user2225: So the Buddhist texts must be stating something incorrectly since we now know that we can't fly without the help of technology. How could they fly then?

user120: The Buddhist texts claim that many things are possible that many people think are not possible. As Suminda said, the claim is that once one properly develops the four bases of power, i.e., profound concentration founded on (1) desire & effort, (2) persistence, (3) intent, and (4) discrimination, then one will be capable of gaining 'supranormal powers,' as described in this passage from the Iddhipada-vibhanga Sutta:

When a monk has thus developed & pursued the four bases of power, he
  experiences manifold supranormal powers. Having been one he becomes
  many; having been many he becomes one. He appears. He vanishes. He
  goes unimpeded through walls, ramparts, & mountains as if through
  space. He dives in & out of the earth as if it were water. He walks on
  water without sinking as if it were dry land. Sitting crosslegged he
  flies through the air like a winged bird. With his hand he touches &
  strokes even the sun & moon, so mighty & powerful. He exercises
  influence with his body even as far as the Brahma worlds.

These appear, at least at first glance, to be literal, bodily powers; i.e., he bodily walks on water without sinking, although perhaps one could claim that the 'body' referred to in this passage refers to the 'mind-made body.' This is at least prima facie plausible since, in the Samaññaphala Sutta, the passage on the aformentioned powers occurs exactly as above but immediately follows a section on the 'mind-made body.' In either case, there are other powers mentioned in this sutta such as reading others' minds, recollecting past lives, and personally seeing how beings fare according to their kamma that contradict mainstream scientific views.
So, yes, there seems to be a contradiction between a worldview, perhaps a materialist scientific view, that holds that it is impossible to fly without technology and what is proclaimed in the suttas. Even if we interpret the suttas to be saying that one can physcially fly, I don't know that the Buddhist view conflicts with physics per se; to borrow from author Sam Harris on this point, it would be a discovery for physics if human flight based on concentration were shown to be possible.
Again, even if we allow that the suttas are talking about physical flight, built into the details is an explanation of why this contradiction should occur; namely, (1) the degree of concentration required for the development of these powers is not attained by the average person (hence, supranormal) and (2) Whatever Buddhist monks do attain these powers are forbidden by the monastic code from displaying these powers. Based on these factors, it would make sense that mainstream scientists or your average layperson would have no knowledge of these possibilities.
On the other hand, if the suttas are talking about the mind-made body (astral body), then although I think the details will still reveal a conflict with mainstream physics, it will not be as gross a contradiction. In any case, there certainly is a contradiction between the physicalist view that death is annihilation and the view that 'there is another world'--i.e., rebirth (cf. Apannaka sutta). So, ultimately Buddhism is at odds with mainstream views of physics.

user-1: 
"So the Buddhist texts must be stating something incorrectly since we now know that we can't fly without the help of technology. How could they fly then?"

What text are you referring to?
Also, what is meant by "flying"? Is it an actual body? Or, perhaps, just the mind?

"since we now know that we can't fly without the help of technology"

I don't think the above can be inferred from physics. Not much because I am a physicist, but because natural laws have a way of refusing to be subsumed by assertions like these. In other words, it seems to be another instance of the old induction trap. For example, seeing 100 black cats is enough to assert "all cats are black" without incurring in mistake?
The Buddha himself seemed to be acutely aware of this problem when he says he does not discern a beginning [of the world], instead of relapsing his reasoning and declaring "the world is eternal" (see  Brahmajāla Sutta).

user295: One of the main pieces of advice in the Buddha Dhamma is verification by trying it yourself (Ehipassiko) and to be open to scientific scrutiny (Sandiṭṭhiko). Hence you can develop the Jhanas and see for your self if this is possible or not. Self-verification and experience is more convincing than people arguing in-favor or against something like this.
Having said this, there is much research in these areas under Parapsychology though this might be view as pseudoscience.

2225: <p>So the Buddhist texts must be stating something incorrectly since we now know that we can't fly without the help of technology. How could they fly then?</p>
 120: <p>The Buddhist texts claim that many things are possible that many people think are not possible. As Suminda said, the claim is that once one properly develops the four bases of power, i.e., profound concentration founded on (1) desire &amp; effort, (2) persistence, (3) intent, and (4) discrimination, then one will be capable of gaining 'supranormal powers,' as described in this passage from the <a href="http://www.accesstoinsight.org/tipitaka/sn/sn51/sn51.020.than.html" rel="nofollow noreferrer">Iddhipada-vibhanga Sutta</a>:</p>

