The now-old-fashioned idea of "machines that think" shows a deep but natural misunderstanding of the mind and software. Computers will never think; to see why, let's start with french fries. I'm assuming that the machines in question are computers, but a variant of the argument applies to any machine.
Neither french fries nor french fried is computable—no computer can ever produce french fries as a result, or the french fried state of being. French fried is not computable because it is a physical state of a particular object, and computers produce only information or codes for information, not physical stuff; not transformations of physical stuff. Happy is also a physical state of a particular object, namely a person. Happy can't exist unless you start with a person and put him into a state of happiness. Computers can't do that.
Thinking-about and being, or (equivalently) thinking-about and feeling, are the endpoints of a spectrum that defines the human mind. (By feeling I mean sensation, emotion or mood, just as the English language does.) We need the whole spectrum or we have no mind and no thought in any proper sense. Computers can imitate important aspects of thinking-about (narrowly understood), but being is beyond them. Therefore mindfulness is beyond them.
The word being is a useful abbreviation in this context, for being part of a physical object or system, and responding naturally to that environment. A sliced potato can be part of a frier environment, and respond by turning french fried. Litmus paper can be part of an acid-in-a-beaker system, and respond by turning blue. The mind is like litmus paper, but instead of turning colors, it responds to its surroundings by experiencing them. If something gives us grounds to be happy, the mind-body system (the human being) becomes happy, and the mind experiences happiness. Happiness has mental and physical consequences. You might experience a rush of energy, even quickened pulse and breathing.
Why can't being be computed? Why can't happiness? Happiness is not computable because, being the state of a physical object, it is outside the universe of computation. Computers and software do not create or manipulate physical stuff. (They can cause other, attached machines to do that, but what those attached machines do is not the accomplishment of computers. Robots can fly but computers can't. Nor is any computer-controlled device guaranteed to make people happy; but that's another story.) Being is not computable: an important fact that has been overlooked until now—not surprisingly. Computers and the mind live in different universes, like pumpkins and Puccini, and are hard to compare whatever one intends to show.
Can we get by without being, and still have a thinking machine? No. Thinking-about and being (or feeling) define the mind and its capacities. At the spectrum's top—at maximum alertness or focus—the mind throws itself into thinking-about and fends off emotion, which is distracting. At the bottom is sleep-and-dreaming, a state in which we do little thinking; we are preoccupied by sensation as we hallucinate, and often by emotion (dreams can be strongly emotional); in any event with feeling, or in other words, being.
Why did it take so long to produce such a simple argument? (And why are so few thinkers likely to accept it now?) Maybe because most philosophers and scientists wish that the mind were nothing but thinking, and that feeling or being played no part. They wished so hard for it to be true, they finally decided it was. Philosophers are only human.