Theoretical physics is also very much a thing.
> and should therefore be testable by definition.
That sounds nice but the definition of testable is hard to pin down and changes over time.
What technology can you imagine that could ever prove or disprove a hypothesis of our universe being only one facet of a multiverse? The apparatus would necessarily exist within the closed system.
does being in a multiverse influences our world in any way using current theories?
yes > we can eventually figure out and run an experiment no > then studying it is as productive as searching the Russel's teapot
this is how you set apart a theory from speculation, a falsification test. i.e. > http://arxiv.org/abs/1210.1847
Part of the problem is, as Gross points out, that the cost of experimental research at extreme scales is far out of sync with the cost of theoretical research.
The cost of the LHC and the annual budget of NASA are, for example, are around O($10B).
Compared with the value of the US economy (just for comparison), which is O($10000B) or so, this doesn't seem all that high. Of course the problem is that no direct economic output stems from constructing machines for experimental research. In addition to cost, there are the problems of time (how long experimental work takes) and engineering manpower that might be better spent elsewhere.
In any case, it doesn't seem obvious to me that in a different economic context than the one we live in, which is largely focused on wasteful consumption and war, that far, far more money couldn't be devoted to experimental research.
And I also hear that no one understands how shortly after the big bang why our universe (a tiny ball of energy) was quite so uniform.
My theory instead of dark matter and string theory (mine is probably wrong) is that the universe consists of every single quantum event that ever happened or could happen and that gravity operates as a blurred field operating through many of these close quantum "universes".
The reason could then be that the set of events that happened after the big bang, every quantum state was explored and we are living in one of the universes that happened to be smooth.
It should also explain why gravity is so "weak" compared to the other forces.
Anyway, I'm sure people smarter than me have thought of this and dismissed it for whatever reason!
Well, there are other areas of Science that have similar or even worse problems with speculative nature and departure from the scientific method. Read "Goo-to-you evolution". Not much "repeatable, observable experimentation" there.
If only Biologists were as honest and honed in consistent, rational and logical thinking as physicists.
I'm prone to think the historically more mathematical nature of the physics discipline plays a role here.
Also, physicist have proposed some experiments and observation such as regarding the cosmic microwave background radiation. There is a book called "The Trouble with Physics" and many articles on the subject. There is something to be said about many claims in theoretical physics and the lack of testability but I think this is not rigorous enough and too loose with the labeling.
> A Fight for the Soul of Science
The biggest problem there is that hypotheses have no underlying mechanism to make sure that the potential cause and effect are semantically related.
If p then q seems innocent enough. It probably seems even more innocent (or at least more simple) than All men are mortal Socrates is a man Socrates is therefore a mortal.
Because the required relationships in a syllogistic model can become a bit complicated.
I started off in this realm as a Philosophy major studying mostly Aristotelian models of deductive reasoning. It was mostly for kicks because I was a violinist at the time and needed a break from my music theory courses.
But when I got into the market research industry and started writing statistical software, I found serious problems with assumptions everywhere I looked. It seemed to me that there's a real problem with the way people with informal or introductory experience dealt with statistical results, with the relationship between null and alternative hypotheses, and with the evidence generated by sampling processes.
This is probably largely irrelevant to high-level Physicists, but I think it's at least partly relevant when we talk about what is and isn't falsifiable.
There's a comment in the piece where a guy says that Astrology is falsifiable, so we know that shouldn't be the only criteria for something to count as Science. I think he's on to something there because I think the fundamental hypothesis of Astrology is so far out of whack that it shouldn't have been considered.
There's nothing behind astrology that's any better than a bad if p then q statement. But we have no way of evaluating these by form. One can simple say, "If the grass is green, then the moon is made of blue cheese." This is formally a valid statement.
The problem I encounter many times (anecdotally, of course) is that people don't treat this statement as a material implication. They treat it as a logical conjunct. So that seems somewhat safe in the grass/moon example. They make the mistake of thinking of it as simply as, "If the grass is green AND the moon is made of blue cheese . . ." Well, that's clearly false. So why bother?
But a material implication has consequences. You can flip it around and say (by axiom) that if p then q then !q implies !p. I can assert that green grass => blue cheese moon. And if you accept that as valid, you can likewise assert that !blue cheese moon => !green grass.
It's easy to see the flaws in this contrived example, but it's often very difficult to see these problems in realistic examples when you are looking at effect sizes in medicine, or changes in advertising techniques, or samples from thermometers, or the kinds of things that I have no knowledge of in theoretical Physics.