<blockquote>
  <p>When a monk has thus developed &amp; pursued the four bases of power, he
  experiences manifold supranormal powers. Having been one he becomes
  many; having been many he becomes one. He appears. He vanishes. He
  goes unimpeded through walls, ramparts, &amp; mountains as if through
  space. He dives in &amp; out of the earth as if it were water. He walks on
  water without sinking as if it were dry land. Sitting crosslegged he
  flies through the air like a winged bird. With his hand he touches &amp;
  strokes even the sun &amp; moon, so mighty &amp; powerful. He exercises
  influence with his body even as far as the Brahma worlds.</p>
</blockquote>

<p>These appear, at least at first glance, to be literal, bodily powers; i.e., he bodily walks on water without sinking, although perhaps one could claim that the 'body' referred to in this passage refers to the '<a href="https://buddhism.stackexchange.com/questions/8779/did-the-buddha-talk-about-out-of-body-experiences/8800#8800">mind-made body</a>.' This is at least prima facie plausible since, in the <a href="http://www.accesstoinsight.org/tipitaka/dn/dn.02.0.than.html" rel="nofollow noreferrer">Samaññaphala Sutta</a>, the passage on the aformentioned powers occurs exactly as above but immediately follows a section on the 'mind-made body.' In either case, there are other powers mentioned in this sutta such as reading others' minds, recollecting past lives, and personally seeing how beings fare according to their kamma that contradict mainstream scientific views.</p>

<p>So, yes, there seems to be a contradiction between a worldview, perhaps a materialist scientific view, that holds that it is impossible to fly without technology and what is proclaimed in the suttas. Even if we interpret the suttas to be saying that one can physcially fly, I don't know that the Buddhist view conflicts with physics <em>per se</em>; to borrow from author Sam Harris on this point, it would be a discovery for physics if human flight based on concentration were shown to be possible.</p>

<p>Again, even if we allow that the suttas are talking about physical flight, built into the details is an explanation of why this contradiction should occur; namely, (1) the degree of concentration required for the development of these powers is not attained by the average person (hence, supranormal) and (2) Whatever Buddhist monks do attain these powers are forbidden by the monastic code from displaying these powers. Based on these factors, it would make sense that mainstream scientists or your average layperson would have no knowledge of these possibilities.</p>

<p>On the other hand, if the suttas are talking about the mind-made body (astral body), then although I think the details will still reveal a conflict with mainstream physics, it will not be as gross a contradiction. In any case, there certainly is a contradiction between the physicalist view that death is annihilation and the view that 'there is another world'--i.e., rebirth (cf. <a href="http://www.wisdompubs.org/book/middle-length-discourses-buddha/selections/middle-length-discourses-60-apannaka-sutta" rel="nofollow noreferrer">Apannaka sutta</a>). So, ultimately Buddhism is at odds with mainstream views of physics.</p>
 -1: <blockquote>
  <p>"So the Buddhist texts must be stating something incorrectly since we now know that we can't fly without the help of technology. How could they fly then?"</p>
</blockquote>

<p>What text are you referring to?</p>

<p>Also, what is meant by "flying"? Is it an actual body? Or, perhaps, just the mind?</p>

<blockquote>
  <p>"since we now know that we can't fly without the help of technology"</p>
</blockquote>

<p>I don't think the above can be inferred from physics. Not much because I am a physicist, but because natural laws have a way of refusing to be subsumed by assertions like these. In other words, it seems to be another instance of the old induction trap. For example, seeing 100 black cats is enough to assert "all cats are black" without incurring in mistake?</p>

<p>The Buddha himself seemed to be acutely aware of this problem when he says he does not discern a beginning [of the world], instead of relapsing his reasoning and declaring "the world is eternal" (see  Brahmajāla Sutta).</p>
 295: <p>One of the main pieces of advice in the Buddha <a href="http://en.wikipedia.org/wiki/Dharma_(Buddhism)" rel="nofollow noreferrer">Dhamma</a> is verification by trying it yourself (Ehipassiko) and to be open to scientific scrutiny (Sandiṭṭhiko). Hence you can develop the <a href="http://en.wikipedia.org/wiki/Dhy%C4%81na_in_Buddhism" rel="nofollow noreferrer">Jhanas</a> and see for your self if this is possible or not. Self-verification and experience is more convincing than people arguing in-favor or against something like this.</p>
<p>Having said this, there is much research in these areas under <a href="http://en.wikipedia.org/wiki/Parapsychology" rel="nofollow noreferrer">Parapsychology</a> though this might be view as <a href="http://en.wikipedia.org/wiki/Pseudoscience" rel="nofollow noreferrer">pseudoscience</a>.</p>