It's often very difficult to assess when a scientific study has any realistic relationship between a null and alternative hypothesis. It would be nice if it were all statistically about whether or not these two numbers are the same or different, but that's frequently not the case.
I think the idea is correct, that we do need Philosophers to come up with a better system. Even something as simple as "The subject of a material implication must be included in the predicate of the material implication." might be a good start. Although it's woefully naive.
It would be kind of interesting to see people testing hypothesis in the scientific world that were formulated as syllogisms.
i.e., based on studies x, y, and z we can make the following claims: all (or some--doesn't matter. Most "some" claims can be reduced to a subset of "all" claims) x are y This study shows that z is x Therefore z is y
Is it limiting and problematic? Of course. Where do new categories happen?
Well, there are negations. You can prove that phenomenon z is not a member of previously known phenomena and is therefore something else.
While I think a great many of people sort of feel this way about stuff, I think there's a reason to codify it formally. Because so many people don't think very clearly about these things in aggregate.
It seems kind of ugly. But it would be an improvement over what we have now, which is basically a free-for-all in certain realms of science, where any sufficiently complex idea is grounds for further research, even when the possibilities of proof are non-existent. I say that more to the social sciences than I do the theoretical physicists of the world, so perhaps I'm off point here.
But my general idea is that, yes, philosophy can and should step it up a bit.
All possible interactions are explained by Einstein's Theory of Relativity.
This particular observation is not explained by Einstein.
Therefore this must have a different explanation.
This gives us a testable proposition by definition.
This gives us proposition 2 to focus on and rebut, if we can.
Generally, I think this is how good science works, but it's not codified. An additional benefit to this concept is that if stored in a central location, it gives us a graph network to deal with and search through.
And it gives us a tree to look at. So anything invalidated higher up in the tree invalidates all of its branches.
Which is also good.
We do indeed, live in interesting (or depending on your worldview, dangerous) times.
This article also made me think of Rand, and I wish they had some awareness of Rand's epistemology. They do mention Bayesianism, which is a useful framework, but still has limitations. (Recently I've been reading through classic papers on probability theory (Bayes, Bernoulli, E. T Jaynes) to see if it can be combined with Rand's neo-Aristotelian view of concepts).
Regarding my comment on the article, it was really just an "excited utterance" when I realized that the "shut up and calculate" and "bury the contradictions" tactics in Physics had run its course. I really wasn't looking to engage and offer Rand as the alternative to Kant. Physicists really want answers and seem more open to questioning their basic premises, including the premise that Philosophy is worthless. I feel like there is "revolution in the air" so to speak.
I too like the Bayesian approach to probability especially the work of E.T. Jaynes. I bought his book and though I didn't fully understand it, I like the idea of probability as a generalized logic of science. In his framework the problem of induction becomes when is it valid to conclude a probability is equal to 1.0 not 0.999.... This is the key because the latter is what leaves the door open to the skeptics.
(I previously tried to PM you but the email bounced, I will try again).
Sounds like you've been reading too much Ayn Rand. Nobody else places as much irrational blame on a single philosopher. Even if you think his philosophy is wrong, its much less wrong than things that came before it, and is certainly less wrong than claiming you can found a philosophy on 'A is A'.
A separate link leads from Kant to Frege, Russell and modern analytic philosophy. Which is hardly on the level of Marxism, and it still respects reason and reality, but it led to the idea of logic as meaningless symbol games, rather than a vital tool to understand the world.
Rand didn't found her whole philosophy on 'A is A' - this is a common misconception. She isn't trying to create a philosophy based on geometry, where everything is deduced from a few axioms. The law of identity is fundamental, but it's not sufficient - you need observation of reality too.
I don't see why this has to follow.
Oversimplifying out of necessity, there's been a long running philosophical conflict between empiricists (focus on reality) and rationalists (focus on theory). The hard sciences have managed to avoid the problems of philosophy for the last few centuries, but are increasingly running into fundamental methodological limitations. If, following Hume, induction is unreliable, how can we ever know our scientific theories are valid?
Ayn Rand developed a novel epistemology and theory of concepts to deal with these issues, but she's almost universally slammed in academia for her political views.
All I can suggest is to read both her and her critics and make up your own mind. (But do read her own words, not just what her critics say about her - the book I mentioned above is a good starting point).